Probabilities, Philosophy, Morality & Illusions #RB24

hello everyone uh today we'll discuss the philosophical essay on priorities by piercing this is a very important essay because it brings together the theory of probabilities and unexpected connections with moral philosophy ethics epistemology the way of thinking correctly et cetera and the the reason why we picked this uh the anecdote why we picked this text to read actually was that a few weeks ago the the statistics community had um had a controversy or whether to rename a a a an award an important award in statistics called after ronald fisher and people were protesting since fisher had some eugeniestic and and racist views and um i was personally wondering uh so so some people argued that fisher in the in the early 20th century was a man of his epoch etc and so i was just personally i was just thinking that um there are many thinkers who who had views that are not necessarily based on the the the generally held opinion of their epoch or of their culture or of their region etc and i thought of laplace because uh he wrote this essay and i just went to the essay and and searched for four key words related to to race or slavery etc and and found out that that laplace was arguing that some commonality and frequently held beliefs that if something is commonly held or frequently held that's not a valid moral or epistemic argument and um i was personally aware of the office thanks to lei but didn't uh didn't read the last edition of it until recently and and it's interesting in the context of our reading group because um as i said so um it discusses at least the three chapters we'll discuss today are applications of probability theory to moral philosophy something that is highly important in the context of ai ethics in particular the second part we'll discuss is the the application of probability theory in in in the judgment um made in a court and the last part we'll discuss um is what laplace called on illusions in estimating probabilities or in what 20th century psychologists would call probably cognitive biases maybe i can even backtrack a little bit and explain the context a bit of of this essay so a bit of the history of the power of poverty theory essay so poverty theory was uh like probably restarted uh around the 17th century with people like with like karma or pascal um and and then the more from bernoulli the more and so on uh but uh before laplace most of the probability theories were in a sense deductive uh meaning that we had a an inertial source of probability and then we try to see the consequences of this uh initial source of probability uh so you start with axioms which are the the axioms of probability typically heads or tails would be one half and half and then you compute the consequences of all of um and in 1776 uh pierre simon laplace uh like so so there was this guy thomas bass who did uh some work uh in the meantime in england but it was like he did not publish it uh it was he did not really believe it in any case like the the most fundamental work an initial work on inductive probability theory was by piercing lapis in 1776 uh and he basically put forward like what we know today as baseball as this uh rule to go from the observations the data uh so go to go from this to uh general theories for instance uh due to infer the laws of the universe from the observations that we make which which if my understanding is correct did that as an attempt to answer hume's induction problem uh so so base so it's not well yeah so it's related to your primary uh by hume so david hume those fields of uh beginning of the 18th century so like a few decades before laplace and base and hume asked this question like if you see the the sun rise every morning uh is it sufficient to say that it will rise every morning from now on like is this generalization uh uh like a a rule uh something that you can uh that you can uh yeah is it a good way to think and hume already had this intuition that no it's not like exactly the right way to think instead we should think in terms of probability the fact that we observe the the sun rising every morning increases the probability that it will be rising tomorrow but hume did not take this follower like he did not formalize uh this idea he did not relate this to the mathematics of probability theory uh base did uh part of this work but laplace this did most of the work and uh especially la plus not only like solved with this this kind of small primer i'd say but he generalized this and he he had this very uh very bold claim and this essay philosophic this philosophical essay from 1814 the first edition and then 1840 the second edition uh is really like the the philosophical approach to probability like like his 1776 essay was memoir was more like mathematical though it has a bit of philosophy of course but it was more mathematical and then laplace taught with this probability course at the corporate technique in france after a while in the late 18th century but probably he felt that people were too stuck too much to the mathematics and did not really see the philosophical uh uh importance of this work and that's probably why he wrote this uh this essay and i think this essay is absolutely fantastic i think this is the i'm not going to make a lot of friends by saying this but i think this is the best philosophical essay ever written yeah and so this is say like well he does discuss a little bit of the mathematics of probability but the main point is that um there's this thing he calls a good judgment bonsang's in french and he he kind of argues that this is what uh bright people are endowed with in some sense maybe this is like one one important uh one important precision here about like good judgments and muscles uh there is a lot of misunderstanding around that often translated in common sense it's his it's not meaning common sense in the term like intuition and the commonly held beliefs actually laplace is writing the last chapter where he mentions like slavery as a commonly held believe that it's okay it's not okay of course uh actually he's against common sense like good judgment not um people translates it to the bosons and then bounce becomes which is common sense and uh those are radically opposed things like it's clear it's really clear from from especially from the french version meaning good judgment and not common sense yeah and he's arguing against actually common sense and commonly held beliefs yeah yeah and his point is that you have this also common sense by held by most people there's this good judgment held by uh some some or some brighter people and what he argues is that uh like when you think longer you get closer to the to the good judgment but what he argues is that good judgment is is still missing some of the important things for one thing it's not very quantitative and what he argues is that uh probability theory is the ultimate way of thinking that there's this quote like he frequently in this essay discusses the fact that good judgment kind of leads us towards the right direction but the computation of probability theory the calculated probability so probability calculus will is what gets us closer to it makes us appreciate what's uh the the exact and right way of thinking in essence so the essay is a lot about this and it draws a lot of applications of this very of a very fundamental and general principle like it's about how to think in general so of course it's going to have a lot of applications to all sorts of fields and those we are going to discuss today uh are mostly uh related to moral sciences and uh and uh and lawsuits so to start by the this first chapter that we read from the book so why is uh why our priority is important in a in discussions about moral moral philosophy so the the main argument of laplace is simply that the the world is extremely complex and even if we take a long time to think and have the highest ability to to provide good judgment uh people will make mistakes at anticipating the effect of return laws on the world so uh if we see for example that there are lots of crimes and we want to to design a law to reduce the amount of crime it's a it can be done obviously but it will sometimes have side effects that are unpredictable and and that's why laplace recommends that we should think of doing this kind of a transformation of changes but in terms of thinking about it in terms of probabilities so simply knowing that the effect of that law is uncertain and what we want is to be able to observe what this law is uh how this law is affecting the world and possibly change it if we see that the transformation is not what we expected and this is this this will be this has been very common that laws are being changed over time as we see that they require improvement uh one thing he discusses in in this uh in this section is uh the fact that um it's often the case that we see maybe part of the law that's never used or that has bad consequences uh in some points and you you may feel like we should remove this part of the law and what laplace argues is that uh it may be dangerous because we we not predicting well enough the consequences of of the law and uh just so that we understand which parts of the laws are important and which are not we should not rely solely on on our judgment but also keep track uh so there's this discussion like it's almost an invitation to do uh data science or to collect data or to have a good database to have a data-driven uh writing of the law uh and jose he he really encourages people to to keep track of all of the cases where the law was applied and for which reasons and to better understand what makes a law good i think this is uh not necessarily specific to you to property theory is more about like the complexity of the world uh i think there's a bit of a computational complexity theory behind it all and uh and i i think it has a lot of consequences to the way we think about safe algorithms for instance algorithms are supposed to make judgment as well and maybe part of the algorithm is not going to be used and you you may want to just keep it because it's slow or something like this but the way you should be doing this according to laplace is that you should actually absolutely keep track of a lot of data and to have a data driven approach to to designing uh what a good judgment is but very well i just like to keep this discussion accessible let's not just mention algorithms because some people think it's something complex just decision making possible like like especially if we're thinking the the error of us to think of decision making procedures if you have a procedure to make decisions uh in a complex world where many data are missing and many phenomenons are interdependent in a complex way in an intractable way you can't track all the dependencies then then this argument from laplace holds it holds especially in the context of decisions made by machines and like with lots of data that humans can process but the argument is valid in in in human judgments in in in in courts etc yeah later laplace compares to two ways of taking decisions the first one is uh using your intuition and the best you can do according to your good judgment and the second one is uh relying on collected data and writing some privileges on paper according to your common sense not your good judgment if you it's uh just keep them separate according to your here you mean common sense or your intuition but it can also be uh the best you can do to achieve good judgment and the the second thing to uh to to compare it with is using collected data and writing some computations of probabilities on a piece of paper and coming up with a result and it's a it's usually a difficult effort to make to to accept that the the computation done on the piece of paper is more trustful than the 10 minutes you spend thinking about uh about an estimation in the general case yeah it's a it's a really a general theme of the of the essay and it is well i guess it's a bit more subtle than this because uh uh laplace acknowledges the fact that most of the time you can't reduce things through computations it's a very frequent uh uh concept in in the in in the essay that he often says that we should try to reduce things to computation but sometimes uh things are too complicated to be a smart organ to be to be submitted to the computations it's like this computation is like an overall it's like a computer you can imagine today and if you can formalize everything like the problem to it then it it will give you an answer but more often than not like the problem is too complex for you to write it down and to ask the computer what do you think and then uh laplace argues that in this sort of situation you could then think in terms of of analogy but you should be careful about to each extent that the analogy holds but the analogy that uh that laplace we currently uh discusses is uh what like having this uh this box with balls inside of it and you don't know what all the balls inside of it and so he uses the the the the was the thought experiment of drawing a ball and for instance observing that you drew a black ball then the question of laplace's what is the probability that all of the balls inside are black or whatever the next ball that you draw is black and he's using this very uh this thought experiment that's very remote from from from the low of from everything but somehow he sees like he constantly in the essay found connections between this very thought simple thought experiment and actual problems that you face from something in the court of law so one example he he gives uh in the essay is the example of a testimony so this is clearly very important uh in the law to have testimonies but there's always the problem of how much you do trust the person who who gives a testimony and so well laplace has all this very really nice discussion but essentially what he says is that um they are like uh if some some event is extremely unlikely uh a period like you you like for instance like uh so a murderer is like very unlikely a period like most people don't murder another person uh then um if somebody tells you that that there was a murder what you should compare is the probability a period of this model with the probability that uh the person who who who gives the testimony is uh either lying or being mistaken now this probability of a person lying or being mistaken can be small but probably like it has to be very very very small to be comparable to the probability of a murder and so this is the kind of probabilistic thinking that uh that this essay is talking a lot about uh and it really answers also like some of the questions that that david hume raised earlier in the century yeah a famous quote mentioned about this topic is that extraordinary claims require extraordinary evidence yeah and this is something you can read if you if you look closely at a base rule whether how much the probability you are assigned to some theories and some unknown theory will change is dependent on the probability of the observation and if you make extremely unlikely observations it will change more the how much you your beliefs in different theories yeah yeah another very interesting aspect of probability theory applied to the to the context of the law is uh the fact that when we rise the law like most laws are written as uh if the person is guilty then uh do something and if the person is not guilty then do not do something else and this kind of of of principle of rule this kind of algorithm uh requires perfect knowledge of the whether the person is guilty or not and yet in practice uh we we have to expect that we're only going to have limited data we're not going to be able to have a mathematical proof of the fact that person the person is guilty or not we only have evidence we only have data that will uh change what we believe that will update our probabilities but there may and quite often there is still a huge amount of uncertainty when the sentence has to be given and so what laplace argues is that the the law we should think more of the law as or we should write more the loop or maybe not right because this is difficult but we should think at least of the law as more something like if the person has a high probability a party larger than 99 of or 90 let's say of being guilty then we should give him this sentence and maybe we can then have a different level of sentences depending on this probability if the priority is between 50 and 90 we have also half half ruling but not as half as it is as if it were larger than 90 another another illustration was just like the introductory paragraph of the the application of poverty is to to to to to to the law and the and and the the court ruling the the the the fact that we have this uh first install like the first tribunal and then you have the appeal and then appeal you go to a tribunal and like argues that in the appeal you need more judges and you need a majority vote etc because like the probability that an error was made in the first uh so just like the this in terms of probability thinking uh this would just boil down to to the wisdom of the crowd like wisdom of the crowd but not every crowd the crowd of churches yeah then he's making a probabilistic argument for the fact that if you go to appeal you need to increase the level the the number of judges uh before you you you finish the procedure yeah and there's also to go back to the threshold that uh that leo was discussing about the fact that we can't be absolutely certain that someone is guilty but we should uh still send that person to jail if there is a high priority that that person is going to do this sounds quite powerful because it means that with some frequency we are going to to put some innocent people in jail and some some something else that is not desirable is that we release free some uh some some murderers that would kill other people so there's this balance between a civil and desirable outcome and because the system is not perfect then we can't have a perfect knowledge so these algorithms should we should not even try to rely on perfect perfect knowledge then we we have to to accept that the the system is going to make mistakes we can think of it as a we can do our best to improve it but there will be some mistakes and choosing this this probability of how should we need to be to send someone in jail it would be a balance between the undisabled effects of uh of putting innocent people to jail and the undisabled effect of reducing a murderer free again just i'm just adding adding just nuance here uh so laplace is not saying that like in all cases it would be impossible to have close to perfect knowledge just arguing that in many cases knowledge is hard so we have to have so then we go to appeal etc but then he says like in easy cases where it is easy to establish close to certain like like everyone in the village so this person murdered this person and then like when the judge saw the killer kill the victim then you don't need to go to appeal you don't need to do this sophisticated probabilistic thing just like just to to close the door because sometimes when we we bring in relativism like this one that's like we can't always know perfectly etc some people interpret it in the wrong way and say okay then everything is relative we can never know no no like laplace is not closing the door to the easy creases there are easy cases and in these easy cases the simple almost binary way of thinking is practical and is enough so we're not ruling out uh simple and close to binary thinking it's just that in complex cases where it is clear that no one has complex like everyone has only partial knowledge for example evidence has been destroyed for example like the the evidence was destroyed either by the the guilty person or the likely guilty person or by someone who would like someone who is really guilty and would like to to make the accused person look guilty so for example those cases those are complex cases where we need this relativistic thinking probabilistic thinking go to appeal include the number of judges laplace is not ruling out uh so so raplace is not a relative is relativist for the sake of being relativist and sometimes i read uh in some part of the literature like people using laplace uh reasoning to say that okay knowledge of truth is always relative and it's like and then they rule out close to certainty cases like there are cases close to sensitivity is useful i agree that is a common mistake and uh it is good to to mention it sometimes it's uh this mistake is described with the with the image that uh people think in black and white so absolute certainty of false absolute certainty of true and this is this is the wrong way to to to to think obviously but then when when they realize that oh nothing is either black or white things are gray they make the mistake of having only one shade of grey and uh and thinking in terms of varieties you should make your priorities go from as close to zero as possible to as close to one as possible obviously in many cases but also have priorities in the middle in for difficult cases that are uncertain and so you should think of all you should think with all the shades of gray from a white as close to one as possible and as close to black zero as possible very dark grey for things that are extremely likely to be false yeah there is some very nice quote in the essay which early on in the essay where he discusses uh the fact that what is probability theory or we can have another episode on this but what is the probability but uh essentially what he says is that a probability is a description of our ignorance and of knowledge where we will discuss the introductory part of the book so it's country intuitive now we're discussing the the final part of the book of the book so moral philosophy or law etc that we will go back and discuss the introductory part of the book why probability theory matters yeah i just like to put this to close this part on relativism so just like to make it short um we like there's a lot of literature on the confrontation between binary thinking and derivativism and actually priority probabilistic thinking uses both like there are cases where it's useful to be a relativist and to have nuances and to to defer your judgment and delay it like to delay it as as as long as possible and there are cases where it's very useful and practical and and fair to have close to binary thinking so you should not through binary thinking when it's useful and you should be aware that you you should be like you should not use it always and you should be aware that complex cases uh are do not like are not solved by binary thinking yeah yeah and so just you to close the the section on uh on the law uh there's also a nice discussion about um so so let's say what we care about is actually uh this probability of the person being guilty and we want to make sure that it's larger than some high threshold so that we can convict the the suspect uh and and then la paz has this discussion about if you grow the size of the assembly of the number of judges to to to give the the ruling um like should you demand that a larger fraction of these or a smaller fraction of these well what is the fraction of these that need to to to say that that the person is guilty so that we conclude that the person is indeed guilty and uh well this next question like if you have a very first hole that's very close to one half uh then um uh then if you have a small number of judges then it's very very bad uh but essentially what but uh the conclusion that laplace uh comes through is that uh with a rough estimate uh is that uh out of an assembly of 12 people maybe there should be something like nine judges that say that the person is guilty in order to convict the the the individual and i think it's it's a nice way of having the prime like you demand more than the majority not because not because well that's a an arbitrary rule but because you want to have a high probability to we want to conduct a person only if there's a high probability that the person is guilty i think it's a it's a nice way of thinking about this problem yeah and it's just uh the fact of accepting that mistake can be made that the jury will not be perfect if the jury is perfect either 12 will always agree or okay 12 the 12 will always agree because they are perfect this is not the case so in the model that laplace discusses the in the model that let us discuss is uh the jury are considered to be quite good better than chance at deciding if someone is guilty or not maybe they they get it right with the priority of 75 percent something like this and this is how laplace run these computations yeah now one caveat to laplace's computation is that laplace assumes in his model that the the the members of the of the of the jury are independent like the opinions they have are independent and unfortunately we know by now that there's a lot of of correlation of group polarization effects when you have an assembly uh so this is a caveat to be given to this analysis of laplace which would demand maybe uh even larger but yeah it's it's a complicated problem because they are shown the same data it's uh surprising to expect that they would be didn't make independent judgments so one of the last sections of the essay this is called on the illusions and estimation probabilities and uh it's also absolutely fantastic like it's uh like 200 years ahead of its time [Music] essentially uh well he he he discusses the way people think poorly i guess that that other philosophers have noticed that people were not always thinking very very clearly but what's really nice is that now that he has this uh post rate that probability theories positive is the right way of thinking then you can measure how people deviate from this right way of thinking and uh in doing so like he discusses essentially all the the best known uh cognitive biases that we we know of today uh like for instance uh the badass policy is like if you only see a stream of like no no if you see a lot of of of uh red uh coming up uh in the roulette in in casino uh lately then you might be tempted to say well the next one is not going to be red because it's come too often something like this but lapis argues that this is a an illusion and then he discusses things that are probably closer to what we would known as call today cognitive bias like familiarity bias motivated reasoning i think these are the two main that he he really stresses uh in this essay and he does this in a very very compelling way so uh i think this is really really really fascinating section yeah one point that i that i that i'd like to write is that uh usually people underestimate how much of what they observe in the world happens simply due to randomness so with the example of the of the lottery a lot of people try to find out explanations of why this this number came out and one of the explanation is that some numbers come the number 47 didn't come for for two years and it it's bound to happen at some point so we bet on this one other sort of explanation is that there are people that would log all the numbers that come out of the lottery and find the numbers that come the most often and then try to bet on these numbers because they have been observed to come more often but but uh and laplace discusses that he simply created a small model of uh of generating uh lottery numbers and finds out that yes we expect that in if you if you observe past data there will be some numbers that came out more than others it's a normal thing simply due to the random process and because you find such a simple explanation you need uniformly random randomly generated numbers to to explain what i've been observing one should not think that there is a different processes for generating these numbers than the simple process that laplace that that that laplace described and that is actually the lottery yeah and it's related to this idea of what poker players call the resulting buyers uh so that's like judging uh the decision of someone like uh like whether he was right to play number five in the lottery based on the result and you say oh i was stupid i did not play fight the number five for instance uh and a poker player would say that uh this is a very very very very bad habit at least in poker because you you give too much attention to things that are just noise and you're going to update your strategy based on this and you you're not going to to focus enough on your decision making because this is what matters this year making so typically in poker players professional poker players uh there are these groups of poker players who who just never discuss like the so-called bad beats the way they they lost in a tournament like the specific hand the larson even though it was highly unlucky because what they care about is like the decision making what it is that you choose to do when you had this uncertainty and based on this uncertainty what whether what you did was good or not and not based on the result you should judge based on the uncertainty and not based on the result i think this was one of the this is one of the the greatest insights of probability theory yeah and this is very hard to do in practice i often reward rewind myself for making decisions that ended up doing good and to punish myself for making decisions that ended up being bad and and i learned because of the result and today it's hard to to do differently yeah think about so to to illustrate this with the example of lottery lottery is well known to be a game with a negative utility negative expectation of gains so if you judge a decision process that either decides to take the lottery or not it is very easy to to to agree right now that the the decision process that decide to play is making wrong decisions when the decision process to decide not to play is making correct decisions but now if you if you imagine you see someone that decided to play and won then it it is very unintuitive to say that the the decision to play for for that person who won was a wrong decision a decision pushed by a decision process that does not correctly maximize its expected utility simply because of the results and this can lead to too difficult discussion if you discuss with someone they might tell you you don't know where they are making a good or not decisions because we haven't seen the result yet yeah yeah that's not politics like let's talk about like uh confirmation bias yeah the confirmation bias and the example of liveness so uh there are like i don't know if like the audience is familiar with like some uh beliefs like a numerology like people who believe in like the power of numbers if this number pops out and then there's i don't know if the the the golden ratio uh in something then there is something special about this object and um this is something still common in today people like uh like believe in in miracles just because some sequence of numbers appeared i don't know in the date of birth of some singer and then the date of release of her album or or his album and then they will start like building up theories and the internet is very good in amplifying these theories that because the the date of birth of the singer and her date of release of the album and then i don't know 9 11 appear like happened and then you the radio between two so so this is this is something that sounds funny but even great minds uh were not immune to it and he he gives the example of leibniz and um and and bernoulli also uh and that's also not like mostly libraries like the bernoullian libraries computer this series like it's a theory of number that gives some special results etc uh done by bermudian lightnings but leibniz used this result to argue with the chinese emperor that god exists [Music] god might exist for other reasons but not because the series is equal to one over two or so he's like he he he he so leibniz who was a strong believer uh knew that the chinese emperor loves mathematics so he thought like yeah maybe like this would convince him of like christian god and christianity and then he sent him like a funny note on the results of his series and say look if you sum these numbers and then you obtain one over two or one or one over four like one over two right one over yeah i think it was one over two yeah one over one over two and then look this this like you create something out of nothing and this is this is how god operates and this is a proof and laplace argues that like this like laplace does not call it confirmation bias but today in light of what we know since the 20th century all the work on cognitive biases this is the clear instance of cognitive bias you believe something is is true so you believe god exists you believe in christianity or islam or judaism or whatever so and then you have a strong bias towards confirming like validating everything that comes from your religion or your ideology communism or capitalism or whatever you want and then he goes on with examples like that and so i believe this this chapter on the illusions of computing probabilities if you want to rename it today in light of the developments we had in psychology it can be called uncognitive biases actually like you can you can argue that what he calls illusions in computing probabilities are cognitive biases actually so that's so so i mentioned this uh so the confirmation bias and the case of leibniz who practice like who's almost falling to numerology to argue for a christian god but then there is the uh i don't know a hybrid between confirmation bias and familiarity bias maybe more like familiarity bias in modern terms which is this this the thing that it's not because slavery is commonly accepted that it is okay so and it's it's not like it's not because in some culture some practice is commonly accepted then this practice is morally good so so maybe we can even argue from this chapter that as as people who who learn political theory we have a moral duty to go beyond the commonly held moral standards of our culture of our time of our era of our i don't know region or and then for example like you mentioned slavery but we can go on make a make a case for like just moral progress for example like moral progress is debated in like moral progress versus uh moral relativism so uh not sure if i'm exact but uh like in moral relativism people would tend to tell you like you have to respect the moral standards of some culture or some region etc uh for example let's say like there is a region where people don't let girls to school for example like should you respect should you respect this practice because it is a it is the commonly held moral standard of that region or or should you like should you try to go beyond that and and the the if you read the the the chapter of labs you can't come up i personally came up with the conclusion that when you when you learn probability theory you have to work with it and think with it and think harder and try to always go beyond the commonly held moral standards of your time and of your of your group your social group whatever that social group yeah uh yeah so the the connection with probability theory may be uh a bit loose in the the essay itself i think it's more like a point that uh well these are quality biases that people have but um and i don't think laplace knew about this but but there are actually a strong connection with povt theory so on the confirmation bias for instance uh parliament there's actually a theorem in uh invasionism that says that the expectation of the posterior is equal to the fire so you should before looking at the data you should expect to have in average the same opinion after looking at the data then prior to looking at the data and intuitively the reason for this is that um uh like the data can make you go both ways uh like if you're surprised that the data is suggesting something like like say like you you sign a probability one half of trump being re-elected i don't know something like this then and then you you you expect that tomorrow you're going to have the same opinion tomorrow at the end of the day it's going to be positive one half as well but this may evolve it's not going to be uh exactly one half for sure even though you see a tumor if tomorrow you see data that suggests actually the popular of the popularity of trump is is decreasing more than you expected then you should decrease your probability but if you're surprised that it's maybe it's decreasing but not as much as you expected then you should increase your probability uh about the reaction of trump uh so whatever happens in average you should have the same so that's actually a theorem just just to make the connection with poverty theory uh even less loose so for example uh uh the what louis said like many things are just due to just to randomness and and like that you don't need sophisticated theory to explain them uh you can you can see that as some form of okan's razor so you don't need sophisticated explanations like it's not because um uh it's not because uh the the moon is like that and the number of girls who were born that month and the number of boys who were born that month and the date of birth of of your husband or your wife is like that that you would have a girl or a boy you would have a girl or a boy just out of probably randomness genetic rankles and how many how many y chromosomes the the the husband produces and and etc and it has nothing to do with the moon and the numerology and sophisticated computation of astrology etc uh and like his book makes a very good case for all comes razor with probabilistic thinking so laplace in in laplace in napla's writing the connection is not straightforward but we can argue that um many of the illusions he talks about laplace talks about are some of them are due to uh a bad application of occam's razor so occam's razor is displayed principle in epistemology that tells you that out of many explanations you should always favor the simplest one the the shortest one the one that does not require a lot of additional assumptions and like in the case of the illusions uh laplace is mentioning a lot of these illusions involve additional assumptions that the moon and astrology or whatever neurology and the number of girls and boys that were born that front and i don't know the existence of christian god so those are like unnecessary assumptions and is very well known for actually uh he uh his way of practicing occam's razor so in his book on mechanic celeste right yeah i can't remember the title but yeah mechanic like it's like the sexual body emotions of the body the whole emotion of celestial bodies there was this famous famous argument he had with napoleon napoleon would tell him i don't see any mention of god in your book and then laplace just replies or is believed to have replied sir i just didn't need this assumption so this is an instance of falcam's laser and we in this group argue that organs razor is just another way of being the union what's uh component it's not sufficient but yeah they still there it is something important to note concerning uh confirmation biases so even though you you you might have a correct prior and uh apply a camera raiser quite well confirmation bias is something that happens at the moment where you you look at evidence and the problem is that sometimes people would look at evidence and no matter what is the evidence they would change their belief in the same direction yeah which is a what cannot happen because as they said that have when you look at the evidence in average depending on what the evidence is you you your change of belief should should serve up to zero in average so that means that if the evidence points one way you should change a beautiful way and if it pulls the other way you should change it in the other way a famous illustrative example for this was the the condemnation of of dreyfus who was accused of of something and when people look for proofs about this they could find no they could find no proof and uh unfortunately uh finding no proof they concluded that oh yes he was guilty and good at hiding that his gucci so i accidentally that's an excellent example let's let's elaborate on this example maybe to conclude so just to put more context uh to the english-speaking audience alfred dreyfus was a captain in the french army and uh they were grouped and the atmosphere was was was uh was so back then in france was uh quite anti-semitic so in an anti-semitic context alfred dreyfus was uh accused of intelligence of being a spy a german spire on english by a german spawn guessing germany uh jerusalem and the evidence against him was a note uh that was presented as a notes dreyfus right to the germans and and then ponca so holy point polymath one of them last 40 months as people say used probabilistic arguments to to to to to prove the innocence or to arch for the innocence of religious if you found no proof and then you change your belief to to increasing how much you think that that person is guilty if you if you are if you correctly apply base law it means that if you had found proof you should have updated your belief in a direction that is not guilty so when you observe a like you you make an observation and you update you believe one way it means that if you had made the opposite observation you should update your beliefs in the opposite direction and obviously finding proof of someone guilty should increase your beliefs in the direction that this person is guilty and it means that not finding proof should always make you update your belief in the direction that that person is not guilty because or at least slightly otherwise otherwise you you are in in the in the failure of a confirmation liars yeah yeah that's like uh like this was that this is uh easy to say in theory in practice it's always harder when you actually presented the evidence and you're always trying to find loopholes and an explanation for why you go in your direction so one way to to better combat this tendency that we all have to motivated reasoning is to pre-commit um so so ideally you just apply baseball you just apply the laws of quality but uh be because we have limited uh we have motivated reasoning one way to to combat it is to pre-commit me meaning that you're going to say well today i believe this i believe that refuse has a 70 percent idea of being here i've been guilty and i know that they are going to look into this uh this piece of evidence and i'm going to do to predict what it is and i'm going to say well i think that uh it's going to be something like that uh and if it's uh so let's say that for instance uh it's the number of uh of messages he sent to some general in the in germany and you say well probably he sent like five messages and you're going to say well that's my prediction and it means that if there are more messages than this then you're going to increase your poverty that is guilty but if you there are less messages than this then you're going to decrease it and you have to well one good way to do is to pre-commit and so uh this is more generally a good habit of a beijing which is to to bet visionism and betting have strong connections uh historically uh and still today and betting is good because it forces you to explicit your prayer and to pre-commit and and to to verify that you're not going to do uh motivated reasoning and so yeah i think this is a one of the important takeaway of probabilistic thinking yeah yeah i really totally agree with that uh advice from lake uh another advice i could be that is slightly less good but uh maybe easier to do in practice also is to simply when you when you see yourself in the process of updating your bills based on evidence so if you are already doing this i think it might be useful to to ask yourself the question how should i update my belief if i had observed the opposite evidence in that case you it might help to detect when you are actually lying to yourself and doing confirmation bias and help you choose in which direction actually the evidence points to so next week we will discuss a very important paper gender shades by joy biolumi uh and uh and the timnit uh that paper was important in in in showing empirical evidence that facial recognition is biased uh and it has strong biases that make it not ready to deploy and thanks to that paper and the research follow-ups by these two researchers and a few others now there is a moratorium on not deploying facial recognition by many companies so ibm then microsoft and many others followed stated they would not deploy facebook recognition and they will not use this especially for police and military use so we'll discuss that paper the some of the follow-ups and and what what does this mean for today's technologies such as so we'll focus on facial recognition but we'll probably discuss other aspects of biases that need more restoration and more work uh by by people who work on artificial intelligence and computer science and moral philosophy of course well thank you and see you next week bye