Notebooks


A place for rough notes. They’re not edited, they’re not even meant to be read. 

6. Divergence

June 14, 2020

As you get older, you move further away from other people in person-space. Your private, unsocialized, incommunicable experiences and thoughts grow faster than the set of thoughts and experience that you do share with other people, leading to you becoming net more isolated from other people over time. The silence grows; true communication becomes harder, rarer.

When you are young, many books can set your soul on fire. Every new classic is a revelation; everything speaks to you. Eventually, very few things speak to you deep down, and the things that used to set you on fire cease to do so. 

Ribbonfarm
Divergentism is the assertion that as time goes on, you are in a net no or silent relationship with an increasing fraction of humanity. Imperceptibly, silence descends on you. At least if you keep seeing, learning, doing and thinking. Or growing, for short.
Bergman’s movie Winter Light is about this. Christianity no longer speaks to the priest, Tomas. Nor does his old flame, Marta, nor do anybody else in the village. Tomas’s experiences in the Spanish Civil War have convinced him that humans are cruel, and gradually his private experiences force him away from the religion which, we assume, at some point moved him enough to motivate him to join the priesthood.

The movie ends with a dialogue about God’s silence during the crucifixion, and some debate about whether to go ahead with the church service. Tomas decides to do so, and the movie ends with him proclaiming that God is holy and that all the earth is full of His glory. A moving gesture because he no longer believes it, but he so deeply wants to. As he’s grown older, Tomas has moved away from all the ideas and experiences that originally gave him life -- Christianity, love, etc. -- into a dark, depressing, shrouded silence.

I read Wong Kar-Wai’s movie 2046 — one of my favourites — in this way too. Mr. Chow aka Tony Leung loses the great love of his life (In the Mood for Love), and he spends this movie escaping this in any way possible, in a haze of sex and womanizing and hedonism and writing. Secretly he yearns to just go back to that time, and his entire life is defined by this yearning as he recedes away from that fixed point in time, when he was happy and things seems like they might have been good. As time goes on, he becomes lonelier and crueller, and all that is left to him is to yearn for 2046, the fictional place where nothing ever changes, there is no loss, and no sadness.

5. Notes on High-Dimensional Spaces

June 13, 2020

I was reading the Hamming book, a gift via Stripe Press (thank you!); the part on n-dimensional space caught my attention, & I wanted to summarize my notes. The whole thing is quite counter-intuitive. 

Elementary result 1: The diagonal length of a unit square is given by Pythagoras’ theorem, i.e. sqrt(2). For a unit cube, this is sqrt(3), easy to see below (length d2).

Similarly, for any cube with dimension d the diagonal length is just sqrt(d).


Here’s where it gets wacky. Consider the “four circles paradox”:


This is a 4x4 square. The “inner sphere” is defined as the sphere that just touches each of the outer spheres. It’s easy enough to see that the radius of the inner circle here is the diagonal length of the unit square minus the radius of the outer circle, i.e. sqrt(2) - 1.

For a cube with 3 dimensions, 4x4x4, this becomes sqrt(3) - 1. There are 8 spheres (2^3).

It’s interesting to pause and think about why the radius of an inner sphere must be bigger than the inner circle above: it’s because the diagonal length of a cube is larger than the diagonal length of a square, so the “inner sphere” grows correspondingly bigger (while the outer spheres remain small, i.e. have unit radius). In general, the diagonal length is increasing with d, and the radius of the inner sphere is also increasing with d.

This leads to a strange result: for a 10-dimensional hypercube (d = 10), the radius of the inner sphere is sqrt(10) - 1, which is greater than 2 (half the length of the sides of the cube) — the inner sphere has grown bigger than the 10-d cube! It “pokes out of the edges”. 

So that’s pretty bizarre.

Even more bizarre than this: the volume of a unit sphere tends to 0 as the dimension tends to infinity

The mathematics of this is a bit more involved (and very fun, involving Euler’s gamma function and various recursion relations), but a simple, albeit not rigorous, way to see this is as follows:

Consider a square with side length 1, and within it a circle of radius 1/2. As you increase the dimensions of the cube and sphere, the volume of the hypercube must always remain at 1 (since volume is just 1*1*1*1*1...) whereas the volume of the hypersphere enclosed within it starts going down exponentially in proportion to d (since r<1), thus becoming a successively worse approximation of the hypercube.

You can also think about a sphere with r = 1 enclosed by a cube (necessarily length 2) and compute the ratio of the volume of the sphere to the cube:

  • V(2) is pi, and the cube’s volume is 2*2 =4, so pi/4 ~ 0.785
  • V(3) is 4/3*pi, and tye cube’s volume is 2*2*2=8, so ~ 0.5225
  • V(4)/16 ~ 0.308
  • V(5)/32 ~ 0.164
  • ... and so on, showing that the ratio tends to 0.

One last fun bit. Consider the following problem: what is the probability that a dart, hitting a square board at random, lands nearer the center than an edge?

It can be shown that the answer is (4*sqrt(2)-5)/3, which is roughly 0.22. What’s interesting is that as you increase the dimensions of the cube your chances of getting closer to the center than to an edge tend to 0. A similar effect is true of hyperspheres: 3/4 of the area of a circle is closer to its circumference than its radius, 7/8 for a sphere, and this tends to 1 as you increase the number of dimensions. At a high enough d, the outer 1% of the d-sphere is responsible for 99% of the volume, i.e. “most of the volume is close to the surface”.

4. Strangeness in art 

May 30, 2020

Enchanted this morning by Gerhard Richter’s painting, Reader.

There is a strangeness to this work: it is so realistic that you think it’s a photograph. Right after that, you notice a faint, barely perceptible blurriness to the girl’s left hand, the page of the brochure, the way her earring is more muted than you’d expect from a photograph. Your mind oscillates between thinking of this as an oil painting, which it is, and a photograph of a girl with blonde hair, beautifully unaware of the camera, unselfconscious, her neck draped in numinous white light. 

Talking to J. last night I realized what an earth-shattering thing it was for me, as a teenager, to read The Waste Land and The Love Song of J. Alfred Prufrock for the first time. Here was poetry, it sounded like poetry, but it was completely incomprehensible. Datta, damyata, etc. Discontinuous, fragmented, a jumble of voices. It was like nothing I had read before.

In film, my favourite directors are Mike Leigh, Yasojiru Ozu, Edward Yang, John Cassavetes, Wong Kar-Wai, Andrey Tarkovsky, and Krzysztof Kieslowski. All of their work is very strange. Those long static shots in Yang, a refusal to zoom into characters’ faces even when they’re undergoing to the worst emotional suffering. The disorienting experience of watching Faces for the first time — my god! An utterly weird movie, sometimes boring, sometimes shocking, but whatever happened there was genius. 

Eliot wrote in a letter:
“As for obscurity, I like to think that there is a good and a bad kind: the bad, which merely puzzles or leads astray: the good, that which is the obscurity of any flower: something simple and to be simply enjoyed, but merely incomprehensible as anything living is incomprehensible.” (source)
Strangeness is important in beauty. The most beautiful things are strange. Strangeness jerks us out of our ordinary, automated perception into a heightened state in which we experience the artwork, and the act of perception itself, more intensely.

Merleau-Ponty writes about this in his essay on Cezanne’s Doubt, in my view the best thing written about art:
Cezanne, in his own words, "writes in painting what had never yet been painted, and turns it into painting once and for all." We, forgetting the viscous, equivocal appearances, go through them straight to the things they present. The painter recaptures and converts into visible objects what would, without him, remain walled up in the separate life of each consciousness: the vibration of appearances which is the cradle of things. Only one emotion is possible for this painter—the feeling of strangeness— and only one lyricism—that of the continual rebirth of existence.
And:
If the painter is to express the world, the arrangement of his colors must bear within this indivisible whole, or else his painting will only hint at things and will not give them in the imperious unity, the presence, insurpassable plenitude which is for us the definition of the real. This is why each brushstroke must satisfy an infinite number of conditions. Cezanne sometimes pondered hours at a time before putting down a certain stroke, for, as Bernard said, each stroke must "contain the air, the light, the object, the composition, the character, the outline, and the style." Expressing what exists is an endless task.

3. Insider Bias

May 27, 2020

Being new to a field and full of questions is the most valuable state to be in if you care about making discoveries; outsiders often spot nonsense quickest.

Over time, they rationalize it to themselves; they stop noticing the weird things, because they were unable to explain them. They become pre-occupied with insider problems, little micro problems that are not on the “critical path” of creating the most value.

(The best demonstration of this is that Feynman chapter in Surely You’re Joking where he plays at being a biologist.)

You stop asking those bigger questions because eventually, if you’re working, you have to start doing things and not just thinking... so you become focused on doing things. But the “doing things” might not make sense in the macro scale; all your effort might be for nothing. 

It takes a special person to develop a synthesized, top down view of a field, and then constantly keep it in mind. An even more special person to use those synthesized models to make bets on the future. (See: Elon Musk). The famous Tesla “master plan” is an example of a synthesized view, a clear plan that is being followed by that company even today.

This is the wisdom behind our instance on only staffing projects with outsiders. Fear of the dreaded “insider bias”, closing you off to opportunities to make things 100x better.

This is also a good reason to keep a research log, a running notebook with one’s observations and questions. Used correctly, it can prevent you from losing sight of the big questions.

2. Koans

May 25, 2020

The “koan” is a paradoxical format: a thing written in words that demonstrates, by its existence, that words are not sufficient to make the point that it futilely tries to make. The koan is a failure by construction. (The best koans know this and play off it, e.g. Nansen’s cat.)

The koan intriniscally points beyond itself. All art does this, too (words are pointers), but only the koan takes this premise and makes it an explicit part of the form. 

This provides one reading of Kafka’s parable of “The Top”: the philosopher, trying to make sense of the mysteries of experience (the spinning top), runs after the top and catches it, but upon catching it, “when he held the silly piece of wood in his hand, [he] felt nauseated”.
A certain philosopher used to hang about wherever children were at play. And whenever he saw a boy with a top, he would lie in wait. As soon as the top began to spin the philosopher went in pursuit and tried to catch it. He was not perturbed when the children noisily protested and tried to keep him away from their toy; so long as he could catch the top while it was still spinning, he was happy, but only for a moment; then he threw it to the ground and walked away. For he believed that the understanding of any detail, that of a spinning top, for instance, was sufficient for the understanding of all things. For this reason he did not busy himself with great problems, it seemed to him uneconomical. Once the smallest detail was understood, then everything was understood, which was why he busied himself only with the spinning top. And whenever preparations were being made for the spinning of the top, he hoped that this time it would succeed: as soon as the top began to spin and he was running breathlessly after it, the hope would turn to certainty, but when he held the silly piece of wood in his hand, he felt nauseated. The screaming of the children, which hitherto he had not heard and which now suddenly pierced his ears, chased him away, and he tottered like a top under a clumsy whip.

1. Alt Identities

May 24, 2020

In quarantine, your mind wanders through your past. The world around you is grey, the world in your memories is full of color. Yesterday I found myself unexpectedly thinking about Burning Man.

IRL alts: people would take on “Burner Names”. What they were called in the real world stopped mattering, and it was taboo to ask. I remember thinking this was cheesy at the time, but now I wonder.

Names are powerful: publishing something as myself constrains me in a million ways, my name is tied to my professional life, for example, hence alts. Why wouldn’t this exist in the physical world too?

I met a man who insisted on being called “Huggy Bear”. We talked for hours. What was his real name? Does it matter?

I met many others there who stick in my memory years after the fact (2013). What were their names? I’ll never know.

Grimes draws a distinction between “Grimes” and “Claire Boucher”. A concert of her goes wrong, she gets nervous:
“It wasn’t a Grimes show,” she said—the illness had made her too weak, and too self-conscious, to give herself over to the performance. “It was Claire pretending to be Grimes.” (The New Yorker)
Later she writes: “claire and grimes are completely different ppl at this point . . . and I can’t tell if I hate her.”

An interview between Tyler Cowen and Emily St John Mandel where she talks about PostSecret, the Tumblr that posted those anonymous postcards with confessions scrawled on them. Sometimes painfully intimate. From the old Internet. She couldn’t stop thinking about one that said: “Everyone who knew me before September 11th thinks I’m dead.”
ST. JOHN MANDEL: Yeah, it’s a great site. It’s wonderful. I’m haunted by this one postcard on the site. I don’t remember what the image is, but let’s say it’s the Twin Towers burning. That’s the theme. The back of it says, “Everyone who knew me before September 11th thinks I’m dead.”

Imagine if that’s true. Of course, there’s no way of knowing if any of the PostSecret secrets are real, but imagine that position. You come up the stairs from the subway into Lower Manhattan. You look up. You see the towers falling, and you think, “This is my opportunity,” and you disappear. So I think if life presents some horrific moment like that, then faking your own death would not be difficult. But otherwise, I think it’s hard to pull off.

COWEN: If I needed to fake my own death today, I think I would go out on a cargo ship manned by people from a fairly corrupt country, and I would offer them money to simply report I had fallen overboard —

ST. JOHN MANDEL: That would do it.

COWEN: — and then walk off in some semi-disguise. How would you fake your own death?

(Conversations With Tyler)
The masks chapter in “Impro”: an actor wears a mask and achieves a terrifying fusion with it, becoming a totally different creature, another example.
‘… My character was different and unfamiliar to the Americans. But with the clothes on I felt he was a reality, a living person. In fact he ignited all sorts of crazy ideas that I would never have dreamt of until I was dressed and made-up as the Tramp.’ 

Elsewhere Chaplin has said, ‘I realised I would have to spend the rest of my life finding out about the creature. For me he was fixed, complete, the moment I looked in the mirror and saw him for the first time, yet even now I don’t know all the things that are to be known about him.’
The masks chapter in that book is so disturbing that we haven’t processed the implications. I read the other chapters very closely in that book. But the masks chapter I skipped and scanned, thinking, this overturns my worldview too much. This is for another time.

I have a Twitter list that is mostly just alts, anonymous accounts that tweet many times an hour, usually with cartoon avatars. Sometimes they are just dumb memes but often they are full of profound insight. Nowadays I find myself checking that list far more than my main list, on which everyone’s tied to their real identities, dull and grey, reliably churning out content, a steady stream of “insights”. 

Certain people are not in the straitjacket. They dance around outside the Overton window. Maybe I don’t always like what they say, maybe I do, but it’s important that people like them exist. A world where all speech is within the policed bounds is not a fun one.

Shakespeare has the Fool character who always pushes the edge of what can be said, who exists as a socially sanctioned vessel for the controversial. After Lear does dumb things he asks for the Fool to be brought to him. You are shocked by how blunt the Fool is and you can tell that Lear gets riled up by the Fool’s words. But he seems to need them, too.
KING LEAR
Dost thou call me fool, boy?

Fool
All thy other titles thou hast given away; that thou wast born with.

KENT
This is not altogether fool, my lord.
The Fool is the best character in Lear. Who is the Fool?