⁠Alex Bilzerian
'Negative probabilities (which could not be justified by Kolmogorov's model) arise with the strange regularity in practically all quantum models.'

"Just like in quantum mechanics--they use negative probabilities."

No we do not. Probabilities are always positive in quantum mechanics because they are defined as the sum of squares of two real numbers (or the square of the modulus of a complex number), and squares of real numbers are always positive! - Nirmalya Kajuri
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⁠Alex Bilzerian
RT @BobMurphyEcon: Among other problems, our Twitter discourse suffers from completely uncharitable readings of people we hate. This physicist is gatekeeping, saying Taleb is wrong for claiming they use negative probabilities in his field. OBVIOUSLY Taleb has this type of thing in mind. https://t.co/Rs2uItg0wd

"Just like in quantum mechanics--they use negative probabilities."

No we do not. Probabilities are always positive in quantum mechanics because they are defined as the sum of squares of two real numbers (or the square of the modulus of a complex number), and squares of real numbers are always positive! - Nirmalya Kajuri
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⁠Alex Bilzerian
RT @alexbilz: "Science is the belief in the ignorance of experts." — Feynman: https://t.co/EvghqgxTHc https://t.co/PHrhnrG18h
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⁠Alex Bilzerian
There may be some truth to this.

@WKCosmo The problem of string theory is that, 10-20 years ago, young theorists had to skip known physics and jump to strings to get a job. They achieved little. Now the old generation who knows physics and developed strings retires. - Alessandro Strumia
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⁠Alex Bilzerian
RT @nntaleb: Academics & X don't go well.
This idiot @Kaju_Nut got involved in a collective troll of yours truly; it keeps being shown that, like the "econometrician" @sndurlauf (on whom, later), he doesn't know his own subject.

'Negative probabilities (which could not be justified by Kolmogorov's model) arise with the strange regularity in practically all quantum models.' - Alex Bilzerian
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⁠Alex Bilzerian
You’re utterly unqualified to teach that, and it shows.

As my first fall econometric lectures are on probability theory and the relationship between probability theory and decision theory, this video is a great help.

PPHA42000 Problem Set 1. Explain why this discussion is complete nonsense. - Steven N. Durlauf
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⁠Alex Bilzerian
Disgusting.

@sndurlauf The only problem is the students might run out of paper - Scott Kominers
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⁠Alex Bilzerian
RT @NoNonsenseQuant: @sndurlauf Why don’t you explain here under the video why and where he is wrong?
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⁠Alex Bilzerian
What is it specifically that you disagree with?

The guy just doesn't quit. - Will Kinney
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⁠Alex Bilzerian
One always hears academics whimpering about "impostor syndrome"—most of them actually happen to be imposters.

Fraud & incompetence in academia are more widespread than many realize.
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⁠Alex Bilzerian
RT @GoujianofYue: @alexbilz https://t.co/VfEgyQuXdp

"In any profession, 90% of people are clueless but work by situational imitation, narrow mimicry & semi-conscious role-playing. Except social "science" and journalism where it is 99% and 100%, respectively."
@nntaleb - Content Philosopher
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⁠Alex Bilzerian
RT @alexbilz: 'The first principle is that you must not fool yourself—and you are the easiest person to fool.'
— Richard Feynman

https://t.co/uBISjy1o9v
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⁠Alex Bilzerian
RT @RDouady: Thank you @nntaleb for raising this question of negative probabilities. As mathematicians, we often use a wording that is not necessarily intuitive and may take a meaning the goes against common sense. This is the price to pay when we need absolute rigor. Too many subtleties in the various concepts we create and not enough words (whatever the language!)

"Negative probabilities" in math or physics don't necessary mean that some event has a negative probability to occur (meaning yet to be made precise) but that we are dealing with quantities we call "probability" that happen to take negative values.

You rightfully took the examples of option prices, or broker's odds in some bets, that reflect a "market implied probability". This "implied probability', given from supply and demand, can possibly negative, meaning that either there is an arbitrage or, if we account for the bid/ask spread, that the remuneration of the market maker is lower than its theoretical value.

There are plenty of other cases where we call "probability" or "volatility" a number that can go negative. For instance, a negative volatility would imply that there are formally no solutions to Kolmogorov's diffusion equation (i.e. Black-Scholes, heat, Fokker-Planck...) But the non-existence relies on a continuous time assumption, which is not necessarily satisfied. Temporarily, we may support an unstable semi-group generator, something that likely occurs in speculative bubbles or market squeezes.

In quantum mechanics, they are related to some negative eigenvalues of operators supposed to be positive, or other issues of this kind. Many paradoxes in here, some being at the source of important phenomena, such as entanglement. The violation of Bell's inequalities, experimentally proven by Aspect, proved that Einstein was wrong in asserting "God doesn't play dice". Basically, one had a choice of accepting negative probabilities or renouncing to the locality principle. It turned out that the latter was the best explanation, and this led to quantum computing.

I also posted about our Antifragility paper, where the non-positiveness of the transfer function between Gamma and Vega can also be interpreted as some negative implied volatility, something physically realizable, which, as we discussed, can be related to Simpson paradox for the far out-of-the-money behavior of stochastic processes.

I wish that the contenders of subtle notions who claim "common sense" would better know what they are talking about and show the necessary rigor in their alleged mathematical criticism!

Academics are so easily busted on X.
Next we deal with that idiot, the econometrician @sndurlauf who isn't aware of its uses in finance, so separated from the real world & unaware of it that it is not even funny.

BTW Espen (my coauthor) & I shared trading office space back in the days in Connecticut. - Nassim Nicholas Taleb
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⁠Alex Bilzerian
RT @alexbilz: 'There is nothing in a stochastic differential equation that is not in a Fokker-Planck equation, but the stochastic differential equation is so much easier to write down and manipulate that only an excessively zealous purist would try to eschew the technique.' - C.W. Gardiner
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⁠Alex Bilzerian
'p-Adic Probability Theory and its Generalizations' - Andrei Khrennikov (2006, PDF):
https://t.co/rpVUR8LN7e
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