Natural Wonder

Another Day for You and Me in Paradise

2023-05-25T00:00:00+00:00

HOW DO YOU COUNT SOMETHING INFINITE?

What does it mean for one set to be larger than another set? Or for two sets to be the same size?

When the two sets are finite, it’s simple: just count them. But when the sets are infinite, what should you do? You can’t actually count them. You don’t have the time! But also, there’s a more difficult problem. Some sets have an obvious place to start and some don’t.

For example, suppose you wanted to count all the numbers which have a decimal expansion (‘real numbers’) in between 0 and 1 (inclusive, if you like). Where should you start?

Well, 0 is least, so maybe start there? Then 1? Then what? You can’t just list them in order of their size. Suppose you started with

    0.00000000000001.

That’s not the next smallest number after 0! For example, what about

    0.00000000000000000001?

But that’s not a good place to start either, if you want to list them in order. What about

    0.000[ ...fifteen thousand more zeros... ]01?

OK, so there’s a practical problem, which is we can’t list all the real numbers between 0 and 1 in order from least to greatest. This is the first hint that there’s something funny about infinite sets and will be related to how we prove that there are more numbers in [0, 1] than positive integers.

COUNTING SHEEP

Let’s return to our starting question: how can you compare the size of sets? We need a procedure that works for finite sets but will generalize to infinite sets. In other words, we’re not looking for “just count them”.

Imagine you were a shepherd thousands of years ago and your language is one that can’t name numbers larger than a certain limit. “One, two, many”, for example. You want to graze your flock in an unfenced pasture but sheep are valuable and you want to make sure that at the end of the day you didn’t lose any.

Here’s something you can do. Get two baskets. Start the day with one empty basket (the ‘counting basket’) and one full of stones (the supply basket). As you let your sheep out of their pen, move one rock from the supply to the counting basket. At the end of the day as they’re rounded up, move a rock from counting basket back into the supply.

Once you are done rounding up the sheep, how many stones should be in the counting basket? None! If you have stones left in the counting basket then there are wayward sheep somewhere. If you ran out of stones early then you gained sheep.

So, we can answer the question: was the number of sheep you let out in the morning equal to the number you rounded up in the evening without ever actually finding out the number of sheep. You don’t have to count the stones in the counting basket in order to answer that size-comparison question.

ONE-TO-ONE CORRESPONDENCE

Why did it work? There was a “one-to-one correspondence” between the outward-bound sheep and the stones, and a similar correspondence between the stones and the inward-bound sheep. That’s enough.

What does the jargon “one-to-one correspondence” mean? It means: in the morning, for each sheep there was exactly one stone and for each stone exactly one sheep. Maybe it was this:

OUTGOING SHEEP	⟷	COUNTING BASKET
Lambchop		smooth gray slate
Fleece Witherspoon		smooth black basalt
Woolverine		coarse gray pebble
Rambo		lumpy speckled rock
…		…
Wooliam Shakespeare		a different coarse gray pebble
Baatman		purple geode
Ewesain Bolt		orange marble cylinder

Where ‘U ⟷ S’ means “Sheep U left the pen and stone S went into the counting basket”.

In the evening, there was also a one-to-one correspondence, but it doesn’t have to be the same one! Maybe it was

COUNTING BASKET	⟷	INCOMING SHEEP
purple geode		Shearlock Holmes
clear quartz crystal		Woolverine
orange marble cylinder		Lady Baabaa
…
petrified wood		Ewen McGregor
lumpy speckled rock		Rambo
smooth gray slate		Baatman

where this time ‘S ⟷ U’ means “Stone S was put back into the supply when sheep U came home.”

If you can construct a one-to-one correspondence between two sets means that there are just as many in one set as in the other.

In the morning you know there are the same number of outgoing sheep as stones. In the evening you know there are the same number of stones as incoming sheep. Therefore you conclude you finished the day with the same number of sheep as you started with. Perhaps Ewesain Bolt made a run for it and the neighbor’s Harry Ewedini appeared in your flock; but this method doesn’t address that question.

Here’s what’s critical: no repeats, and nothing left out. You’ve always got to make sure there’s exactly one stone for one sheep. That makes it one-to-one. And that guarantees the sets are the same size.

You DON’T have to match the stones and sheep up in the evening as you did in the morning. Rambo happened to get paired up with the lumpy speckled rock both times, but Woolverine was paired with the coarse gray pebble in the morning and the clear quartz crystal in the evening. The orange marble cylinder was paired with Ewesain Bolt in the morning but Lady Baabaa in the evening. No problem. We still know the number of outbound sheep was the same as the number of stones in the morning and the number of stones was equal to the number of incoming sheep in the evening. Therefore the number of outbound sheep and the number of inbound sheep were the same.

This method of constructing one-to-one correspondences works for finite sets, as good as counting. But we go further: we define two sets to be the same size when they can be put in a one-to-one correspondence. Two sets are of different size when there is no possible one-to-one correspondence.

SOME EXAMPLES

Let’s use this definition a little bit.

I have the same number of fingers and toes. If I sit in butterfly pose it’s easy for each finger to touch exactly one toe and for each toe to touch exactly one finger: left thumb touches the left big toe, left pointer was left at home, the left middle finger left their roast beef over, the left ring finger left none, and the left pinky went wee wee wee all the way to it’s home last on the left. Same for the right fingers and right toes. Each finger touches exactly one toe, each toe touches exactly one finger. Therefore the number of fingers and the number of toes are the same. I could make up a different choice (left hand touches right toes, or whatever) but I don’t need to. I demonstrated even a single one-to-one correspondence, that is enough.

I have more fingers than nostrils. Suppose each nostril can fit only one finger. Then, no matter how I stick my fingers in my nose I always have clean fingers left. It is NOT enough to say: I stuck my pinkies in my nose and had clean fingers left over. You have to know that every way of pairing fingers and nostrils leaves clean fingers.

There are more counting numbers (1, 2, 3, and on and on…) than any finite number. For instance, there are more than 3 counting numbers. One correspondence you might try is

Set containing three items	⟷	Counting numbers
1		2
2		3
3		5

but we’ve got counting numbers left over. Try any choice of counting numbers on the right hand side of the correspondence, you’ll always have at least one left over. Here’s a proof: find the maximum of all the numbers on the right. Add one. That number is a counting number but didn’t appear! So there are more counting numbers than 3.

This argument doesn’t just show that the particular thing I tried failed. It shows that any attempt is bound to fail.

The same argument works for any finite number! 3 wasn’t important, could have been 17. So there are more counting numbers than any finite number. That’s what we mean by infinite. We call the number of counting numbers “countable infinity”.

If a set is finite we can definitely count it. We call finite sets and infinite sets the same size as the counting numbers “countable”. Sets that are bigger are “uncountable”.

THE BURDEN OF PROOF

You can’t just say “I tried one [or two, or fifty-three] correspondence[s], didn’t find any one-to-one.” and declare victory. You’ve got to show that NO possible correspondence is one-to-one. And there are a lot of possible ways to try!

Here’s why it’s important to rule out the success of any arbitrary attempt: some tries are better than others.

For example, let’s compare the counting numbers and the even numbers. There’s an infinite number of both. But somehow it’s intuitive that there’s only half as many even numbers? Because you left half out! In other words, here’s a correspondence

Even numbers	⟷	Counting numbers
2		2
4		4
6		6
…		…
x		x

but it’s not one-to-one, because there are counting numbers that don’t appear: all the odd numbers. So maybe there really are more counting numbers than even numbers?

But here’s another correspondence

Even numbers	⟷	Counting numbers
2		1
4		2
6		3
…		…
x		x/2

Every even number appears on the left exactly once and every counting number appears on the right exactly once! There are no repeats, and nothing left out! So it’s one-to-one. There are a countably infinite number of even numbers. Just as many as the counting numbers.

There are an infinite number of prime numbers. Are there more counting numbers than primes? Or maybe there are the same number of primes as counting numbers? (It seems unlikely there are more primes than counting numbers, since each prime is a counting number.)

Here’s a way to build up a one-to-one correspondence between counting numbers and primes. The first prime number is 2. The next prime number is 3. 4 isn’t prime, so the next prime number is 5. Always find the least prime that isn’t yet on the list.

Counting numbers	⟷	Prime numbers
1		2
2		3
3		5
4		7
5		11
…		…

Is this one-to-one? Yes. Here’s why: There is always a smallest prime not yet on the list, because we can increase the most recent addition to the list one by one until we find a prime. So, this is a one-to-one correspondence between the counting numbers and the primes. Therefore there are as many primes as counting numbers. Since there are as many even numbers as counting numbers, there are also as many primes as even numbers. (We can use the two one-to-one correspondences to construct a one-to-one correspondence between even numbers and primes: the correspondence is basically to go to the counting numbers as an intermediate step.)

There are the same number of integers (… -3, -2, -1, 0, +1, +2, +3, …) as counting numbers. One one-to-one correspondence basically puts the integers in order, but by absolute value:

Counting numbers	⟷	Integers
1		0
2		–1
3		+1
4		–2
5		+2
6		–3
…		…

So the integers are countable. Notice that unlike the primes, there is no smallest integer; integers can get as negative as you like. So we can’t order the correspondence by the value of the integers; we could never get started, just like the beginning of this story.

Constructing a one-to-one correspondence of a set with the counting numbers is called “enumerating the set”; the correspondence is “an enumeration”.

AN ASIDE ON DENSITY

So, it’s a bit unintuitive, but there really are as many even numbers as counting numbers. How can we make sense of our intuition that there’s only half as many?

We can do that by computing the density of the evens in the counting numbers. But we’ve got to do it carefully. Let’s pick a really high number N. How many counting numbers are there up to and including N? Not a trick question: there are N. How many even numbers are there up to and including N? Well, it’s about N/2. If N is even it’s exactly N/2. If N is odd it’s (N-1)/2. So the ratio is

$\frac{\#(\textrm{even numbers} \leq N)}{\#(\textrm{counting numbers} \leq N)} = \frac{(N - [0\textrm{ or } 1])/2}{N} = \frac{N/2}{N} - \frac{[0\textrm{ or } 1]/2}{N}$

The first term of the last expression is $N/2/N = 1/2$ no matter what N is. The subtracted term is $[0\textrm{ or } 1]/2/N$ which gets smaller and smaller as N gets bigger and bigger. So as N gets large the ratio of the sizes of these finite sets approaches 1/2. But if you don’t put a cutoff N there’s an equal number of counting and even numbers!

Essentially what we have found is that if you count up one by one, only half of the numbers you count are even, the intuitive result. The surprise is that this fact is compatible with the assertion that there just as many even numbers as counting numbers! But our one-to-one correspondence above proves it!

An interesting theorem due to Riemann is that the number of the primes less than N is proportional to $N / \log N$ as N gets large and the density is therefore proportional to $1 / \log N$ , which goes to 0 as N gets large. In other words, the primes get rarer and rarer. But there’s still an infinite number of them!

THE RATIONALS ARE COUNTABLE

The rational numbers are numbers that can be written as fractions with integers upstairs and downstairs. ⊕Just don’t put 0 downstairs please! Let’s consider just the positive rationals for simplicity. ⊕A similar trick sign-alternating scheme that we used to show the integers are countable works for the rationals but adds complication.

Here’s an enumeration of the positive rational numbers: for each counting number list every pair of counting numbers that sum to that number (let different orders matter). To build a fraction put the first one upstairs, put the second downstairs, for example:

Total	Sum	Rational
1		no two counting numbers sum to 1.
2	1+1	1/1
3	1+2	1/2
	2+1	2/1 = 2
4	1+3	1/3
	2+2	2/2 = 1 which is a repeat so skip it
	3+1	3/1 = 3
5		1/4, 2/3, 3/2, 4
6		1/5, 5 [the others have appeared already, so skip them]
7		1/6, 2/5, 3/4, 4/3, 5/2, 6
…		…

and so on. Note that for a given sum the number of possible rationals is one less than the total.

Now just string these lists together in order:

Counting numbers	⟷	Positive Rationals
1		1
2		1/2
3		2
4		1/3
5		3
6		1/4
7		2/3
8		3/2
9		4
…		…

Does every positive rational number appear? Yes. Suppose the fraction was $n/d$ (numerator divided by denominator; you might have to use d=1). The total is n+d, and all those numbers appear in the (n+d)th row; in the concatenated list before item (n+d)². Therefore every positive rational appears on the list; the rationals are countable. It doesn’t matter that the rationals aren’t in order by value, that’s fine. What matters is that none are missing and none appear twice: the correspondence is one-to-one.

NUMBERS BETWEEN 0 AND 1

The rationals between 0 and 1 are countable too; just repeat the above construction but require the upstairs be less than the downstairs.

So, there are a countably infinite number of rationals between 0 and 1. They’re also “dense” which means that no matter which two rationals you pick you can always find one in between ⊕The average of two rationals is rational, for example. (and then you can use that new in-between number as a new starting point). So there’s no “getting away” from the rationals. Famously π is not rational, but if we play a game where you say some small positive number ε ⊕ε is the Greek letter epsilon, and is often used in math to represent some tiny positive number I can always find a rational number closer to π than the number you said. That is, I can always name a rational r such that π-ε < r < π+ε, as long as you name ε first.

At the beginning of this story we tried to list the real numbers between 0 and 1 in order and found that we couldn’t, because no matter where we started we could always find a smaller number. That’s true of the rationals! You can’t list them in order of size, because there’s always a smaller one, but you can list them in this other funny order.

Does that mean there are as many numbers between 0 and 1 as there are rationals (which are countably infinite)?

This is a very subtle question, but the answer is no. There are more numbers between 0 and 1 than counting numbers, as we will now show.

The numbers between 0 and 1 all have a unique decimal expansion, which is just a list of digits. ⊕Let’s agree that expansions that end in repeating 9s aren’t allowed, for example 0.499999… is just 0.5 For example, here are some numbers between 0 and 1 and their decimal expansions:

    1/2:        0.5000000000000000[0 forever]
    π-3:        0.1415926535897932...
    √(2)-1:     0.4142135623730950...

Remember: we need to show that no matter what correspondence we try to make between the countables and the reals in [0,1] we have some reals left over. For example, this correspondence

Counting numbers	⟷	Real numbers in [0, 1]
1		1
2		1/2
3		1/3
4		1/4
5		1/5
…		…
n		1/n

leaves out a lot of numbers. 3/4 and 5/12 and π-3 for example. But maybe this choice is like the evens and the countables and there’s some non-obvious way to enumerate every real number?

George Cantor proved that no, there is NO way to pair up the reals and counting numbers without having reals left over. The proof proceeds by contradiction.

Suppose I claimed to have such a one-to-one pairing. Let’s list them by their counting number.

Counting numbers	⟷	Real numbers in [0, 1]
1		0.1234567890123456789…
2		0.2222222222222222222…
3		0.1415926535897932384…
4		0.1011011101111011111…
5		0.5000000000000000000…
6		0.6660000000000000000…
7		0.7777770777777077777…
8		0.2139046935690214393…

You’re suspicious that my list is incomplete, which would mean it’s not a one-to-one correspondence. So it’s your job to find a number that’s not in the right column of this list; something I left out. Here’s how you build a missing number:

Look at the first digit of the first number. It happens to be a 1. So the first digit of your number should be some other digit. Say 7. Now we know that the number you’re building isn’t the first number on my list, because it disagrees in the first digit.
Look at the second digit of the second number. It’s a 2. So the second digit of your number shouldn’t be 2. Maybe you pick 3. Now we know that the number you’re building isn’t the second number on my list, because it disagrees in the second digit.
Look at the third digit of the third number on my list. It’s a 1. Again, pick a different digit. 8. Now we know the number you’re building isn’t the third number on my list, because it disagrees in the third digit.

and so on and so on. So you build 0.7384517… This number is not on my list, because we know it differs from each number on my list in at least one digit.

“Oh sorry, I just forgot that one!” I say. “Just take my list, shove each item down one, and put this number at the front. That patches the hole.” No. You do the procedure again, this time building 0.47384517…

No matter the pairing I present to you, claiming it to be an enumeration, you can always find a missing number. So there are more real numbers than counting numbers!

How many more? A LOT MORE! One way to see this is that at each digit you’ve got to pick a digit and only one is forbidden, 9 are allowed. So instead of 0.738… you could have picked 0.238, 0.338, 0.438, 0.538, 0.638, 0.738, 0.838, 0.938, and that’s only fiddling with the first digit. In fact, as long as your number doesn’t start 0.12110009… it’s guaranteed to be different.

If we just look at the first d digits of the first d numbers on my list, how many numbers could you write that are guaranteed not to be in these first d numbers? There’s 10^d possible strings of digits and you just cannot write d of them. In this sense there are exponentially more real numbers than counting numbers: just let d get larger and larger and larger.

The number of real numbers in [0, 1] is infinite. But it’s bigger than the countable infinity. It’s the “size of the continuum”, the continuum being a fancy name for “the entire number line with no holes”.

This method for finding omissions is called “Cantor’s diagonal argument” because the missing number is different from the list of real numbers along the diagonal digits.

OK BUT THAT’S IT RIGHT? JUST TWO?

No. There’s a whole hierarchy like this! But it’s much harder to give a concrete example; things get abstract quickly.

Mathematicians found a way to take Cantor’s argument and pull itself up by its bootstraps. ⊕Famous, contemporary mathematicians accused Cantor of being a scientific charlatan. He had a number of mental health episodes and died in involuntary commitment in a sanitorium. On the other hand David Hilbert proclaimed ‘No one shall expel us from the paradise Cantor has created.’ So Cantor’s difficult ideas were not universally derided in his day. The idea at each level is roughly the same idea: Given a nonempty set (finite or infinite) it’s possible to construct a set exponentially larger, and to show there is no possible one-to-one correspondence between the starting set and this exponentially larger set.

Are there any sets with more elements than the counting numbers but fewer elements than the continuum? The claim that there are no such sets is called the Continuum Hypothesis.

Surprisingly, this question is independent of the standard choice of axioms of mathematics. If all you pick are the standard axioms (called ZFC), you can’t decide. Fucking hellish answer.

I HATE THIS INFINITY PLUS ONE!

The entire discussion above is about comparing sizes (“cardinality”) of sets. But that’s not about counting something in order. In fact, we explicitly gave this whole story about how to compare sizes you don’t have to actually count all the elements.

But, like, maybe if you just keep counting up higher and higher you … get? … to infinity? Like, infinity comes … after? all the counting numbers?

George Cantor’s answer was: YEAH MAN, JUST FUCKING KEEP GOING! You can put anything in order if you’re brave enough!

He said: I’m just going to put numbers in order, like I was counting. “After” all the natural numbers comes ω (omega). “After” comes in quotes because if you set out to do it you’d never finish counting the counting numbers, so “After” doesn’t mean in time.

1, 2, 3, … ω, ω+1, ω+2, …, ω×2, ω×2+1, ω×2+2, …, ω×3, …, ω×4, …, ω×ω = ω^2, … ω^3, … ω^ω, and so on…

where the first few … all stand for the same amount of counting, but “then” [it never happens in time] you hit ω^2 and I use each … to elide a lot more numbers, to show the pattern. Also “and so on…” is carrying a lot of water; we’ve counted an infinite infinite number of numbers and yet compared to what mathematicians call, with dramatic understatement, “large ordinals”, they’re just the start.

I understand these “ordinals” a lot less. But these explanations by John Baez are pretty good! ⊕John is Joan Baez’s cousin.

Met her in a club down in old Soho

2021-04-03T00:00:00+00:00

Washington, DC

Their Eyes Gazed Straight Ahead

2020-09-25T00:00:00+00:00

Eisenhower Memorial, Washington DC

I Was Rolling Down The Road In Some Cold Blue Steel

2020-03-08T00:00:00+00:00

The National Mall

Washington, DC

Mighty Fine Wine

2019-04-17T00:00:00+00:00

⊕Previously
November 2017
September 2018

Trento, Italy, Atomic Nuclei as Laboratories for BSM Physics

Kindly State the Time of the Year

2019-04-06T00:00:00+00:00

Burg Eltz, Rheinland-Pfalz

My friends and I took a day trip to Burg Eltz, a castle in Rheinland-Pfalz. We made a short hike from the parking lot to the castle grounds. After a quick look around we hiked up the road for a scenic overlook, which we took in as the passenger shuttle went back and forth.

We had an excellent picnic of home-made curry and rice, and surprise chocolate birthday cake! We played by the river bank, wandered the castle’s treasury, and took a tour of the unoccupied parts of the castle ⊕The castle is privately held and the rear section is currently occupied by the thirty-third generation of the Eltz family. from a very peculiar guide who stuck to his very formal script even though the tour group was only us.

We returned to Köln, enjoying so-called flapjacks and selinamosas en-route and listening to 70s classics.

A Coat of Gold, A Coat of Red

2019-03-17T00:00:00+00:00

Muiderslot, The Netherlands

Turn My Face to the Wall

2019-01-20T00:00:00+00:00

Heidelberg, Baden-Württemberg

A Band Beyond Description

2018-09-15T00:00:00+00:00

Roboter-Kunst-Festival, Köln

Lasciate Ogne Speranza

2018-09-01T00:00:00+00:00

Trento, Italy

I arrived in Trento on Saturday night after an all day trip through Düsseldorf, Venizia, and Verona. Next time I’ll take the train through München. I had an absolutely fantastic pizza with tomato sauce, fresh basil, mozzarella di bufala, dizzled with a reduced balsamic vinegar at Anfiteatro, a new restaurant. Sunday it rained but I did some indoor and underground archaeological tourism and visited the cathedral.

During the week I was busy with a program at ECT*, but also had a free Friday afternoon and evening. I returned to Anfiteatro to have the pizza, but accidentally walked into their grand opening! They had a free buffet with a free glass of wine, and live music. The food was delicious—some kind of roasted pork, a variety of roasted and pickled vegetables, fried dough of some kind—but I kind of wished for that pizza! The musician performed popular and classic English-language songs. He could sing but sprinkled every song with mondegreens, which I found amusing at first and distracting by the end.

A Bold Deceiver

2018-08-04T00:00:00+00:00

Maynooth and Glendalough, Ireland

The Nucleon Axial Coupling

2018-05-30T00:00:00+00:00

⊕Nature, DOI:10.1038/s41586-018-0161-8

My collaborators and I are glad to announce that the Standard Model of particle physics predicts that $g_A$ , the axial coupling of the nucleon, is 1.271±0.013. The experimentally measured value is 1.2723±0.0023.

A neutron β-decays into a proton, electron, and antineutrino.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

Introduction

Protons and neutrons, collectively known as nucleons, are the particles that compose atomic nuclei. Nucleons, in turn, are made out of quarks and gluons, particles which are dominantly governed by quantum chromodynamics (QCD) and—as far as we know—are fundamental. Nucleons are baryons, and thus contain three “valence” quarks in addition to a big roiling mess of gluons and quark-antiquark pairs. Protons have two valence up quarks and one valence down quark, while neutrons have two valence down quarks and one valence up quark.

⊕
A free neutron decays into a proton, an electron, and an antineutrino.

The proton’s mass is 938.2 MeV, while the neutron’s mass is 939.6 MeV. That slight imbalance means that, by itself, a neutron can β-decay into a proton, an electron, and an antineutrino. But the rate of that decay isn’t controlled only by the masses involved. The decay rate also depends on the nucleon axial coupling, $g_A$ ⊕For experts, the axial coupling controls the Gamow-Teller transitions. . In the same way that electrons and protons have familiar electric charges which dictate how strongly they feel the influence of the electromagnetic interaction, nucleons have a charge, or coupling which dictates how strongly they feel the influence of the weak nuclear force, which causes β-decay, but also dictates how strongly they feel the influence of pions, which are the composite particles made of a quark-antiquark pair that bind nucleons into a nucleus.

Since nucleons are composite particles, this coupling can be determined by understanding the behavior of its constituents. However, unlike electric charge, which is conserved, determining the axial coupling of a neutron isn’t as simple as summing up properties of its valence quarks.

⊕
The nucleon coupling to the pion, drawn in the language of pions and nucleons and as the behavior of valence quarks.

You might wonder: if nucleons are composite objects without sharp edges, is there even any meaningful sense in which this coupling can be defined? Interestingly, the answer is yes. When trying to describe nuclear physics, we can write down a theory of pions and nucleons with all the same symmetries as QCD but which doesn’t talk about quarks and gluons any more. Matching the symmetries ensures we can force these theories to make the same predictions.

The cost of changing our picture is the introduction of a variety of unknown parameters ⊕These unknown parameters are called low energy constants, or LECs, in the parlance of effective field theory. . That is, symmetry is strong enough to dictate the form of the theory, but isn’t enough to quantitatively match the two together. But, in principle, if we know enough about the underlying behavior of quarks and gluons we can match the two theories’ predictions to determine these numbers. Put another way, in the Cosmic Control Booth, God doesn’t have a dial that controls these numbers independently: she sets only the parameters of the fundamental theory, and all else is consequence.

Once determined, these parameters can be used to make predictions about the nuclear interaction. These numbers can be measured experimentally. Indeed, $g_A$ is known experimentally to be 1.2723±0.0023. These numbers can also be determined theoretically. We found that the underlying theory of quarks and gluons predicts 1.271±0.013.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

Motivation

If $g_A$ can be determined experimentally with better precision, why bother calculating it in the first place? The answer is three-fold.

⊕
Colleagues generously provided us with this updated version of their Figure 12, showing three constraints on model-independent parameters that characterize new physics. The red ellipse comes from muonic pion decays, the blue circle from LHC W+Higgs production data, and the orange band is controlled by our result.

First, we want to make sure that the measured quantity is what it ought to be, assuming the Standard Model. If there were some new physics that modified this quantity, its effects would show up in experiments. But, in our calculations, we work only with physics described in the Standard Model. So, if there were a significant difference, it could be an exciting sign of new physics. That our result so closely matches what is found experimentally places tight limits on right-handed beyond-the-Standard-Model currents.

Second, we want to stress-test our calculating methods. Computing $g_A$ isn’t so straightforward, as I’ll explain below. In the future we will calculate quantities that aren’t measured well by experiment yet, and knowing we have our calculation under control will prove important. Having a benchmark quantity is a useful check that we know what we’re doing. The axial coupling is in some sense the simplest quantity in a larger set of observables, so it’s a good testbed for making sure we know where all the bodies are buried.

Finally, we like the laws of physics to be as unified a whole as possible. In principle, all of nuclear physics, from the simplest nuclei to neutron stars, should have a single, far-reaching description that originates in fundamental particle physics. While the method of summarizing the theory of quarks and gluons into a theory of nucleons and pions is perfectly well justified, as mentioned it comes with a cost of new, unknown parameters. Without calculation, these new parameters break the quantitative foundation of nuclear physics in particle physics. Computing the nucleon axial coupling is the first step in forging a quantitative connection that anchors nuclear physics in the underlying particle physics and reduces the number of input parameters one needs when describing physics as a whole.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

Why Do We Need Computers?

In many circumstances, when we want to extract information from a physical theory, we can use the following perturbative strategy:

Make a good approximation to the answer, and get an answer that is accurate but approximate.
Fix up the approximation, yielding a more daunting calculation, but improving the precision of the answer.
Make ever-better approximations, undertaking ever more daunting calculations, and achieving better and better precision.

The theory of quantum electromagnetism is a theory where this strategy has enormous success, because there is a small parameter, the fine structure constant α, which is very small—about 1/137 ⊕For experts, the perturbative expansion in quantum electrodynamics, and in most field theories, is thought to be an asymptotic expansion. . When we execute the above improvement scheme, the difference between each generation of results keeps getting smaller by factors of α. So, if you know to what precision you need your answer, I can tell you just how hard you need to work, in terms of how many times you have to go and fix up your approximation. Unless your problem is extraordinarily simple or has astounding mathematical properties, this fix-it-up strategy is the usual approach for pen-and-paper calculations.

The analogous number for QCD is about 1.5—a disaster for this perturbative method! Suppose you’ve worked very hard and made the third-least-stupid approximation. How many digits of accuracy can you expect? None, because there’s no sense in which the corrections get smaller and smaller. If you would only go and make the fourth-least-stupid approximation, you’d find your answer changes dramatically: your current result might even have the wrong sign. So you go and fix up your approximation further. How hard must you work to achieve a particular reliability? Hopefully it’s clear that with this perturbative strategy you can never stop and trust your result—the next piece will always dominate the answer and the work you’ve done so far is largely irrelevant.

Because this strategy fails, we call QCD a strongly interacting, or nonperturbative theory. ⊕Interestingly, QCD becomes perturbative at high energies, such as those found in colliders, where it has been tested vigorously and yielded predictions crucial for eliminating known signals from experiments and discovering new physics. To avoid this runaway disaster, we need a different strategy. We put QCD on a computer, and try to solve the whole thing without making any uncontrollable approximations. It could be that tomorrow someone has a new insight that allows us to solve QCD without computers. But the above argument about the failure of perturbation theory gives us a ‘folk theorem’ that no tractable pen-and-paper solutions exist.

Wielding Lattice QCD to Calculate $g_A$

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

⊕
A cartoon of a four-dimension lattice used in lattice QCD. The interior sites and links have been omitted for clarity.

Lattice QCD is the formulation of QCD on a finite, discrete spacetime. This transforms the problem from a horrible infinite-dimensional integral to a still-horrible but finite-dimensional integral, which we attempt to evaluate via importance sampling Monte Carlo methods.

Typically we use a square lattice, but in four dimensions. We put the quarks on sites—the intersections of the grid—and the gluons on links—the lines that connect the sites. The gluons determine how the quarks can move around, and so naturally live on the connections between sites. We have to sample many different possible configurations—arrangements of fields in spacetime—to correctly capture the quantum-mechanical properties. The more configurations we can sample, the better our answer. We generate these configurations with a Markov chain, and each configuration is computationally expensive to create. In other words, if someone is willing to pay the electric bill, we can drive down the uncertainty on our answer further and further, but it ain’t cheap.

The day-to-day activities of a lattice QCD practitioner look a lot like an experimentalist—there’s statistical data analysis, curve fitting, and understanding and quantifying uncertainties. We often refer to the quantities we compute on each configuration as “measurements”—although of course we’re aware that we’re not poking and prodding Nature itself. Instead, just as a telescope lets you see deep into space, a computer lets you see deep into the Platonic mathematical realm. At the end, we quote an answer with a controlled uncertainty that accounts for both the statistical nature of the approach, and any systematic difficulties, just as an experimentalist might.

There are three standard sources of systematic uncertainty in lattice QCD which must be addressed. Obviously, we use a discrete spacetime even though we are interested in the continuum. Although we’re interested in physics in an infinite spacetime volume, we use only a finite spacetime volume so that our problem fits in a finite-size computer memory and our calculations finish in a finite amount of time. We have another trick as well: we can change the parameters of QCD! ⊕So, the computational physicist can answer questions the experimental physicist cannot, such as what would happen if one could adjust the dials in the Cosmic Control Booth that are impossible to adjust experimentally. Experimentalists are stuck with the true values—we have to make sure we can ultimately get to the experimental values.

At short distances, QCD is perturbative and we know the exact theory we are interested in. That means we can take our lattice spacing—the length of the links—finer and finer so as to match QCD, and then let the computer handle the long-distance, nonperturbative mess. We calculated at three lattice spacings: 0.15, 0.12, and 0.09 fm ⊕1 fm, a femtometer, or fermi, is 0.000000000000001 meters. A proton is about 1 fm across. and extrapolated to the continuum limit. We avoid going to ultrafine lattices because the numerical cost grows quickly as the lattice spacing shrinks.

Of course, the computational cost also grows with the number of sites in each direction, yet we want to make sure our calculations aren’t too badly distorted by being in a finite volume. One helpful technique is to use periodic boundary conditions—like in Pac-Man—to ensure the lattice has no edges or walls and no site is privileged to be in “the middle”. Still, we calculated at a variety of different volumes, making sure to carefully take the infinite-volume limit.

Finally, for technical reasons, some numerical steps become very expensive as the quark masses get close to zero. ⊕This growth in cost is caused by the Dirac operator becoming more-and-more ill conditioned. Multigrid methods alleviate this problem. In nature, the up and down quark masses are just a few MeV while the natural scale of QCD is a few hundred MeV (for example, the proton and neutron masses, as mentioned, are about 940 MeV) and in this sense are very small; only in the last 10 years or so have calculations with physical parameters been achieved. We calculated on five quark masses from 130 MeV to 400 MeV, allowing us to interpolate to the near-physical pion mass of about 138 MeV.

Numerical results for the nucleon axial coupling for a variety of different pion masses (along the x-axis) and the three different lattice spacings (red being coarsest, blue being finest), as well as the infinite-volume-and-continuum-limit function as the dashed purple line (with its corresponding 1σ uncertainty band). The physical parameters of QCD are given by the dashed vertical gray line, and our final result is the intersection of this line with the purple band. The experimental result is shown in black.

By calculating at three different lattice spacings, different volumes, and different quark masses, we control all three sources of systematic uncertainty and recover a function (and its uncertainty band) that describes the axial coupling as a function of the pion mass in the continuum and in infinite volume. Our final quoted result

$g_A = 1.271\pm0.013$

is the value of that function at the physical pion mass, the error accounting for statistical uncertainties, uncertainties from interpolating/extrapolating to the physical parameters of QCD, to the continuum, to an infinite volume, from omitting the small mass splitting between up and down quarks, and from fitting.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

Methodological Improvements

⊕
A comparison of previous calculations, our result (purple, with an error band to guide the eye), and the experimental determination given in the PDG.

We are by no means the first group to compute the nucleon axial coupling using lattice QCD. However, the 1% uncertainty we achieved is an enormous improvement over previous results. This marked improvement wasn’t simply a matter of using a larger amount of computer time, but relied on new methods. In fact, people expected that a 2% uncertainty would be achieved by 2020, possible only with the next generation of supercomputers. It’s natural to ask: what did we do differently that unlocked this precision result?

The quantities we need to determine $g_A$ are correlation functions, which tell you how quantities change across the spacetime volume. In particular, we need to know the long-time behavior of those functions. Unfortunately calculations with baryons have an exponentially-bad-in-time signal-to-noise problem, which means that the later we look in time the larger the statistical fluctuations are and so the less reliable the measurements are. One expensive way to overcome this problem is through sheer strength, overcoming this difficulty with ever-increasing statistics. ⊕If you know a funding agency with an exponentially large computer or an exponentially large budget, point me their way! Previous calculations focus on a few values of these functions, at just a few intermediate and late times, hoping to get a good signal that still captured the late-time behavior without breaking the bank.

An example correlation function on an ensemble with a lattice spacing 0.09 fm and a pion mass of 310 MeV. The gray points come directly out of the improved method; the black and white points are those same data, after fitting in the white region and subtracting away the early-time behavior. The blue band indicates the long-time limit. Simply examining the late-time points cannot provide comparable precision, because the statistical noise explodes the error bars.

Instead, we use a different method to determine these functions, which, for the same computational cost as a single point, gives us access to the functions at all times. The benefit of this approach is that it yields access to points at early times which are exponentially better in terms of a signal-to-noise precision. While these early-time points don’t accurately capture the late-time behavior, knowledge of how these functions evolve in time allow us to fit and make a reliable late-time extrapolation. The drawback of this method is that we only have access to the axial coupling in this calculation, while the more common method yields access to many different nucleon properties; we can compute these other properties, but at additional cost.

The clear reliability of our late-time extrapolation depends on computing these functions at all times, and leveraging the precision of the early times, where the noise isn’t bad.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Outlook
Acknowledgements
Press Releases and Mentions

Outlook

With this determination of the axial coupling, we have demonstrated the potency of lattice QCD for nuclear physics. But, this is by no means the end of the story—indeed, it is just the beginning. There are many interesting single-nucleon properties important for translating experimental results into knowledge of new physics. The hunt for exotic, ultra-rare processes, such as neutrinoless double beta decay, requires quantitatively connecting very high energy particle physics with very low energy nuclear physics with controlled errors, and lattice results will form an important link in that chain of evidence. Ultimately, a quantitative understanding of one-, two-, and other few-nucleon systems from lattice QCD will supplant phenomenological modeling as the basis of nuclear physics.

Acknowledgements

⊕

The computing power for the calculation was provided by the Department of Energy’s Innovative and Novel Computational Impact on Theory and Experiment (INCITE) program to CalLat (2016) as well as by Lawrence Livermore National Laboratory (LLNL) Multiprogrammatic and Institutional Computing program through a Tier 1 Grand Challenge award.

We used Titan, an NVIDIA GPU-accelerated supercomputer, at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC05-00OR22725, and the GPU-enabled Surface and RZHasGPU and BG/Q Vulcan clusters at LLNL.

As explained, lattice QCD calculations are performed with Monte Carlo ensembles of field configurations. Most of the ensembles we used were produced by the MILC Collaboration, though we generated some of our own as well.

⊕

We were supported by our employers and funding agencies, NVIDIA, the DFG and NSFC Sino-German CRC 110, Lawrence Livermore and Lawrence Berkeley National Laboratories’ Lab Directed Research and Development (LDRD) programs, the RIKEN Special Postdoctoral Researcher Program, the Leverhulme Trust, the Department of Energy Offices of Science’s Nuclear Physics, Advanced Scientific Computing Research, SciDAC and Early Career Research programs, as well as through its Nuclear Theory for Double Beta Decay and Fundamental Symmetries Topical Collaboration.

We had helpful input on our work, in its various stages, from C. Bernard, A. Bernstein, P.J. Bickel, C. Detar, A.X. El-Khadra, W. Haxton, Y. Hsia, V. Koch, A.S. Kronfeld, W.T. Lee, G.P. Lepage, E. Mereghetti, G. Miller, A.E. Raftery, D. Toussaint and F. Yuan.

⊕ Introduction
Motivation
Why do we need computers?
Wielding Lattice QCD to Calculate $g_A$
Methodological Improvements
Acknowledgements
Press Releases and Mentions

Press Releases and Mentions

This list will be updated sporadically.

A Demon Cannot Be Hurt

2018-02-07T00:00:00+00:00

Mysore, Karnataka, India

The Palace of Mysore still belongs to the Wadiyar dynasty, the titular monarchs of the Kingdom of Mysore, and can be toured with an excellent audioguide app. The well-kept walled grounds have two temples, a stable of elephants, and multiple large gateways. On display in the palace are a small portion of the Wadiyar traditional figurine collection, portraits, and a set of caskets used by supplicants to deliver written requests and mementos to the maharaja. The highlight is certainly the architecture—the palace, built after the previous wooden palace burned, is stone, and has enormous spaces with rich tilework, frescoes, bright colors, and stone and ivory inlay.

I walked through the nearby market, where flowers, spices, vegetables, dyes, and other everyday goods are sold in a loud, frenetic, chaos. Many vendors approached me, followed me, or otherwise tried to get my attention, though a quick pace and polite but firm insistence that I didn’t need a wooden cat puzzle box, junky souvenirs, or ingredients for dinner got my message across.

I had an fantastic onion dosa from a stall on the main market square.

The final stop was at the Sri Chamundeshwari temple, which is the main temple dedicated to the state’s local goddess. A complex of many temples, the main focus is the shrine and idol of Sri Chamundeshwari, who myth claims defeated a snake-wielding demon. This victory is commemorated annually with a 10-day festival, while other nearby regions share the festival and the vanquishing of evil is always accomplished by a deity, Mysore is unique in both celebrating and being the seat of this important regional goddess. The temple is located atop a huge hill that overlooks the whole city of Mysore, and the palace grounds and palace itself are oriented so as to face the temple, to identify the dynasty and the goddess.

From Mysore, it was a bit more than 3 hours to the Bangalore airport. My flight was at 3:30 in the morning, which put me in Frankfurt at about 9 am.

Wine For The Woman Who Made The Rain Come

2018-02-06T00:00:00+00:00

Ooty, Tamil Nadu, India

I woke up early in Bandipur and my driver and I left for Ooty at about 6 am, shortly after the road through the tiger reserve opens. It was a long trip, which crossed from the state of Karnataka to Tamil Nadu and took me high into the mountains. I was warned to dress for the cold, which turns out to be a laughable concern for someone more used to a continental European climate.

My first stop was the botanical gardens, which I found to be lackluster. Very few of the flowers were in season, the grounds were poorly maintained, and some of the water was standing rather than flowing as designed. It was quiet and cool, however, and a nice way to spend the morning.

I had lunch at the Lake & Boat House, which had some amusements and rides that I didn’t ride, and also had paddle boats and powered boats for rent. A class from a local all-girls high school was there, and clandestinely took selfies with me in the background. A family gave me a “butterscotch fruit”A quick search yields only western baked goods. that was unusual in that it had a thin but inedible peel, a center with lots of little black seeds in a goop, and a mushy flesh. It was good, but messy and a lot of work.

I visited the park atop Doddabetta peak, which, as the highest nearby peak, has phenomenal view of both Ooty and the valley on other side of the ridge. On the way back into the main part of town I stopped at Benchmark Tea Factory.

Ooty is surrounded by mountains, with large tea plantations covering entire mountainsides. One of the chief employees gave me and my driver our own tour of their little plantation and took us onto the factory floor to see the machines close-up and to watch the women sort and pack the tea. In addition to an educational time, they also provided samples of green, black, white, and ginger tea.

I had a late lunch at a restaurant in the town center, where I met Tom and Sue, two older British people on their fifth trip to India. I had a nice lunch of paratha and grilled paneer and vegetables, while they shared a masala and some naan. After an hour we parted ways and I walked around downtown Ooty and the market. The most dangerous part, as always, was crossing the street.

At 5 pm we left Ooty and returned to Bandipur. The way down had less traffic, both factors conspiring for a much shorter trip on the way down. I had dinner at the lodge, and met a nice couple from California, their two children, and grandma, who had just arrived that day. I told them about Ooty, and they told me about their first and incredibly successful trip into the forest. The next morning we went into the park and ate breakfast together before checking out and saying goodbye.

What Immortal Hand or Eye Dare Frame Thy Fearful Symmetry?

2018-02-05T00:00:00+00:00

Bandipur Tiger Reserve, Karnataka, India

Although Your Mind's Opaque

2018-02-03T00:00:00+00:00

International Centre for Theoretical Sciences, Tata Institute for Fundamental Research, Bangalore, India.

My Sweet Lord

2018-01-30T00:00:00+00:00

Bangalore, India

Nonperturbative and Numerical Approaches to Quantum Gravity, String Theory, and Holography, the program I attended, had a half-day Tuesday program with a free afternoon. We arranged cabs into Bangalore, where we visited the summer palace–which could be better kept up–and followed the audiotour through the public areas, court, and private residence of the British-collaborating rulers of the state of Karnataka.

We stopped at a souvenir shop, where I spotted a lassee shop across the street. The traffic in India is controlled chaos—there are essentially no stop lights and no pedestrian crossings: one must simply cross with caution and confidence. I enjoyed a falooda, which my friend Vesna recommended before my trip. It was… weird. There were small tapioca balls and shredded rice noodles, topped with vanilla ice cream and yellow raisins.

From there we made a short stop at the Parliament and High Court en route to the botanical gardens. Parts of the gardens are very nice, but it’s very hard to ignore the abundance of litter. The highlights were the greenhouse seen above, an abundance of beautiful, wild song birds, bonsai trees, and a still lake with lotus lillies.

The cabs then took us through rush-hour Bangalore traffic to Ishkon temple, a main temple of the Hare Krishna. As I was wearing shorts, I had to put on a doti before proceeding to the shrines. As we made our way to the first shrine, we passed a special staircase for worshipers where with every step they alternate the mantras “Hare Krisha, Hare Krishna, Krishna Krishna, Hare Hare” or “Hare Rama, Hare Rama, Rama Rama, Hare Hare”.

When we reached the main shrine, a monk or priest had us touch flower blossoms and sprinkled us with perfumed water. Then we joined a group of worshipers as another monk rang a bell and sprinkled the blossoms around an idol. He swung incense and chanted, and finally sprinkled the crowd with the remaining perfumed water. As worshipers leave the shrine, they put their hands over the flames of candles and touch their faces with their warmed hands.

For dinner the different cabs split up before heading back to campus.

Things That Didn't Suck 2017

2017-12-23T00:00:00+00:00

⊕TTDS 2011
TTDS 2012
TTDS 2013
TTDS 2015
TTDS 2016

BOOKS + SHORT FICTION

The Man In The High Castle, by Philip K. Dick
The Ice Dragon and Knight of the Seven Kingdoms, by George R.R. Martin
The Three Body Problem and The Dark Forest by Cixin Liu

ARTICLES + SERIOUS VIDEO

A Bigger Problem Than ISIS? - The Mosul Dam is failing, and a breach would cause a colossal wave that could kill as many as 1.5M people.
What Charlie Hebdo Taught Me About Freedom of Speech
The Birth of An Ocean - How did I not know that in 2005 a giant rift 60 km long and 8 m wide opened in the Earth over the course of 10 days?
Steve Wozniak Was My Computer Teacher in 1995
12 Letters that Didn’t Make the Alphabet
How Do People Get New Ideas?, by Isaac Asimov
The World’s Worst Skier
The Future of Not Working - Give Directly experiments with guaranteed basic income.
What Writers Do When They Write
Product 19 Is Discontinued
Norway’s graphic identity is killing it: new banknotes and new passports.
London Bridge is Down - the plan for when Queen Elizabeth dies.
What It’s Like to Watch Your Life’s Work Blow Up on a Rocket SPOILER: it’s kind of the same as watching American science implode!
Secrets of the Magus - a profile of Ricky Jay, magician.
Five Minutes Early is On Time; On Time is Late; Late is Unacceptable - if you respect someone else’s time, show up early.
Is an Open Marriage a Happier Marriage?
In Lieu of Money, Toyota Donates Efficiency to New York Food Bank and Meals Per Hour
The Selfie Monkey Goes to the 9th Circuit
How Checkers Was Solved
Doctor Elaborates on New Study Showing Prevalence of CTE in Football Players - one of my good friends who studies CTE on All Things Considered. Also received the greatest honor available to scientific work.
Sfyrizo - a whistling language goes extinct.
Better Business through Sci-Fi
The Legion Lonely
Arks of the Apocalypse
Where Are the Brave Military Voices Against Forever War?
Branded in Memory - a study on how well corporate logos are remembered.
Demisexuality
SPORT DEATH: The end of Senior House and the spirit of the Institute
I invented Baileys
Left-Handers Struggle to Mate
Scientists Aren’t Stupid, and Science Deniers are Arrogant
If Your Vibrator Is Hacked, Is It A Sex Crime?
Can Germany Fix Facebook?
The Last of the Iron Lungs
Curvature Blindness
Faster, Faster, Must Go Faster
Don’t Make Fun of Renowned Dan Brown
Poor Millennials
Queens has more languages than anywhere in the world
Enlightenment Principles Emerged in Africa before Europe

PHYSICS

PUBLICATIONS

TRAVEL & CONFERENCES

UMass Amherst, for an interview.
Matter over Antimatter: The Sakharov Conditions after 50 Years
Bochum and Mainz for talks.
OLCF User’s Meeting
LATTICE 2017 in Granda, Spain.
Neutrinoless Double Beta Decay INT-17-2a and INT-17-67W in Seattle, WA.
Computational Sciences and Reality, Bad Honnef, Germany
Axions at the Crossroads: QCD, Dark Matter, Astrophysics in Trento, Italy
Technical Advances in Lattice Field Theory

SERIOUS

What Does Any of This Have to do with Physics? Reflections on pursuit of a life in theoretical physics.
The Principle of Sufficient Reason - The PSR seems to miss the possiblity of logical fixed points. That is, that the “deeper” reasons and explanations can be nontrivially isomorphic to the thing you wish to explain—much as happens under the renormalization group flow—so that the system pulls itself up by its own bootstraps.
Maryam Mirzakhani’s Pioneering Mathematical Legacy
The Scariest Nuclear Threat May Be Coming from Inside the White House
The Art of Teaching Math and Science
Why I Left Academia - in which a professor plagiarizes their student.
R.R. Wilson’s Congressional Testimony, April 1969
Don’t Fall for Babylonian Trigonometry Hype - I mean, seriously, there’s no way “the wisdom of the ancients” was going to go beyond the understanding of modern mathematics.
The CIA Staged Sham Academic Conferences to Thwart Iran’s Nuclear Program
Science Denier, House Science Commitee Chairman, National Embarrassment Lamar Smith Retires - let’s see what regressive reality-denier will take his place!
Astronomy Prepares for a Flood

FUN

${(1 + 9^{-4^{6*7}})}^{3^{2^{85}}}$ uses every digit 1-9If you want to include 0 just add “0+” basically anywhere in there. and is ALMOST equal to e. How close? It gets the more than 18 TRILLION TRILLION digits right.
Richard Feynman on the True Meaning of Physics
Unexpected Mathematical Images
Reuters’ World’s Most Innovative Research Institutions - 2017I've worked at two!
Self-Referential Aptitude TestI now have a headache
The Best Demo of Gravitational Waves Yet
Whispers of String Theory
How Quantum Theory is Inspiring New Math
Enhacement of human color vision by breaking the binocular redundancy
Creating the Never-Ending Bloom
Mass Extinction and the Structure of the Milky Way
The TSA Asks: How do you milk a fur seal? and Carrying your Nobel Prize through Airport Security
Double-blind testing
Math vs. Physics - I object to some of his characterizations of quantum mechanics, including his glossing over of important aspects of the sum-over-histories idea that makes it sound dumb rather than specific and consistent.
The Librarian Who Guarded the Manhattan Project’s Secrets
Visualizing Algorithms: Sampling, Shuffling, Sorting, and Maze Generation
On The Unreasonable Effectiveness of Mathematics in Science - a podcast where smart people discuss Wigner’s famous question.
Aronson’s Sequence - “‘T’ is the first, fourth, eleventh, sixteenth, twenty-fourth, twenty-ninth, thirty-third…”
The Eclipse Conspiracy
On Crackpots
Mathematical games interesting to both you and a 5-year-old
Black Art: On the History of Mathematical Typography
Marjorie Rice’s Secret Pentagons, her website Intriguing Tessellations, and the ultimate classification of convex pentagons that tile the plane
Sorting algorithms, visualized
Chalkboards and whiteboards.

TOOLS

The Well-Tempered Clavier - I bought a mechanical keyboard (Das Keyboard 4 Ultimate). It’s great. Phenomenal tactile feedback and sound, and the blank keys look bad ass.
The Sword - I bought two nice pens from Faber-Castell. Heavy, good grip, cartridges write like a dream. Still wish left-handed people could use a fountain pen.
Left-Handed Scissors - I can make a clean cut without applying an absurd amount of torque.
Left-Handed Ruler - No longer do I have to do subtraction to measure.

RELIGION

A Lizard With Scales That Behave Like Cellular Automata
Timeline of the Far Future - “Sorry, did you say ten million or ten billion?”

TV SHOWS

Man in the High Castle
Stranger Things - Oh man, I loved this. I started listening to The Adventure Zone podcast (TTDS2016), and I think this plays to the same predilictions. But the production quality is substantially higher.
Arrested Development - I hadn’t seen season 4 before. It’s a tangled-up mess, trying to pull off over the course of a whole season what an individual episode in the previous seasons accomplished. I’d love to see it re-cut into chronological order, or something. Maybe a movie?
Easy
Penn & Teller: Fool Us
Master of None - This show is awesome. My biggest problem with it is the happy ending. Buncha bullshit.
Atypical
Game of Thrones? - Honestly… while this season had a few great moments, the plot and storyline has become too predictable and less dangerous. When Jon falls into the lake and doesn’t die I no longer fear for any character’s safety from repercussions.
Rick and Morty - simply hilarious.

MOVIES / DOCUMENTARIES

The Day Prince’s Guitar Wept the Loudest - I never noticed that at the end he just throws his guitar straight up into the air.
Arrival
The Lego Batman Movie
The Man Who Knew Infinity
Logan
Passengers
Moneyball
Weiner
One of Us
Star Wars: The Last Jedi

MUSIC

I absolutely loved reading about Fyre Festival. “Let’s just do it and be legends, man.”
In the Air Tonight, cover by Chris Daughtry
Grateful Dead Fan Sends Women Unsolicited Dick’s Picks
Happy Birthday, Jerry Garcia
The Story of the DuckTales Theme Song
Despacito but it’s played on two calculators
Tiny Desk Concert Podcast
All Songs Considered
The Other One: The Long Strange Trip of Bob Weir
Fredrika Stahl: Tributaries
Mark Gillespie: Real to Reel and In Your Hands
Astrud Gilberto’s Finest Hour
Long Strange Trip Soundtrack
Paramore: After Laughter
Darrell Scott & Tim O’Brien: Real Time
30 Days of Dead
In B Flat, a collaborative music / spoken word project combining 20 youtube videos.

ACTIVISM

I longed to join the various protest groups in the US. From abroad, the only thing I could help organize was my local March for Science.

AUDIO / PODCASTS

S-Town - 7-hours dropped all at once. I listened over a weekend. It felt much more like a novelization than journalism. Consistently held my attention, substantially more than Serial Season 2. Might be worth a re-listen now that I have the whole picture.
The West Wing Weekly
What Trump Can Teach Us About Con Law
The Allusionist
The Adventure Zone concluded its first campaign.
The Tobolowsky Files came back for a 12-episode season.
What Trump Can Teach Us About Con Law
Heavyweight
The Adventure Zone
More Perfect
My Brother, My Brother, and Me
Reply All
Every Little Thing
The Indicator from Planet Money

GAMES

Most Complicated Board Game Ever
Mad Science Foundation - a gamified version of “I cut, you choose” that’s quite fun.
Just Make Paperclips - a parable on artificial intelligence.
Dutch Blitz, which I played with some hostel friends in Copenhagen.
Gorogoa
Super Mario Run!

SPIEL 2017

Tag 1: Pyramis, Nonaga, Hack Trick, Cthulhu: Rise of the Cults, Enchantment, 27. Purchased: Nonaga, Hack Trick
Tag 2: Sector 6, Dragon Keeper, Qango, Vortex, Ringfield, Paco Saco, Captains of the Golden Age, “the pipe game”. Purchased: Dominion promotional swag card, Paco Saco, misc. small expansions from BGG.
Tag 3: Outlive, Il Diagonale, Azul. Purchased: Alien Artifacts, Imperial Settlers, Azul, green dice.
Tag 4: Merlin, watched some of the Carcassonne World Championship, Urbino

TRAVEL

The experience of air travel has improved tremendously since I got Global Entry, an EU Aufenthaltstitel, and my credit card gave me free entry into many airport lounges. Except that the one time I really needed a shower the lounge’s showers were under construction.

Cornwall, for New Years.
Boston-Amherst-NYC for an interview at UMass Amherst.
A weekend in Brussels.
A day Antwerp to see my great aunt and uncle.
Leiden, NL for a week-long workshop. Also visited Amsterdam and the Hague (mostly for the Escher Museum).
Mainz for a talk.
Vienna for a long weekend.
Oak Ridge, Tennessee for a computer users’ group meeting and to give a talk.
A long weekend in Luxembourg and Koblenz with my mom and her boyfriend.
Granada, Spain for LATTICE 2017, with an amazing visit to Alhambra, and a day in Malaga on the way home.
Bochum for a talk.
Seattle, for a workshop on neutrinoless double beta decay.
DC, for a wedding and to visit with friends and my colleagues.
NY
Essen, for SPIEL 17.
Trento, for an axion workshop at ECT*.
München, for ex-pat Thanksgiving
Billund
Odense, for Technical Advances in Lattice Field Theory at CP3 Origins.
Copenhagen

FOOD + DRINK

Oral Allergy Syndrome - I finally have a name for this extremely annoying allergy.
The best true dive bars in the DC area.
Parody is the truest mirror.

YOUTUBES

How to write like an architect
Raymond Smullyan on Carson, 1982 - it’s not too often a mathematician gets on a late night show. Especially one who sounds like the Tin Man. Or maybe the Cowardly Lion?
Game of Thrones / A Song of Ice and Fire Geek-Out Channels: Alt Shift X really draws a lot of material and evidence together. Also their April Fool’s Day episode covering GoT porn parody “Game of Bones” was inspired. Secrets of the Citadel goes deep and covers a LOT of canonical material that is not explored at all in the show or even in the main text.
Nerdwriter - I got hooked after watching his disection of Bob Dylan’s “All Along the Watchtower”
Extremely good version of the cups and the balls
P-Town - S-town parody brought to you by the guy who did the Serial parody (TTDS2015).
Brothers of Climbing - fixing the primary thing wrong with climbing.
Biisuke Ball’s Big Adventure Part 2
Downward Dog
Rick and Morty do State of Georgia vs. Denver Fenton Allen
Does Bob Mortimer Do His Own Dentistry?

LEGO

Space Shuttle Launching
2017: A LEGO ODYSSEY
Slow-motion LEGO Porsche Crash Test
LEGO Saturn V
Hajj to Billund, staying at Hotel LEGOLAND and visiting the Lego House

TRUMPOCALYPSE

2017 was a waking nightmare in many ways. We’ve witnessed a war on truth, the undermining of public institutions, attempts to roll back civil liberties, and a resurgence of white nationalism. It was impossible to engage with every outrageous action, simply because there were too many.

Washington Post changed its motto to the most metal motto of any paper of record: “Democracy Dies in Darkness”.
Billy Goats Gruff: 4chan: the Skeleton Key to the Rise of Trump - “Support for Trump is an acknowledgement that the promise is empty.” See also Trolling Scholars Debunk the Idea That the Alt-Right’s Shitposters Have Magic Powers, a strong critique of the previous article.
Milo. Oh man I love to hate this guy: I’m With The Banned, The Lost Boys of America’s New Right
Vice: What Nuclear War Would Look Like
How to Beat Trump
Trackdown Shakedown - an episode of the 1950s western TV series ‘Trackdown’ featured a character named Walter Trump who claimed he would build a wall in order to protect a town from the end of the world.
Correction: Republican Bloodsuckers who Sentenced Poor to Die Didn’t Drink Bud Light
Blue State Exit
His Kampf - a discussion with and profile of Richard Spencer, American definitely-not-a-Nazi.
It’s just the nonsense that it seems - PM May gets ready to censor and fundamentally break the internet.
Hannity on NSA Surveillance
Stephen Fry, Blasphemer
People Outside a Trump Rally Told Vice Why They Hate the Media
The Mooch is a crazy person
The Republican’s Guide to Presidential Etiquette
The Witch-King of Angmar was an Insignficant Volunteer in the Great Army of the Dark Lord Sauron
Schmabeas Schmorpus
One way to stand up to the experts is to eliminate them
Nobel, Schmobel
The problem with Article VI is that who has an attention span long enough to get through the first V Articles?
Trump Dismisses Accusers as Women
The Nationalist’s Delusion

How Many Wonders Can One Cavern Hold?

2017-12-12T00:00:00+00:00

København, Danemark

On the way home from Technical Advances in Lattice Field Theory I stopped in Copenhagen. The city is beautiful, although it doesn’t get much light in early December. I made some nice friends at a hostel, enjoyed some walking tours, and had a great hotdog. Tivoli Gardens is open for Christmas-time. We rode the roller coaster while wearing virtual-reality headsets, which was phenomenal and so obviously the future it’s hard to overstate.

Everything Is Awesome

2017-12-03T00:00:00+00:00

Billund, Danemark

On my way to Odense for Technical Advances in Lattice Field Theory I flew through Billund. LEGOLAND itself was closed for the winter, but the recently-opened LEGO House was great. Very interactive, with lots of creative opportunities and amazing exhibits.

I'll Meet You Any Time You Want

2017-11-25T00:00:00+00:00

Trento, Italia

I was invited to Axions at the Crossroads: QCD, Dark Matter, Astrophysics at ECT*, the European Center for Theoretical Studies in Nuclear Physics and Related Areas in Trento, Italy. It was a productive, educational workshop and Trento itself is beautiful and full of interesting history. We ate an absurd amount of carbs—the most delicious pizza I had included gorgonzola, pears, and thinly-cut strips of lard.

Orangutans are Skeptical

2017-07-22T00:00:00+00:00

If you’re going to guess the name of an animal in German, the best strategy is to think “What kind of pig is this?” and guess the most naïve adjective-pig compound word that fits. If it doesn’t look like a pig, try again for a horse, bear, chicken, toad, fish, or mouse. You’ll probably get it.

Kölner Zoo

His Tears Fall And Burn The Garden Green

2017-06-25T00:00:00+00:00

Alcazaba, Málaga, Spain

If We Travel By My Dragonfly

2017-06-18T00:00:00+00:00

Alhambra, Granada, Spain.

I'd Forsake Them All for Your Sweet Kiss

2017-06-17T00:00:00+00:00

Granada, Spain

All the King's Men

2017-06-04T00:00:00+00:00

Koblenz, Germany

Be Like the Squirrel

2017-06-03T00:00:00+00:00

Luxembourg City, Luxembourg

Be On My Side, I'll Be On Your Side

2017-06-02T00:00:00+00:00

Luxembourg City, Luxembourg

Your Technicolor Motor Home

2017-05-28T00:00:00+00:00

Aachen, Germany

The Hush of Falling Leaves

2017-05-12T00:00:00+00:00

Den Haag, The Netherlands

Just A flower I Can Help Along

2017-05-07T00:00:00+00:00

Keukenhof, Holland

Longer Boats Are Coming

2017-05-06T00:00:00+00:00

Leiden, The Netherlands

Stray Cavaliers

2017-03-24T00:00:00+00:00

Brussels, Belgium.

METAQ

2017-02-22T00:00:00+00:00

⊕
Tasks of one sort naïvely bundled, wasting a substantial amount of cycles ⊕
Tasks of many sorts bundled with METAQ, wasting far fewer cycles.

METAQ is a small suite of bash scripts I wrote to increase the ease and efficiency with which my collaborators and I use supercomputing resources.

Supercomputing time is almost always awarded through a competitive proposal process, and there’s usually not enough to make everybody happy. So, if you receive an allocation, you want to be sure you use it as best you can.

METAQ helps you avoid wasted cycles, by making it simple to group computational tasks together and to slot smaller and shorter tasks into otherwise-wasted cycles.

I wrote up a description of METAQ for the arχiv.

Update 2017-03-21: METAQ was covered by The Next Platform!

The Heat Came 'Round and Busted Me For Smilin' On A Cloudy Day

2017-02-14T00:00:00+00:00

⊕There's a cryptographically signed version, too.

There is a war coming on general-purpose computing. It starts with, of course, forcing child pornographers to provide evidence against themselves and fighting terrorism. We have progressed into demanding a scientist’s telephone and passwords at the border, demanding access to citizens’ social media, and using log files from a person’s implanted medically-necessary heart monitor to indict them. It creeps in as Hollywood and the RIAA search for ways to make your web browser obey them, rather than obey you.

General purpose computing is essential for freedom of thought, freedom of speech, and freedom of association. Only if you can trust your computer—only if your computer obeys you alone—is it a reliable means of resistance. Compromised electronics can be used as means of surveillance, blackmail, identity theft, and other terrible compromises. Strong cybersecurity and the ability to freely encrypt is essential. Moreover, as electronics become further integrated into human identity, their compromise amounts not just to the compromise of the unchangeable biometric data that might be used to unlock your phone, but to the compromise of the self. Indeed, I already anthropomorphize my computer as… me. I browse the web. I check my email. I post on Facebook. The computer is a transparent medium for the projection of my will and identity.

There is some concern that strong encryption poses a challenge for law enforcement, and that therefore we need some kind of compromise. You hear complaints about “going dark”. You hear police departments and the FBI make suggestions that we come up with alternative encryption standards that can be broken with a warrant. You know who never makes these suggestions? The NSA. NIST. The experts. The mathematicians who study, design, and attempt to break cryptosystems all agree that any possible government mandate for access simply provides a route for hostile attack. If you roll your eyes when people deny climate change, remember that searching for political compromises around encryption is literally math denialism, and the foundations of mathematics are substantially stronger than those of climate scienceI'm not trying to undermine climate science with this comparison. . Moreover, there’s the gun control analogy: if strong encryption is criminalized, then only criminals will have the protection of strong encryption.

So what can be done? We can adopt widespread encryption across the internet. We can make security-conscious design decisions. We can adopt free software whenever possible and recognize that its motivating principles are aligned with social justice. We can use encrypted communications channels by default even when we don’t need security, to help obscure those who do. I donate to the Electronic Frontier Foundation, the Free Software Foundation, and the Internet Archive. We must adopt the mindset that even though we might have nothing to hide, we value our privacy. We can insist that our politicians embrace cybersecurity rather than attempt to fundamentally undermine it. We can value our metadata.

Public key cryptography is a method by which you can encrypt a message with a public key, but that same key cannot be used to decrypt it—for that you need the private key. This is an excellent tool for establishing a secure channel across an unsecure channel. The private key can be used to encrypt a message that can be decoded with the public key, providing a cryptographically secure signature. This is signed with my public key, and the cryptographic signature is at the bottom.

My PGP public key, which I generated in 2013, recently expired. In the four years that passed since it was first generated, nobody ever needed it. Nevertheless, here is my new one:

- -----BEGIN PGP PUBLIC KEY BLOCK-----
Comment: GPGTools - https://gpgtools.org

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=5hH1
- -----END PGP PUBLIC KEY BLOCK-----

It has fingerprint 7171 57C8 50B6 0C96 FB21 C9EA 7C82 C5B5 4672 A784. The private key is… just kidding. You can verify it on any of the public key servers—I default to the MIT key server.

The current situation is a nightmare come true. We must value and defend our civil liberties. We must put our foot down, or imagine a boot stamping on a human face – forever.

A Modern Major General

2016-12-31T00:00:00+00:00

Minack Theatre, Porthcurno in Penzance, Cornwall, England.

Live and Die a Pirate King

2016-12-30T00:00:00+00:00

Porthchapel Beach, St. Levan, in Penzance, Cornwall, England.

Things That Didn't Suck 2016

2016-12-15T00:00:00+00:00

⊕TTDS 2011
TTDS 2012
TTDS 2013
TTDS 2015

I kept track as the year progressed, so preparing this was substantially easier than in the past.

BOOKS + SHORT FICTION

The Slow Regard of Silent Things, by Patrick Rothfuss - This book will make no sense to you unless you’ve read The Name of the Wind / The Wise Man’s Fear (TTDS 2015), and even then… It’s a weird book. There’s only one alive character. But there are plenty of not-alive objects in the story. IDK, just read it. Also, I love that Vi Hart and Patrick Rothfuss are friends.
Animal Farm, by George Orwell

I feel like I read more than this, but I cannot remember! I worked a lot this year.

ARTICLES + SERIOUS VIDEO

The Blood Harvest Possibly the most metal thing I’ve ever heard: we strap down horseshoe crabs and steal their blood for our own healthcare.
Groundbreaking Computers are revolutionizing paleogeology.
The Dragnet Stingray Cell-Site operators get caught.Bum-badum-dum. Bum-badum-daDUM. The story you are about to read is true…
The 30th Anniversary of the Challenger Disaster
- The Crew Fell To Their Deaths Alive and Aware of What Was Happening
- Sally Ride passed Information Regarding O-rings
- Feynman wrote a special appendix to the ultimate report, and it’s the only one that’s easy to read and totally frank.
- An Engineer Still Blames Himself
What Makes Mathematics Difficult To Learn by Marvin Minsky
Campaign Against Sex Robots - interesting, but ultimately wrong.
How New York Gets Its Water
The Day We Discovered Our Parents Were Russian Spies - the true story The Americans is loosely based on.
The Curse of the People Who Can’t Stop Making Puns It’s no laughing matter.
What It’s Like to ‘Wake Up’ From Autism After Magnetic Stimulation
Aphantasia is when you have a blind mind’s eye. I scored 15/40 (low, but not low enough to qualify as aphantasia) on an abridged test. I’ve noticed that I am extremely bad at visualizing specific colors, or biologically-reasonable motion. I can imagine what it feels like t to kick a soccer ball. But if asked me to draw someone mid-strike, it’d be extremely difficult. I think I could do it, ultimately, but there’d be a lot of injected reasoning and personal experience, rather than transferring a clear image in my mind to the paper. I’m good with directions, and do well at Pictionary, where stick figures or outlines suffice, but that has a lot more to do with abstract communication than faithful visual depiction.
Colors!⊕
Plaid patterns can change their appearance in da club.
So Many Research Scientists, So Few Openings as Professor Science is the dumbest thing. I wish my field were one in six!
Inside the World’s Only Surviving Tattoo Show for Medieval Pilgrims
Who Will Command the Robot Armies I laughed, but it’s not funny.
Inside a Moneymaking Machine Like No Other: Renaissance Medallion
The Last Unknown Man A man is no one.
Media Lab Director Ito interviews President Obama about AI
Lego is the Perfect Toy

PHYSICS - SERIOUS

Black holes are known to have a negative specific heat: they heat up as they radiate! We show how to derive the fact that black holes have negative specific heat from gauge theory and earned an honorable mention for our brief introductory essay.For physicists.
The holographic principle is the conjecture that certain gravitational theories and certain quantum field theories are equivalent. We numerically computed certain quantities on the gauge theory side and found excellent agreement between gravity and QFT in one example.
Neutrinoless double beta decay is a hypothetical ultra-rare nuclear decay that could shed light on the fundamental symmetries of Nature. We performed the first calculation of properties of fundamental nuclear physics needed to quantify our expectations.
Nuclear Physics from Lattice QCD INT-16-1, Institute for Nuclear Theory, Seattle WA, Spring 2016.
LATTICE 2016, University of Southampton, Southampton, United Kingdom, July 2016.
Frontiers in Nuclear Physics, Kavli Institute for Theoretical Physics, Santa Barbara CA, Summer 2016.

PHYSICS - FUN

Why is the integral of 1/x equal to the natural logarithm of x?
John Baez’s Favorite Numbers: 5, 8, and 24. The lecture on 24 has more details and background on the identity $1+2+3+4+\ldots = -\frac{1}{12}$ .
The Difference Between Entropy and Complexity
8 Is Enough

RELIGION

Meat by Terry Bisson. Will computers ever “think like a human”? Perhaps only in the same sense that air planes “fly like a bird”.
LIGO found gravitational waves.
SPECTRAL GAP is Undecideable - Seth Lloyd and the original authors compare and contrast new results with known results (continued from TTDS 2015).
Evolution in Action: Lizard Moving From Eggs to Live Birth

TV SHOWS

Law & Order SVU - The whole spiel with Benson and the guy she beat the shit out of a few seasons back… man. And the whole thing with Rollins accidentally going under cover? Can’t we just have the tried-and-true rape ⟶ investigation ⟶ trial ⟶ possible sickening loophole.
Breaking Bad - OK, I get what all the fuss was about.
Orange is the New Black - Well, that turned pretty quickly.
Game of Thrones - The Winds of Winter better be damn good if Martin is going to let the TV get so far ahead. I’m still hype for Cleganebowl.
Sports Night - Sorkin sure does have some go-tos.

MOVIES

The Secret World of Lego
GNAR - Ski hooligans turn Squaw Valley into a game. I can’t believe you’re a pro—I’m so much sicker than you.
Independence Day - I had never seen the original before.

MUSIC

Bruce Springsteen & the E Street Band at the Oracle Colliseum, Oakland CA, 2016-03-13 .
Mavis Staples opened for Bob Dylan at The Greek, Berkeley CA, 2016-06-09. Eh. He can’t really sing any more. I’m glad to cross him off the bucket list. He ended with Freebird.
Steve Winwood opened for Steely Dan at the Shoreline in Mountainview CA, 2016-06-16. Concert was great. I love Steve Winwood. Steely Dan was exactly what you expect and it was good. No ticket stub, dumb e-ticket.
Four Organs - It doesn’t really improve at all but I still found myself listening to the whole thing. There are some aural illusions, I think.
Hey Joe as covered by bluegrass musician Tim O’Brien.
მამა სერაფიმეს გალობა არამეულ ენაზე The Georgian Orthodox sang for the Pope. I have a hard time imagining what it must have been like to be a serf a thousand years ago and then hearing this.
Can’t Find My Way Home - Just Steve Winwood and a guitar. Honestly I love just about every variant of this song on YouTube.

THEATER

Latin History for Morons - John Leguizamo’s one-man show.

PODCASTS

A Canticle for Liebowitz In 1960 NPR produced A Canticle for Liebowitz (TTDS 2015) by Walter M. Miller Jr. for radio. The story tracks an abbey in the American southwest whose mission is to preserve the Memorabilia—the technical knowlege of the society from before the Flame Deluge—as post-nuclear-apocalypse society comes out of a technological dark age.
More Perfect - Radiolab covers the Supreme Court.
The West Wing Weekly - Song Exploder Guy and Will Bailey go in-depth
In Our Time With Melvyn Bragg (TTDS 2011)
This American Life
StartUp
Freakonomics
Planet Money
99% Invisible
Radiolab
Heavyweight The episode with Moby is the best one.
The Adventure Zone

GAMES

San Juan - Like Puerto Rico, but fast.
Indigo This is basically a head-to-head version of the flash game Entanglement (TTDS 2011), so I predictably LOVED IT.
Boss Monster You are the villain of an 8-bit video game and you have to make your dungeon dangerous enough to kill the heros the game throws at you. I only played this once but loved the idea and would play it again. The art is perfect and the rules and other box contents feels like an NES game.
What’s My Word - Mastermind, but for words.
Velocity Raptor - Special relativity is CRAZY!
One Night Ultimate Werewolf - I played a perfect round in LA.
Codenames Easily the best game of the year, and the first Spiel des Jahres winner I predicted in advance.
Vive VR - I played with a Vive, which is like an Occulus Rift. It was AMAZING. I played a tower defense archery game, where I actually had to nock, draw, and loose. Also some other games. It was SWEET.
Obduction - I haven’t put too much time in yet, but I’m extremely excited for the latest game from the makers of Myst.

TRAVEL

Skied often in Lake Tahoe, CA. Regained a lot of my confidence on skis after my fall. Still nervous depending on steepness.
Los Angeles, CA
- Lei Out - Beach Frisbee.
- Jurassic Restaurant which was delicious.
- The La Brea Tar PitsA very redundant name, translating to “The The Tar Tar Pits”. - The most metal science museum?
Pinnacles National Park - Pinnacles is simply amazing. Craziest damn rocks I’ve ever seen.
Seattle, WA - Seattle is the best in the spring time.
Camping in Santa Cruz - Camping at a secret beach campsite.
Detroit MI for a wedding. Detroit seemed perfectly nice.
Marine Mammal Center, Marin CA It’s a hospital for seals, sea lions, dolphins, etc. The back-stage tour is fantastic.
Jülich, Germany - Stayed in Jülich, spent two days in Cologne, one in Bonn. Looking at neighborhoods, getting a feel for the place. Fooled a few people into just speaking to me in Deutsche.
Southampton, England for LATTICE 2016. Conference went well, learned a lot, had some exciting ideas. Southampton leaves something to be desired, though Stonehenge was great.
NUCLEAR 16 at Kavli Institute for Theoretical Physics at UC Santa Barbara, Labor Day in LA, and hiking and kayaking in Santa Cruz on the way down.
I moved to Köln, Germany!
- OK, really I moved to a beet farm in Jülich.
Hannover for expat Thanksgiving.

FOOD + DRINK

Döner Kebap. I don’t know why it ends in a ‘p’, but it does. It’s guuuuuuuuuuuuut. And just a few euro.
Really cheap ok-quality wine? Like 3€ for a huge bottle.
Wurst: The Best?
Kartoffelpuffer. I get to eat latkes all the time? SIGN ME UP.

YOUTUBES

Real Life SkiFree
Confessions of a Tetris Addict - Not quite Ecstasy of Order (TTDS 2015) but made by the Numberphile people.
Spinning Levers - How a transmission works, explained by Chevrolet in 1936.
Interview with Arthur C Clarke - He was smart.
HYPER-REALITY - When we all have digital implants, the world is going to be awesome (wc?).
Magnets and Marbles - A clever Rube Goldberg machine / marble relay
Intelevator - Ylvis has a string of funny bits where they add a voice activated “feature” to everyday objects, like an elevator.
KSK Key Signing Ceremony - The creation of the cryptographic key that secures the domain name system of the internet is a serious, formal, and human activity.
Ambiguous Cylinder Illusion - Probably the best illusion I’ve ever seen?
Very Clever 3D Printed Zoetrope - Man I want a 3D printer.
Memory Lane - Gizmodo gets a tour of LEGO’s vault of all sets ever made.
Lego Yellow Submarine
Primitive Technology - This guy… he never says anything to the camera. He uses no words. Just clear filming and editing. He has a piece of remote property in the Australian bush. He builds everything from scratch or using tools he himself has made already. Basically, if the world ends, this guy is going to be fine.
Never Happened - An 8 minute episode of Black Mirror: what if we could erase our memories easily?
Is Mir Egal - A funny ad by the Berlin transit authority (turn on closed captions).
SHAME! - The Soda Stream / Game of Thrones crossover advertisement we’ve all been waiting for.
Protegion - Stop motion photography + geometry.
Ice Call - Skiing on and in a glacier.

TRUMPOCALYPSE

DC Wants Statehood - If you don’t support statehood because DC is heavily democratic, I don’t support your right to vote because you’re an unprincipled partisan.
Nation Elects First Black-Hearted President
Letter from Leslie Knope
Michael Moore on Morning Joe - Scarborough waved off every advertising break.
Historians find German Decree Banishing Trump’s Grandfather
Are Jews White?
Millennial Jews Awake to Anti-Semitism
States Rights for the Left
But let’s insist that tech vendors insert backdoors into everything!
What Was Comey Thinking?

THOUGHTS ON GERMANY

Registration - What is the point of having a unified person registration system if, when they move, they still have to go to the DMV to change their car registration?
The Poop Shelf - Only the Germans could have invented the poop-shelf toilet. It is really completely inexplicable. I am thankful every day that my home and office do not have them.
Deutsche Post - I live in the middle of no where. Nobody is going to steal my packages. Just leave them. Don’t make me come to the post office to sign for them! What good is Amazon Prime if I have to go to the post office every time I order something? The line on Saturday morning was 20 minutes long! Fire those 4 Saturday-morning employees and easily recoup the cost of insurance against stolen packages. This is not the only example I have noticed where I think basically everybody would be better off if certain jobs didn’t exist but they’re not eliminated (I assume) out of consideration to the employee.
Sunday - I imagine it’s great to have a nothing-open-on-Sunday enforcement of getting your errands done on Saturday, if you have family or friends to see on Sunday. If you have nobody, it’s not so good. OK, you can go for a walk. In an emergency you can go to the train station, where, if place you are is big enough, there will be a convenience store and a bookstore.
Bread - It’s good. It’s cheap.
Bakery - Standards are high, competition is fierce.
Quark - It’s like… somebody whipped yogurt?
Schocolade - Even the chocolate from AldiMore than a 7-11 but not a full grocer, either. is delicious. Also in Köln there is a chocolate museum, whichhaving not yet been, I assume is made out of chocolate and has a memorial to Augustus Gloop.
Cost of Living - I make less, but I need less too. Fresh-baked rolls for 0,19€. 3€ bottles of wine. Decent 2€ beers in a bar. Gasoline is more expensive. I bought a decent bicycle, not outrageous in cost.
Water - Seltzer is plentiful. Water is not free.
Weihnachtsmarkt - Christmas markets are nice. Glühwein, brezeln, sweets.
Alte Kacke - It’s weird to walk around and then BAM there’s something 1000 years old, or there’s a huge beautiful monument with a carved wreath and then inside the wreath the swastika has been removed.

Beets - Man, fuck beets.

Don't the Sun Look Good Going Down Over The Sea?

2016-11-27T00:00:00+00:00

Hannover, Germany

I traveled to Hannover to see a friend from grad school and to have ex-pat Thanksgiving, which was great. Turkey, cranberry sauce, delicious veggies, and only a small amount of beets.

I stayed with a friend of a friend who showed me around Hannover on Sunday before my train back to Köln. We walked by a very sharpSeriously, it is awesome looking natural gas processing plant, over a bridge with terrifying aquatic animals and inviting mermaids, saw the Nanas, the Opera House, and the Rathaus.

The Rathaus is open to the public and the main, vaulted room houses models of Hannover at different eras—1639, 1939, immediately post-war, and today. It sits a short walk from the end of the Maschsee, a huge artificial lake built as a public works project during the Nazi era.

Hannover’s Weihnachtsmarkt is different from the others I have seen—there is a part that is more Renaissance Fair than others: a temporary forest of evergreens, rope-making demonstrations, axe throwing. I shot crossbow bolts for a few Euro with decent accuracy—only to notice that there were fletched bolts available.

The Weihnachtsmarkt is very close to the Hannover HauptbahnhofCentral Station, abbreviated Hbf , a bustling station with many open-on-Sunday shops and quick bites to eat. The train back to Köln was very crowded—I stood for an hour of the three-hour journey. But the ride was relatively smooth and I listened to Heavyweight.

Back in Köln, I walked from the Hbf, which is right at the cathedral, through the Christmas markets at the cathedral, in Neumarkt, and Rudolfplatz.

Heavy Horses, Move the Land Under Me

2016-11-19T00:00:00+00:00

Stetternich, Germany

Somebody Holds the Key

2016-11-18T00:00:00+00:00

After Tuesday’s predicament things started happening fast.

Wednesday afternoon I met with the International Employees Officer again. This time she was extremely warm. She basically said there was no hope to expedite anything, and the only route to starting my contract at FZJ was to accept the offer on the beet farm. She walked me through the health insurance application.

I sent my future landlady an email during that meeting.

Thursday morning, I went to the laboratory to meet with herShe has worked there 40 years. . I gave her the deposit and November’s half-month of rent in cash, as my online banking account isn’t activated yet. She signed the WohnungsgeberbestätigungHousing-giver-confirmation. , which I took to the Jülich municipal hall. There, I got my Jülich Anmeldebestätigung. I took that paper back to the International Employees Officer, who copied it and had me sign the application for the residence permit.

⊕
Meine Anmeldebestätigung

By Thursday afternoon the Immigration Officer approved it verbally, and agreed to back-date it to Monday. So I retroactively am saved from facing the choice of breaking my employment contract or working illegally. I will have the paper copy of the temporary work paper on the 29th, when I also have an appointment with the Immigration Officer to have my fingerprints taken and complete requirements for the complete residence permit.

I sit here on Friday night, writing from the beet farm. If anyone had told me any time in my life before Tuesday that I’d live on a beet farm in Germany with 3 ponies and 4 horses, I’d have laughed at the absurdity of the suggestion. I would never have picked this. But it was a solution to acompletely absurd problem.

At least three months in Jülich. That’s 3 months of not meeting the people I want to meet. Of not establishing my routine. Of not really settling in. Of not living the adventure I had hoped.

Ultimately, I am here because ich bin physiker, and I want to physik! If to this I must consent, I consent.

Stuff that's scuzzy

2016-11-16T00:00:00+00:00

Well. I had a bit of a day on Tuesday. When I was hired I was told “You’re American? Just come on a tourist visa and we’ll convert you to a work visa when you arrive.” OK, seems easy enough. I went to the ForschungszentrumResearch Center last week to sign the contract, and I scheduled a meeting with the International Employees Office (which is just 1 person) for the first day (Monday). Nobody said “Do you have a work permit? Where are you registered?”

Registration is something Americans would never put up with—you must tell the police where you live in order to have any legal status, and as proof you registered you receive a MeldebescheinigungRegistration certificate . Every government service is contingent upon your registration, and you must go to your local office or the central city office (which has a huge line). Different municipalities may have different requirements or charge different fees for the same service. The visa change I need is €20 in Jülich but €100 in Köln.

⊕
Canal in Lindenthal, near Dürenerstraße in Köln, where I hope to live, eventually.

I get to the meeting, where we’re supposed to sign me up for health insurance and switch the visa over.

Where are you registered?

Köln.

Oh, that is outside of my geographical jurisdiction for switching the work visa. I cannot help you. You must take your Meldebescheinigung, your passport, and your employment contract to the local government office tomorrow. If you have a problem, here is my card and please have them call me. And you should not sign up for the health insurance until your job starts, because the laboratory pays for a big fraction of it.

OK.

Here is my card, so that you can have the officer call if you have a problem.

⊕

Get up Tuesday morning, go to the government office with the 3 important documents. Nope. Sorry. You are missing X, Y, and Z papers, and you don’t have the proof of health insurance. I cannot give you the work visa, and if you come back with the proper papers, it will take up to two months for processing, even for the temporary work permit. You understand that you cannot currently work, even with this contract?

WTF.

I get the government employee and my helper on the phone together. They speak Deutsch very fast together for a few minutes and I have no idea what is going on. “Ja… OK… Please take the phone Mr. Berkowitz.”

[from Jülich:] Mr.It’s Dr. Berkowitz. I don’t usually offer the correction, but people take it seriously in Germany. Berkowitz please come to my office at 2:30 PM tomorrow.

But my advi…

Mr. Berkowitz, I cannot spend any more time on you today, I have many appointments.

:blink: :blinkblink: You sent me here today and told me to call if I had a problem!

I cried as I walked down the straße back to my AirBNB, completely frustrated and defeated and alone.

So now I’m in a scramble.

The only plausible solution is to move as quickly as possible into the jurisdiction of the person who can help me at the laboratory, and she goes on holiday at noon on Friday, and there is no substitute who can perform her job. Moreover, her jurisdiction is in the middle of goddamn nowhere.

I saw a room in a house in Jülich that same day. The house has 3 ponies, 4 horses, and beets. Fields and fields of beets as far as the eye can see. And I must sign a lease for at least 3 months, and must by law give 3 months notice before moving out. The first 3 months may not be a problem, because if I move during the processing of my work permit, it will have to transfer between offices and then the requirements can change! So, 3 months amongst the Pferde und Rüben.

I’m eager to try the Chinese restaurant to the east by southeast. I have brought the entirety of my creative imagination to try to guess what it might be like, with no success. My colleagues tell me there is what sounds like duckpin bowling in the basement.

The lab I’ll be working at has 6000+ people. How are they totally unprepared for my circumstance? Why didn’t someone give me a checklist? I could have done this stupid thing at a consulate while I was in the US! Why didn’t anybody ask me when I was in last week to sign the contract? Why didn’t the International Employees’ Officer warn me that being in the geographical region where she has sway is extremely important? Why didn’t she know that more than 3 papers are required?! Then there’s a Catch-22 on the health insurance. I was totally unpreparedperhaps “misinformed” is fairer , and the lab was wildly unprepared for me.

So I have an AirBNB in Düren, which is the “big” place near JülichRead: boasts its own radio station , but I won’t be here for long—I will move all of my things into my room in Jülich in the next few days.

Jülich is known for the Forschungszentrum, stallions to put out to stud, and beets. In the winter time, they process the beets into sugar. The whole place smells vaguely of ash and muted beets. Like a beet brewery burned down. Mild but off-putting and entirely pervasive.

If you need me, I’m the one doing computational nuclear physics and tending the ponies.

When I told this to a PhD student I’ll be working with this whole spiel, they asked me if I knew the word “Schadenfreude”. I am aware that this will make a funny story some day / may currently be funny if it’s not happening to you.

Otherwise, Germany has been great!

The day of my arrival was AllerheiligenAll Saint’s Day which is a recognized holiday in this portion of Germany. I walked around Köln a lot—everything was closed.

Köln

I got sick on the airplane. I thought at first it was just jet lag, but then it turned into a nasty cough and a really stuffy nose. But: no health insurance!

The next day, I got a Handytelephone service and a bank account. My research group’s leader won the Lise Meitner Prize so there was a symposium at the Forschungszentrum, and I got to see many people in my field.

⊕

The next day was the Trumpocalypse. I woke up just as PA was being declared. I basically read all day, and looked for flats.

⊕
Kölner Dom

Finding a flat is very difficult. There’s a huge market problem, which is that it is way too cheap. I’m not sure if it is by law, or just custom. The demand is therefore through the roof, and any opening gets 100+ applicants, so the supply is washed out. When I told my AirBNB host that I had two weeks to get settled before starting work she just laughed. Most flats or shared flats are secured by the I-know-a-guy method, and I don’t know any guys. So if you know a guy in Cologne who isn’t me, let me know.

I got a car (which required me registering in Köln). Driving stick was new—I’m still not perfect at it. That switch from 1st to 2nd gear…

This most recent Friday was the start of Carneval (11:11 on 11/11).⊕
Carneval My AirBNB host brought me along with her friends, which was great. They have Carneval celebrations straight up until Lent, but the kickoff and the Fat Tuesday celebrations are the biggest. A lot of “We are Köln, We are the best” kinds of singing, and schunken—traditional “dancing” which is really just locking arms in a big circle, swaying back and forth, and singing. Not knowing or understanding any of the words makes it a little bit confusing. I grasped “Schön ist liebe”Life is Beautiful and then logicked out that the following line is along the lines of “Even if you’re really old.” Many old people were superpronounced “zoo-per” into it. They either dress like (non-scary) clowns or in red and white (the Kölsch colors). But people of all age participate. I don’t understand. It’s just some random Friday. Don’t these people need to be at work?

Saturday I spent in Aachen, ⊕
Aachener Domlooking at a potential flat, before I knew I’d need to live on the farm to solve my visa problem. Their Christmas Mark[e]t was under construction, and sits just outside the huge cathedral and Charlemagne’s seat.

People have made many jokes about me being the first American refugee. Which is… yeah. Especially in light of my hilariousword choice? visa difficulties. It’s funny. But also it’s not funny.

Soagain, pronounced “zo” : it’s been up and down. Once things settle down and the visa issues get fixed, I think it will get better.

I already didn’t really like beets. I mean, once in a while, fine. But, and I think I know enough Deutsch to say it: beets up der wazoo?

The Döner is fücking goooöoood though.

⊕

Thinkin' and drinkin' are all I have today

2016-11-09T00:00:00+00:00

I believe in reason. I believe in facts. I believe in a shared, underlying reality. I believe in the Enlightenment. I believe women are as smart as men. I believe in listening. I believe that my experience is not the only valid one. I believe in trying to understand another point of view. I believe in changing my mind. I believe it is valuable to admit ignorance.

The issue, of course, is that if you don’t believe in a shared reality, if everything is a partisan position, if you don’t have an open mind, if you cannot challenge your prejudices, if you have no empathy, if you don’t desire informed, inclusive governance, if you jump to conclusions, or if your emotions take control, it may not be possible to free your mind. Irrationality is something you can’t talk yourself out of.

It is apparent that the Democrats were out of touch with the reality of the electorate.

It is apparent that cynical, manipulative, vacuous propaganda can overcome Enlightenment values.

Reality must take precedence over public relations, for Nature cannot be fooled.

Where Your Gentle Wing Rests

2016-08-03T00:00:00+00:00

Bonn, Germany

A Golden Winged Ship Is Passing My Way

2016-05-28T00:00:00+00:00

Santa Cruz, CA

We drove down on Saturday, through the hills west of Palo Alto to the coast.

We knew of a secret beach campsite, where you leave your car on some nearby private property with a friendly donation and short hike down from Highway 1 to the beach. The site is on public grounds, but not visible from the road and the segment of beach is disconnected from the beach to the north by impassable rocks.

We somehow left the hotdogs at the grocery store (after purchase) so we had a light dinner of lousy salad and delicious, albeit a bit sandy, artichoke bread. We drank beers and sat around the fire.

The morning brought biologists looking for a nearby dolphin carcass, which was pretty interesting—they took samples, poked and prodded, and made some measurements.

We had brunch at the Main Street Grill in Half Moon Bay on the way back to San Francisco.

Steal Your Face Right Off Your Head

2015-12-27T18:00:00+00:00

Things That Didn't Suck 2015

2015-12-27T12:00:00+00:00

⊕TTDS 2011
TTDS 2012
TTDS 2013
I was delinquent in 2014, so this contains approximately twice as much as it should.

BOOKS + SHORT FICTION

Thinking In Pictures, by Temple Grandin - Explains what it’s like to be autistic. Helped me figure out that I’m not autistic.
What is Life? (1944), by Erwin Schrödinger - Tries to explain what it could mean to be alive.
American Gods, by Neil Gaiman - Weaves a story whose premise is that all the gods of the Old Country migrated to America with their believers.
In The Beginning… Was The Command Line, by Neal Stephenson - covers the history of computers.
The Name of the Wind and The Wise Man’s Fear by Patrick Rothfuss - A story about an unreliable narrator orphan who goes to magic school and (maybe?) nothing really happens, but it’s really fucking good.
A Canticle for Liebowitz (1960), by Walter M. Miller Jr. - Tracks a post-nuclear-apocalypse society coming out of a technological dark age. Motivated me to give to the Internet Archive.
Seveneves, by Neal Stephenson (Snow Crash, Cryptonomicon, Anathem (TTDS 2012)) - What happens if the moon suddenly explodes? Went to a reading / Q&A and got my copy inscribed.
What If?, by Randall Munroe - Tackles bar-room speculation with research and physics
Our Mathematical Universe, by Max Tegmark - Proposes a serious and compelling form of Mathematical Platonism.
The Secret Number (TTDS 2012) was made into a 15 minute short.

ARTICLES + SERIOUS VIDEO

The Greatest Juggler Alive Drops Everything
The Knowledge - Uber Ruins Everything.
Sisyphus Kinetic LEGO Sculpture
Update to Could Conjoined Twins Share A Mind? (TTDS 2011)
The Moral Character of Cryptographic Work - Seriously, though, all this nonsense about outlawing strong crypto is scary.
The Great Paper Caper - Counterfeiting is legitimately interesting. Canadian man counterfiets $250M USD and essentially gets away with it.
The Great Chain of Being Sure About Things - This title sucks, but it’s about the consensus technology behind bitcoin
8 Adults, 3 Kids: Modern, Intentional Families are on the Rise
The Secret Life of Yo-Yos
The Case of the 500-Mile email bug - Computers are hilarious.
One Man’s Quest To Rid Wikipedia of Exactly One Grammatical Mistake - This article is comprised of hilarious anecdotes, grammatical arguments, and Wikipedia palace intrigue.
John Horton Conway: The World’s Most Charismatic Mathematician
The Wall of Sound - The Grateful Dead’s crew were sonic pioneers.
How the Talmud became as Best-Seller in South Korea
Nick Offerman at the Congressional Radio and TV Correspondent’s Dinner
The Press Your Luck Scandal (1984) - Unemployed Ice Cream Truck Driver beats Press Your Luck
God, The Universe, and Everything Else (1988) - Hawking, Sagan, and Clarke shoot the shit.

PHYSICS - SERIOUS

Stealth Dark Matter - What experimental constraints can we place a particular kind of strongly-interacting dark matter?
Axions - We offer the first constraint the mass of the hypothetical QCD axion from SU(3) Yang–Mills, and I show that constraint should get tighter with a complete calculation from QCD by studying properties of the strong force at Big Bang temperatures.
Nucleon-Nucleon Scattering - We calculate how protons and neutrons interact, in a modified version of reality. We employ new techniques to go beyond the spherically-symmetric interactions previously studied, crucial for studying parity-violating interactions.
LATTICE 2014
Bay Area Science Festival
Organized LLNL Beyond the Standard Model Workshop
LATTICE 2015, Kobe, Japan
Numerical Approaches to the Holographic Principle, Quantum Gravity, and Cosmology, Yukawa Institute for Theoretical Physics, Kyoto University, Kyoto, Japan
INT-15-3 Intersections of BSM Phenomenology and QCD
INCITE Proposal was funded (Page 20)

PHYSICS - FUN

Is The Universe A Simulation?
I got an acknowledgement in second printing of Quantum Computing Since Democritus (TTDS 2013)
Best Math Puns Contest 2014
Fermat’s Little Theorem
Computational Hydrographic Printing - The with-computers version of The Art of the Marbler (TTDS 2015).
The Best (and Worst) Ways to Shuffle Cards
LISP as the Maxwell’s Equations of Software - Swim in the purity of quantified conception and of ideas manifest.
In Mathematics, Mistakes Aren’t What They Used To Be
This philosopher has a new definition of “nature,” and it includes traffic jams - At once totally trivial and deep. I’d go further and put culture inside of nature, too.
Too Many Worlds - The absolutely dumbest possible objections to the Many Worlds Interpretation of Quantum Mechanics, but the author doesn’t know that.
The First Light of Trinity
A Career In Science Will Cost You Your Firstborn - Seems about right.
A Few Goodmen - Goodman, Goodman, Goodman, and Goodman explore the phenomenon of coauthorship by economists who share a surname.

RELIGION

Truth, Provability, and the Fabric of the Universe
Our Mathematical Universe (also under BOOKS)
Physicists and Philosophers Hold Peace Talks
SPECTRAL GAP is Undecidable - And Aaronson’s take

TV SHOWS

Man in the High Castle
Would I Lie To You? - I don’t understand why there isn’t an American version of this. Could be a podcast. Also I identify with David Mitchell.
Black Mirror - The Twilight Zone for the technological era.
Only Connect - Another British show that could be a podcast.
Silicon Valley - Seems eerily accurate.
Connections (1978)

MOVIES

The Lego Movie
Particle Fever
Tim’s Vermeer
The Theory of Everything
Interstellar
The Martian
Ex Machina
Predestination
Stripped - Feature-length documentary about comic strips, with a good interview of Bill Watterson.
Ecstasy of Order - Tetris is the best video game ever.
Star Wars: The Force Awakens

MUSIC

I went on a kick of listening to Tuvan throat singing for like two weeks. I was in a weird place. I still can’t do it. I think you probably have to be alone on the steppe with only your herds to get really good.
Miles Davis improvises over LCD Soundsystem
Fredrika Stahl
Merry Clayton’s part in Gimme Shelter
2015-05-01 The Decemberists at The Greek Theater - They can really put on a show.
2015-07-03 and 05: Grateful Dead’s Fare The Well Concerts, in Chicago - This was really unbelievable.
2015-12-27 Dead & Company at Bill Graham Civic Auditorium - THIS IS TONIGHT!

THEATER

Improv 4 Humans Live Taping at SF Sketchfest - 2014, 2015.
Mortified
Nerd Nite (both East Bay and SF) - The best one I went to included a guy who draws realistic dinosaurs for scientific publications and museums using the best knowledge available.
Emperor Norton’s Fantastic San Francisco Time Machine - A historial interpreter gives walking tours of SF as an 1800s San Francisco eccentric who proclaimed himself Emperor of the United States
Festival of Bad Ad-Hoc Hypotheses (SF 2014)
Festival of Bad Ad-Hoc Hypotheses (Seattle 2015)

PODCASTS

GAMES

Kye (1992)
Portal - I know, I’m late to the game on this one.
Mini Metro
Super Mario Maker
Ducktales Remastered - The NES game was remade for Wii U
Terra Mystica - Only played it once, but liked it.
It might be that I didn’t Settle Catan once this year, which would be the first time since… 2004?
Dominion expansions
Twilight Struggle - I’ve only played as the USSR.
Space Alert - It’s a real-time board game. It’s kind of like the Space Team App (which is also super fun) but more serious and gamer-esque.
Pandemic
Betrayal at House on the Hill
Munchkin
Last Will - This was very fun, and it’s extremely confusing that the goal is to get rid of as much money as you can as quickly as possible.

TRAVEL - 2014

Minnesota for a wedding. - Nye’s Polonaise Room with live piano karaoke and The World’s Most Dangerous Polka Band. I sang Charlie on the MTA, to tremendous applause.
Big Sur
Zion National Park for some excellent canyoneering. I ran into a rock climbing instructor I had in college in Springdale.

TRAVEL - 2015

DC ⟶ Boston ⟶ Fermilab / Chicago - Organized around going to the Fare The Well Dead50 concerts.
Japan for a month - Kobe ⟶ Kyoto / Nara ⟶ Fuji ⟶ Tokyo ⟶ Osaka ⟶ Mineyama ⟶ Nagano Prefecture ⟶ Tokyo
Backpacking at Devil’s Postpile
Road trip to Seattle for INT 15-3 workshop - Berkeley ⟶ Lassen Volcanic NP (2 days) ⟶ Crater Lake NP (2 days) ⟶ Mt. Rainier ⟶ Seattle ⟶ Cape Disappointment ⟶ Eugene ⟶ Redwood NP ⟶ Berkeley
Sequoia

FOOD + DRINK

Sushi Dai, Tsukiji fish market
Russian River Brewing Company
Mammoth Brewing Company
Falling Sky, Eugene OR
Growler USA, Eugene OR
Steak and brussel sprouts at Mikkeller Bar
Toast
Umami Burger

MISC

A one-off glassblowing workshop that was fun.
I tried to bike to work, and discovered a crucial mistake in Strava’s maps at the top of an 1000+ft climb instead.
Bay to Breakers was zany.

YOUTUBES

Master Blacksmith Forges a Knife
Meet the Mennonites Behind One of the World’s Best Syrups - I still don’t really know what sorghum is, but I want it.
Weird Canadian Guy Works Wood
Physics GirlSometimes she goes by Girl and sometimes by Woman. , especially Crazy Pool Vortex - Apparently she and I were at MIT at the same time? How did I not know her then?!
How Money is Made and Printed
What if Episode III Were Good? - The final installment of What if the Star Wars Prequels Were Good (TTDS 2013) - If Star Wars is ever rebooted, I hope they do it like this. Also I hope that Jar Jar is actually a Sith master.
The Seinfeld Situation - Indian Comics make a Seinfeldesque video about Seinfeld’s Mumbai Performance being cancelled. It’s spot on. It helps to know that Tatkal is an Indian website for booking train tickets.
The Engineer Guy - Especially his dive into aluminum cans
The 8-Bit Guy - Especially the Graphics episode Learn how old tech works.
Truth or Drink - It’s a whole series (people dating, parent/child, exes, etc.)
Adam Sandler’s Channukkah Song (Part 4)
Coldplay’s Game of Thrones: The Musical
Jožin z bažin (1978) (Joey the Swampthing) - I don’t know. I like it. Made me realize I dance like a Soviet from 1978. Also why does that guy show us the inside of his mouth?
Crows Understand Water Displacement
Hot Bagels
Satanists Unveil Statue - The best acting I’ve ever seen is in this video.
The Triangle - Macarthur Genius Michael Moschen juggles inside a triangle.
Treehouse Bicycle Elevator - Some day.
Nick Offerman’s Shower Thoughts - Once you have a PhD, every meeting you go to is a doctor’s appointment.
Serial Parody
Synchronized Juggling
The Art of the Marbler
Numberwang
Amelymeloptical Illusion - Beautiful contact juggling.

This World Was Made For All Men

2015-10-17T00:00:00+00:00

Cape Disappointment, Washington

Nicer than it sounds.

Show the Bastards Up With Our Divine Light

2015-10-16T00:00:00+00:00

Seattle, Washington

Dungeons Deep and Caverns Old

2015-10-04T00:00:00+00:00

Mount Rainier, Washington

Tore Me All to Pieces, Nothing Else Remains

2015-10-03T15:00:00+00:00

Salt Creek Falls, Oregon

See the Colors Floating in the Sky

2015-10-03T09:00:00+00:00

Crater Lake National Park, Oregon

The Deep Forbidden Lake

2015-10-02T14:00:00+00:00

Crater Lake National Park, Oregon

Wild Mountain Honey

2015-10-02T09:00:00+00:00

Mount Shasta, California

Flame From Your Stage Has Now Spread to the Floor

2015-10-01T00:00:00+00:00

Lassen Volcanic National Park, California.

In the morning I moved from the Manzanita Lake Campground to the Butte Lake campground, which is towards the other end of the park. It has substantially less infrastructure and is less scenic, resulting in a substantially smaller crowd—there were only two other occupied campsites.

I got off to an early start, mentioning to an older Scottish couple my plan to hike all day, and that they should get concerned if I was not back by 6 PM.

From the campground it was a nice walk to the base of Cinder Cone.

The hike up Cinder Cone is difficult on a very steep, totally featureless slope of small loose black rubble. With every step the earth slides a bit. There is no place to rest, sit, or find purchase with your hands.

Once on top, the views are spectacular. Back from where you came you see pine forests heading into the mountains. The caldera is a mix of blacks and reds, and on the other side of the mountain are the Fantastic Lava Beds—lava flows from previous eruptions—and Snag Lake, with other volcanoes in Lassen National Park visible in the distance.

Coming down is substantially easier—the path is longer and thus less steep. Towards the bottom the scoria gives way to larger stones, with some scrambling or larger steps between boulders.

I followed along the edge of the lava beds until I came to Snag Lake. I considered scrambling along the boulders to cut the path short, but decided against it, as the boulders were piled steep, and looked sharp.

I stopped for a snack, and when I continued, I walked for a few minutes before realizing I had left my hiking poles. The best decision I may have ever made was to go back for them.

I walked along the shore of Snag Lake, which was substantially lower because of the prolonged California drought.

When full, Snag Lake has a spit of land that stretches towards the right shore. In the drought conditions, though, the spit was a full isthmus, partitioning the lake. Cutting across would save about 1.5 miles and some substantial time.

⊕
My approximate route, on the NPS Map. Dashed lines indicate off-trail hiking. I hiked about 14 miles.

I took a few steps towards the birds. My hiking boots got a little muddy.

A few more steps, a little bit more muddy. Well, they were going to need a wash at the end of this road trip anyway.

A few more steps and the hems of my jeans were muddy. Well, that’s to be expected on a hike. I was going to have to do laundry anyway.

A few more steps, and I was up to my ankles. Who cares? The pants were already muddy anyway.

A few more steps. About a third of the way across. Up to my shins. Well, what’s the difference at this point.

A few more steps. The mud is up past my knees.

Oh.

This must be how animals got trapped in muck and turned into fossils.

It’s a good thing I tied my boots tight. Every step was a struggle as the mud fought to keep my feet.

I’m half way. What do I do? I can go back, but I’m half way! If I’m going to fight my way back, I might as well fight my way across. I use my hiking poles to probe ahead of me, ensuring they find the solid lakebed below the mud, and planting them for balance and leverage.

I manage not to fall.

I get across. I am soaked, and covered in mud up to my thighs.

I was lucky to be free. I hadn’t seen a single person for hours—since leaving the campground. Had I gotten exhausted, who knows if I would have been rescued.

I sat on a log for a rest. I had another snack and drank a huge fraction of my water. I was sweating, and my legs were tired. I swore never to attempt a similar crossing ever again.

Now, to find the trail. How hard could it be? It just runs along the lake!

But the water level is down, and “along the lake” ain’t what it used to be. I couldn’t find it. I don’t know how. If you walk away from the water, you have to cross it eventually! I missed it.

Once I realized I had gone too far I turned left, knowing that I would cross the trail again. There were many downed trees that I needed to climb over. Some hiking in relatively flat woods. Some traversable ravines.

Even watching closely, I missed the trail a second time. But at least this time I was heading back towards the lava beds, and even in the worst case would be making progress home.

I continued off trail.

I finally came to Butte Lake. The trail was unmistakable. Thank goodness.

I hiked another mile or two along Butte Lake, and looked for the shorter path back to the campground. I could not find it. Not so bad—only an extra half mile.

The hike back to the campsite from the edge of Butte lake was lovely. Pines, gentle hills, and two serene, hidden lakes.

I got back to the campground at about 6:15, and checked in with the Scottish couple.

I must have been quite a sight. Sun-dried mud from the waist down, sweat and sun from the waist up. They took one look at me and raised their eyebrows.

We were just starting to wonder where you were…

I told them the whole spiel. They shook their heads. They laughed. They went on about the folly of youth.

I went back to my campsite, pitched my tent in the last light, and cooked myself some rehydrated mountain chili. I slept very well, glad to be alive.

Take a Whole Pail of Water Just to Cool Him Down

2015-09-30T00:00:00+00:00

Bumpass Hell, Lassen Volcanic National Park

I Set Out Running But I Take My Time

2015-09-07T00:00:00+00:00

Devil’s Post Pile National Monument, Mammoth Lakes, CA

Eat them up, yum!

2015-08-07T00:00:00+00:00

¥4000, or (at the time) about $30. Easily the best sushi I ever had, breakfast or otherwise.

Sushi Dai, Tsukiji Market

Let Me Wander In Your Garden

2015-08-06T00:00:00+00:00

Besso Onsen and Ueda, Japan

Wrapped In The Old School Song, We Fly Our Colours High

2015-08-05T00:00:00+00:00

Matsumoto, Japan

The Locomotive Jumped The Gun

2015-08-04T00:00:00+00:00

Yudanaka, Japan

Its Ribs are Ceiling Beams

2015-08-01T00:00:00+00:00

Osaka, Japan

Oh, Mountain of Our Eyes, What Do You See?

2015-07-25T00:00:00+00:00

Mt. Fuji, Japan.

A Tingling Recognition

2015-07-19T00:00:00+00:00

Nara, Japan.

The Ink Is Black, The Page Is White

2015-07-16T00:00:00+00:00

Himeji Castle, Himeji, Japan.

They're A Band Beyond Description

2015-07-05T00:00:00+00:00

Soldier Field, Chicago IL

Dust off those rusty strings just one more time…

First Set:

China Cat Sunflower > I Know You Rider
Estimated Prophet
Built to Last
Samson and Deliliah > Mountains of the Moon > Throwing Stones

Second Set:

Truckin’ > Cassidy > Althea
Terrapin Station > Drums > Space > Unbroken Chain > Days Between
Not Fade Away

Encore:

Touch of Grey

Encore:

Attics of My Life

Where Little Cable Cars Climb Halfway To The Stars

2015-01-31T00:00:00+00:00

San Francisco, California, and Emperor Norton’s Fantastic San Francisco Time Machine.

Rainbows End Down That Highway Where Ocean Breezes Blow

2014-10-18T00:00:00+00:00

Big Sur, California

The Lunatic Is On The Grass

2014-10-08T00:00:00+00:00

I left the house around 1:30 and made it to Ocean Beach by 2. Unfortunately, contrary to the prediction of a clear night, it was quite foggy. Moreover, the parking at Ocean Beach is weirdly 100% restricted between 2 and 5 a.m. I thought I might try and leverage Twin Peaks’ altitude, but the fog unfortunately thickened as I ascended.

I considered retreating to the East Bay, where, though San Francisco is quite bright, the observing conditions were at least clear. However, as I came down from Twin Peaks and headed east on Haight at around 2:30, the sky cleared up. This was fortunate timing, as the first edges of the Earth’s shadow impinged on the Moon at around 2:24. I found a parking spot and made it to Duboce Park without missing too much.

I set up my tripod and put on my telephoto lens, which served as a reasonable telescope substitute. Over the course of a few hours I took over 250 photographs. From the previews on the LCD screen on my camera, they were coming out amazing. Unfortunately, once I got them on a higher-res screen, it was apparent that they were mostly blurry or dark. If I adjusted the exposure time to capture enough light to see details of the moon and a few stars, those few seconds were enough for the Earth to rotate slightly and alter the positions in the sky, blurring the photo. That disappointment means it is worth it to buy a telescope with an equatorial mount for the future.

I spent the evening with two nice people who live across the street from Duboce Park, Kemrexx and Kyla, and their dog Pablo, plus some transient people walking through the park. We shared some beers, geeked out about astronomy, and watched the moon together. Two cop cars scoped us out, seemingly unaware of the ongoing wonder in the heavens.

Though I wish it had been darker, the field in Duboce park is big enough to get you away from the immediate glare of any streetlights, and the night was clear enough to see many stars. Uranus, which ought to have been visible through my camera, was outshone even by the eclipsed Moon.

The Moon itself was red. Really red, and very pretty.

It's Stormin', Stormin' Rain

2014-06-07T00:00:00+00:00

Spotted jellies at the Monterey Bay Aquarium, Monterey CA.

Listen to Those Rails A-Thrumming All Aboard

2014-05-24T00:00:00+00:00

To convert from Fahrenheit to Celsius and back again is often a pain in the neck. Do you multiply by 5/9 first, and then subtract 32? The other way around? Add 32? How does it go, again?

Most people know that water freezes at 32˚F / 0˚C, and boils at 212˚F / 100˚C (at standard pressure). ⊕Why was 212˚F chosen as the boiling point? Well, freezing and boiling are in some sense opposite, and they are separated by 180˚…

This information is enough to convert. But most people don’t want to solve two equations in two unknowns on the fly. So people make up rules of thumb.

A rule of thumb that isn’t so bad at temperatures near freezing is that each degree Fahrenheit is half a degree Celsius. It is only off by 1 part in 18 so that it’s off by only 1˚C at 50˚F. But the error gets worse as you get further from freezing.

Luckily, I know another rule of thumb that stays within 1˚C of the true value. It has to do with the 6 train, also called the Lexington Avenue local train, in New York City. The rule is this: the stop at 33rd street is 0˚C, each stop (thought of as ˚F) farther up town is another 5˚C.

That is:

Stop	Exact Conversion	Rule of thumb
[Street or ˚F]	[˚C]	[˚C]
33rd	0.555	0
42nd	5.555	5
51st	10.555	10
59th	15	15
68th	20	20
77th	25	25
86th	30	30
96th	35.555	35
103rd	39.444	40

which is good to 5/9˚C all the way through 103rd street. After that, it sort of… goes off the rails.

Another Brand New Day

2014-04-27T00:00:00+00:00

San Francisco, CA.

A Cave Up In The Hills

2014-04-26T00:00:00+00:00

Mount Diablo, California.

Smiles Await You When You Rise

2014-04-06T00:00:00+00:00

The golden ratio $\phi = \frac{1+\sqrt{5}}{2}\approx 1.618\ldots$ can be represented by a beautiful repeated fraction and a beautiful repeated square root. This leads to the mystical-looking identity:

\[1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}} = \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}}.\]

Let’s try to understand the origin of this identity.

The golden ratio is the solution to the equation

\[\phi^2 - \phi - 1 = 0\]

which can be rearranged in two different ways.

The more common, perhaps, is to rearrange it into

\[\phi = 1+\frac{1}{\phi}\]

This rearrangement gives us a method for generating approximations to $\phi$:

Make an initial guess.
Plug that guess into the right-hand side and
Use the result as your next guess for $\phi$.

Notice that if your initial guess is perfect (meaning you guessed the true value of $\phi$), the next guess (and all subsequent guesses) are also perfect. We call “perfect guesses” fixed points because when you put them through this little procedure they come out unchanged.

So, if our initial guess for $\phi$ is $\phi_0$, our first improved guess would be

\[\phi_1 = 1+\frac{1}{\phi_0}.\]

Our second improved guess would be

\[\phi_2 = 1+\frac{1}{\phi_1} = 1+\frac{1}{1+\frac{1}{\phi_0}},\]

the third improved guess would be

\[\phi_3 = 1+\frac{1}{\phi_2} = 1+\frac{1}{1+\frac{1}{1+\frac{1}{\phi_0}}},\]

and so on. As we continue this process our initial guess becomes less and less important to our later guesses, and when we repeat this process infinitely many times the influence of our initial guess vanishes entirely, so that the “infinityth” guess must be some value independent of our initial guess. This means it must be a fixed point, a true solution to the defining equation, or equivalently, a perfect guess:

\[\phi = \phi_\infty = 1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{1+\ddots}}}}\]

Another rearrangement of the equation that defines $\phi$ is

\[\phi = \sqrt{1+\phi}.\]

We can use this rearrangement in the same fashion as we did the other: view it as a pattern for generating improved guesses. If our initial guess is again $\phi_0$ then

$\phi_1 = \sqrt{1+\phi_0},$ $\phi_2 = \sqrt{1+\phi_1} = \sqrt{1+\sqrt{1+\phi_0}},$ $\phi_3 = \sqrt{1+\phi_2} = \sqrt{1+\sqrt{1+\sqrt{1+\phi_0}}}$

and so on, so that an infinite number of guesses later we wind up with

\[\phi = \sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\sqrt{1+\cdots}}}}},\]

demonstrating the mystical-looking equality.

There is one loophole to this whole story: there are actually two “perfect guesses” that yield themselves when you try to improve them in the first iterative manner. The first is the golden ratio, the one we actually want. The other is $-1/\phi$. If you use this value as your initial guess, you will get stuck. However, if your initial guess differs from this value in any miniscule amount, you are guaranteed to wind up with the golden ratio eventually. We express this by calling $\phi$ a stable fixed point of this procedure and $-1/\phi$ an unstable fixed point. The second iterative procedure has only one fixed point, ($\phi$), because we implicitly mean that we want the positive square root and not the negative square root.

California, Preaching On The Burning Shore

2014-03-23T00:00:00+00:00

Muir Beach, CA

Ain't Gonna Stop Until The 25th Hour

2014-03-22T00:00:00+00:00

2048 is a game by Gabriele Cirulli based on 1024 and similar to Threes. More than one person I know has likened it to a mind virus.⊕
xkcd/1344

The game is played on a 4x4 grid, and each cell can either be empty or contain a tile with a power of two on it. The game starts with a few cells filled with some 2s and 4s.

Using the arrow keys, one can send all of the tiles as far in a given direction as possible. If two tiles with the same power of two would collide as a result of this movement then they combine into a single tile with the next higher power of two, and your score increases by this higher power. When you move any tiles, a new tile that contains a 2 is generated in a random empty cell with 90% probability and a 4 is generated with 10% probability. If it’s not clear what I’m talking about, you should simply play yourself.

The object of the game is to continue this procedure until you get the 2048 tile, but you can continue playing past 2048 to attain higher and higher scores. The game is lost when the board is full and no tiles may be combined.

⊕
The queue snaking from the 2048 tile to the left, up one row, and to the right to the 8 tile. My strategy is stuck, because no tiles can now be combined.

My strategy has been to move tiles down and to the right, never ever pressing up, so that the largest number is in the lower right-hand corner, and so the numbers decrease across the bottom. Once the bottom row is full, moving the tiles left and right will leave this row alone, locked in place. Then I move tiles down and to the left, so that the largest number of the row one from the bottom touches the smallest number of the bottom row. This generates a queue or snake that tends to ensure that you don’t get stuck with two tiles that could be combined far away from one another on the board.

An example of this strategy can be seen in the screenshot, which was taken in my highest scoring game (so far…).

⊕
After getting stuck the 2 in the bottom row disrupted the queue and quickly led to the end of the game.

The main fault of this strategy is that once in a while (as shown above) pressing down, left, and right will move no tiles at all. Then one must press up, get a small tile “stuck” underneath the high-value tiles, disrupting the queue and hampering your ability to combine tiles efficiently. If this happens, the strategy is bound to lose soon. The loss that followed the above situation is shown below.

Because the code for this game is available on GitHub under the MIT License it has spawned a bunch of fun and interesting variations. These include:

2048 3D, which is played on three side-by-side 3x3 grids.
2048 4D, which is played on four 2x2 grids laid out in a square.
8192, which asks the player to keep playing past 2048.
65536, which increases the board size to 5x5 and sets the target at 65536.
9007199254740992, which is played on an 8x8 grid, with the object being to get the 2^53 tile. Estimated time to complete with a move a second is between 15 and 286 million years. I played until 65536. You can also have the game play itself, making a random move at a specified interval.
16384 Hex, which is played on a hexagon, with 3 independent directions of motion. Estimated playing time to win is 4-5 hours. I was defeated with an 8192 tile on the board.
2048 Hard, which is designed to not place a new tile randomly but instead to give you the least help.
8402, where you put down the tiles with the intent of preventing an AI from getting 2048.
243, where you combine 3 tiles into one: 1+1+1 = 3, 3+3+3=9, etc.
2048-tetris, a mashup with the classic game of falling blocks.
2584, where you combine tiles whose values are consecutive Fibonacci numbers.
2048 Automatic Win, full of snark.
DOGE2048, which is a joke version where instead of numbers you combine tiles with goofy doge-meme images.
2048 Numberwang, which is inspired by Numberwang, the maths quiz show that’s simply everyone.

My Will Is Prophecy, My Own Mythology

2014-03-17T00:00:00+00:00

\[\frac{1}{8} = \frac{1}{9} + \frac{1}{81} + \frac{1}{729} + \cdots\]

Whispering Hallelujah Hatrack

2014-03-16T00:00:00+00:00

\[\frac{1}{7} = \frac{1}{8} + \frac{1}{64} + \frac{1}{512} \cdots\]

They Carry News That Must Get Through

2014-03-15T00:00:00+00:00

\[\frac{1}{3} = \frac{1}{4} + \frac{1}{16} + \frac{1}{64} + \cdots\]

One heat up, and one cool down

2014-02-15T00:00:00+00:00

Grandma Betty’s Chopped Liver

2 lbs. chicken livers
3 hard-boiled eggs
4 large onions

Dice up onions and sauté in pre-heated oil on low flame.

When onions have turned light brown add livers, season with salt.

Drain off the oil.

Put onion/liver combo and hard-boiled eggs into a chopping bowl and chop.

What Shall We Say, Shall We Call It By A Name?

2014-02-02T00:00:00+00:00

An aptronym is a name that serendipitously reflects the character of its referent. Familiar examples include Chris Moneymaker, Anthony Weiner, Marilyn vos Savant, Price Club, Usain Bolt, and almost everybody who worked for Car Talk.

There are a few quantities in physics which have aptronyms.

The most familiar, since it is typically taught in introductory electromagnetism, is the Poynting vector, which poynts in the direction that energy flows in an electromagnetic field (eg. in the direction light is shining).

However, there are other good, less-familiar aptronyms:

The Schwarzschild radius is the size of the event horizon of a black hole. “Schwarzschild” translated literally means “black shield”, which is apt, as the outside universe is… shielded from anyone who has had the misfortune to fall pass the horizon.
The Heaviside function $\theta(x)$, or the unit step function, is 0 if $x < 0$ and 1 if $0 < x$ (the definition at $x=0$ is sometimes taken to be $\frac{1}{2}$, 1, and sometimes 0). The name can be considered apt for two reasons: some say it looks like an imbalanced two pan balance (in which case $x < 0$ is the “heavy part”), while others say that the mass of the function is where $0 < x$ in the sense that
$$\\ \int_{-\infty}^x \theta(x)\ dx = x \theta(x).$$
The Unruh effect is the fact that an accelerating observer will measure that the vacuum of space has a non-zero finite temperature, whereas an observer at rest (or, by relativity, an observer coasting at a constant velocity) will measure the vacuum to be at absolute zero. “Unruhe” translates to “unrest” from German, but was actually named after W.G. Unruh. This was pointed out to me by my friend Will Donnelly.

There May Be Many Others But They Haven't Been Discovered

2014-01-24T00:00:00+00:00

Spotted in downtown Livermore.

Your Golden Sun Will Shine For Me

2014-01-18T00:00:00+00:00

San Francisco, California

A Marvelous Night for a Moondance

2014-01-10T00:00:00+00:00

⊕
Hexagonal ice crystal in a 22˚ halo. CC BY-SA 2.5 from Wikimedia Commons. When it is cold enough for hexagonal ice crystals to form in the sky, you can sometimes see the 22˚ halo. Its angular radius, as the name suggests, is about 22˚, which means that it is about half as wide as a rainbow (which has an angular radius of around 42˚).

To make the 22˚ halo, light only gets refracted, which just means that it gets bent when entering and leaving the ice crystal.

⊕
Water droplet in a rainbow. Public domain from Wikimedia Commons.

In contrast, to make a rainbow the light also has to reflect off the back surface of the water droplet.

This has a few effects:

You can only see a rainbow if you look in the direction opposite the light source. Instead of being centered on the position of the sun (or moon) in the sky, like the 22˚ halo is, a rainbow is centered 180˚ away from there.
The colors are reversed, so that red is on the outside of the primary rainbow, but the inside of the 22˚ halo.
Rainbows are much larger than the 22˚ halo. The reflection explains why it’s roughly a factor of 2 larger.

On 2014-01-10 there was a magnificent lunar halo in Tahoe.

So that you can see the reversed colors and dramatically larger size of a rainbow, here is a photo I took in 2009 of a brilliant rainbow in DC. You can also tell from the shadows that the sun is behind me in this photo, in contrast to the halo.

STAR Struck

2014-01-08T00:00:00+00:00

STAR is one of the experiments at RHIC, which collides heavy nuclei to study the ultra-hot quark-rich medium called the quark-gluon plasma (or QGP) that existed shortly after the Big Bang.

The QGP created at RHIC has a temperature of around 350 MeV (in units where $k_B$ $=1$ or $4\cdot 10^9$ Kelvin in more familiar units). For comparison, the sun’s photosphere temperature is a few thousand Kelvin and its core temperature is around 15 million Kelvin. So the QGP is hot.

RHIC is essentially a long and skinny donut, and electromagnets are precisely coordinated so that ions whip around in both directions of the evacuated inside very quickly. Then, at certain points the beams which are traveling in opposite directions are crossed. These are the points where you build your detector, because it’s where the collisions happen.

The detector goes around the pipe, and tries to catch all the junk that comes out of the collisions. Knowing where the particles hit the detector and how fast they were going allows us to “rewind the tape” and see where the particles were created and what they might have interacted with.

STAR is getting an enhancement, called the Heavy Flavor Tracker, which recently completed construction at Lawrence Berkeley Laboratory, the lab responsible for STAR, and was shown off to fellow scientists not involved in the project on 2014-01-08, before it got packed up for shipment to RHIC. I am lucky enough to be an affiliate of LBL, so I could not pass up the opportunity to see this device.

⊕
Half the HFT, which is quite pretty. The other half was inserted into a mock-up of the full detector, so that we could get a feel for how it would be put into the detector.

The Heavy Flavor Tracker is designed to be inserted into the STAR detector, but around the beam pipe. Heavy quarks flavors decay much faster, so that the signal gets jumbled up before reaching the pixels of the current detector. By adding a precision instrument so close to the collisions, the experiment will get much better data about how heavy quarks interact and behave in the QGP.

Roughly in the middle of that photo is a black tube with an aluminum box on the end, which is a mirror copy of the aluminum box at the left end of that photo. That box is connected to a long metal tube, which is connected to two black panels. Those panels are the detector and some accompanying electronics. The close-up above is from the other side, and the shiny panels are mounted to the black carbon-fiber panels you see in the panorama.

⊕
Gigantic autoclave The carbon-fiber panels were made in the gigantic autoclave which was two rooms over from where the HFT was assembled and shown off.

For the desired improvement in experimental precision, the HFT requires positioning that is more certain than just a few microns, so the scientists who built it have measured its surface and its response to mechanical and thermal stresses. In order to maintain the integrity of the device, the shiny part will be packed up into a cushioned and stabilized box and flown to RHIC, while the big rig you see in the panorama will be sent by truck.

Things That Didn't Suck 2013

2013-12-27T00:00:00+00:00

⊕TTDS 2011
TTDS 2012

THE BOOKS

Quantum Computing Since Democritus, by Scott Aaronson
World War Z, by Max Brooks
Word Freak, by Steven Fatsis
I Am A Strange Loop, by Douglas Hofstadter
The Mind’s I, by Douglas Hofstadter and Daniel C Dennett
Chesapeake, by James Michener

THE MOVIES

Star Trek: The Next Generation - The Best of Both Worlds - OK, it’s really a TV show, but it was a 2-parter played back-to-back in a theater.
Oblivion
World War Z / Man of Steel double feature at a real-life drive in theater - Man of Steel was stupid, WWZ was great, until I read the book, and then I thought it was bad.
Deceptive Practice - Ricky Jay is the most interesting magician alive.
Catching Fire
All is Lost - I was stressed out the whole time. I learned a lot about sailing that I didn’t already know.
American Hustle
The Hobbit: Desolation of Smaug - I saw this last night. I liked the dragon, was largely unimpressed otherwise. WTF is a Tauriel? And was there a character briefly mentioned named Elros? What?

THE ARTICLES

Apollo Robbins is a Pickpocket
- A Pickpocket’s Tale
- The Secrets of a Master Pickpocket
- TED Talk
North Korea
- Dear Leader Dreams of Sushi - Japanese man makes sushi for Jung-il and Jung-un
- The Forbidden Railway - Turns out you can/could until recently take a train from Vienna to North Korea.
It Takes Planning, Caution to avoid being ‘It’ - High school friends play a game of tag spanning 2 decades.
This Russian family was lost in the taiga for 40 years.
How the Chess Set Got Its Look and Feel
On Getting Drunk in Antarctica
How Does Copyright Work In Space?
The 150 Things The World’s Smartest People Are Afraid Of
The Great Canadian Maple Syrup Heist
- What
- Why
- Conclusion
A whole bunch of Aaron Swartz stuff, none of which in particular stand out to me.
Similarly for Edward Snowden.
Similarly for BitCoins, except this one

MATH & PHYSICS FUN TIMES

Chain of balls jumps out of container - I am working on doing the physics of this on the side now. Lots of smartness.
The Big Move - There was a magnet at Brookhaven on Long Island that they needed at Fermilab outside of Chicago. So they moved it. The magnet is 50 feet in diameter, and weighs 700 tons, and needed to be kept within a quarter inch of its true shape during transit to do science.
Helium (P)reserved -The government established a strategic helium reserve in order to flood the sky with dirigible warships. Even though that didn’t pan out, the helium reserve is incredibly important.
The Dwarves Delve Deeply and Greedily. You Know What They Hope to Find in The Darkness of Khazad-dum - dark matter.
Magnetic Putty is Super Weird.
Professor Team Teaches With A Recorded Video of Himself
Water & Sound - It’s as though there were a strobe light, but there isn’t.
Many Worlds & The Copernican Principle - You sort of have to read back and forth between Aaronson’s blog and Landsburg’s blog to understand the discussion.
Nobody Agrees what Quantum Mechanics Means, but Everyone Agrees What it Predicts.
Feynman explains what a computer is and how it works.

THE TV SHOWS

Mostly just the Red Wedding over and over again. I was sitting at home, reading a book. I heard a scream, and immediately recognized it as Catelyn’s. I ran downstairs and my roommate was just staring at the TV with wide eyes and agape.

THE YOUTUBES

Triathalon Juggling World Record - If you don’t yell at your computer when he gets in the water…
No Direction, Period - Bob Dylan wrote every pop song since 1965.
NYC Subway Train Conductors are obligated to point at the black and white ///////////// sign
Crazy Combination of Sculpture, Machine, and Movie
Marble Adding Machine - This is how your computer works, basically.
Interesting People Who Make Fonts
What if the Star Wars Prequels Were Good?
Louis CK Tells The Classics

THE MUSIC

Heart performs Stairway to Heaven at the Kennedy Center for Led Zeppelin
The Takoma Park Folk Music Festival
Katie and Joe - The Revolution
Sheltered Turtle - Runaway Sketchbook
A whole bunch of classical music and a whole bunch of CDs I brought home from India got me through my thesis.

THE THEATER

Louis CK live at the Kennedy Center
American Utopias, by Mike Daisey - Let’s go to Burning Man!
Romeo and Juliet in the round at Signature Theatre in DC.
Punderdome 3000
Second City
The Neuroscience of Magic - A magician and neuroscientist team-teach a lecture, where the magician does a trick, the neuroscientist explains why you don’t understand what happened, the magician re-does the trick, explaining to you how he fooled you, and then the magician does some more tricks using the same kind of technique that you can’t catch even though you know exactly what to look for.

THE PODCASTS / AUDIOBOOKS

True Story
The Lord of the Rings, by BBC Radio
The Martian Chronicles, by Ray Bradbury
A Game of Thrones

THE GAMES

Thurn & Taxis - Spiel de Jahres 2006
Dominion
Qwirkle Cubes
Quoridor - It’s a maze game.
Lost Cities
Liar’s Poker - I played it a lot in India. My grad school friends a lot like it now.
Ginkgopolis - I played this in Seattle at a game store.
Boardgame Remix Kit - I haven’t actually played with this, but I want to.
Gerrymandering Puzzle
Geoguessr
Color Zen - It’s a fun, beautiful puzzle app.

TRAVEL

India & Nepal
DC ⟶ CA Road Trip
Camping at Pismo Beach and seeing the monarch butterfly grove there.

THE OTHER MISCELLANEOUS THINGS

Sugru - Magical, moldable rubber that cures in 24 hours.
DCist Exposed 2013 photo gallery.
My roommate got a dog, which was fun.

I'm As Free As A Bird Now

2013-12-20T00:00:00+00:00

Lawrence Berkeley Laboratory, Berkeley, CA

Is this place at your command?

2013-11-17T00:00:00+00:00

Oceano Dunes, CA

It's Not Hard, Not Hard To Reach

2013-11-16T12:00:00+00:00

Pismo Beach and Piedras Blancas.

This Dichromatic Vision

2013-11-16T09:00:00+00:00

The Monarch Grove at Pismo Beach.

Lake Ogallala, We Hold You In Our Hearts

2013-10-08T00:00:00+00:00

To call the Lake Ogallala Beachside Campgrounds civilized is only true to the most fundamental requirements of the word. There are some fire rings, a few picnic tables, a toilet, and a suspicious fresh water source that you manually pump to get water, I feel certain, from the lake.

Sunset was beautiful, the sky first pastel pinks and then vivid reds and yellows. If you look closely at the second photo, a bright red 22˚ halo is also faintly visible.

I stayed there on a night with a new moon, so it was dark. Really dark. There were some houses about a mile away, and some rare commerce on the distant shore, but they could not light the night. The night was cold and beautiful, and the Milky Way could be seen dimly spilled across the sky. I had not seen it before, at least not like that.

Ring-ding-ding-ding-dingeringeding!

2013-10-03T00:00:00+00:00

Lake Calhoun, Minneapolis MN.

It's A Light And Tumble Journey

2013-09-14T00:00:00+00:00

I've Been Stretching My Mouth

2013-06-12T00:00:00+00:00

My friend Brian posted on social media:

On a brief break from proposal-ing, I was pondering the statement in computer science that “a function is entirely defined by its inputs and outputs.” At first I thought, “yep, that sounds about right. In the sort of idea of function-as-mapping, two identical mappings should be the same function. I think. But then I thought, “but I can write two functions to compute the fibonacci sum up to a given integer, and they may have vastly different orders of computation time. And, at least I think in principle, I might be able to write two algorithms with the same order of computation time but different memory needs. Are those all really the same function? Is the input-output mapping sufficiently descriptive to stand for the entire DNA of a function?”

I’m not sure if all of the words I wrote were strictly necessary to convey my point, but I love computational complexity and I found that once I got going I was making connections that weren’t obvious to me when I simply stated what my opinion was.

Let’s set aside the issue of side effects and state variables and deal with pure functions. We know we can always rewrite a program that has state and functions with side effects into a program that is composed of pure functions that are stateless (though perhaps might involve closures). Finally, let’s also set aside uniqueness issues by demanding that the inputs to our functions belong to some set that is at most countably infinite, so that the pairs are enumerable and we don’t have to worry.

With these caveats aside, to me, the issue raised strikes at the core of distinguishing definability, computability, and complexity. Any mathematical mapping for which a computer scientist can write a program (lambda calculus, pseudo code, C++, whatever) is called computable.

I cannot in any way tell you a non-definable function. If I could tell you (or even come up with one myself), I’d have defined it. A definable function is just some big list of (input output) pairs. But definability is important because not all definable functions are computable. I’m not sure definability is the right technical term. But whatever.

It’s hard to think of specific mathematical functions that are definable but aren’t computable; the canonical one the Halting Problem: there is no function that can take a description of a Turing machine and an initial input tape and tell you if the machine halts or loops forever. So, even though there exists an (input, output) pairing for this function ({turing machine description, tape-input}, output-or-LOOPS_FOREVER) that entirely defines the function, nobody knows how to mechanically generate such a list of pairs. So while the list of (input, output) pairs is enough, in a mathematical sense, to entirely define a function, that function might not be computable. Another example of a well-defined but uncomputable function is the busy beaver function. It’s also merely a list of (input, output) pairs, but it is known that no algorithm can tell you how to generate such a list (because you could then solve the Halting Problem). ⊕See also Scott Aaronson’s essay Who Can Name the Bigger Number?

That doesn’t mean that no such list exists. Such a list of pairs certainly exists—we even know the first few pairs. If some oracle handed us a list of busy beaver numbers, that would be quite interesting. For two reasons: first, how did it get the list?An out-of-bounds question for both computational and mystical oracles Second, let’s run a theorem-proving program on all sorts of stuff–either we’ll find a proof or know the input string we fed in is not a theorem. Creating the list of the busy beaver numbers is at least as hard as doing all of mathematics.

The fibonacci sequence is obviously definable. In the sense of computability, Fib(n) doesn’t care about how long you’ve got or how much hard drive space you need or whatever, so your different implementations of Fib(n) all show that Fib is computable equally well.

The computational complexity of Fib(n) is not a property of the list of (input, output) pairs. Indeed, asking what the computational complexity of a function is sort of assumes you don’t have such a list, because otherwise there’s always an algorithm that’s very fast: look up the output in the list! Fastness is under the assumption that the list is ordered by the inputs, but the point remains. Let’s exclude this algorithm from consideration. One reason is that that algorithm doesn’t give a finite upper bound on Kolmogorov complexity, which means, in my opinion, that even though you wrote down an algorithm you didn’t grok the function.

Instead complexity is a property of the algorithms themselves. Assuming that the cost of the arithmetic is constant even for large numbers and we have enough floating point precision, the obvious recursive method is exponentially expensive, the iterative method linear in n, and the best method actually only costs $\log(n)$ . People might say something like “Fib(n) takes $\log(n)$ ” which can be desugared into “The Best Possible Implementation® of Fib(n) takes $\log(n)$ ” where ® is a special form conveying the agreed-upon caveat “aside from already having the answer and just looking it up”. I always know how to make a function take longer

(define slowfunc (lambda (n) (begin (pause (anyPositiveFunctionOf n)) (func n))))

but unfortunately I don’t know how to develop a working implementation of (pause (anyNegativeFunctionOf n)); indeed, some levels of the complexity hierarchy collapse if you have access to a closed timelike curve ⊕Closed timelike curves can cause other concerns, because you can wind up with paradoxes such as the grandfather paradox. Interestingly, quantum mechanics cures these issues! . What I’m driving at is that if you want to define the complexity of a function itself and not just an algorithm, one sensible way is to ascribe it the minimum over all possible correct algorithms.

If you’re a mathematical constructivist, you might object to the idea that the busy beaver exists in any meaningful sense, since nobody can tell you how to make such a list. If you’re even more “practical” than a constructivist you might decide that only functions whose minimum computational complexity is small enough are useful/good/handy/etc. In particular functions whose min complexity are polynomial in the size of the input are considered tractable. These problems form the class FP. Under polynomial time reductions, these functions are all equivalent. For functions that are easier than FP, you’ve got to use reductions that take less time, but for functions that are harder than FP, continuing to use polynomial reductions seems to make sense since such reductions are fast to make.

SO FINALLY let me get to the question about tuples like ((input/output pairs) big-O space-requirements). First, the only thing I can meaningfully imagine adding to this list to characterize an algorithm is how many random bits are required as a function of n—which is not quite the same as allowing for state, though it kind of feels similarly disruptive to the notion of a pure function. Even pure functions, though, can have probabilistic algorithms that compute them. You might also want to characterize how the algorithm parallelizes.

I would say that the only really meaningful function-describing tuples are tuples like ((input/output pairs) complexity-class), while the only meaningful algorithm-describing tuples are tuples like ((i/o) big-O space randomness). Two algorithms that are the same in big-O are, in broad strokes, usually implementing the same idea, while two functions differing in big-O might be in the same complexity class but are nonetheless really different ways of thinking about the problem. A great example is sorting. Insertion and selection sort are the same $\mathcal{O}(n^2)$ and really embody the same way of thinking: go get the next one from the remaining ones. Contrast them with merge sort $\mathcal{O}(n \log n)$ and radix sort $\mathcal{O}(\text{numDigits} * n)$ which are qualitatively different thinking: divide-and-conquer and wait-what-oh-that’s-cool. So even though these algorithms are all poly time, I’d classify the first two as the same and the others as different.

Once In A While You Get Shown The Light In The Strangest Of Places If You Look At It Right

2013-05-24T00:00:00+00:00

While giving an introduction to the amplituhedron:

We can also generalize a triangle in a different way. Consider a square…

–Nima Arkani-Hamed

People Say We Monkey Around

2013-04-24T00:00:00+00:00

Duke Lemur Center, Raleigh NC.

People –– What Have You Done?

2013-04-20T00:00:00+00:00

Send the Sunshine Down My Way Whenever You Call My Name

2013-04-10T00:00:00+00:00

Cherry Blossom Festival

How Can the Wind With So Many Around Me?

2013-01-21T00:00:00+00:00

Washington, DC

Come On Children, Now Learn How To Run

2013-01-12T00:00:00+00:00

Sunrise over the Himalayas, Nagarkot, Nepal.

The valley is filled with music emanating from the local monastery.

Almost Aflame, Still You Don't Feel The Heat

2013-01-11T00:00:00+00:00

Sunset at The Hotel At The End Of The Universe, Nagarkot, Nepal.

Near The Village, The Peaceful Village

2013-01-11T00:00:00+00:00

Bhaktapur, Nepal.

Walking Through Forests of Palm Tree Apartments

2013-01-10T00:00:00+00:00

Chitwan National Park, Nepal.

By The Ranks Or Single File Over Every Jungle Mile

2013-01-09T00:00:00+00:00

We walked from our resort to the Elephant Breeding Center. For Rs. 50 you have free range over the grounds of the EBC and access to a little museum with some information about the biology of elephants, how to care for them, and their relationship with their mahouts and humans more broadly. Of course, the main attraction is being able to see the elephants!

A year or two before our visit a pair of elephant twins were born, which is quite rare. They were curious and friendly, and unchained, unlike the rest of the elephants. They came right up to the fence to interact!

The larger elephants were chained to posts that were planted in the ground. Many of them were rocking back and forth and exhibiting other behaviors that, were a human doing them, would indicate psychological disstress, which is quite upsetting. However, we did see the mahouts take them their mounts into the jungle, and were told that they would not be back for many hours, so at least the elephants are getting some time to exercise and explore.

On the way back we stopped at a factory where they make paper goods from elephant dung, which is a plentiful and renewable natural resource. They make a slurry with water and then pour that slurry over framed grates. A day drying in the sun and the sheets are ready to be cut and processed.

In the afternoon we went on an elephant ride through the jungle. We saw a rhino up-close and some other animals. Rhinos typically flee when they smell humans but the elephant scent is strong enough to cover up the scent of the riders.

Chitwan National Park, Nepal.

If I Ever Get Out Of Here, I'm Going To Kathmandu!

2013-01-08T00:00:00+00:00

I Can Tell My Sister By The Flowers In Her Eyes

2013-01-07T00:00:00+00:00

You're Tired Of Yourself And All Of Your Creations

2013-01-04T00:00:00+00:00

It Takes A Lot To Laugh

2013-01-03T00:00:00+00:00

Tinsel Tigers

2013-01-02T00:00:00+00:00

Played War Games In The Woods

2013-01-01T00:00:00+00:00

The train to Agra from New Delhi left very early in the morning, was quite cheap, and came with a delicious meal and tea service. We took two cabs from the station to the grounds of the Taj Mahal. We paid our entry fee and entered. The fog hid the mausoleum from view until we were quite near.

Up close it is quite something to behold, the stylized caligraphy and intricate carved panels, the geometrical mosaics and inlays, and the grandness of it all lend it a feeling of impossibility.

Unfortunately the fog hindered any good photographs, and photography inside is prohibited. The fog also made the marble slick and a bit muddy, making the sanctity-preserving booties a bit useless from a practical point of view.

We left the grounds and ate lunch at a small restaurant. For just a few hundred rupees six of us ate like kings, with pineapple lassis and a dessert of banana pakora.

Once we had left the restaurant, the day became absolutely beautiful and clear, but our tickets could not get us readmitted to the grounds of the Taj Mahal.

We walked around Agra a bit and took tuk-tuks to Agra Fort, which we kept jokingly referring to as the Red Keep. It is gargantuan, and when it was first built not only served as a palace but also as the military headquarters and as a busy commercial center.

For dinner we ate at an otherwise-empty restaurant and had outstanding biryani. We spent some time at the bar, and talked with some local construction workers who bought us some Kingfishers.

We made it to the train station with plenty of time to spare, which was a terrible mistake, because the train was delayed by many hours.

Some of us successfully slept on the train, others had a tough time. We got back to New Delhi by the hour of the wolf. A short walk to our hotel, and we passed out quite quickly.

Then A Silence That Chilled My Soul

2012-12-31T00:00:00+00:00

Things That Didn't Suck 2012

2012-12-21T00:00:00+00:00

⊕Previously

BOOKS & SHORT FICTION

The Beginning of Infinity, by David Deutsch - Philosophy, Computer Science, Physics, and more. Deutsch is a physicist; his philosophy closely reflects this and nonetheless is not morally empty.
Anathem, by Neal Stephenson - This book + The Beginning of Infinity turned me into a Platonist. Seriously.
The Golden Apples of the Sun, by Isaac Asimov
Dark Integers - What if the rules of mathematics were physical and were dynamical?
The Secret Number - Did Dr. Tomlin discover Bleem, the integer between 3 and 4?
The Source, by James Michener - I read this before, during, and after my trip to Israel. It was an important part of understanding what the hell was going on.
The Information, by James Gleick

MOVIES

The Dark Knight Rises
Argo
The Hobbit
Apocalypse Now
Up

ARTICLES

Don’t Turn Left - Every highway intersection is obsolete.maybe
Safety Through Asymmetry - Burt Rutan designed a plane that can lose either engine but remain completely stable.
Fashioning Apollo - SPACE TAILORS
Cookies, by Douglas Adams - A true tale demonstrating that quiet desperation is the English way.
Falsehoods Programmers Believe About Names - Context: G+ required your real name.
‘Underground Railroad’ Carries Slaves From Brooklyn To Manhattan
Glass Works: How Corning Created the Ultrathin, Ultrastrong Material of the Future
The Heinlein Maneuver - Heinlein gives a friend ideas for stories.
As We May Think, by Vannevar Bush - In which Vannevar Bush describes, in 1945, the internet.
Playboy Interview: George Carlin
Science Is Our Human Heritage
The Bookstore Strikes Back - One can only hope.
The Most Dangerous Gamer - Can Jonathan Blow make video games into a respected art?
Who Is Tom Bombadil? - If you haven’t read The Silmarillion, this will not make any sense to you at all. Inside the Secret Program to Build the World’s Best Maps - The notion that Apple was going to replace or beat Google at mapping is hilarious.
Realistic Space Combat - This guy is a nerd. His argument that belligerents in real space combat will have total situational awareness and its implications on strategy are convincing.
The Hazards of Growing Up Painlessly - Not as cool as Could Conjoined Twins Share A Mind? from last year, but interesting nonetheless.
List of Films that Most Frequently Use the Word “Fuck” - Exactly what it sounds like.
Unabomber lists self as ‘prisoner’ in Harvard directory - “Awards: Eight life sentences, issued by the United States District Court for the Eastern District of California, 1998.”
French phone bill waved after 12qn-euro blunder - A woman was charged 11,721,000,000,000,000.00 euros. That is more than the economic output of the world, by a large margin.
Manhattan Evacuation Plan Reveals Island’s Old Contours - It’s almost as though the surface of the Earth was shaped over eons by natural forces.

MATH & PHYSICS POPULAR-LEVEL THINGS

Factorization Diagrams
Divisibility by 7 is a Walk on a Graph - ÷7 is the first one where the divisibility rule is not “easy”. The complete rule is shown. The method promptly generalizes, though becomes more complex when the divisor has more digits.
Just what do you mean by “number”? - Hmm.
The Mystery of the Menger Sponge - Fractals at MoMath
The Philosophy of Computer Science - The Stanford Encyclopedia of Philosophy is what Wikipedia would be if it were written by experts.
Advice to a Young Mathematician - Sir Michael Atiyah was the president of the Royal Society and has a Fields Medal.
Manifold Destiny - Gregori Perelman is a crazy person; he proved one of the most difficult mathematical theorems.
Neutrino Detector Will Be Second-Biggest Human Structure - The Mediterranean itself will be part of the detector.
Who Needs The Higgs Boson? - Raman knows what he’s talking about.

TV

Game of Thrones
Louie

THE YOUTUBES

It’s Painting It’s Pouring - Some people make really interesting looking art by pouring paint on a thing.
The Connected States of America - You can learn a lot by understanding who’s calling who.
Stephen Fry on The Joys of Swearing
Social Networking in its Oldest Form - A guy throws messages in bottles into the ocean.
Baby birds - They grew up in the bush by my house’s stoop.
Vi Hart - Everybody should make hexaflexagons. It’s a fun project and they are zany objects.
What Color is a Mirror? - Surprise! It’s green.
Paul Erdős: N is a number
Pendulum Waves - Pendula are mesmerizing.
What Earth Would Look Like With Rings Like Saturn - Hint: it’d be pretty.

MUSIC

Dispatch - Live in concert. They were awesome. I ran into Jake Itzkowitz.
The Cranberries had a new album.
So did Jethro Tull.
Punch Brothers - modern take on bluegrass.

PODCASTS / RADIO

How Fake Money Saved Brazil - cf. the onion
A Man, A Van, A Surprising Business Plan - Turns out you can make $500/day helping the individual defeat moronic bureaucracy.
StoryCorps - I just wish they came out more quickly.

THE GAMES

Dream of Pixels - It’s reverse tetris. I can’t really explain it better than that. I paid for the app.
Tigris & Euphrates - The Gamer’s Game.
Agricola - I have played a handful of times and have systematically gotten destroyed.
Maps Tower Defense - Play a tower defense game anywhere in google maps.
Open Face Chinese Poker
DrawSomething
Scramble With Friends
Kerning: The Game

THE OTHER MISCELLANEOUS THINGS

Infrequently Used Punctuation Marks
Tig Notaro’s “Live” set that I bought at Louis CK’s website.
Trip to Israel
The American Craft Beer Festival
Snallygaster
The National Aquarium
Night Life at the California Academy of Sciences
I caught a t-shirt at a Nat’s game.
Wind Map
Green Twilight Publication Party
That time the Space Shuttle Discovery flew over DC.
A 63-comment long facebook thread filled with puns that followed my quip “Are baking scholarships knead-based?”

I Sail Above Your Inlets and Interstates

2012-12-08T00:00:00+00:00

Lake Union, Seattle WA.

Let It Blossom, Let It Flow

2012-07-05T00:00:00+00:00

Princeton, NJ.

We Know We Can't Be Found

2012-06-28T00:00:00+00:00

At the National Aquarium in Baltimore.

A Hiding Place Where No One Ever Goes

2012-04-26T00:00:00+00:00

We noticed a robin’s nest in the bush out side of our house.

One of my roommates made a video:

They Came In Peace For All Mankind

2012-04-17T00:00:00+00:00

The Space Shuttle Discovery moved to its new home at the Udvar-Hazy Center of the Smithsonian Institution’s National Air and Space Museum. Discovery was transported on the back of a Shuttle Carrier Aircraft and was escorted by fighter jets.

Discovery is the oldest remaining spacefaring shuttle, traveled 149 million miles, and is the most-flown human-carrying spacecraft.

I went down the the National Mall and watched the Shuttle make a few passes around DC landmarks.

All the Wrong Fuses and Splices

2012-03-07T00:00:00+00:00

There are a few different conventions for electromagnetism, and keeping them straight can be a headache.

Here I collect the differences between the particle physics convention

$\mathcal{L}=-\frac{1}{4}F^2$

and the… other convention

$\mathcal{L}=-\frac{1}{16\pi}F^2.$

The particle physics convention is the same as SI if you replace $\varepsilon_{0}$ , $\mu_{0}$ , and $c \rightarrow 1$ , so you can use any result in e.g. Griffiths easily.

	$\mathcal{L}$	$-\frac{1}{4}F^2$	$-\frac{1}{16\pi}F^2$
Units		“Particle Physics”	“Gaussian”
		“Rationalized”
Lagrangian Density	$\mathcal{L}$	$\frac{1}{2}\left(E^2-B^2\right)$	$\frac{1}{8\pi}\left(E^2-B^2\right)$
Hamiltonian Density	$\mathcal{H}$	$\frac{1}{2}\left(E^2+B^2\right)$	$\frac{1}{8\pi}\left(E^2+B^2\right)$
Maxwell’s Equations	$\partial_\mu F^{\mu\nu}$	$j^\nu$	$4\pi j^\nu$
Fine Structure Constant	$\alpha$	$\frac{e^2}{4\pi}$	$e^2$
Flux quantum	$\Phi_0$	$\frac{2\pi}{e}$	$\frac{1}{2e}$
Coulomb’s Law	$\vec{E}$	$\frac{Q}{4\pi r^2}\hat{r}$	$\frac{Q}{r^2}\hat{r}$
Biot-Savart Law	$\vec{B}$	$\frac{1}{4\pi}\oint \frac{I d\vec{\ell}\times \hat{r}}{r^2}$	$\oint \frac{I d\vec{\ell}\times \hat{r}}{r^2}$

You can see it’s just a matter of keeping track of where the $4\pi$ goes, which is what makes it so tough to remember.

Things That Didn't Suck 2011

2011-12-22T00:00:00+00:00

One of my friends suggested we each compile a list of things we enjoyed reading, watching, listening, or otherwise consuming in the past year. He titled his email “things that didn’t suck”.

Here is my list.

BOOKS

Basically in the order I read them, with quite a few books not making the list for being not outstanding

The Soul of a New Machine - Tracy Kidder’s biography of the digital computer and the people who build it
The Man Who Loved Only Numbers - the biography of Erdös, the most prolific mathematician of the 20th century.
The Man Who Knew Infinity - the biography of the genius Ramanujan by My Close Personal Friend Robert Kanigel. Contains almost no math, and is an interesting story of an unusual mind.
The Worthing Saga - if I had to recommend one sci-fi book that I read this year, this would be it.
Pastwatch: The Redemption of Christopher Columbus - future- and past- historical fiction which is hard to describe but really masterly executed.
Flowers for Algernon - I read this in less that 12 hours, and I cried at the end.
Footfall - Space elephants conquer Earth.
A crapload of not-the-usual Heinlein
Game of Thrones and the rest of A Song of Ice and Fire - This was the fastest that I’ve ever burned through 2000 pages, and I loved almost every page of it. Valar morghullis.
The Hobbit I reread this in about a week, because I had forgotten almost all of it but the broadest generalities. Now I am psyched for the movie.

MOVIES

The Fighter
The Adjustment Bureau - which only makes the list because Joe Biden was there, and I imagine him laughing at my laugh in response to this trailer for Paul.
Bridesmaids - Did you know that air marshall jon and the woman who figures out he’s an air marshall are married in real life?
Crazy Stupid Love - I really like Steve Carell.
Contagion
One Flew Over The Cuckoo’s Nest
In The Heat of the Night
Cool Hand Luke

ARTICLES

Roughly in reverse chronological order.

Lockhart’s Lament - a mathematician’s perspective on math education and the value of math as a human activity.
African American Atheists
Many of the written works of John Perry Barlow, EFF founder and Grateful Dead lyricist
Steve Jobs’ eulogy, authored by his sister
The Royal Society opened their historical archives
The Food Bubble - Goldman Sachs plays with its food. It was in Harpers, but I think it probably needs a grain of salt. Because otherwise this should be an absolutely huge story, and I haven’t really seen it anywhere else.
Is Shyness an Evolutionary Tactic?
Could Conjoined Twins Share A Mind?
The Document Which Used To Be Called The MIT Lockpicking Guide
The $700 Million Yogurt Startup - The story of the ascent of Greek yogurt. It’s perishable, must be kept cold, &c, but this company is kicking ass and taking names nonetheless.
Why Philosophers Should Care About Computational Complexity - This is a very long article. 50 pages, and it’s not all light. But Aaronson is a good explainer, and the essay is digestible in pieces, and harder parts can just be skipped.
Gold Coins: The Mystery of the Double Eagle
The Beer Archaeologist

TV

Carl Sagan’s Cosmos - Once you get over the hokey 80s graphics, the astronomy and philosophical considerations are timeless, and Sagan’s somber awe is enthralling.
Louie CK in all his various instantiations
It’s Fun To Imagine, with Richard Feynman
Tales of Mere Existence
Game of Thrones

MUSIC

Listening to these things in a serious way was new.

David Gilmour
Fiona Apple
Harry Chapin
Johnny Cash
Joni Mitchell
Warren Zevon

THEATER

Too Much Light Makes The Baby Go Blind - 30 plays in 60 minutes. Some funny, some serious. Mostly funny. I laughed so hard the performers commented on it during the performance. If you are in Chicago or if the Neo-Futurists visit New York, I strongly recommend seeing it.
The Story Collider - I’d never been to a story slam before. It was great.
Various public lectures at the Air and Space Museum
Company - the broadway show with Stephen Colbert + whats his name on the silver screen.
You, Me, Them, Everybody - they live-record an improv, story-telling, stand-up, and music podcast.

PODCASTS

I have become a podcast fiend.

The Moth
The Story Collider - The Moth, but about science in some capacity
Radiolab
The Tobolowsky Files - The guy that Bill Murray hits in Groundhog’s day/the guy who forgets everything in Memento is a character actor with an exceedingly interesting life and a real talent for stories.
In Our Time With Melvyn Bragg - 3 scholars and a moderator discuss a big idea, a historical figure, a cultural development, etc.
A History of the World in 100 Objects
NPR’s Sunday Puzzle
Wait Wait Don’t Tell Me
This American Life

GAMES

GENERAL

Feb-run-uary, the sequel to Veganuary - Although running sucked at the beginning, by the end I could actually run. This achievement was quickly undone by the the trees conquering my sinuses for a month and a half, making it impossible to breathe.
Race to the End of the Earth exhibit at AMNH.
Vi Hart’s math doodle youtubes
Great Migrations at the National Geographic Society
Rock climbing twice a week during the summer. - I find rock climbing to be a giant puzzle where you coincidentally have to exercise, too.

Hey Now, All You Lovers

2011-12-04T00:00:00+00:00

The National Zoo puts on ZooLights every December.

Twisting Burning, My Thoughts Turning

2011-12-04T00:00:00+00:00

These whirls come from accumulating numerical errors.

Tyger Tyger, burning bright

2011-10-03T00:00:00+00:00

⊕Rev. Mod. Phys. 23, 21 (1951)
hep-th/9405029
Ohanian Ch. 6+8

⊕I first prepared these notes for a 90-minute lecture for the first semester of Graduate Quantum Mechanics in 2011.

The Factorization, Operator,

or Supersymmetric Method

In quantum mechanics we are, quite generally, intersted in studying Hamiltonians (in rescaled variables) like

$H = - \frac{d^2}{dx^2}+V(x).$

In one dimension we usually mean $x\in (-\infty,\infty)$ , while in three dimensions we usually mean $x = r \in [0,\infty)$ and $V=V_\ell$ where $\ell$ is a partial wave label, so that we just worry about the radial pieceReducing to just a radial coordinate only works for spherically symmetric potentials. .

Let us focus on a special class of Hamiltonians: those derivable from a superpotential $W(x)$ . Let’s defineRecall $i \frac{d}{dx}$ is Hermitian, so $\frac{d}{dx}^\dagger = -\frac{d}{dx}$

$A = \frac{d}{dx} + W(x) \hspace{3em} A^\dagger = - \frac{d}{dx} + W(x)$

From these operators we can build two Hamiltonians,

$H_1 = A^\dagger A = - \frac{d^2}{dx^2} - \frac{dW}{dx} - W \frac{d}{dx} + W \frac{d}{dx} + W^2 = - \frac{d^2}{dx^2} - \frac{dW}{dx} + W^2$

and its partner

$H_2 = A A^\dagger = - \frac{d^2}{dx^2} + \frac{dW}{dx} + W^2$

where the sign of the second term is the only difference between the two.

Immediately we can prove a nice theorem:

Theorem: The eigenenergies of these Hamiltonians are nonnegative.

Proof: For any state $\left|\phi\right\rangle$ the matrix element of $H_1$ is

$\left\langle \phi \mid H_1 \mid \phi \right\rangle = \left\langle \phi \mid A^\dagger A \mid \phi \right\rangle = \left|A \left|\phi\right\rangle\right|^2 \geq 0,$

and similar reasoning establishes the claim for $H_2$ .∎

The two Hamiltonians differ only by the sign of the derivative term for the superpotential—does this establish a deep connection?

Theorem: They have almost the same spectrum!

Proof: Suppose $\left|\phi_n\right\rangle$ are the energy eigenstates of $H_1$ :

$H_1 \left|\phi_n\right\rangle = A^\dagger A \left|\phi_n\right\rangle = E_1^{(n)} \left|\phi_n\right\rangle.$

Applying $A$ to the above,

$A H_1 \left|\phi_n\right\rangle = A A^\dagger A \left|\phi_n\right\rangle = A E_1^{(n)}\left|\phi_n\right\rangle$

but we know $H_2 = AA^\dagger$ so the second equality can be written

$H_2 A \left|\phi_n\right\rangle = E_1^{(n)} A \left|\phi_n\right\rangle$

so if we let $\left|\psi_n\right\rangle = A \left|\phi_n\right\rangle$ then $\left|\psi_n\right\rangle$ is an eigenstate of $H_2$ with energy $E_1^{(n)}$ !

This of course works the other way—hit

$H_2 \left|\psi_n\right\rangle = E_2^{(n)}\left|\psi_n\right\rangle$

with $A^\dagger$ and you will find

$H_1 A^\dagger \left|\psi_n\right\rangle = E_2^{(n)} A^\dagger \left|\psi_n\right\rangle$

That’s it. The two Hamiltonians have precisely the same spectrum. Any loopholes?

Just one.

If $A \left|\phi_n\right\rangle = 0$ or $A^\dagger \left|\psi_n\right\rangle = 0$ —i.e. if one of the Hamiltonians has a zero-energy eigenstate, then we cannot successfully do the regrouping because the state is destroyed.

Can we find these destroyed states?

Yes! $A \left|\phi_n\right\rangle = 0$ and $A^\dagger \left|\psi_n\right\rangle = 0$ are linear, first-order ODEs:

$\frac{d\phi_0}{dx}+W(x)\phi_0(x) = 0$

$\frac{d\psi_0}{dx}-W(x)\psi_0(x) = 0.$

We can use the method of the integrating factor. It is simple to check thatThe lower bounds on the integrals simply readjust the proportionality constant.

$\phi_0(x) \propto e^{- \int^x dy\; W(y)} \hspace{3em} \psi_0(x) \propto e^{+ \int^x dy\; W(y)}$

solve those differential equations, respectively.

Now we can check the normalizability of these states. For $\phi_0(x)$ ,

$\infty \stackrel{?}{>} \int_{-\infty}^{+\infty} dx\; \left|\phi_0(x)\right|^2 \propto \int dx\; e^{-2 \int^x dy\; W(y)}$

so we need $\int^x dy\; W(y)$ to go to $\infty$ as $x\rightarrow\infty$ , so that $W(x)$ must fall slowly or grow at large $x$ .

On the other hand, for $\psi_0(x)$ , we find

$\infty \stackrel{?}{>} \int_{-\infty}^{+\infty} dx\; \left|\psi_0(x)\right|^2 \propto \int dx\; e^{+2 \int^x dy\; W(y)}$

so we need $\int^x dy\; W(y)$ to go to $-\infty$ as $x\rightarrow\infty$ .

These two behaviors are clearly incompatible, so we conclude that $H_1$ and $H_2$ have the same spectrum except at most one has a zero energy eigenstate.∎

In one dimension, for any Hamiltonian $H$ , if you can find its ground state and adjust the constant part correctly, you can get $W(x) = -\frac{d}{dx}\ln \phi_0(x)$ so that $H=H_1$ and you can build $H_2$ . But $H_2$ is not generically simple, so this is not a good way of solving most problems.

In three dimensions, it isn’t always possible to perform this feat, but it is in a large number of cases. In fact, Schrödinger solved the hydrogen atom this way in the 1940s.Proc. Roy. Irish Acad. A 48, 9-16 (1940/1941).

The Harmonic Oscillator $W(x) = x$

⊕
Using the shift and ladder operator to find new higher-energy states in the spectrum of $H_1$.

$H_1 = - \frac{d^2}{dx^2} + x^2 - 1$

$H_2 = - \frac{d^2}{dx^2} + x^2 + 1$

$H_1$ and $H_2$ have the same spectrum, but are only different by a constant. How could that be?

For every energy eigenvalue there must be another one a constant amount higher, because we can do the constant shift from $H_1$ to $H_2$ and then use $A^\dagger$ to find a state in the spectrum of $H_1$ .

⊕

Going to higher energies forever in this fashion is perfectly fine. Going down is doable too, but can create issues.

Since the equation $\frac{d\phi_0}{dx}+W(x)\phi_0(x) = 0$ is a first order, linear ODE, it has only one solutionUp to an overall normalization. . So, if there are multiple towers of evenly-spaced states, only one of them can have a state that gets destroyed. The spectra of the two Hamiltonians still match exactly but for this destroyed state. But, since no other state can get destroyed, one can forever find states with less energy (again, by a constant amount), and this must eventually violate the non-negativity theorem we proved above.

So, these extra states cannot be in the spectrum, by reductio ad absurdum. Moreover, you cannot find multiple perfectly-aligned towers of states because of the uniqueness theorem for $\frac{d\phi_0}{dx}+W(x)\phi_0(x) = 0$ . The harmonic oscillator has but one semi-infinite tower of evenly spaced states.

Have we done anything new? No, not for this example. If you check you will find $A^\dagger = \sqrt{2}a^\dagger$ and $A = \sqrt{2}a$ where $a$ and $a^\dagger$ are the usual ladder operators for the harmonic oscillator.

The Coulomb Potential $W^{(\ell)}(r) = -\frac{\ell+1}{r} + \frac{1}{2(\ell+1)}$

⊕Again, first presented by Schrödinger, Proc. Roy. Irish Acad. A 48, 9-16 (1940/1941).

The way the three-dimensional central potential problems tend to work is that you can, by a clever choice of superpotentials, construct relationships between $H_2^{(\ell)}$ and $H_1^{(\ell+1)}$ .

For the Coulomb superpotential

$W^{(\ell)}(r) = -\frac{\ell+1}{r} + \frac{1}{2(\ell+1)}$

one finds

$H_2^{(\ell)} = H_1^{(\ell+1)} + \frac{1}{4(\ell+1)^2} - \frac{1}{4(\ell+2)^2}$

so there is a constant shift between different $\ell$ and supersymmetric partners.

The Coulomb spectrum up to n=4 with the ladder operators and constant shifts that connect the states.

This method also works for the three-dimensional isotropic harmonic oscillator,

$W^{(\ell)}(r) = - \frac{\ell+1}{r}+r$

but I will not go through the algebra or logic here.

Infinite Square Well

Suppose you restrict, in one dimension, to $-\frac{\pi}{2} \leq x \leq \frac{\pi}{2}$ and let

$W(x) = \tan(x)$

Then,

$H_1 = - \frac{d^2}{dx^2} - 1$

a constant potential with hard boundaries—the infinite square well—and

$H_2 = - \frac{d^2}{dx^2} + \sec^2(x) + \tan^2(x)$

This potential looks like it ought to be extremeley difficult to solve, except that we know its spectrum matches the infinite square well. That is,

$E_n \sim n^2-1.$

You can figure this out more precisely.

What’s In A Name?

⊕Caveat Lector: this section is not very precise. I welcome pedagogical clarifications or simplifications.

Supersymmetry, or SUSY, is a symmetry that theorists like for its beauty and its ability to resolve some of the theoretical problems in quantum field theory:

Gauge coupling unification
Provides dark matter candidates
Solves the hierarchy problem / provides naturalness.

It guarantees that particle species come in pairsOr larger multiplets, depending on the amount of supersymmetry of equal mass called superpartners.

It is unclear if SUSY is a symmetry of nature: we know of no superpartners, even though we expected them to be produced at the Large Hadron Collider.

If you restrict to particles at rest, a state with one boson species and one fermion specied can be specified by

$\left| n_b, n_\uparrow, n_\downarrow \right\rangle$

where $n_b$ is a nonnegative integer representing how many bosons there are, and $n_\uparrow, n_\downarrow$ are either 0 or 1by Pauli exclusion and describe how many fermions there are.

A state is bosonic if $n_\uparrow + n_\downarrow \equiv 0$ (mod 2) and fermionic otherwise.

We can partition all the states into bosonic and fermionic sectors and define the Hamiltonian of this system to be

$H = \left(\begin{matrix} H_b & \\ & H_f \end{matrix}\right)$

which can be constructed out of

$Q = \left(\begin{matrix} & 0 \\ A & \end{matrix}\right) \hspace{3em} Q^\dagger = \left(\begin{matrix} & A^\dagger \\ 0 & \end{matrix}\right)$

with $A$ a fermionic operator. One can check that $\{Q,Q^\dagger\}=H$ , if we recognize $H_b=H_1$ and $H_f=H_2$ .

$Q$ and $Q^\dagger$ are supersymmetry generators in the superalgebra that take us between the bosonic and fermionic sectors.

The full superalgebra is

$[H,Q] = [H,Q^\dagger] = 0$

$\{Q,Q^\dagger\} = H \hspace{2em} \{Q,Q\} = \{Q^\dagger,Q^\dagger\} = 0.$

The first lines imply that the fermion number is conserved.

I got better!

2011-08-25T00:00:00+00:00

Newton’s Method is an iterative numerical technique for finding the roots, or zeroes, of a function. You pick an arbitrary point, and perform a procedure on that point using the function of interest, getting another, new point, which you perform the same procedure on, getting a new point, and so on.

This procedure is constructed so that its fixed points are the zeroes of the function you’re insterested in, and is guaranteed to yield an approximation to one of the zeroes… given enough time.

We can naturally extend this procedure into the complex plane, where we then can color each point based on which zero it approaches, and how long it takes for this procedure to “settle down”. When we make this coloring we get objects known as Newton’s Fractal.

No Straight Lines Make Up My Life

2011-08-08T00:00:00+00:00

⊕
One example ($N=6$).

Take a unit circle, and inscribe a regular $N$-gon.

Pick one vertex. Draw lines from that vertex to all the other vertices (two of these lines are edges of the $N$-gon, the rest are interior to the $N$-gon).

What is the product of the lengths of these lines?

⊕
$N=3$, with additional lines that help us deduce the side length.

We can start with simple examples. For $N=3$ we need to know the lengths of the sides of an equilateral triangle whose center is 1 unit from the vertices. By drawing the angle bisectors / medians / altitudes (which are all the same for an equilateral triangle) we can decompose the triangle in 30˚-60˚-90˚ right triangles with hypotenuse 1. The side of interest of one of those smaller triangles has length $\frac{\sqrt{3}}{2}$, so the equilateral triangle has side $\sqrt{3}$ and the product we’re after is $\sqrt{3}\times\sqrt{3}=3$.

Curious. Let’s check $N=4$.

The decomposition in this case is even simpler! We can draw just four 45˚-45˚-90˚ triangles with side length 1 and hypotenuse $\sqrt{2}$. So, the product we’re after is $2\times\sqrt{2}\times\sqrt{2}=4$, where the terms are the inner diagonal and the two sides of the square, respectively.

⊕
$N=2$

In fact, if $N$=2, the polygon is degenerate, but we can consider the points at ±1—so the length of the one line 2!

$N$	product of lengths
2	2
3	3
4	4

Does this pattern hold forever? Does it generalize into higher dimensions?

I immediately checked the tetrahedron and cube inscribed in the unit sphere, and found that there was no obvious pattern in 3 dimensions.

I struggled to find a proof in 2D. I was able to reduce the problem to proving

$\prod_{n=1}^{N-1} \sin\left( \frac{n \pi}{N} \right) = \frac{N}{ 2^{N-1}}$

but got no further.

My friend Will offered the following proof:

Consider a regular $N$-gon in the complex plane with vertices at the $N^{th}$ roots of unity $\omega^n$ where $\omega=e^{2\pi i/N}$. Let 1 be the distinguished vertex, so the product of the lengths to all the other vertices is

$\prod\text{lengths} = \prod_{n=1}^{N-1} |1-\omega^n| = \left|\prod_{n=1}^{N-1} (1-\omega^n) \right|$

Now consider the polynomial identityThis is in some sense the definition of the roots of unity.

$z^N-1 = \prod_{n=0}^{N-1} \left(z-\omega^n\right)$

which is just the factorization of the left hand side into linear factors. Differentiating both sides with respect to $z$ and setting $z=1$,

$N = \sum_{k=0}^{N-1}\prod_{n=0,n\neq k}^{N-1}\left(1-\omega^n\right).$

But now note that if $k\neq 0$ then the product on the right hand side includes a factor of $1-\omega^0=0$ and so vanishes. Thus only $k=0$ contribues,

$N = \prod_{n=1}^{N-1}\left(1-\omega^n\right).$

Combining this with the first equation yields

$\prod\text{lengths} = N.$

QED.

The reliance on complex numbers immediately explains why there was no pattern in three dimensions. I would be interested to learn if there is any similar identity that takes advantage of the quaternions or octonions.

I designed a graphic inspired by this identity, and gave Will a printed copy as thanks for this enlightening proof.

A high-resolution version is available.

If we take the bounding circle to have radius 1, the product of length of all the lines in this figure is exactly

230 843 697 339 241 380 472 092 742 683 027 581 083 278 564 571 807 941 132 288 000 000 000 000

or $54!$, as it is all the figures for $N=2$ to $N=54$, each a different color, superimposed.

Subsequently, I came across a purely algebraic proof that does not require differentiation.

Spirals Round and Round

2011-08-01T00:00:00+00:00

I saw a glassbow in the wild! That is, on the corner of 17th and Kilbourne Streets in Washington, DC.

Unfortunately, my glassbow was largely obscured by a tree’s shadow, and my phone’s camera is not the greatest, so my photo is nowhere near the quality of the gold standard.

The very fact that I noticed this bow at all is due to Walter Lewin and his masterfully taught course 8.03 Vibrations and Waves, which I was lucky enough to take in the fall of 2005. I still carry my wallet-sized linear polarizer. What kind of physicist would I be if I didn’t?

Don't Believe A Thing They Say

2010-11-28T00:00:00+00:00

If I am traveling out of Penn Station and have some time to kill before my train, I like to get a street meat gyro with tzatziki and hot sauce from the guy on the southeast corner of 33rd Street and 8th Avenue. If the weather’s not too bad I take it across the street and sit in front of the colonnade of the Post Office.

The pigeons were surprisingly outgoing.

Out Of Control On A Breeze

2010-10-17T00:00:00+00:00

The National Mall, Washington DC

never trust a man with a typewriter between his lips

2010-07-31T00:00:00+00:00

⊕Images from the Special Collections of the University of British Columbia.

Stan

⊕

 I only met you yesterday, uncle                                   
 though you did not meet me
 as I poured through the endless papers
 sitting in cartons
 organized artificially
 by a librarian named Cynthia.
 Yellowed and creased I hear your words
 spoken through the typewriter between your lips,                  
 set within your bearded face, 
 injected between the lines by your bobbing blue fountain pen
 floating on the paper and the words and the ideas
 marking measuredly, unsatisfied.

⊕

 We shared an original thought about the endless tombstone
 fields marching forth to the factory that can only be glimpsed
 from the LIE as one is lured into the city by the other
 stone monuments that stick out of the ground in planned, regular rows
 while ascending the hill, Manhattanbound.

⊕

 I see the reflections of my father's signature in yours,
 hear my grandmother's voice in the recordings of your readings
 echoing through the tapes that have been sitting in the stacks
 waiting
 for me to request them
 waiting
 for 34 for years.
 Your deep tone and hearty laugh and throaty cough
 sound so familiar, at yet so foreign
 as I record them on my laptop, 
 piped in from a reel-to-reel player that was dusted off upon my request.
 It brags in an unmistakably 70s font of playing in stereo!
 Your voice is in mono.
 Nonetheless it reaches my ears and I can see you
 sitting behind your desk or rocking on a cool leather chair
 with a tremendous microphone, stroking your beard and inspecting
 the world in your own way and your own time.
 
 I miss you uncle, though I only met you yesterday, as
 I sorted through the papers you left when you left.

Can I Step Into Your World For A While?

2010-07-13T00:00:00+00:00

Seattle, Washington

Carved Like a Dwarf Tree On A Mountain

2010-06-27T00:00:00+00:00

Stanley Park, Vancouver BC

It's Easy as 1-2-3

2009-01-12T00:00:00+00:00

Bonaire, Leeward Antilles

Laid Back In An Old Saloon, With A Peso In My Hand

2008-03-29T00:00:00+00:00

Cancun, Mexico

Come On Ye Childhood Heroes!

2008-02-24T00:00:00+00:00

⊕I first wrote this piece for Robert Kanigel’s class 21W.774 Invention and Ingenuity, which I thoroughly enjoyed.

Imagine a world devoid of hate. No race to divide. No politics. Everybody and everything working together to form a better place. There’s no conflict. Everything just works out. Everything has its place. It’s not far off. It’s the world of Lego®.

LegosI understand that by not capitalizing and using the colloquial plural I am jeapordizing my chances of an awesome life as a Lego Certified Professional and am inherently choosing sides in a protracted battle over dialect and trademark. I’ve always said ‘Legos’. , the classic Danish building block of your childhood is a marvel of engineering. With only a few kinds of pieces you can build a car or a castle, a frigate or a fighter jet, a submarine or a spaceship. The Lego manAnd women! is truly a Jack-of-all-trades. He can do anything. He always fits in. Of course he does. He was designed that way.

But I don’t need to tell you this. Chances are, you know. Chances are, you can tell me the standard Lego colorsThe Classic 8 are red, yellow, blue, black, white, green, brown, and grey. . If you’re anything like me, your pieces were sorted by them (and then again by shape, of course). If you’re anything like me, those few colors were all you needed. Bricks and plates, doors and wheels, and the occasional windshield are all you needed. With these came endless diversion. And at the end you had a definite creation, a toy. The fun didn’t end with assemblyThe LEGO Group understands the importance of the subsequent storytelling that takes place after building is complete, and its ambitious licensing is one of its major stragic business advantages over Mega Bloks and other Lego-compatible competitors. . What you made became its own world. You had a day at the track, a protracted castle siege, or a voyage a-seaI have been told that “a-sea” is not a real word or phrase, but it is most definitely a common answer to the New York Times crossword puzzle. .

And as much as you would look at the picture on the box before opening up a new set, you couldn’t imagine that there was a combination of pieces that would turn out that fun.

Yet, without fail, you would put it together. And along the way, the set designers taught you new ways to put those familiar pieces together. They’d expose you to more interesting and clever constructs. Interesting ways to mount wheels. New ways to support roofs. Things that you never would have dreamed of. But it all fit together. And as you assembled more and experienced more you anticipated more. You could see how this combination strengthened the car’s chassis or how adding some extra pieces now would alleviate the lack of studs later, and it was extremely satisfying when the wordless directions bore out your predictions.

But those guys always had something up their sleeve. They knew exactly which piece would be absolutely perfect for that next step. What a fun job. When I was six or seven, after my garbage man stint (they get a cool truck) I imagined growing up and working at Lego, designing sets for people to build. I couldn’t imagine a better way to get paid.

But I grew up, and I moved on. I was no longer satisfied to make something that stood still. I wanted to build something that itself could do something. I wanted to engineer, though if you had asked me at the time, I wouldn’t have known it.

Luckily for my parents, those Danish wizards anticipated my maturity, and had just the remedy. Lego Technic. Sprockets and gears, racks and pinions. Motors. Motion. And the most amazing part? All of the big-boy pieces fit together with the pieces they would have otherwise antiquated. Surely this was no coincidence! The engineers at Lego certainly thought this through. Legos developed and whetted your palette, and Technic was the reward. Legos were the hook, Technic the twist, revitalizing your interest with new surprises and new questions.

How do you get the gear ratio in the drive train right? How do you build a worm gear housing? How can you transmit one motor’s power to both the helicopter’s rotor and its relatively distant stabilizing fan? When you were ready to set aside the bricks and plates, suddenly you got beams and axles and new dynamics. And then you have to ask, “How do you do it right?”

That was always a problem. If you were building something big, you either needed to draw plans (unlikely) or to have the engineering equivalent of Kasparov’s foresight. Otherwise what you just built now would, by the end, wind up in the way of that most crucial shaft or gear.

And in thinking everything through, and putting the small pieces into functional modules, and assembling the modules into a model, you were indoctrinated. The definition of effective propaganda is that it draws you in without you noticing.

That’s what they had done.

They got me.

And my parents had paid them to do it.

Mom and dad didn’t know then, but those were certainly the most expensive toys they ever bought. They came with four years at MIT.

By the time I got to high school, I knew I wanted to be an engineer. And when I finally could choose my courses, I loaded up with sciences, that being the closest thing to engineering available. And I didn’t just stick to pulleys and ramps and projectiles. I made it a point to take chemistry and computer science too. Who knew what subject would capture my attention?

I was lucky to wind up at a school with strong science, because after a few college-level science classes, I was converted. Studying those subjects you learn little pieces here and there, but what you come away with isn’t a set of single-purpose facts, it’s a full picture of how the world works and a broad understanding of how your facts fit together. It’s difficult to explain many phenomena with a single framework, because you never know what kinds of questions will arise. Yet someone, Boyle or Newton or Turing, found the right one. They had discovered the pieces, and people have added new pieces now and then. But the magic isn’t in the pieces provided.

A lot of learning science is learning new tricks. Having a million different ways to look at a problem, and to say “Oh, this kind of like that.” You arm yourself with little pieces here and there. But understanding science isn’t about the tricks. The magic is that once you understand, you can take the principles and solve your own problems. It’s freeform, a bunch of loose pieces in a crowded plastic tub.

Natural Wonder

Another Day for You and Me in Paradise

HOW DO YOU COUNT SOMETHING INFINITE?

COUNTING SHEEP

ONE-TO-ONE CORRESPONDENCE

SOME EXAMPLES

THE BURDEN OF PROOF

AN ASIDE ON DENSITY

THE RATIONALS ARE COUNTABLE

NUMBERS BETWEEN 0 AND 1

OK BUT THAT’S IT RIGHT? JUST TWO?

I HATE THIS INFINITY PLUS ONE!

Met her in a club down in old Soho

Their Eyes Gazed Straight Ahead

I Was Rolling Down The Road In Some Cold Blue Steel

Mighty Fine Wine

Kindly State the Time of the Year

A Coat of Gold, A Coat of Red

Turn My Face to the Wall

A Band Beyond Description

Lasciate Ogne Speranza

A Bold Deceiver

The Nucleon Axial Coupling

Introduction

Motivation

Why Do We Need Computers?

Wielding Lattice QCD to Calculate ​g_A

Methodological Improvements

Outlook

Acknowledgements

Press Releases and Mentions

A Demon Cannot Be Hurt

Wine For The Woman Who Made The Rain Come

What Immortal Hand or Eye Dare Frame Thy Fearful Symmetry?

Although Your Mind's Opaque

My Sweet Lord

Things That Didn't Suck 2017

BOOKS + SHORT FICTION

ARTICLES + SERIOUS VIDEO

PHYSICS

PUBLICATIONS

TRAVEL & CONFERENCES

SERIOUS

FUN

TOOLS

RELIGION

TV SHOWS

MOVIES / DOCUMENTARIES

MUSIC

ACTIVISM

AUDIO / PODCASTS

GAMES

SPIEL 2017

TRAVEL

FOOD + DRINK

YOUTUBES

LEGO

TRUMPOCALYPSE

How Many Wonders Can One Cavern Hold?

Everything Is Awesome

I'll Meet You Any Time You Want

Orangutans are Skeptical

His Tears Fall And Burn The Garden Green

If We Travel By My Dragonfly

I'd Forsake Them All for Your Sweet Kiss

All the King's Men

Be Like the Squirrel

Be On My Side, I'll Be On Your Side

Your Technicolor Motor Home

The Hush of Falling Leaves

Just A flower I Can Help Along

Longer Boats Are Coming

Stray Cavaliers

METAQ

The Heat Came 'Round and Busted Me For Smilin' On A Cloudy Day

A Modern Major General

Live and Die a Pirate King

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