The following is a conversation with Roger Pan-Rose, physicist, mathematician, and philosopher
at University of Oxford.
He has made fundamental contributions in many disciplines, from the mathematical physics
of general relativity and cosmology, to the limitations of a computational view of consciousness.
In his book, The Emperor's New Mind, Roger writes that, quote,
Children are not afraid to pose basic questions that may embarrass us as adults to ask.
In many ways, my goal with this podcast is to embrace the inner child that is not constrained
by how one should behave, speak, and think in the adult world.
Roger is one of the most important minds of our time, so it's truly a pleasure and an
honor to talk with him.
This conversation was recorded before the outbreak of the pandemic.
For everyone feeling the medical, psychological, and financial burden of the crisis, I'm sending
love your way.
Stay strong.
We're in this together.
We'll beat this thing.
This is the Artificial Intelligence Podcast.
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it on Patreon, or simply connect with me on Twitter at Lex Freedman, spelled F-R-I-D-M-A-N.
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And now here's my conversation with Roger Penrose.
You mentioned in conversation with Eric Weinstein on the portal podcast that 2001 Space Odyssey
is your favorite movie.
Which aspect, if you could mention, of its representation of artificial intelligence,
science, engineering connected with you?
There are all sorts of scenes there, which are so amazing.
And how the science was so well done.
I mean, people say, you know, Interstellar is this amazing movie, which is the most scientific
movie.
I thought it's not a patch on 2001.
I mean, 2001, they really went into all sorts of details regarding, you know, getting the
free fall, well done and everything.
I thought it was extremely well done.
So just the details were mesmerizing.
And also things like the scene where at the beginning they have these sort of human ancestors,
which is sort of apes becoming monolith.
Yes.
And well, it's the one where he throws the bone up into the air and then it becomes this.
I mean, that's an amazing sequence there.
What do you make of the monolith?
Does it have any scientific or philosophical meaning to you?
This kind of thing that sparks innovation?
Not really.
That comes from Arthur C. Clarke.
I was always a great fan of Arthur C. Clarke.
So it's just a nice plot device.
Yeah.
Oh, that plot is excellent.
Yes.
So Hal 9000 decides to get rid of the astronauts because he, it, she believes that they will
interfere with the mission.
That's right.
Yeah, well, there you are.
It's this view.
I don't know whether I disagree with that question.
In a certain sense, it was telling you it's wrong.
See the machine seemed to think it was superior to the human.
And so it was entitled to get rid of the human beings and run the show itself.
Do you think Hal did the right thing?
Do you think Hal is flawed, evil?
Or if we think about systems like Hal, would we want Hal to do the same thing in the future?
What was the flaw there?
Well, you're basically touching on questions.
You see, it's one supposed to believe that Hal was actually conscious.
I mean, it was played rather that way as though Hal was a conscious being.
Because Hal showed some pain, some cognizant, Hal appeared to be cognizant of what it means
to die and therefore had an inkling of consciousness.
Yeah.
I mean, I'm not sure that aspect of it was made completely clear whether Hal was really
a just a very sophisticated computer, which really didn't actually have these feelings
and somehow, but you're right.
It didn't like the idea of being turned off.
How does it change things if Hal was or wasn't conscious?
Well, it might say that it would be wrong to turn it off if it was actually conscious.
I mean, these questions arise if you think, I mean, AI, one of the ideas, it's sort of
a mixture in a sense.
You say, if it's trying to do everything a human can do, and if you take the view that
consciousness is something which would come along when the computer is sufficiently complicated,
sufficiently whatever criteria you use to characterize its consciousness in terms of
some computational criterion.
So how does consciousness change our evaluation of the decision that Hal made?
Yes.
I guess I was trying to say that people are a bit confused about this.
Because if they say these machines will become conscious, but just simply because it's the
degree of computation, and when you get beyond that certain degree of computation, it will
become conscious.
Then, of course, you have all these problems.
I mean, you might say, well, one of the reasons you're doing AI is because you're going to
send a device out to some distant planet, and you don't want to send a human out there
because then you'd have to bring it back again, and that costs you far more than just sending
it there and leaving it there.
But if this device is actually a conscious entity, then you have to face up to the fact
that that's immoral.
And so the mere fact that you're making some AI device and thinking that removes your responsibility
to it would be incorrect.
So this is a sound of flaw in that kind of viewpoint.
I'm not sure how people who take it very seriously, I mean, I had this curious conversation
with, I'm going to forget names, I'm afraid, because this is what happens to me at the
wrong moment.
Hofstadter, Douglas Hofstadter, and he'd written this book, I wish I liked, I thought it was
a fantastic book.
But I didn't agree with his conclusion from Gerdl's theorem, I think he got it wrong,
you see.
Well, I'll just tell you my story, you see, because I'd never met him, and then I knew
I was going to meet him, the occasion I realized he was coming and he wanted to talk to me
and I said, that's fine.
And I thought in my mind, well, I'm going to paint him into a corner, you see, because
I'll use his arguments to convince him that certain numbers are conscious, you know, some
integers, large enough integers are actually conscious.
And this was going to be my reductio, I'd absurd him.
So I started having this argument with him, he simply leapt into the corner, he didn't
even need to be painted into it, he took the view that certain numbers were conscious.
I thought that was a reductio, I'd absurd him, but he seemed to think it was perfectly reasonable
point of view.
Without the absurdum there, yes, interesting.
But the thing you mentioned about how is the intuition that a lot of the people, at least
in the artificial intelligence world had and have, I think, they don't make it explicit,
but that if you increase the power of computation, naturally consciousness will emerge.
Yes, I think that's what they think, but basically that's because they can't think of anything
else.
Right.
And so it's a reasonable thing.
I mean, you think, well, the brain does do a lot of computation.
I think most of what you actually call computation is done by the cerebellum.
I mean, this is one of the things that people don't much mention.
I mean, I come to this subject from the outside and certain things strike me, which you hardly
ever hear mentioned.
I mean, you hear mentioned about the left-right business, the move your right arm, that's
your left side of the brain, and so on and all that sort of stuff.
And it's more than that.
If you have these plots of different parts of the brain, there are two of these things
called the homunculi, which you see these pictures of a distorted human figure and showing
different parts of the brain controlling different parts of the body.
And it's not simply things like, okay, the right hand is controlled and both sensory
and motor on the left side, left hand on the right side, it's more than that.
Vision is at the back, basically, your feet at the top, and this is though it's about
the worst organization you could imagine.
Right.
Yeah.
So it can't just be a mistake in nature.
There's something going on there.
And this is made more pronounced when you think of the cerebellum.
The cerebellum has, when I was first thinking about these things, I was told that it had
half as many neurons or something like that, comparable.
And now they tell me it's got far more neurons than the cerebrum.
The cerebrum is this sort of convoluted thing at the top, people always talk about.
Cerebellum is this thing, just looks a bit like a ball of wool, right at the back underneath
them.
Yeah.
It's got more neurons.
It's got more connections.
Computationally, it's got much more going on than the cerebrum.
But as far as we know, although it's slightly controversial, the cerebellum is entirely
unconscious.
So the actions, you have a pianist who plays an incredible piece of music, and you think
of, and he moves his little finger into this little key to get it hit at just the right
moment.
Does he or she consciously will that movement?
No.
Okay.
The consciousness is coming in.
It's probably to do with the feeling of the piece of music is being performed and that
sort of thing, which is going on, but the details and what's going on are controlled.
I would think almost entirely about the cerebellum.
That's where you have this precision and the really detailed.
Once you get, I mean, you think of a tennis player or something, does that tennis player
think exactly which muscles should be moved in what direction and so on?
No, of course not.
But he or she will maybe think, well, if the ball is angled in such a way in that corner,
that will be tricky for the opponent.
And the details of that are all done largely with the cerebellum.
That's where all the precise motions, but it's unconscious.
So why is it interesting to you that so much computation is done in the cerebellum and yet
is unconscious?
Because it's the view that somehow it's computation, which is producing the consciousness.
And here you have an incredible amount of computation going on.
And as far as we know, it's completely unconscious.
So why, what's the difference?
And I think it's an important thing.
What's the difference?
Why is the cerebrum, all this very peculiar stuff that very hard to see on a computational
perspective, like having everything have to cross over under the other side and do something
which looks completely inefficient.
And you've got funny things like the frontal lobe and the, what do we call the lobes?
And the place where they come together, you have the different parts, the control, you
just want to do with motor and the other to do with sensory.
And they sort of opposite each other rather than being connected by, it's not as though
you've got electrical circuits, there's something else going on there.
So it's just the idea that it's like a complicated computer just seems to me to be completely
missing the point.
There must be a lot of computation going on, but the cerebellum seems to be much better
at doing that than the cerebrum is.
So for sure, I think what explains it is like half hope and half we don't know what's
going on and therefore, from the computer science perspective, you hope that a Turing
machine can be perfectly, can achieve general intelligence.
Well, you have this wonderful thing about Turing and Gertl and Church and Cary and various
people, particularly Turing, and I guess Post was the other one, these people who develop
the idea of what a computation is.
And there were different ideas of what a computer developed differently.
I mean, Church is where they're doing it was very different from Turing's, but then they
were shown to be equivalent.
And so the view emerged that what we mean by a computation is a very clear concept.
And one of the wonderful things that Turing did was to show that you could have what we
call a universal Turing machine.
You just have to have a certain finite device.
Okay, it has to have an unlimited storage space, which is accessible to it, but the
actual computation, if you like, is performed by this one universal device.
And so the view comes away, well, you have this universal Turing machine and maybe the
brain is something like that, a universal Turing machine, and it's got maybe not an
unlimited storage, but a huge storage accessible to it.
And this model is one, which is what's used in ordinary computation.
It's a very powerful model.
And the universalness of computation is very useful.
You can have some problem and you may not see immediately how to put it onto a computer,
but if it is something of that nature, then there are all sorts of sub-programs and sub-routines
and all the...
I mean, I learned a little bit of computing when I was a student, but not very much.
But it was enough to get the general ideas.
And there's something really pleasant about a formal system like that where you can start
discussing about what's provable, what's not, these kinds of things.
And you've got a notion, which is an absolute notion, this notion of computability and address
when mathematical problems are computably solvable and what chance.
So then it's a very beautiful area of mathematics and it's a very powerful area of mathematics
and it underlies the whole sort of, I wouldn't say, the principles of computing machines
that we have today.
Could you say what is Gato's incompleteness theorem and how does it, maybe also says
it heartbreaking to you and how does it interfere with this notion of computation and consciousness?
Sure.
Well, the ideas, basically ideas, which I formulated in my first year as a graduate
student in Cambridge.
I did my undergraduate work in mathematics in London and I had a colleague, Ian Percival.
We used to discuss things like computational and logical systems quite a lot.
I'd heard about Gerdl's theorem, I was a bit worried by the idea that it seemed to
say there were things in mathematics that you could never prove.
And so when I went to Cambridge as a graduate student, I went to various courses.
You see, I was doing pure mathematics.
I was doing algebraic geometry of a sort, a little bit different from all my supervisors
and people.
But it was algebraic geometry.
And I was interested.
I got particularly interested in three lecture courses that were nothing to do with what
I was supposed to be doing.
One was a course by Herman Bondi on Einstein's general theory of relativity, which was a
beautiful course.
He was an amazing lecturer, brought these things alive, absolutely.
And now there was a course on quantum mechanics, given by the great physicist Paul Dirac.
It was a beautiful course in a completely different way.
He was very kind of organized and never got excited about anything, seemingly.
But it was extremely well put together and I found that amazing too.
The third course that was nothing to do with what I should be doing was a course on mathematical
logic.
And I got excited, as I say, my discussions with Ian Percival.
There's an incompleteness theorem already deeply within mathematical logic space.
Were you introduced to it?
I was introduced to it in detail by the course by Steen.
And it was two things he described, which were very fundamental to my understanding.
One was Turing machines and the whole idea of computability and all that.
So that was all very much part of the course.
The other one was the girdle theorem, and it wasn't what I was afraid it was to tell
you there were things in mathematics you couldn't prove.
It was, basically, and he phrased it in a way which often people didn't.
And if you read Douglassoff's status book, he doesn't, you see, but Steen made it very
clear and also in a sort of public lecture that he gave to a mathematical, I think it
may be the Adams Society, one of the mathematical undergraduate societies, and he made this
point again very clearly, that if you've got a formal system of proof, so suppose what
you mean by proof is something which you could check with a computer.
So to say whether you've got it right or not, you've got a lot of steps, have you carried
this computational procedure, well, following the proof, steps of the proof correctly, that
can be checked by an algorithm, by a computer.
So that's the key thing.
Now what, you have to, now you see, is this any good?
If you've got an algorithmic system which claims to say, yes, this is right, no, you've
proved it correctly, this is true, if you've proved it, if you made a mistake, it doesn't
say it's true or false, but if you've done it right, then the conclusion you've come
to is correct.
Now you say, why do you believe it's correct?
Because you've looked at the rules and you said, well, okay, that one's all right, yeah,
that one's all right, what about, oh, yeah, I see, I see why it's all right, okay.
You go through all the rules, you say, yes, following those rules, if it says yes, it's
true, it is true.
So you've got to make sure that these rules are ones that you trust.
If you follow the rules and it says it's a proof, is the result actually true?
And that your belief that it's true depends upon looking at the rules and understanding
them.
Now what Goethe shows is that if you have such a system, then you can construct a statement
of the very kind that it's supposed to look at, a mathematical statement.
And you can see by the way it's constructed and what it means that it's true, but not
provable by the rules that you've been given.
And it depends on your trust in the rules.
Do you believe that the rules only give you truth?
If you believe the rules only give you truth, then you believe this other statement is also
true.
I found this absolutely mind-blowing when I saw this, it blew my mind, thought, my God,
you can see that this statement is true, it's as good as any proof, because it only depends
on your belief in the reliability of the proof procedure, that's all it is, and understanding
that the coding is done correctly and it enables you to transcend that system.
So whatever system you have, as long as you can understand what it's doing and why you
believe it only gives you truth, then you can see beyond that system.
Now how do you see beyond it?
What is it that enables you to transcend that system?
Well, it's your understanding of what the system is actually saying and what the statement
that you've constructed is actually saying.
So it's this quality of understanding, whatever it is, which is not governed by rules.
It's not a computational procedure.
So this idea of understanding is not going to be within the rules of the formal system.
Yes, you only use those rules anyway because you have understood them to be rules which
only give you truth.
There'd be no point in it otherwise.
I mean, people say, well, okay, this is one set of rules as good as any other.
Well, it's not true.
You see, you have to understand what the rules mean.
And why does that understanding of the mean give you something beyond the rules themselves?
And that's what it was.
That's what blew my mind.
It's somehow understanding why the rules give you truth enables you to transcend the rules.
So that's where, I mean, even at that time, that's already where the thought entered
your mind that the idea of understanding, or we can start calling it things like intelligence
or even consciousness is outside the rules.
Yes.
I've always concentrated on understanding.
People say, people are talking about creativity.
That's something a machine can't do.
It's great.
Well, I don't know.
What is creativity?
And I don't know.
Somebody can put some funny things on a piece of paper and say that's creative and you could
make a machine do that.
Is it really creative?
I don't know.
I worry about that one.
I sort of agree with it in a sense, but it's so hard to do anything with that statement.
But understanding, yes, you can.
You can go see that understanding whatever it is, and it's very hard to put your finger
on it.
That's absolutely true.
Can you try to define or maybe dance around a definition of understanding?
To some degree, but I often wondered about this, but there is something there which is
very slippery.
It's something like standing back, and it's also got to be something which was of value
to our remote ancestors, because sometimes there's a cartoon, which I drew sometimes
showing you how all these, in the foreground, you see this mathematician just doing some
mathematical theorem.
There's a little bit of a joke in that theorem, but let's not go into that.
He's trying to prove some theorem, and he's about to be eaten by a saber-toothed tiger
who's hiding in the undergrowth, you see.
In the distance, you see his cousins building growing crops, building shelters, domesticating
animals.
In the slight foreground, you see they built a mammoth trap, and this poor old mammoth
is falling into a pit, you see, and all these people around them are about to grab him,
you see.
Well, you see, those are the ones who, the quality of understanding, which goes with
all these, it's not just the mathematician doing his mathematics, this understanding
quality is something else, which has been a tremendous advantage to us, not just to
us.
See, I don't think consciousness is limited to humans.
That's the interesting question, at which point, if it is indeed connected to the evolutionary
process, at which point, did we pick up this...
A very hard question.
It's certainly, I don't think it's primates, you see these pictures of African hunting
dogs and how they can plan amongst themselves how to catch the antelopes.
Some of these David Attenborough films, I think this probably was one of them.
You could see the hunting dogs, and they divide themselves into two groups, and they go in
two routes, two different routes.
One of them goes and they sort of hide next to the river, and the other group goes around
and they start yelping at these, they don't bark, I guess, whatever noise hunting dogs
do, the antelopes, and they sort of round them up and they chase them in the direction
of the river.
And they're the other ones just waiting for them just to get, because when they get to
the river, it slows them down, and so they pounce on them.
So they've obviously planned this all out, somehow, I have no idea how.
And there is some element of conscious planning, as far as I can see.
I don't think it's just some kind of, so much of AI these days is done, they call bottom
up systems.
Is it, yeah, where you have neural networks and you give them a zillion different things
to look at, and then they sort of can choose one thing over another just because it's seen
so many examples and picks up on little signals, which one may not even be conscious of.
And that doesn't feel like understanding.
There's no understanding in that whatsoever.
Well, you're being a little bit human-centric, so I think I would expect…
Well, I'm talking about, yeah, I'm not with the dogs, am I?
No, you're not.
Sorry, sorry, not human-centric, but I misspoke, biology-centric.
Is it possible that consciousness would just look slightly different?
Well, I'm not saying it's biological, because we don't know.
I think other examples of the elephants is a wonderful example, too, where the elephants
have to go from the long… the troop of them have to go long distances, and the leader
of a troop is a female, they all are apparently.
And this female, she had to go all the way from one part of the country to another.
And at a certain point, she made a detour, and they went off in this big detour.
All the troop came with her, and this is where her sister had died.
And there were her bones lying around, and they go and pick up the bones, and they hand
it around, and they caress the bones, and then they put them back, and they will go
back again.
What in the hell are they doing?
That's so interesting.
I mean, there's something going on.
There's no clear connection with natural selection.
There's just some deep feeling going on there.
We have to do with their conscious experience.
And I think it's something that, overall, is advantageous, a natural selection, but
not directly to do with natural selection.
I like that.
There's something going on there, like I told you, I'm Russian, so I tend to romanticize
all things of this nature, that it's not merely cold, hard computation.
Perhaps I could just slightly answer your question.
You were asking me, what is it?
There's something about standing back and thinking about your own thought processes.
I mean, there is something like that in the girdle thing, because if you're not following
the rules, you're standing back and thinking about the rules.
And so there is something that you might say, you think about you're doing something, and
you think, what the hell am I doing?
And you sort of stand back and think about what it is that's making you think in such
a way.
Just take a step back outside the game you've been playing.
Yeah.
You back up and you think about, you're just not playing the game anymore.
You're thinking about what the hell you're doing in playing this game.
And that's somehow, it's not very precise, descriptive, but somehow it feels very true
that that's somehow understanding, this kind of reflection.
A reflection, yes.
Yeah.
It's a bit hard to put your finger on, but there is something there which I think maybe
could be unearthed at some point and see this is really what's going on.
Why conscious beings have this advantage?
What it is that gives them advantage.
And I think it goes way back.
I don't think we're talking about the hunting dogs and the elephants.
It's pretty clear that octopuses have the same sort of quality.
We call it consciousness.
Yeah, I think so.
I've seen enough examples of the way that they behave and the evolution route is completely
different.
Does it go way back to some common ancestor or did it come separately?
My hope is it's something simple, but the hard question, if there's a hardware prerequisite,
that we have to develop some kind of hardware mechanisms in our computers, like basically,
as you suggest, we'll get to in a second, we kind of have to throw away the computer
as we know it today, the deterministic machines we know today to try to create it.
My hope, of course, is not.
Well, I should go really back to the story which, in a sense, I haven't finished because
I went to these three courses, you see, when I was a graduate student.
And so I started to think, well, I'm really, I'm a pretty, what you might call a materialist
in the sense of thinking that there's no kind of mystical or something or other which comes
in from who knows where.
You still that?
Yeah, you still throughout your life been a materialist.
I don't like the word materialist because it suggests we know what material is.
And that is a bad word because there's no mystical.
It's not some mystical something which is not treatable by science.
That's so beautifully put, just to pause on that for a second.
You're a materialist, but you acknowledge that we don't really know what the material
is.
That's right.
I mean, I like to call myself a scientist, I suppose, but it means that, yes, well, you
see, the question goes on here.
So I began thinking, okay, if consciousness or understanding is something which is not
a computational process, what can it be?
And I knew enough for my undergraduate work, I knew about Newtonian mechanics and I knew
how basically you could put it on a computer.
There is a fundamental issue which is this important or not that computation depends
upon discrete things, so using discrete elements, whereas the physical laws depend on the continuum.
Now, is this something to do with it?
Is it the fact that we use the continuum in our physics?
And if we model our physical system, we use discrete systems like ordinary computers.
I came to the view that that's probably not it.
I might have to retract on that someday, but the view was no, you can get close enough.
It's not altogether clear, I have to say, but you can get close enough.
And I went to this course by Bondi on general relativity and I thought, well, you can put
that on a computer.
Of course, that was a long time before people, and I've sort of grown up with this, how people
have done better and better calculations and they could work out about black holes and
they can then work out how black holes can interact with each other, spar around and
what kind of gravitational waves can out, and there's still a very impressive piece
of computational work, how you can actually work out the shapes of those signals.
And now we have LIGO seeing these signals and they say, yeah, those black holes spiral
into each other.
This is just a vindication of the power of computation in describing Einstein's general
relativity.
So in that case, we can get close, but with computation, we can get close to understanding
the physics.
You can get very, very close.
Now, is that close enough, you see?
And then I went to this course by Dirac.
Now, you see, I think it was the very first lecture that he gave, and he was talking about
the superposition principle, and he said, if you have a particle, you usually think of
particle can be over here or over there, but in quantum mechanics, it can be over here
and over there at the same time, and you have these states which involve a superposition
in some sense of different locations for that particle.
And then he got out his piece of chalk, and some people say he broke it in two as a kind
of illustration of how the piece of chalk might be over here and over there at the same
time.
And he was talking about this, and my mind wandered.
I don't remember what he said.
All I can remember, he just moved on to the next topic, and something about energy he'd
mentioned which I had no idea what had to do with anything.
And so I'd been struck with this and worried about it ever since.
It's probably just as well, I didn't hear his explanation, because it was probably one
of these things to calm me down and not worry about it anymore, whereas in my case, I've
worried about it ever since.
So I thought, maybe that's the catch.
There is something in quantum mechanics where these superpositions become one or the other,
and that's not part of quantum mechanics, there's something missing in the theory.
The theory is incomplete, it's not just incomplete, it's in a certain sense not quite right.
Because if you follow the equation, the basic equation of quantum mechanics, that's the
Schrodinger equation, you could put that on a computer too, there are lots of difficulties
about how many parameters you have to put in and so on, that can be very tricky.
But nevertheless, it is a computational process.
Modulo this question about the continuum as before, but it's not clear that makes
any difference.
So our theories of quantum mechanics may be missing the same element that the universal
term machine is missing about consciousness.
Yes, this is the view I held, is that you need a theory and that what people call the
reduction of the state or the collapse of the wave function, which you have to have,
otherwise quantum mechanics doesn't relate to the world we see.
To make it relate to the world we see, you've got to break the Schrodinger equation.
Schrodinger himself was absolutely appalled by this idea, his own equation.
I mean, that's why he introduced this famous Schrodinger's cat as a thought experiment.
He's really saying, look, this is where my equation leads you into it.
There's something wrong, something we haven't understood, which is basically fundamental.
And so I was trying to put all these things together and said, well, it's got to be the
non-competitive credibility comes in there.
And I also can't remember when I thought this, but it is when gravity is involved in quantum
mechanics.
It's the combination of those two, and it's that point when you have good reasons to believe,
this came much later, that I have good reason to believe that the principles of general
relativity and those of quantum mechanics, most particularly, it's the basic principle
of equivalence, which goes back to Galileo.
If you fall freely, you eliminate the gravitational field.
So you imagine Galileo dropping his big rock and his little rock from the leaning tower,
whether he actually ever did that or not, is it pretty irrelevant?
And as the rocks fall to the ground, you'll have a little insect sitting on one of them
looking at the other one.
And it seems to think, oh, there's no gravity here.
Of course, it hits the ground and then you realize something's different going on.
But when it's in free fall, the gravity has been eliminated.
Galileo understood that very beautifully.
He gives these wonderful examples of fireworks.
And you see the fireworks and explode, and you see the sphere of sparkling fireworks.
It remains a sphere as it falls down, as though there were no gravity.
So he understood that principle, but he couldn't make a theory out of it.
Einstein came along, used exactly the same principle, and that's the basis of Einstein's
general theory of relativity.
Now, there is a conflict.
This is something I did much, much later, so this wasn't those days, much, much later.
You can see there is a basic conflict between the principle of superposition, the thing
that Dirac was talking about, and the principle of general covariant.
Well, principle of equivalence, gravitational field is equivalent to an acceleration.
Can you pause for a second?
What is the principle of equivalence?
It's this Galileo principle that we can eliminate, at least locally.
You have to be in a small neighborhood, because you see if you have people dropping rocks
all around the world somewhere, you can't get rid of it all at once.
But in the local neighborhood, you can eliminate the gravitational field by falling freely
with it.
And we now see this with astronauts, and they don't, you know, the Earth is right there.
You can see the great globe of the Earth right beneath them, but they don't care about it.
As far as they're concerned, there's no gravity.
They fall freely in the gravitational field, and that gets rid of the gravitational field.
And that's the principle of equivalence.
So what's the contradiction?
What's the tension with superposition and equivalence?
Well, that's technical.
So it's just a backtrack for a second, just to see if we can weave a thread through it
all.
Yes.
So we started to think about consciousness as potentially needing some of the same, not
a mystical, but some of the same magic.
You see, it is a complicated story.
So you know, people think, oh, I'm drifting away from the point or something.
But I think it is a complicated story.
So what I'm trying to say, I mean, I tried to put it in a nutshell, but it's not so easy.
I'm trying to say that whatever consciousness is, it's not a computation.
Yes.
Or it's not a physical process which can be described by computation.
But it nevertheless could be, so one of the interesting models that you've proposed is
the orchestrated objective reduction, which is stuck.
You see, that's going from there, you see.
So I say I have no idea.
So I wrote this book through my scientific career.
I thought, you know, when I'm retired, I'll have enough time to write a sort of a popularish
book, which I will explain my ideas and puzzles, what I like, beautiful things about physics
and mathematics, and this puzzle about computability and consciousness and so on.
And in the process of writing this book, well, I thought I'd do it when I was retired.
I didn't actually, I didn't wait that long because there was a radio discussion between
Edward Fredkin and Marvin Minsky.
And they were talking about what computers could do.
And they were entering, entering a big room.
They imagined entering this big room where at the other end of the room, two computers
were talking to each other.
And as you walk up to the computers, they will have communicated to each other more
ideas, concepts, things than the entire human race had ever commuted.
So I thought, well, I know where you're coming from, but I just don't believe you.
There's something missing.
So I thought, well, I should write my book.
And so I did.
It was roughly the same time Stephen Hawking was writing his brief history of time.
In the 80s at some point.
The book you're talking about is The Emperor's New Mind.
The Emperor's New Mind, that's right.
And both are incredible books, The Brief History of Time and The Emperor's New Mind.
Yes.
It was quite interesting because he told me he'd got Carl Sagan, I think, to write it
forward.
It's a good get.
The book you see.
So I thought, gosh, what am I going to do?
I'm not going to get anywhere unless I get somebody.
So I said, well, I know Martin Gardner, so I wonder if he'd do it.
So he did.
And he did a very nice forward.
So that's an incredible book.
And some of the same people you mentioned, Ed Franken, which I guess of expert systems
fame and Minsky, of course, people know in the AI world, but they represent the artificial
intelligence world.
Absolutely.
That's right.
That do hope and dream that AI's intelligence is probably the best.
Well, you see, it was my thinking.
Well, you know, I see where they're coming from.
And from that perspective, yeah, you're right.
But that's not my perspective.
So I thought I had to say it.
And as I was writing my book, you see, I thought, well, I don't really know anything about neurophysiology.
What am I doing writing this book?
So I started reading up about neurophysiology and I read another thing and I try to find
out how it is that nerve signals could possibly preserve quantum coherence.
And all I read is that the electrical signals which go along the nerves create effects through
the brain.
There's no chance you can isolate it so that this is hopeless.
So I come to the end of the book and I more or less give up.
I just think of something which I didn't believe in, that's maybe this is the way around it,
but no.
And then you say, I thought, well, maybe this book will at least stimulate young people
to do science or something.
And I got all these letters from old retired people instead.
He's the only people who could have time to read my book.
So I mean, except for Stuart Hammerhoff.
Except for Stuart Hammerhoff.
Stuart Hammerhoff wrote to me and he said, I think you're missing something.
You don't know about microtubules, do you?
He didn't put it quite like that, but that was more or less it.
And he said, this is what you really need to consider.
So I thought, my God, yes, that's a much more promising structure.
So I mean, fundamentally, you were searching for the source of non-computable source of
consciousness within the human brain in the biology.
And so if I may ask, what are microtubules?
Well, you see, I was ignorant and what I'd read, I never came across them in the books
I looked at.
Perhaps I only read rather superficially, which is true, but I didn't know about microtubules.
Stuart, I think one of the things he was impressed him about them was that when you
see pictures of mitosis, that's a cell dividing and you see all the chromosomes and the chromosomes
get, they all get lined up and then they get pulled apart.
And so as the cell divides, the half the chromosomes go, you know, they divide into the two parts
and they go two different ways.
And what is it that's pulling them apart?
Well, those are these little things called microtubules.
And so he starts to get interested in them.
And he formed the view when he was at his day job or night job, or whatever you call it,
just to put people to sleep, except he doesn't like calling it sleep because it's different.
General anaesthetics in a reversible way.
So you want to make sure that they don't experience the pain that would otherwise be something
that they feel and consciousness is turned off for a while and it can be turned back
on again.
So it's crucial that you can turn it off and turn it on.
And what do you do when you're doing that?
What do general anaesthetic gases do?
And see, he formed the view that it's the microtubules that they affect.
And the details of why he formed that view is not, or they're clear to me, but there's
an interesting story he keeps talking about.
But I found this very exciting because I thought these structures, these little tubes which
inhabit pretty well all cells, it's not just neurons, apart from red blood cells, they
inhabit pretty well all the other cells in the body.
But they're not all the same kind.
You get different kinds of microtubules.
And the ones that excited me the most, this may still not be totally clear, but the ones
that excited me most were the ones that, the only ones that I knew about at the time because
they were, they're very, very symmetrical structures.
And I had reason to believe that these very symmetrical structures would be much better
at preserving a quantum state, quantum coherence, preserving the thing without, you just need
to preserve certain degrees of freedom without them leaking into the environment.
Once they leak into the environment, you're lost.
So you've got to preserve these quantum states at a level which the state reduction process
comes in and that's where I think the non-computability comes in and it's the measurement process
in quantum mechanics, what's going on?
So something about the measurement process and what's going on, something about the structure
of the microtubules, your intuition says, maybe there's something here, maybe this kind
of structure allows for the mystery of the quantum mechanics.
There was a much better chance, yes.
It just struck me that partly it was the symmetry because there is a feature of symmetry you
can preserve quantum coherence much better with symmetrical structures.
There's a good reason for that.
And that impressed me a lot.
I didn't know the difference between the A-lattice and B-lattice at that time, which could be
important.
Now that could be, which isn't talked about much.
But that's in some sense details.
We've got to take a step back just to say in case people are not familiar.
So this was called the orchestrated objective reduction idea or ORC-OR, which is a biological
philosophy of mind that postulates that consciousness originates at the quantum level inside neurons.
So that has to do with your search for where, where is it coming from?
So that's counter to the notion that consciousness might arise from the computation performed
by the synapses.
Yes.
I think the key point, sometimes people say it's because it's quantum mechanical.
It's not just that.
See, it's more outrageous than that.
You see, this is one reason I think we're so far off from it because we don't even know
the physics right.
You see, it's not just quantum mechanics.
People say, oh, you know, quantum systems and biological structures.
No, will you starting to see that some basic biological systems does depend on quantum?
I mean, look, in the first place, all of chemistry is quantum mechanics.
People got used to that.
So they don't count that.
So he said, let's not count quantum chemistry.
We sort of got the hang of that, I think.
But you have quantum effects, which are not just chemical, in photosynthesis.
And this is one of the striking things in the last several years, that photosynthesis
seems to be a basically quantum process, which is not simply chemical.
It's using quantum mechanics in a very basic way.
So you could start saying, oh, well, with photosynthesis is based on quantum mechanics.
Why not behavior of neurons and things like that?
Maybe there's something which is a bit like photosynthesis in that respect.
But what I'm saying is even more outrageous than that, because those things are talking
about conventional quantum mechanics.
Now my argument says that conventional quantum mechanics, if you're just following the Schrodinger
equation, that's still computable.
So you've got to go beyond that.
So you've got to go to where quantum mechanics goes wrong in a certain sense.
You have to be a little bit careful about that, because the way people do quantum mechanics
is a sort of mixture of two different processes.
One of them is the Schrodinger equation, which is an equation Schrodinger wrote down, and
it tells you how the state of a system evolves, and it evolves accordingly.
This equation is completely deterministic, but it involves inter-ridiculous situations.
And this was what Schrodinger was very much pointing out with his cat.
He said, you follow my equation, that's Schrodinger's equation, and you could say that you have
a cat which is dead and alive at the same time.
That would be the evolution of the Schrodinger equation would lead to a state, which is the
cat being dead and alive at the same time.
And he's more or less saying, this is an absurdity.
People nowadays say, oh, Schrodinger said you can have a cat which is dead, and that's not
that.
You see, he was saying, this is an absurdity.
There's something missing.
And that the reduction of the state, or the collapse of the wave function, or whatever
it is, is something which has to be understood.
It's not following the Schrodinger equation.
It's not the way we conventionally do quantum mechanics.
There's something more than that.
And it's easy to quote authority here, because Einstein, at least three of the greatest physicists
of 20th century, who were very fundamental in developing quantum mechanics, Einstein,
one of them, Schrodinger, another, Dirac, another.
You have to look carefully at Dirac's writing, because he didn't tend to say this out loud
very much, because he was very cautious about what he said.
You find the right place, and you see, he says quantum mechanics is a provisional theory.
We need something which explains the collapse of the wave function.
We need to go beyond the theory we have now.
I happen to be one of the kinds of people, there are many, there is a whole group of
people, they're all considered to be a bit, you know, a bit mavericks, who believe that
quantum mechanics needs to be modified.
There's a small minority of those people, which are already a minority, who think that
the way in which it's modified has to be with gravity, and there is an even smaller minority
of those people who think it's a particular way that I think it is, you see.
So those are the quantum gravity folks, but what's what?
You see, quantum gravity is already not this, because when you say quantum gravity, what
you really mean is quantum mechanics applied to gravitational theory.
So you say, let's take this wonderful formalism of quantum mechanics and make gravity fit
into it.
So that is what quantum gravity is meant to be.
Now I'm saying, you've got to be more even-handed, that gravity affects the structure of quantum
mechanics too.
It's not just you quantize gravity, you've got to gravitate quantum mechanics.
And it's a two-way thing.
But then when you even get started, so that you're saying that we have to figure out
a totally new idea isn't it?
Exactly.
No, you're stuck.
You don't have a theory, that's the trouble.
So this is a big problem if you say, okay, well, what's the theory?
I don't know.
So maybe in the very early days sort of...
It is in the very early days, isn't it?
But just making this point, if you Stuart Hammerhoff tends to be, oh, Penrose says that
it's got to be a reduction of the state and so on, so let's use it.
The trouble is Penrose doesn't say that, Penrose says, well, I think that.
We have no experiments as yet, which shows that.
There are experiments which are being thought through and which I'm hoping will be performed.
There is an experiment which is being developed by Dirk Baumeister, who is known for a long
time, who shares his time between Leiden in the Netherlands and Santa Barbara in the US.
And he's been working on an experiment which could perhaps demonstrate that quantum mechanics,
as we now understand it, if you don't bring in the gravitational effects, has to be modified.
And then there's also experiments that are underway that kind of look at the microtubule
side of things to see if there's, in the biology, you could see something like that.
Could you briefly mention it?
Because that's really sort of one of the only experimental attempts in the very early days
of even thinking about caution.
I think there's a very serious area here, which is what Stuart Hamaroff is doing, and
I think it's very important.
One of the few places that you can really get a bit of a handle on what consciousness is,
is what turns it off.
And when you're thinking about general anesthetics, it's very specific.
These things turn consciousness off.
What the hell do they do?
Well, Stuart and a number of people who work with him and others happen to believe that
the general anesthetics directly affect microtubules.
And there is some evidence for this.
I don't know how strong it is and how watertight the case is, but I think there is some evidence
pointing in that kind of direction.
It's not just an ordinary chemical process, there's something quite different about it.
And one of the main candidates is that these anesthetic gases do affect directly microtubules.
And how strong that evidence is, I wouldn't be in a position to say.
But I think there is fairly impressive evidence.
And the point is that the experiments are being undertaken, which is a very clear direction
where you can think of experiments which could indicate whether or not it's really microtubules,
which the anesthetic gases directly affect.
That's really exciting.
One of the sad things is, as far as I'm from my outside perspective, is not many people
are working on this.
So there's a very, like with Stuart, it feels like there's very few people carrying the
flag forward on this.
I think it's not many in the sense it's a minority, but it's not zero anymore.
You see, when Stuart and I were originally close friends, we were just us and a few of
our friends, there weren't many people taking it, but it's grown into one of the main viewpoints.
There might be about four or five or six different views that which people hold, and it's one
of them.
So it's considered as one of the possible lines of thinking, yes.
You describe physics theories as falling into one of three categories, the superb, the useful
or the tentative.
I like those words, it's a beautiful categorization.
Do you think we'll ever have a superb theory of intelligence and of consciousness?
We might.
We're a long way from it.
I don't think we're even, we're in the tentative scale.
I mean, it's...
You don't think we've even entered the realm of tentative?
Probably not, I think.
Yeah, that's right.
When you see this, it's so controversial, we don't have a clear view which is accepted
by a majority.
I mean, you say, yeah, people, most views are computational in one form or another.
They think it's some, but it's not very clear, because even the IIT people who think of them
as computational, but I've heard them say, no, consciousness is supposed to be not computational.
I say, well, if it's not coming, what in the hell is it?
What's going on?
What physical processes are going on which are that?
What does it mean for something to be computational then?
So is...
Well, there has to be a process which is, you see, it's very curious the way the history
has developed in quantum mechanics, because very early on, people thought there was something
to do with consciousness, but it was almost the other way around.
Obviously, you have to say the Schrodinger equation says all these different alternatives
happen all at once, and then when is it that only one of them happens?
Well, one of the views, which was quite commonly held by a few distinguished quantum visitors,
is when a conscious being looks at the system or becomes aware of it, and at that point,
it becomes one or the other.
That's a role where consciousness is somehow actively reducing the state.
My view is almost the exact opposite of that.
It's the state reduces itself in some way, in some non-computational way, which we don't
understand, we don't have a proper theory of, and that is the building block of what
consciousness is.
So consciousness is the other way around.
It depends on that choice which nature makes all the time when the state becomes one or
the other rather than the superposition of one and the other.
And when that happens, we're saying now an element of proto-consciousness takes place.
Proto-consciousness is, roughly speaking, the building block out of which actual consciousness
is constructed.
So you have these proto-conscious elements which are when the state decides to do one
thing or the other, and that's the thing which, when organized together, that's the
OR part and ORCOR, but the ORC part.
That's the OR part, at least one can see when we're driving it as a theory.
You can say it's the quantum choice of going this way or that way.
But the ORC part, which is the orchestration of this, is much more mysterious.
And how does the brain somehow orchestrate all these individual OR processes into a
genuine, genuine conscious experience?
And it might be something that's beautifully simple, but we're completely in the dark about.
Yeah.
I think at the moment, that's the thing.
We happily put the word ORC down there to say orchestrated, but that's even more unclear
what that really means.
Just like the word material orchestrated, who knows.
And we've been dancing a little bit between the word intelligence or understanding and
consciousness.
You can see those as sitting in the same space of mystery as with this place.
Yes.
You see, I tend to say you have understanding and intelligence and awareness.
And somehow understanding is in the middle of it, you see.
I like to say, could you say of an entity that is actually intelligent if it doesn't
have the quality of understanding?
You say, I'm using terms I don't even know how to define, but who cares?
I'm just relating.
They're somewhat poetic, so if I somehow understand them.
Yes.
That's right.
Exactly.
But they're not mathematical in nature.
Yes.
You see, as a mathematician, I don't know how to define any of them, but at least I can
point to the connections.
So the idea is, intelligence is something which I believe needs understanding, otherwise you
wouldn't say it's really intelligence.
And understanding needs awareness, otherwise you wouldn't really say it's understanding.
Do you say of an entity that understands something unless it's really aware of it,
you know, normal usage?
So there's a three sort of awareness, understanding, and intelligence.
And I just tend to concentrate on understanding because that's where I can say something.
Okay.
And that's the girdle theorem, things like that.
But what does it mean to perceive the color blue or something?
I mean, I'm a foggiest.
That's a much more difficult question.
I mean, is it the same if I see a color blue and you see it?
If you're assembling with what is this condition, what does it call them?
Over your sign, like a sound to a color.
Yeah, that's right.
You get colors and sounds mixed up.
And that sort of thing.
I mean, an interesting subject, I mean.
But from the physics perspective, from the fundamentalist perspective, we don't.
I think we're way off and having much understanding what's going on there.
In your 2010 book, Cycles of Time, you suggest that another universe may have existed before
the Big Bang.
Can you describe this idea?
First of all, what is the Big Bang?
Sounds like a funny word.
And what may have been there before it?
Yes.
This is a matter of terminology.
I don't like to call it another universe, because when you have another universe, you
think of it kind of quite separate from us.
But these things, they're not separate.
Now, the Big Bang, conventional theory, you see, I was actually brought up in the sense
of when I started getting interested in cosmology, there was a thing called the steady state model,
which was sort of philosophically very interesting.
And there wasn't a Big Bang in that theory that somehow new material was created all
the time in the form of hydrogen and the universe kept on expanding and expanding and expanding
and there was room for more hydrogen.
It was a rather philosophically nice picture.
It was disproved when the Big Bang, well, when I say the Big Bang, this was theoretically
discovered by people trying to solve Einstein's equations and apply it to cosmology.
Einstein didn't like the idea.
He liked a universe which was there all the time.
And he had a model which was there all the time.
But then there was this discovery, accidental discovery, very important discovery of this
microwave background.
And if you, there's the crackle on your television screen, which is already sensing this microwave
background, which is coming at us from all directions, and you can trace it back and
back and back and back, then it came from a very early stage of the universe.
Well, it's part of the Big Bang theory.
The Big Bang theory was when people tried to solve Einstein's equations.
They really found you had to have this initial state where the universe, it was used to be
called the primordial atom and things like this.
This Friedman and Lemaître, Friedman was a Russian, Lemaître was a Belgian, and they
independently, well, basically Friedman first, Lemaître talked about the initial state,
which is a very, very concentrated initial state, which seemed to be the origin of the
universe.
Primordial atom.
Primordial atom is what he called it, yes.
Beautiful term.
And then it became, well, Fred Hoyle used the term Big Bang in a kind of derogatory
sense.
He said, well, didn't he have that?
Just like with the shorting or the cats, right?
Yes, it's like sort of got picked up on, whereas it wasn't his intention originally.
But then the evidence piled up and piled up, and one of my friends I learned a lot from
him when I was in Cambridge, just Dennis Sharma, he was a very proponent of steady state,
and then he got converted, just said, no, I'm sorry, I had a great respect for him.
He went around lecturing, said, I was wrong.
This steady state model doesn't work.
There was this Big Bang, and this microwave background that you see, okay, it's not actually
quite the Big Bang, when I said not quite.
It's about 380,000 years after the Big Bang, but that's what you see.
But then you have to have had this Big Bang before it in order to make the equations work,
and it works beautifully, except for one little thing, which is this thing called inflation,
which people had to put into it to make it work.
When I first heard of it, I didn't like it at all.
What's inflation?
Inflation is that in the first, I'm going to give you a very tiny number.
Think of a second.
That's not very long.
Now, I'm going to give you a fraction of a second, one over a number.
This number has 32 digits, well, let's say between 36 and 32 digits, tiny, tiny time
between those two, tiny, ridiculous seconds, fraction of a second, the universe was supposed
to have expanded in this exponential way, in an enormous way.
For no apparent reason, you had to invent a particular thing called the inflaton field
to make it do it, and I thought this is completely crazy.
There are reasons why people stuck with this idea.
You see, the thing is that I've formed my model for reasons which are very fundamental,
if you like.
It has to do with this very fundamental principle, which is known as the second law of thermodynamics.
The second law of thermodynamics says, more or less, things get more and more random as
time goes on.
Now, in other words, saying exactly the same thing, is things get less and less random.
As things go back, as you go back in time, they get less and less random.
They go back and back and back and back, and the earliest thing you can directly see is
this microwave background.
What's one of the most striking features of it is that it's random.
It has what you call this spectrum, which is what's called the Planck spectrum, of frequencies,
different intensities for different frequencies, and there's this wonderful curve, there's
a max Planck, and what's it telling you?
It's telling you that the entropy is at a maximum, start is off at a maximum, and it's
going up ever since.
I call that the mammoth in the room.
I mean, it's a paradox.
The mammoth, yeah, it is.
So people, why don't cosmologists worry about this?
So I worried about it, and then I thought, well, it's not really a paradox because you're
looking at matter and radiation at a maximum entropy state.
What you're not seeing directly in that is the gravitation.
It's gravitation, which is not thermalized.
The gravitation was very, very low entropy, and it's low entropy by the uniformity, and
you see that in the microwave too.
It's very uniform over the whole sky.
I'm compressing a long story into a very short few sentences.
And doing a great job, yeah.
So what I'm saying is that there's a huge puzzle.
Why was gravity in this very low entropy state, very high organized state, everything
else was all random?
And that, to me, was the biggest problem in cosmology.
The biggest problem?
Nobody seems to even worry about it.
People say they solved all the problems, and they don't even worry about it.
They think inflation itself says it doesn't, it can't, because it's just...
Just to clarify, that was your problem with the inflation describing some aspect of the
moment right after the Big Bang?
Inflation is supposed to stretch it out and make it all uniform, you see.
It doesn't do it, because it can only do it if it's uniform already at the beginning.
You just have to look...
I can't go into the details, but it doesn't solve it, and it was completely clear to me
it doesn't solve it.
But where does the conformal cyclic cosmology of starting to talk about something before
that singularity of the Big Bang?
And I was just thinking to myself, how boring this universe is going to be.
You've got this exponential expansion, this was discovered early in this 21st century.
People discovered that these supernova exploding stars showed that the universe is actually
undergoing this exponential expansion.
So it's a self-similar expansion.
And it seems to be a feature of this term that Einstein introduced into his cosmology
for the wrong reason.
He wanted a universe that was static, he put this new term into his cosmology, to make
it make sense, it's called the cosmological constant.
And then when he got convinced that the universe had a Big Bang, he retracted it, complaining
that this was his greatest blunder.
The trouble is it wasn't a blunder, it was actually right, very ironic.
And so the universe seems to be behaving with this cosmological constant.
So this universe is expanding and expanding, what's going to happen in the future?
Well, it gets more and more boring for a while, what's the most interesting thing in the
universe?
Well, there's black holes.
The black holes more or less gulp down in entire clusters of galaxies, it'll swallow
up most of our galaxy, we will run into our Andromeda galaxies, black hole, that black
hole will swallow our one, they'll get bigger and bigger and they'll basically swallow
up the whole cluster of galaxies, gulp it all down, pretty well all, most of it, maybe
not all, most of it, that'll happen to, they'll be just these black holes, pretty boring,
but still not as boring as it's going to get, it's going to get more boring because
these black holes, you wait, you wait, and you wait, and you wait, and you wait, and
you wait, an unbelievable length of time, and Hawking's black hole evaporation starts
to come in.
And the black holes, you just, it's incredibly tedious, finally evaporate away, each one
goes away, disappears with a pop at the end.
What could be more boring, it was boring then, now this is really boring, there's nothing,
not even black holes, universe gets colder and colder and colder and colder, and I thought,
this is very, very boring, now that's not science is it, but it's emotional, so I thought,
who's going to be bored by this universe, not us, we won't be around, it'll be mostly
photons running around, and what do photons do, they don't get bored because it's part
of relativity, you see, it's not really that they don't experience anything, that's not
the point, that photons get right out to infinity without experience any time, it's the way
relativity works, and this was part of what I used to do in my old days when I was looking
at gravitational radiation and how things behaved in infinity, infinity is just like
another place, you can squash it down, as long as you don't have any mass in the world,
infinity is just another place, the photons get there, the gravitons get there, what do
they get, they run to infinity, they say, well, now I'm here, what do I, there's something
on the other side, is there, the usual view, it's just a mathematical notion, there's
nothing on the other side, that's just the boundary of it, a nice example is this beautiful
series of pictures by the Dutch artist MC Escher, you may know them, the one's called
Circle Limits, they're a very famous one with the angels and the devils, and you can see
them crowding and crowding and crowding up to the edge, now the kind of geometry that
these angels and devils inhabit, that's their infinity, but from our perspective, infinity
is just a place, okay, there, sorry, can you just take a brief pause, and just the word
you're saying, infinity is just a place, so for the most part, infinity, sort of even
just going back, infinity is a mathematical concept, you think there's an actual physical
manifest, like in which way does infinity ever manifest itself in our physical universe?
Well, it does in various places, you see, it's a thing that, if you're not a mathematician,
you think, oh, infinity, I can't think about that, mathematicians think about infinity
all the time, they get used to the idea, and they just play around with different kinds
of infinities, and it becomes no problem, but you just have to take my word for it.
Now, one of the things is, you see, you take a Euclidean geometry, well, it just keeps
on going, and it goes out to infinity.
Now, there's other kinds of geometry, and this is what's called hyperbolic geometry,
it's a bit like Euclidean geometry, it's a little bit different.
It's like what Asher was trying to describe in his angels and devils, and he learned about
this from Coxeter, and he think that's a very nice thing, I try and represent this
infinity to this kind of geometry.
So it's not quite Euclidean geometry, it's a bit like it, that the angels and the devils
inhabit.
And there infinity, by this nice transformation, you squash the there infinity down, so you
can draw it as this nice circle boundary to their universe.
Now, from our outside perspective, we can see their infinity as this boundary.
Now, what I'm saying is that it's very like that.
The infinity that we, might experience like those angels and devils in their world, can
be thought of as a boundary.
Now, I found this a very useful way of talking about radiation, gravitational radiation,
and things like that.
It was a trick, mathematical trick.
So now what I'm saying is that that mathematical trick becomes real, that somehow the photons,
they need to go somewhere, because from their perspective, infinity is just another place.
Now this is a difficult idea to get your mind around, so that's why one of the reasons cosmologists
are finding a lot of trouble taking me seriously.
But to me, it's not such a wild idea.
What's on the other side of that infinity?
You have to think, why am I allowed to think of this?
Because photons don't have any mass.
And we in physics have beautiful ways of measuring time.
They are incredibly precise clocks, atomic and nuclear clocks, unbelievably precise.
Why are they so precise?
Because of the two most famous equations of 20th century physics.
One of them is Einstein's E equals MC squared, what's that tell us?
Energy and mass are equivalent.
The other one is even older than that, still 20th century, only just.
Max Planck E equals H nu.
Nu is a frequency, H is a constant again like C, E is energy.
Energy and frequency are equivalent.
Put the two together, energy and mass are equivalent to Einstein, energy and frequency
equivalent, Max Planck, put the two together, mass and frequency are equivalent.
Absolutely basic physical principle.
If you have a massive entity, a massive particle, it is a clock with a very, very precise frequency.
It's not, you can't directly use it, you have to scale it down, so your atomic and
nuclear clocks, but that's the basic principle.
You scale it down to something you can actually perceive, but it's the same principle.
If you have mass, you have beautiful clocks.
But the other side of that coin is, if you don't have mass, you don't have clocks.
If you don't have clocks, you don't have rulers.
You don't have scale.
So you don't have space and time.
You don't have a measure of the scale of space and time.
You do have the structure, what's called the conformal structure.
You see it's what the angels and devils have, if you look at the eye of the devil, no matter
how close to the boundary it is, it has the same shape, but it has a different size.
So you can scale up and you can scale down, but you mustn't change the shape.
So it's basically the same idea, but applied to space-time now.
In the very remote future, you have things which don't measure the scale, but the shape,
if you like, is still there.
Now that's in the remote future.
Now I'm going to do the exact opposite.
Now I'm going to go way back into the Big Bang.
Now as you get there, things go hotter and hotter, denser and denser.
What's the universe dominated by?
Particles moving around almost with the speed of light.
When they get almost with the speed of light, okay, they begin to lose the mass too.
So for a completely opposite reason, they lose the sense of scale as well.
So my crazy idea is the Big Bang and the remote future, they seem completely different.
One is extremely dense, extremely hot.
The other is very, very rarefied and very, very cold.
But if you squash one down by this conformal scale and you get the other.
So although they look and feel very different, they're really almost the same.
The remote future on the other side, and I'm claiming as that, where do the photons go?
They go into the next Big Bang.
You've got to get your mind around that crazy idea.
Taking a step on the other side of the place that is infinity.
Yes.
Okay, but...
So I'm saying the other side of our Big Bang, now I'm going back into the Big Bang.
Back, backwards.
There was the remote future of a previous Eon.
Previous Eon.
And what I'm saying is that previous Eon, there are signals coming through to us which
we can see and which we do see.
And these are both signals, the two main signals are to do with black holes.
One of them is the collisions between black holes and as they spiral into each other,
they release a lot of energy in the form of gravitational waves.
Those gravitational waves get through in a certain form into the next Eon.
That's fascinating that there's some, I mean, maybe you can correct me if I'm wrong, but
that means that some information can travel from another Eon.
Exactly.
That is fascinating.
I mean, I've seen somewhere described sort of the discussion of the Fermi Paradox, you
know, that if there's intelligent life, communication immediately takes you there.
We have a paper, my colleague, Vaheguzhe Jan, who I worked with on these ideas for a while,
we have a crazy paper on that, yes.
Looking at the Fermi Paradox, yes.
So if the universe is just cycling over and over and over, punctuated by the singularity
of the Big Bang, and then intelligent or any kind of intelligent systems can communicate
through from Eon to Eon, why haven't we heard anything from our alien friends?
Because we don't know how to look.
That's fundamentally the reason.
I don't know.
You see, it's speculation.
I mean, the SETI program is a reasonable thing to do, but still speculation.
It's trying to say, okay, maybe not too far away with a civilization which got there first
before us, early enough that they could send us signals, but how far away would you need
to go before, I mean, I don't know, we have so little knowledge about that.
We haven't seen any signals yet, but it's worth looking.
It's worth looking.
And what I'm trying to say, here's another possible place where you might look.
Now you're not looking at civilizations which got there first.
You're looking at those civilizations which were so successful, probably a lot more successful
than they were likely to be by the looks of things, which knew how to handle their own
global warming or whatever it is, and to get through it all and to live to a ripe old
age in the sense of a civilization to the extent that they could harness signals that
they could propagate through for some reason of their own desires, whatever we wouldn't
know, to other civilizations which might be able to pick up the signals, but what kind
of signals would they be?
I haven't the foggiest.
Let me ask the question, what do you use the most beautiful idea in physics or mathematics
or the art at the intersection of the two?
I'm going to have to say complex analysis.
I might have said infinities.
One of the most single most beautiful idea, I think, was the fact that you can have infinities
of different sizes and so on, but that's, in a way, I think, complex analysis.
It's got so much magic in it.
It's a very simple idea.
You take these, you take numbers, you take integers, and then you fill them up into the
fractions and the real numbers, you imagine you're trying to measure a continuous line,
and then you think of how you can solve equations, and what about x squared equals minus one?
Well, there's no real number which satisfies that, so you have to think of, well, there's
a number called i, you think you invent it, well, in a certain sense it's there already,
but this number, when you add that square root of minus one to it, you have what's called
the complex numbers, and they're an incredible system.
If you like, you put one little thing in, you put square root of minus one in, and you
get how much benefit out of it, all sorts of things that you'd never imagined before,
and it's that amazing, all hiding there in putting that square root of minus one in.
So, in a sense?
I think that's the most magical thing I've seen in mathematics or physics, and it's
in quantum mechanics.
In quantum mechanics.
You see, it's there already.
You might think, what's it doing there?
Okay, just a nice beautiful piece of mathematics, and then suddenly we see, nope, it's the very
crucial basis of quantum mechanics, it's there in the way the world works.
So, on the question of whether math is discovered or invented, it sounds like you may be suggesting
that partially it's possible that math is indeed discovered.
Oh, absolutely, yes.
No, it's more like archeology than you might think.
Yes.
So, let me ask the most ridiculous, maybe the most important question.
What is the meaning of life?
What gives your life fulfillment, purpose, happiness, and meaning?
Why do you think we're here on this, given all the big bang in the infinities of photons
that we've talked about?
All I would say, I think it's not a stupid question.
I mean, there are some people, many of my colleagues, new scientists, they say, well,
that's a stupid question, meaning, well, we're just here because things came together and
produced life and so what?
I think there's more to it, but what there is that's more to it, I have really much idea.
And it might be somehow connected to the mechanisms of consciousness that we've been talking about,
the mystery there.
Yeah, yeah.
It's connected with all sorts of, yeah, I think these things are tied up in ways which,
you see, I tend to think the mystery of consciousness is tied up with the mystery of quantum mechanics.
And how it fits in with the classical world, and that's all to do with the mystery of complex
numbers.
And there are mysteries there, which look like mathematical mysteries, but they seem to have
a bearing on the way the physical world operates.
We're scratching the surface, we have a long, huge way to go before we really understand
that.
And it's a beautiful idea that the depth, the mathematical depth could be discovered.
And then there's tragedies of ghettos and completeness along the way that we'll have
to somehow figure our ways around.
Yeah.
So, Roger, it was a huge honor to talk to you.
Thank you so much for your time today.
It's been my pleasure.
Thank you.
Thanks for listening to this conversation with Roger Penrose, and thank you to our presenting
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And now let me leave you with some words of wisdom that Roger Penrose wrote in his book,
The Emperor's New Mind.
Beneath all this technicality is the feeling that it is indeed, quote unquote, obvious that
the conscious mind cannot work like a computer, even though much of what is involved in mental
activity might do so.
This is the kind of obviousness that a child can see, though the child may later in life
become brow-beaten into believing that the obvious problems are quote unquote, non-problems
to be argued into nonexistence by careful reasoning and clever choices of definition.
Children sometimes see things clearly that are obscured in later life.
We often forget the wonder that we felt as children when the cares of the quote unquote
real world have begun to settle on our shoulders.
Children are not afraid to pose basic questions that may embarrass us as adults to ask.
What happens to each of our streams of consciousness after we die?
Where was it before we were born?
Might we become or have been someone else?
Why do we perceive it all?
Why are we here?
Why is there a universe here at all in which we can actually be?
These are puzzles that tend to come with the awakenings of awareness in any of us, and
no doubt with the awakening of self-awareness within whichever creature or other entity
it first came.
Thank you for listening and hope to see you next time.