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Nicolas Gisin on Free Will, Quantum Gravity, Superdeterminism, and Time NOT Being an Illusion
February 13, 2022
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The Economist covers math, physics, philosophy, and AI in a manner that shows how different countries perceive developments and how they impact markets. They recently published a piece on China's new neutrino detector. They cover extending life via mitochondrial transplants, creating an entirely new field of medicine. But it's also not just science they analyze.
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This is a desultory interview in keeping with the theme of the indeterminate and unfolding nature of time. For those who were intrigued by Lou Alessandro's comments on the blurred notion of the present, i.e. his metaphor of the cigarette that burns unevenly, Nicolas Gisson's concept of thick time is the closest I've heard to a rigorous account of it.
Nicolas Gisson is a professor at the University of Geneva working on the foundations of quantum mechanics and quantum information, both experimentally and theoretically. In this episode, we talk about the existence of free will, the indeterminacy of reality, and the unreality of the real numbers. Nicolas is one of the world-renowned experts in quantum theory, and we're extremely grateful that his first podcast appearance
is on the Theories of Everything channel. Thank you, Professor. Click on the timestamp in the description if you'd like to skip this intro. My name is Kurt Jaimungal. I'm a Torontonian filmmaker with a background in mathematical physics dedicated to the explication of the variegated terrain of theories of everything.
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I'm also interested in the topic of free will. That's why you're here. I was speaking with a professor of the philosophy of mathematics who referenced me an article of yours quite some time ago. And ever since then, I thought, okay, I want to speak to this person, but I didn't have a reason to but now I do. So thank you.
So which paper is that? Do you remember? I don't remember. You had the Baker map and you were showing that there is indeterminacy with classical laws of physics and you don't need quantum mechanics to have that. I don't recall exactly. Okay, so it's not very old. Yeah, yeah, I know. I know which paper it is. From what I gathered, I've been watching plenty of your talks recently, plenty and plenty of them, and even I went through your book, which is almost a decade old now called Quantum Chance, which is a wonderful book, delightful book. Most books about physics are
or can be intimidating to someone who's not familiar with mathematics. But this book was so winsome and childlike in its curiosity, instead of Bell's inequality, you have Bell's game. You give the reader the impression that you're not speaking above them. Just changing Bell's inequality to Bell's games, it's a delightful conceptual shift that makes it much more lucid for those who are ordinarily intimidated by mathematics.
You know, the subject, I find the subject fascinating. I mean, that's spent my life on quantum physics, quantum chance, and so on, indeterminacy. And I wanted to allow everyone to share that fascination. So without mathematics, indeed, but also without hiding the conceptual difficulties. It's not trivial these things. It's a major change in our worldview.
So it is, I wouldn't say it's an easy book, but the goal was indeed to allow everyone who is willing to make an intellectual effort to be able to share some of this fascination and gain some understanding of why physicists are so excited about Bell inequalities, games and indeterminism and so on.
Even something as complicated sounding as a quantum random number generator, which to many people they're like, well, firstly, what is random? And then it generates numbers and is quantum on top of that. Well, you explain it's just a beam splitter and just think of it like zeros and ones on each side. It's a splendid explanation of what's customarily complicated. Yeah. And actually what is even very nice here. So, you know, there is all these conceptual issues that you just mentioned, which are not trivial.
can make it relatively simple, but not completely trivial, certainly not. But it goes all the way that now actually this startup company from my university group IDQ, they may put everything into a little chip, which is just a few millimeter in size. And it's also low power consumption. So it's a quantum random number generator that actually is used by Samsung in some of their smartphones.
Have you done much thinking about the nature of consciousness? I know that you've spoken about free will and time and indeterminacy. Consciousness, no, you know, I'm a physicist and not a philosopher. So even about free will, which is certainly something which I think is an important concept, but it's not a concept of physics. So, you know, and consciousness
Maybe I should indeed warn you and everyone listening to this that I'm not a philosopher. I don't claim to be a philosopher. And I certainly claim that consciousness, free will, the mind or things like that,
fascinating concepts. We all know that we have that. But these are not concepts that belong to today's physics, possibly not even to future physics. From what I gathered from my research into your views, your philosophy, so to speak, you see free will and indeterminacy as not tied. Now, is this correct? Why is it so?
I'm sure you know the ordinary view, or not the ordinary, I'm sure you know the common view in philosophy, and even in physics, some people who dabble in philosophy, who are physicists, think if you're going to have a notion of free will, it's predicated on indeterminacy. Yeah, so I'm certainly not a compatibilist. I don't really understand how one could claim that the future is already given, is already determined by the present, and nevertheless, we have free will. I think that's a more
a game of words. So indeterminism is necessary, but indeterminism is certainly also not sufficient because free will is also not just randomness. We don't want to make random decisions. So it's much more complicated. Never determinism or pure indeterminism is sufficient to explain free will. In this sense, again, free will is not part of today's physics. And I would probably go even further and say that
So I'm now going to give some arguments and so on. And everyone can then buy these arguments or reject them. But in order to buy or reject these arguments, you need some free will. So somehow you need free will to start arguing, to start doing philosophy or to start doing physics. So probably the best I can say about free will is that is a prerequisite
In order to start arguing, so in particular for philosophy and science in general. When you say that free will is necessary in order to choose between truths, in order for you to say this one is true and not this one, then it sounds like you're tying free will to reason, is that the case? Or to rationality? To rationality, yes, absolutely. Now it's not a matter of being true or not true, you know, I mean you may
buy an argument or not, and you may even change your mind in course of time. But you need to be able to decide, yeah, now this argument that I just listened to is convincing or no, this is not convincing enough. I'm not going to change my mind because of that little argument. So you need to make decisions about what kind of arguments you're going to buy and which one you're going to reject.
I have a quote from you which says, free will comes first in the logical order. Indeed, without free will, there's no way to make sense of anything. And in particular, there would be no understanding. Remember, earlier in the conversation, I said, I'm interested in the notion of time,
Maybe not exactly. I've read many things from Penrose, so probably it's maybe in the back of my mind. But indeed, I mean, absolutely correct. I mean, free will, in my opinion, comes first in the logical order.
And because of that, you know, physics or science or psychology, whatever, cannot argue against free will, because it rests on free will. Yes, then now let's explain that because even to me as someone who has been looking into this, I found that to be a new notion. I didn't encounter that before. So firstly,
How did you come to that conclusion and then can you explain that conclusion?
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I was thinking about free will and randomness and determinism and passage of time ever since I was a teenager. And so I don't, there's not really one point in time when suddenly, aha, now it works. So it's really something that evolved. And at some point I was invited to a conference to deliver a talk, of course. And the conference was actually about time.
I was a bit surprised to be invited but okay I thought this is really a good chance and so I went to it and I had of course to prepare myself and that's actually when I started really formulating these ideas a bit more in a more articulated way like you know stating that free will comes first in the logical order there is no understanding without free will and so on but then also when I
During, I think it was during that conference, some colleagues mentioned in particular, Chris Fuchs mentioned to me that there is an old unknown, essentially a French philosopher, Le Cuyet, who actually had very similar thoughts. He was, Le Cuyet was also very much influenced much more by myself, certainly by religious beliefs.
So God was his problem. How could God know everything and me still having free will? That's the old version. Is it a pre-Scientist version of the free will debate? And L'Equiel came to the similar conclusion as myself, but of course centuries before, saying that actually free will comes first and without free will we cannot even start this kind of argument about God having
Now, let's explain what it means that free will comes first in the logical order.
and don't have any free will, whether this argument is going to resonate is a purely, let's say, mechanical stuff. You know, if I hit my table here, whether the table is going to resonate is just a matter of the mechanics of the resonant frequencies of this table and so on, and how I hit it and so on. But for an argument to resonate,
In me, it's I think not just a matter of, I don't know, it's not a mechanical question. Some arguments are convincing, some of us are not convincing. And again, that may change in the course of time, you don't need to always be convinced by the same argument during all your lifespan. So there must be something more. And this something more is actually what we name free will. This table has no free will.
doesn't decide to resonate to my hitting it, while you and me and everybody listening here and so on, they may find for instance now my argument in that it resonates to them,
Or that they are willing to buy it, or at least to consider it, or on the contrary, they will just reject it. But whatever they do, it's a free decision. It's something that depends on them. I don't think it is just a mechanical consequence of their bodies and their brain and so on.
So the way that I understand it is if I was to make a bridge resonate, I throw wind at it and then it wobbles and that's a physical process. Now, if I throw an idea at you or you to me, if it resonates with me, we use the same word resonate, but we just mean, well, we use the same word resonate. That is dependent not on the physics, but on free will. Exactly. I think that's correct.
Of course, I know that some people will say, no, no, this is a purely physical phenomenon. We don't, I mean, we, first of all, don't exist. Everything is just pure physics. But I think going that far first assumes that physics really explains everything. It almost assumes in between the line that today's physics is close to an end, which I consider ridiculous.
Yeah, and I think it bypasses the beauty of life, the beauty of human beings, including animals, of living beings. What do your colleagues say to you when you say, well, perhaps physics doesn't explain everything. The reductionist account, including our actions, it goes from our actions to our neurobiology, to the chemistry, to the physics. And that's it. Physics, that's it.
Again, here depends where we are talking about today's physics or even near future physics or physics in general. Science is not at the end and will continue to develop and there will be new ideas and completely new things which will be totally surprising to today's physicists like quantum mechanics and relativity are completely foreign to 19th century physics.
So there will be more revolutions and so maybe there is one thing which seems pretty clear is that today's physics doesn't explain free will, consciousness or things like that. Could it be that future physics explain it? Certainly not near future. Now what is really the very far future of physics or science more generally? Of course I don't know but my claim is that free will being
First, in the logical order, physics or science more generally and philosophy will never be able to fully explain free will. Of course, we can explain part of it. For instance, today we understand much better, I find in the 19th century, the difference between hardware and software. And this distinction
which is very common today. But this is a useful distinction to study and to think about the brain as just being the material part and maybe based on software, whatever that exactly means and things like that. But at least we can start articulating ideas thanks to this distinction between software and hardware that were completely unthinkable 200 years ago, 150 years ago.
So we can also expect that in the future there will be new concepts that we master or that the future scientists will master and that will help better articulating the problem of free will and consciousness and so on. But I don't think we will ever come to an end in that. Free will will somehow, some essence of free will will always remain
There are many colleagues, and I would say the vast majority of the physicists just don't care. They are not going to listen at all. They just don't care. Now, among those that care, they care after a few beers, usually.
Most of them which then, I don't know, they would listen to what I have to say, they would not necessarily agree. Okay, some have very strong opinions, they are strongly compatibilist, but they really thought about it. That's okay. And I guess we also quite a lot and I have already experienced quite a lot of my colleagues who are happy with what I'm saying.
But you know, the happy is a small minority. The seriously unhappy is also a small minority and the enormous majority just doesn't care. And why do you think the majority doesn't care? It's too ill-defined, they'll say? Yeah, it's too ill-defined. I don't exactly know how they cannot care about such important and deep questions.
Maybe we just think that, you know, they have not been trained in that. They don't feel competent in this respect somehow. Probably also if some of my colleagues I tell them about some subtleties in biology, they may also just say, oh, I don't understand it. It's outside my field of competence. Actually, nowadays we get so specialized that you don't even need to change field and go outside of physics for not understanding what the colleague is saying.
Do you think what governs free will is mathematics or you think it's something completely different? And this goes back to our reductionist account. Okay, yeah, mathematics. We should talk about mathematics and determinism. But no, I think
Mathematics again, especially today's mathematics has very, very little to say on, probably nothing to say on free will and consciousness. The reason I say that is that when one says, well, it's first in the logical order, the way I'm thinking is of the traditional reductionist view. And you go down and down until you get to physics. And then sometimes people encapsulate physics into math.
and then if free will is first well then free will is prior to math is that the correct way of looking at it as these nested sets or is that different i shouldn't be thinking about it like that i don't think you should be thinking of nested sets mathematics is i guess it's really a kind of different branch of uh of science and of understanding um
And again, mathematics, in French, we say the mathematics, it's really a plural. And indeed, there are different sorts of mathematics, you can really think of mathematics as kind of, you know, this purely platonistic view where there are these mathematical objects existing, you know, outside of time, outside of the physical world.
They just have their own existence with their own rules. I'm probably not prepared to really argue how these rules depend on the axioms in principle. But there are quite a lot of basic things like the integers, for instance. The integer 5, does it exist by itself in this Platonistic world?
I guess that's the view that most mathematicians would approach, would admit. But there are different sorts of mathematics. You have also mathematics where people were more thinking in terms of that the mathematical objects would themselves be processes that develop and evolve in time.
The best example here is intuitionistic mathematics that was mostly developed by Brouwer about 100 years ago. There are still today some people developing this form of mathematics that come under the general umbrella of constructivists. But in this specific form of constructivism called intuitionism,
you really have that already at the mathematical level, even numbers, like what we call real numbers, are really evolving in time. And then if mathematics includes that kind of and needs the concept or introduces the concept of time already, even at the level of numbers, then that makes this sort of mathematics much closer and possibly better suited for physics or for science in general.
So when you say mathematics, it's not clear what you mean. Many of the people watching don't know what constructivism... what is it? Constructionist? It's not constructivism, is it? Well, the physical... Social constructivism and social constructionism. I don't want to mix that up.
I know intuitionism, and I've always seen intuitionism as the same as the constructionist view in mathematics, but you just said that intuitionist is a specific subset of constructionist. What would be an example of a constructionist that is not an intuitionist? Hear that sound?
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and period is done, or is it enough to have a rule that tells you how the process of constructing these objects develops in time? So somehow they are never finished, there are at least some of these processes that will never finish, so they evolve in time, and that's then intuitionism. So intuitionism, the intuition is that things can evolve in time,
admittedly Brouwer, when he developed that, he was thinking about, you know, you may define a number depending on some mathematical conjecture and depending how this conjecture will turn out, you know, true or false, the number may be zero or one, let's say. And so the number is undefined until this conjecture, this specific conjecture is solved.
But that brings now mathematics or this form of intuitionistic mathematics very much to what human are able to do, prove or not prove this conception. While my understanding and other people's understanding of intuition is just that as time passes, new information gets created continuously and hence a number may evolve according to this new information.
So the standard view in mathematics is classical mathematics. And that is to say that we're discovering it and it's timeless. So the Pythagorean theorem is timeless. We just found it and it existed before humans. Now, Brouwer would say, well, it didn't exist until we discovered it. And then Brouwer was a type of intuitionist, but that's a bit too anthropocentric. So we say now, well, there's still intuitionism. It's just that the universe itself reveals new information. Exactly.
It is correct. But of course, about the Pythagorean theorem, once it is on the table, there's nothing more to add on that. But you can imagine just a number that starts as a zero dot, and then you have all the digits that come afterwards. And some of these far away digits may not yet be determined. But as new information gets created, these far down the series,
You should know that the audience for this is generally upper year undergrads in math and physics. So for them, can you explain how indeterminacy arises in classical physics? Like a few arguments and you can also outline your views on the real numbers aren't real and so on because those are tight. Yeah, it's all connected indeed.
So very important to understand first is chaos. So in classical mechanics, you have Newton's law and all that, and you may use Hamiltonian's equation, whatever the equation that you learn at school and university. And usually one then gives some examples, and the examples will be a harmonic oscillator, you know, just a kind of pendulum that oscillates very regularly. Or you may have, I don't know,
a star, a planet orbiting its star, like Earth orbiting the Sun, which again is a very, very regular motion. But actually, when you look at all the possible configurations of these matter particles, you notice that almost all, actually with probability one, the system that you're going to consider actually is not regular, but it's chaotic. And by chaotic, it means that's the
the future of this set of particles depends super sensitively on the initial condition. So you take an initial condition, which is usually defined by a real number. I know you change the digits number 1000 or 1 million, whatever. And of course, initially, you don't see any difference if you let the systems evolve.
But if the system is chaotic, pretty quickly, the system will evolve completely differently, although you have only changed the digit 1000 positions down the string of digits. And then comes the question, is that still a deterministic system or not? So first of all, obviously, it is not deterministic in the sense that you cannot control all these digits. It's beyond our technology.
But see, you can now go more on the ontology side. Does this 1,000 or 1 million digits really exist since ever? And hence, this chaotic system actually evolved in a fully deterministic way. We don't know which way, but it is deterministic. Or is it the case that this billion for million digits actually is undetermined at time t0?
and hence the evolution of this chaotic system will be also undetermined. As time passes, this digit will get determined, gain a determined value, but initially at time t0 it has no determined value. And if you think like that, so if you replace classical mathematics by intuitionistic mathematics, you make the same predictions, statistical predictions anyway,
But very importantly, with intuitionistic mathematics, you see that a chaotic classical system is no longer deterministic. It becomes indeterministic, although it is classical physics still, although the equations are still Newton's equations and all that. And so, indeed, I like to argue that is, first of all, that it already shows that just by changing the mathematics,
Contrary to what we learned, there are more than one mathematics. And if you go to another form of mathematics, you don't change the prediction since all the empirical confirmation of physics remains. But instead of presenting you with a deterministic worldview, the same theory, Newton's theory in this case, classical mechanics, presents you with an indeterministic worldview.
So you see, it's really, you can choose, you can use your free will to choose where you prefer one or the other, but it's not the facts that are going to choose for you. And then there's one more argument, which I like to put on the table. You know, a real number, a typical real number, you know, this integer dot, and then all these digits that contains actually an infinite amount of information, because the series of digits, they typically contain no structure at all.
It's not like one third. One third is zero dot and then you have only three, three, three, three that just repeats itself. But a typical real number will have no structure at all. And that means that if you want to describe it, you have to give everything, every, every digit. Hear that sound?
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Go to Shopify.com slash theories now to grow your business no matter what stage you're in Shopify.com slash theories. Infinity many digits. So that's infinitely many. It's an infinite amount of information. I know if you think that's, you know, you make the assumption that in a finite volume of space, you have only a finite
amount of information. We cannot pack infinite information into a finite volume. Then the natural consequence of this assumption is that if you have now a beard ball or anything in your small volume, finite volume, the center of mass of that or any other degree of freedom cannot be faithfully described by a real number, because if it would be a real number you would have to pack all this infinite information into your finite volume.
From that I concluded, and I have a paper with this nice title, real numbers are not really real. These real numbers were called real by Descartes for historical reasons, and we still use this terminology of real numbers, but if you look at them from a physics point of view, they're not really real.
Usually people who say that the real numbers aren't real are a fan of digital physics, but there's computation underneath and the laws of physics are computation. So Stephen Wolfram, for example, do you subscribe to this? Not entirely. I guess in part, yes. But what I add to that, what I think is important to add is really this idea that these numbers are evolving in time. So you still have, for instance, the continuum.
Wolfram would not have the continuum in this sense but with intuitionistic mathematics you have these numbers evolve and so this digit which is initially undetermined will get determined in proper time and so the yeah first of all if this digit becomes very important let's say in a week time because it would determine the weather in a week
It cannot be that the weather, in one week from now, the weather will be determined. It will be sunny or rainy or in between, but it will be something. So at some point in time, these chaotic systems, they must settle down, they must get determined.
It's not enough to have some granularity in it. You need that they settle. And in this sense, I think that intuitionistic mathematics is an appropriate language, mathematical language, to describe this idea that although things may not be determined today, the weather in a week time from today is not yet determined, but it will be determined in a week time.
How do you get from this intuitionist view to the view that time is thick, that you can't pull out a single point of time? It's much like molasses. Yeah, yeah. Okay, the argument here is, if you have, let's say, imagine two processes or two numbers that initially are exactly the same, but they evolve in time. And maybe after some time, they may split.
these new information that gets created as time passes may be different and so these two numbers at now or even in the near future we can just not distinguish them because so far they are exactly the same but they may become different and so somehow you know these numbers they are they stick together they are a bit like yeah yeah this this last that you cannot really
or honey, you cannot really take out a molecule of honey, they stick together. And these numbers also kind of stick together. And that's where the intuition of this thick time in intuitionistic mathematics comes from. But I'm not really... Okay, I don't claim that I have a full understanding of time in intuitionistic mathematics, let's say.
Can you give an example more simply?
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So they still stick together. Although they are different in the sense that as you said, I mean, in a second or maybe in a day, it will be 2.001 for one of them and 2.005 for the other. So they clearly are different. But nevertheless, today they stick together. Ah, okay. So time gets increasingly more specific. I mean, sorry.
Is it? It's not. I don't think I said that correctly. So correct what I said. I said time gets increasingly more specific, but it's more like the quantities that we're measuring it or the quantities that exist get more specific. Exactly. The quantities that exist get more specific or I would use the terminology, they get more determined. I'm trying to understand. How is it that the present is thick? So you're saying the present is thick because it then fractionates later. And that means that any moment in the future is actually less thick than a moment in the past.
No, I don't think so, because it can happen again in the future, even once it's 2.001, let's say it settles for 2.001, but you still have the same kind of thickness for the next digit. Ah, so they're all equally as thick. It evolves forever. Okay, and they're all equally as thick because they're all just indeterminate at the last digit, whether the time is T010. Okay. Yeah, if you want to be more precise, it's not a matter of the digit, it's really additional information.
But never mind, the intuition is good with these digits, yes. Many younger people especially don't know about intuitionist mathematics. They don't even know that there's a difference in mathematics. They just think it's classical mathematics. So I'm going to outline some of how, and I'm going to place a slide of yours up on the screen, how indeterministic physics and intuitionist mathematics map onto one another.
Yeah, probably. Yes, yes, yes. And there's a paper in the philosophy journal Sintesa that appeared, I think, last summer, I think, which is indeed an indeterministic physics and intuitionistic mathematics. Something like that is the title.
Maybe you can just give a give a link to that. It's not a difficult paper. Great, great. I'll give a link to that. Now the future is open in indeterministic physics, that gets analogized or mapped on to or made equivalent with the law of the excluded middle not being there. Okay, so firstly, can you explain what the law of the excluded middle is? And then why the heck that means that the future is open?
Yeah, so this law of the excluded middle says, so it's a part of, let's say, classical logic, classical mathematics, that says that every statement, every proposition, is either true or false. It cannot be something else. It's either true or false. So if I'm now saying it will be raining in exactly a year time in Geneva, in my garden, let's say, this statement, according to classical logic, has to be either true
I mean, for sure it will rain, or it is false, and then for sure it will not rain. Of course, I may be ignorant about whether it is true or false, and for sure I'm ignorant about that, but the fact is that this proposition has a true value. Consequently, the future, because my statement, my proposition here is about the future, but if now this proposition has a true value, it means that this future somehow already exists, or at least is already determined.
Let's determine this. Now, if I want to have a different view, saying that this weather in a year time, not only do I not know whether it will be sunny or rainy, but it is truly undetermined. It's not yet settled whether it will be one way or the other. And then it means that a proposition about this future weather is neither true nor false.
It takes a third value, and this third value is just indeterminate. Indeterminate, sorry, indeterminate. So you have now a new sort of logic, which is no longer with two values, it has this third value, but the third value is not, I don't know, 50-50 or gray, it just says it is indeterminate. And this is certainly part of intuitionistic mathematics,
You made me think of some personal questions. So this young Nicholas, when you're sitting and philosophizing about the nature of time and indeterminacy and free will, etc.
And you meddled, you meddled with mathematics at the logical level. So there's different types of logic. Mathematics is based on logic, classical logic and intuitionist logic. Did you meddle so far outside of intuitionist logic, such as grand priests, paraconsistent logic or other forms of logic? Or have you settled on intuitionist and why? Well, so actually the situation is following. I was
Okay, thinking about that, and indeed the young Nicolas was already thinking about randomness. I think it's a super complicated concept. And I don't remember now, let's say five years ago, I was writing a paper that appeared in another philosophy journal, their Kindness. That's the paper which has the subtitle, real numbers are not really real. And okay, and so when at some point I presented that at the conference,
And one of the participants, Carl Posse, who is actually a professor of philosophy and logic in Jerusalem, mentioned to me this intuitionistic mathematics. So I didn't know intuitionistic mathematics, but clearly what I was at with my real numbers and it's really real, I was somehow rediscovering intuitionistic mathematics, trying to reinvent it.
Of course, I didn't went as far as all these people doing that. It's an entire community. But so then thanks to Karl Posse, I learned about it and he taught me about it. And it's not difficult to understand because it really just corresponds quite closely to my intuition about how things are going. And so I understood it. And then I wrote this other paper, the Synthese one about indeterminacy.
Hear that sound?
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Sign up for a $1 per month trial period at shopify.com slash theories, all lowercase. Go to shopify.com slash theories now to grow your business, no matter what stage you're in shopify.com slash theories. You know, we all think, we all, many of us think, you know, a real number, you get all these digits and then, you know, we can think of the other digits. They come one after the other.
And they come one after the other in time. You know, one is here, then it comes the next, then comes the next, then comes the next. But actually, proper classical mathematics says something very different. Proper classical mathematics claims that a real number is this infinite series of numbers, of digits, this infinite amount of information that comes all at once in zero time.
So when you say let x0 be the initial condition and x0 you assume it's a real number or even a bunch of real numbers if you have many degrees of freedom it actually means let there be instantaneously infinite information and that's an enormous assumption and I don't think most physicists really think that way they really think okay there is this number and there are some digits and then well who cares anyway but
These numbers, these digits, they come really one after the other, and now we say one after the other in time, and then you have intuitionistic mathematics.
Part of the reason why many physicists don't have much of a trouble with real numbers is that I don't think they think in terms of a billiard ball carrying its position with it. If it carried it like on a piece of paper on a sticky note, metaphorically, it would create a black hole instantly, typically, unless it's because the typical real number has infinite. Okay, so then the way that you've explained it to me is that you imagine it like the
electron or the billiard ball does carry with it its position. Is that still a metaphor or is that meant to be taken more literally? If it's just the center of mass of course then it depends on a reference frame anyway but you could imagine the kinetic momentum or you could also imagine just you have a molecule or you have a little system with more than one particle and then the relative
degrees of freedom, you know, the distance between a planet and its sun. This is really within the system, the system being the global thing. And then you can really think, I mean, then it makes sense to think that these relative degrees of freedom are really represented by numbers carried by the system. It's really internal of it. Now you may say, okay, it depends if I'm measuring that with miles or kilometers or whatever.
But that is indeed where if we think in terms of the amount of information, it's the same. Now, if I really think in terms of the digits, of course, if I change my units, the digits will change, but the amount of information will in both cases be infinite.
Okay, now getting to the reality of time, again, the commonplace view in physics is that arrow of time is an illusion. In fact, time itself may be an illusion like Carlo Rovelli suggests, because the laws of nature as far as we have are symmetric, except for the second. Do you see the second law as being what engenders the arrow of time, or you see it as being so much more fundamental? It's more fundamental, it comes already in the basic mathematics. In the basic mathematics, we don't erase
information, we create information as time passes. So the direction of time is already built into our mathematical language. And I think, again, that comes much closer to the intuition that everyone has. Of course, if you learn too much of classical mechanics or quantum mechanics with the Schrodinger equation, you may get the feeling that because the equations are time reversal, then time is an illusion.
That's because you use classical mathematics to describe the initial condition for these evolution equations. If you just use this different form of mathematics, then even if the equation has still the symmetry, the initial condition no longer has that symmetry.
Something I'm extremely excited about exploring on this channel are different approaches to quantum gravity. And you said in an offhand statement, you said, I think we need a different understanding of time in order to make a breakthrough in quantum gravity. Please explain that. Yes, yes. Yeah, so indeed. So quantum gravity, that's of course a huge challenge and a very little progress in the last decades.
Okay, maybe I'm going to annoy a few of my colleagues, but I don't think we have made any breakthrough. I think that's a fair statement. To be fair, professor, almost everyone has a variation of that statement that we need a new understanding of X in order to make progress in quantum gravity, whether we need a new understanding of space, we need a new understanding of strings, we need a new understanding of holography. So why time? Okay, good. So why time? So time plays a completely different role in relativity, so gravity, and in quantum mechanics.
In relativity, I mean that the usual picture is this block universe where everything is kind of frozen since ever, forever, and there is no present. You have to add it by hand. And even Einstein was a bit concerned with the lack of the present. In quantum mechanics, at least the standard view is this indeterminacy. On the beam splitter with the two detectors, for instance,
And so there is clearly a process going on. Before the photon hits the detector and gets localized in one or the other detector and there is a time after it has triggered one and only one of the detectors. So there is clearly a passage of time there. And now we have these two basic theories which
they fundamentally disagree about what time is and then how do you want now to develop a dynamical theory of quantum gravity if we don't even agree on what time is and whether this is you know whether the passage of time is a real phenomenon as in standard quantum mechanics or is it
just the kind of illusion us in the block universe presented by relativity. So I think this is really a fundamental issue and we need to be able to, if we want to do quantum gravity, we need to have one concept that is going to unify that. I know I wouldn't say that I have solved the problem, I mean, certainly not, but my hope is that my
Introducing indeterminism also in classical pre-relativity mechanics, so Newtonian mechanics, but I have already introduced indeterminism there, so somehow I have brought at least classical mechanics and quantum mechanics closer together. I have also one paper on the indeterminacy is relative, so going one more step in the direction of relativity, but okay this is maybe it's
I don't think we should enter that kind of debate anyway, it is still under development. But the goal is indeed to bring also indeterminism to relativity. Professor, whenever you speak, I have so many questions that are there's so many that come to my mind. Okay, so first, do you have an idea as to the discretization of space and time? Do you think it's discrete? Okay, let me just be fair, I don't know.
The way I describe time in this, well, like all the others in intuitionist mathematics, it is discrete. Is it fundamentally discrete? Is it a technical problem today? I don't know. Also, you mentioned that you were similar to that philosopher, which I forgot the name of. I know William James was influenced by someone who published that person's work because that person died young. Yeah. So, okay, the guy I mentioned before is Le Cuyet.
Jacques Lecuyer, I think. And then there was indeed a person in between Lecuyer and William James, and that's Renouvier, I think. Also a French philosopher. The first one I'm not going to even try to pronounce. Now that person, Lecuyer, so I tried to pronounce it, Lecuyer, was spurred by a religious instinct, or these religious questions. You mentioned you feel similar to him, so I'm curious about your religious views.
Well, okay, in some sense, I'm certainly not a religious person. So I never go to church or things like that. My children are not baptized and so on. But you know, the fact that I spent time thinking about free will, consciousness, time, you know, it's really taking physics, a stretch maybe physics a bit beyond the
standard physics to go in the direction of philosophy. And I mentioned already two of my papers in philosophy journals. Actually, I have very little publications in philosophy journals. I think I have four of them, if I remember well. So it's very few compared to the numbers of papers I have in physics. So I'm mostly really a physicist, but I'm a physicist with a kind of, I like kind of broad view. And by that, I mean that these questions are important to me.
Now you may say, okay, is that a religious feeling or something like that? I'm certainly not following any, you know, book, religious book or things. Yeah, no. Okay, let's talk about Sabine Hassenfelder, who says that the idea of free will is both incompatible with the laws of nature and entirely meaningless. Okay, what are your thoughts on that statement? Yeah, so I know Sabine.
and I use actually, so she does a lot of these videos and I love most of them. Now she has one indeed on freewheel and actually I use that one when I give some of my lectures to illustrate how extreme some physicists, including very good physicists, can become. And indeed in this video Sabine goes really a very long way and
claiming that if you believe in free will you are denying science. So she's really claiming that actually science has answered the question in the negative, there is no free will. And this is, in my opinion, a clear overstatement. It's taking physics as a religion somehow, and it's physics with classical mathematics. Again, we just discussed that.
It's pretty strange that Sabine Ofenfelder makes that kind of mistake because one of her books, which I like very much, I think it's called Lost in Mathematics, actually says we have to be careful, we the physicists have to be careful not to overestimate mathematics. In high energy physics, people try to
to guess the future theories just by the beauty of mathematics, by symmetries and elegance and things like that. And so she says, no, but maybe actually the correct mathematics of the next physics theory will not be as elegant as we think or would like it to be. So, okay, that's a reasonable argument. And I certainly buy that argument, but then herself
takes classical Platonistic mathematics of the truth. And because Platonistic mathematics considers only objects, mathematical objects that are outside of time, it's a timeless language, classical mathematics. And so when she concludes that time cannot exist and that everything has already to be settled. So she also believes strongly in super determinism.
You know, everything is already determined. There is no quantum randomness. Bail inequality violations can be explained by super determinism. And yeah, at least she's very consistent that I certainly grant her. But when she claims that science has proved it, for instance, that free will is an illusion, she goes too far.
She goes too far by taking mathematics too literally. Can you quickly outline to the audience what super-determinism is? Perhaps what you dislike about it? Well, actually, there are two things that I dislike. Firstly, it's already determinism. Let me come back to that. The entire future, like the entire past, everything is already determined. It doesn't mean that we know it or it doesn't even mean that we have any ability to get that knowledge.
ontologically, fundamentally, it is already determined. That's determinism. Now when people say super determinism, they add an extra little assumption, namely that everything is coordinated. Because you could still imagine that this part of the universe is entirely determined, that part is also entirely determined, but they are not yet connected.
So we are still independent systems that exist in the world. Now, if you also reject the existence of independent systems, then this is super determinism. Some other people would probably say that the super of super determinism means a kind of conspiracy, because when these different things not only need to be already connected, so not
independent, but they have to be not independent in a very specific way, for instance, to explain the violation or the apparent violation of bail inequality. So I certainly dislike completely the idea that there exist no independent systems in the universe, and actually my view is very clearly, I mean, physics has to be able to tell stories. Physics should make predictions, we all know that, and predictions of course should agree with the experiments,
But physics is not only about sophisticated theories, physics is also about telling a story. When you go to a class or if you teach, you never start by writing an equation, you start by telling a story. For instance, most people know that
The tides are due to the moon that attracts the water from the ocean and so on and so on. And you don't need an equation for that story. So the stories are super important in science in general and also in physics. But there are no stories without time. You need to be telling something in time. An event takes place in time. That the moon attracts this water is something that takes place in time.
If you remove the time, there is no story any longer. And how does time come in? For me, time is very, very much connected to the actualization of potentialities, as Aristotle would have said, to the fact that there is new information created during the course of time. So it has to do with indeterminism. And also that already explains you why I think if
Earlier in the conversation, you said indeterminacy is a necessary condition for free will. It's not sufficient. However, any indeterminate theory can be made determinate with supplementary variables. We can talk about that just for people who are wondering what that means. And then similarly, a determinate theory can be made indeterminate, so they're equivalent. And thus, is determinacy truly a necessary condition for free will?
The way to make an indeterministic theory deterministic is by adding variables. The trivial way of adding variables is just to add all the future results of all future events or future measurements. It's a trivial way of doing it, it's not very practical, it's not very useful, but obviously you can always do that. Somehow maybe one could say that instead of God playing dice when an event happens,
God played all dyes at the initial condition at the Big Bang and coded all this information of all these dyes that he played initially, he coded it into the initial conditions, the initial conditions of you know these real numbers that contain all this information of all future events or in Bohmian quantum mechanics it's a similar idea you have
So you can always do that, but you don't want just to be able to do it. You want to be able to do it in a faithful way. You want to describe nature in a faithful way. And adding the result of future measurements
When I was speaking with Carlo Rovelli, he said there are two interpretations of quantum mechanics that he feels like are consistent, relational quantum mechanics, and then the many worlds. Of course, but he doesn't like the many worlds interpretation, so he chooses the relational one.
Now, from my understanding of your views, there can't be a wave function of the universe, because this can't just simply evolve in time determinately. Is that an incorrect way? Correct, correct. Okay. Now, does that mean that you don't believe in the many worlds interpretation? No, not at all. I think that's quite an empty concept. And I think the explanatory power of many worlds is essentially zero.
again it's again one of these things which is super deterministic you know there is the initial wave function of the universe and then everything evolves according to that and there is never any event that happens nothing really happens it just is this unitary evolution which is an enormous rotation in this gigantic Hilbert space so I think that there's nothing happening there you cannot tell a story here no no so so my view I'm much closer
I'm not claiming that I have the solution to all these problems, but my feeling is much closer, my heart is much closer to a spontaneous localization theory, so stochastic evolution of the Schrodinger equation. And so in this way also, as time passes, this Schrodinger equation, this wave function gets added additional information
bit like my numbers for classical mechanics and as time passes this additional information that gets added to the
I won't keep you for much longer. I know that you probably have to get going soon. So I'll just ask a couple more questions. Now, going back to when you were younger and your little Nicholas was philosophizing in his armchair and you dabbled with different logical systems. So we talked about periconsistence and intuitionist. Did you dabble with questioning even if logic should be the basis of mathematics itself?
Well, when I did my PhD in Geneva, indeed a long time ago, my PhD advisor, Professor Piron, was actually a guy working in quantum logic. I don't think himself really believed in quantum logic, but there are many people around and so we had visitors who were really
thinking of this quantum logic and that by changing the laws of logic, we could make sense of better sense of quantum mechanics. I don't think that this is an interesting approach. I think that that's okay. No. So my answer to your question is no. And again, this is so I'm rejecting the law of the excluded middle.
essentially about propositions that concern the future. You know, my bicycle, now you may ask, is my bicycle on that side or on that side? Well, maybe I forgot. Actually, I know, but I suppose I forgot. Even if I forgot where my bicycle is, my bicycle is definitely either there or there. It's not in an indeterminate position. Now, if you ask me, where will my bicycle be in a weak time?
One of my favorite ways of showing that classical mechanics has indeterminacy built in it is Norton's Dome. Have you heard of Norton's Dome? Yes, yes, I know that. Yeah, well, but this is, okay, it's a very nice example that shows that indeed you may have initial conditions that don't determine the future of these dynamical systems, but you need very specific
dynamical systems. You need this dome, that's why it's called a dome, in such a way that if you have a particle coming to that dome, it will, okay, if you don't throw it hard enough, it will just go up and back again. If you throw it too far, it goes over it and goes to the other side. So there's precisely an initial condition, an initial velocity, such that it will stop at the top. And that doesn't exist for all domes. It exists only for
very specific domes and for these very specific domes so of course we have another ball comes from that side or from any side and suppose it's a two-dimensional thing but from any direction it can stop at the top which means now the initial condition it may go at any time in any direction and that will always be a solution of the newton's equation but so this is fascinating indeed but i don't think it's super convincing because
You know, if you change the shape of that dome by an epsilon, by a little bit, it's gone. I mean, this peculiarity is gone. So it is not a generic feature. It's a feature of some very, very specific domer potential, as we call it. The reason why I like it is because I know that it's predicated on real numbers and so on. So maybe that's another dispute you have with it.
the reason why I like it is that even in the classical domain we can show that it doesn't have certain continuity condition and then because of that it allows for multiple solutions and not only that but you mentioned that it's not a generic feature I don't know if there's a result that says much like we can say that the typical real number has infinite information in it I don't know if there's a result that says the typical configuration of matter is that which has a Lipschitz continuity condition I would think it's the opposite I would think that not satisfying the Lipschitz continuity condition would be
typical if we have the general space of functions. But I don't know if that's true. I don't know if there's a result like that. Okay, I also don't know. My bet is that this is very, very specific, and that generically, we don't have this phenomenon, but I cannot. I'm not sure about that. My last question is, with regard to quantum gravity, is there an approach that you favor?
Make relativity deterministic. But you know, that's a vast program. Okay, now let's get to the audience questions. This one comes from Stephen E. Robbins. A great question to ask Nicholas is, I'm curious if he has looked at Bergson, Time and Free Will. Wait, yes, I'm curious if he's looked at Bergson. So that's it. Yeah, yeah. So I looked at it. I read some of it. I mean, it's too large. I didn't read everything.
Certainly a lot of his writing resonates, but somehow that's where I'm a physicist much more than a philosopher, and Bergson was clearly a philosopher, so at some point it is kind of too vague, I cannot really, you know, grasp it, I cannot really anchor on it, and yeah, so for that reason I
This question comes from Complex Plane.
Does he think that the denial of free will by physicists is an attempt to make evidence fit a model? Chomsky says that it may be something outside human cognitive abilities to understand. Does he hold a similar view?
I don't really know. Again, I mean, for me, free will comes first in this logical order. So you need it to start arguing about the existence of free will. So somehow you cannot really deny the existence of free will because if you want to argue against the existence of free will, you need free will to be able to buy or not buy the argument.
Then someone may say, well, how is it that you're choosing so-and-so? Because we use our free will to choose among possibilities. Are you saying there's nothing that influences that? Is it random? How does that work? No, no, no, no. So of course we get influenced. I mean, obviously we are under very heavy influence. And so free will is not something that we use continuously and so on. I mean, most of our decisions are not so important and so on. And we get influenced by ads and whatever.
And they're also not random. I mean, they might be partially random. You can, for instance, decide whether you go to a restaurant tonight by just tossing a coin. So sometimes it will be, but most of the time it will be not random and not predetermined. Now you may say, but who is now
making the decision, is there a little guy in my brain? Well, it should be myself, so I'm not sitting in my brain or whatever. So that's where our understanding of what free will is, is limited. We don't have this kind of understanding. Maybe it comes also back to what you asked initially about consciousness. I'm making conscious decisions,
Not always, by the way, but sometimes I'm making conscious decisions. I'm not sure I have much more to add on that. Our decisions are extremely determined by our environment, but being extremely determined is not the same as being fully determined. Exactly. There is room for some decisions. There are clearly some decisions
Professor, thank you so much for spending some of your time with me.
I appreciate it. I know it's late where you are. No, it's okay. It's 20 past 8. So no, that's perfect. So thank you very much for your time and tell me when that will be online. Very good. Thank you. Thank you for your interest in physics, in science, in free will and in my poor understanding of all those. Thank you, sir.
The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash c-u-r-t-j-a-i-m-u-n-g-a-l. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you.
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"text": " Nicolas Gisson is a professor at the University of Geneva working on the foundations of quantum mechanics and quantum information, both experimentally and theoretically. In this episode, we talk about the existence of free will, the indeterminacy of reality, and the unreality of the real numbers. Nicolas is one of the world-renowned experts in quantum theory, and we're extremely grateful that his first podcast appearance"
},
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"text": " is on the Theories of Everything channel. Thank you, Professor. Click on the timestamp in the description if you'd like to skip this intro. My name is Kurt Jaimungal. I'm a Torontonian filmmaker with a background in mathematical physics dedicated to the explication of the variegated terrain of theories of everything."
},
{
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"start_time": 157.483,
"text": " from a theoretical physics perspective, but as well as analyzing consciousness and seeing its potential connection to fundamental reality, whatever that is. Essentially, this channel is dedicated to exploring the underived nature of reality, the constitutional laws that govern it, provided those laws exist at all and are even knowable to us. If you enjoy witnessing and engaging with others on the topics of psychology, consciousness, physics, etc., the channel's themes,"
},
{
"end_time": 199.428,
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"start_time": 182.363,
"text": " then do consider going to the Discord and the subreddit which are linked in the description. There's also a link to the Patreon, that is patreon.com slash KurtGymungle if you'd like to support this podcast as the patrons and the sponsors are the only reasons that I'm able to have podcasts of this quality and this depth."
},
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"end_time": 219.121,
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"text": " Given that I can do this now, full-time, thanks to both the patrons and the sponsors' support. Speaking of sponsors, there are two. The first sponsor is Brilliant. During the winter break, I decided to brush up on some of the fundamentals of physics, particularly with regard to information theory, as I'd like to interview Chiara Marletto on constructor theory, which is heavily based in information theory."
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"text": " Now, information theory is predicated on entropy, at least there's a fundamental formula for entropy. So, I ended up taking the brilliant course, I challenged myself to do one lesson per day, and I took the courses Random Variable Distributions and Knowledge Slash Uncertainty. What I loved is that despite knowing the formula for entropy, which is essentially hammered into you as an undergraduate,"
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"text": " It seems like it comes down from the sky arbitrarily. And with Brilliant, for the first time, I was able to see how the formula for entropy, which you're seeing right now, is actually extremely natural. And it'd be strange to define it in any other manner. There are plenty of courses, and you can even learn group theory, which is what's being referenced when you hear that the standard model is predicated on U1 cross SU2 cross SU3. Those are Lie groups, continuous Lie groups. Visit brilliant.org slash totoe to get 20% off an annual subscription."
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"text": " And I recommend that you don't stop before four lessons. I think you'll be greatly surprised at the ease at which you can now comprehend subjects you previously had a difficult time grokking. The second sponsor is Algo. Now, Algo is an end-to-end supply chain optimization software company with software that helps business users optimize sales and operations, planning to avoid stockouts, reduce return and inventory write downs while reducing inventory investment."
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"text": " It's a supply chain AI that drives smart ROI headed by Amjad Hussein, who's been a huge supporter of this podcast since near its inception. In fact, Amjad has his own podcast on AI and consciousness and business growth. And if you'd like to support the Toe podcast, then visit the link in the description to see Amjad's podcast because subscribing to him or at least visiting supports the Toe podcast indirectly. Thank you and enjoy."
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"text": " I'm also interested in the topic of free will. That's why you're here. I was speaking with a professor of the philosophy of mathematics who referenced me an article of yours quite some time ago. And ever since then, I thought, okay, I want to speak to this person, but I didn't have a reason to but now I do. So thank you."
},
{
"end_time": 364.019,
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"start_time": 334.684,
"text": " So which paper is that? Do you remember? I don't remember. You had the Baker map and you were showing that there is indeterminacy with classical laws of physics and you don't need quantum mechanics to have that. I don't recall exactly. Okay, so it's not very old. Yeah, yeah, I know. I know which paper it is. From what I gathered, I've been watching plenty of your talks recently, plenty and plenty of them, and even I went through your book, which is almost a decade old now called Quantum Chance, which is a wonderful book, delightful book. Most books about physics are"
},
{
"end_time": 387.329,
"index": 16,
"start_time": 364.343,
"text": " or can be intimidating to someone who's not familiar with mathematics. But this book was so winsome and childlike in its curiosity, instead of Bell's inequality, you have Bell's game. You give the reader the impression that you're not speaking above them. Just changing Bell's inequality to Bell's games, it's a delightful conceptual shift that makes it much more lucid for those who are ordinarily intimidated by mathematics."
},
{
"end_time": 417.807,
"index": 17,
"start_time": 388.592,
"text": " You know, the subject, I find the subject fascinating. I mean, that's spent my life on quantum physics, quantum chance, and so on, indeterminacy. And I wanted to allow everyone to share that fascination. So without mathematics, indeed, but also without hiding the conceptual difficulties. It's not trivial these things. It's a major change in our worldview."
},
{
"end_time": 439.701,
"index": 18,
"start_time": 418.387,
"text": " So it is, I wouldn't say it's an easy book, but the goal was indeed to allow everyone who is willing to make an intellectual effort to be able to share some of this fascination and gain some understanding of why physicists are so excited about Bell inequalities, games and indeterminism and so on."
},
{
"end_time": 465.316,
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"start_time": 440.247,
"text": " Even something as complicated sounding as a quantum random number generator, which to many people they're like, well, firstly, what is random? And then it generates numbers and is quantum on top of that. Well, you explain it's just a beam splitter and just think of it like zeros and ones on each side. It's a splendid explanation of what's customarily complicated. Yeah. And actually what is even very nice here. So, you know, there is all these conceptual issues that you just mentioned, which are not trivial."
},
{
"end_time": 492.671,
"index": 20,
"start_time": 465.623,
"text": " can make it relatively simple, but not completely trivial, certainly not. But it goes all the way that now actually this startup company from my university group IDQ, they may put everything into a little chip, which is just a few millimeter in size. And it's also low power consumption. So it's a quantum random number generator that actually is used by Samsung in some of their smartphones."
},
{
"end_time": 521.425,
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"start_time": 493.626,
"text": " Have you done much thinking about the nature of consciousness? I know that you've spoken about free will and time and indeterminacy. Consciousness, no, you know, I'm a physicist and not a philosopher. So even about free will, which is certainly something which I think is an important concept, but it's not a concept of physics. So, you know, and consciousness"
},
{
"end_time": 551.715,
"index": 22,
"start_time": 521.92,
"text": " Maybe I should indeed warn you and everyone listening to this that I'm not a philosopher. I don't claim to be a philosopher. And I certainly claim that consciousness, free will, the mind or things like that,"
},
{
"end_time": 577.875,
"index": 23,
"start_time": 552.278,
"text": " fascinating concepts. We all know that we have that. But these are not concepts that belong to today's physics, possibly not even to future physics. From what I gathered from my research into your views, your philosophy, so to speak, you see free will and indeterminacy as not tied. Now, is this correct? Why is it so?"
},
{
"end_time": 606.049,
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"start_time": 578.916,
"text": " I'm sure you know the ordinary view, or not the ordinary, I'm sure you know the common view in philosophy, and even in physics, some people who dabble in philosophy, who are physicists, think if you're going to have a notion of free will, it's predicated on indeterminacy. Yeah, so I'm certainly not a compatibilist. I don't really understand how one could claim that the future is already given, is already determined by the present, and nevertheless, we have free will. I think that's a more"
},
{
"end_time": 635.759,
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"start_time": 606.51,
"text": " a game of words. So indeterminism is necessary, but indeterminism is certainly also not sufficient because free will is also not just randomness. We don't want to make random decisions. So it's much more complicated. Never determinism or pure indeterminism is sufficient to explain free will. In this sense, again, free will is not part of today's physics. And I would probably go even further and say that"
},
{
"end_time": 664.616,
"index": 26,
"start_time": 636.408,
"text": " So I'm now going to give some arguments and so on. And everyone can then buy these arguments or reject them. But in order to buy or reject these arguments, you need some free will. So somehow you need free will to start arguing, to start doing philosophy or to start doing physics. So probably the best I can say about free will is that is a prerequisite"
},
{
"end_time": 694.189,
"index": 27,
"start_time": 664.906,
"text": " In order to start arguing, so in particular for philosophy and science in general. When you say that free will is necessary in order to choose between truths, in order for you to say this one is true and not this one, then it sounds like you're tying free will to reason, is that the case? Or to rationality? To rationality, yes, absolutely. Now it's not a matter of being true or not true, you know, I mean you may"
},
{
"end_time": 721.817,
"index": 28,
"start_time": 694.394,
"text": " buy an argument or not, and you may even change your mind in course of time. But you need to be able to decide, yeah, now this argument that I just listened to is convincing or no, this is not convincing enough. I'm not going to change my mind because of that little argument. So you need to make decisions about what kind of arguments you're going to buy and which one you're going to reject."
},
{
"end_time": 751.834,
"index": 29,
"start_time": 722.517,
"text": " I have a quote from you which says, free will comes first in the logical order. Indeed, without free will, there's no way to make sense of anything. And in particular, there would be no understanding. Remember, earlier in the conversation, I said, I'm interested in the notion of time,"
},
{
"end_time": 777.466,
"index": 30,
"start_time": 752.039,
"text": " Maybe not exactly. I've read many things from Penrose, so probably it's maybe in the back of my mind. But indeed, I mean, absolutely correct. I mean, free will, in my opinion, comes first in the logical order."
},
{
"end_time": 797.722,
"index": 31,
"start_time": 778.08,
"text": " And because of that, you know, physics or science or psychology, whatever, cannot argue against free will, because it rests on free will. Yes, then now let's explain that because even to me as someone who has been looking into this, I found that to be a new notion. I didn't encounter that before. So firstly,"
},
{
"end_time": 813.899,
"index": 32,
"start_time": 798.131,
"text": " How did you come to that conclusion and then can you explain that conclusion?"
},
{
"end_time": 840.145,
"index": 33,
"start_time": 814.377,
"text": " Jokes aside, Verizon has the most ways to save on phones and plans where you can get a single line with everything you need. So bring in your bill to your local Miami Verizon store today and we'll give you a better deal. Rankings based on root metrics, root score, report data to 1-H-2025, your results may vary. Must provide a post-paid consumer mobile bill dated within the past 45 days. Bill must be in the same name as the person who made the deal. Additional terms apply. How did I came to it? I don't know. You know. Of your own free will you came to."
},
{
"end_time": 867.5,
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"start_time": 841.357,
"text": " I was thinking about free will and randomness and determinism and passage of time ever since I was a teenager. And so I don't, there's not really one point in time when suddenly, aha, now it works. So it's really something that evolved. And at some point I was invited to a conference to deliver a talk, of course. And the conference was actually about time."
},
{
"end_time": 895.452,
"index": 35,
"start_time": 867.995,
"text": " I was a bit surprised to be invited but okay I thought this is really a good chance and so I went to it and I had of course to prepare myself and that's actually when I started really formulating these ideas a bit more in a more articulated way like you know stating that free will comes first in the logical order there is no understanding without free will and so on but then also when I"
},
{
"end_time": 924.821,
"index": 36,
"start_time": 895.879,
"text": " During, I think it was during that conference, some colleagues mentioned in particular, Chris Fuchs mentioned to me that there is an old unknown, essentially a French philosopher, Le Cuyet, who actually had very similar thoughts. He was, Le Cuyet was also very much influenced much more by myself, certainly by religious beliefs."
},
{
"end_time": 952.278,
"index": 37,
"start_time": 925.196,
"text": " So God was his problem. How could God know everything and me still having free will? That's the old version. Is it a pre-Scientist version of the free will debate? And L'Equiel came to the similar conclusion as myself, but of course centuries before, saying that actually free will comes first and without free will we cannot even start this kind of argument about God having"
},
{
"end_time": 982.21,
"index": 38,
"start_time": 952.927,
"text": " Now, let's explain what it means that free will comes first in the logical order."
},
{
"end_time": 1011.288,
"index": 39,
"start_time": 983.422,
"text": " and don't have any free will, whether this argument is going to resonate is a purely, let's say, mechanical stuff. You know, if I hit my table here, whether the table is going to resonate is just a matter of the mechanics of the resonant frequencies of this table and so on, and how I hit it and so on. But for an argument to resonate,"
},
{
"end_time": 1041.647,
"index": 40,
"start_time": 1012.449,
"text": " In me, it's I think not just a matter of, I don't know, it's not a mechanical question. Some arguments are convincing, some of us are not convincing. And again, that may change in the course of time, you don't need to always be convinced by the same argument during all your lifespan. So there must be something more. And this something more is actually what we name free will. This table has no free will."
},
{
"end_time": 1059.923,
"index": 41,
"start_time": 1042.005,
"text": " doesn't decide to resonate to my hitting it, while you and me and everybody listening here and so on, they may find for instance now my argument in that it resonates to them,"
},
{
"end_time": 1079.036,
"index": 42,
"start_time": 1060.282,
"text": " Or that they are willing to buy it, or at least to consider it, or on the contrary, they will just reject it. But whatever they do, it's a free decision. It's something that depends on them. I don't think it is just a mechanical consequence of their bodies and their brain and so on."
},
{
"end_time": 1104.599,
"index": 43,
"start_time": 1079.804,
"text": " So the way that I understand it is if I was to make a bridge resonate, I throw wind at it and then it wobbles and that's a physical process. Now, if I throw an idea at you or you to me, if it resonates with me, we use the same word resonate, but we just mean, well, we use the same word resonate. That is dependent not on the physics, but on free will. Exactly. I think that's correct."
},
{
"end_time": 1132.363,
"index": 44,
"start_time": 1105.026,
"text": " Of course, I know that some people will say, no, no, this is a purely physical phenomenon. We don't, I mean, we, first of all, don't exist. Everything is just pure physics. But I think going that far first assumes that physics really explains everything. It almost assumes in between the line that today's physics is close to an end, which I consider ridiculous."
},
{
"end_time": 1165.401,
"index": 45,
"start_time": 1135.469,
"text": " Yeah, and I think it bypasses the beauty of life, the beauty of human beings, including animals, of living beings. What do your colleagues say to you when you say, well, perhaps physics doesn't explain everything. The reductionist account, including our actions, it goes from our actions to our neurobiology, to the chemistry, to the physics. And that's it. Physics, that's it."
},
{
"end_time": 1194.974,
"index": 46,
"start_time": 1166.937,
"text": " Again, here depends where we are talking about today's physics or even near future physics or physics in general. Science is not at the end and will continue to develop and there will be new ideas and completely new things which will be totally surprising to today's physicists like quantum mechanics and relativity are completely foreign to 19th century physics."
},
{
"end_time": 1224.411,
"index": 47,
"start_time": 1195.708,
"text": " So there will be more revolutions and so maybe there is one thing which seems pretty clear is that today's physics doesn't explain free will, consciousness or things like that. Could it be that future physics explain it? Certainly not near future. Now what is really the very far future of physics or science more generally? Of course I don't know but my claim is that free will being"
},
{
"end_time": 1245.879,
"index": 48,
"start_time": 1224.94,
"text": " First, in the logical order, physics or science more generally and philosophy will never be able to fully explain free will. Of course, we can explain part of it. For instance, today we understand much better, I find in the 19th century, the difference between hardware and software. And this distinction"
},
{
"end_time": 1273.831,
"index": 49,
"start_time": 1246.34,
"text": " which is very common today. But this is a useful distinction to study and to think about the brain as just being the material part and maybe based on software, whatever that exactly means and things like that. But at least we can start articulating ideas thanks to this distinction between software and hardware that were completely unthinkable 200 years ago, 150 years ago."
},
{
"end_time": 1302.79,
"index": 50,
"start_time": 1274.326,
"text": " So we can also expect that in the future there will be new concepts that we master or that the future scientists will master and that will help better articulating the problem of free will and consciousness and so on. But I don't think we will ever come to an end in that. Free will will somehow, some essence of free will will always remain"
},
{
"end_time": 1332.534,
"index": 51,
"start_time": 1303.524,
"text": " There are many colleagues, and I would say the vast majority of the physicists just don't care. They are not going to listen at all. They just don't care. Now, among those that care, they care after a few beers, usually."
},
{
"end_time": 1355.077,
"index": 52,
"start_time": 1332.995,
"text": " Most of them which then, I don't know, they would listen to what I have to say, they would not necessarily agree. Okay, some have very strong opinions, they are strongly compatibilist, but they really thought about it. That's okay. And I guess we also quite a lot and I have already experienced quite a lot of my colleagues who are happy with what I'm saying."
},
{
"end_time": 1383.507,
"index": 53,
"start_time": 1356.288,
"text": " But you know, the happy is a small minority. The seriously unhappy is also a small minority and the enormous majority just doesn't care. And why do you think the majority doesn't care? It's too ill-defined, they'll say? Yeah, it's too ill-defined. I don't exactly know how they cannot care about such important and deep questions."
},
{
"end_time": 1413.933,
"index": 54,
"start_time": 1384.053,
"text": " Maybe we just think that, you know, they have not been trained in that. They don't feel competent in this respect somehow. Probably also if some of my colleagues I tell them about some subtleties in biology, they may also just say, oh, I don't understand it. It's outside my field of competence. Actually, nowadays we get so specialized that you don't even need to change field and go outside of physics for not understanding what the colleague is saying."
},
{
"end_time": 1443.729,
"index": 55,
"start_time": 1414.445,
"text": " Do you think what governs free will is mathematics or you think it's something completely different? And this goes back to our reductionist account. Okay, yeah, mathematics. We should talk about mathematics and determinism. But no, I think"
},
{
"end_time": 1468.848,
"index": 56,
"start_time": 1443.916,
"text": " Mathematics again, especially today's mathematics has very, very little to say on, probably nothing to say on free will and consciousness. The reason I say that is that when one says, well, it's first in the logical order, the way I'm thinking is of the traditional reductionist view. And you go down and down until you get to physics. And then sometimes people encapsulate physics into math."
},
{
"end_time": 1496.613,
"index": 57,
"start_time": 1469.241,
"text": " and then if free will is first well then free will is prior to math is that the correct way of looking at it as these nested sets or is that different i shouldn't be thinking about it like that i don't think you should be thinking of nested sets mathematics is i guess it's really a kind of different branch of uh of science and of understanding um"
},
{
"end_time": 1524.206,
"index": 58,
"start_time": 1498.148,
"text": " And again, mathematics, in French, we say the mathematics, it's really a plural. And indeed, there are different sorts of mathematics, you can really think of mathematics as kind of, you know, this purely platonistic view where there are these mathematical objects existing, you know, outside of time, outside of the physical world."
},
{
"end_time": 1552.039,
"index": 59,
"start_time": 1524.821,
"text": " They just have their own existence with their own rules. I'm probably not prepared to really argue how these rules depend on the axioms in principle. But there are quite a lot of basic things like the integers, for instance. The integer 5, does it exist by itself in this Platonistic world?"
},
{
"end_time": 1575.469,
"index": 60,
"start_time": 1552.432,
"text": " I guess that's the view that most mathematicians would approach, would admit. But there are different sorts of mathematics. You have also mathematics where people were more thinking in terms of that the mathematical objects would themselves be processes that develop and evolve in time."
},
{
"end_time": 1603.985,
"index": 61,
"start_time": 1576.237,
"text": " The best example here is intuitionistic mathematics that was mostly developed by Brouwer about 100 years ago. There are still today some people developing this form of mathematics that come under the general umbrella of constructivists. But in this specific form of constructivism called intuitionism,"
},
{
"end_time": 1633.404,
"index": 62,
"start_time": 1604.753,
"text": " you really have that already at the mathematical level, even numbers, like what we call real numbers, are really evolving in time. And then if mathematics includes that kind of and needs the concept or introduces the concept of time already, even at the level of numbers, then that makes this sort of mathematics much closer and possibly better suited for physics or for science in general."
},
{
"end_time": 1653.336,
"index": 63,
"start_time": 1634.735,
"text": " So when you say mathematics, it's not clear what you mean. Many of the people watching don't know what constructivism... what is it? Constructionist? It's not constructivism, is it? Well, the physical... Social constructivism and social constructionism. I don't want to mix that up."
},
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"end_time": 1671.135,
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"start_time": 1653.763,
"text": " I know intuitionism, and I've always seen intuitionism as the same as the constructionist view in mathematics, but you just said that intuitionist is a specific subset of constructionist. What would be an example of a constructionist that is not an intuitionist? Hear that sound?"
},
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"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
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"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone."
},
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"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com slash theories, all lowercase."
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"text": " Razor blades are like diving boards. The longer the board, the more the wobble, the more the wobble, the more nicks, cuts, scrapes. A bad shave isn't a blade problem, it's an extension problem. Henson is a family-owned aerospace parts manufacturer that's made parts for the International Space Station and the Mars Rover."
},
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"text": " Now they're bringing that precision engineering to your shaving experience. By using aerospace-grade CNC machines, Henson makes razors that extend less than the thickness of a human hair. The razor also has built-in channels that evacuates hair and cream, which make clogging virtually impossible. Henson Shaving wants to produce the best razors, not the best razor business, so that means no plastics, no subscriptions, no proprietary blades, and no planned obsolescence."
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"text": " It's also extremely affordable. The Henson razor works with the standard dual edge blades that give you that old school shave with the benefits of this new school tech. It's time to say no to subscriptions and yes to a razor that'll last you a lifetime. Visit hensonshaving.com slash everything."
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"text": " If you use that code, you'll get two years worth of blades for free. Just make sure to add them to the cart. Plus 100 free blades when you head to H E N S O N S H A V I N G dot com slash everything and use the code everything. So constructivist just means that every object one should be able to construct them. Now it depends. Do you want to be able to construct them now?"
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"text": " and period is done, or is it enough to have a rule that tells you how the process of constructing these objects develops in time? So somehow they are never finished, there are at least some of these processes that will never finish, so they evolve in time, and that's then intuitionism. So intuitionism, the intuition is that things can evolve in time,"
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"text": " admittedly Brouwer, when he developed that, he was thinking about, you know, you may define a number depending on some mathematical conjecture and depending how this conjecture will turn out, you know, true or false, the number may be zero or one, let's say. And so the number is undefined until this conjecture, this specific conjecture is solved."
},
{
"end_time": 1938.029,
"index": 74,
"start_time": 1909.701,
"text": " But that brings now mathematics or this form of intuitionistic mathematics very much to what human are able to do, prove or not prove this conception. While my understanding and other people's understanding of intuition is just that as time passes, new information gets created continuously and hence a number may evolve according to this new information."
},
{
"end_time": 1968.183,
"index": 75,
"start_time": 1939.991,
"text": " So the standard view in mathematics is classical mathematics. And that is to say that we're discovering it and it's timeless. So the Pythagorean theorem is timeless. We just found it and it existed before humans. Now, Brouwer would say, well, it didn't exist until we discovered it. And then Brouwer was a type of intuitionist, but that's a bit too anthropocentric. So we say now, well, there's still intuitionism. It's just that the universe itself reveals new information. Exactly."
},
{
"end_time": 1997.961,
"index": 76,
"start_time": 1969.684,
"text": " It is correct. But of course, about the Pythagorean theorem, once it is on the table, there's nothing more to add on that. But you can imagine just a number that starts as a zero dot, and then you have all the digits that come afterwards. And some of these far away digits may not yet be determined. But as new information gets created, these far down the series,"
},
{
"end_time": 2026.886,
"index": 77,
"start_time": 1998.439,
"text": " You should know that the audience for this is generally upper year undergrads in math and physics. So for them, can you explain how indeterminacy arises in classical physics? Like a few arguments and you can also outline your views on the real numbers aren't real and so on because those are tight. Yeah, it's all connected indeed."
},
{
"end_time": 2055.998,
"index": 78,
"start_time": 2027.244,
"text": " So very important to understand first is chaos. So in classical mechanics, you have Newton's law and all that, and you may use Hamiltonian's equation, whatever the equation that you learn at school and university. And usually one then gives some examples, and the examples will be a harmonic oscillator, you know, just a kind of pendulum that oscillates very regularly. Or you may have, I don't know,"
},
{
"end_time": 2086.084,
"index": 79,
"start_time": 2056.561,
"text": " a star, a planet orbiting its star, like Earth orbiting the Sun, which again is a very, very regular motion. But actually, when you look at all the possible configurations of these matter particles, you notice that almost all, actually with probability one, the system that you're going to consider actually is not regular, but it's chaotic. And by chaotic, it means that's the"
},
{
"end_time": 2111.988,
"index": 80,
"start_time": 2087.108,
"text": " the future of this set of particles depends super sensitively on the initial condition. So you take an initial condition, which is usually defined by a real number. I know you change the digits number 1000 or 1 million, whatever. And of course, initially, you don't see any difference if you let the systems evolve."
},
{
"end_time": 2140.418,
"index": 81,
"start_time": 2112.722,
"text": " But if the system is chaotic, pretty quickly, the system will evolve completely differently, although you have only changed the digit 1000 positions down the string of digits. And then comes the question, is that still a deterministic system or not? So first of all, obviously, it is not deterministic in the sense that you cannot control all these digits. It's beyond our technology."
},
{
"end_time": 2170.213,
"index": 82,
"start_time": 2140.794,
"text": " But see, you can now go more on the ontology side. Does this 1,000 or 1 million digits really exist since ever? And hence, this chaotic system actually evolved in a fully deterministic way. We don't know which way, but it is deterministic. Or is it the case that this billion for million digits actually is undetermined at time t0?"
},
{
"end_time": 2195.469,
"index": 83,
"start_time": 2170.64,
"text": " and hence the evolution of this chaotic system will be also undetermined. As time passes, this digit will get determined, gain a determined value, but initially at time t0 it has no determined value. And if you think like that, so if you replace classical mathematics by intuitionistic mathematics, you make the same predictions, statistical predictions anyway,"
},
{
"end_time": 2225.606,
"index": 84,
"start_time": 2197.602,
"text": " But very importantly, with intuitionistic mathematics, you see that a chaotic classical system is no longer deterministic. It becomes indeterministic, although it is classical physics still, although the equations are still Newton's equations and all that. And so, indeed, I like to argue that is, first of all, that it already shows that just by changing the mathematics,"
},
{
"end_time": 2252.398,
"index": 85,
"start_time": 2226.34,
"text": " Contrary to what we learned, there are more than one mathematics. And if you go to another form of mathematics, you don't change the prediction since all the empirical confirmation of physics remains. But instead of presenting you with a deterministic worldview, the same theory, Newton's theory in this case, classical mechanics, presents you with an indeterministic worldview."
},
{
"end_time": 2282.551,
"index": 86,
"start_time": 2253.166,
"text": " So you see, it's really, you can choose, you can use your free will to choose where you prefer one or the other, but it's not the facts that are going to choose for you. And then there's one more argument, which I like to put on the table. You know, a real number, a typical real number, you know, this integer dot, and then all these digits that contains actually an infinite amount of information, because the series of digits, they typically contain no structure at all."
},
{
"end_time": 2299.326,
"index": 87,
"start_time": 2282.841,
"text": " It's not like one third. One third is zero dot and then you have only three, three, three, three that just repeats itself. But a typical real number will have no structure at all. And that means that if you want to describe it, you have to give everything, every, every digit. Hear that sound?"
},
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"end_time": 2326.374,
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"start_time": 2300.213,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 2352.466,
"index": 89,
"start_time": 2326.374,
"text": " There's also something called Shopify Magic, your AI-powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the next level. Join the ranks of businesses in 175 countries that have made Shopify the backbone."
},
{
"end_time": 2378.217,
"index": 90,
"start_time": 2352.466,
"text": " of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklinen. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story? Sign up for a $1 per month trial period at Shopify.com slash theories, all lowercase."
},
{
"end_time": 2403.848,
"index": 91,
"start_time": 2378.217,
"text": " Go to Shopify.com slash theories now to grow your business no matter what stage you're in Shopify.com slash theories. Infinity many digits. So that's infinitely many. It's an infinite amount of information. I know if you think that's, you know, you make the assumption that in a finite volume of space, you have only a finite"
},
{
"end_time": 2433.985,
"index": 92,
"start_time": 2404.292,
"text": " amount of information. We cannot pack infinite information into a finite volume. Then the natural consequence of this assumption is that if you have now a beard ball or anything in your small volume, finite volume, the center of mass of that or any other degree of freedom cannot be faithfully described by a real number, because if it would be a real number you would have to pack all this infinite information into your finite volume."
},
{
"end_time": 2458.422,
"index": 93,
"start_time": 2435.35,
"text": " From that I concluded, and I have a paper with this nice title, real numbers are not really real. These real numbers were called real by Descartes for historical reasons, and we still use this terminology of real numbers, but if you look at them from a physics point of view, they're not really real."
},
{
"end_time": 2485.538,
"index": 94,
"start_time": 2459.394,
"text": " Usually people who say that the real numbers aren't real are a fan of digital physics, but there's computation underneath and the laws of physics are computation. So Stephen Wolfram, for example, do you subscribe to this? Not entirely. I guess in part, yes. But what I add to that, what I think is important to add is really this idea that these numbers are evolving in time. So you still have, for instance, the continuum."
},
{
"end_time": 2512.381,
"index": 95,
"start_time": 2486.101,
"text": " Wolfram would not have the continuum in this sense but with intuitionistic mathematics you have these numbers evolve and so this digit which is initially undetermined will get determined in proper time and so the yeah first of all if this digit becomes very important let's say in a week time because it would determine the weather in a week"
},
{
"end_time": 2534.548,
"index": 96,
"start_time": 2512.91,
"text": " It cannot be that the weather, in one week from now, the weather will be determined. It will be sunny or rainy or in between, but it will be something. So at some point in time, these chaotic systems, they must settle down, they must get determined."
},
{
"end_time": 2562.278,
"index": 97,
"start_time": 2535.333,
"text": " It's not enough to have some granularity in it. You need that they settle. And in this sense, I think that intuitionistic mathematics is an appropriate language, mathematical language, to describe this idea that although things may not be determined today, the weather in a week time from today is not yet determined, but it will be determined in a week time."
},
{
"end_time": 2592.108,
"index": 98,
"start_time": 2563.063,
"text": " How do you get from this intuitionist view to the view that time is thick, that you can't pull out a single point of time? It's much like molasses. Yeah, yeah. Okay, the argument here is, if you have, let's say, imagine two processes or two numbers that initially are exactly the same, but they evolve in time. And maybe after some time, they may split."
},
{
"end_time": 2622.807,
"index": 99,
"start_time": 2593.166,
"text": " these new information that gets created as time passes may be different and so these two numbers at now or even in the near future we can just not distinguish them because so far they are exactly the same but they may become different and so somehow you know these numbers they are they stick together they are a bit like yeah yeah this this last that you cannot really"
},
{
"end_time": 2652.671,
"index": 100,
"start_time": 2623.183,
"text": " or honey, you cannot really take out a molecule of honey, they stick together. And these numbers also kind of stick together. And that's where the intuition of this thick time in intuitionistic mathematics comes from. But I'm not really... Okay, I don't claim that I have a full understanding of time in intuitionistic mathematics, let's say."
},
{
"end_time": 2666.681,
"index": 101,
"start_time": 2653.166,
"text": " Can you give an example more simply?"
},
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"end_time": 2689.036,
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"start_time": 2667.227,
"text": " This Marshawn beats my old Lynch. Prize pick is making sports season even more fun. On prize picks where the"
},
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"end_time": 2711.664,
"index": 103,
"start_time": 2689.411,
"text": " football fan, a basketball fan, it always feels good to be ranked. Right now, new users get $50 instantly in lineups when you play your first $5. The app is simple to use. Pick two or more players. Pick more or less on their stat projections. Anything from touchdowns to threes and if you're right, you can win big. Mix and match players from"
},
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"end_time": 2721.527,
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"text": " any sport on PrizePix, America's number one daily fantasy sports app. PrizePix is available in 40 plus states including California, Texas,"
},
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"end_time": 2751.766,
"index": 105,
"start_time": 2721.766,
"text": " Florida and Georgia. Most importantly, all the transactions on the app are fast, safe and secure. Download the PricePix app today and use code Spotify to get $50 in lineups after you play your first $5 lineup. That's code Spotify to get $50 in lineups after you play your first $5 lineup. PricePix. It's good to be right. Must be present in certain states. Visit pricepix.com for restrictions and details. Well, it means that at any time now, for instance, you cannot distinguish"
},
{
"end_time": 2774.753,
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"start_time": 2752.654,
"text": " So they still stick together. Although they are different in the sense that as you said, I mean, in a second or maybe in a day, it will be 2.001 for one of them and 2.005 for the other. So they clearly are different. But nevertheless, today they stick together. Ah, okay. So time gets increasingly more specific. I mean, sorry."
},
{
"end_time": 2803.729,
"index": 107,
"start_time": 2775.401,
"text": " Is it? It's not. I don't think I said that correctly. So correct what I said. I said time gets increasingly more specific, but it's more like the quantities that we're measuring it or the quantities that exist get more specific. Exactly. The quantities that exist get more specific or I would use the terminology, they get more determined. I'm trying to understand. How is it that the present is thick? So you're saying the present is thick because it then fractionates later. And that means that any moment in the future is actually less thick than a moment in the past."
},
{
"end_time": 2832.978,
"index": 108,
"start_time": 2805.145,
"text": " No, I don't think so, because it can happen again in the future, even once it's 2.001, let's say it settles for 2.001, but you still have the same kind of thickness for the next digit. Ah, so they're all equally as thick. It evolves forever. Okay, and they're all equally as thick because they're all just indeterminate at the last digit, whether the time is T010. Okay. Yeah, if you want to be more precise, it's not a matter of the digit, it's really additional information."
},
{
"end_time": 2855.316,
"index": 109,
"start_time": 2833.643,
"text": " But never mind, the intuition is good with these digits, yes. Many younger people especially don't know about intuitionist mathematics. They don't even know that there's a difference in mathematics. They just think it's classical mathematics. So I'm going to outline some of how, and I'm going to place a slide of yours up on the screen, how indeterministic physics and intuitionist mathematics map onto one another."
},
{
"end_time": 2870.503,
"index": 110,
"start_time": 2855.418,
"text": " Yeah, probably. Yes, yes, yes. And there's a paper in the philosophy journal Sintesa that appeared, I think, last summer, I think, which is indeed an indeterministic physics and intuitionistic mathematics. Something like that is the title."
},
{
"end_time": 2891.544,
"index": 111,
"start_time": 2871.203,
"text": " Maybe you can just give a give a link to that. It's not a difficult paper. Great, great. I'll give a link to that. Now the future is open in indeterministic physics, that gets analogized or mapped on to or made equivalent with the law of the excluded middle not being there. Okay, so firstly, can you explain what the law of the excluded middle is? And then why the heck that means that the future is open?"
},
{
"end_time": 2921.032,
"index": 112,
"start_time": 2893.507,
"text": " Yeah, so this law of the excluded middle says, so it's a part of, let's say, classical logic, classical mathematics, that says that every statement, every proposition, is either true or false. It cannot be something else. It's either true or false. So if I'm now saying it will be raining in exactly a year time in Geneva, in my garden, let's say, this statement, according to classical logic, has to be either true"
},
{
"end_time": 2949.77,
"index": 113,
"start_time": 2921.408,
"text": " I mean, for sure it will rain, or it is false, and then for sure it will not rain. Of course, I may be ignorant about whether it is true or false, and for sure I'm ignorant about that, but the fact is that this proposition has a true value. Consequently, the future, because my statement, my proposition here is about the future, but if now this proposition has a true value, it means that this future somehow already exists, or at least is already determined."
},
{
"end_time": 2979.36,
"index": 114,
"start_time": 2950.503,
"text": " Let's determine this. Now, if I want to have a different view, saying that this weather in a year time, not only do I not know whether it will be sunny or rainy, but it is truly undetermined. It's not yet settled whether it will be one way or the other. And then it means that a proposition about this future weather is neither true nor false."
},
{
"end_time": 3009.633,
"index": 115,
"start_time": 2979.889,
"text": " It takes a third value, and this third value is just indeterminate. Indeterminate, sorry, indeterminate. So you have now a new sort of logic, which is no longer with two values, it has this third value, but the third value is not, I don't know, 50-50 or gray, it just says it is indeterminate. And this is certainly part of intuitionistic mathematics,"
},
{
"end_time": 3039.104,
"index": 116,
"start_time": 3010.452,
"text": " You made me think of some personal questions. So this young Nicholas, when you're sitting and philosophizing about the nature of time and indeterminacy and free will, etc."
},
{
"end_time": 3063.643,
"index": 117,
"start_time": 3039.906,
"text": " And you meddled, you meddled with mathematics at the logical level. So there's different types of logic. Mathematics is based on logic, classical logic and intuitionist logic. Did you meddle so far outside of intuitionist logic, such as grand priests, paraconsistent logic or other forms of logic? Or have you settled on intuitionist and why? Well, so actually the situation is following. I was"
},
{
"end_time": 3093.643,
"index": 118,
"start_time": 3064.189,
"text": " Okay, thinking about that, and indeed the young Nicolas was already thinking about randomness. I think it's a super complicated concept. And I don't remember now, let's say five years ago, I was writing a paper that appeared in another philosophy journal, their Kindness. That's the paper which has the subtitle, real numbers are not really real. And okay, and so when at some point I presented that at the conference,"
},
{
"end_time": 3123.422,
"index": 119,
"start_time": 3094.138,
"text": " And one of the participants, Carl Posse, who is actually a professor of philosophy and logic in Jerusalem, mentioned to me this intuitionistic mathematics. So I didn't know intuitionistic mathematics, but clearly what I was at with my real numbers and it's really real, I was somehow rediscovering intuitionistic mathematics, trying to reinvent it."
},
{
"end_time": 3150.196,
"index": 120,
"start_time": 3123.712,
"text": " Of course, I didn't went as far as all these people doing that. It's an entire community. But so then thanks to Karl Posse, I learned about it and he taught me about it. And it's not difficult to understand because it really just corresponds quite closely to my intuition about how things are going. And so I understood it. And then I wrote this other paper, the Synthese one about indeterminacy."
},
{
"end_time": 3169.172,
"index": 121,
"start_time": 3150.674,
"text": " Hear that sound?"
},
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"end_time": 3195.981,
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"start_time": 3169.889,
"text": " That's the sweet sound of success with Shopify. Shopify is the all-encompassing commerce platform that's with you from the first flicker of an idea to the moment you realize you're running a global enterprise. Whether it's handcrafted jewelry or high-tech gadgets, Shopify supports you at every point of sale, both online and in person. They streamline the process with the internet's best converting checkout, making it 36% more effective than other leading platforms."
},
{
"end_time": 3214.974,
"index": 123,
"start_time": 3195.981,
"text": " There's also something called Shopify Magic, your AI powered assistant that's like an all-star team member working tirelessly behind the scenes. What I find fascinating about Shopify is how it scales with your ambition. No matter how big you want to grow, Shopify gives you everything you need to take control and take your business to the"
},
{
"end_time": 3240.828,
"index": 124,
"start_time": 3214.974,
"text": " Join the ranks of businesses in 175 countries that have made Shopify the backbone of their commerce. Shopify, by the way, powers 10% of all e-commerce in the United States, including huge names like Allbirds, Rothy's, and Brooklynin. If you ever need help, their award-winning support is like having a mentor that's just a click away. Now, are you ready to start your own success story?"
},
{
"end_time": 3270.145,
"index": 125,
"start_time": 3240.828,
"text": " Sign up for a $1 per month trial period at shopify.com slash theories, all lowercase. Go to shopify.com slash theories now to grow your business, no matter what stage you're in shopify.com slash theories. You know, we all think, we all, many of us think, you know, a real number, you get all these digits and then, you know, we can think of the other digits. They come one after the other."
},
{
"end_time": 3298.66,
"index": 126,
"start_time": 3270.981,
"text": " And they come one after the other in time. You know, one is here, then it comes the next, then comes the next, then comes the next. But actually, proper classical mathematics says something very different. Proper classical mathematics claims that a real number is this infinite series of numbers, of digits, this infinite amount of information that comes all at once in zero time."
},
{
"end_time": 3328.712,
"index": 127,
"start_time": 3299.445,
"text": " So when you say let x0 be the initial condition and x0 you assume it's a real number or even a bunch of real numbers if you have many degrees of freedom it actually means let there be instantaneously infinite information and that's an enormous assumption and I don't think most physicists really think that way they really think okay there is this number and there are some digits and then well who cares anyway but"
},
{
"end_time": 3338.746,
"index": 128,
"start_time": 3328.899,
"text": " These numbers, these digits, they come really one after the other, and now we say one after the other in time, and then you have intuitionistic mathematics."
},
{
"end_time": 3365.606,
"index": 129,
"start_time": 3340.691,
"text": " Part of the reason why many physicists don't have much of a trouble with real numbers is that I don't think they think in terms of a billiard ball carrying its position with it. If it carried it like on a piece of paper on a sticky note, metaphorically, it would create a black hole instantly, typically, unless it's because the typical real number has infinite. Okay, so then the way that you've explained it to me is that you imagine it like the"
},
{
"end_time": 3393.012,
"index": 130,
"start_time": 3365.998,
"text": " electron or the billiard ball does carry with it its position. Is that still a metaphor or is that meant to be taken more literally? If it's just the center of mass of course then it depends on a reference frame anyway but you could imagine the kinetic momentum or you could also imagine just you have a molecule or you have a little system with more than one particle and then the relative"
},
{
"end_time": 3422.739,
"index": 131,
"start_time": 3393.541,
"text": " degrees of freedom, you know, the distance between a planet and its sun. This is really within the system, the system being the global thing. And then you can really think, I mean, then it makes sense to think that these relative degrees of freedom are really represented by numbers carried by the system. It's really internal of it. Now you may say, okay, it depends if I'm measuring that with miles or kilometers or whatever."
},
{
"end_time": 3438.422,
"index": 132,
"start_time": 3423.336,
"text": " But that is indeed where if we think in terms of the amount of information, it's the same. Now, if I really think in terms of the digits, of course, if I change my units, the digits will change, but the amount of information will in both cases be infinite."
},
{
"end_time": 3466.305,
"index": 133,
"start_time": 3439.292,
"text": " Okay, now getting to the reality of time, again, the commonplace view in physics is that arrow of time is an illusion. In fact, time itself may be an illusion like Carlo Rovelli suggests, because the laws of nature as far as we have are symmetric, except for the second. Do you see the second law as being what engenders the arrow of time, or you see it as being so much more fundamental? It's more fundamental, it comes already in the basic mathematics. In the basic mathematics, we don't erase"
},
{
"end_time": 3492.91,
"index": 134,
"start_time": 3466.817,
"text": " information, we create information as time passes. So the direction of time is already built into our mathematical language. And I think, again, that comes much closer to the intuition that everyone has. Of course, if you learn too much of classical mechanics or quantum mechanics with the Schrodinger equation, you may get the feeling that because the equations are time reversal, then time is an illusion."
},
{
"end_time": 3515.265,
"index": 135,
"start_time": 3493.951,
"text": " That's because you use classical mathematics to describe the initial condition for these evolution equations. If you just use this different form of mathematics, then even if the equation has still the symmetry, the initial condition no longer has that symmetry."
},
{
"end_time": 3542.705,
"index": 136,
"start_time": 3516.493,
"text": " Something I'm extremely excited about exploring on this channel are different approaches to quantum gravity. And you said in an offhand statement, you said, I think we need a different understanding of time in order to make a breakthrough in quantum gravity. Please explain that. Yes, yes. Yeah, so indeed. So quantum gravity, that's of course a huge challenge and a very little progress in the last decades."
},
{
"end_time": 3572.346,
"index": 137,
"start_time": 3543.148,
"text": " Okay, maybe I'm going to annoy a few of my colleagues, but I don't think we have made any breakthrough. I think that's a fair statement. To be fair, professor, almost everyone has a variation of that statement that we need a new understanding of X in order to make progress in quantum gravity, whether we need a new understanding of space, we need a new understanding of strings, we need a new understanding of holography. So why time? Okay, good. So why time? So time plays a completely different role in relativity, so gravity, and in quantum mechanics."
},
{
"end_time": 3599.633,
"index": 138,
"start_time": 3572.739,
"text": " In relativity, I mean that the usual picture is this block universe where everything is kind of frozen since ever, forever, and there is no present. You have to add it by hand. And even Einstein was a bit concerned with the lack of the present. In quantum mechanics, at least the standard view is this indeterminacy. On the beam splitter with the two detectors, for instance,"
},
{
"end_time": 3626.869,
"index": 139,
"start_time": 3600.23,
"text": " And so there is clearly a process going on. Before the photon hits the detector and gets localized in one or the other detector and there is a time after it has triggered one and only one of the detectors. So there is clearly a passage of time there. And now we have these two basic theories which"
},
{
"end_time": 3652.927,
"index": 140,
"start_time": 3627.875,
"text": " they fundamentally disagree about what time is and then how do you want now to develop a dynamical theory of quantum gravity if we don't even agree on what time is and whether this is you know whether the passage of time is a real phenomenon as in standard quantum mechanics or is it"
},
{
"end_time": 3679.804,
"index": 141,
"start_time": 3653.473,
"text": " just the kind of illusion us in the block universe presented by relativity. So I think this is really a fundamental issue and we need to be able to, if we want to do quantum gravity, we need to have one concept that is going to unify that. I know I wouldn't say that I have solved the problem, I mean, certainly not, but my hope is that my"
},
{
"end_time": 3709.275,
"index": 142,
"start_time": 3680.111,
"text": " Introducing indeterminism also in classical pre-relativity mechanics, so Newtonian mechanics, but I have already introduced indeterminism there, so somehow I have brought at least classical mechanics and quantum mechanics closer together. I have also one paper on the indeterminacy is relative, so going one more step in the direction of relativity, but okay this is maybe it's"
},
{
"end_time": 3733.37,
"index": 143,
"start_time": 3709.855,
"text": " I don't think we should enter that kind of debate anyway, it is still under development. But the goal is indeed to bring also indeterminism to relativity. Professor, whenever you speak, I have so many questions that are there's so many that come to my mind. Okay, so first, do you have an idea as to the discretization of space and time? Do you think it's discrete? Okay, let me just be fair, I don't know."
},
{
"end_time": 3758.695,
"index": 144,
"start_time": 3733.985,
"text": " The way I describe time in this, well, like all the others in intuitionist mathematics, it is discrete. Is it fundamentally discrete? Is it a technical problem today? I don't know. Also, you mentioned that you were similar to that philosopher, which I forgot the name of. I know William James was influenced by someone who published that person's work because that person died young. Yeah. So, okay, the guy I mentioned before is Le Cuyet."
},
{
"end_time": 3787.398,
"index": 145,
"start_time": 3759.258,
"text": " Jacques Lecuyer, I think. And then there was indeed a person in between Lecuyer and William James, and that's Renouvier, I think. Also a French philosopher. The first one I'm not going to even try to pronounce. Now that person, Lecuyer, so I tried to pronounce it, Lecuyer, was spurred by a religious instinct, or these religious questions. You mentioned you feel similar to him, so I'm curious about your religious views."
},
{
"end_time": 3815.674,
"index": 146,
"start_time": 3789.002,
"text": " Well, okay, in some sense, I'm certainly not a religious person. So I never go to church or things like that. My children are not baptized and so on. But you know, the fact that I spent time thinking about free will, consciousness, time, you know, it's really taking physics, a stretch maybe physics a bit beyond the"
},
{
"end_time": 3845.828,
"index": 147,
"start_time": 3816.442,
"text": " standard physics to go in the direction of philosophy. And I mentioned already two of my papers in philosophy journals. Actually, I have very little publications in philosophy journals. I think I have four of them, if I remember well. So it's very few compared to the numbers of papers I have in physics. So I'm mostly really a physicist, but I'm a physicist with a kind of, I like kind of broad view. And by that, I mean that these questions are important to me."
},
{
"end_time": 3876.203,
"index": 148,
"start_time": 3846.698,
"text": " Now you may say, okay, is that a religious feeling or something like that? I'm certainly not following any, you know, book, religious book or things. Yeah, no. Okay, let's talk about Sabine Hassenfelder, who says that the idea of free will is both incompatible with the laws of nature and entirely meaningless. Okay, what are your thoughts on that statement? Yeah, so I know Sabine."
},
{
"end_time": 3905.145,
"index": 149,
"start_time": 3877.688,
"text": " and I use actually, so she does a lot of these videos and I love most of them. Now she has one indeed on freewheel and actually I use that one when I give some of my lectures to illustrate how extreme some physicists, including very good physicists, can become. And indeed in this video Sabine goes really a very long way and"
},
{
"end_time": 3933.353,
"index": 150,
"start_time": 3905.589,
"text": " claiming that if you believe in free will you are denying science. So she's really claiming that actually science has answered the question in the negative, there is no free will. And this is, in my opinion, a clear overstatement. It's taking physics as a religion somehow, and it's physics with classical mathematics. Again, we just discussed that."
},
{
"end_time": 3964.394,
"index": 151,
"start_time": 3934.531,
"text": " It's pretty strange that Sabine Ofenfelder makes that kind of mistake because one of her books, which I like very much, I think it's called Lost in Mathematics, actually says we have to be careful, we the physicists have to be careful not to overestimate mathematics. In high energy physics, people try to"
},
{
"end_time": 3994.65,
"index": 152,
"start_time": 3965.111,
"text": " to guess the future theories just by the beauty of mathematics, by symmetries and elegance and things like that. And so she says, no, but maybe actually the correct mathematics of the next physics theory will not be as elegant as we think or would like it to be. So, okay, that's a reasonable argument. And I certainly buy that argument, but then herself"
},
{
"end_time": 4024.445,
"index": 153,
"start_time": 3995.299,
"text": " takes classical Platonistic mathematics of the truth. And because Platonistic mathematics considers only objects, mathematical objects that are outside of time, it's a timeless language, classical mathematics. And so when she concludes that time cannot exist and that everything has already to be settled. So she also believes strongly in super determinism."
},
{
"end_time": 4052.415,
"index": 154,
"start_time": 4025.077,
"text": " You know, everything is already determined. There is no quantum randomness. Bail inequality violations can be explained by super determinism. And yeah, at least she's very consistent that I certainly grant her. But when she claims that science has proved it, for instance, that free will is an illusion, she goes too far."
},
{
"end_time": 4082.637,
"index": 155,
"start_time": 4052.722,
"text": " She goes too far by taking mathematics too literally. Can you quickly outline to the audience what super-determinism is? Perhaps what you dislike about it? Well, actually, there are two things that I dislike. Firstly, it's already determinism. Let me come back to that. The entire future, like the entire past, everything is already determined. It doesn't mean that we know it or it doesn't even mean that we have any ability to get that knowledge."
},
{
"end_time": 4112.312,
"index": 156,
"start_time": 4083.063,
"text": " ontologically, fundamentally, it is already determined. That's determinism. Now when people say super determinism, they add an extra little assumption, namely that everything is coordinated. Because you could still imagine that this part of the universe is entirely determined, that part is also entirely determined, but they are not yet connected."
},
{
"end_time": 4139.991,
"index": 157,
"start_time": 4112.637,
"text": " So we are still independent systems that exist in the world. Now, if you also reject the existence of independent systems, then this is super determinism. Some other people would probably say that the super of super determinism means a kind of conspiracy, because when these different things not only need to be already connected, so not"
},
{
"end_time": 4168.524,
"index": 158,
"start_time": 4140.503,
"text": " independent, but they have to be not independent in a very specific way, for instance, to explain the violation or the apparent violation of bail inequality. So I certainly dislike completely the idea that there exist no independent systems in the universe, and actually my view is very clearly, I mean, physics has to be able to tell stories. Physics should make predictions, we all know that, and predictions of course should agree with the experiments,"
},
{
"end_time": 4192.21,
"index": 159,
"start_time": 4169.275,
"text": " But physics is not only about sophisticated theories, physics is also about telling a story. When you go to a class or if you teach, you never start by writing an equation, you start by telling a story. For instance, most people know that"
},
{
"end_time": 4220.725,
"index": 160,
"start_time": 4192.449,
"text": " The tides are due to the moon that attracts the water from the ocean and so on and so on. And you don't need an equation for that story. So the stories are super important in science in general and also in physics. But there are no stories without time. You need to be telling something in time. An event takes place in time. That the moon attracts this water is something that takes place in time."
},
{
"end_time": 4250.64,
"index": 161,
"start_time": 4221.067,
"text": " If you remove the time, there is no story any longer. And how does time come in? For me, time is very, very much connected to the actualization of potentialities, as Aristotle would have said, to the fact that there is new information created during the course of time. So it has to do with indeterminism. And also that already explains you why I think if"
},
{
"end_time": 4280.862,
"index": 162,
"start_time": 4251.34,
"text": " Earlier in the conversation, you said indeterminacy is a necessary condition for free will. It's not sufficient. However, any indeterminate theory can be made determinate with supplementary variables. We can talk about that just for people who are wondering what that means. And then similarly, a determinate theory can be made indeterminate, so they're equivalent. And thus, is determinacy truly a necessary condition for free will?"
},
{
"end_time": 4309.121,
"index": 163,
"start_time": 4281.22,
"text": " The way to make an indeterministic theory deterministic is by adding variables. The trivial way of adding variables is just to add all the future results of all future events or future measurements. It's a trivial way of doing it, it's not very practical, it's not very useful, but obviously you can always do that. Somehow maybe one could say that instead of God playing dice when an event happens,"
},
{
"end_time": 4333.08,
"index": 164,
"start_time": 4310.026,
"text": " God played all dyes at the initial condition at the Big Bang and coded all this information of all these dyes that he played initially, he coded it into the initial conditions, the initial conditions of you know these real numbers that contain all this information of all future events or in Bohmian quantum mechanics it's a similar idea you have"
},
{
"end_time": 4358.592,
"index": 165,
"start_time": 4333.404,
"text": " So you can always do that, but you don't want just to be able to do it. You want to be able to do it in a faithful way. You want to describe nature in a faithful way. And adding the result of future measurements"
},
{
"end_time": 4381.766,
"index": 166,
"start_time": 4359.172,
"text": " When I was speaking with Carlo Rovelli, he said there are two interpretations of quantum mechanics that he feels like are consistent, relational quantum mechanics, and then the many worlds. Of course, but he doesn't like the many worlds interpretation, so he chooses the relational one."
},
{
"end_time": 4407.927,
"index": 167,
"start_time": 4382.176,
"text": " Now, from my understanding of your views, there can't be a wave function of the universe, because this can't just simply evolve in time determinately. Is that an incorrect way? Correct, correct. Okay. Now, does that mean that you don't believe in the many worlds interpretation? No, not at all. I think that's quite an empty concept. And I think the explanatory power of many worlds is essentially zero."
},
{
"end_time": 4438.439,
"index": 168,
"start_time": 4409.428,
"text": " again it's again one of these things which is super deterministic you know there is the initial wave function of the universe and then everything evolves according to that and there is never any event that happens nothing really happens it just is this unitary evolution which is an enormous rotation in this gigantic Hilbert space so I think that there's nothing happening there you cannot tell a story here no no so so my view I'm much closer"
},
{
"end_time": 4466.049,
"index": 169,
"start_time": 4438.695,
"text": " I'm not claiming that I have the solution to all these problems, but my feeling is much closer, my heart is much closer to a spontaneous localization theory, so stochastic evolution of the Schrodinger equation. And so in this way also, as time passes, this Schrodinger equation, this wave function gets added additional information"
},
{
"end_time": 4473.882,
"index": 170,
"start_time": 4466.442,
"text": " bit like my numbers for classical mechanics and as time passes this additional information that gets added to the"
},
{
"end_time": 4503.08,
"index": 171,
"start_time": 4474.138,
"text": " I won't keep you for much longer. I know that you probably have to get going soon. So I'll just ask a couple more questions. Now, going back to when you were younger and your little Nicholas was philosophizing in his armchair and you dabbled with different logical systems. So we talked about periconsistence and intuitionist. Did you dabble with questioning even if logic should be the basis of mathematics itself?"
},
{
"end_time": 4525.811,
"index": 172,
"start_time": 4505.35,
"text": " Well, when I did my PhD in Geneva, indeed a long time ago, my PhD advisor, Professor Piron, was actually a guy working in quantum logic. I don't think himself really believed in quantum logic, but there are many people around and so we had visitors who were really"
},
{
"end_time": 4551.766,
"index": 173,
"start_time": 4526.408,
"text": " thinking of this quantum logic and that by changing the laws of logic, we could make sense of better sense of quantum mechanics. I don't think that this is an interesting approach. I think that that's okay. No. So my answer to your question is no. And again, this is so I'm rejecting the law of the excluded middle."
},
{
"end_time": 4582.363,
"index": 174,
"start_time": 4552.671,
"text": " essentially about propositions that concern the future. You know, my bicycle, now you may ask, is my bicycle on that side or on that side? Well, maybe I forgot. Actually, I know, but I suppose I forgot. Even if I forgot where my bicycle is, my bicycle is definitely either there or there. It's not in an indeterminate position. Now, if you ask me, where will my bicycle be in a weak time?"
},
{
"end_time": 4611.766,
"index": 175,
"start_time": 4583.404,
"text": " One of my favorite ways of showing that classical mechanics has indeterminacy built in it is Norton's Dome. Have you heard of Norton's Dome? Yes, yes, I know that. Yeah, well, but this is, okay, it's a very nice example that shows that indeed you may have initial conditions that don't determine the future of these dynamical systems, but you need very specific"
},
{
"end_time": 4640.043,
"index": 176,
"start_time": 4612.022,
"text": " dynamical systems. You need this dome, that's why it's called a dome, in such a way that if you have a particle coming to that dome, it will, okay, if you don't throw it hard enough, it will just go up and back again. If you throw it too far, it goes over it and goes to the other side. So there's precisely an initial condition, an initial velocity, such that it will stop at the top. And that doesn't exist for all domes. It exists only for"
},
{
"end_time": 4668.933,
"index": 177,
"start_time": 4640.742,
"text": " very specific domes and for these very specific domes so of course we have another ball comes from that side or from any side and suppose it's a two-dimensional thing but from any direction it can stop at the top which means now the initial condition it may go at any time in any direction and that will always be a solution of the newton's equation but so this is fascinating indeed but i don't think it's super convincing because"
},
{
"end_time": 4695.759,
"index": 178,
"start_time": 4669.804,
"text": " You know, if you change the shape of that dome by an epsilon, by a little bit, it's gone. I mean, this peculiarity is gone. So it is not a generic feature. It's a feature of some very, very specific domer potential, as we call it. The reason why I like it is because I know that it's predicated on real numbers and so on. So maybe that's another dispute you have with it."
},
{
"end_time": 4724.94,
"index": 179,
"start_time": 4696.22,
"text": " the reason why I like it is that even in the classical domain we can show that it doesn't have certain continuity condition and then because of that it allows for multiple solutions and not only that but you mentioned that it's not a generic feature I don't know if there's a result that says much like we can say that the typical real number has infinite information in it I don't know if there's a result that says the typical configuration of matter is that which has a Lipschitz continuity condition I would think it's the opposite I would think that not satisfying the Lipschitz continuity condition would be"
},
{
"end_time": 4750.469,
"index": 180,
"start_time": 4725.213,
"text": " typical if we have the general space of functions. But I don't know if that's true. I don't know if there's a result like that. Okay, I also don't know. My bet is that this is very, very specific, and that generically, we don't have this phenomenon, but I cannot. I'm not sure about that. My last question is, with regard to quantum gravity, is there an approach that you favor?"
},
{
"end_time": 4785.555,
"index": 181,
"start_time": 4755.725,
"text": " Make relativity deterministic. But you know, that's a vast program. Okay, now let's get to the audience questions. This one comes from Stephen E. Robbins. A great question to ask Nicholas is, I'm curious if he has looked at Bergson, Time and Free Will. Wait, yes, I'm curious if he's looked at Bergson. So that's it. Yeah, yeah. So I looked at it. I read some of it. I mean, it's too large. I didn't read everything."
},
{
"end_time": 4814.428,
"index": 182,
"start_time": 4785.981,
"text": " Certainly a lot of his writing resonates, but somehow that's where I'm a physicist much more than a philosopher, and Bergson was clearly a philosopher, so at some point it is kind of too vague, I cannot really, you know, grasp it, I cannot really anchor on it, and yeah, so for that reason I"
},
{
"end_time": 4831.51,
"index": 183,
"start_time": 4815.043,
"text": " This question comes from Complex Plane."
},
{
"end_time": 4848.114,
"index": 184,
"start_time": 4832.108,
"text": " Does he think that the denial of free will by physicists is an attempt to make evidence fit a model? Chomsky says that it may be something outside human cognitive abilities to understand. Does he hold a similar view?"
},
{
"end_time": 4873.097,
"index": 185,
"start_time": 4852.585,
"text": " I don't really know. Again, I mean, for me, free will comes first in this logical order. So you need it to start arguing about the existence of free will. So somehow you cannot really deny the existence of free will because if you want to argue against the existence of free will, you need free will to be able to buy or not buy the argument."
},
{
"end_time": 4903.097,
"index": 186,
"start_time": 4874.36,
"text": " Then someone may say, well, how is it that you're choosing so-and-so? Because we use our free will to choose among possibilities. Are you saying there's nothing that influences that? Is it random? How does that work? No, no, no, no. So of course we get influenced. I mean, obviously we are under very heavy influence. And so free will is not something that we use continuously and so on. I mean, most of our decisions are not so important and so on. And we get influenced by ads and whatever."
},
{
"end_time": 4926.613,
"index": 187,
"start_time": 4904.121,
"text": " And they're also not random. I mean, they might be partially random. You can, for instance, decide whether you go to a restaurant tonight by just tossing a coin. So sometimes it will be, but most of the time it will be not random and not predetermined. Now you may say, but who is now"
},
{
"end_time": 4956.067,
"index": 188,
"start_time": 4926.783,
"text": " making the decision, is there a little guy in my brain? Well, it should be myself, so I'm not sitting in my brain or whatever. So that's where our understanding of what free will is, is limited. We don't have this kind of understanding. Maybe it comes also back to what you asked initially about consciousness. I'm making conscious decisions,"
},
{
"end_time": 4982.363,
"index": 189,
"start_time": 4956.288,
"text": " Not always, by the way, but sometimes I'm making conscious decisions. I'm not sure I have much more to add on that. Our decisions are extremely determined by our environment, but being extremely determined is not the same as being fully determined. Exactly. There is room for some decisions. There are clearly some decisions"
},
{
"end_time": 5012.022,
"index": 190,
"start_time": 4982.739,
"text": " Professor, thank you so much for spending some of your time with me."
},
{
"end_time": 5040.367,
"index": 191,
"start_time": 5012.363,
"text": " I appreciate it. I know it's late where you are. No, it's okay. It's 20 past 8. So no, that's perfect. So thank you very much for your time and tell me when that will be online. Very good. Thank you. Thank you for your interest in physics, in science, in free will and in my poor understanding of all those. Thank you, sir."
},
{
"end_time": 5061.493,
"index": 192,
"start_time": 5042.346,
"text": " The podcast is now finished. If you'd like to support conversations like this, then do consider going to patreon.com slash c-u-r-t-j-a-i-m-u-n-g-a-l. That is Kurt Jaimungal. It's support from the patrons and from the sponsors that allow me to do this full time. Every dollar helps tremendously. Thank you."
}
]
}No transcript available.