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Understanding is a poor substitute for convexity (2012)

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Re: Understanding is a poor substitute for convexity (2012)

#51

Post by hannasanarion »

yesenadam wrote: post #25
hannasanarion wrote: post #17

Earlier quoted context omitted.

Falsification is something that you do to hypotheses, not data. Experiments that Aristotle performed to demonstrate classical elemental theory are still valid and useful, his incorrect interpretation of the underlying mechanisms notwithstanding

I thought Aristotle didn't do experiments.

Sure he did. He didn't follow the modern Bacon/Popper empirical method with testable hypotheses, but he still performed experiments and drew conclusions based on what he saw.

All beside the point: his observations are not invalid, his conclusions are

Re: Understanding is a poor substitute for convexity (2012)

#52

Post by [deleted] »

thaumasiotes wrote: post #49
hannasanarion wrote: post #17

Earlier quoted context omitted.

Falsification is something that you do to hypotheses, not data. Experiments that Aristotle performed to demonstrate classical elemental theory are still valid and useful, his incorrect interpretation of the underlying mechanisms notwithstanding

> Falsification is something that you do to hypotheses, not data. Nonsense. Falsification of data happens all the time. But more importantly, falsification as applied to hypotheses and falsification as applied to data are two completely different concepts. Falsification in the sense "we tried this, and got unexpected results, disconfirming our hypothesis" is something you do to hypotheses. This is Popperian falsifica…

[deleted]

Re: Understanding is a poor substitute for convexity (2012)

#53

Post by fujimotos »

The basic point of this article seems valid to me.

The point the author is trying to make is that the structure of the payoff function matters a lot. Specifically, you need it to be convex for a try-and-error (or random walk) process to become very rewarding.

For example, think about fuzzing C programs, which has been proven to be very productive in terms of software security. But why is it so productive? This is essentially because a bug in a C program can have a quite significant implication (e.g. remote code execution), thus its payoff function is extremely convex. If there was no such property, fuzzing just wouldn't be so much rewarding (This explains why fuzz tests are less used for programs written in memory-safe languages).

The author believes this idea of "convexity" can explain a broad range of phenomena in the human world. I'm not so sure about its applicability, though.

Re: Understanding is a poor substitute for convexity (2012)

#54

Post by mattkrause »

hannasanarion wrote: post #51
yesenadam wrote: post #25

Earlier quoted context omitted.

I thought Aristotle didn't do experiments.

Sure he did. He didn't follow the modern Bacon/Popper empirical method with testable hypotheses, but he still performed experiments and drew conclusions based on what he saw. All beside the point: his observations are not invalid, his conclusions are

So women do have fewer teeth?!

Re: Understanding is a poor substitute for convexity (2012)

#55

Post by fujimotos »

mr_toad wrote: post #44
jjk166 wrote: post #2

"The point we will be making here is that logically, neither trial and error nor "chance" and serendipity can be behind the gains in technology and empirical science attributed to them. By definition chance cannot lead to long term gains (it would no longer be chance); trial and error cannot be unconditionally effective: errors cause planes to crash, buildings to collapse, and knowledge to regress." This is an extrem…

The first two paragraphs of the article are a straw man. I think most of us were biting our tongues at that point. The thesis of the rest of the article contradicts the initial premise. Your scenario of ramdomly digging holes are a perfect example of what the author is explaining: “Critically, convex payoffs benefit from uncertainty and disorder.“

IMHO, the author tries to argue that we can get a better understanding by thinking in term of the structure of the payoff function, rather than focusing on the input itself.

Yes, the try-and-error process and chance are important, but the convexity of the output function is exactly what makes them so rewarding.

Re: Understanding is a poor substitute for convexity (2012)

#57

Post by klipt »

User23 wrote: post #50
buboard wrote: post #18

Earlier quoted context omitted.

> This is an extremely flawed initial assumption. that was not an initial assumption but (presumably) the subject of the essay. its not clearly stated in the text though > you can certainly win on chance in the long run No you can't ; both casinos and insurance companies make choices that give them an assymetry in gains, and thus they benefit from the randomness of events. Chance is by definition centered around the…

This is the concept of ergodicity. The fun fact is that even if casinos offered a game with 50% odds players without unlimited bankrolls would still always bust eventually[1]. It's similar to why betting $1 to make $1 million at million to one odds is a smart bet, but betting $1 million to make $1 at the equivalent odds isn't, unless you have an unlimited bankroll. [1] If they use the Kelly criterion they won't bust…

But real world casinos also have limited bankrolls and can go bust given 50% odds. Which is why they never offer 50% odds.

Re: Understanding is a poor substitute for convexity (2012)

#59

Post by systoll »

hannasanarion wrote: post #17
bchjam wrote: post #15

Earlier quoted context omitted.

> No experiment could ever possibly hurt scientific knowledge what about one with a falsified result? fwiw I think convexity and understanding are relatively orthogonal, but how could one employ the former without the latter? However the author's position seems to be more that gaming systems works better than exploring their contexts. Sometimes you might make more money in less time, but the money is all you'll get o…

Falsification is something that you do to hypotheses, not data. Experiments that Aristotle performed to demonstrate classical elemental theory are still valid and useful, his incorrect interpretation of the underlying mechanisms notwithstanding

You’re using a different meaning when you talk about falsifying a hypothesis.

From Oxford via https://google.com/search?q=falsify :

1. alter (information, a document, or evidence) so as to mislead. "a laboratory which was alleged to have falsified test results"

vs

2. prove (a statement or theory) to be false. "the hypothesis is falsified by the evidence"

Re: Understanding is a poor substitute for convexity (2012)

#60

Post by sooheon »

pazimzadeh wrote: post #4

“By definition chance cannot lead to long term gains (it would no longer be chance)“ If this was modified to “chance alone” then it might be correct. The way it’s worded now makes it sound like chance cannot contribute to long term gains, which is clearly false. Evolution depends on chance (generation of diversity) followed by a selection process and clearly that works pretty well.

Yes. Chance + opportunism can lead to plenty of long term gains.
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