A conversation between Nassim Nicholas Taleb and Stephen Wolfram at the Wolfram Summer School 2021
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Taleb argues that economics fundamentally differs from physics because it lacks energy constraints and exhibits fat-tail distributions, requiring risk management frameworks that prioritize survival over scientific prediction, and that single numeraire (currency) systems are essential for arbitrage-free markets.
- Economics has no binding constraint like energy in physics, allowing prices to move from $1 to a billion arbitrarily
- Fat-tail distributions dominate economic variables, making law-of-large-numbers approaches fail and tail risk unobservable
- Survival constraints create absorbing barriers that break ergodicity; time-average and ensemble-average outcomes diverge in economics unlike physics
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Option pricing reveals a systematic bias: when volatility is variable (stochastic), taking the average option price across two volatility states produces different results than pricing an option at average volatility, because the Black-Scholes formula is nonlinear in volatility.
“you take the black trolls you price the option at 10 percent higher volatility which was about the the variation of volatility that we had and you know over time and then you should explain for people that volatility is is the the variance of this time series for exactly the square square the the square root of the variance of that that the expected time series annualized”
The Romans built self-reinforcing concrete (opus caementicium) that becomes stronger under stress and whose recipes were completely lost; engineering as technique often preceded explicit knowledge and modern 'science-first' approaches would have prevented such discoveries.
“and then the other uh the branch that we we we should look at that was monstrously successful and a catalog an anti-fragile how it it preceded knowledge in it procedure science or technique procedure estimate is engineering the the romans had phenomenal and we had recipes then that definitely were vastly more effective than medicine okay because it's an easier field you would say less complex in engineering and they had a self reinforcing concrete the concrete that that under stress get stronger and recipes we have lost completely”
Connectivity and transportation costs are the primary determinants of tail risk in economic distributions: as connectivity increases (fewer barriers to goods transport, fewer geographic monopolies), previously-local income distributions become winner-take-all (fat-tailed), transforming an opera singer's income distribution from thin-tailed (local monopoly) to fat-tailed (global competition where the perceived-best takes most income).
“and this has to do with connectivity which is the most important thing for economics is connectivity so to explain the dynamics and why things are getting more fat-tailed let's say that you're an opera singer in and that's the example i've used okay in naples in the 1800s okay you have a good life because nobody can transport goods from new york namely singing so so you know so people can sing in milan and they don't no threat to you so therefore you're gonna have the income local income determined locally okay now let's say that someone invented something called the vcr or stuff like that where suddenly now you've been displaced by audiovisual and and and they didn't have planes and now people can fly and go to milan new york other places see other opera singers okay now that creates a winner take all effect or a smaller and probably the let's say perceived to be the best okay we'll take all the money and this applies to practically everything like google today taking all the money for browser worldwide or in the past no farmer could take all the money for farming worldwide all right you're very local so things are being delocalized in many respects they've been localized”
Market makers make money by buying on the bid and selling on the ask, maintaining positive spreads regardless of directional accuracy; this simple edge works better than trying to model 'the world' because it is model-independent and profits from order flow.
“okay buying on the bid it's like i'm a car dealer i buy for ten thousand i sell for twelve right and i have it's worth eleven thousand in my mind i have that edge all right so that's what a market maker does right so of course it's you're going to be wrong about valuation but it washes out if you buy and sell a lot”
P-values are random variables themselves; observing a p-value of 0.12 means the true parameter could produce p-values ranging widely, so approximately 53% of repeated experiments could yield p < 0.05 even though the true p-value is 0.12, making thresholds like p < 0.05 arbitrary.
“p value is a random variable if i have an example and it has one property p-value that say the true p-value is 0.12 it means that you repeat the same experiment and you get long-term distribution around 0.12 53 of the observation will be below 0.05 okay so so it means you you can get at 0.01 by two or three by repeating two or three times the experiment okay with a different the same knowing the p-value is 0.12”
The function of an average is not equal to the average of a function; this inequality (Jensen's inequality) is the foundational error in economics, statistics, and medicine, where practitioners compute E[f(X)] when they should compute f(E[X]) or vice versa.
“the function of an average is not an average of a function so it all comes from that by saying i'm adding a layer of stochasticity to things”
Computational irreducibility means that even when you have the complete underlying rules for a system, you cannot predict the outcome by any shortcut more efficient than running the simulation forward step-by-step.
“computational irreducibility is the story of the extent to which that is not possible that is you might have thought once you have a scientific theory of you know how the pandemic is going to develop or how you know the climate is going to change or whatever it is once you have a scientific theory you're done you can you know you can figure out everything you can base your behavior on what's what's being um uh uh on on that sort of scientific knowledge but one of the things that's come out of science i've done is that that's just not true that science in a sense sort of eats itself from the inside because even when you know the scientific rules by which something should operate knowing what's actually going to happen is something that's kind of computationally irreducible”
Fat tails emerge from a Gaussian distribution when volatility itself is variable; by constructing a mixture of Gaussian distributions with different variance parameters, the resulting composite distribution exhibits heavier tails and higher shoulders than a single Gaussian.
“and we do a control with it okay plot i do two things i do and i do a control with it as a normal distribution okay pdf normal distribution with x uh at just one okay yep all right now we do manipulate you can see that they coincide okay they don't concern no more right okay you got fat tails uh-huh higher shoulders okay”
Long-Term Capital Management blew up in 1998 because 52+ PhDs in finance ignored tail risk and ruin, treating options pricing as if it worked in the real world; they were 'short volatility' (selling tails) when they should have avoided ruin.
“and it was uh people who loved financial theory and and they said they they really believed that whatever financial economics and all the techniques they had work in the real world and my belief was that these guys are called considering ducks because you can make some money off of them so and of course in 1998 there was a blow up and we counted something like 52 phds in finance or right who are involved and blow up”
A numeraire (unit of account) is essential for economics to function; without a single numeraire, arbitrage cannot be defined and the law of one price cannot be enforced, making pricing incoherent and allowing circular arbitrage loops.
“okay that you're going to have to have a home currency what we call a home currency and the home currency doesn't can be expressed in beanie in baseball cards you can have your home currency in anything okay but why is it obvious that there has to be a scalar measure of value why is it obvious that transactions can be and then you no longer have you cannot enforce the law of one price if if you don't have one unit you're valuing everything else this is where and also you cannot have arbitrage if you have one unit”
Dynamic hedging and replication strategies break down in fat-tail environments because the continuous rebalancing required to maintain perfect replication cannot execute at theoretical prices when large dislocations occur.
“except that when when you're under fat tail these don't work dynamically now with my subspecialties breakdown of these theories locally and and where they don't break down”
Price (what something sells for) and valuation (what something is fundamentally worth) are distinct; some assets Taleb values at zero trade at positive prices due to speculation, while others may trade at prices below their valuations.
“a lot of people say bitcoin for me is valued at zero but the price is 34. and a lot of people don't get it say well sell it to me for zero i paid a thousand for it i said no you idiot if i want to show it i said it's 34. you see but i value it at so you have new valuation and you have the price there are two different items okay”
Financial institutions use value-at-risk (VaR) as their primary risk metric, but VaR only measures the loss at a specific quantile (e.g., 95th percentile) and tells you nothing about losses beyond that quantile—in fat-tailed domains, most catastrophic losses occur in the tail that VaR ignores, making it a dangerously flawed risk metric that persists in use because it is simple and fits institutional incentives.
“systems still don't handle this still use something called the value at risk and they still use all the crap that was there still being used why because you don't have learning you don't have a skill in the game”
Time-average and ensemble-average outcomes diverge fundamentally in systems with absorbing barriers (like bankruptcy or death); a bet with positive expected value can bankrupt an individual if they keep taking it over time, even though an ensemble of people taking it once would gain on average.
“if i take a hundred gamblers i send them to the casino okay and for one each for one day uh okay come back i get the average uh expected return from the casino and a lot of large numbers works beautifully tell them gamble for eight hours all right or whatever or whatever you lose your money and come back okay with your p l right so you can figure out the return you can get from a casino for a certain number of bets the the works beautifully because casinos are we built casinos because we know probability that's another one where science but the rest of the world doesn't work that way now if i sent one single uh trader okay one single person to the casino for 100 days okay have complete different picture”
Medicine confuses evidence-based aggregate statistics with individual treatment, incorrectly generalizing claims about populations to individuals; the proper framework requires three separate methodologies: clinical (apprenticeship-based), empirical (statistical), and theoretical (mechanistic), each with different validity domains.
“the mistake of evidence-based medicine is that they often make the mistake of saying okay let's bring an ethiopian to run a marathon or let's let's bring a uh swede to lift uh uh or sorry a bulgarian truth wait all right because statistically bulgarians are better at deadlifts whatever it is okay so let's go bring a bulgarian no i mean you don't have to go call build gear and consulate right you you go to the gym”
Inequality measured as a static snapshot (Gini index) is misleading; social mobility requires measuring the probability that someone in a high-income state exits it, or tracking whether the same families remain in top quantiles across generations, not comparing income distributions at two points in time.
“so it's like taking a markov chain and make sure that they are no absorbing barrier no absorbing probabilities no unit one or zero probabilities in the markov chain so so that's the problem with uh with taking not looking at dynamics for uh for inequality”
In domains with fat-tail distributions or high uncertainty, the precautionary principle should guide action: avoid actions with unbounded downside even if you don't fully understand the mechanism; the variance of climate model predictions is more informative than their means.
“the more the less we understand the world the less risk we should take with things that are no dumping in large quantities in the atmosphere plus there's a notion of non-linearity like if i jump 10 meters as i'm harmed more than uh uh ten times that if i jump one meter so if you know there's a non-linearity in those response okay there's always some kind of s-curve”
The central limit theorem and law of large numbers only hold when variance is bounded and finite, but in fat-tailed distributions like Pareto distributions these conditions fail, requiring sample sizes of 10^13 instead of 30 to achieve the same statistical stability.
“to compress the variance enough in other words to get the mean and you're the same reliability for the mean for a sample of 30 you need 10 to the 13”
Dimensionality in finance creates spuriousness: as you add more securities to a portfolio, you add O(n^2) correlations but only O(n) observations per security; with high dimensionality, you will find spurious correlations by chance that don't persist.
“so when you have a high dimensionality you end up having a lot of securities and not enough data per security so to give you a very simple example let's say i have a thousand securities okay how many coordination do i have i have say a thousand uh one half of a thousand uh it's about one half thousand square and n minus one all right uh so one half thousand square you remove the diagonal and then you count okay so and now i add one security now that additional security you got to look at correlation with the with the other thousand now i add one so so every time i add a security okay i add the spuriousness because people look at the extreme correlation or the high correlations you see”
Divergence between price and value can persist for years in illiquid or isolated markets, but the 'law of one price' tends to hold in efficient, liquid markets over long periods; exceptions occur when barriers to arbitrage exist (shipping costs, regulatory restrictions, illiquidity, or active agents with irrational preferences preventing arbitrage).
“you cannot arbitrage it because you have some idiot holding on to shares and doesn't want to sell it to you okay so for example so you have things that make uh markets uh not as you know frictionless and efficient but in general in general in general uh market tend to be not that stupid so in other words you can have stupid pockets of inefficiencies but they don't last for a long time they may last a year two years they don't last decades”
There is no successful use of automated predictive models for price forecasting in finance beyond short-term market making; the recursive problem of knowing that others know that you know prevents stable prediction; successful automated strategies (like Renaissance Technologies) work by doing order-flow arbitrage in high dimensions rather than by forecasting.
“the only successful use of automated models i've seen is in doing short term uh brokerage when i was a pit trader how do you make money at betrayal you mean by being stupid all right and buying on the bid selling on the offer and going home flat”
Pandemics are the fattest-tailed random variable on the planet; studying 500 pandemics and removing any subset still shows fat tails, making single-point epidemic predictions useless because the tail contains all the information.
“we discovered that the fattest tailed random variable on the planet is by far pandemics and you take 500 pandemics and we know they're fat tails you remove half you remove this you find fat it's very robust”
The mental accounting bias Richard Thaler discovered—that people treat 'house money' (winnings) differently from endowment—is actually rational and essential for survival; treating new wealth as different enables compounding and avoids ruin.
“and and and also i'm going to tell you about when i talk about racism for example racism is the same problem all right let's assume let's talk about that but let's let's finish our medicine for a second because there are interesting points to make i mean so one question is current the current practice of medicine is all about statistics you know it's all about we've done this trial this happens that happens what's the alternative view of medicine alternative view of medicine is to have a theory but medicine is extremely allergic to theories”
The dividend discount model applied to bitcoin is invalid because bitcoin produces no cash flows; the only way to justify its price is via 'greater fool' dynamics where you assume someone even more foolish will buy it later, distinguishing it from stocks which eventually generate cash flows.
“the difference between a ponzi and that the ponzi is something where that had absolutely no value and we know it has no value okay it's a pyramid scheme and and hopefully we won't stuck with it we're going to sell it to someone even more foolish than we are it's a greater fool okay so so your stocks are priced off of some kind of expected cash flow in the future”
Bitcoin cannot function as a currency because it exhibits volatility far exceeding the minimum frictional volatility required for commerce (5-7%) and because its value depends entirely on continued network maintenance, creating an absorbing barrier where abandonment leads to zero value unlike gold.
“so bitcoin must have exactly the volatility all right of zero or close to frictional okay with respect to the us dollar and stuff like that for it to be adopted and if anything's volatility have been increasing over time”
Correlation is a meaningless metric outside of linear relationships; it is not transitive and exhibits paradoxes that make it unsuitable for causal reasoning, yet it is routinely misused in psychology and social science to claim causal relationships.
“correlation correlation is a metric that has no meaning all right outside linear relationships and uh i have a paper called uh fooled by correlation on you know on the web uh waiting to be fixed um and and that food by correlation papers you know suppose shows a bunch of things like for example uh a lot of paradox that people don't know okay that uh it's not transitive”
Science is an incomplete methodology, not a complete answer; it is a process for arriving at the most coherent and least-hole-riddled story so far, and claiming completeness is conflating the map with the territory.
“and the preparing view of science which philosophers like and now no longer like all right is that science is fundamentally incomplete and you're adding something and it must have holes in it so we know where it doesn't work and update progressively based on that so that's my understanding of science is that we know just as we know more today than we did 10 years ago or definitely i don't know uh 20 years ago and we'll know a lot more in 20 years so therefore it's not complete nothing is closed it's not settled”
The average human has one breast and one testicle; using group averages to make claims about individuals or to derive prescriptions for individuals is a category error—it conflates collective properties with individual properties.
“if i uh want to know okay something about attributes of individuals okay uh i may be inspired by results from a collective but they may not necessarily apply to give you a idea if i take the average human then the average human must have one breast right and uh and uh and one testicle on average”
Human height is bounded (cannot be fat-tailed) for scientific reasons: humans need wombs for gestation, and if heights were fat-tailed, occasionally someone would be 1,000 kilometers tall, which is physically impossible; therefore, you can rule out fat-tailed distributions for human height using a priori scientific reasoning rather than just fitting distributions to data.
“the human height is fat-tailed because if human heights were fat-tailed okay you would have p most people have to have a mother so you have to have a womb that's a another human height being fat-tailed means once in a while you observe someone who's a thousand kilometers at all okay so this we can rule out on scientific grounds based on the way humans are built and the way they scale and all of that so you can rule out”
Arbitrage in real markets is frequently impossible to execute despite theoretical profitability because of liquidity constraints, idiosyncratic holding costs, and timing mismatches between buying and selling legs; someone can make the perfect trade and still go bankrupt.
“but i mean because you have all kind of crazy things happening and because of very good decision you may go bankrupt on a good trade and i've seen someone go bankrupt on on excellent trade like you can convert to put into a call all right where you you you you can convert it it's called convert whatever and and the the but the problem is uh put uh a put plus underlying is called a call minus short underlying okay and the problem is he converted it so he had a there was a rally and you're losing money on the underlying that you have to pay cash for and the call is a book entry you know that's making money but you he couldn't cash it out okay”
Psychological concepts like 'cognitive dissonance' and behavioral patterns like the 'sunk cost fallacy' are not modern discoveries but observations known since antiquity; Erasmus compiled them 500 years ago, magicians knew optical illusions, used car salesmen knew persuasion tricks.
“so i said whatever is not there okay ozar is and uh and as we know you know there's all these tricks that psychologists try to figure out about humans the other statement i said it's if it's not an erasmus explicitly or it must be known by used car salespeople all right or and and effectively you know the all these uh richard taylor theories and stuff like that were well known by advertising agencies”
The Kelly criterion tells traders how to size bets to maximize long-term growth rate (geometric mean) while avoiding ruin, and it involves logarithmic sizing (bet size proportional to edge divided by odds), which is fundamentally different from arithmetic sizing that assumes independent outcomes; most traders who go bankrupt are using arithmetic sizing when they should be using log sizing.
“you got to take a strategy that compounds a return this is one example of things that in economics that practitioners know”
Restaurants succeed or fail based on customer satisfaction (skin in the game), but awards and peer-review systems (Michelin stars, critic rankings) are less predictive of survival than market selection; organic market selection outperforms expert consensus.
“in in skin in the game okay uh restaurants uh have skin in the game in a sense that it's your credit card that counts okay but there are prizes so whatever system but there is a peer review system for restaurants where they have awards and and says a peer review system and journalists and stuff like that so there are two mechanisms and a friend a former trader who decided to lose his money slowly in a in a restaurant business reported that he said you go you know you have all these prices and they don't make it to the gala dinner you see they don't make it to the gala dinner just to tell you the mechanism of peer review is not as good a mechanism as survival you know organic survival”
Skin in the game creates appropriate risk management because decision-makers bear consequences of their choices; when institutional decision-makers are insulated from consequences (banks bailed out, academics with tenure), incentives are misaligned.
“and it's very strange out of the we counted how many we we call it we call people the short vowel we call these people all right how many people were short tales out of the 53 financial economists or phds in economics or finance who went to wall street it went because it was not only the ltcm that blew up so many other firms blew up they were they were the same kind of people it's the same ecology they're emitting like a crypto firm blows up you're gonna have four or five blowing up because they do have the same strategy okay so one out of 53 was not short volatility their risk because they came in and said oh risk is to be sold let's sell the tail”
The wealth of the top 1% is not merely concentrated; what matters is social mobility—how quickly someone exits the top 1% and how many Americans ever spend time there; in the US, 15% spend at least one year in the top 1%, suggesting high mobility.
“what you must do is take the find a metric that takes an individual okay today and see or based on experience or someone uh 50 20 years ago 30 years ago all right and see how many times on average they spend in every state to give you a very simple idea the and this was larry summers actually although i had a a little uh run in with him over uh misuse of math in in economics he actually has a good metric he took the forbes 1980 and took the 4th 2010 or 82 or 2012 and then 30 years later he showed it's not the same people of course it's not most of them have died”
Hedge funds are more robust than large financial institutions in managing tail risk because they have skin in the game—owners must invest personal wealth in their funds—creating natural selection against ruin-ignoring strategies.
“and it's very strange out of the we counted how many we we call it we call people the short vowel we call these people all right how many people were short tales out of the 53 financial economists or phds in economics or finance who went to wall street it went because it was not only the ltcm that blew up so many other firms blew up they were they were the same kind of people”
Steroid dosing for COVID should account for body weight and individual risk class, not assume the population average from clinical trials applies to all individuals; Taleb's 220-pound weight and isolation on a third floor differed substantially from the trial population.
“i say okay i weigh 220 pounds okay you have 145 uh you know uh people in the samples sample 45 okay so there's got to be some variation that's the first one and two gonna be something interesting age and stuff like that that you can increase the dosage and i realized that for example why my situation was different from the aggregate okay i was uh in lebanon on the third floor of my house with no contact with anyone everything foods count via an elevator all right so so therefore i had absolutely not the same risk class as others”
Throat cancer in young non-smokers is statistically rare, but Taleb was a victim of it; doctors discounted the possibility despite his symptoms because of base rate neglect, treating statistical rarity as individual impossibility.
“i had i was 30 in my 30s and i had throat cancer and i wasn't smoking and and all doctors they were too young to have throat cancer and uh so uh so you you should uh stop shouting and i was a pit trader where you shout a lot so they say you have a singer's uh nodule that's you know it was they ruled it out because it was i was it's the exception but the young person did not having this experience that wasn't smoking and i had throat cancer”
Physics has achieved success by building tall towers of interconnected theories where each level follows from prior levels; medicine has no such tower and attempts to build one on statistical foundations that don't support it.
“notice an important point you know one of the things that physics has achieved is it's built these pretty big towers of theories that is you start off from some underlying set of principles and you build this whole tower of this follows from this this follows from this et cetera et cetera mathematics is probably built the tallest such towers but physics is about fairly tall towers in medicine i don't think they build towers if they did they would all fall down”
Ricardo's theory of comparative advantage becomes invalid when parameters are stochastic; the calculus of specialization based on average cost/price ratios breaks down if costs or prices vary, making static comparative advantage a theoretical artifact that doesn't survive introducing a second layer of stochasticity.
“i came up with what if there's a fatwa on wine in portugal right now what would ha or what if you something so if the average is let's say the come up with 70 and 70 equivalent okay the price and they give you the calculus of that the calculus falls apart under introducing a very simple layer of stochasticity in other words making these numbers random okay that's very simple”
Risk management supersedes science because survival is a prerequisite for doing science; when faced with tail risks that could cause absorption (death or extinction), decision-making must prioritize avoiding ruin even without complete scientific understanding.
“risk survival supersedes science and let me explain why risk management and science are two different professions so to speak and why one supersedes the other because there's a conditioning on you need to survive to do science you see”
In a hypothetical economy where everything is transacted through bots doing barter (no explicit money), an implicit numeraire would still emerge because the system must be coherent, meaning that exchange ratios would form a consistent system that can be viewed as if there were a numeraire chosen by the system, even though no currency is explicitly used.
“if for the system to be coherent okay i think this i i this is exactly what i suspect is the case very similar to physics where you have the observer traveling at different speeds and stuff like that but the system stays coherent yeah it's coherent for every observer okay and it's also coherent in transaction intro observers right”
Economics differs fundamentally from physics because while physics has energy as a binding constraint on systems, economics has no comparable boundary condition on prices, allowing them to theoretically range from one unit to a billion units or higher without physical constraint.
“in other words and i i traded securities as as a trader looking for similarities between island price differently so for example if you have a an option on this item and correlates heavily on that other item i can use one a substitute for the other at a cheaper cost”
There are multiple layers of risk that differ in importance: individual death, death of loved ones, species extinction, planetary destruction; the precautionary principle applies most strongly to systems with no expiration date (humanity, the planet); an individual human has an expiration date, so protecting humanity is more important than maximizing individual lifespan.
“i have layers okay whereas the first thing is you want to survive because yeah there are mistakes you don't recover from uh-huh so so whatever strategy you do it needs to ensure not just your survival but the survival of your species okay so you want to avoid that worst case scenario”
You can rule out probability distributions and rank them by explanatory power even without knowing the true distribution; if you observe a 10-sigma event and the Gaussian distribution would assign it probability 10^-100, then the true distribution is ~10^100 times more likely to be non-Gaussian than Gaussian; this approach (Popperian falsification applied to distributions) is more powerful than trying to estimate the distribution directly.
“you can start you can have a hierarchy of distributions that if you if i've observed tail of a large deviation i can rule out gaussian okay so it's it is very similar to preparing falsification i can rule out that this thing is degenerate determined means no distribution everything's moving and okay if i see something 10 sigma events i can it's much more likely that the distribution is not gaussian it's 10 to the 100 times more likely distribution than gaussian right then it being a 10 to the 10 an event of such low probability in the gaussian okay so you can rank them”
Decisions under uncertainty are easy: if you are uncertain about something that could harm you and you have an alternative, choose the alternative (water purity example—if uncertain, don't drink it; pilot skills uncertain, take a different plane); the hard problem is when all doors lead to uncertainty, in which case you rank options by worst-case scenario severity.
“if i have uncertainty it's easier to make a decision okay under uncertainty than uncertainty this water for example i'm uncertain about uh let's assume that i give you a glass of water i tell you i'm concerned about the purity of the water what would you do i don't know smell the water see what it smells disgusting the the first thing you'd say no okay you say i want this other uh glass of water”
Knowledge transfer in finance has degraded from practitioner-to-practitioner chains to professor-to-student chains, breaking implicit knowledge transmission; doctors still learn from doctors, which is why medicine has some accumulated wisdom despite being scientifically disorganized.
“in my days when i started training there are two kind of traders there's the old traders who didn't like formulas they priced an option organically you know with the whims and then the relationship between items and and stuff like that and and then there was a the scientific uh crowd they formed us so what happened is that because of there's something called mba that came about so people started getting classes in mba and learning finance from professors so instead of having a practitioner teacher practitioner teacher practitioner teacher practitioner you had the old days to be not an option trader or to be a trader you go work for a trader you clear for a trader you pick her or his brain and then you become a trader”
Medical textbooks from antiquity (Maimonides, Avicenna) were highly theoretical, making explicit causal models about humors and treatments, yet modern 'evidence-based' medicine claims to be more scientific while actually being less theoretical and more purely empirical.
“but in fact it doesn't work that way people learn from seeing patients well i mean developing experience what you're describing and i'm curious actually to what extent that's i haven't looked at galen in a very very long time and i had no idea that um dominated uh gain galen actually was lost in greek uh text and it was recovered in syria it was very present in syriac has to be called in the ancient world the syriacs were the doctors all right”
The central limit theorem ensures that the sum of many independent random variables converges to a Gaussian distribution, even if the underlying distribution is uniform or other shapes, and this convergence happens very quickly (by 3 samples for uniform distribution you see non-flat distribution, by 10 samples you are approaching Gaussian).
“so as you see now already you see the distribution is already not flat anymore the sum two distribution two two numbers and you already have this distribution now let's do it this way plus r your or you almost have a gaussian by summing up three numbers okay look all right so this is called the central limit theorem”
Entropy is often conflated with disorder in common usage, but in statistical mechanics and thermodynamics it has a precise mathematical meaning: the entropy of a distribution is -Σ p(x) log p(x), and entropy is maximized when the distribution is uniform (maximum disorder) subject to constraints like fixed mean and variance.
“if i maximize entropy under constraint of variance and mean and variance i think i have the mathematica file here somewhere you get a gaussian so you have to realize that you're you're bounding the equivalent in physics would be by you know you're putting a boundary on energy because it varies is energy or whatever you want to define it okay”
Pareto distribution (80/20 distribution) is characterized by having the property that 80% of values lie in 20% of the range, which implies that if you recurse it, 1% of people own 50% of wealth, and this is used to illustrate fat tails because the distribution has most values concentrated but with extreme tail events.
“pareto 80 20 pareto distributions yeah right so anything or any distribution let's say let me take a student t distribution okay fat tails student t is uh has parental tales okay the let me see pedagogically since we have high school people and we have physicists i don't want to board the physicist and i don't want to upset the high school students so let me find the most well-known distribution is the pareto 80 20. okay this maps to pareto distribution one okay it's about one and one point one uh four okay”