MATHEMATICIANS GONE WILD: Livio's magical mystery tour!

FRIDAY, MARCH 22, 2019

Things that go bump in the night:
Was man [sic] ever "the rational animal" is any essential way?

This morning, right in his opening paragraph, Paul Krugman helps answer that question. Don't let your children read this:
KRUGMAN (3/22/19): We’re now in the silly season of the Democratic primary—a season that, I worry, may last all the way to the nomination. There are many honorable exceptions, but an awful lot of reporting seems to be third order—not about the candidates, let alone their policy proposals, but about pundits’ views about voters’ views of candidates’ electability. It’s a discussion in which essentially nobody has any idea what he or she is talking about.
So it goes as the rational animals pretend to cover another White House campaign. And while we're at it, make no mistake:

Many of these "rational animals" went to "the finest schools." It doesn't much seem to have helped!

In truth, Krugman is being too kind. It's hard for us to understand how anyone can still be watching "cable news," a profit-seeking corporate enterprise which now centers, with numbing repetition, on The Chase And Nothing Else.

No one is more obsessive in this regard than Rachel Maddow. Maddow is Our Own Rhodes Scholar and a Stanford/Oxford grad. That said, she continues to center on one entertainment product—Manafort Pictured In Chains.

Public schools don't exist on this program; neither does America's struggle with health care. In fairness, though, the Green New Deal has finally been mentioned.

The plan was designed to save the world; it was released on February 7. Maddow finally mentioned it at the start of Tuesday evening's program, during the throw from Chris Hayes. This is what was said:
HAYES (3/19/19): The Rachel Maddow Show starts right now. Good evening, Rachel.

MADDOW: Chris, I am super-excited about your Green New Deal town hall thing. That's awesome.

HAYES: I am too. You know what? Here's a great detail. It's in the Bronx. It's in the hospital I was born in, which is in Alexandria Ocasio-Cortez's district.

MADDOW: That is going to be amazing. That is the last Friday in March, that's Friday, the 29th. Awesome.

HAYES: Yes, Friday next.

MADDOW: I have to find out about these things watching TV!

HAYES: That's how you get it.

MADDOW: Jeez, you know, I work down the hall. You could—

HAYES: Well, you're welcome to come if you want, although you've got to a show to do. All right.

MADDOW: Yes. Thanks. Well done! And thanks to you at home for joining us this hour.

We've got a lot to get to tonight. You can always tell that when my desk is piled up like this before we even gotten started talking about anything.
Maddow told us that her desk was piled up. "I I I I I I I," the analysts quickly said.

At any rate, Rachel Maddow, Our Own Rhodes Scholar, had finally mentioned the Green New Deal! As it turns out, she "has to find out about these things from watching TV!"

In fairness, Maddow probably meant that she'd just found out that Hayes would be holding a town hall program. That said, if Maddow's viewers want to find out about the environment (or about any significant part of their world), they'll have to go somewhere else, to some other TV show, perhaps to a show which originates in some Platonic realm.

What you see in that exchange with Hayes is Maddow's most extended discussion of the Green New Deal since the program was unveiled on February 7. That said, what did she quickly "get to" after speaking with Hayes? In accord with the laws of Pandering Tribal Entertainment, she quickly "got to" this:
MADDOW (continuing directly): But we're going to start tonight with something that arrived in today's news as a surprise.

About a week and a half ago, the Washington Post filed a motion with the federal court in Washington, D.C. that was handling the criminal case of the president's campaign chairman, Paul Manafort...
As always, she turned to Manafort In Chains. Why that would come as some sort of "surprise" is anybody's guess!

Despite this amazingly useless diet, the Maddow Show remains the cable program most heavily watched by us pseudo-liberals. For ourselves, we persistently marvel at the idea that anyone could still be watching this ridiculous program by choice.

In that opening paragraph, Krugman describes the fatuous way our White House campaigns typically get covered. In the case of Maddow, children being born today are going to drown in future years because corporate multimillionaire "rational animals" conduct themselves as she does.

So it goes as our theoretically brightest "rational animals" agree to destroy the earth. Elsewhere, our highest ranking intellectuals—our astrophysicists, mathematical physicists, philosophers and mathematicians—continue to stage their endless pseudo-debate about where "you can find" the number 3, about where such "mathematical objects" "reside."

Where do the numbers 3, 4 and 5 reside? According to Professor Livio, Professor Penrose believes that they resides in "the Platonic world of mathematical forms, which to Penrose has an actual reality"—an "actual reality comparable to that of the physical world."

Newton's laws "reside" there too—or so says Livio, though only while reporting what Penrose, "a renowned Oxford mathematical physicist," allegedly thinks.

In fairness, this is Livio's account of what Penrose thinks; at no point does Livio quote Penrose speaking in his own words. That said, Livio presents this peculiar set of ideas in a fully respectful way, as if the ideas he ascribes to Penrose might seem to make some sort of sense.

It isn't until page 37 that Livio tips his hand. We're going to guess that Professor Livio isn't a "devout Platonist," the term he ascribes to Penrose.

Indeed, we'll guess that Livio, like Professor Goldstein before him, isn't a Platonist at all! We say that because, on that page, he writes this:
LIVIO (page 37): Platonism has become one of the leading dogmas when it comes to the foundations of mathematics.

But does the Platonic world of mathematics really exist? And if it does, where exactly is it? And what are these "objectively true" statements that inhabit this world? Or are the mathematicians who adhere to Platonism simply simply expressing the same type of romantic belief that has been attributed to the great Renaissance artist Michelangelo? According to legend, Michelangelo believed that his magnificent sculptures already existed inside the blocks of marble and that his role was merely to uncover them.
"Where exactly is this world?" Livio skeptically asks. But uh-oh! On its face, his question doesn't exactly seem to make sense, since he has earlier said that the Platonic world of mathematical forms "exists outside space and time."

Whatever! We have to say we're inclined to count Livio among the group to whom we've affixed the moniker, "mathematicians [and others] gone wild." We say that because we've read the first two pages of his book, in which he travels to a dream state which almost certainly has Michelangelo shaking his head.

Like others in his high academic class, Livio has invented a "fairyland" (page 9) by the end of his own fourth paragraph. We'll examine what he says in two steps.

As you can see at this NPR link, Livio starts his book with an explanation of its eye-catching title:
LIVIO (page 1): A few years ago, I was giving a talk at Cornell University. One of my PowerPoint slides read: "Is God a mathematician?" As soon as that slide appeared, I heard a student in the front row gasp: "Oh God, I hope not!"

My rhetorical question was neither a philosophical attempt to define God for my audience nor a shrewd scheme to intimidate the math phobics. Rather, I was simply presenting a mystery with which some of the most original minds have struggled for centuries—the apparent omnipresence and omnipotent powers of mathematics. These are the type of characteristics one normally associates only with a deity. As the British physicist James Jeans (1877-1946) once put it: "The universe appears to have been designed by a pure mathematician." Mathematics appears to be almost too effective in describing and explaining not only the cosmos at large, but even some of the most chaotic of human enterprises.
Please note: before the professor has completed his first page, he is attributing "omnipotent powers" to mathematics—"the type of characteristics one normally associates only with a deity."

Already, Livio is flirting with a highly peculiar "romantic belief" all his own! In part, he gets there by way of a logical error—through his conflation of the terms "describing and explaining" in this particular context.

Can mathematics "describe" the cosmos at large? In many ways, yes, it can.

A few pages later, Livio describes the way Newton was able to formulate "unbelievably accurate mathematical laws of nature" based on a set of observations—observations of the moon and of a falling apple. Those "laws of nature" can be said to describe the way physical bodies act across the cosmos at large.

Newton's laws can be said to describe major parts of the way the cosmos works. But do they "explain" the way physical bodies act? Not exactly, no—and when an astrophysicist blows past this fact, he may soon be indulging himself in things that make us go hmmm:
LIVIO (continuing directly): Whether physicists are attempting to formulate theories of the universe, stock market analysts are scratching their heads to predict the next market crash, neurobiologists are constructing models of brain function, or military intelligence statisticians are trying to optimize resource allocation, they are all using mathematics. Furthermore, even though they may be applying formalisms developed in different branches of mathematics, they are still referring to the same global, coherent mathematics. What is it that gives mathematics such incredible powers? Or, as Einstein once wondered: "How is it possible that mathematics, a product of human thought that is independent of experience [the emphasis is mine], fits so excellently the objects of physical reality?"

This sense of utter bewilderment is not new. Some of the philosophers in ancient Greece, Pythagoras and Plato in particular, were already in awe of the apparent ability of mathematics to shape and guide the universe, while existing, as it seemed, above the powers of humans to alter, direct, or influence it.
By paragraph 4, Livio seems to be saying that mathematics is somehow "shaping and guiding" the universe. Mathematics is no longer being used to provide a description of the way physical bodies move. It's now somehow said to be guiding the moon, and falling apples, in the way they move.

It now seems to exhibit "the type of characteristics one normally associates only with a deity."

In just four paragraphs, while still on page 2, mathematics has been turned into something resembling a god. It's no longer describing the universe. It how has the power to guide it!

This is foolish, incompetent work. It's also the product of our highest-order rational animals—and a great deal follows from that.

This is what happens when mathematicians and physicists leave their areas of expertise and head down to the corner bar for a couple of cool ones. Given the way we humans are, silly "things which make us go hmmm" are the inevitable product.

We debate where the number 3 resides; along the way, we decide that mathematics is "guiding the universe!" This is the apparently endless product of mathematicians, and humans, gone wild.

You'll note that Livio tells us, right in paragraph 1, that he'll be discussing the work of "some of the most original minds" of the past few centuries. We humans have always flattered ourselves in such ways. This helps explain how we came to think of ourselves as "rational animals" to begin with.

In the middle part of the last century, a logician tried to put a stop to this manifest foolishness. According to Professor Horwich, "professional philosophers" in the academy have chosen to throw him away.

Livio's book is a record of primitive thought—primitive thought as conducted by our highest-ranking intellectuals. The fact that nonsense like this can seem deep and wise helps explain the past thirty-five years, in which professional journalists have run wild in the way Krugman describes, with almost none of our vaunted intellectuals stepping forward to offer critiques, objections or correctives.

Our journalists clown as Krugman describes. Our foremost thinkers continue to wonder where the number 3 "can be found."

The clowning and the manifest nonsense have become increasingly general. Are we supposed to be surprised to see climate change threatening the world, to see Donald J. Trump where he is?

Coming: Horwich on Wittgenstein

BREAKING: News from the Platonic realm!

THURSDAY, MARCH 21, 2019

Natural numbers gone wild:
In response to this morning's report, comedian [NAME WITHHELD] has emailed us with an anecdotal further report.

"I'd not sure if 3 lives next to 4," he admits, but he's "heard that 7 ate 9."

We've received partial confirmation of this unusual breaking report. According to Future Anthropologists Huddled in Caves, it happened one block over, not too far from the gated community where the trapezoids live.

A chance to review such actual facts!

THURSDAY, MARCH 21, 2019

What college enrollments look like:
Very few seats at a handful of schools were involved in the current "college admissions scandal."

Despite this fact, the scandal has been getting maximum play. That's pretty much the basic way we rational animals roll.

The coverage has involved a fair amount of obvious inanity. Tomorrow, we'll cover the silliest moment of them all, taken from—where else?—CNN's Don Lemon program.

For today, let's use this as an opportunity to review such actual data. On Sunday, in a high-profile essay, the New York Times was making it sound like it's still 1955, with elite colleges doing everything they possibly can to keep out students of color.

Is that really the way our "elite" campuses currently roll? We were struck by these in-house data from Harvard concerning its current freshman class:
Ethnicity, Harvard College, admitted class of 2022
African American: 15.2%
Asian American: 22.9%
Hispanic or Latino: 12.3%
Native American: 1.9%
Native Hawaiian 0.4%
Somewhat oddly, "white" is neither a race nor an ethnicity within these Harvard statistics. The data seem to cover the number of admissions offered to various students as opposed to the number of enrollments, although thanks to Harvard's murky work, we can't really be sure.

That said, if those in-house data are accurate, Harvard offered admission to black kids in a number which matches the percentage of black kids within American public schools. If Harvard is trying to ban students of color, it's doing a terrible job.

Those are in-house data from just one class at just one famous college. For today, let's look at NCES data from some of the schools involved in the current (quite limited) scandal, with a few other schools thrown in.

For starters, what does Stanford's enrollment look like? The NCES says this:
Undergraduate enrollment, Stanford
White students: 36%
Black students: 7%
Hispanic/Latino students: 16%
Asian-American students: 22%
Two or more races: 10%
Race/ethnicity unknown: 0%

Foreign students: 9%
Remember—foreign students are treated as a separate category in these NCES statistics. Among American students enrolled at Stanford, the NCES says that white students made up 36% of overall undergraduate enrollment. Students of color stood at 45%, with an additional 10% biracial students.

Stanford is not all white. What do other upper-end schools look like? To simplify matters, we'll show you the data in a three-part format. For any school's data, start here:
Undergraduate enrollment at various schools
White students/Students of color/Biracial students

Harvard: 43% / 35% / 6%
Yale: 45% / 38% / 6%
Princeton: 42% / 39% / 4%
Columbia: 37% / 38% / 6%

Cornell: 38% / 39% / 5%
Duke: 44% / 40% / 2%
Georgetown: 53% / 25% / 4%
Stanford: 36% / 45% / 10%

USC: 39% / 39% / 6%
UCLA: 27% / 53% / 5%
Texas/Austin: 42% / 48% / 4%
Georgetown is an outlier here. That said, it's the only one of these schools in which white American students constitute even half of the overall undergraduate enrollment.

Try comparing that to the impression the New York Times pimped to the world in this essay in last weekend's Sunday Review. In that essay, readers were told that these schools do everything they can to deny admission to students of color. We've included Cornell on our list because the Times' grossly misleading essay mainly concerned that school.

Meanwhile, take a look at UCLA's breakdown. Last Saturday, Times readers were given the impression, in this news report, that it's extremely hard for students of color to get admitted there. This is the way the New York Times rolls, though mainly the paper's just stupid.

The Times is a pernicious force in the intellectual life of the nation. They've been such a force for a very long time. There's no sign that they plan to change.

One final point:

Black enrollments at the private schools on this list tend to stand at roughly 7 percent. According to the NCES, undergraduate black enrollment at Harvard was 7 percent when these data were compiled, as opposed to the higher number to whom the school says it offered enrollment in this year's freshman class.

(Note: The NCES data aren't directly comparable to the in-house data from Harvard.)

Why are black enrollments so low? We'll be discussing that question all next week, in line with this latest report from the Times about New York City high schools.

The Times strikes us as a pernicious pseudo-liberal upper-class force. This helps explain why black kids are under-represented at upper-end schools. It helps explain how Donald J. Trump got where he currently is.

One further note: As we've told you, you won't be seeing data like these in the New York Times. Information is boring! And hard!

Instead, you'll be seeing human interest stories concerning what Olivia Jade deeply prefers for breakfast. This is very much the way our dumbest big newspaper rolls.

MATHEMATICIANS GONE WILD: Fields Medal winners get tons of respect!

THURSDAY, MARCH 21, 2019

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?"

Berkeley and Harvard and Stanford oh my!

WEDNESDAY, MARCH 20, 2019

Top schools admit no one but white kids:
When the current "college admission scandal" broke, the New York Times swung into action, doing the one thing it knows.

The New York Times began working from script. In this circumstance, this meant that the New York Times began telling black kids that they were getting royally hosed and should feel deeply aggrieved.

In fact, very few students were affected, in any way, by the recent scandal. But this is the one thing the Times does well. Last Saturday, we showed you one of the more unfortunate passages produced in the Times' blizzard of misleading coverage.

"So disheartening," the headline says. This is the passage in question:
LEVIN, DE LEON AND ASSAN (3/16/19): At the University of California, Los Angeles—among the campuses ensnared in the shocking scheme—students like Ayesha Haleem said she and her classmates were both heartbroken and fuming.

“The higher education system has always benefited people who come from privileged backgrounds,” said Ms. Haleem, a Pakistani 23-year-old senior. “Students of color have it so much harder to even get to these places.”
At UCLA, the New York Times said, a heartbroken student was fuming. “Students of color have it so much harder to even get to these places," she was quoted saying.

By Sunday, the Times had refined its message. An essay in the Sunday Review seemed to say that admission procedures at these upper-end schools were designed to admit as few "students of color" as possible.

That essay principally dealt with Cornell. Yesterday, we showed you the current enrollment figures there—figures which are impossible to square with the Times' ugly, dim-witted propaganda.

Today, let's return to UCLA, the school which is so hard for students of color to get in to. Have they managed to keep the school all white? According to the NCES enrollment data, the answer would seem to be no:
Undergraduate enrollment, UCLA
White students: 27%
Black students: 3%
Hispanic/Latino students: 22%
Asian-American students: 28%
Two or more races: 5%
Race/ethnicity unknown: 2%

Foreign students: 12%
As we noted yesterday, the NCES data treat foreign students as a separate category, with no race or ethnicity recorded. At UCLA, that accounts for 12% percent of the undergraduate student body.

Among UCLA's undergraduate American kids, 27 percent were white; 53% were students of color, with an additional 5% listed as biracial. Compare that with the fuming quotation the Times had chosen to run.

It's hard to have sufficient contempt for a lazy, upper-class newspaper which functions the way the Times does—for a newspaper which aims to mislead its readers about elementary facts, then builds on that by filling good, decent American kids with waves of resentment and grievance.

In fairness, UCLA is a bit of a special case; California is different. These are the enrollment figures for Cal Berkeley, one of the nation's most elite state universities:
Undergraduate enrollment, Cal Berkeley
White students: 26%
Black students: 2%
Hispanic/Latino students: 15%
Asian-American students: 35%
Two or more races: 6%
Race/ethnicity unknown: 4%

Foreign students: 12%
It's true, of course, that black enrollment is quite low at both these upper-end schools. We'll be discussing that general topic all next week, when we focus on the latest front-page report by the Times about New York City's high-powered "specialized high schools."

That said, Berkeley currently enrolls 26% white students and 52% "students of color," with an additional 6% biracial kids. If current admission procedures are intended to keep enrollment by students of color as low as possible, the powers that be at Westwood and Berkeley are doing a rather poor job.

You don't, and you won't, see data like these in the New York Times. Tomorrow, we'll look at Harvard and Yale and Stanford and such—at elite private schools, where you'll see a higher black enrollment.

Deeply serious national issues are involved in the data we've shown you. The New York Times, working from script, continues to propagandize and misinform. It's behaving like the pseudo-liberal, upper-class clown car it has long been.

Are the most elite private schools trying to admit the fewest possible students of color? Tomorrow, we'll show you the data for a range of such schools, and we'll quote that pitiful New York Times essay again.

The Times has played it this way for decades. Rather clearly, this helps explain why Donald J. Trump is in power.

MATHEMATICIANS GONE WILD: "When language goes on holiday!"

WEDNESDAY, MARCH 20, 2019

Hardy and Godel gone wild:
Just for today, let's be fair.

Professor Livio didn't invent the cultural phenomenon which is, in fairness, on full display at the very start of his well-received 2009 book, Is God A Mathematician?

As we noted yesterday, the cultural practice is on full display by page 3 of Livio's book. At that point, in just the fifth paragraph of his book, we're confronted by the spectacle of a ranking astrophysicist citing a renowned Oxford mathematical physicist, with the latter said to have made incoherent remarks about the constitution of this big crazy cosmos of ours.

For the fuller text, see yesterday's report. Meanwhile, this is a taste of the oddness:
LIVIO (page 3): The Platonic world of mathematical forms, which to [the mathematical physicist] 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, [the mathematical physicist] 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 the astrophysicist's account of the views of the mathematical physicist, the Platonic world of mathematical forms doesn't just "have a reality," whatever that means. It has an actual reality!

Through a process which doesn't get explained, that "motherland of mathematics" is said to be "where you will find the natural numbers 1, 2, 3, 4,...," along with Newton's laws of motion. Later in the passage, we're told that's where they "reside."

In what way will you "find" the natural numbers there? Readers, please don't ask! But that's the world where the natural numbers "reside." Rather, that's where the number 3 "actually resides," or so we're crazily told.

A peculiar culture is on quick display in Livio's well-received book. In fairness, though, he didn't invent it. This puzzling culture of apparent incoherence has been around for an extremely long time.

Within this puzzling culture, peculiar metaphysical statements are hatched by physicists, astrophysicists and mathematicians gone wild. One such earlier adept was the brilliant British mathematician G. H. Hardy (1877-1947), whose famous treatise, A Mathematician's Apology, was reverentially quoted by Professor Goldstein in her well-received 2005 book, Incompleteness: The Proof and Paradox of Kurt Godel:
HARDY (1940): I believe that mathematical reality lies outside us, that our function is to discover or observe it, and that the theorems which we prove, and which we describe grandiloquently as our "creations," are simply our notes of our observations. This view has been held, in one form or another, by many philosophers of high reputation from Plato onwards, and I shall use the language which is natural to a man who holds it...

[T]his realistic view is much more plausible of mathematical than of physical reality, because mathematical objects are so much more than what they seem. A chair or a star is not in the least like what it seems to be; the more we think of it, the fuzzier its outlines become in the haze of sensation which surrounds it; but "2" or "317" has nothing to do with sensation, and its properties stand out the more clearly the more closely we scrutinize it. It may be that modern physics fits best into some framework of idealistic philosophy—I do not believe it, but there are eminent physicists who say so. Pure mathematics, on the other hand, seems to me a rock on which all idealism founders: 317 is a prime, not because we think so, or because our minds are shaped in one way rather than another, but because it is so, because mathematical reality is built that way.
Warning! In this passage, the terms "realism" and "idealism" are technical terms taken from a long, less-than-coherent "philosophical" tradition. Having allowed for that, let's consider what Hardy does in this passage.

In this hoary, much-quoted passage, Hardy invents a construct called "mathematical reality." He then starts debating where it "lies" (i.e., where it "resides") and the way it is "built."

For reasons which go unexplained, he refers to numbers like 2 and 317 as "mathematical objects." In this way, he continues venturing down as unfortunate road, in which, to quote the later Wittgenstein, "language goes on holiday," generally with bad results.

The numbers 2 and 317 have now been classified, somewhat oddly, as "mathematical objects." Having introduced that strange formulation, Hardy tells us that such objects "are much more than what they seem."

More specifically, he tells us that the chair on which you're currently sitting "is not in the least what it seems to be," while the properties of the number 2 "stand out the more clearly the more closely we scrutinize it."

From there, we're invited to wonder about what makes 317 a prime. It isn't a prime "because we think so," this brilliant mathematician somewhat peculiarly says. Instead, he says that 317 is a prime "because mathematical reality," whatever that is, "is built that way," whatever that might mean.

Why is 317 a prime? Within the context of Hardy's rumination, the question starts to seem odd, but we'll offer an extremely simple answer:

Once you know what it means to say that some number is a prime, it's very easy to determine that 317 qualifies. First you try to divide it (evenly) by 2. Then you try to divide it evenly by 3, and then by 5, and then 7.

By the time you've been unable to divide it evenly by 17, your search is over, though people like Hardy—mathematicians who have wandered outside their field of expertise—will try to engage you in a debate about a range of fuzzy concepts they couldn't explain or clarify if they were competently asked to.

Alas! Within our academic world, such challenges are rare. In that famous passage from Hardy's famous essay, we're looking at the ruminations of a brilliant mathematician gone wild.

Hardy's ruminations are barely coherent. But Professor Goldstein presented the passage with full respect, and she tends to treat Godel's crazy ideas about "Platonism" in a similar way.

Livio behaves the same way in his opening chapter. He quotes a string of award-winning mathematicians as they make fatuous remarks about the structure of the cosmos—after they have strayed beyond the bounds of their expertise.

In effect, Livio treats these mathematicians' fuzzy statements as "things that make us go hmmm." In his years on late-night TV, Arsenio Hall performed that trademark bit as a rollicking entertainment. But at the higher ends of the academy, astrophysicists, mathematicians and "philosophers" gone wild still play the game for real.

In the first two paragraphs of his book, Livio starts taking us down the amusing road of "things that make us go hmmm." Tomorrow, we'll review those opening paragraphs to see what can happen when the mind of a ranking astrophysicists is allowed to stray.

For today, we'll only say this. Once we start down that road—the road where language has gone on holiday—we can reach some very strange destinations. By page 9 in his opening chapter, Livio is offering the following passage as he tries to fight his way through a long-standing semantic muddle:
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?...
We're now being asked to consider the possibility that mathematics "exists in some abstract fairyland"—in some sort of "mystical world," which lies "outside of space and time." This is where we can get by page 9 when, on pages 1-3, language has been allowed to go on a bit of a journey.

The later Wittgenstein warned about this ubiquitous practice. According to Professor Horwich, his work has been thrown under the bus because our "professional philosophers" still want to gambol and play.

According to Horwich, they want the right to retain their long-standing "linguistic illusions and muddled thinking. This helps explain why so little aid has come from the academy as our journalistic discourse has descended into inanity and grinding technical incompetence—and by the way:

This is the type of work which is done by our highest-order thinkers! By our astrophysicists, our mathematicians, our winners of all those medals!

Man [sic] is the rational animal? As we await the start of Mister Trump's War, is it possibly time to thrown that pleasing old story away?

Tomorrow: Things that make us go hmmm

From the original text: "Philosophical problems arise when language goes on holiday."

So said the later Wittgenstein, in Philosophical Investigations.

To review the original text, click here, then move to page 19—though, as Wittgenstein essentially acknowledged, the writing is quite obscure.