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Understanding is a poor substitute for convexity (2012) (edge.org)
130 points by alrex021 8 months ago | hide | past | web | favorite | 64 comments

"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 extremely flawed initial assumption. There is no requirement for chance to be centered around zero. Consider rolling a dice: sometimes you'll get more than the mean, sometimes less, but you'll never roll a negative number. You can certainly win on chance in the long run, that's the foundation of casinos and insurance companies. It's hard to imagine a scenario where trial and error can possibly lead to knowledge regressing.

Consider randomly digging holes in the ground: after enough holes you will eventually strike gold, and you will never lose physical gold in the process. However, you may lose significant time, wealth, and effort that could have been better converted to gold. The optimal way to strike gold is not to dig more, shallower holes, but to learn enough geology to understand where gold is likely to be found and concentrate your prospecting there.

No experiment could ever possibly hurt scientific knowledge. People tinkering will certainly make occasional discoveries. In a brand new field with a lot of low hanging fruit, these discoveries will be numerous and the cost will be low. But in a developed field where people have a good idea where the remaining discoveries are likely to be found and the effort to conduct such experiments is substantial, targeted approaches become optimal. Reducing the unit cost of experiments is always nice, but is not generally feasible. This strategy of "convexity" is a very poor substitute in the real world for understanding.

Yeah, it's badly written in a way to provoke controversy, but fundamentally, I'm not sure there's any real disagreement here?

In simple terms, he's just saying that it needs to be safe to take chances in order for it to be worthwhile to take chances. As you say, science is an example of a system where it's often safe to take chances, because you don't risk losing any knowledge from a failed experiment. (But that doesn't mean there are no costs! You can lose time and money. And I'll also point out that some experiments can be dangerous.)

In any search, whether you can find something interesting is going to depend at least partly on the landscape, so understanding the landscape better will improve the search process, along with your estimates of whether it's worth doing at all. Calling this property of a desirable landscape "convexity" doesn't, in itself, help you understand the landscape, but it doesn't seem wrong?

> Yeah, it's badly written in a way to provoke controversy

I’m not sure it is worth my time to read something that is badly written to provoke controversy, even if it does make good clickbait.

Yeah, I used to go out of my way to follow links to Taleb’s writing, but then I kept running into pieces like this one, where it wasn’t clear if he knew he was fundamentally (if not subtly) wrong. He seems to welcome controversy, and his recent childish attack on guy from 538 means I won’t give him more than a paragragh to convince me the rest of the piece is worth my time.

I hate it when smart, competent people become famous, and a few years later they become total loons. Happens way too often.

>* but then I kept running into pieces like this one, where it wasn’t clear if he knew he was fundamentally (if not subtly) wrong*

He is not "fundamentally" wrong here though. The parent comment misread what TFA says (as I replied above).

It is worth the time for those that can read beyond the title or opening paragraphs.

There's nothing against a work with a clickbait title or opening being the most important thing one would read all year.

Like whether an author is a "bad man" in their personal life tells us nothing about the worth of their work, the ways an author/editor tries to attract viewers do not mean that the actual content is also of bad quality.

My take was that he is using a slightly different definition of "chance" or "trial and error" than what is perhaps common. I don't quite grasp his definition enough to be able to do it justice.

I don't know enough about geology to be able to comment intelligently on your digging holes in the ground point. However, from my own background in biology research, a lot of what he writes strikes true with some caveats.

Biological systems are highly complex, and a lot of reductionist basic research work does seem to be driven by understanding along the forms of "I have a mental model of this subsystem, if I do X, then I expect Y." However, a lot is also discovered via his "convexity" principles (which I agree most laypeople would label as "trial and error"). Biologists often discover functions by randomly mutating billions or trillions of individual microbes, screening for interesting phenotypes, and then sequencing to discover the supposedly causal mutations.

Where the understanding approach really breaks down is in engineering systems -- which I believe requires an even higher level of understanding than the qualitative mental models bandied about in biology. We simply don't understand enough to be able to develop most drugs with that sort of rational approach, so reducing costs per attempt (while keeping all else equal, which is something often overlooked) would be beneficial. Unfortunately, things in the industry appear to be heading the other direction.

I'd say the zero is where you don't do anything. There's no gain and no loss. Once you decide to do something, you have to spend to make it happen. The dice example is pointless when the roll is assumed to be zero effort and you get a random number for it. Where's the gain?

> No experiment could ever possibly hurt scientific knowledge.

Sure could. An experiment might yield a false result. You might get a false negative and abandon a promising discovery. You might get a false positive and waste more experiments on an impossible setup. It's all about opportunity cost.

But overall I couldn't follow Taleb's writing. It's not accessible to me anymore.

> 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 mean.

The question of scientific research directions is interesting , but i m not sure that research is a random walk. There are biases and "hunches" that guide scientists.

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 hard, but they'll still lose most of their bankroll.

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

thaat's only because they have "chosen" to not allow players with negative balances or margins.

> 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 out of it. In practice, maybe understanding and convex payoff functions are both useful at different scales.

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"


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

> 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 falsification.

In the sense of what happens to data, falsification is "we tried this, and got data that disconfirmed our hypothesis. But instead of recording that data, we recorded spurious data which confirms our hypothesis". (Or, of course, "we didn't try anything, but here are some numbers that we feel reflect what would have happened if we had".) This is falsification in the same sense you'd see it applied to, say, accounting records.

If someone knowingly uses bad data, aren't the claims supported by it false?

Technically that is fallacious - a lie doesn't make the claim false it not being true does. Rarely frauds can be accidentally accurate.

It has a bit of a meta role I suppose - a system must be robust enough with replication that it shouldn't matter. Knowing bad actors are about can promote better verification practices than a blind trust.

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

He made observations, sure, but what are some actual experiments he did? (Or where to read about that?)

So women do have fewer teeth?!

No, but not because Aristotle was against observation. Just because he either miscounted or trusted a wrong earlier observation. What he wrote is:

"”Males have more teeth than females in the case of men, sheep, goats, and swine; in the case of other animals _observations have not yet been made_”

Emphasis mine.

> This is an extremely flawed initial assumption. There is no requirement for chance to be centered around zero. Consider rolling a dice: sometimes you'll get more than the mean, sometimes less, but you'll never roll a negative number. You can certainly win on chance in the long run, that's the foundation of casinos and insurance companies. It's hard to imagine a scenario where trial and error can possibly lead to knowledge regressing.

Casinos and Insurance companies don't win on "chance". There is an expected value of the events that are in consideration here, and these firms price their services such that their return is higher than the expected value...very little down to chance. It's as if we played a die roll game where I paid you the value on the dice each time you rolled it and you paid me >3.5 units per roll to take your turn. That's the house edge.

>No experiment could ever possibly hurt scientific knowledge. (...) This is an extremely flawed initial assumption. There is no requirement for chance to be centered around zero. Consider rolling a dice: sometimes you'll get more than the mean, sometimes less, but you'll never roll a negative number.

That's the convexity property Taleb argues must lie underneath research though.

So, you're saying the same thing.

What he means with the first paragraph is not that chance can't lead to gains -- it's that chance alone cannot lead to gains. There should be an additional property, and that's what the article is about.

Consider your counter-argument: "You can certainly win on chance in the long run, that's the foundation of casinos".

And yet, that's not the foundation of casinos. That's what the article speaks against. For if it was chance + long run alone the "foundation" then it would work for the players too. But players face ruin in the long run (unless they have an infinite supply of money), while casinos do not.

The foundation of casinos is chance + resilience to chance events (a casino doesn't go under from this or that player winning) -- e.g. the exact convexity the author talks about.

I think another way to put this is that betting on convexity still requires a formal theory of costs and benefits, even if not of the risks involved.

There are some cases where that model can itself seem pretty fragile (like estimating the opportunity cost on your hole digging), but others where it night feel reasonable. Pick your poison!

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.

I read this from the perspective of money. If an invention or discovery makes some organisation, company or government a lot of money, then that money can be ploughed back into research. If on average science and technology is making us more money than it costs it will be "antifragile".

The expected value of an infinite series of coin flips centers on 0. Sure, you might get lucky, but you can't leverage that as a strategy to ratchet up value. That's the point about luck in the non convex case.

To your mining example, that's where prospecting comes in. Use your knowledge to make checking candidate locations cheaper (increasing convexity) - knowledge of geology to approximate likelihood, improvements to technology to determine if gold exists, etc. Then go check as many candidate mines as possible. It's much more cost effective to have a lot of shallow mines than it is to extract every ounce all the way down to the crust from a single mine.

If heads is 1 and tails is 0 then the expected value is 0.5. The expectation really depends on what values your random variable can take.

That's not the non convex case though (as e.g. 1 and -1 is). You're right that chance can be convex; the premise of the article is that that's the property of interest, and that randomness alone isn't sufficient.

You could conceivably have a number of related experiments that lead you to conclude that phlogiston exists.

Is anyone surprised by the notion that ratcheting is critical for consolidating gains made from chance events? I thought that was a trivial observation (maybe my biologist bias is showing here).

It might be obvious but worth saying anyway. Giving something a name can help you use it as a unit of work, or reason more effectively/accurately/mechanically.

A lot of arguments are built on abstractions like "competition" and "chance", and having a short list of common exceptions to those heuristics on hand is pretty useful. Now when discussing federalism in the U.S., I'll not only wonder whether there are free-rider problems or economies of scale missed out on, I'll also think about whether local decisions are effectively "locked in" forever.

Biology, game theory, informatics, and complexity are full of ideas that one can pluck out in isolation and look like a hero for injecting into other areas. I think its because those fields are insufficiently studied by those outside them.

Yeah it’s like - OK what systems are not like that? Pre written technology eras where one could lose knowledge if a tribe member died?

Maybe The Great Leap Forward when Mao killed a bunch of intellectuals?

yeah the message here is pretty basic. Would be more intersting if he would expand on the process of scientific research which is an open problem.

“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.

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.

Isn't he basically saying the economics of research works up to a point but there is an inflection point after which it's broken?

And he's saying you can't just keep the model as is, but you need to make certain adjustments to the incentive structures.

It's becoming blindly obvious that this is the case in psychology at least with the replication crisis and the "publish or perish" mentality. We can see these things playing out.

Does the economics of the scientific machine need to be revisited and tweaked? I'd say there is a good conversation to be had about that. I can already see a little evidence of a minor self-correction, but given economics drives absolutely everything then yeah I'd say it's likely there are some changes that would produce different results that might be better than what the current system is producing. Though it's not easy to compute ahead of time whether changes themselves would have unintended consequences.

He probably needs to spend more time trying to explain things to 5 year olds to offset his "I am so smrt" persona.

I think an important way to understand the optionality/convexity is to imagine science without it. Here is a paper about that: https://nickbostrom.com/papers/vulnerable.pdf - the idea is: what if there are inventions that could destroy our civilisation? One example of such invention would be a bomb as powerful as an atomic bomb - but from materials and technologies readily available to anyone. Surely there would be terrorist/mafias/suicidal individuals who would build and use them.

From the title I assumed that the author was going to make a different point: that understanding a problem does not mean that said problem can be represented by a convex function, i.e. it still may have many local optima that a problem solver may get stuck in, rather than a single global optimum.

So, I expected some more general point about theoretical understanding of a thing being distinct from the actual computation of that thing, and that theoretical understanding does not necessarily lead to optimal outcomes.

I wish he’d made that point instead.

I'm not certain where the author wants to go with this. Comparing research with an Airplane flight seems not correct to me.


> By definition chance cannot lead to long term gains (it would no longer be chance)

Heh. The whole universe might be made by "chance". It is, in fact, quite possible that the total energy of the universe is 0. Our existence is a fluctuation.

Define long term gains. Since infinity is out of our possible reach, it is possible (though unlikely) to make long term gains just by chance. Especially, if you have a large audience. Some of them will get lucky.

"an army of pompous phrases moving across the landscape in search of an idea."

>A "1/N" strategy is almost always best with convex strategies (the dispersion property): following point (1) and reducing the costs per attempt, compensate by multiplying the number of trials and allocating 1/N of the potential investment across N investments, and make N as large as possible. This allows us to minimize the probability of missing rather than maximize profits should one have a win, as the latter teleological strategy lowers the probability of a win. A large exposure to a single trial has lower expected return than a portfolio of small trials.

Isn't that YC Combinator in a nutshell?

I read the article in full but still have no idea what he is trying to say. Perhaps someone can explain what he is talking about? Because as far as I'm concerned its postmodernism meets statistics.

Amazing how Taleb can write such utter banalities and yet utterly believe he is writing novel and important things.

I'm not sure he thinks what he's writing is novel. But he does seem to think it's important and if you consider his earnings as signal, he does have signal in that direction. To whom is it important? Not academia. But probably socially, it is. You have to convince a lot of people before you convince a politician...

The writing style of this article strikes a tone that seems overly eager to place an eloquent vocabulary on display.

  Hey guys! Look at all the
  big, big words I can use!

  Don’t I sound smart???
Seriously. It’s like they wrote, and proof read the original draft, then performed a search/replace for any polysyllabic synonym they could opportunistically inject.

Why do they need to sound smart? Is it really because they know they’ve got nothing to say? Is this an SAT reading comprehension test?

You could sum up the sentiment with an anaology to paraphrase the concept: “defensive programming is no replacement for accomplished programming skill” (to borrow a concept comparable to investing)

Big words, small mind.

This comment breaks the site guidelines, which ask: "Please don't post shallow dismissals, especially of other people's work. A good critical comment teaches us something."

Could you please not create accounts to break the guidelines with?


Or, he has over a long time tricked himself into thinking in that language style and otherwise has trouble (or at least no desire for) expressing himself otherwise.

I might be taking bait here. I guess I take umbradge at the post I am replying to because it has insults in it, which is not so pleasant. Maybe it's just the hypocrisy, as its language is also verbose. To paraphrase:

> The writing style of this article strikes a tone that seems overly eager to place an eloquent vocabulary on display.

"This article uses too many big words"

> You could sum up the sentiment with an anaology to paraphrase the concept: “defensive programming is no replacement for accomplished programming skill” (to borrow a concept comparable to investing)

"You could sum up his article as: 'following best practices won't replace programming skill'"

You might argue that paraphrasing like I have detracts meaning but I'm sure the original author of the article would say that too.


To further boil down what the article tries to distill, but never explicitly states as a revealed conclusion: Success requires agency. The positive outcomes must be recognized and selected for, to produce gains.

Correct. We live in a world where sentient intelligence persists upon a substrate of inert, newtonian determinism. Life, itself, stands bound by gravity, upon a rock floating in space. So where’s the investment tactics?

Meanwhile, mysogyny as a personality flaw of the author would not invalidate the merit of any ideas expressed into a vacuum devoid of mysogyny. As adults, individuals should be capable of reading and digesting a non-inflamatory article, if its ideas have merit, and it doesn’t seek emotional agitation.

You should be able to read an article, and ignore the name of the author. Ask yourself: If it were the same article written under a pseudonym, could it still be found valuable?

That sounds so logical, but the truth is that reputation is a useful time saver. I don't have time to read the vast majority of what is written in the world, why should I make time to read stuff written by someone who I know is an arrogant ass?

If that's it, it's not exactly a novel idea.

Are there actually people who argue that brute trial and error with nothing else in play can yield structured knowledge? Note that biological evolution doesn't count because it is not mere trial and error.

I'm curious why you think Taleb is a misogynist. A quick Google didn't turn up anything other than a few posts of his where mentions the word. He seems like an abrasive ass in general, but he's only a misogynist if he's more of an abrasive ass to women than men.

Have a look out for his appalling attack on renowned clacissist Dame Mary Beard. Actually I suggest you don't.

I just read Pagliucci's summary of the exchange [1]. Taleb's disdain for academics is well known, particularly the humanities, and that seems on full display here. I don't see anything specifically misogynistic though. Did Pagliucci simply not quote what you're referring to?

Edit: by which I mean, what definitively demonstrates his misogyny as opposed to a gender neutral disdain for historians in general? He's definitely the abrasive ass I described earlier, but misogynist doesn't seem warranted, and it's a label that's thrown around far too freely these days.

[1] https://iainews.iai.tv/articles/beard-nassem-taleb-twitter-f...

It is a fair question I suppose. I watched the incident at the time and I felt Taleb was being a misogynist yes. However I am not prepared to go trawling through the bile again to find specific quotes.

I acknowledge that there is a chance I am remembering it incorrectly. Lots of people who joined in his appalling baiting were certainly openly misogynist in their language, and maybe I am accusing him of being guilty-by-association. However perhaps joint-enterprise is a fair stick to beat him with, he certainly and very deliberately tries to get his fan club to wade in on social media. Maybe people who do this bear some responsibility for what their followers inevitably say?

The further complication is that Dame Professor Mary Beard is an outspoken feminist, and this has caused her to receive more than her fair share of misogynist abuse both on social and mainstream media (incidentally her book Women and Power is very readable and I see now in paper-back). Therefore it could be that I was showing my prejudice in assuming that a man attacking Mary Beard was automatically misogynist. Then I think to myself that a man who has no credentials at all in that field attacking a renowned person in that field (from one of the worlds great institutions) in such a vile way must have some special reason to do so.

I guess the final thing is that he did indeed accuse her of having "used feminist cover" (Damn I said I wasn't going to look up quotes). What he seemed to be saying is that she was trying to be exempt from criticism because she was a feminist. I would actually say that that was very misogynist thing to say. It reminds me of the people who try and perpetuate racial slurs an say things like, 'you can't even criticise them for (insert racist trope) for fear of being called racist'.

What is worse, is I came out thinking that he was wrong, and badly wrong at that, but was trying to bully his view to the forefront. But as you can see from reading what I wrote, I am not a scholar of the humanities at all. It is still my personal opinion that he is a misogynist bully, and his ego is so big that it compromises his objectivity.

> Did Pagliucci simply not quote what you're referring to?

Before I finally posted I read the article you linked, I think you have missed this bit

"It isn’t because of the not-so-subtle sexist undertone (not just of Taleb’s, but of many of his Twitter-based supporters)"

So indeed Pagliucci does mention it.

BTW, I predicted the financial crisis of 2008 too. I say that as it seems to be Taleb's main claim to fame. I was wrong about what the trigger would be, but what I identified as a potential cause certainly helped it spread (mind you I could have changed that around when I wrote my book). But then so did my dad, and a plumber I remember talking to at the time. I heard mainstream radio shows about it. In fact it only seemed to be people who were in the financial game who couldn't see it. So what? We could just have easily been wrong.

Thanks for the key phrase, actually found most of the original thread (I think), and the feminist cover one you mentioned [1], but not what apparent revision Beard made that led that reply. I don't really use twitter, partly because it's such a terrible place to begin with and I get into enough arguments on HN and Reddit as it is.

Taleb is unsurprisingly obnoxious and inflammatory, and you're right that his ego is huge. I don't see anything specifically misogynist from in that thread (although maybe that last one crossed the line, hard to say without context), but if you're right that he encourages his followers in that manner, that's skirting that line pretty damn closely.

At the very least, this is an interesting case study in historical scholarship and philosophy of language for sure (does Beard calling it "accurate" entail that it's "representative" and thus "typical"?). I would have to read a lot more to take a side, but I probably won't. Thanks for the info though!

[1] https://mobile.twitter.com/nntaleb/status/894316405365100544

I dunno. An ego size comparison between Taleb and Wolfram would be pretty epic. Get both in a room and the resulting ego singularity could damage local space-time.

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