MATHEMATICIANS GONE WILD: Professor Livio's well-received book!

TUESDAY, MARCH 19, 2019

High-order rational animals: Nothing we discuss this week will make any sense unless we agree to the following stipulation:

As determined by any conventional norm, Mario Livio is smart.

As a matter of fact, Livio is surely very smart. You see, he isn't just smart, he's an astrophysicist—and, as best we can tell, he seems to be a ranking astrophysicist to boot:

Mario Livio (born 1945) is an Israeli-American astrophysicist and an author of works that popularize science and mathematics. From 1991 till 2015 he was an astrophysicist at the Space Telescope Science Institute, which operates the Hubble Space Telescope.

He isn't just an astrophysicist. He's an astrophysicist who worked on, or at least around, the Hubble Space Telescopr for roughly 25 years!

In the way we assess such things, Professor Livio is extremely smart. You'll note that he also writes books "that popularize science and mathematics." With that in mind, we offer the fuller capsule bio from the leading authority on Livio's life and career:

Mario Livio (born 1945) is an Israeli-American astrophysicist and an author of works that popularize science and mathematics. From 1991 till 2015 he was an astrophysicist at the Space Telescope Science Institute, which operates the Hubble Space Telescope. He is perhaps best known for his book on the irrational number phi: The Golden Ratio: The Story of Phi, the World's Most Astonishing Number (2002). The book won the Peano Prize and the International Pythagoras Prize for popular books on mathematics.

He's best known for his book on an irrational number? We'll use that as a hook!

This week, we'll be looking at early passages from another book Livio wrote for general readers. This well-received book, Is God a Mathematician?, was published in 2009. Its publisher, Simon and Schuster, describes the book like this:

SIMON AND SCHUSTER: Bestselling author and astrophysicist Mario Livio examines the lives and theories of history’s greatest mathematicians to ask how—if mathematics is an abstract construction of the human mind—it can so perfectly explain the physical world.

Nobel Laureate Eugene Wigner once wondered about “the unreasonable effectiveness of mathematics” in the formulation of the laws of nature. Is God a Mathematician? investigates why mathematics is as powerful as it is...

Physicist and author Mario Livio brilliantly explores mathematical ideas from Pythagoras to the present day as he shows us how intriguing questions and ingenious answers have led to ever deeper insights into our world. This fascinating book will interest anyone curious about the human mind, the scientific world, and the relationship between them.

Does mathematics "explain" the physical world. Or does it simply describe its various processes? Right in the first sentence of this blurb, we may have hit our first snag.

Set that to the side for now; the publisher isn't the author. That said, the publisher vouches for the author's brilliance—and, without any possible question, Livio is, by normal standards, a highly intelligent person.

That's why it's interesting to note the fact that his book is routinely a jumbled sub-logical irrational mess right from its opening pages. Tomorrow, we'll look at Livio's first two paragraphs, but suffice to say that, by paragraph 5 as found on page 2, we're asked to grapple with this:

LIVIO (pages 2-3): 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. 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...

In that passage, an astrophysicist is describing the views of a "renowned mathematical physicist." On their face, those views seem to make no earthly sense, a point we'll further explore before the week is through.

Let's restate the key point:

As described by Livio, the views of this renowned mathematical physicist seem to make no sense at all. Or do you think you have some idea what it might mean to say that "you will find" numbers and circles and mathematical laws in a "Platonic world"—a world which has "an actual reality" (our emphasis), a world where Newton's laws of motion "actually reside?"

Reader, tell the truth! On its face, does any of that seem to make any sense at all? Or do you just feel that it has to make sense, given the academic standing of the authority figures who emit such strings of words?

College freshmen have always suspected that people like these are nuts. In the middle part of the last century, Ludwig Wittgenstein finally said that those traditional, mystified freshmen just weren't all that wrong after all.

If we might borrow from Professor Horwich, Wittgenstein said that our "philosophical" theories and claims tend to be "misbegotten products of linguistic illusion and muddled thinking." And alas! In the highest realms of our persistently bungling world, that muddled thinking remains comically widespread today.

In Is God A Mathematician?, a ranking astrophysicist steps outside his area of expertise and starts to deal in what would typically be called the philosophy of mathematics. When he does this, "linguistic illusion and muddled thinking" quickly start having their way.

Livio is an astrophysicist; we assume he's a very good one. That said, he isn't a "philosopher," and we'd have to say this starts becoming clear in the first pages of his book.

Let's be clear! The later Wittgenstein said that "linguistic illusion and muddled thinking" were the traditional stuff of academic philosophy itself.

Indeed, he said we humans—we famously self-impressed rational animals—are most likely to commit the types of errors he diagnosed "when doing philosophy." We're going to spend some time this year exploring this comical story.

"Man [sic] is the rational animal," we self-impressed humans have long said. The later Wittgenstein showed the way our rational abilities quickly break down when we start "doing philosophy."

These comical errors are constantly being made on our highest academic platforms, the later Wittgenstein said. That's what makes this a comical story—a comical story which helps explain the very poor work you persistently encounter in a silly, upper-class newspaper like the New York Times.

At the start of last year, we made a gloomy proclamation: "It's all anthropology now." We gloomily meant that the time was past when it made any sense to expect good work from our leading journalists, or to expect significant corrective work from our leading professors.

That said, the later Wittgenstein produced a type of anthropology. He diagnosed a basic way our species' rational thinking breaks down.

This doesn't just happen on "cable news," or in the hopeless work routinely found in the New York Times. According to the later Wittgenstein, these extremely basic errors dog the sorts of work which emerge from our highest and most-respected intellectual platforms.

In our view, Livio's book is a case study in this anthropological mess.

We assume that Livio is a brilliant astrophysicist. By way of contrast, his popular book for general readers offers a remarkable though familiar portrait of physicists, philosophers and mathematicians gone wild.

Tomorrow: Things that make you go hmmm