Mathematicians gone crazy: Friend, do you believe that the numbers 3, 4 and 5 can be said to "reside" somewhere?
Does the number 3 "reside" next door to the number 4? Do Newton's laws of motion inhabit a larger residence in this same immutable "world?"
We ask these questions after perusing Mario Livio's well-received book, Is God A Mathematician?
Livio is an astrophysicist—a ranking astrophysicist at that. As is required by Hard Pundit Law, his book was chosen by the Washington Post as one of the best science books of 2009.
You can read Livio's entire first chapter thanks to the people at NPR. The Washington Post decided to publish the bulk of the first chapter too.
Rather famously, Rodney Dangerfield got no respect at all. But astrophysicists get tons of respect within our routinely comical press corps, even when they, in turn, are displaying tons of respect for mathematicians gone wild.
If you're a ranking astrophysicist, or even a ranking philosophy professor, you can say any darn thing you please and journalists will rush to affirm you. And so it was when, right on page 2, Livio respectfully described the views of Roger Penrose, a "renowned Oxford mathematical physicist" seemingly gone wild:
LIVIO (pages 2-3): Penrose identifies three different "worlds": the world of our conscious perceptions, the physical world, and the Platonic world of mathematical forms. The first world is the home of all of our mental images—how we perceive the faces of our children, how we enjoy a breathtaking sunset, or how we react to the horrifying images of war. This is also the world that contains love, jealousy, and prejudices, as well as our perception of music, of the smells of food, and of fear. The second world is the one we normally refer to as physical reality. Real flowers, aspirin tablets, white clouds, and jet airplanes reside in this world, as do galaxies, planets, atoms, baboon hearts, and human brains. The Platonic world of mathematical forms, which to Penrose has an actual reality comparable to that of the physical and the mental worlds, is the motherland of mathematics. This is where you will find the natural numbers 1, 2, 3, 4,..., all the shapes and theorems of Euclidean geometry, Newton's laws of motion, string theory, catastrophe theory, and mathematical models of stock market behavior. And now, Penrose observes, come the three mysteries. First, the world of physical reality seems to obey laws that actually reside in the world of mathematical forms...Let's be clear—we're looking here at Livio's account of Penrose's views, not at the work of the renowned Oxford mathematical physicist himself.
But as Livio describes those views, he seems to be describing the thoughts of a person who's stark raving mad. Respect for authority apparently keeps him from making this rather obvious statement—respect for authority, or perhaps the lack of intellectual ability which has long characterized the comical efforts of us "rational animals," especially those who work on the highest academic platforms.
Let's summarize what Livio says there:
According to Livio, Penrose believes that the numbers 3, 4 and 5 "reside" in "the Platonic world of mathematical forms." Penrose allegedly further believes that this Platonic world "has a reality comparable to that of the physical world"—indeed, that it has an actual reality of that type, whatever that one extra word might be thought to add.
Newton's laws of motion can also be "found" in that Platonic world, possibly in a larger residence than the one where the number 3 lives. You see, those laws "reside" in that world too. They "actually" reside there, in fact!
Except in the disordered world described by Andersen in The Emperor's New Clothes, the views attributed to Penrose would seem to be those of a madman. But because our frequently comical human world is frequently extremely irrational, such apparently peculiar views are routinely treated with full respect.
As Livio proceeds through Chapter 1, he quotes one mathematician after another making "philosophical" statements which seem to be fatuous, crazy, incoherent or bizarre pretty much on their face.
On page 9, for example, we encounter one of those "things that make us go hmmm," if we might quote Professor Hall. We encounter it in the form of a quote from French mathematician Alain Connes:
CONNES: Take prime numbers, for example, which as far as I'm concerned, constitute a more stable reality than the material reality that surrounds us. The working mathematician can be likened to an explorer who sets out to discover the world. One discovers basic facts from experience. In doing simple calculations, for example, one realizes that the series of prime numbers seems to go on without end. The mathematician's job, then, is to demonstrate that there exists an infinity of prime numbers. This is, of course, an old result due to Euclid. One of the most interesting consequences of this proof is that if someone claims one day to have found the greatest prime number, it will be easy to show that he's wrong. The same is true for any proof. We run up therefore against a reality every bit as incontestable as physical reality.Do prime numbers "constitute a more stable reality than the material reality that surrounds us?" It's hard to know why anyone would raise such a peculiar point, and Livio makes no attempt to speak to this obvious question.
In fairness, "the material reality which surrounds us" is subject to earthquakes, tidal waves, nuclear war and the gruesome effects of bomb cyclones. As best we can tell, prime numbers are subject to no such forces, nor do we have the slightest idea what it could mean to say such a thing.
In that sense, you might decide to say that prime numbers "constitute a reality" (whatever that formulation might mean) which is "more stable" than the physical reality of farmland in Nebraska. You might decide to make that statement if you're very, very strange, though it's unlikely you'd be able to explain why your statement made any recognizable sense if you were subjected to something like competent intellectual challenge.
Mathematicians like Connes don't get that kind of challenge in Livio's book. Again and again, their puzzling, often fatuous statements are presented as if they make full and complete perfect sense.
Why is apparent nonsense of this type afforded so much respect? We'll only say that, on page 9, Livio describes Connes as "winner of two of the most prestigious prizes in mathematics, the Fields Medal (1982) and the Crafoord Prize (2001)."
Apparently for that reason, Connes' fatuous statements in other areas will be treated with full respect, even when he's ventured far outside his field of expertise.
The comical aspects of this culture seem to know no bounds. Professor Goldstein took the same approach to the "Platonism" of leading intellectual lights in her own remarkable book, Incompleteness: The Proof and Paradox of Kurt Godel.
As we've noted in earlier reports, Goldstein's ridiculous treatment of ludicrous claims won her accolades from a long string of name-brand intellectuals. That's the way the game is played within this high-ranking class.
Along the way, Goldstein dropped hints that the views she was describing were in fact the crazy views of irrational people gone wild. But she never came out and made this blindingly obvious statement. Livio follows suit.
We'll have a lot of nonsense to get to in tomorrow's final report. We'll want to look at the peculiar way Livio starts his book, right there on page 1. We'll also want to touch on his respectful treatment of a hoary semantic morass, the utterly pointless pseudo-debate about whether mathematics is "discovered" or "invented."
Before we hit those topics, let's agree that we'll begin tomorrow on page 37, where Livio finally rolls his eyes at all this "Platonist" foolishness. That said, he does so very respectfully. These are the emperors' theories, the theories of Fields Medal winners gone wild.
As you know, we're just killing time at this site as we await the start of Mister Trump's Fully Dispositive War. Future Anthropologists Huddled in Caves (TM) have told us, in a set of convincing nocturnal submissions, that the conflagration is coming.
Convincingly, they've told us that the road to this war involved the ineptitude of our mainstream press corps over the past thirty years or so, mixed with the failure of leading academics to step in with helpful correctives.
Was man [sic] ever "the rational animal," as sacred Aristotle is widely said to have said? These future anthropologists tend to respond to that question with short bursts of mordant laughter.
At such times, they point to the highly irrational claims of physicists, philosophers and mathematicians gone wild. "Look upon the works of these mighties," they mordantly say, "and join us in joyful despair!"
Tomorrow: "But does the Platonic world of mathematics really exist? And if so, where is it?"