Episode Transcript
[00:00:00] Speaker A: Foreign.
[00:00:05] Speaker B: The Future, a podcast about evolution and intelligent Design.
[00:00:12] Speaker C: Welcome to ID the Future. I'm your host, Andrew McDermott. Today I'm very pleased to bring back on the show Dr. David Berlinski to finish discussing his book Signs After Babel in the final episode of a three part interview. Dr. Berlinski is a senior Fellow at Discovery Institute's center for Science and Culture. He received his PhD in Philosophy from Princeton University and was later a postdoctoral fellow in mathematics and Molecular biology at Columbia University. Dr. Berlinski has taught philosophy, mathematics and English at such universities as Stanford, Rutgers, the City University of New York and the University of Paris. He is author of numerous books including A Tour of the Calculus, the Advent of the Algorithm, Newton's Gift, and the Devil's Delusion. His latest, Signs After Babel is a collection of essays challenging the prevailing beliefs and pronouncements of contemporary science with his unique blend of deep learning, close reasoning and sharp wit. In it, he reflects on everything from Newton, Einstein and Godel to catastrophe theory, information theory, and the state of modern Darwinism.
Mathematician, philosopher and author of the Design Inference. William Dembsky says Science After Babel masterfully exposes the hubris of scientific pretensions with a wit that dances deftly between the lines, unveiling profound insights with a refreshing candor. David, welcome back to Idea the Future.
[00:01:39] Speaker A: Thank you so much.
[00:01:40] Speaker C: Absolutely. Well, I've thoroughly enjoyed our first two conversations together where you covered your appraisal of modern Darwinism as well as the enduring problem of the origin of life and the physicist's quest to explain everything.
Listeners are encouraged to go back and listen to parts one and two in this episode. I wanted to touch on the last two sections of your book. The first of these is titled Deep Dive and the first essay in this Deep Dive section is a review of Michael Ruse's book, the Philosophy of Biology. Who is Michael Ruse? What does he see as the proper philosophy of biology? And what's your beef with the fellow?
[00:02:19] Speaker A: I would like to think of myself that I do not have a beef with Michael Ruse. I don't know him. He's now a man of my old the same age as me, an old, old man.
And the book was written quite a while ago. It is the expression of a certain point of view in the philosophy of biology. It is the point of view, I would say, of an analytic philosopher, not a continental philosopher, but Anglo American philosopher with a very good background in logic and entirely persuaded that the role of the philosopher is to be in effect, a handmaiden to the sciences and to clarify and to round out arguments for their philosophical significance that really have a scientific basis.
And like many other philosophers of biology, Rouss went back and this was at the moment of efflorescence for Darwinian theory, when it increasingly seemed to the biologists that, hey, my goodness, we have a terrific theory and we haven't been spreading the word around sufficiently. I would say this was taking place roughly 1973, 1974. That's when it began. It reached its peak, I think, 25 years later in a real propaganda effort to persuade every man, woman and child in the United States to genuflect before the image of Charles Darwin. It's tapering off now.
That's a movement in social as well as intellectual history. But Roos offered, so far as I can tell, a very orthodox view of the philosophy of biology in which a great many things were purged of their teleological implications and reduced essentially to very, very straightforward orthodox Darwinian biology. Survival of the fittest, natural selection, entirely adequate mechan.
And that's really what prompted me to write the review, the sheer and commendable orthodoxy of the position.
[00:04:26] Speaker C: Okay, well, other essays in this deep dive section look at the great mathematician Giuseppe Piano or Pinot, and the great logician Kurt Godel. Also at Rene Thom and catastrophe theory, and at the question of how mathematics does and does not relate to the world. I wanted to ask you about that last one. Is this a complicated question? Math helps us figure out how planets revolve around the sun, how entropy works, Einstein's theory of relativity, and so on. What's puzzling or challenging about mathematicians and mathematics? Relation to reality?
[00:05:02] Speaker A: Well, everything as far as I'm concerned. Look, in the 13th century, a very little known philosopher of the high Middle ages, Thierry of Chartres, he made an aphoristic remark which I think is very pregnant. He said, the beginning of numbers, the beginning of numbers was the beginning of things.
When you think about the simplest application of numbers, which after all are not created entities, you can't say the number one was created on February 3, 1852. That makes no sense.
But equally, it doesn't make a whole lot of sense to say they're eternal, they last forever, because lasting is not something that numbers do.
When you ask about how numbers apply to things as simple as finger counting, you get yourself in kind of an intellectual muddle. What is it to say that one finger is one?
What is the predicate one doing? I mean, quite clearly, if we have a finger to begin with, there's just one of them. Otherwise we'd say fingers, two of them or three, so we know it's one.
What is added by saying it's one finger, as opposed to saying it's a finger, is saying one finger is one. Identifying oneness in a figure, what does that mean? Is there a mapping from one to a finger? Is there a mapping from the natural numbers to things? If there's a mapping from natural numbers to things, as for example, Bertrand Russell and many other philosophers of mathematics argued, how can it have numbers in its domain if it has fingers in its range? That's a mixed marriage. Numbers going to fingers is not mathematical and it's not physical. How can it be both without violating or encountering Aristotle's third man argument? There's no natural mapping from an ostensibly Platonic object like a number, to a perfectly ordinary physical object like a thing.
When we say two fingers plus two fingers equal four fingers, if we divide through by the fingers, we get two plus two equals four. There's no sneezing at that. But how do you divide anything by fingers? And if you can divide by the fingers, what does two fingers plus two fingers equal four fingers even mean?
I'm not saying these questions are unanswerable, but the very long, fairly complicated paper that I wrote is an attempt to answer them.
[00:07:30] Speaker C: Yeah, it's a fascinating section here, and you're breaking it down in an interesting way here. Well, the book's final section returns to the more accessible mode of the book's first four sections. It's titled Titans and it contains reflections on Isaac Newton. And there's a final essay there that I wanted to discuss for a moment.
The second essay, however, is about Alan Turing. Some listeners may be familiar with Turing from the Movie Back in 2014, the Imitation Game, with Turing played by British actor Benedict Cumberpatch. Turing is famous of course, for cracking the Nazis Enigma code, which helped the Allies win World War II. But that isn't the focus of your essay. You focus on Turing's so called Turing machine and on something it revealed about the nature and reach of the mathematical enterprise. I'd like to take this in three parts. First, can you briefly explain to listeners who are unfamiliar with Turing, who was he besides a code breaker?
[00:08:24] Speaker A: Alan Turing was an extraordinary, extraordinarily gifted mathematician Englishman, and he became captivated by mathematical Logic, which in 1934, 1935 or 1936 was still at its beginnings.
I mean, mathematical logic reached a point of dazzling maturity only in 1931 with the publication of Kurt Godel's Incompleteness Theorem. It had been a subject before, but nothing like the incompleteness theorem had ever been seen, either in mathematics, medical logic, or in mathematics. It's completely, completely sophisticated professional publication which just lifted the entire discipline so that it was visible everywhere.
But it took a long time for these ideas to be absorbed. You know, when I was at Columbia College in the 1950s, nobody ever heard of Godel.
It was just not there. The first English translation of the German version didn't appear to them until the mid-1950s. And Nagel and Newman's very important book, Godel's Proof, appeared a few years thereafter. We're talking about a lag of almost 25 years, which is quite astonishing for a major intellectual achievement. A major intellectual achievement. So that by the time that Turing wandered from England to Princeton to study with Alonzo Church, he was participating in a discipline that was virtually new. Not new, but virtually new. I mean, Russell and Whitehead had written Principia Mathematica many years before for. But in comparison to anything. And this Russell acknowledged handsomely that Godel was advancing in the early 1930s. Or Alonzo Church, it was simply primitive by comparison.
[00:10:07] Speaker C: Yeah, and we also see this, this. This time frame, the turn to machines and. And the effort to. To control natural processes and exploit them. So what was Turing's machine? How does that figure in?
[00:10:22] Speaker A: Well, in his great incompleteness proof, Godel had introduced a class of functions that he called recursive functions. These were functions that build on predecessor functions. For example, if you want to know what two plus three is, you ask what two plus two is, and you define two plus three in terms of two plus two plus one.
It goes all the way back to the base at 0 or 1. That's a recursive function. It eats its own tail, in effect.
And he introduced them, and he gave them a careful mathematical description. Alonzo Church, a few years later, gave them a very careful definition in terms of lambda definable functions. But these were quite difficult mathematical ideas, and only mathematicians really could follow it. What Turing did was smash through these definitions to come up with an intuitive idea that was so radically clear and so successful intuitively that it became the standard. And that was the idea of a Turing machine.
And the idea is very simple. Imagine an infinite tape divided into squares.
I mean, literally an infinite tape, paper tape, if you will, divided into squares. There's a machine with a reading head poised over the tape. The machine can be in several different states, finite states. Call them state one, state two, state three, whatever you want to call them. And it can also read what's on a square and then either erase what it sees and move on, or print something new, move on, or stay where it is. In other words, it's step by step. Behavior is controlled by a program and what it does is controlled by a program as well, that it prints something on the square and then finally it stops. And that's all that there is to a Turing machine. But it turns out that can do anything computable that's completely equivalent theoretically to a full fledged von Neumann machine. It is as powerful as any machine could possibly be devised.
It's called a Turing machine. It can compute all the computable functions. And Godel, and of course Alonso Church and later Emil Post and Turing all came to the conclusion that these different definitions were defining one idea. That was the idea of a computable function, something that could be done by a machine. And Turing had said, here, here's the machine. Go do it. And he was right.
He was right. Godel was moved to say this was one of the very few examples of an absolute definition in mathematics. All the concepts coincided, coincided perfectly. And of course, based on Turing's work at the end of the Second World War, the development of the computer needed only von Neumann's genius, actually to put these steps into place and make a mechanical machine. Turing's machine was simply an idealization of a computer.
By 19, or at the latest, 1950, the first mechanical devices were in place. This is an enormous contribution to thought.
[00:13:12] Speaker C: And thus begins the computing age and the pursuit of artificial intelligence. Exactly what did Turing's work reveal about mathematics then in general?
[00:13:21] Speaker A: It's really hard to say. Don't forget Turing died prematurely. He died by his own hand, tragic death.
What he could have contributed addressing these questions is simply unclear. They're an enormous class of computable functions, but we know perfectly well that the class of functions that cannot be computed is just infinitely greater. Most things can't be computed.
What does this say about mathematics? It's really, really hard to say because the time lag, the time dilation between the enunciation of These ideas in 1931, 1935, 6, 1940, and their percolation throughout the entire scientific establishment has taken almost a century. We're just now, just now seeing the fruits of this work.
When I started my education in the late 1950s and when I was at Princeton, this stuff was invisible. It really was invisible. It seemed to be a very peripheral activity.
Now it seems to occupy something like the center stage. What it means for mathematics itself, very difficult to say. There are a Lot of new proof verifiers, that is automatic systems which will check a mathematical proof for consistency, for logical accuracy and things like that.
And those are very helpful. I mean, a great many extremely good mathematicians have said, you know, even me, sometimes I look at my own proofs and I say, h is step 97, really hard as a rock. There's some famous examples, but. But every mathematician has said. Every mathematician presiding over a complex body of work has said the same thing. I hope to God some colleague gotten the other part of the world in Japan doesn't notice a mistake. I can find the mistake, but who knows? I'm awfully tired in checking these things. Maybe I just nodded off at the wrong moment. Now we have systems that to some extent, to some extent can do a verification. Peter Schultz is an extremely good young mathematician, a field medalist, and he's got a very elaborate new part of arithmetic geometry. He calls it liquid tensor.
It's quite complicated. Trust me, it's complicated mathematics, not unintu.
I don't know how interesting, but not simple.
And he said to the mathematical community, you know, even though I believe everything I put down in my proof is correct, I have my doubts about Lemma 6 point. I think it was 6.4, 6.5. It's been a long time since I looked at. What I'd really like is a hard and fast computer to take a look, check all the steps. That's not simple to take a mathematical proof written in a mathematical language and translate it into a computer language. But they did it. They did it. And yes, the proof was correct, but now he has a computer to say it was correct.
Of course, I believe deep down he always knew it was just a way of drawing attention to the importance of the work. But there are other cases where people really don't know. Not quite sure. Mitchizaki in Japan, ostensible proof of the ABC conjecture, which has been rejected by Schultz, that would certainly profit from a computer proof. Certainly profit, because nobody can understand it right now.
Clearly mathematics is changing under the influence of computers. It's changing. It has changed more radically under their influence in the last 20 years than it changed in the years from the introduction of these ideas in the 1930s to say, 1980.
That's another interesting historical question. In one of the previous episodes, we asked, why no science in China? Why no science in the Arab world? Why no science in the Greek world? Science in the modern sense, theoretical science.
Here's another question. Why time lags in certain disciplines and not in others? You know, when Einstein published relativity in 1905. Within six months, Max Planck said, yeah, it's right. He published it.
General relativity the same. A few years later, there was an expedition, I don't know where it went to, to verify Einstein's calculation. But everybody knew, though. But in logic, no. Long time delay. Long time. I don't know why.
Maybe the Second World War had a. Had a part in that.
[00:17:30] Speaker C: Yeah. Yeah, well. And before we move into the final essay, just a little aside while we're on the topic of Turing. Do you think Chat GPT has answered the Turing test or do you think there's trickery involved?
[00:17:44] Speaker A: Oh, yeah. Oh, I think there's no question about it. You know, you, you can interact with Chat GPT. I defy most people to figure out whether it's a human being or a computer. It just sailed right by the Turing Test, that that means less than you would think. The Turing Test says if you're interrogating an object and don't know whether it's a human being computer and can tell after you talk to it, it's passed the Turing test. It's intelligent. Yeah, these systems certainly are. Are intelligent.
Modulo the obvious objection. We really don't know what intelligence is because so far we've only defined it in human terms.
And the inference to a machine intelligence has all of the disadvantages of a leap into the dark. We don't know what's there. We just don't know.
We don't know how it works. We have no dynamic theory of its mechanism, no way of predicting what it does. It seems to be fumbling huge matrices, things like that. But what it's actually doing, whether it's a form of intelligence or we can do, is look at what it says. And as far as what it says goes, yeah, it seems perfectly intelligent.
[00:18:51] Speaker C: Yeah, it's. It's an interesting phenomenon and something wholly modern that we're wrestling with today. Before we finish up here, you had an essay called Life Itself, which was a rather beautiful way to. To finish things up. It's only four paragraphs long, but it really packs a punch. You begin by noting in the essay the majestic advances that physics saw in the first 30 years of the 20th century. Science seemed as if it might extend without limit, conquering every snow capped vista and sight and rushing on from there. Tell us about this moment in the first part of the 20th century, this heady chapter in the history of science.
[00:19:27] Speaker A: Well, if you look at the great achievements, certainly special relativity. Einstein wasn't the only person to think of special relativity. He was the only one confident enough to complete it. That's 1905.
And you see that there are absolutely stunning new ideas entering into physical thought. And then 10 years later, the culmination, the apotheosis of special in general relativity, which brought all the notions of relativity from uniform motion into accelerated motion. Uniform motion completely satisfies the postulates of special relativity that speed of light is absolute and laws of physics look the same to every inertial observer. But that's just motion in a straight line. Uniform, uniform, straight line, any speed. General relativity is far more general because it incorporates acceleration, which means it incorporates curvature. Curvature is the mark of acceleration.
So this was a great achievement, spectacular achievement.
But then the remarkably swift progress of quantum mechanics, from the Bohr model of the hydrogen atom in the first part of the second decade of the 20th century to the culmination of a serious theory of Quantum mechanics by 1929-30, and the Dirac equation, which introduced relativistic concerns into special relativity. This was unparalleled in the entire history of thought in the human race. And to a certain extent, everything from 1930, 1935, say, to 2023 has been the elaboration, the culmination, the apotheosis, the elaboration of these ideas, which has been a magnificent story, which over the last 50 years, has seemed to some observers as if it had begun to sputter.
Doesn't mean that there hasn't been remarkable achievements. I don't want to say that for a moment. You know, every now and then, a physicist will get on YouTube or Twitter and say, no, no progress in particle physics since the 1970s, the standard model of particle physics. That's obviously not true. Lots of progress, especially in solid state physics. What is meant is that we are still in a universe where there are two majestic theories, general relativity and quantum field theory.
And for the life of us, we don't know quite how they fit together. Theoretically, practically, there's no problem. We can do lots of calculations with both theories, but theoretically, they don't quite fit because they don't seem to belong to the same universe of thought. One's classical, one's modern, one's completely quantum, one's not quantum at all. One has a fixed spatial temporal background, one doesn't. One is dynamical in terms of the interaction between a gravitational object and the surrounding space time. One's not. One's renormalizable, and one's not renormalizable. And nobody knows what does this really mean? That physics is a divided heart, that it has two parts and nobody for the life of them can figure out how to put it back together.
Interesting question, huh?
[00:22:31] Speaker C: Well, I just love your example of, of humility there and, and honesty. And as you explore in your book, you know, parts of the physical world just simply refuse to yield to scientific reductionism. And it's important to note, you know, it's important to remember and again, have that humility, no matter what scientific field you're in. Well, I'd like to close by reading the final paragraph of the volume's last essay. It's a rather beautiful way to end this discussion. You say. More than any particular thing that lives, life itself suggests a kind of intelligence evident nowhere else. Reflective biologists have always known that in the end they would have to account for its fantastic and controlled complexity, its brilliant inventiveness and diversity, its sheer difference from anything else in this or any other world. David, we've run out of time here, but over the course of three episodes, we've unpacked just a little bit of the richness that you've put into science After Babel and All this Life now is that our readers pick it up and. And read it.
[00:23:35] Speaker A: Let's hope.
[00:23:36] Speaker C: Well, you heard the man. Pick up your copy of Signs After Babel at The website science afterbabble.com couldn't be easier. Science afterbabble.com and again, you can listen to parts one and two of our discussion anytime you feel like it. The quicker the better, because this is. This is quite something. This is a great work by a great man. David, it's. It's been amazing. Thank you so much for spending this time with me.
[00:24:02] Speaker A: You're so welcome. It was entirely, entirely my pleasure, I assure you.
[00:24:06] Speaker C: Thank you, David. For ID the Future, I'm Andrew McDermott. Thanks for listening.
[00:24:14] Speaker B: Visit us at idthefuture. Com and intelligentdesign. Org. This program is Copyright Discovery Institute and recorded by its center for Science and Culture.
