Geometry is Heroic

Why study Euclid?

Euclid’s geometry shows you that you, personally, can know truth without taking anything on faith.

You don’t have to believe Euclid, you just have to walk the same road that Euclid and millions of others have walked, and see what’s there: truth that’s available to everyone, that doesn’t rely on faith, popular consensus, or opinion. The truth found in geometry is not an expression of power relations; it was constructed by people of many cultures but isn’t “socially constructed”. It is not moral, it does not demand obedience, it does not yield to hegemony, it does not submit to authority. You can only attain it by your own efforts, but you can still communicate it and share it with others.

Knowing this kind of truth, and knowing that you can know this kind of truth, is a power that can be gained no other way.

The Mark of an Ergodic Crab

I. Chasing ergodic crabs

Yes! Ergodicity is interesting and very useful. At least in statistics. Don’t ask me what physicists do with the thing though. Those guys are crazy. The problem with ergodicity is that it’s pretty complicated. Go ahead, take a look at the Wikipedia page, I’ll wait a minute.

Ok, good. The math geniuses are gone now. You know the type – they can look at some math they’ve never seen before and understand it in minutes. Right now they’re busy proving theorems about ergodic flows on n-dimensional locally non-Hausdorff manifolds. And twitching at that last sentence. You and me? We’re going to learn about ergodicity with a pretty crabby extended metaphor.

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How We Frame the Value of “Experimental” Art Badly

Gabe and I were talking about the Harvard Sensory Ethnography Lab the other day. For context: the HSEL is an experimental form of documentary-making. Each film places you, without narration, into some unfamiliar situation, about which you become educated, ideally, solely by the power of your own observations. It’s as much experimental anthropology as it is experimental art.

I’m not about to say that experimental art is inevitably shitty nonsense and shouldn’t exist. Experimental art should definitely exist. But the fact that it is experimental should not be grounds to claim that it is better than other art. In fact, I find the idea of expecting experimental art to be good or complete to be totally crippling of its possibilities. The point of an experiment is the potential for failure. Continue reading “How We Frame the Value of “Experimental” Art Badly”

Gödel for Dummies

Gödel’s theorems say something important about the limits of mathematical proof.

Proofs in mathematics are (among other things) arguments. A typical mathematical argument may not be “inside” the universe it’s saying something about. The Pythagorean theorem is a statement about the geometry of triangles, but it’s hard to make a proof of it using nothing but points and lines in a plane! For instance, Euclid’s own proof (per Wikipedia) starts like this:

  1. Let ACB be a right-angled triangle with right angle CAB.
  2. On each of the sides BC, AB, and CA, squares are drawn, CBDE, BAGF, and ACIH, in that order. The construction of squares requires the immediately preceding theorems in Euclid, and depends upon the parallel postulate.[13]
  3. From A, draw a line parallel to BD and CE. It will perpendicularly intersect BC and DE at K and L, respectively…

The proof uses words, symbols and other tools that aren’t points and lines in a plane. Euclid’s proof thus is about geometry but isn’t inside geometry.

How does this apply to logic? Logic is (among other things) the mathematics of arguments. It’s reasonable to wonder if proofs about logic fit inside logic! More precisely, given a particular system of logic S, we can ask what S can and can’t say about itself.

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What is intelligence?

Intelligence as Awareness and Response

The most primordial kind of intelligence is awareness of relevant features in the environment, coupled with responses to relevant information. This environmental awareness-response type of intelligence only makes sense in the light of goals (“relevant” to what?) – from a single-celled organism responding to the presence of food by consuming it, to a human noticing that a plant is dry and watering it.

Evolution itself has acquired a great deal of intelligence; DNA is the transmissible record of the information evolution has acquired about the environment, from the perspective of billions of organisms with future existence as a “goal.” Simple organisms are still very viable, but the computational process of evolution has revealed that increasingly complex organisms that extract a great deal of information (and energy) from their surrounding systems are also extremely viable, especially over short time frames. Organisms have evolved increasingly complex neural systems and senses that reach into new domains of relevant information. Humans have created instruments that do the same.

Games vary in the amount of “luck” that is available. A solved game presents no opportunities for randomness, no luck – but even very complex games present different amounts of luck depending on the level of play. One measure of luck available in a game is the distance from the best player to the ideal player; as chess becomes computationally solved, its skill component overtakes its luck component. Games, like awareness-response intelligence, only make sense in the context of goals. Awareness-response intelligence extracts as much information as it can about the world relevant to its goals so that “luck” is as small a factor as possible. Sources of apparent randomness must either be controlled, studied until predictable, or, if these are not possible, responded to with optimal probabilistic strategies.

The “intelligence” apparently contained in complex economies (the “invisible hand” of the market, ecosystems) is of the awareness-response type.

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What is statistics?

I put the call out on twitter for ideas for my first post, and Gabe asked this:

https://twitter.com/GabrielDuquette/status/488858307885424640

I suppose I did ask for statistics questions. This one is a bit tough to answer because, like I hinted at on twitter, a wide variety of things get called statistics by the people doing them, statisticians do an even wider variety of things, and to muddy the waters even more, lots of things that typically get categorized as statistics often are also categorized as other things like machine learning or computer science. I suppose I should blame the computer people.

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Rationality Is Not A Martial Art

From the beginning, Yudkowsky’s sequences follow a running metaphor of rationality as martial art. This implies a bunch of shitty stuff. I’m going to describe why it’s shitty, and then propose an alternative metaphor that I think is somewhat less shitty.

  • Martial arts are individual pursuits. They are typically practiced in a social context, yes, students practicing together, masters passing their wisdom on to students. But they’re mostly not about fighting together, just training. Rationalists, like other humans, need to work together to complete large projects.
  • Martial arts are personal. They are specifically about what a human mind can do with a human body. Rationalists are encouraged to make and use tools.
  • Martial arts are only good for one thing: physical conflict with other humans. Rationality is broadly applicable, in almost any context or for any purpose.
  • It’s straightforward to identify skilled martial artists by holding fighting tournaments. What sort of tournament do you hold to test rationalists? Assessing rationality in humans is Hard.
  • Martial arts are competitive. They are about becoming the best fighter (comparative) and not about becoming the true fighter (absolute), whatever that would even mean.
  • In martial arts, your opponents are always human.

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