The Gaussian distribution, aka ‘the bell curve,’ is what Herr Taleb calls The Great Intellectual Fraud. Strong words, no ?
And I’m very much inclined to agree, for in essence, the bell curve is an over-used and oft-abused platonicity upon which far too much pseudoscience is predicated, all of it attempting to wedge the vast and unpredictable complexity of reality into a knowable schemata upon which further models can be built and, yes, policy decisions divined with shamanistic precision. It’s upon this corrupt foundation that the Soviet-Harvard illusion rests,i what with its pretended powers of prediction and perverted political panderings. It’s this that is the cause of so much pain and suffering in this world. It’s this that I’m so hellbent on destroying if it’s the last thing I do.
Technically speaking, the reason that the Gaussian so frequently fails to model reality, as Taleb describes it, is this :
The main point of the Gaussian, as I’ve said, is that, as we kept saying, that most observations hover around the mediocre, the average; the odds of a deviation declining faster and faster (“exponentially”) as you move away from the average. If you must one single piece of information, this is the one: the dramatic increase in the speed of decline in the odds as you move away from the center or the average.
Yet despite this inapplicability of such models to anything but the most mundane and mediocre, Gaussian distributions are quite so loved by that entire sub-human class of intellectual louts know as “economists” and “cognitive scientists” because it allows them to lazily and “efficiently” take smaller sample sizes and still feel confident in the accuracy of their predictions, trusting that additional samples won’t appreciably skew or fatten the tails of their results. So an experimental group comprised of a few dozen college students just read a handful of “priming” words about being aged and slow then proceed to walk down a hallway more slowly than the control group therefore words matter, which must surely mean that democracy matters, right ?
All of which, as far as discussions of statistics go, brings us around to a recent conversation in channel regarding a few other distributions, namely human intelligence and skill :
mats: AMZN ticker is ridiculous
pete_d: +15%. Whoa.
mats: Closed yesterday at $390 with uncertainty premium due to earnings report, opens at $440.
funkenstein_: People love the unverifiable numbers they reported I guess.
funkenstein_: I should take that back, I have no clue who the relevant market makers are here.
pete_d: Figure it’s banks and whatever funds.
mats: I started buying AMZN after it became clear they had intentions of becoming a USG contractor.
pete_d: Well played. When was this ?
pete_d: http://business.financialpost.com/news/fp-street/here-are-the-most-cringeworthy-chat-message-that-landed-deutsche-bank-with-a-record-us2-5b-fine << speaking of market makers. “COULD WE PLS HAVE A LOW 6MTH FIX TODAY OLD BEAN?”
williamdunne: Nice to see some civility in the markets.
Pierre_Rochard: What’s cringeworthy about those chat messages ?
williamdunne: I suppose the “cringe” is about how brazen it was. Like “ooohhh and theres 2.5b gone. There is the near entirety of bitcoin’s market cap gone.”
Pierre_Rochard: Also, traders getting blamed for poorly designed “market” mechanisms… I liken it to the Stanford prison experiment – what exactly were you expecting ?
pete_d: ‘Don’t blame the bankers / jooz‘
williamdunne: What do “jooz” have to do with it?
pete_d: Scapegoat par excellence ?
williamdunne: “COULD WE PLS HAVE A LOW 6MTH FIX TODAY OLD YID?”ii
Pierre_Rochard: Well – some of the execs who designed this certainly deserve blame, some of which may coincidentally be bankers/jooz… All of them likely long retired/dead. But really I’d cast blame on the lemmings who use LIBOR for everything and anything
pete_d: Not sure how much of a coincidence it is that those in positions of influence, who needed to be leveraged by the state and ‘the consumers who’ve come to expect’, would be bankers and/or jooz. So the state leveraged those of influence, and were leveraged in turn. and both grew larger. And larger. And the incentives inherent in large organisations became manifest until we arrived here.
Pierre_Rochard: My point was only that traders gonna trade. The real cringeworthiness happened in 1984 when some old beans decided this was an acceptable way of doing business.
williamdunne: Is it not generally accepted that banking/law etc is engrained into Jewish culture ?
pete_d: If it is, where would that leave us ?
williamdunne: Exactly where we are now.
pete_d: Which is where ?
williamdunne: A world where Jews are over-represented in banking and law ?
pete_d: Define ‘over-represented’. Compared to what ? Somalis ?
williamdunne: The statistical average.
pete_d: Human skill and intelligence aren’t on a Gaussian distribution.iii Average is meaningless in this context and by extension any relationship to it.
williamdunne: Doesn’t seem irrelevant when comparing subsets of the wider context.
pete_d: That’s like saying that crack cocaine makes a lot of sense when you’re living among homeless people in dumpsters. You have no business over there in the first place.iv
williamdunne: I’m not suggesting I have any issue with it, if that’s what you mean.
pete_d: Not at all. And nor do I. Just that the context has never and will never be evenly distributed.v So no averages. So no predictions. No ‘over-represented’
williamdunne: Fair nuff’.
Life is complex and largely unpredictable, which is also why purposes are so pointless. So throw away your bell curves, walk away from the rigged fiat markets of yesteryear, and embrace uncertainty. And if you absolutely cannot for the life of you embrace uncertainty on your own, and you wouldn’t be alone in this, cling dearly and obediently to someone who can.
Your survival depends upon it.
___ ___ ___
- Shakily, tremoringly it all rests, this entire stack of un-good democratic Scheisser. From software on up. ↩
- Heh. Old yid.↩
- Wealth wasn’t on a perfectly knowable distribution either, primarily because wealth instead follows Mandelbrotian, or power law, distributions, meaning that one new observation can throw whatever average you thought you had right out the window. This, and the fact that no one knows how many dollars/euros/yuan/rubles there are. They can be counterfeited, so they are counterfeited, so who the fuck knows ?
…until Bitcoin was discovered. Now, for the first time in history, we know exactly what fraction of the monetary base we hold (if any). Even if we don’t know how many public keys belong to a single private key, much less a single individual, we still know the number of large addresses that exist. FYI there are currently 16,151 addresses with 100+ BTC.↩
- Or maybe you do have business lighting up rocks in a back alley behind a smelly downtown restaurant, but it doesn’t speak very highly of you if this is indeed the case.↩
- As MP points out, “you know the mathematical criteria for a set to include its average is not ‘even distribution’ “. This is obviously true and I should’ve been more clear so as to state that for the domains of skills and intelligence, the distributions aren’t even knowable and whether or not one additional sample with throw the curve right off, which is really why averages and predictions aren’t possible, but black swans are. This, of course, ties into MP’s splendid “Genetics of intelligence” piece.↩
In WWI, something like 99% of naval tonnage sunk by u-boats was attributable to 1% of captains. On Wall St., outsized gains attributable to fraction of a percent of money managers. etc. Yet, nearly all social science “research” assumes the population is normally distributed…
No matter what “the research” says, Margaret Mead’s line holds true as ever : “Never doubt that a small group of thoughtful, committed citizens can change the world; indeed, it’s the only thing that ever has.”
Cows are not spherical. Does that mean spheres are useless or fraudulent concepts? Not at all. 1st order Hermite expansions, Maxwellian distributions, Gaussian approximations, are things we should learn about and use correctly, pointing out when higher order effects are important, and not throw out with the bathwater because some idiots were waving them about claiming they were cows.
I’m not saying that Gaussian distributions don’t work for sports games, coin flips, human height, etc. I’m saying that the stupid idea of children should be confined to the sandbox where they are not only most applicable but also least likely to harm others.
Spheres aren’t useless or fraudulent, but a baseball thrown at your skull can do some damage.
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