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okay today i have the pleasure speaking with machaz leonardus manchas is covered in a paper with david deutsch about the problem miller theorem and we get into that as well as the dangers of the scientific identity the nature of scientific progress advice
to young people who want to be polymaths matjaz is one such as you will see he's a fascinating person that have had the pleasure of getting to know he has a broad range of interesting ideas which we get into so without further ado here's matcha's leonardus
okay masha's you have court written a paper with david deutsch about uh bass theorem but before we get into that let's talk about the big picture questions science uh what is it and is it somewhat of a is it somewhat of a confusion to even talk about it distinctly from other disciplines
um well so my view on that subject is that is that um often a lot of a lot of talk about science ends up being quite counterproductive i'm not saying that there is no such thing as science but i definitely think that um that sort of um that people identify with science too
much they they wonder whether what they are doing is science um they they think they are scientists and wonder what is it that they should do in their capacity as scientists um and i think that often has a counterproductive effect on on on basically what they do now one
interesting thing to note is that is that you know the name scientist is actually um an early 19th century invention um it was traced back to i think two um two to professors at i think trinity college in cambridge um and it's uh and you know people were
able to do science before that um quite well um and uh so so one of the problems that i see i guess in that in that respect is just that uh people people perhaps think about you know uh what what is a scientist and uh sorry who is a scientist and what is science a
bit too much but i don't know the history here do people not consider themselves natural philosophers before then um there is definitely been sort of names for for um for this role um the the so so one way to sort of think about it is that people
people have always thought about the natural world though right so people have always you know tried to understand you know how um you know how how machines work how nature works how sort of everything does and and they often did that without you know ever becoming conscious of the
idea that they were doing anything special or that they are playing a special role by doing so um and you know they were they were able to sort of do it just fine and one of the things that uh you know at some point that obviously changed um you know
uh this sort of idea that that one is engaged in some sort of a special activity when one is trying to understand nature and uh you know there'll be kind of a special social role for that like all of that obviously had to develop um but but it does seem to be the case
that you can reach a better understanding of the natural world without it sorry sorry go ahead oh no and therefore there is a question about you know whether it is actually helpful okay well if the identity of scientists is not that useful then why do we have universities that we
consider to be special places and we employ people with tax dollars to do special things that i mean clearly they're not doing construction or um you know building archers or something like that so so like there is an activity ie trying to understand
natural world that seems to work better when it is supported uh sort of both kind of that it is that is institutionally um and culturally supported um so you know it is useful to have institutions that you know kind of keep all the relevant books at the same place
and kind of get some of the same people um um you know at the same place that sort of organize you know events and sort of where people can sort of meet each other um and and i think that that you know that so so i'm not disputing that um there is an activity that is sort of
worthy of of of being supported um but but whether that sort of particular way of looking at that activity is is the right one um is is less clear okay so you do identify there's a special role for universities and they're doing a distinctive distinctive activity well if it's not
science they're doing how would you describe what the thing they're doing is right so so well okay so perhaps to illustrate this right one um needn't need to think of this activity in a unified way so for example like imagine that we had an institution
and in this institution there would be you know somebody who was interested in you know liquid helium and uh he would be writing about it and talking with all the people that were interested in it and then you would have another person and that person um
would be you know interested in in you know the way star swarm and and their you know evolution and that person would be sort of you know again writing about this talking with other people about it and you know you could have so on for for just a bunch of other
things now you can easily have an institution that would be sort of supporting all of these people in that in that endeavor um but you know that you know but now for example if one if one were to just kind of stop there right it's it's not possible yet at that stage
you know to sort of say okay well well all of these people are are engaged in this you know unified activity you know called science and oh are some of them really doing it or or not right everybody is just it's just you know one one person is doing this one person is
doing that you know one person is doing the third thing so perhaps i mean these interesting right uh comparison might be um um for kind of the the particular review that i have it's just like you know um um you know um like like people have this idea of an
entrepreneur right um well you know in a certain sense um you know and all these entrepreneurs are kind of trying to construct different companies right but nobody nobody nobody is kind of asking the question well you know is any one of these people
actually entrepreneuring right um that that is not a conversation that ever arises so um it is in that sense that that i think that um that you can have an institution that supports that activity uh but you don't need to like understand it in this particular way that
that science is often understood and so what's counterproductive about the current understanding of science and scientists right so so one problem um with this idea is that the idea of sort of science and scientists comes with this idea that there is this particular method
in other words um that that you know one that one is somehow doing something more other than just being engaged um you know with a particular problem or question and pursuing it you know wherever it might lead there is this idea that there is a specific method
that that one ought to use to think about this particular question rather than just you know where were sort of the the question naturally leads you and i think that that um uh this attitude or this idea can often stop people from doing sensible things that
that that um would otherwise be that that would help with sort of pursuing pursuing their their problem right so um uh you know the thinking is that you need to pursue the various questions with a specific method as opposed to just where kind of the logic of the problem
itself leads you and i'm not saying this that this actually affects everybody or that this is a sort of an across-the-board thing but it but it is sort of an argument that that often features um the current conception of this therefore you know as i said sort of before
kind of allows you to make criticism of somebody you know you can say well are they really doing this thing or not which is not a thing you could really do you know where it just were people just started thinking about specific issues and what they did was understood in that
way um and in general um i i do think that like making making you know becoming conscious of what one is doing um and and uh uh um you know kind of being um and sort of classifying it or telling yourself the story about it um is is one thing that is known you
know in several other fields to sometimes lead to problems um you know hence the term self-consciousness and uh it being sort of productive it being deemed counterproductive in many areas but let me make the counter argument there is a specific method or at least a
family of methods right we have proper we have you know um falsifiability accessibility and you know we privilege these over other methods we could be using like myth making and so on so what's wrong with somebody understanding their position at institution
as to understand the world through a specific family of methods well um i would i would perhaps funny funny mention popper there because i would actually dispute that premise um he wrote this uh i mean there is there is i think a very nice set of undergraduate lectures
that has been recorded from him um where where he says that he was i think a professor of scientific method at the london school of economics or something like that and he says in that lecture that that he is uh is a professor of of a subject that uh
that he thinks does not exist um um his student firearm and uh i think uh actually wrote a book against method um which is which is sort of yet another kind of philosopher of science arguing against that idea um and uh um now it um it is true that that
there are certain i guess patterns of thought that are more conducive to under that seem to at least be more conducive to understanding um the natural world than others um but i think that that that is still like what what patterns work you know how one thinks about them and
so on all of these things are kind of um more of a great mystery than an exact science to put it to put it like that so then um to paraphrase you let me just see if i'm understanding you correctly it's that scientists should consider certain methods better than others but
they shouldn't identify themselves with some of them um well i mean okay that i'm not sure if that is sort of paraphrasing it exactly as i see it because it's um um like this it is very unclear if one is ever is ever using a method um because you
know like like people people as i said at the beginning people have been thinking about the natural world without being conscious of it in in any way and and you know it is it is you know like thoughts are constantly arising in the mind right
and it's it's it often feels like a bit of a stretch to say that you know all these different thoughts one is having um are arising as a result of a method um as opposed to just just arising there is a certain level of ambiguity that i think sometimes occurs there so
people have been trying to solve problems for a long time but only recently well i would argue that only recently um for maybe like the past 500 years they've been very productive in understanding the natural world and it does seem to be because of a
family of methods right so doesn't the case of the success of the enlightenment lend credence to the idea that um certain methods are to be privileged and are more productive um well um i uh i do not exactly have a view on that on that on that subject for example um there to be honest i i
just sort of don't know i kind of have various passing thoughts um on that issue but um i mean for example there is this sort of question of there is a sort of narrative about um the importance of the enlightenment and uh it's uh it's it's not exactly obvious if that
to me if that if that narrative is in fact true or if that narrative is more of a fiction um and um you know uh there are there are strong proponents for one of that positions and there are strong proponents for the other um and uh what what they have in common uh
ironically is that i think that they both sort of agree that there was something very important about the enlightenment uh because there is perhaps yet another third explanation where you know it was it was you know it you know all of this had nothing to do to do
with anything else maybe it was just you know economic progress that that allowed for you know like uh all this thought to be produced at the time like it's very very difficult to sort of figure out exactly how causality works with with most of these things
um but but to this idea that it was due to to um a change in method i mean like well that's like a lot of people at the time had that idea but a lot of people kind of subsequently criticize that idea by sort of pointing out well i don't know maybe something did change
in the way we thought about things but but nobody can really understand that change right because a huge part of that um idea was that was that you know what is that is that what was this idea of reason really that that somehow or other reason is the way to
to understand the natural world and what for example hume and other skeptics subsequently pointed out is just that well like like this like this can't possibly really work as as you know um you guys are imagining it because for example i mean as human pointed out this is kind of
the famous problem of induction you know there is no way to kind of proceed logically i.e by reason from experience to you know the the the celebrated you know general theories of the enlightenment such as newton's theory and such like um and uh so i do not know what
what opinion exactly i have on that issue uh but these are some of my thoughts yeah that was a very interesting answer uh speaking of induction let's get into the paper you co-wrote with david that's coming out uh soon um so do you want to describe it
oh sure so we um we wrote a paper on something called the popper miller theorem uh popper miller theorem was a theorem that popper that we previously mentioned in this podcast and um david miller um basically they published a short letter in nature in 1983
where they presented um this this very kind of short paradox where they basically claimed that um that pro the way they explained it was the idea that probabilistic support is not inducted um that is quite vague and and this was conceded by by many people
kind of subsequently um but the basic idea is is something like um so basically there is this there is this idea that somehow and this idea is very much a part of common sense and was a part of various attempts to build an inductive logic at the time which is simply this idea that
that that evidence somehow confers support on general theories um and figuring out the right model of that of that support um of how this sort of support works um you know has been kind of one of the challenges that people have basically been trying
trying to figure out at the time and one of the ideas was that basically probability is is what you know probability was considered as one of such possible sort of support measures and um basically uh um what what their what their theorem aimed to show was that was that this
that this probabilistic support that evidence sort of confers on theories i you know a piece of evidence comes in and the probability of a particular theory you know increases by 10 that that 10 increase can't really be understand as in any way
being due to that evidence conferring some kind of inductive support on that theory um and the way they made the argument is that they basically said um they basically identified two propositions they said look this theory relative to this evidence like really this first proposition
is a kind of a the deductive part of the theory relative to the evidence and this other part of the theory is uh the inductive part of the theory relative to the evidence and they showed that um the evidence always decreases the probability of this inductive part
now um there are sort of two there was a lot of kind of subsequent commentary on this on this result and the main the main sort of the main points that people kind of made were well you know the main points of the spirit were well in what sense is
this proposition that they said was the inductive part in what sense does it kind of capture you know all of a you know all of this theory that goes beyond the evidence as they put it um and then the other issue was was just was just you know because there is
a vague notion of of you know inductive support and what exactly that means um and so that was kind of another source of objections and what and i think that the conversation has in many ways sort of moved on from there um but we sort of thought that that that
argument is sort of still interesting we found sort of a couple of other ways of explaining it um and uh i think they you know present kind of a very interesting challenge to this idea of of um you know sort of kind of trying to use bayesian reasoning to
to either build an agi or or for various other purposes and we thought it would be sort of a very interesting thing to present okay did this serum for the broader theme and popper's work um well it sort of did right so so the basic idea that that popper had um
um that i think kind of sort of came out this theorem i think came out of kind of the same way of thinking about this was basically just this idea that that um so he was interested in the idea of logical content of a theory uh there was this idea that just like you could have
you know this probability measure that you assigned to theories you can assign a content measure so the idea is that some theories say more than others um and you know the question was can you construct a measure of that kind and one of the interesting observations in
in thinking about that measure is simply the fact that kind of the the the constraints or the rules it has to obey are exactly the same as as the probability calculus basically so so in a certain sense you can um you can always interpret some assignments
or probabilities right as as really being a kind of a statement of um as he put it a degree of logical weakness so you know if i say that one theory is um more likely than another theory um i you know there is a per there is always this perfectly consistent interpretation where
what i'm actually just saying is that um um you know if i say that this theory is more likely than that theory i can say this theory says less than this theory um that was kind of the idea of it and um and and basically um what the the reason therefore he i think
kind of became skeptical of scam these probabilistic approaches to knowledge is simply the fact that um is simply the fact that that as he saw it um and i think that there are some reasons to to kind of think that this is in fact how people think um is that is that what people actually
want what they believe in what they seek are not kind of these sort of tautology like contentless but likely theories as it were but kind of these incredibly informative um and and therefore um you know informative explanatory and therefore kind of less likely theories um and if
you want kind of an example of the fact that that people do seem to think about that way right there is something known as the conjunction fallacy um that would seem to sort of support that so um there is this famous experiment i think it was popularized by
uh daniel kahneman in his book thinking fast and slow um which was i think the sort of case of linda so um the you know in this in this experiment you're told about a woman and you're given a bunch of information that would kind of you know that are kind of
stereotypically associated with being a feminist and then the question is well is it more likely that linda is a a banker or b a banker and a feminist and a lot of people uh pick option b even though um the probability calculus kind of tells you that
that that you know option a has to be more likely than option b and so the question can be why that is um but i think that this tendency that he talked about sort of explains this phenomenon right the second fact explains the facts you were initially given
but option a as i called it doesn't um and and i think that this is sort of a part of a general theme where people really do um you know sort of look for and as i said believe in explanatory general theories not by by um not this sort of content you know not
not kind of the most likely theory i mean there are several european languages i think the the german um german and slovenian are the two that i know where i think that um like if you were translate the word for probability into english it would be something like
believability um and uh and uh i i think that you know if you if you interpret probability in that way sort of um i think that you know the believability of explanatory theories is always higher than the believability of of these sort of less likely theories
and therefore believability isn't really probability okay and can you explain why explanatory theories uh should be preferred well i'm i'm not saying that they should be i'm you know um i i do i do like explanatory theories i find them interesting to think about
and and kind of much more fun to engage with um i mean i can i can give you his arguments for it um i'm not sure if i entirely agree with them but actually i'm more interested in where you might disagree or where might i disagree um well um well he there so for example he points
so so the so there is this interesting question right of what exactly is the role of this universal theories like why why do we have them why do we think about them why do we try to improve them and so on um and his argument was that that that that people actually his argument was
actually quite psychological it was that people seem to have this need for regularity um and and you know if you put them in an environment um without regularity uh people kind of go mad or or you know at least uh uh you know kind of kind of kind of
invent regularity out of thin air um and i think that's a very interesting argument i you know like there is this interesting question of why if this is true i can't quite exactly see why this need for regularity exists um but it is it is something that that that
i think is is uh is a is a kind of worthy of exploration on the other hand i think that's another thing that is great about explanatory theories is that is that they allow and i think that this was another point that you would make is that is that they sort of
allow for progress right because it's only if you kind of create this universal explanatory theories and you go out there um you know you will eventually find that something about it doesn't quite work so you will replace it with another and then another one after that but what
is kind of happening in that process is that your um is that your kind of knowledge of the world is increasing um in a way it wouldn't if you just accumulated experiences um because you know if you were just accumulating experience you might never
go out there and try you know things that your universal theory says you should do and therefore discover that is false and another thing that can happen um in this process of is that is that kind of various kinds of truth can accumulate in this in these general
theories that are not present just in the experience alone um and so i i get i i'm not sure if this thing that i just said is his argument or something that uh or not but but it is i think another reason why explanatory theories play such an interesting role in in
in life in general i completely agree with everything there but you didn't explain where you disagree with popper well i mean i i said that that that that you know it's it's somewhat unclear to me um this thing that i mentioned about the need for regularity
um i i'm not sure if it exists uh it's plausible that it exists but if it does i don't quite understand how it works um so that's that's kind of that okay let me ask about being polymathic so this paper clearly pulls from a lot of disciplines and i think a lot of the work you do
generally does um what advice do you have to a young person who's trying to be a polymath um well uh first of all the first piece of advice is is that is that i would give is that no you should never take advice from me uh the second piece of uh the second
thing i would say though is um is a um it actually relates so so um again this sort of relates to just a particular um problem that i think i i think people are naturally interested in everything um and it is only through through um again it's actually it's
actually very similar to the thing we talked about at the beginning i think that um i think that the same the same phenomenon that happens with the way people think about science sort of happens with learning um so you know people learn or all their life um you you
and in fact people learn all the time like you interact with information all the time it changes you but you never think you never consciously think of changing yourself by doing that or um you know uh uh trying to change it it's only in very special circumstances
that that you kind of try to think of yourself in that way and i think a lot of what happens when one tries to do that is actually quite counterproductive um like for example there are a lot of ideas that that that if you want to learn something you can't just
do it through osmosis you have to be very very systematic about it um and i think that is basically completely false um i think that um uh and again this sort of leads people in in sort of very very counterproductive direction where they think they need to study the
fundamentals of something and then there are first of all they think they need to study a subject then you think okay first then you just study the fundamentals then the intermediate level then the advanced levels and all of these levels are fiction the there is
sort of not none of that there and all of these ideas were actually developed um to oh oh they have always been developed to solve a particular problem or advance a particular need and and i think what what is what is you know um most imp if one wants to just have broad
interest i think the most important thing is is to just um you know pursue whatever you're interested in not be afraid or think that you can't understand it and paradoxically um not not actually trying to achieve any particular change in yourself
uh but rather just sort of going going where the story goes um reading history is perhaps perhaps sort of helpful because because um a lot of books are kind of written with the with these ideas that i think are misconceptions in mind um but uh you know there is a there is a
substantial uh uh but history often history of things often gets around that because um like you know as i said like every single one every single thing you see in a textbook wasn't written to be put in a textbook wasn't developed so that somebody could
learn it it was it was created by somebody who was trying to do something or understand something and it was useful in a particular context and that's why people adopted it and that's why it eventually ended up in that textbook but what often happens is that then that
context goes away and all that remains is a textbook and so you are left with all of these irrelevant seeming information that was actually relevant to somebody at some point but is no longer relevant to to anybody that reads it or at least not immediately relevant
um to how they approach it so that are some of my basic thoughts on like what i sometimes see kind of go weird but i think people you know polymath is not something you learn to be it's something you unlearn to be as some people would put it awesome that's very liberating advice
but let me ask you this um should you just should a young person just be focused on learning what they find interesting or as as you mentioned like people are trying to find solutions to the problem situations they're in should they be purposefully
trying to identify problem situations in existing knowledge yeah so so i think that when it comes to that i think my impression at least is that the most important thing is to connect um with other people or groups of people that are doing something because there you will
um you know again find find something that you can contribute to um as well as um you know sort of gets get support for doing so and and so on um i think that that that is sort of very much an unsolved problem as a thing to to kind of do at scale um as i think we
we uh talked about at some point um like there is this idea that you could create a kind of a um there is often this idea that that that you that one could easily create kind of a list of all unsolved problems in a given field and just put it on the internet um and
many people kind of think well this this seems so simple like why doesn't anybody ever do that and i think that is that it's actually incredibly difficult to do i think that the kinds of information that you would have to put um online is just it's just incredibly
it's very very unclear how one does that and um the key the key thing is that is that the key thing to realize is that well um first of all that there really is no such thing as a as an unsolved problem i think as conventionally understood they're just a bunch of people and you
know like one can form a view that that creating something would be valuable to them um it often won't be valuable to everybody it will only be valuable to a subsection of those people um and those people might not actually know in advance that that's what they
would want and for that reason it's actually quite difficult to sort of put um you know that seems to be a kind that's that is kind of dif it's a difficult thing to kind of put online um for that reason um and uh yeah oh so but if you're uh but if you're a
young person who needs to connect to people to um who are solving the right problems or about to solve the right problems but you yourself don't know what the right problems are because you haven't connected to them yet i mean how do you solve that
circle right so i think that that that that is sort of quite a challenge and as i said i'm i think i'm terrible at this uh there are people who i think are are sort of because i i think you know it is very much the case as you sort of say that that the whole thing has a bit of a sort
of a chicken and egg problem to it right because the whole idea is well you can't really contribute anything valuable because you don't know anything about you know what these people's lives are like what you can contribute to it and on the other hand it's kind of difficult to
join the conversation because you don't have anything yet to contribute to it right and so the the there already sort of all kinds of idiosyncratic ways that that i think this this sort of happens and gets solved uh but there isn't anything as it's not an
impossible problem to solve but but it does require i think quite a bit of an experimentation um i don't think i'm i'm the best person at this by by any stretch uh but these are i guess are just some general thoughts in that okay so then young people
connecting to mentors who are solving the right problems is this very hard is this impossible almost um i i actually no i don't think i don't think so at all i think that the main problem is just that it is somewhat idiosyncratic right so you you cannot just sort of
give give uh give a give a universal answer um but i think that the it's definitely not the case that that the world is hostile to it i think people are very sympathetic to attempts to do that um um you know and and you know as i'm as basically you illustrate i think uh a
lot of a lot of that is very very possible and there's tremendous goodwill for young people out there so so that's yeah i i have sort of the same impression and uh so so so yeah i don't want to like i think i think one one of the worst
things perhaps perhaps the reason i sort of bringing this up is just because um i think people often just lack awareness of this uh they they they kind of lack the awareness of the fact that that is kind of the main challenge uh or at least i think that the thing
that one ought to do um and uh yeah i guess for that for that reason i i think it is sort of worth mentioning on that hopefully and obviously mystic note master us thank you for being on the show this is very fascinating thanks thanks for having me it's been a pleasure