bookmark_borderWholesale Wikipedias – July 2021

https://en.wikipedia.org/wiki/Concealed_shoes

https://en.wikipedia.org/wiki/Umm_al-Qura_Mosque

https://en.wikipedia.org/wiki/Operation_Vegetarian

https://en.wikipedia.org/wiki/Retired_husband_syndrome

https://en.wikipedia.org/wiki/Berners_Street_hoax

https://en.wikipedia.org/wiki/Gilles_de_Rais

https://en.wikipedia.org/wiki/Love_Jihad

https://en.wikipedia.org/wiki/Ejaculatory_prayer

https://en.wikipedia.org/wiki/Herma

https://en.wikipedia.org/wiki/St._Petersburg_paradox

bookmark_borderA Random Clock

I may have found a solution to one of my biggest, longest-standing, most irredeemable problems. For most of my life, I have been consistently late. Whether it’s appointments, attending events, taking trains or joining a zoom call, I’m typically 10 minutes late for everything and it’s ruining my life – not because I actually miss the train (though that happens too) but because I’m constantly rushing and panicking. Whatever I do, I start it in a state of maximum stress and guilt. Obviously, I tried pretty much everything to address the problem, including various artificial rewards and punishments, telling a therapist about it, having people call me to remind me to get ready, taking nootropics, and many more ridiculous ideas. So I thought, “how do all these well-adjusted adults manage to be perfectly on time all the time?” and I did what any well-adjusted normie would do: I tried to formally frame the problem in terms of expected utility theory.

Tricking myself: single-player game theory

Imagine I have to attend a very important scientific conference on the effect of dubstep on mosquitos. The figure below plots how much I enjoy the event depending on the time I arrive.

Arriving early by ten minutes or one hour does not make any difference (or so I presume – this never happened to me). Being just a few minutes late is not a big deal either, since it’s just going to be the speaker testing her microphone or other formalities of no importance. Beyond that, it starts becoming really rude (with some variation depending on which culture you live in) and I risk missing some crucial information, like the definition of a crucial concept central to understanding the equations of mosquitos’ taste for Skrillex.

The second aspect of the problem is how much time I can save by arriving later, which is just a straight line:

Why would I arrive ten minutes early to the Skrillex-as-a-cure-for-dengue talk, when I could spend ten more minutes reading about exorcism under fMRI? Summing both aspects of the problem, the grand unified utility curve looks something like this:

There you have it: the utility peak, the most rational outcome, is obtained by being just a few minutes late. I suppose for most people, this basically means you should arrive on time, since the peak is not that far from the start of event. But chronically-late people like myself have a distorted vision of the utility curves, that looks more like that:

This might look like a desperate situation, but there is one spark of hope: even in this wildly-distorted version of the utility function, the downward part of the curve (problems with being late) is much steeper than the upward part of the curve (time saved by being late). This asymmetry makes it possible to change the location of the peak by adding some uncertainty, in the form of a random clock. Let me explain.

A rookie approach to not-being-late is to shift your watch 10 minutes in the future. This way, it “looks” like you’re already 10 minutes late when you are actually on time, which might make you speed up through some obscure psychological mechanism. Of course, this does not work since you know perfectly well your clock is 10 minutes early and you compensate accordingly. But what if you ask a friend to shift your watch by a random number of minutes, between 0 and 10? Then, you don’t know how much to compensate. Coming back to the utility function above, we are effectively blurring out the utility function. Here is what happens:

Thanks to the asymmetry of the original peak, the maximum utility is now shifted to the left! Say the mosquito conference starts at 8:00, and the random clock says 7:59. Best case scenario, the clock is 10 minutes in advance, and I still have 11 minutes left, so everything is fine and I can take my time. Worst case scenario, the clock is exactly on time, and the show starts in one minute, and I can’t wait any longer. Since I would rather be 10 minutes early than 10 minutes late, I stop reading this very important exorcism paper, and hurry to the conference room.

Self-blinding in practice

In the early development phase I asked a trusted friend to pick a number between 0 and 10 and shift my watch by this amount in the future without telling me. This was for prototyping only, since it has some disadvantages:

  • I don’t want to ask friends to change my watch all the time, especially if I have to explain the reasoning behind it every time,
  • My friend could totally troll me in various ways, like shifting my clock two hours in the future. I’m clueless enough not to notice. But she is an amazing person and did not do that.

Then, I used this very simple python command:

#!/usr/bin/python3
import time,random
print(time.ctime(time.time()+60*10*random.random()))

It takes the current time, draws a random number between 0 and 10, and adds the same number of minutes to the time.

I have an advantage for this project: I usually wear a wristwatch at all times. This makes the practical implementation of the random clock much easier – I just need to shift my wristwatch, and rely exclusively on it without ever looking at any other clock. I also have an alarm clock and a regular clock on the wall of my room, so I simply shifted them to match my watch. I also had clocks on my computer and my phone, and there is surely a way to shift them too, but I was lazy and just disabled the time display on both devices1In hindsight, I think removing the clock from computers/smartphone is also a healthy decision in its own right, as it forces you to get your eyes off the screen from time to time, you should give it a try. Here is my full randomization procedure:

  • Shuffle my watch and alarm clock by a large amount, so I can’t read the time when I randomize them,
  • Wait until I can no longer tell what time it is (to a 10 minutes margin of error),
  • Run the script,
  • Set my watch and clocks to the time prescribed by the script.

And then, it is all about avoiding looking at the various clocks in my environment that display the true time (sometimes the microwave will just proudly display the time without warning). Who will win – my attempt at deliberately adding uncertainty to the world, or my microwave? Let’s do the experiment.

Putting a number on it

For a few days before and after trying out the random clock, I kept track of the time when I arrived to various appointments and events. For the random phase, I would just write down the raw time displayed on my watch, then, before re-randomizing it, I would check what the shift was and subtract it to the data to know at what time I really arrived. My astonishing performance can be witnessed in the figure below:

The horizontal segments represent the median. As you can see, I went from a median lateness of nine minutes to only one minute. I’m still not perfectly calibrated, but this might be the first time in my whole life I am so close to being on time, so I’d consider this a success. In both series, there are a few outliers where I was very very late (up to 35 min), but those are due to larger problems – for example, the green outlier was when my bicycle broke and I had to go to a band rehearsal on foot. Apparently, I am so bad at managing time that my lateness undergoes black swan events.

Contrary to what I expected, it is very easy to just stop looking at all the clocks in the outside world, and only rely on my watch. Of course, the world is full of danger and sometimes I caught a glimpse at whatever wild clock someone carelessly put in my way. In that case, I just had to avoid checking my watch for a few minutes to avoid breaking the randomization. A bigger problem is seeing when events actually start. Whether I like it or not, my system 1 can’t help but infer things about the real time by seeing when other people arrive, or when the conference actually starts, or when some !#$@ says “alright, it’s 10:03, should we start?”. If this narrows the distribution too much, I have to randomize again. I did not find it to be a major problem, only having to re-randomize about once a week. In fact, when I revealed the real shift to myself before re-randomizing, I often found that what I inferred about the true time was completely wrong. Thus, even if I believe I’ve inferred the real time from external clues, I can tell to myself it’s probably not even accurate. This only makes my scheme stronger.

A continuously-randomizing clock

Since no randomization is eternal, am I doomed to re-randomize every few weeks all my life? There is actually a pretty simple solution to avoid this, which is to use a continuously-randomizing clock. Instead of manually randomizing it from time to time, the clock is constantly drifting back and forth between +0 min and +10 min, slightly tweaking the length of a second. A very simple way to do that is to add a sine function to the real time:

#!/usr/bin/python3
import time, math
real_time = time.time()
shift = (1+math.sin(real_time/1800))/2 # Between 0 and 1
wrong_time = real_time + shift*60*10
print(time.ctime(wrong_time))

In this example, the clock shift will oscillate between 0 and 10 once every π hours. Of course it is not really random anymore, but it does not matter since we are just trying to trick our system 1 so it cannot figure out the real time against our will. Finding the real time might be possible with some calculations, but those would involve your system 2, and that one is supposed to be under your control. All that matters is that the oscillation period is not an obviously multiple of one hour. The snippet above uses a period of π, which is not even rational, so we are pretty safe.

The advantage of using a sine function rather than a fancy random variable is that it is magically synchronized across all clocks that use the same formula. If you use this on two different computers, they will both give the same (wrong) time, without the intervention of any internet. As I said, I am fine with my old needle watch, but if you are the kind of person who uses a smartwatch, give it a try and tell me how it went. Or perhaps I will try to build one of these Arduino watches.

In my tests, I found that my archaic wristwatch-based system is already good enough for my own usage, so I will stick to this for the moment. Maybe it will keep on working, maybe the effect will fade out after a while, once the novelty wears out. Most likely, I might have been more careful than usual because I really wanted the experiment to succeed. Maybe I will get super good at picking up every clue to guess the real time. I will update this post with the latest developments. Anyways, there is something paradoxical about manipulating oneself by deliberately adding uncertainty – a perfectly rational agent would always want more accurate information about the world, and would never deliberately introduce randomness. But I am not a perfectly rational agent, I did introduce uncertainty, and it worked.

bookmark_borderWholesale Wikipedias – June 2021

Chemistry edition. Anyone has a few milligrams to spare?

https://en.wikipedia.org/wiki/Magic_acid

https://en.wikipedia.org/wiki/Chlorine_trifluoride

https://en.wikipedia.org/wiki/Bremelanotide

https://en.wikipedia.org/wiki/Fenestrane

https://en.wikipedia.org/wiki/Resiniferatoxin

https://en.wikipedia.org/wiki/Megaphone_(molecule)

https://en.wikipedia.org/wiki/Isosorbide_dinitrate%2Fhydralazine

https://en.wikipedia.org/wiki/Olympiadane

bookmark_borderWholesale Wikipedias – May 2021

I almost forgot about this.

https://en.wikipedia.org/wiki/Oil_futures_drunk-trading_incident

https://en.wikipedia.org/wiki/Lady_tasting_tea

https://en.wikipedia.org/wiki/Ribs_(recordings) (see also, samizdat)

https://en.wikipedia.org/wiki/Long_line_(topology)

https://en.wikipedia.org/wiki/Bald-hairy

https://en.wikipedia.org/wiki/Blind_Willie_Johnson

https://en.wikipedia.org/wiki/Non-human_electoral_candidates

https://en.wikipedia.org/wiki/Osama_Vinladen

https://en.wikipedia.org/wiki/List_of_lists_of_lists

bookmark_borderWholesale wikipedias – April 2021

https://en.wikipedia.org/wiki/Curse_of_the_Colonel

https://en.m.wikipedia.org/wiki/Anthropodermic_bibliopegy

https://en.wikipedia.org/wiki/Mhoon_Landing

https://en.wikipedia.org/wiki/Lyman-alpha_forest

https://en.wikipedia.org/wiki/Mobro_4000

https://en.wikipedia.org/wiki/Lacrymaria_olor (https://www.youtube.com/watch?v=ZquzlvEEZq8)

https://en.wikipedia.org/wiki/Mathematical_coincidence

bookmark_borderThe Holy Algorithm

As it will surely not have escaped your insight, this weekend is Easter. Why now? The date of Easter is determined by a complicated process called the Computus Ecclesiasticus. I will just quote the Wikipedia page:

The Easter cycle groups days into lunar months, which are either 29 or 30 days long. There is an exception. The month ending in March normally has thirty days, but if 29 February of a leap year falls within it, it contains 31. As these groups are based on the lunar cycle, over the long term the average month in the lunar calendar is a very good approximation of the synodic month, which is 29.53059 days long. There are 12 synodic months in a lunar year, totaling either 354 or 355 days. The lunar year is about 11 days shorter than the calendar year, which is either 365 or 366 days long. These days by which the solar year exceeds the lunar year are called epacts. It is necessary to add them to the day of the solar year to obtain the correct day in the lunar year. Whenever the epact reaches or exceeds 30, an extra intercalary month (or embolismic month) of 30 days must be inserted into the lunar calendar: then 30 must be subtracted from the epact.

If your thirst of knowledge is not satisfied, here is a 140-page document in Latin with more detail.

As far as I understand, during the Roman Era the Pope or one of his bureaucrats would perform the computus, then communicate the date to the rest of Christianity and everybody could eat their chocolates at the same time. Then, the Middle-Ages happened and communication became much harder, so instead they came up with a formula so people could compute the date of Easter locally. Of course, the initial formulas had problems – with the date of Easter dangerously drifting later and later in the year over centuries, and don’t even get me started on calendar changes. Eventually Carl Friedrich Gauss entered the game and saved humanity once again with a computationally-efficient algorithm (I am over-simplifying the story so you have more time to eat chocolate).

But now is 2021, and I’m wondering how they run the algorithm now, in practice. I looked up “how is the date of Easter calculated” but all the results are about the algorithms themselves, not about their practical implementation. I have a few hypotheses:

  1. There are responsible Christians everywhere who own printed tables with the dates of Easter already computed for the next few generations. If your Internet goes down, you can probably access such tables at the local church.
https://upload.wikimedia.org/wikipedia/commons/e/e4/DiagrammePaques_Flammarion.jpg
Here is such table from 1907 (Wikimedia commons)

Of course this does not really solve the problem: who comes up with these tables in the first place? Who will make new ones when they expire?

2. There is a ceremony in Vatican where a Latin speaker ceremoniously performs the Holy Algorithm by hand, outputs the date of Easter, prints “Amen” for good measure and then messengers spread the result to all of Christianity.

3. Responsible Christians everywhere own a Computus Clock, a physical device that tells you if it is Easter or not. When in doubt, you just pay a visit to that-guy-with-the-computus-clock. Then, it is like hypothesis 1 except it never expires.

4. There is software company (let’s call it Vatican Microsystems®) who managed to persuade the Pope to buy a license for their professional software solution, Computus Pro™ Enterprise Edition 2007 – including 24/7 hotline assistance, that only runs on Windows XP and they have a dedicated computer in Vatican that is used once in a while to run these 30000 lines of hard Haskell or something. Then, it goes just like hypothesis 2.

(Of course, all of these solutions are vulnerable to hacking. It might be as easy as sneaking into a church and replace their Easter tables with a fake. A talented hacker might even have it coincide with April fools.)

If an active member of the Christian community reads this and knows how it is done in practice, I am all ears.

Anyways, happy Easter and Amen, I guess.

bookmark_borderWholesale wikipedias – March 2021

Wikipedias for the wikipedia God.

https://en.wikipedia.org/wiki/Everyday_life

https://en.wikipedia.org/wiki/999-year_lease

https://en.wikipedia.org/wiki/UEFA_Champions_League_Anthem

https://en.wikipedia.org/wiki/Artificial_cranial_deformation

https://en.wikipedia.org/wiki/Metro-2

https://en.wikipedia.org/wiki/Cookiecutter_shark

https://en.wikipedia.org/wiki/Quantum_tic-tac-toe

https://en.wikipedia.org/wiki/Rolling_coal

bookmark_borderAverage North-Koreans Mathematicians

Here are the top-fifteen countries ranked by how well their teams do at the International Math Olympiads:

When I first saw this ranking, I was surprised to see that North Koreans have such an impressive track record, especially when you factor in their relatively small population. One possible interpretation is that East Asians are just particularly good at mathematics, just like in the stereotypes, even when they live in one of the world’s worst dictatorships.

But I don’t believe that. In fact, I believe North Koreans are, on average, particularly bad at math. More than 40% of the population is undernourished. Many of the students involved in the IMOs grew up in the 1990s, during the March of Suffering, when hundreds of thousands of North Koreans died of famine. That is not exactly the best context to learn mathematics, not to mention the direct effect of nutrients on the brain. There does not seem to be a lot of famous North Korean mathematicians either1There is actually a candidate from the North Korean IMO team who managed to escape during the 2016 Olympiads in Hong-Kong. He is now living in South Korea. I wish him to become a famous mathematician.. Thus, realistically, if all 18 years-old from North Korea were to take a math test, they would probably score much worse than their South Korean neighbors. And yet, Best Korea reaches almost the same score with only half the source population. What is their secret?

This piece on the current state of mathematics in North Korea gives it away. “The entire nation suffered greatly during and after the March of Suffering, when the economy collapsed. Yet, North Korea maintained its educational system, focusing on the gifted and special schools such as the First High Schools to preserve the next generation. The limited resources were concentrated towards gifted students. Students were tested and selected at the end of elementary school.” In that second interpretation, the primary concern of the North Korean government is to produce a few very brilliant students every year, who will bring back medals from the Olympiads and make the country look good. The rest of the population’s skills at mathematics are less of a concern.

When we receive new information, we update our beliefs to keep them compatible with the new observations, doing an informal version of Bayesian updating. Before learning about the North Korean IMO team, my prior beliefs were something like “most of the country is starving and their education is mostly propaganda, there is no way they can be good at math”. After seeing the IMO results, I had to update. In the first interpretation, we update the mean – the average math skill is higher than I previously thought. In the second interpretation, we leave the mean untouched, but we make the upper tail of the distribution heavier. Most North Koreans are not particularly good at math, but a few of them are heavily nurtured for the sole purpose of winning medals at the IMO. As we will see later in this article, this problem has some pretty important consequences for how we understand society, and those who ignore it might take pretty bad policy decisions.

But first, let’s break it apart and see how it really works. There will be a few formulas, but nothing that can hurt you, I promise. Consider a probability distribution where the outcome x happens with probability p(x). For any integer n, the formula below gives what we call the nth moment of a distribution, centered on \mu.

\int_{\mathbb{R}}p(x)(x-\mu)^ndx

To put it simply, moments describe how things are distributed around a center. For example, if a planet is rotating around its center of mass, you can use moments to describe how its mass is distributed around it. But here I will only talk about their use in statistics, where each moment encodes one particular characteristic of a probability distribution. Let’s sketch some plots to see what it is all about.

First moment: replace n with 1 and μ with 0 in the previous formula. We get

\int_{\mathbb{R}}p(x)(x)dx

which is – suprise – the definition of the mean. Changing the first moment just shifts the distribution towards higher or lower values, while keeping the same shape.

Second moment: for n = 2, we get

\int_{\mathbb{R}}p(x)(x-\mu)^2dx

If we set μ to be (arbitrarily, for simplicity) equal to the mean, we obtain the definition of the variance! The second moment around the mean describes how values are spread away from the average, while the mean remains constant.

Third moment (n = 3): the third moment describes how skewed (asymmetric) the distribution is, while the mean and the variance remain constant.

Fourth moment (n = 4): this describes how leptokurtic or platykurtic your distribution is, while the mean, variance and skew remain constant. These words basically describe how long the tails of your distribution are, or “how extreme the extreme values are”.

You could go on to higher n, each time bringing in more detail about what the distribution really looks like, until you end up with a perfect description of the distribution. By only mentioning the first few moments, you can describe a population with only a few numbers (rather than infinite), but it only gives a “simplified” version of the true distribution, as on the left graph below:

Say you want to describe the height of humans. As everybody knows, height follows a normal distribution, so you could just give the mean and standard deviation of human height, and get a fairly accurate description of the distribution. But there is always a wise-ass in the back of the room to point out that the normal distribution is defined over \mathbb{R}, so for a large enough population, some humans will have a negative height. The problem here is that we only gave information about the first two moments and neglected all the higher ones. As it turns out, humans are only viable within a certain range of height, below or above which people don’t survive. This erodes the tails of the distribution, effectively making it more platykurtic2If I can get even one reader to use the word platykurtic in real life, I’ll consider this article a success..

Let’s come back to the remarkable scores of North Koreans at the Math Olympiads. What these scores teach us is not that North Korean high-schoolers are really good at math, but that many of the high-schoolers who are really good at math are North Koreans. On the distribution plots, it would translate to something like this:

With North Koreans in purple and another country that does worse in the IMOs (say, France), in black. So you are looking at the tails and try to infer something about the rest of the distribution. Recall the plots above. Which one could it be?

Answer: just by looking at the extreme values, you cannot possibly tell, because any of these plots would potentially match. In Bayesian terms, each moment of the distribution has its own prior, and when you encounter new information, you could in principle update any of them to match the new data. So how can we make sure we are not updating the wrong moment? When you have a large representative sample that reflects the entire distribution, this is easy. When you only have information about the “top 10” extreme values, it is impossible. This is unfortunate because the extreme values are precisely what gets all our attention – most of what we see in the media is about the most talented athletes, the most dishonest politicians, the craziest people, the most violent criminals, and so forth. Thus, when we hear new information about extreme cases, it’s important to be careful about which moment to update.

This problem also occurs in reverse – in the same way looking at the tails doesn’t tell you anything about the average, looking at the average doesn’t tell you anything about the tails. An example: on a typical year, more Americans die from falling than from viral infections. So one could argue that we should dedicate more resources to prevent falls than viral infections. Except the number of deaths from falls is fairly stable (you will never have a pandemic of people starting to slip in their bathtubs 100 times more than usual). On the other hand, virus transmission is a multiplicative process, so most outbreaks will be mostly harmless (remember how SARS-cov-1 killed less than 1000 people, those were the days) but a few of them will be really bad. In other words, yearly deaths from falls have a higher mean than deaths from viruses, but since the latter are highly skewed and leptokurtic, they might deserve more attention. (For a detailed analysis of this, just ask Nassim Taleb.)

There are a lot of other interesting things to say about the moments of a probability distribution, like the deep connection between them and the partition function in statistical thermodynamics, or the fact that in my drawings the purple line always crosses the black like exactly n times. But these are for nerds, and it’s time to move on to the secret topic of this article. Let’s talk about SEX AND VIOLENCE.

This will not come as a surprise: most criminals are men. In the USA, men represent 93% of the prison population. Of course, discrimination in the justice system explains some part of the gap, but I doubt it accounts for the whole 9-fold difference. Accordingly, it is a solid cultural stereotypes that men use violence and women use communication. Everybody knows that. Nevertheless, having just read the previous paragraphs, you wonder: “are we really updating the right moment?”

A recent meta-analysis by Thöni et al. sheds some light on the question. Published in the journal Pyschological Science, it synthesizes 23 studies (with >8000 participants), about gender differences in cooperation. In such studies, participants play cooperation games against each other. These games are essentially a multiplayer, continuous version of the Prisoner’s Dilemma – players can choose to be more or less cooperative, with possible strategies ranging from total selfishness to total selflessness.

So, in cooperation games, we expect women to cooperate more often than men, right? After all, women are socialized to be caring, supportive and empathetic, while men are taught to be selfish and dominant, aren’t they? To find out, Thöni et al aligned all of these studies on a single cooperativeness scale, and compared the scores of men and women. Here are the averages, for three different game variants:

This is strange. On average, men and women are just equally cooperative. If society really allows men to behave selfishly, it should be visible somewhere in all these studies. I mean, where are all the criminals/rapists/politicians? It’s undeniable that most of them are men, right?

The problem with the graph above is that it only shows averages, so it misses the most important information – that men’s level of cooperation is much more variable than women’s. So if you zoom on the people who were either very selfish or very cooperative, you find a wild majority of men. If you zoom on people who kind-of cooperated but were also kind-of selfish, you find predominantly women.

As I’m sure you’ve noticed, the title of the Thöni et al paper says “evolutionary perspective”. As far as I’m concerned, I’m fairly skeptical about evolutionary psychology, since it is one of the fields with the worst track record of reproducibility ever. To be fair, a good part of evpsych is just regular psychology where the researchers added a little bit of speculative evolutionary varnish to make it look more exciting. This aside, real evpsych is apparently not so bad. But that’s not the important part of the paper – what matters is that there is increasingly strong evidence that men are indeed more variable than women in behaviors like cooperation. Whether it is due to hormones, culture, discrimination or cultural evolution is up to debate and I don’t think the current data is remotely sufficient to answer this question.

(Side note: if you must read one paper on the topic, I recommend this German study where they measure the testosterone level of fans of a football team, then have them play Prisoner’s Dilemma against fans of a rival team. I wouldn’t draw any strong conclusion from this just yet, but it’s a fun read.)

The thing is, men are not only found to be more variable in cooperation, but in tons of other things. These include aggression, exam grades, PISA scores, all kinds of cognitive tests, personality, creativity, vocational interests and even some neuroanatomical features. In the last few years, support for the greater male variability hypothesis has accumulated, so much that it is no longer possible to claim to understand gender or masculinity without taking it into account.

Alas, that’s not how stereotyping works. Instead, we see news report showing all these male criminals, and assume that our society turns men into violent and selfish creatures and call them toxic3Here is Dworkin: “Men are distinguished from women by their commitment to do violence rather than to be victimized by it. Men are rewarded for learning the practice of violence in virtually any sphere of activity by money, admiration, recognition, respect, and the genuflection of others honoring their sacred and proven masculinity.” (Remember – in the above study, the majority of “unconditional cooperators” were men.). Internet people make up a hashtag to ridicule those who complain about the generalization. We see all these male IMO medalists, and – depending on your favorite political tradition – either assume that men have an unfair advantage in maths, or that they are inherently better at it. The former worldview serves as a basis for public policy. The question of which moment to update rarely even comes up.

This makes me wonder whether this process of looking at the extremes then updating our beliefs about the mean is just the normal way we learn. If that is the case, how many other things are we missing?

bookmark_borderArgumentative prison cells

Two persons are trapped in a prison cell. The warden gives them a controversial question they disagree about, and promises to set them free if they manage to reach an honest agreement on the answer. They can discuss and debate for as long as they need, and all the relevant empirical data are available. Importantly, they are not allowed to just pretend to agree: they must genuinely find common ground with each other for the door of the prison cell to open. Needless to say, both participants want to escape the room as soon as possible, so they will do their best to reach a honest agreement1I know some of you would love to stay forever in a room with unlimited time and data – just pretend you want to leave the room for the sake of the thought experiment..

In most cases, a handful of good arguments from each side may be enough to settle the case. Sometimes, they would disagree on the meaning of the question itself, in which case they would first spend some time arguing about terminology, before arguing about the content of the question. In more complicated cases, the subjects might turn to a meta-discussion about the best method to reach agreement and get out of the room. If they must debate about whether to rely on the Scientific Method or the double-crux or any other advanced epistemic jutsu, they have all the time in the world to do that. The question is, is it always possible to escape the Argumentative Escape Room? Given unlimited time, will any two persons necessarily reach an agreement on any possible question, or are there cases where the two persons will never agree, despite their best efforts?

Of course, it is easy to find trivial cases where this will not work. For sure, if one participant is a human and the other is a pigeon, agreement might be hard to reach (although, you can’t say the pigeon really disagrees either, right?). If one participant has Alzheimer’s and forgets everything you say after two minutes, it will be hard to change their mind on any somewhat complicated topic. But these are edge cases.

A more difficult question is whether some people just lack the fundamental intelligence to understand certain arguments, or if anybody can eventually understand anything given enough time. To take an extreme case, suppose one of the participants is a rudimentary AI with a very limited amount of memory space. Some arguments based on experimental data will never fit in that memory. It might be possible, in principle, to compress the data by carefully building layers of abstraction on top of each others, but there is a limit. Likewise, many mathematical proofs require logical disjunction, where you split the claim into a number of particular cases, and prove you are right for each case taken separately. If you are arguing with an AI who firmly disbelieves the 4-color theorem but lacks the hardware to survey the 1482 distinct cases, it is going to be very hard to truly convince it. Without knowing how the brain works, I am not sure how this would translate to humans debating “normal” controversial questions. Let’s say your argument involves some advanced quantum mechanics. Most people won’t understand it at first, but since you have all the time you want, you could just teach QM to the other participant until she gets your point and can agree/disagree with you. I have good hopes that most humans could eventually understand QM given enough time and patience. But it is not clear what are the absolute limits of one particular human brain, and whether these limits differ from person to person.

The problems I mentioned so far are merely “technical” difficulties. If we leave these aside, it seems reasonable to me that the two players will reach agreement on pretty much any factual statement or belief. If everything else fails, both parties can agree that they do not know the correct answer to the question, that more research is needed, that the question does not make sense, that the problem is undecidable. The real problem lies on the other branch of Hume’s fork. What happen if we ask the two participants to agree on moral values?

Is it okay to kill a cow for food? Is it okay to steal bread if your family is starving? Is it okay to kill a stolen cow for food if your family is starving? There is a Nature Versus Nurture kind of problem here. If values are entirely cultural, or come entirely from lived experience, then there is no reason to think that, after a sufficient time spent together, the two participants will never put their sacred values into perspective and find common ground about what is okay or not. On the other hand, if values are in part influenced by your brain’s mechanisms for emotion, empathy or instinct, like the structure of your amygdala or the sensitivity of your oxytocin receptors, then it’s entirely possible that two people will simply have different values, no matter how long they discuss it. We already know from classical twin studies that political opinions are in large part influenced by genetics. In developed countries, genetic factors are responsible for about half of the variance in attitudes towards egalitarianism, immigration and abortion. They might explain one third of the variance in patriotism, nationalism, and homophobia. One study suggested that an intra-nasal administration of oxytocin leads to increased ethnocentrism (but check out this skeptical paper for good measure). There is even a strange study were researchers could bias the reported political opinions of participants by stimulating parts of their brain with magnetic fields2That’s right, scientists MANIPULATED people’s views on IMMIGRATION using MAGNETS. Please, never tell my grandmother about this study.. Thus, it is pretty clear that our opinions and values are not just the result of experience and reasoning, but also involve a lot of weird brain chemistry that we might no be able to change. Genetic differences are only one obvious factor of inescapable disagreement, but they are likely not the only one. For example, it is easy to imagine that some experiences will leave irreversible marks on one’s psyche (for an interesting illustration, look at the story of Gudrun Himmler). Can such barriers ever be overcome through discussion? I’m not sure.

But that is just a fun thought experiment with mildly philosophical implications about the existence of objective truth. Since unlimited time is quite uncommon in the real world, and since reaching honest agreement is rarely the only goal of people who argue with each other, does it ever matter in practice? I think this thought experiment is important, because it clarifies our underlying assumptions about how we collectively handle disagreement.

When one defends the marketplace of ideas, deliberative democracy and absolute free speech, it is implicitly assumed that, for all practical purposes, any disagreement can eventually be solved through discussion and explanation. If it turns out some people will simply never agree because their minds operate in fundamentally different ways, then the marketplace of ideas probably needs a patch. The scenario that Karl Popper describes in his “paradox of intolerance” is precisely such a situation: there are very intolerant people out there who simply can’t be reasoned with, so the best thing you can do is silence them. One essay from Scott Alexander describes two approaches to politics: mistake and conflict. Mistake theory is when you believe everybody wants to benefit the collective, and disagreements come from people being mistaken about the best way to achieve that. Conflict theory is when you believe that people are just advocating for their own personal advantage, and disagreements come from people serving different goals. On first sight, those who believe it is usually possible to escape the room might gravitate towards Mistake Theory, while those who think otherwise might be driven to Conflict Theory. However, things are more complicated.

In a recent study, Alexander Severson found that, when people are presented evidence that political opinions have genetic influences, they typically become more tolerant of the other side. From the conclusion part:

“We proudly weaponize bumper stickers and traffic in taunt-infused comment-thread witticisms in the war against the political other, all in part because we believe that the other side chooses to believe what they believe freely and unencumbered. […] In disavowing this belief and accepting that our own ideologies are partially the byproduct of biological and genetic processes over which we have no control, we may end up promoting a more tolerant and kinder civil society.”

Somehow, since the outgroup’s obviously wrong opinions are altered by their genes, it’s not entirely their fault if they disagree with you, so it becomes a forgivable offense. Alternatively, if differences in our opinions partially reflect differences in our bodies, then peace is only possible if we accept the coexistence of a plurality of opinions, and we may as well embrace it. Interestingly, in this study, about 20% of the participants ignored all the presented evidence, firmly rejecting the idea of any possible genetic influence on opinions. Perhaps the evidence that Severson showed them was not all that convincing, or perhaps the belief that genetics can influence beliefs is itself influenced by genetics, which, at least, would be fun to argue.

I’m curious about whether this question has already been treated by other people, in theory or – even better – experimentally. If you know of anything like that, please let me know.

bookmark_borderWholesale wikipedias – Feb 2021

https://en.wikipedia.org/wiki/List_of_proposed_etymologies_of_OK

https://en.wikipedia.org/wiki/Mariko_Aoki_phenomenon

https://en.wikipedia.org/wiki/Junk_fax

https://en.wikipedia.org/wiki/The_Thing_(listening_device)

https://en.wikipedia.org/wiki/Animal-borne_bomb_attacks

https://en.wikipedia.org/wiki/Collyer_brothers (s/o Gwern)

https://en.wikipedia.org/wiki/Lenin_was_a_mushroom (s/o VeryWhen)

https://en.wikipedia.org/wiki/Cable_bacteria

https://en.wikipedia.org/wiki/Maxine_Asher