Matjaž Leonardis - Science, Identity, and Probability

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Okay, today I have the pleasure of speaking with Machoz Leonardis. Machoz is co-written a paper with David Deutsch about the Palmer-Miller theorem, and we get into that, as well as the dangers of the scientific identity, the nature of scientific progress, and advice to young people who want to be polymaths.
Machoz is one such, as you will see. He's a fascinating person that I've 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 Matjaz Lernardis.
Okay, Matjaz, you have, of course, written a paper with David Deutsch about Bay theorem, but before we get into that, let's talk about the big-picture questions. Science, What is it? And 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 people identify with science too much. They wonder whether what they are doing is science.
They think they are scientists and wonder what is it that they should do in their capacity as scientists. And I think that often has a counterproductive effect on basically what they do.
Now, one interesting thing to note is that the name scientist is actually an early 90th century invention. It was traced back to, I think, two professors at, I think, Trinity College in Cambridge.
And, you know, people were able to do science before that quite well. And so one of the problems that I see, I guess, in that respect is just that people perhaps think about, you know, what is a scientist and sorry, who is a scientist and what is science a bit too much.
But I don't know the history here. Did people not consider themselves natural philosophers before then? There has definitely been sort of names for this role.
So one way to sort of think about it is that people have always thought about the natural world though, right? So people have always tried to understand how machines work, how nature works, how sort of everything does. And they often did that without ever becoming conscious of the idea that they were doing anything special or that they are playing a special role by doing so.
And, you know, they were able to sort of do it just fine. And one of the things that, you know, at some point that obviously changed, you know, this sort of idea that one is engaged in some sort of a special activity when one is trying to understand nature and uh you know there being kind of a special social role for that like all of that obviously has to develop uh but but it does seem to be the case that you can reach a better understanding of the natural world without it and therefore this question sorry sorry go ahead oh no and therefore there is a question about whether it is actually helpful.
Okay. Well, if the identity of scientist 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.
I mean, clearly, they're not doing construction or building archers or something like like that so so like there is an activity i.e trying to understand the natural world that seems to work better when it is supported uh sort of both kind of that 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 that so i'm not disputing that um there is an activity that is sort of worthy of being supported.

But whether that sort of particular way of looking at that activity is the right one is less clear. Okay, so you do identify there's a special role for universities and they're doing a distinctive activity.
Well, if it's not science they're doing, how would you describe what the thing they're doing is? Right. So, well, okay.
So, so perhaps to illustrate this, right? One needn't, needn't think of this activity in a unified way. So for example, like imagine that we had an institution and then this institution that would be, you know, somebody who was interested in, you know, liquid helium and he 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 would be, you know, interested in, in, you know, the way stars form 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 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 endeavor.

But, you know, that, you know, but now, for example, if one were to just kind of stop there, right, it's not possible yet at that stage, you know, to sort of say, okay, well, all of these people are engaged in this, you know, unified activity, you know, called science. And, oh, are some of them really doing it or not, right? Everybody is just, you know, one person is doing this, one person is doing that, you know, one person is doing the third thing.
So perhaps, I mean, an interesting, right, comparison might be for kind of the particular view that I have.

It's just like, you know, like people have this idea of an entrepreneur, right?

Well, you know, in a certain sense, you know, and all of these entrepreneurs are kind of trying to construct different companies, right?

But nobody is kind of asking the question, well, you know, is any one of these people actually entreprene companies, right? But nobody is kind of asking the question, well,

you know, is any one of these people actually entrepreneuring, right? That is not a conversation that ever arises. So it is in that sense that I think that you can have an institution that supports that activity, but you don't need to understand it in this particular way that

science is often understood.

And so what's counterproductive about the current understanding of science and scientists?

Right.

So one problem with this idea is that the idea of science and scientists comes with this

idea that there is this particular method.

In other words, that one is somehow doing something more other than just being engaged with a particular problem or question and pursuing it wherever it might lead. There is this idea that there is a specific method that one ought to use to think about this particular question rather than just where you know, where, where sort of the, the question naturally leads you.
And I think that that this attitude or this idea can often stop people from doing sensible things that, that, that would otherwise, that, that, you know, that, that would help with sort of pursuing, pursuing their, their problem. Right.
So, 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 that this actually affects everybody or that this is a sort of an across the board thing, but it is sort of an argument that often features.
The current conception of this, therefore, 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 uh which is not a thing you could really do you know where it just were people just sort of thinking about specific issues and what they did was understood in that way um and in general um i do think that like making, you know, becoming conscious of what one is doing and, you know, kind of being and sort of classifying it or telling yourself the story about it is one thing that is known, you know, in several other fields to sometimes lead to problems. You know, hence the term self-consciousness and 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, falsifiability, testability.
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 in institution as to understand the world through a specific family of methods? Well, I would perhaps, funny you mentioned Popper there, because I would actually dispute that premise.
He wrote this, I mean, there is, I think, a very nice set of undergraduate lectures that has been recorded from him 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 he is a professor of a subject that he thinks does not exist his student Feyerabend 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's um it is true that that there are certain i guess patterns of thought that are more conducive to, that seem to at least be more conducive to understanding the natural world than others.

um but i think 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 more of a great mystery than an exact science to put it to put it like that so then 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. Well, I mean, okay.
That's, I'm not sure if that is sort of paraphrasing it exactly as I see it, because it's like this, it is very unclear if one is ever, is ever using a method. 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 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 certain methods are to be privileged and are more productive? Well, I do not exactly have a view on that subject.
For example, there, to be honest, I just sort of don't know. I kind of have various passing thoughts on that issue.
But, I mean, for example, there is this sort of question, there is this sort of narrative about the importance of the Enlightenment. And it's not exactly obvious to me if that is in fact true, or if that narrative is more of a fiction.

And, you know, there are strong proponents for one of that positions and there are strong proponents for the other. And what they have in common, ironically, is that I think that they both sort of agreed that there was something very important about the Enlightenment.
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 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. 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 criticized that idea by 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 possibly really work as, as, you know, you guys are imagining it.
Because for example, I mean, as Hume 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 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 wrote a paper on something called the Popper-Miller theorem. Popper-Miller theorem was a theorem that Popper, that we previously mentioned in this podcast, and David Miller, basically, they published a short letter in Nature in 1983 where they presented this very kind of short paradox where they basically claimed that, the way they explained it was the idea that probabilistic support is not inducted.
That is quite vague, and this was conceded by many people kind of subsequently. But the basic idea is something like, so basically, 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 evidence somehow confers support on general theories.
and figuring out the right model of that support,

of how this sort of support works,

you know, has been kind of one of the challenges that people have basically been trying to figure out at the time.

And one of the ideas was that basically probability is, you know, probability was considered as one of such possible sort of support measures.

And basically, what their theorem aimed to show was that this probabilistic support

that evidence sort of confers on theories,

i.e., 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. And the way they made the argument is that they basically said, they basically identified two propositions.
They said, look, this theory relative to this evidence, like really this first propositions is a kind of a, the deductive part of the theory relative to the evidence. And this other part of the theory is the inductive part of the theory relative to the evidence.
And they showed that the evidence always decreases the probability of this inductive part. Now, there are sort of two, there was a lot of kind of subsequent commentary on this result.
And the main points that people kind of made were, well, you know, the main points of the dispute 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. And then the other issue was just, you know, because there is this sort of vague notion of, of, you know, inductive support and what exactly that means.
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.
But we sort of thought that, that, that that argument is sort of still interesting, we found sort of a couple of other ways of explaining it.

And I think they, you know,

present kind of a very interesting challenge

to this idea of, you know,

sort of kind of trying to use Bayesian reasoning

to either build an AGI or for various other purposes.

And we thought that would be sort of

a very interesting thing to present.

Okay. Did this theorem fit a broader theme in Popper's work? Well, it sort of did, right? So the basic idea that Popper had that I think kind of sort of came out, the theorem I think came out of kind of the same way of thinking about this, was basically just this idea that, so he was interested in the idea of logical content of a theory.
There was this idea that just like you could have this probability measure that you assign to theories, you can assign a content measure. So the idea is that some theories say more than others.
And the question was, can you construct a measure of that kind? And one of the interesting observations in thinking about that measure is simply the fact that kind of the constraints or the rules it has to obey are exactly the same as the probability calculus, basically. So in a certain sense, you can always interpret some assignment of probabilities, right, as really being a kind of a statement of, as he put it, a degree of logical weakness.
So, you know, if I say that one theory is more likely than another theory, you know, there is always this perfectly consistent interpretation where what I'm actually just saying is that, you know, if I say that this theory is more likely than that theory, I can say this theory says less than this theory. That was kind of the idea of it.
And basically, the reason, therefore, he, I think, kind of became skeptical of these probabilistic approaches to knowledge is simply the fact that as he saw it, and I think that there are some reasons to kind of think that this is in fact how people think, 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, and therefore, you know, informative, explanatory, and therefore kind of less likely theories. And if you want kind of an example of the fact that people do seem to think about that way, right, there is something known as the conjunction fallacy that would seem to sort of support that.
So there is this famous experiment, I think it was popularized by Daniel Kahneman in his book, Thinking Fast and Slow, which was, I think, the sort of case of Linda. So in this experiment, you're told about a woman and you're given a bunch of information 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 pick option B, even though the probability calculus kind of tells you that, you know, option A has to be more likely than option B. And so the question can be why that is.
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. And I think that this is sort of a part of a general theme where people really do, you know, sort of look for, and as I said, believe in explanatory general theories, not by, by, not the 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, German and Slovenian are the two that I know, where I think that, like, if you were translate the word for probability into English, it would be something like believability.
And, and I think that, you know, if you interpret probability in that way, sort of, I think that, you know, the believability of explanatory theories is always higher than the believability of these sort of less likely theories.

And therefore, believability isn't really probability.

Okay.

And can you explain why explanatory theories should be preferred?

Well, I'm not saying that they should be.

I do like explanatory theories.

I find them interesting to think about and kind of much more fun to engage with. I mean, I can give you his arguments for it.
I'm not sure if I entirely agree with them, but- Actually, I'm more interested in where you might disagree. Where might I disagree? Well, so for example, he pointed- So there is this interesting question, right? of what exactly is the role of this universal theories? Like why do we have them? Why do we think about them? Why do we try to improve them and so on? And his argument was that people actually, his argument was actually quite psychological.
It was that people seem to have this need for regularity. and you you know, if you put them in an environment without regularity, people kind of go mad or, you know, at least, you know, kind of invent regularity out of thin air.
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 um is is uh is a is a uh kind of worthy of exploration on the other hand i think that 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 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, is that your kind of knowledge of the world is increasing in a way it wouldn't if you just accumulated experiences. 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 discovered it is false.
And another thing that can happen in this process of, of, is that, is that kind of various kinds of truth can accumulate in this, in this general theories that are not present just in the experience alone. And so I get, I'm not sure if this thing that I just said is his argument or something that, or not, but it is, I think, another reason why explanatory theories play such an interesting role in life in general.
I completely agree with everything there, but you didn't explain where you disagree with Popper. Well, I mean, I said that, you know, it's somewhat unclear to me.
This thing that I mentioned about the need for regularity. I'm not sure if it exists.
It's plausible that it exists, but if it does, I don't quite understand how it works. So 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.
What advice do you have to a young person who's trying to be a polymath? Well first of all the first piece of advice is that is that I would give is that you should never take advice from me. The second piece of the second thing I would say though is, it actually relates,

again, this sort of relates to just a particular problem

that I think people are naturally interested in everything.

And it is only through, again,

it's actually very similar to the thing we talked about

at the beginning.

I think that the same phenomenon that happens with the way people think about science sort of happens with learning. So, you know, people learn all their life.
And, in fact, people learn all the time. Like, you interact with information all the time.
It changes you. But you never consciously think of changing yourself by doing that or, you change it.
It's only in very special circumstances 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.
Like, for example, there are a lot of ideas that if you want to learn something, you can't just do it through osmosis. You have to be

very, very systematic about it. And I think that is basically completely false.
I think that,

and again, this sort of leads people in this 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 I need to study the

fundamentals, then the intermediate level, then the advanced levels. And all of these levels are

Thank you. And then there are, first of all, they think they need to study a subject.
Then you think, okay, first I need to study the fundamentals, then the intermediate level, then the advanced levels, and all of these levels are fiction. There is sort of none of that there.
And all of these ideas were actually developed to, they have always been developed to solve a particular problem or advance a particular need. and and I think what is what is you know um most if one wants to just have broad interests, I think the most important thing is to just, you know, pursue whatever you're interested in, not be afraid or think that you can't understand it.
And paradoxically not, not actually trying to achieve any particular change in yourself, but rather just sort of going, going where the story goes. reading history is perhaps perhaps sort of helpful because because um 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 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 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 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 it's no longer relevant to to anybody that reads it or at least not immediately relevant 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 should you just should a young person just be focused on learning what they find it 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 uh 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 get 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 would create a kind of a there is often this idea that often this idea that one could easily create kind of a list of all unsolved problems in a given field and just put it on the internet. And many people kind of think, well, this seems so simple.
Like why doesn't anybody ever do that? And I think that is actually incredibly difficult to do. I think that the kinds of information that you would have to put online is just incredibly, it's very, very unclear how one does that.
And the key thing to realize is that, well, first of all, there really is no such thing as an unsolved problem, I think,

as conventionally understood. There are just a bunch of people and, you know,

like one can form a view that,

that creating something would be valuable to them.

It often won't be valuable to everybody.

It will only be valuable to a subsection of those people.

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, you know,

I've done it. 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, you know, that seems to be a kind of, that is kind of, it's a difficult thing to kind of put online for that reason. um and uh yeah oh interesting so but if you're uh but if you're a 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 think I'm terrible at this. Uh, there are people who I think are i think are are sort of because i i think you know it is very much the case as you sort of said that the whole thing has a bit of a sort of 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 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 are these sort of all kinds of idiosyncratic ways that, that I think this sort of happens and gets solved.
But there isn't anything as it's not an impossible problem to solve, but it does require I think, quite a bit of an experimentation. I don't think I'm the best person at this by any stretch.
But these are, I guess, are just some general thoughts in that. So then young people connecting to mentors who are solving the right problems.
Is this very hard? Is this impossible almost? I actually, no, I don't think so at all. I think that the main problem is just that it is somewhat idiosyncratic, right? So you cannot just sort of give a universal answer.
But I think that it's definitely not the case that the world is hostile to it. I think people are very sympathetic to attempts to do that.
you know and you know as basically you illustrate

I think 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 oh there's tremendous goodwill for young people out there so so that's yeah i have sort of the same impression and uh so so so yeah i don't want to like i think i think one of the worst things perhaps perhaps the reason I sort of bring this up is just because I think people often just lack awareness of this.

They kind of lack the awareness of the fact that that is kind of the main challenge.

Or at least a thing that one ought to do.

And, yeah, I guess for that reason, I think it is sort of worth mentioning.

On that hopeful and optimistic note, Masjass, thank you for being on the I think it is sort of worth mentioning. On that hopeful and optimistic note,

Masjass, thank you for being on the show.

This is very fascinating.

Thanks.

Thanks for having me.

It's been a pleasure.