And other high-end mumbo-jumbo: We asked the question yesterday. What goes through the mind of a very smart person who writes something like this?
LIVIO (page 2): Millennia of impressive mathematical research and erudite philosophical speculation have done relatively little to shed light on the enigma of the power of mathematics. If anything, the mystery has in some sense even deepened. Renowned Oxford mathematical physicist Roger Penrose, for instance, now perceives not just a single, but a triple mystery. Penrose identifies three different "worlds": the world of our conscious perceptions, the physical world, and the Platonic world of mathematical forms....Roger Penrose "identifies" three different "worlds," including "the Platonic world of mathematical forms?" So this author said.
That passage was written by Mario Livio, who is, by any normal metric, an extremely smart person. By any normal metric, Penrose is extremely smart too.
That said, what goes through the mind of a person who writes something like that? Also, what goes through the mind of a major publisher who puts such work into print?
What went through the mind of NPR when it decided to highlight Livio's 2009 book, Is God A Mathematician? What went through that upper-end news org's mind when it decided to post the very excerpt from Livio's book in which this passage occurs?
What goes through the minds of these high-end players? We ask because of what happened when Livio tried to explain what Penrose was said to believe.
Few people will be puzzled by the claim that a "physical world" exists. Is there also a "world of our conscious perceptions?" That's a slightly awkward construction, but most people would understand what such a claim probably means.
But how about that third alleged belief by Penrose—the belief that a third "world" exists, "the Platonic world of mathematical forms?" Will anyone reading Livio's book know what claim could possibly mean? We ask because of the mess which occurs when Livio tried to explain what Penrose means:
LIVIO (continuing directly): 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.According to Livio, "the physical world" is "the one we normally refer to as physical reality!"
With that, we're off to a possibly unimpressive start. But then, we see the remarkable way Livio explains what Penrose means when he says that there is a "Platonic world of mathematical forms."
What does Penrose mean by that? According to Livio, Penrose means this:
According to Livio, Penrose thinks this Platonic world "has an actual reality!" What kind of reality wouldn't be actual? We're left to guess about that.
Let's set that aside as nitpicking. As he continues, Livio says that Penrose believes that the Platonic world of mathematical forms is "the motherland of mathematics."
He then says that Penrose believes that this motherland is "where you will find the natural numbers 1, 2, 3, 4,..." It's also where you will find "all the shapes and theorems of Euclidean geometry [and] Newton's laws of motion," among other assorted entities.
Question: Will any reader have any idea what this mumbo-jumbo means?
According to Livio, Penrose believes that the world of Platonic forms is a motherland which has an actual reality. It's where you'll find the number 1! Can this be distinguished from madness?
Will any reader have any idea what this presentation means? The reader is told that she will find the number 1 in the world of Platonic forms. What can that possibly mean?
Will the number 1 introduce itself when she finds it there? It's been claimed that one is the loneliest number. Will it ask her to stop for a chat?
Meanwhile. what does it means when we're told that we'll also find Newton's laws there? In what form will those laws exist when we find them in this motherland, which has an actual reality?
So far, no one reading this mumbo-jumbo could possibly have any hope of explaining what it might mean. At this point, we're on page 3 of an extremely smart person's book. But if we're sensible and experienced, we're probably already looking around, hoping to locate the exits.
If we're perhaps a bit more trusting, we may have a different reaction. We may assume that Livio—by any normal metric, he's one of the smartest people around—will start to untangle those problems.
Experienced people will be less sanguine. Indeed, by the time we hit page 9 of this well-regarded book, Livio will be saying this:
LIVIO (page 9): As I noted briefly at the beginning of this chapter, the unreasonable effectiveness of mathematics creates many intriguing puzzles: Does mathematics have an existence that is entirely independent of the human mind? In other words, are we merely discovering mathematical verities, just as astronomers discover previously unknown galaxies? Or, is mathematics nothing but a human invention? If mathematics indeed exists in some abstract fairyland, what is the relation between this mystical world and physical reality? How does the human brain, with its known limitations, gain access to such an immutable world, outside of space and time?Ignore the useless semantic debate about discovery versus invention. This debate has long been loved by high-end mathematicians, people who aren't logicians—by very smart people who are, in effect, playing out of position.
Instead, look at where we find ourselves after nine pages of this discussion. It seems that we're now being told that the world of Platonic forms can be thought of as "some abstract fairyland"—as a "mystical world."
Apparently, that's the actual reality of the "world" where we "will find the number 1" (along with Newton's laws). We'll find it in a mystical world, whatever that will be like.
True believers may assume that we're being unfair to Livio. Such true belief will be wrong.
We will extend the basic fairness to which we've just alluded. Livio, an extremely smart person, is a high-ranking astrophysicist. More specifically, he's a high-ranking astrophysicist who is playing out of position when he heads down the road which takes us to the actual reality of this mystical fairyland.
Livio isn't a professor of philosophy. More specifically, he isn't a logician. Presumably, he's never been trained to avoid the shoals on which his discussion quickly foundered.
Livio is extremely smart, but he's playing out if position. That said, here's the saddest point of all:
When our logicians threw the later Wittgenstein under the bus, they sanctioned high-end mumbo-jumbo of this familiar type. This mumbo-jumbo exists today because our logicians have walked off their posts—because our logicians permit it.
The later Wittgenstein's seminal text, Philosophical Investigations, was published in 1953. Almost seventy years later, the kinds of conceptual confusion it clumsily diagnosed are still taken seriously by major publishing houses and by major news orgs like NPR. And alas:
These kinds of confusion are still OK within the high professoriate. When people like Livio offer mumbo like this, no one says a world.
The most troubling point is this:
When logicians go on holiday, their intellectual squalor trickles down through the national discourse. When our smartest people write nonsense like this, what can anyone expect from the grasping clawing lesser beings who crawl all over cable news and high-end op-ed pages, building their gonzo careers?
The number 1 lives in a fairyland! Also, Al Gore said he invented the Internet, and Donald Trump sits in the Oval.
Tomorrow: "Rogers does this every year." In the winter of 68, the book was just 15 years old!