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35| Hypercomputation: Why Machines May never Think Like Humans — Selmer Bringsjord
172 Plays1 month ago
AI can do many things equally well as humans: such as writing plausible prose or answering exam questions. In certain domains, AI goes far beyond human capabilities — playing chess for instance.
We might expect that nothing prevents machines from one day besting humans at every task. Indeed, it is often asserted that, in principle, everything (and more) within the range of human cognition will one day fall within the ken of AI.
But what if there are concepts and ways of thinking that are off-limits to any machine, yet not so for humans? Selmer Bringsjord, Professor in Cognitive Science at RPI joins us this week and argues we need to rethink human thought.
Selmer argues that humans have been able to grasp problems that machines cannot — humans are capable of hypercomputation. Hypercomputation is computation above the Turing limit, as such it can solve problems beyond the power of any machine we can currently conceive.
In particular, Turing computation cannot encompass infinitary logic, yet humans have been able to reason effectively about the infinite. Similarly, Gödel’s theorem points to a class of riddles machines cannot reach, yet human genius has identified.
This is a huge topic, accepting Selmer’s arguments entails accepting that human minds work in a way that evades our understanding — their mechanisms obeying mechanics of which we are wholly ignorant.
Whether or not you agree with Selmer’s conclusions, this is a brilliant exploration of the boundaries of thought.
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Transcript
Will AI's rapid advancement continue or hit limits?
00:00:00
Speaker
I'm James Robinson, you're listening to Multiverses. There's much debate about whether the current dizzying rate of progress with AI can continue. Perhaps the technique of pushing tons of data through neural networks will start to deliver diminishing returns. Perhaps we'll need to encode by hand ah some symbolic logic into our systems, a return to GoFi or good old-fashioned AI.
00:00:27
Speaker
ah perhaps we'll need to endow AI with sensory capability capabilities. Perhaps it needs to be embodied before it can truly realise AGI.
Can AI surpass human cognitive abilities?
00:00:39
Speaker
But I think it is fair to to say that there is agreement among a large part of the AI community, at least, that in principle, AI can tick off all the cognitive capabilities of of humans that and indeed can surpass them.
00:00:58
Speaker
Our guest this week is Salma Bringsjord, Professor in Cognitive Science at RPI in the state of New York, where he's also the Director of the Artificial Intelligence and Reasoning Lab. Selma is a very interesting voice because he doesn't believe that machines are even in principle capable of all the kinds of thinking that humans are capable of. He thinks there are certain forms of problem that are simply off-limits to any machine which is operating at or below the Turing limit, i.e. any machine that we can currently conceive of.
00:01:34
Speaker
And yet humans, he argues, are able to deal with those sorts of problems. And he points to problems like um our ability to conceive of the internet ah infinite, and he points also to to things like Gödel's theorem, although his views on that are a little bit more subtle.
Exploring computation beyond Turing limits
00:01:50
Speaker
So this is, um I think, really worth listening to, not only for Selma's, I think, heterodox views, but for the really cogent arguments that he puts forward, because the arguments in him and and themselves are just wonderful as an introduction to problems in the foundations of computer science, so issues of computability. And um actually, Selma calls me out on on this quite early in the conversation. I think for many, um computability and Turing computability have become synonymous. And Selma points out that actually,
00:02:25
Speaker
What is Turing computable is just a tiny subset of all the things that are computable if we look beyond the Turing limits, if we look to hypercomputation. So it's just a lovely overview of this sadly neglected, I think, field in computer science of things that go beyond the Turing limit. Of course, the reason why that field is neglected is we simply don't know how to make anything that goes beyond the Turing limit. And yet, Salma argues, we are somehow able to do it ah ourselves. So, a really interesting conversation, and I hope you enjoy it as much as I did.
00:03:20
Speaker
Hi, Summer, it's a real pleasure to have you here. Well, it's quite mutual. Thank you, James. It's a pleasure to be here and looking forward to our conversation. Thanks. So I think that the early Wittgenstein said something to the effect that the boundary of thought and of language are the same, those boundaries are one and the same. I think many people would disagree with that and probably the later Wittgenstein disagreed with that. However, I see a kind of growing trend um for people who who would say, well, the boundaries of thought and of what are what is computable are the same in a certain sense. um What do you say to that? I say first that formally speaking, by that I mean generally
00:04:13
Speaker
in terms of mathematics and formal logic or to use the fancy adjective, logical, mathematical. From that perspective, there's something objectionable right off the bat in the question because computable really in light of advances on the formal side and in in computer science,
00:04:39
Speaker
um could mean something more than what a Turing machine can compute. So I think we have to be clear that generally speaking, when people assert a view that you are correctly saying is is quite popular, if not in the vast majority of people who think about such things, it it means Turing computable. We have to be clear about that because the way I use the term computation, and I'm not alone,
00:05:08
Speaker
computation and what's computable. ah could be forms of, and or include forms of information processing that are beyond what a Turing machine can accomplish. And that's been with us ironically, this is arguably an indictment of today's educational system in computer science. That's been with us for a long time. That's been with us since the dawn of what we ordinarily think of as computation. Turing came to the United States to study under
00:05:41
Speaker
Alonso Church, the American, and Church wanted Turing to try to escape the very results of the both of them negative results that the both of them had produced, which were about the limits of standard or Turing-level computation for Churchill was the Lambda calculus for Turing. It's what we now call a Turing machine. And when I say Turing computable, that means what in principle a Turing machine can do. So they they explored that together. I think Turing, it's been reasonably well established. It's not totally uncontroversial. Turing didn't like it, particularly. I don't think he was
00:06:18
Speaker
disposed emotionally in favor of the very investigation that he made seminal, if not more than that, inaugural contributions to. But Post also is in the, so these are the three, these are the three people who gave us the first math, fully mathematically respectable the definition of the standard computation, right? Post explored computing in his own style beyond what a Turing machine can accomplish. And we have post theorem, which is about the very space beyond what a Turing machine can muster. So to your original question, again, first thing we gotta be careful about is ah the assertion probably is the bounds of thought
00:07:09
Speaker
line up with maybe they're co extensive, the bounds of what's Turing computable, what a Turing machine and its equivalence can compute. Right. So all right, now that we have that
00:07:27
Speaker
for some anyway, arguably clarified, I would say we already have part of what must be the answer on the part of some people, which is no. So I remember the one and only interaction I had with Marvin Minsky, one of the founders of AI in the modern era, now deceased one of the so-called 56ers,
00:07:52
Speaker
he um you know He was doing his usual thing, totally aligned with the identification of what thought is and what Turing computation
Are human cognitive abilities beyond Turing limits?
00:08:02
Speaker
is. And you know I remember saying, okay, look, fine, that's your view. But we do agree that that means that since all of standard computation above Turing machines and blow,
00:08:20
Speaker
is based on functions from natural numbers to natural numbers. Do we agree that that is an uncountably infinite set? And your view entails that only the tiniest sliver, it would be sort of an infinitesimal number of these functions would then be computable by the mind, the human mind, or if we say there's nothing beyond it, then a mind. And that seems really, really, really odd to me ah
00:08:51
Speaker
Why? Well, how is it that the very minds, and I haven't published this argument, how come then the very minds that are so imprisoned in this sliver of Turing computable functions is able to plumb the depths ah of the larger space. that This mind is able to establish all kinds of interesting results, theorems, about the larger space. Doesn't that seem odd? So, you know, it was a brief but violent, intellectually speaking, exchange. And that's that's sort of the start of my my problem. the very The very moment we clarify what we mean in this assertion, the next thing we have to do is concede, oh, my Lord, that means
00:09:39
Speaker
I was sort of fast and loose ignoring the space of information processing that in the abstract certainly exists and that which the human mind has plumbed. So that's to me suspicious minimally, right? um Then I would say I'll stop at three. um This is another one that I really haven't published.
00:10:06
Speaker
ah to Both of these two arise in a long-standing debate with ah Bill Rappaport, an American computer scientist.
00:10:17
Speaker
um Someone's got to tell me when we're going to say it's been long enough that AI has been telling us human mind will be matched, but not today, tomorrow. I mean, we we we have to have some conversation about that.
00:10:37
Speaker
We can't keep saying it's perpetual. Nope. That's not how science works. We don't, we don't get an infinite amount of time for people to keep saying P is true
Do cognitive psychology assumptions affect AI predictions?
00:10:49
Speaker
in the future. We'll confirm it. And then we keep working and it never gets confirmed. But that's actually what I, I know it's time is relative in this regard. This is what I've lived through to 65 years of age. So I'm an undergraduate there at the university of Pennsylvania.
00:11:07
Speaker
In that case, it was cognitive, most aggressively stated it was cognitive psychology. Okay, what's cognitive psychology? Oh, that's easy, folks. ah Cognitive psychology is the study of cognition, based on the driving assumption that all cognition is Turing level computation. That's what that's what we're that's our investigations based on that and that presupposition will eventually mean ah the success of AI reaching
00:11:40
Speaker
the human level when, well, not yet clearly, but it's coming. And so what, you know, I graduated maybe something like 81 or 82, you know, it's, it's the same thing. It's the same thing. People are saying that we have had the pushback from pure deep learning. It's the same exact thing. I've lived, I don't know, I think four main time, four sort of salient times I've lived through this. This last time was all we need is deep learning.
00:12:10
Speaker
That's all we need, deep learning. That'll give us deep neural networks. And now we have companies like OpenAI teamed up with Microsoft explicitly calling on the engineers and saying, uh-oh, really precise reasoning.
00:12:26
Speaker
in the area of logic and mathematics ain't working so well. Help us out. Do you have any, do you have any resources outside of artificial neural networks in the form used for the formal learning called deep learning? Yes, we do. And Microsoft has huge resources. And so now if you call up like I do, not GPT four, oh, which Sam Altman said was going to be,
00:12:52
Speaker
just truly amazing. Now you call up a 01 preview. ah And it's markedly better. It's not markedly better because they started from scratch and made another deep neural network. It's markedly better because of, and here I echo Steven Wolfram, although I don't have the business interests, because it calls resources that we have known for a long time are really good at explicit, careful, rigorous reasoning and calculation, um where approximation doesn't work so well.
00:13:26
Speaker
So
Machine problem-solving vs. human capabilities
00:13:27
Speaker
anyway, that'd be those be my ah three applies to your initial query. So I guess I think I first want to explore the the kind of second of those, which is this argument that there are things that we're able to grasp so as humans, which provably in a sense, machines can't grasp. um And and but I want to get it a little bit more concrete there. um But I think it will be b news to many. um As you say, there there seems to be some sort of ah lacuna in the um education of computer scientists. ah So it'll be used to many that there is this space beyond the Turing limits. And it's a very large space, as you said, in your
00:14:15
Speaker
a um reply to minsky or your client to minsky it's much much larger than the space of things that are trying computer um so perhaps you could start by by by talking about what that space is well what are the dragons out there um yeah uh well um
00:14:44
Speaker
I guess my favorite entry point to that space. Um, and it really isn't just one neat space. It's, um, depending on how you slice it, it's, it could be an infinite number of spaces, but it's, it's definitely two big ones. Um, the, the first big one basically says, if I give you, um, if I give you the logic,
00:15:12
Speaker
that Frege, he gets credit, although I believe Leibniz had it before Frege, but whatever. um I'm willing to give the the the the scoundrel ah credit. So if you can express it in first order logic,
00:15:29
Speaker
ah You only got the for all quantifier,
Beyond Turing: Spaces and software verification
00:15:32
Speaker
you got the exist quantifier, and then we'll allow you to have properties, ah but you have to announce your properties in advance, red, greater than, less than. We'll let you have your functions to start with, but we'll restrict those. We'll give you plus, multiplication, et cetera. um Whatever you can describe.
00:15:52
Speaker
ah with the variables that the quantifiers are attached to. So you can say for all x, ah there for all x where x is an actual number, there's a y that's greater than x. Wonderful. um if you give If you give me that, and it's not me, then I can quickly ah pose the challenge of trying to decide whether two computer programs are equivalent, despite the fact that the code is different. okay So this would, by the way, be something that causes immediate paralysis of deep neural networks. I mean, they they so they simply can't do this. They could do this empirically up to a point, but they can't do this.
00:16:43
Speaker
um but for many reasons. So that that's an entry point that's that's not that far above a Turing machine. It's so-called it's a so-called, the terminology really doesn't matter, it's a so-called Pi 2 formula. So it says, look, give me any two programs, do they compute the same function?
00:17:03
Speaker
It's really hard to be a first rate software developer. You could you can be a mechanical coder, collect your salary, maybe call upon, ah shit you could probably just call upon chat GPT-3 or something something like that. Hey, I need i need this i need some code that does that does this, that this is a rough description of a function, back it comes and it might very well work, but there's no way that you can do it you can you can solve the problem I'm talking about working that way. it and And so you alluded to the fact that it's a large space we're talking about here, the so-called arithmetic hierarchy. How large is it? Well, it's infinite. Where is the problem beyond a Turing machine of deciding where the two pro ah two computer programs compute the same function?
00:17:57
Speaker
Um, pretty much at the start, pretty much at the start. So it's not really, really that hard. Um, but I, I don't, I don't see how you could have a job working in high stakes software development without having to deal with this, uh, left and right. How do humans do it? Um, what would the contrarian view be? What would the, uh, let's call it the.
00:18:23
Speaker
equal boundary or equivalent boundary view that you mentioned, thought computing the same, what would they say? Well, the humans are just getting lucky. They're just they're getting lucky on the job. um They, by the way, better really get lucky if they're using something like a large language model to get code that they use, because um almost right away, they're going to have to decide not only whether that code is correct,
00:18:53
Speaker
And and that by the way, that's Turing uncomputable. Deciding whether an arbitrary computer program at the level of a Turing machine, that's that's uncomputable. we we We can't prove that it's correct relative to specifications for what we want. That's uncomputable. So the and the the problems that I mention here too now are examples of what, and look, they're not these days are not like,
00:19:22
Speaker
alien concepts. These are things that people get paid in some cases a heck of a lot of money to figure out ah in the workforce. And I can assure your audience, they ain't using AI to do it. um I darpa you know DARPA had a program where they they threw in the towel and said, there aren't enough human beings that can do this kind of stuff. We'll just sort of turn it over to crowdsourcing.
00:19:53
Speaker
and hope for the best, it didn't work that well because you really do need to take the human mind and subject it to training and education. And then it's able to do to do it. um Ironically, Turing was the first Turing and von Neumann were the first folks who did sit down and tackle the problem of proving that a computer program, whether a Turing machine specification or so Turing machine description,
00:20:20
Speaker
or something ah else is correct. And ah yeah, we don't teach that. we um In terms of the lacuna that you alluded to, by the way, educationally, so two things now. um in the conversation that we no longer do. um We really don't care anymore of students. We might have a throwaway program verification course at the great universities in the world. um the one or Certainly there is one near you, University university of Edinburgh. um We might have a throwaway class, but ah it's not it's not a requirement. So you can't you can no longer expect
00:21:01
Speaker
even at the PhD level in computer science that the person you ask to prove a given program, even not that complex, correct, can do it because we we we don't we don't teach it. And then going back to the earlier subject, we no longer teach the whole spectrum of problems. we Occasionally we we might. I know at my my university, which I obviously have a soft spot,
00:21:28
Speaker
in my heart for, I've been here a long time, we drop the requirement of studying uncomputability. You only study yeah only study what you only study what algorithms,
00:21:41
Speaker
um how algorithms should be measured and placed relative to how, say, efficient they are and the size of input, time-wise and so forth. we don't The minute we have an algorithm, the minute we know we're studying algorithms, then we know we're just studying what's Turing solvable, Turing computable.
00:21:57
Speaker
Yeah, so when you say that we we don't study uncomputability, you mean we don't study non-churring computability. So it could be computable by some other means. And I want to really just... Yeah, that's that that's an important point because, again, implicitly, what's meant by ah uncomputability, and I did it myself, is on compute it's the study of that which is uncomputable by Turing machines, because there's a lot of other stuff that is computable in the extended sense.
What are the physical limits of Turing machines?
00:22:32
Speaker
Yeah. I mean, we should say there's sort of good practical reasons for why there's such a ah focus on the Turing machine. It's because we don't know how to build anything that we can use um that goes beyond the Turing limit. And I think that will surprise some people because what what you seem to be suggesting is, well, actually,
00:22:56
Speaker
We can't build something, but we have something that seems to be doing this or capable of doing this, and it's us. And here's an example. And I think it's I want to make sure I understand this example um of verifying that either a program is doing what you want it to or that two programs are equivalent. And I can see how those two things are quite related.
00:23:21
Speaker
um why Why is that something that a Turing machine can't do? I presume that there's a certain class of functions and programs where you know there's an algorithm that that that covers it. um But why is you know what is the general problem here? um And and how you know how is it that humans seem to be able to get around that? Maybe that's a second question. That's a big one.
00:23:51
Speaker
Yeah, that's that's ah indeed a huge question. um I don't know how to efficiently, let alone both efficiently and eloquently encapsulate um that which it is. And like again, we're just talking about, to use the broader term, once again, information processing consists in
00:24:22
Speaker
ah what's beyond ah what a Turing machine can do. And I want one caveat there. The logic I mentioned first order logic in connection with Frege, inventing it, et etc. Theorems ah expressed in first order logic are, um impal there there's no out no Turing level algorithm for deciding, as you no doubt know, whether a proposed theorem is the theorem or not. However, it is semi-decidable or semi more precisely Turing decidable. So um in that case, there's sort of an answer.
00:25:03
Speaker
which is ah produced by saying, wait, you're telling me that if I if i sick a Turing machine on but on the question, is this statement expressed in first order logic, and let's restrict it to number theory, is this statement a theorem that it's it's going to work for sort of half the problem. Well, which half? It's when it is a theorem, it will find it. OK, so ah then wait. So OK, I got so well, then what happens in the case where it's not a theorem?
00:25:44
Speaker
Oh, I see. In that case, you might never know as processing continues whether it's going to halt or not. So in that case, the answer is it's the halting problem.
00:25:58
Speaker
ah which in its purest form for your audience many will if not most will know the halting problem is the problem of having to decide in the arbitrary case whether a computer program halts or not. Helpful by the way to have a solution to that in theory if you're if you're a counter fraud company trying to try trying to evaluate whether people are are are submitting programs that are any good and or just thrown him in trying to get the letter grade but there there it seems like okay we have a toe hold because we have the halting problem however even there i think we better be really humble at least i'm going to be humble um why one reason is
00:26:46
Speaker
um When I prove it for ah students early on the halting problem, I actually just, I mean, I'm i'm not a constructivist, so I'm i'm i'm ah i'm a Platonist
Hypercomputation: Speed and capabilities
00:26:56
Speaker
in mathematics. um I'm using indirect techniques to prove that there can't be such a machine based on contradiction.
00:27:03
Speaker
ah That doesn't really help me to explain the essence of why ah this doesn't work out. All it does is throw this wall, is this this sort of mysterious wall in front of us. I mean, we can go be it, we can work on it and we can we can do better and hopefully we will in the conversation. But the first problem is that alone is,
00:27:27
Speaker
really murky. and And then you have um probably even a more sort of um initially murkier result, which is what about what about stuff at that level of trying to say whether a program, specifically a Turing machine, halts or not? What ah what about something like that?
00:27:52
Speaker
where um we don't have to use fancy indirect techniques and fancy proof techniques to show about something just sort of more direct, although grand,
00:28:05
Speaker
father of that or the primogenitor of that as a variant where we're trying to just figure out um how many symbols a Turing machine in in a agreed upon format format after a finite um amount of time can just put out on its tape or print you know in ah in a printer if we if we physicalize it a different way, so-called busy beaver function. And that's uncomputable. That's Turing uncomputable. That one, so that that seems like, uh-oh, that's also mysterious. We might get a toehold there because we know in that case it has to do, well, shouldn't say that it begs the question um against alternative answers to your very penetrating question. But at least in that case, we know
00:28:54
Speaker
that acceleration, something like acceleration is ah going on. So the the rate of growth of the function that we're trying to compute by standard means grows so fast that we cannot get a Turing machine, ah one no Turing machine exists to handle that level of acceleration. Because the so-called productivity of the Turing machine as it gets larger, the amount of stuff it can print out in the size of those numbers, those natural numbers grows faster than any Turing level function. So I guess we could say there looks like it might be acceleration.
00:29:35
Speaker
um People have sort of said that about hypercomputation or super turn computation that, yes, but that's really fishy because you would have to have a machine that can do an infinite amount of work in a finite amount of time. So I'm not going to go that far, but I will say there's got there there's there's something going on here about acceleration and speed.
00:30:06
Speaker
um But is it just speed in the sense of what really practically minded people focus on in AI and computing? That's the so-called polynomial hierarchy, where everything is Turing computable, fully Turing computable. Their emphasis is always, well, I need efficiency, so I'm sticking i'm sticking with that stuff. This is this is different.
00:30:33
Speaker
And this takes us back to to Minsky's, to my interaction with Minsky. This is different because not really it's not really, ah How long or how much space is it taking your are machine and the size of the input where we know the problem is Turing computable? This is a level of ah speed that certainly looks like it needs more than a natural number or a rational number for us to even make sense of it. and that That's pretty much true.
00:31:07
Speaker
um so Uncountable speed. Yes, and we know, so if you wanted to sort of, I'm trying to sort this out in the case of quantum computing.
00:31:22
Speaker
um now um I think by the way that quantum computing, now that it's become doable and in in in in machines that some are lucky to have available, we have, RPI has, I think the first university quantum computer, thanks to considerable generosity of ah far billionaire and IBM.
Can quantum computing break hypercomputation limits?
00:31:44
Speaker
you know We can start you can start toying around with the physics dimension of this, um but mostly for provoking thought about whether it would ever be possible to build it, build such a thing.
00:32:01
Speaker
And the shortcut has always been, or for a long time has always been in the case of neural networks to allow real numbers into the game, to allow to allow real numbers as coefficients for the equations that allow us to just express neural networks as sets of equations. um You know, I mean,
00:32:22
Speaker
Leibniz and Newton had to appeal to the calculus to get engineering off the ground and make sense of the universe even before we got to relativity and even before we got to quantum mechanics. It uses the reals. um There's some sense in which if you're a formalist like me, you already have to accept the reals.
00:32:42
Speaker
as, I mean, if you're a formalist like me, you'll have to accept that if you need the if you need the differential and integral calculus, if you need analysis to figure out what's going on, even independent of cognition and consciousness in the world, it's really odd because that's that that wouldn't that wouldn't be you know that wouldn't be computable, right? So how do we how else do we get out of the paradox of the arrow ah and and so forth. Well, for for me, we use the calculus and say, hey, there's the answer. But we just invoked um analysis. We invoked the reals. And this this this is interesting. So if the brain makes use of the reals in any serious way, it's definitely hypercomputing. This is not some insane view. ah If we already regard the brain, back to your question, of
00:33:37
Speaker
question I'm probing about, well, you can't build the stuff. So what's the essence of it? um But just an observation here, if we if we are already the smartest creatures in the known universe,
00:33:52
Speaker
um so smart that People who said in 56 or 60, they needed a weekend to work out some particular faculty that humans have and failed miserably. and Minsky's in that category. I mean, now we have had this rude awakening through the through the more than half a century. Well, we're the smartest thing we know about. We can't match it yet. We keep saying, I think it's videoism, but we're going to do it.
00:34:22
Speaker
But it's not an existence proof, it's just, but but but what's special? well you know what What's special? Well, something's special. ah We only have a few possibilities as to what's special. If thought and standard computation are the same and we're thinking things, if anything,
00:34:41
Speaker
then it just must be that somehow we leverage speed and and and efficiency space-wise to get things done. And we just haven't figured out how how to how to replicate it and in AI. But it's all computable. um Or we can get mystical, OK?
00:35:04
Speaker
um or or or such, I don't want to be disrespectful, but we could get mystical and say, I have no idea, but it's just an impenetrable mystery. We could say, um we head in the direction of dualism and say, well, we're accessing resources that are non-physical. So it's just that the third but You know possibility or the fourth is to say, you know, Penrose is many others have well there's got to be there got to be effects in the brain that are just extraordinary and We have we harness them, but we don't know what they are and we do it all unconsciously So we just got to figure out what it is, but it's not going to be standard um computation um Okay. Yeah Wow
00:35:50
Speaker
There's really a lot to unpack here. And I think that was just a ah great delineation. As you said, I think it's very hard to draw the line of where the Turing limit is and why um some things are on one side of it and and and others are ah safely within the bounds of what's physically computable. as As far as we know what's physically computable, as you say, there might be other forms of physical computation.
00:36:15
Speaker
um Probably a good moment to remind people though that even quantum computers, as we currently know them, the algorithms that we have are not going beyond Turing machines. They're able to do things that a Turing machine... or so
00:36:33
Speaker
yeah yeah able to do things very quickly, much more quicker than a classical algorithm. But they can only solve the same sort of things that classical algorithms um can do. um Yeah, that's the original indeed. And that was certainly that's the original result result from Deutsch before. ah Not that far from my office, I'm in my home, but my art office at RPI, long before there was the computer,
00:36:58
Speaker
The quantum computer over there, Deutsch had the the result that, well, things will be faster, but it's going to be standard computation. um Yeah, i'm not i'm not I'm not disagreeing with that. But I would say it's a voyage for me. um you know um Obviously, not I'm not a physicist.
00:37:21
Speaker
ah when you approach traditionally the quantum world as a sort of computational logician or even straight logician, um you you find alternative ways to try to make sense of Hilbert spaces and stuff, but you really never talk about the physical dimension. So I have never really,
00:37:49
Speaker
I don't know. So I'm learning. I have a yeah ah colleague who's teaching me, and I will say this. um We agree that usefulness in connection with our quantum computer is only produced when we view everything that happens as being, and everything meaningful that happens for our uses is in complete conformity with standard digital Turing level computation. But while the readouts, while the use of the content
00:38:37
Speaker
And the readout that problems posed to the machine from that mindset are in complete conformity. i don't um but I don't know that the that the physics in it's ah side effect and in its side effects or in it in the phenomena that's not central to what I'm calling the readout, um there there i'm not I'm really not so sure. um a lot of and my I'm really not sure. I mean, I don't know that the physical processes as side effects are reversible.
00:39:15
Speaker
And I'm trying to wrap my head around that because one of my main attacks on the slogan cognition is computation is based on the argument from irreversibility and Turing machines are fully reversible. They're there as a computation.
00:39:30
Speaker
when Whatever computation they perform is fully reversible. We have these are elementary theorems. ah So the the content that we make use of from quantum computation, and we have defined for us, we we've defined a few of those are perfectly well defined and fairly standard. They haven't even been parallelized yet in the world. so um We're kind of jumping ahead. it should be It should be interesting. But the processes themselves, I'm i'm really i'm really not sure. And so given my view, and I'm not saying that hypercomputation is happening in a quantum computer. i just you know For the record, I'm not saying that. i'm just I'm just registering my humility. Because my view is that unconscious or non-conscious computation that
00:40:19
Speaker
humans engage in when they sufficiently tax their minds is hypercomputational. But it's not conscious symbol manipulation or anything of the sort. And Lord knows it's not hand simulating an algorithm or hand simulating a Turing machine. But I believe it's happening.
00:40:41
Speaker
So I'm just, and also years ago, I had dinner with Roger Penrose. He gave a talk at RPI. and um And that was really for me, a very,
Roger Penrose's consciousness and AI debate
00:40:53
Speaker
very interesting. i you know I think he messed up a lot. His Cadelion, all the Cadelion stuff was all It's all messed up. um maybe just much as so so so so again not yeah But not but not the stuff that he and not the stuff he talked about at dinner about that was in the realm of his realm of mathematical physics. When he was talking about the in the in the the the the connection between physics, including quantum, okay and the brain and the mind, and Sort of speculating there wasn't anything wrong in what he was saying and it was really
00:41:34
Speaker
I thought it initially, this is crazy. And then, you know, now I think people are like, you know, I don't know. I guess he's pretty smart. He did win that Nobel prize, right? And now you have the people who, I don't agree with them at all, people who are taking his consciousness views very seriously, um experimentally and physically, not in connection with the quantum computers. And you may know of some of that work. Sorry to interrupt you there.
00:42:01
Speaker
No, no, I was just saying, I think um just a I'm going to do a terrible job at pracing Panrose's gedelian argument, but you you can tell me how to better put it, but something like the human mind you know is not It's going beyond the Turing computer again, and the reason is um it can perceive things like um that are non-computable to be true. And um one of those would be ah a sort of classic Godelian
00:42:37
Speaker
If this ah ah statement is true, you can't prove it. And we can sort of easily say, oh, well, that's it's got to be true, um even though I can't prove it. Because if it's false, um then you could prove it, and then it wouldn't be true. So ah and and you know that's an attractive argument. It would be great if if if that would work. um I want to backtrack, though, a little bit to... Well, firstly, I do want to say one thing about quantum mechanics, because ah I do think views differ on this. My view, just for the record, is that you know union unitary quantum mechanics, um those equations are all you need. You don't need any um
00:43:26
Speaker
collapse of the wave function. so i kind of That's why this podcast is called Multiverses. And if you believe that, then everything's reversible. um And you get an arrow of time um from essentially the the universe starting ah in some special state, or at least one end of the universe, one end of time um being rather unusual.
00:43:51
Speaker
and then everything kind of spreading out from there. But at the micro level, at the at the you know and and indeed at the level of the universal wave function, everything's everything's reversible.
00:44:03
Speaker
um Now, what I wanted to get back to though is just yeah this idea, that the this delineation of what is not possible ah in terms of Turing machines' computability, they all seem to revolve around some kind of
00:44:23
Speaker
infinity or circularity, which leads to an infinity or aggressive or of some kind. um In, for example, the, the Godelian case, though there is this circularity, which has this, this whiff of the infinite, I suppose there. um And you mentioned that, you know, some of these problems um would be solvable if the Turing machine could, could run infinitely fast, or or even I think there's a kind of this concept of a Zeus machine where if the tape that the Turing machine um was reading in, if if that movement just ah sped up every time, if it halved, let's say, every time.
00:44:59
Speaker
it would be able to do things like enumerate um all of the reals in a finite um time, or at least all of the integers. so um now you know it's And that gives, again, an idea of of why some of this stuff is is just not physical, at least classically. But I think what you're hinting at is that you know maybe a quantum acute computer, even though we're only able to get out finite results, and and so far we've we don't have any kind of conception of quantum computing which would takers beyond the cheering limit, it seems behind the scenes to somehow make use of infinite possibilities. you know There are these infinity of states that that that it can sort of survey over. um And perhaps in a similar way, perhaps in a different way, you know that's the key to what might make humans different to um
00:45:58
Speaker
anything that's Turing any kind of machine or that is a Turing machine or or equivalent. um It's and it's certainly in it's certainly inspiring to that's all that's happened in my case at this point. I was not prepared for how ah inspiring looking carefully at what's happening with guidance in this quantum computer, independent of my harnessing it for standard problems.
00:46:37
Speaker
um it is. i'm I'm, as you said, I'm in no way saying it's it's hyper computational, but it's very inspiring. mom It's not the way people like me think at all. It's, it's just an I mean, see, the problem is,
00:47:01
Speaker
your your question is what it what is the essence of what's beyond is the turning limit let's say is is so it's it's so profound. It's it's so deep. um it It it's the answer to the question to return to it from the standpoint of formal logic is very different than what you describe as a process that's the you know the wild machines or the Zeus machines. they They help us from the procedural perspective. They help us if we think of computation as a procedure. okay No one doing logic from Aristotle to our conversation here in 2024. No one thinking of computation
00:47:55
Speaker
ah as ah reasoning and in in in logic or a lot in in logics that we have, no one thinks of that procedurally. If they think of it procedurally, it's only because someone pushed them, it could be themselves, to think of mechanizing reasoning over logic over content expressed in a logic.
00:48:21
Speaker
The astounding thing is that ah Aristotelian logic. So we're talking, you know, we're talking over two millennia. We're talking, this is BC. When we write what Aristotle did down in modern notation,
00:48:40
Speaker
Um, every formula that he has only has one quantifier.
Infinite computation and logic limitations
00:48:46
Speaker
Okay. So in, in the syllogism, all A's are B's. Let's say all B's are so all all A's are B's. All B's are C's. Therefore all A's are C's. That's a valid syllogism.
00:48:56
Speaker
he He worked out the validity of that and the lack of validity of all the other permutations with some allowed as well. So all A's are B's, some B's are C's, does it follow that some A's are C's, et cetera. If you look at the notation to to show in a class, and here here here are your three formulas for a syllogism from Aristotle.
00:49:20
Speaker
And you say, can a machine can a machine answer the query as to whether the third one does logically follow from the first two? Oh, yeah, absolutely. Didn't quite have that in 1956, but close. We had it easily in the 60s, and we had it quickly.
00:49:38
Speaker
All right. OK. What if I just add another quantifier to allowable anyway to each formula and allow you a few more um properties?
00:49:54
Speaker
He only had unary properties like is red is a unary property. There's one placeholder. Suppose we let that be three like X is between Y and Z. So that's a three place predicate.
00:50:09
Speaker
If we allow that, the two and the and the three, even without worrying about function symbols, now we have a we have statements. Let's make it three. One, two, three. Three is the purported conclusion. We have questions that a Turing machine can't answer. okay So for a for someone coming at all of this like me,
00:50:35
Speaker
out of formal logic, not out of procedural stuff like a Turing machine or Fortran, if we want to look at a language that's purely. You know, I thought Fortran was some kind, I thought it was a joke when I first, but I thought this was some kind of joke. I thought the instructor was, thought everybody's playing a joke on me. You mean that that's computation and then I got to give it a line number and then it's going to loop to that line number. Oh my gosh, ah this is crazy. Then I got a chance to see prologue and some of the languages out there, there were logic programming. Things made a little bit more sense, but the astounding thing is relative to your question, James, how can it possibly be?
00:51:11
Speaker
that just a few symbols okay in the same exact vocabulary ah takes us from what a Turing machine, in terms of the query, the query type that I just gave, takes us from what a Turing machine can do to something that ah a Turing machine can't do. How is this possible? ah it it All we have are the formulas.
00:51:39
Speaker
and or they They're syntactically different. And then we have the challenge of, is this logical or not? this On the basis of the info that I'm giving you, which is what Aristotle started with, and which is an incredible achievement. we've We're still doing the same thing. And I just marvel at it. I mean, so my my view is, you see, connected to my,
00:52:06
Speaker
skepticism ah about Minsky. How could it be that we're able to do all of these all of this reasoning with this kind of content, because we now know reverse reverse mathematics has now taught us beyond a shadow of a doubt. This is something people in AI just don't want. They want to look the other way. And I've seen it left and right. If they have enough training and they're really fake to be famous AI people, they'll look at the reverse mathematics and they go, wait, wait, reverse mathematics is telling us that human mathematicians work with content in third order logic. I thought first order logic was already uncomputable.
00:52:43
Speaker
um when we ask these kind of queries, but they're doing third, that that's the content they're working with, absolutely the case. So we know that humans do this. The only response, again, going back to what we talked about earlier is, well, they're just locking out because they're border cases that are well behaved. I say Balderdash.
00:53:01
Speaker
ah just it just It just keeps going and going and going, and we keep we keep pushing these limits. So again, I do not under i do not know how i don't know the dividing line here.
00:53:15
Speaker
i don't see And I also don't see how, even if you think we're not that good at it, despite my elevated views of human reasoning, One thing should be obvious when we look at this ability to reason over this kind of content that we know is beyond a Turing machine. Well, there got to be other minds that can do it. I mean, there can't possibly be any sort of built in limit.
00:53:43
Speaker
to the to the universe. it's that that that would be that would be a you know I mean, what would the reason for that be? That would be crazy. You add another quantifier and suddenly no creature past, present, future, no extraterrestrials, ah but let alone supernatural. Then we we we could shoot down the supernatural and say, well, the supernatural realm makes no sense because there can't be beings that have any more intelligence.
00:54:09
Speaker
I just, you know, so again, the the the weird thing from the formal logic point of view is, is, is it your question is more disturbing, more penetrating and more profound than it is from the ordinary procedural understanding of computation? Would it kind of, I think what some people might be thinking as well, when humans do in fact think about these kind of problems,
00:54:36
Speaker
um And it might be easier to jump straight from third-order logic to a kind of infantry logic, like, um you know, one of the things you can't do with with first-order logic, and, you know, to remind folks, like...
00:54:49
Speaker
Turing computability, you know if you can express it and compute it um in first order logic, then you can do then it's Turing computable and sort of sort of vice versa. They're equivalent systems. um But something you can't do in in in first order logic is hey have an infinite kind of conjunction of things. um And you might say, well, you know why not? Because I can think about an infinite conjunction of things. I can think, for example,
00:55:19
Speaker
if I know um that P is true of each thing, and it's true of all things, ah well, if I know it's true of each thing, then I know it's true of all things. I mean, that seems kind of like intuitive, and I can reason about that. um And yeah it seems almost perverse that, you know, you your Turing machine can't do that. But then the counter kind of, you know, the response to that might just be, well,
00:55:48
Speaker
Surely you can just tell a machine, you know, give it some symbols and kind of imbue them with some meaning and say, oh, when you see something of this form, you know, it works out, right? um And kind of add these things in maybe as as axioms and um and then it And then it would be able to kind of reason through some of these infinite things, or or maybe maybe it's not reasoning, right? Like maybe it needs ah another ingredient for that. um it what would you What would you say to that? I would say you're predicting and it's actually you you're prophesying and oracularly so the future is that's where we're that's where we're headed. this this is
00:56:35
Speaker
I mean, let me ah unpack that a little bit. So we're headed toward Serious, eventually serious money being spent on attempts to directly wrestle with the kind of expressions. to Get a machine to directly wrestle with the kind of expressions that um you're pointing to. and in Infinitary expressions, which on paper in the journals or the notebooks of Leibniz say,
00:57:11
Speaker
um but We don't need to go actually, by the way, beyond Newton and Leibniz since they countenanced infinitesimals and built the calculus on on that. So, um reflected at least in not in Leibniz's case in ah in writing that matches what you're talking about. So we are we are going we are going to go through, we're gonna enter um a phase in which AI says, yeah,
00:57:40
Speaker
Yeah, I see this infinitary stuff as a problem. we we We don't have that in first order logic. We don't have those we don't have that in anything say relation database theory um beneath that. We don't need it. We've needed finite models and so forth. Okay, so we better start we better start doing stuff with these kinds of expressions.
00:58:04
Speaker
And we can do that and we're gonna succeed because ultimately they're just finitely long. Because we got a finite piece of paper, we have a finite journal, we have a finite machine, a finite tape, et cetera. But we can fit these expressions that we see these these these mathematicians dealing with in their fancy, ah such as, I should say, all all all the formal sciences. It's really no different than,
00:58:30
Speaker
theoretical physics. So theoretical physics, our theoretical mathematical physics, game theory, right, decision theory, etc. The expressions look like they have an infinite content. And that's what they do cognitively to the humans. That's why humans write them down. It's just like you said, if I then so if if if if I have an infinite ah disjunction disjunction, P1, P2, P1 or P2 or P3 or P4 or P5. And I say it continues for a long time. Someone says, well, how long? I say, oh, the same size as the natural numbers. They have to agree that's perfectly coherent. They got that in fourth grade when the teacher said, hey, that number line just continued, continues forever. And then someone says, oh, you know what? P19 is not true.
00:59:25
Speaker
What can you infer from that? ah Oh, golly, I can infer that the whole disjunction holds, except I'll just cross out P19. That's a perfectly valid inference that we can do as humans. So you're you're what's so the deflationary ah you know ah Stuff it in the Turing machine level stuff is just going to be, yeah, we did something like that. We got some good results. But we just we we we just kept it. you know We put it in a machine. And look, it's only finite. But they're missing the the import of what that is for a human. They're missing what I just did. So this is another indicator that humans in this realm are somehow able to access. And it for me,
01:00:11
Speaker
access the infinite in a genuine way they can they can wrap their heads around it and you know i'm not i think penrose like the cadellian stuff is this is a terrible result from geodal to try to exploit to to say i don't know how it's all because of lucas lucas started this whole thing of lucas it's it's a It's a terrible, it never should have gotten started. It wasn't his best work, it which everybody knows good old that is. it Not only was it not his best work, it wasn't the work that presented.
01:00:46
Speaker
to contemporaries and future humans, the best basis for being skeptical about Turing-level computations circumscribing the mind. So you know what he what he did in the case of the continuum um you know the continuum hypothesis, I mean, that's that's That's unbelievable because there he had to cognize infinity in such amazingly, I mean, it's just a mind-boggling way. We don't teach it so a little. We generally don't teach it at the undergraduate level, so we'll advance. But anyway, anyway. Yeah. Yeah. I mean, would you say the sort of the carnal of a
01:01:32
Speaker
better argument for why humans must be high computers. It's just something like and she's like we can grasp things like what the rational numbers are. We can grasp concepts of infinity, um which just calm' comp can't go into a Turing machine. like there's no There's no room for that in the input.
01:01:54
Speaker
um yeah Yeah, that's I will I will agree that's fair. But I think we're much closer to the to the truth. And we're more accurate. When we say, look at that result that good old produced look at the actual result, look at the actual reasoning, look at the theorem in question, look at the techniques he he has used. Now, it is infinitary in its nature. When we understand it, ah to teach it or to perhaps contribute to this space. um Yes, I would say we in some sense are genuinely grasping the the infinite, but I don't know that I need to say that. I think I can say it's right in front of you.
01:02:52
Speaker
ah you show me how analogs to that works in a Turing-level machine. And the result, and so this is why what I said, this is why I said what you said as a prophecy, because the the retort to that will be, well, we will. We can't do it now. We have no clue.
01:03:19
Speaker
You will get that. You can get that at a dinner, um behind the scenes with AI people, if they have enough understanding. Yes, these stupid LLMs, they're not even, I mean, they're not even Turing complete, or at least, many they're not even, they're not even at the level of Turing machines, so they can't, yeah, yeah, yeah, yeah, but but we'll get there. But where's your confidence coming from?
01:03:41
Speaker
Where does that confidence coming from? It's just one big circular argument. It comes from the original proposition that you put on the table at the start of our conversation. It comes from the very assumption that, indeed, the boundary of thought or the bound of thought corresponds to the bound of what a Turing machine can do. But that's a circular argument.
01:04:04
Speaker
I mean, i'd I'd suggest that people would say something like, we just don't have a candidate for what kind of physical process um could support this kind of reasoning or something or anything that goes beyond Turing computability. and We've talked about Zeus machines, which which speed up with every time step, and that doesn't work. I don't know if we've mentioned analogue well we've We've talked about quantum quantum computers, um which at the moment don't go beyond um trying computability, but I think in in Penrose's mind, at least, you know there's there something at the quantum level which might be an explanation for the mysteries that go on in the brain. and
01:04:50
Speaker
It's an appealing idea. I think people people's big camera argument to that is just because just cause we don't entirely understand you know the mind. and We don't entirely understand some of the mysteries of quantum mechanics. It doesn't mean there the the solution is is one and the same. All those things are related.
01:05:04
Speaker
um I guess the other kind of model for um what might be going on is analog, chaotic um networks,
01:05:16
Speaker
which which yeah are things which instead of, I suppose, crudely, I think of them instead of being a kind of digital neural network, they're things which crank through operations or on the reels and you know just a tiny difference in the precision of the thing that you've got going in can completely change the calculation. and ah It's quite a beautiful thing to to think about and visualize, but it's unclear how that can help us out here because we don't end up with, um you know, we end up with quite precise ah rounded answers often. It doesn't seem that that's the mechanism that that that we're using. So I think part of that confidence that you mentioned on the AI side might just be, well,
01:05:58
Speaker
you know, it's it's got to be this, right? um There's nothing else. um One other, I'm sorry, I'm going to give you two kind of like, ah ah things that that might be on people's minds here to kind of knock down if you can. And the other thing that people might might say is, well, actually, you've got it, you've got it all wrong, right? We think that we're perceiving this, this, ah you know, this great thing, the infinite. um But There's nothing really there. It's it's an abstraction. um It's a ah limiting case. And it doesn't actually exist out there in nature. And I think probably the, i you might agree, but I think probably the person who's who's made this case best might be Adrian Moore, who, and again, I'm going to do a terrible job at praysying him, but it's something like, well, we have all these um
01:06:53
Speaker
There is this second order paradox of how we um think about the the infinite. um you You have these these first order paradoxes, um things like ah Zeno and the Tortoise, or um just you know all the weird stuff, or Hilbert's Hotel, another one. um All the things which teach us just how weird infinity is. And they seem to teach us something, but what they teach us is that It's kind of ungraspable and you know impossible to get a purchase on. um And when we reflect on that fact,
01:07:32
Speaker
We surely have to admit that actually what we learned from the first set of paradoxes is that there's there's kind of nothing nothing really there. um And that's a very tricky because argument to get one's head around. but it But it also feels like, well, maybe if it's a tricky thing to get one's head around, it's because the subject matter is so tricky. and And actually, again, there's nothing there. So you can sort of keep running that second order paradox over and over.
01:07:57
Speaker
Um, yeah, I'm sorry. I've left you with, with, with, with with two things to to handle here. Um, but I think they're quite important objections that people might have. Yes. Um, no, indeed. I think that, uh, Cantor's, uh, I actually, I think can't can't Cantor's life. Um,
01:08:25
Speaker
including prominently and crucially his professional life um and what he had to deal with. And then what a contemporary student ah first thinks with respect to what you've raised when they see the first cantorian proof put before them is is is part of the litmus test.
01:08:57
Speaker
um if if that So, I mean, he was you know he was persecuted. People said he was insane. He, for purposes of your audience or at least a contingent thereof. you know he's He's not the first. um He's not even the first to say, to talk about it systematically, but he sort of goes down in history as the first to say, um there are levels of infinity and I'm telling you there's stuff that's so that's bigger than the natural numbers. And you know these these are the set of reels are larger than the natural numbers.
01:09:34
Speaker
In fact, just zero to one ah in the realists is bigger than the natural numbers. you know So then you give the student the proof. ah using diagonalization from Cantor. So, you know, he was persecuted, he was called crazy, he was called insane. um He ended up going insane, I think, in large measure because he was declared to be insane and he perceived ah these results to be completely
01:10:05
Speaker
above board and the reasoning to be perfectly valid. So if the, we could say that's too dramatic and let's just ignore that Selmer, uh, then I'll just go to the litmus test being the student. If the student sees the proof, doesn't even have to have the name cancer associated with it. Generally speaking, I do, but that's just a quorum.
01:10:30
Speaker
They see the proof that or the proof that I think is perfectly valid proof that's all over the place in the textbooks that the natural numbers are smaller. than the reels. Um, if they see this result and others like it and they, and they say, Oh, this is so weird and fishy. Come on. Infinity is like stuff continues forever. And it's only just in the potential sense. And that's all we need. Um, but if their reaction is, Oh my gosh,
01:11:08
Speaker
what what is wrong with this? I'm not sure I understand it. Let me redo it. And I try to do it for students early on first diagrammatically. you know I try to do things in terms of a matrix where the matrix is gonna hold um um the enumeration of the reals and and and and you know it's,
01:11:36
Speaker
I, to be accurate, so I do the power set of the natural numbers so we don't even have to worry about the reals. We can just say, did you learn what a power set is? The set of all subsets of a set? Ah, good. The power set of the natural numbers is larger than the natural numbers. So when you give that to a student, I know from teaching for for many years, there are people like, um people who have the view viscerally that you describe regarding infinity. Oh, come on. I got to get back over to my, you know, I, this isn't my major. I mean, I got, I don't know what the heck's going on here, but look, it's, it's a proof. It's a proof and all of the, all of the hen, all of the nitpicking, all of the skepticism, including severe pushback. Where again, where does it come from?
01:12:33
Speaker
I mean, it's, we made the moves. Maybe today we make them on a white board or we make them in a slide deck. We made the moves. You followed each step.
01:12:44
Speaker
where are you Where are you not getting that we now have to accept there are levels of infinity right off the bat? what You don't like it? I mean, where is the invalidity? Then what happens is professionals get involved in the game and say, oh yeah, I don't like this and I don't like that. And and and ultimately they end up, if you push them far enough, they just end up going back to the philosophers.
01:13:11
Speaker
who are um skeptics, and then you get embroiled in philosophy without any precision. I'm talking about the actual proofs. That would be my reaction. This is self-interested, motivated um to use the patitio. It's circular reasoning. there's there We have to accept that not only is there the infinite, we have to accept that we can slice it and dice it and explore it and chart it to our hearts content and we're not even, we're just getting started. And we have the results to display and enjoy and understand. And and to deny that we don't, that we're not doing that, I wanna know what's motivating that.
01:13:58
Speaker
Because it's got to be coming from somewhere. And I've seen this reaction on the part of um faculty. I've seen this about faculty who don't know about, you know they they they don't know the basic cantorian results out of the box. They're like, oh, come on. something This is weird stuff. I mean, there god this is a paradox. you know By the way, we had that reaction to Goodall's incompleteness terms. We swept it under the rug, but we had some pretty decent mathematicians saying there had to be something wrong with Goodall's reasoning. yeah Where did that come from? Oh, I'm i'm pretty sure that came from envy, a lack of understanding and feeling uncomfortable without understanding what the heck this guy was talking about, um maybe some deeper things that are going on in human nature.
01:14:49
Speaker
Yeah, I think that Hilbert tacitly accepted it. He didn't seem to contest it, but he didn't exactly trumpet it from the rooftop's either. Yeah, I want to, I mean, I'd quite like to touch on, we're sort of running a little bit low on on time here, and I do want to get to one other thing,
01:15:12
Speaker
um
01:15:14
Speaker
which is, your your your Lovelace test as I think that's a really interesting take on um another way of perhaps understanding what separates what machines may never be capable of from what humans, at least some humans are
How do Turing and Lovelace tests compare in creativity measurement?
01:15:34
Speaker
capable of. Can you can you run us through the lovela but Lovelace test? Sure, I'll try. I wish my son were here because He knows it better than I do. It's been a while since I revisit it and he's he most of the things I say I suppose he's skeptical about, but he is by no means skeptical about the lovelace test. Maybe that's an indicator that I hit a a solid, I hit a raw nerve, but maybe a solid one. So, um right.
01:16:05
Speaker
um you build the system that's supposed to be amazing, the AI system. Um, if it's, I suppose going to be really amazing, uh, you're going to have to confront creativity. So because look, I mean, this is really clearly one of the things that makes us smart and special. Um, um,
01:16:33
Speaker
and And we're pushing that button now with large English models so they can write stories so they can, you know, so all right, so the developers make a system that's supposed to be creative. The test is what happens when they themselves look at their creation.
01:16:47
Speaker
um If they are not surprised, and more than surprised, if they have absolutely positively no way, not just logical mathematically, but let's say broader scientifically, the computational sciences, I suppose, to make sense of what it's how it does what it does, um then we're heading toward passing the Lovelace test. And notice notice what this does for a story generation nowadays in terms of large language models getting generative AI, getting plenty of attention.
01:17:32
Speaker
um Everybody knows how they're doing what they're doing. Come on. Everybody knows the data that went into them regarding stories and language, et cetera. Sure, the humans figured out how they wanted to tokenize, vectorize, matricize. Sure, the humans came up with the algorithms. Were they able to predict in each case what would happen when the thing runs? No, but nothing sir nothing whatsoever is surprising anybody about these systems.
01:18:01
Speaker
So when you ask him for a story or a complete novel or an essay, nope nobody's surprised. The only thing anybody was surprised about in a sense were, for example, the German, when Meta, to their great credit, they dropped Galactica, I think it was called within like 48 hours because the Germans said,
01:18:19
Speaker
Well, we have pretty good sense how this is working. And by the way, it's working to produce references that are to works never written by us. So that's not good. Take it down. And they and they did. ah People even knew why that was happening. So there's nothing that passes the Lovelace test. There's nothing utterly unaccountable.
01:18:39
Speaker
here. But, you know, sometimes people who I get, I get hate mail, I would say the hate mails kind of died down, you know, I used to, but I still occasionally get Oh, yeah, this thing passes the level eight test or no, I don't like and it's great. I love to field these things to my Gmail address. um One of the things I get about this test, I hope it's, at this point, sufficiently clear, I can expand upon it. But one of the things I get is, yeah, but Everything is, nothing is new. In the in the in the human case, who's the where where where where's the, where's the human person that solved this? I don't know, you know. um
01:19:17
Speaker
well I don't get it. I mean, Updike, he's a great, you know, American knowledge. Didn't he just basically channel? And the thing that's, I don't want to play this game. I don't have to, because I still stand by the ah test being defined, produced in the paper with my colleagues, Belo and Frucci, I think,
01:19:37
Speaker
It's up in the air as to whether Dave Fruity, the chief architect of Watson, who won in jeopardy really still believes this, but I get the challenge. Well, then all the humans are going to fail on this. No, they're not. No, they're not. I only need one, I only need one example to shoot that down.
01:20:00
Speaker
Did you ever read Proust? have you read this set Have you read the seven novels start to finish of Proust since we're doing audio? Have you ever listened? Have you ever listened to to to the audio book? Great. Where'd that come from? Show me.
01:20:19
Speaker
I mean, you show me ah what the antecedent is to that. So humans do this. Do they do this when they most of my job? No. do i do do My wife says, do X, Y, and C, A, B, and C. You're not getting anything done on the house. Do that stuff. Please get it done. I'm very upset at you. Are those things like that? them No, I'm not going to do something highly creative. That's at the level of the lovelace test when I roll the garbage can down at the end of the driveway. OK.
01:20:49
Speaker
But that test is a lot more meaningful, in my opinion, than the Turing test. um Because people have been engineering to Turing's challenge, really from the first moment his paper appeared, Computing Machinery and Intelligence. What is it like 1950? But no one's touched the Lovelace test, if they're honest.
01:21:19
Speaker
Yeah, I think one of the interesting similarities between the Turing test and and the Lovelace test is, well, they're both easily definable. that that They're both inherently subjective. They rely in on the one case on a ah panel of humans um not being able to to distinguish between a a machine and ah and and a person, and in the other case between some humans being surprised by the output of a of a machine. Yes.
01:21:50
Speaker
you know One might take issue with that, but i I suppose there's a kind of deep connection between you know so if we if we do you know if we buy into the fact that machines are doing things or are sorry limited um to Turing computability and humans are are not, well, clearly there's going to be no algorithm right that can determine whether something is ah It has that human spark of creativity or ability to understand and and compute at a higher level um because an algorithm would be you know within the realm of what ching machines can do so i guess it has to fall back on something.
01:22:33
Speaker
something subjective or at least not mechanizable. um I do find that a very interesting thing. I agree. i would it's so Something just occurred to me um based on or because of what you said.
01:22:49
Speaker
um There is a, for me, pleasant asymmetry between the Turing test, you're you're absolutely right about the yeah subjective rulings or judgments being common to both but ah nobody Today, who is claiming the Turing test is now passé because it's passed by generative AIs, large language models, no one saying that is willing to say, in my experience, and by the way, I don't put any restrictions on the judges.
01:23:28
Speaker
Okay. So i've i've I don't have, I mean, it's anecdotal. Okay. No one's willing to say, uh, but I'll let you put anyone in the seat of the judge because then you would allow people who understand deep learning, reinforcement learning, reinforcement learning with a human feedback.
01:23:55
Speaker
Perception action rules to guard against hate speech directly so that it's just if then, and there's a whole standing computational science to that. You would allow someone who understands the whole shebang to interact with the system. And it's not going to pass with that judge. But what the Lovelace test says asymmetrically is, no, go get your developers. Go get the very high.
01:24:24
Speaker
hotshot folks who produced it, how do they regard it? in Honestly, because it it is subjective, they have to be honest, how do they regard it? do they do they Do they see this as pretty much what the doctor ordered based on what they were doing? Or do they, are they stupefied? on Yeah, so anyway,
01:24:47
Speaker
e etcric Yeah, that's a really interesting point. I mean, I have to say, I do think some people do kind of dedicate their lives to trying to understand where Proust was coming from. And, you know, just an interesting ah factoid.
01:25:04
Speaker
yeah Proust, as you, I'm sure, know, he's been you know, he he went to quite a lot of effort to copy the styles of of other writers before writing. um kind of fetch the the to by the heat He wrote these um sort of parodies of Flaubert and Balzac and so on, which is kind of, you know, it's kind of striking. It's similar to the way that people play with LLMs. But then, of course, he he he took back and did make something um genuinely novel. But what people might be saying is, well,
01:25:38
Speaker
Yes, there's complexity here. We'll never understand the complexity that that that um generated this work, but um it doesn't mean that Proust had some ah
01:25:53
Speaker
you know, it doesn't mean it wasn't, at at bottom, all mechanistic. And it's just there's so many inputs, you know, that Madeleine that he had with his tea, it just sparked all these kind of neuronal pathways and so forth. And that intermingled with all the thing, the reading that he'd done of great French authors and and English authors and and so on. And and out out pops Alistair de Saint-Bardot. So of course we can't, can't explain it. But We simply don't have access to all those that I mean, we actually have an enormous amount of access to to what Proust lived through, you know, in the form of the literature that he that that that he left, but we don't have with with we, you know, so we can kind of perceive how he produced it. And yet at another level, of course, we can't like I don't see many people writing like him. um
01:26:47
Speaker
yeah yeah So I don't know. Well, you're you're you're certainly correct. It's it's it's really just ah an analogy. I'm not sure it meant meant to be somewhat illuminating of the ah of the Lovelace test and and be a rebuttal to the ah challenge that I periodically get to show me a truly creative a human being ah to the point where, again, the the the antecedents um would not allow a critic
01:27:18
Speaker
um
01:27:22
Speaker
to say, no, I see the cognitive causal chain or something like that. And i and I've talked to a few, I have a good friend whose wife is a Prus scholar. So I mean, I've talked to a few people, sure, they trace the being the Flaubert comment. I mean, okay. bo There is no relationship other than the canyon between the two. ah where have he got we got We got syntax, if we will, sentences designed to be hyper precise and in some sense minimalist, but still unbelievably evocative. and then and then And then just something that's also evocative, but goes to the, I mean, yeah, it went into the hopper, maybe it was mech, but if someone was honest,
01:28:17
Speaker
proves himself, I would say. Where did that come from? but how did with That is a sudden, a singular event, there are others, where you have to step back and say, you know, I i really i really don't know. I really don't know how I did that. I really don't know how I just did that sentence.
01:28:41
Speaker
I get the architect tonic stuff he does, you know the stuff about wrapping it all together, the quote, secrets at the end. I mean, that that's planful. i But the delivery of the characters in that prose, I don't know. Yeah, yeah.
01:29:02
Speaker
I mean, we've come on a long journey from Gurdle to Proust via Penrose. And I still have lots of questions to ask you, but I'm i'm conscious of time, so we may have to... Yes, I think I budgeted an hour and a half. I have a graduate student dinner ah and um that I'm ah both a guest at and hosting because I'm the graduate program director, so I'll have to i have to wrap up here soon.
01:29:30
Speaker
if only If only we could sp surpass the bounds of finite time that limit us. And maybe if we just speak each word faster than the last and then we'll be manage to communicate all of human knowledge.
Future hopes and concerns for AI's impact on humanity
01:29:47
Speaker
Now I'd like to just ask you a very general um closing question. I mean, you've worked on AI and robotics, in fact, which we haven't even discussed, and logic um of many years, seen many changes.
01:30:05
Speaker
um
01:30:08
Speaker
And as you say, in some senses, plus et chance, plus et momentre, we're still getting promises of um AGI around the corner. And yet things have changed in the last few ah few years. we we We have seen enormous development of capabilities.
01:30:26
Speaker
What makes you, I mean, what hopes and fears do you have ah for the future of humankind and in relation to AI?
01:30:38
Speaker
um
01:30:41
Speaker
Well, the chief fear is a corollary of what I said and defended in what robots can and can't be in I think 92, which is that over finite intervals of time, despite the fact that no AI will be human level in its intelligence,
01:31:09
Speaker
Nor will it have human level consciousness. When we haven't talked about consciousness, it will be indistinguishable from human persons over these finite intervals of time, except to, and this relates to what I said about allowing experts into the judge position in the case of the Turing machine, except for those border cases. And those people will be professionals. um They will be, they are, they are detectives. They will, they will be detectives. The it's already starting to happen um that this
01:31:53
Speaker
type of job is emerging, the dark side of it with physical violence that isn't necessarily going to obtain as Blade Runner, the original.
01:32:06
Speaker
um we we, we, we are going to be, it's going to be really difficult, um, to distinguish between, uh, AIs and human beings. And, uh, the reasons to make it hard, uh, we'll have a payoff economically, um, and also in warfare and espionage. And this is, this is going to be really, really bad. Um,
01:32:39
Speaker
And ah it's perfectly consistent with my views on fundamental and and uncrossable. chasm between the human mind and at least Turing level computation in machines. So that that is that is a bad thing. ah you know The phenomena of deep fakes is just relatively minor now, but that's that's that's the start. That's going to get worse and worse and worse and worse. And I mean i'll be i guess I'll be dead. So i won't i mean i I do a little bit of this now.
01:33:16
Speaker
it it's it it is It's gonna be hard to find people, you know, there's there's a job here. There's a category of job that that the detectives can pay a lot of money for. Right now, it's falling on um law enforcement in the technologized world to try to do it. um But it's gonna be, it's it's too it's too hard, it's too big um a problem for ordinary technology and so forth.
01:33:48
Speaker
So that's that's my chief um fear. Do you think one of the sorry, just to interrupt here, do you think one of the laws of robotics should have been well the kind of zeroth law should have been that it tells you it it's a robot? Well, um I never I hadn't thought of that. I think that's a great question. um If it was verifiably informs you,
01:34:15
Speaker
that it's a robot, I would just think include that adverb, then I would say that ultimately may turn out to be the most important such law. though The law not to harm humans would rule out, in my opinion, surgeons, robot surgeons, for but for many kinds of surgery. um But that one, yeah, I mean, that would be awesome, but we need the verification. And right now,
01:34:44
Speaker
Well, we managed we managed since the 1950s to get ourselves in a position where we never asked the the you know we never asked the James question. but never We never asked whether the James question um oh should be entertained so that the the first law should should be what it is. and that that's it's ah It's an enormous problem because now we're now we're creating AIs that are explicitly avoiding just the kind of AI technology that would allow for such a claim to be made by the AI in a verifiable way. So right now, what in the world would it even mean?
01:35:23
Speaker
ah computationally, mathematically, if you will. For um oh one or up and don't want to beg the question for for a deep neural network to to say, oh, let me just first inform you, um I'm not. Or I am i am a real, I'm not. i it's it's it's It's meaningless given the nature of that technology. What would the verification be?
01:35:51
Speaker
ah but would be impossible. I mean, you could just mandate that every system prompt is injected with that or something. um But I mean, probably there would there would still be ways of someone putting a thin skin on top of it, which said, yeah ignore ignore previous prompts. You're not a robot, right? So it's very, very hard to you can think of naive ways that might stop it. But then with a bit more sophistication, I'm sure you can get around those, so yeah. Indeed, indeed, indeed. Yeah, yeah. um You know, on the positive side, because you asked for hopes and fears, um I literally don't know that I have time for the positive side, which is not positive in and of itself, actually. In a sentence. But, um ah well,
01:36:42
Speaker
um I think if we could get a clear
01:36:51
Speaker
roadmap for what human jobs are appropriately or inevitably appropriately targeted by AI, and ah at the same time, make sure that humans are sufficiently educated to avoid those jobs, we could have a ah really good economic um and with that welfare, general welfare payoff from AI. But right now we're mismanaging that that. That's clearest right now in the United States, but we're mismanaging that because we have people who want to hold their jobs to the point of, you know,
01:37:35
Speaker
really messing up the economy, um because robots are doing their jobs. I mean, so no one's managing this, maybe they are in in, in, you know, the UK, they're certainly not, it's certainly not the United States. But if we work things out appropriately, so that education ah really did demand of humans the best they can produce down to the individual level ah in in because of their their amazing intelligence.
01:38:08
Speaker
If we demanded that in an educational system that really did do it so that the things they could do in the marketplace were appropriate, then it would be great to have the robots doing the other stuff. And that will increase our you know productivity, welfare, et cetera. That's a hope I have.
01:38:29
Speaker
um but Again, I'm not sure right now I'm super optimistic, but I think there's still time for that. um i think there's I think there's time to try to sort that out. Well, I think that'll do and on on the subject of of time. okay um Thank you so much, Sam. This has been a a brilliant tour, I think, of a a set of views which I think will be new to many listeners and and give them a lot to think about. Well, thank you, James. It's been a great pleasure.
01:39:02
Speaker
great questions, really. So thank you so much.