"During the Cold War, we classified entire areas of physics and took them out of the research community—entire branches of physics went dark..."

"... and didn’t proceed. If we decide we need to, we’re going to do the same thing to the math underneath AI."

Said Marc Andreessen, on the podcast "Honestly with Bari Weiss."

Marc Andreessen (@pmarca) says he attended “absolutely horrifying” meetings where Biden’s government vowed to take “complete control” over AI technology:

“They basically said AI is going to be a game of 2 or 3 big companies working closely with the government… We’re going to… pic.twitter.com/REjkfgJkyV

— Honestly with Bari Weiss (@thehonestlypod) December 10, 2024

Here's a transcript of the entire podcast. Excerpt, giving context to the quote above:

Stephen King helps J.K. Rowling with the mathematics of fuck-giving.

I think you may mean "not giving a fuck squared." The square root, I believe, would mean a *smaller* amount of giving a fuck. I could be wrong. https://t.co/7lzylpInVV

— Stephen King (@StephenKing) July 17, 2024

Help me with the math here. Seems to me, if you don't give a fuck, you're already at zero. Rowling is talking about the smallest possible amount of fuck-giving and being silly about the math. King admits he could be wrong, and isn't he? She doesn't want more than zero, and zero times zero wouldn't give you more than zero anyway. But she wants to go smaller. 

Ah, wait! Rowling writes back: "But I was going for a fraction of a fuck. I barely give a tenth of a fuck. So I stand by my square root. What we really need here is a certified fuckologist."

 

Perfect. JK won. Reeled him in and won. Good for King, though, for expressing his idea with respect.

ADDED: Actually, JK's explanation — that she was talking about fractions (and not 0, as I assumed) — put King in the right. As Matt says in the comments: "King is correct. The square root of 1/4 is 1/2. For numbers less than 1 the square root makes it larger. 1/2 * 1/2 = 1/4." 

"That’s why middle school math is this flashpoint. It’s the first moment where you potentially make it very obvious and explicit that there are knowledge gaps opening up."

Said Joshua Goodman, an associate professor of education and economics at Boston University, quoted in "The Algebra Problem: How Middle School Math Became a National Flashpoint/Top students can benefit greatly by being offered the subject early. But many districts offer few Black and Latino eighth graders a chance to study it" (NYT).

"You live as if without history, as if you throw no shadow behind you."

Saw a play.

From the New Yorker review:

The first scene is a welter of references to Viennese thought and art—Freud, Mahler, Klimt—and the coming destruction of that golden culture is one of the tragedies of the play. Over whiskey, Hermann and his mathematician brother-in-law, Ludwig Jakobovicz... argue about Hermann’s blithe disregard of Austrian anti-Semitism. Hermann is joining the Jockey Club and—a mathematician, you say? Your inner Stoppard gong should ring at that; this is the playwright who taught us chaos theory and probability. When Ludwig later tries to demonstrate coördinate geometry using a cat’s cradle, we can see that one of Stoppard’s famous Knowledge Metaphors is twisting itself into view. And, indeed, like the knots on Ludwig’s cat’s-cradle string, family members change positions yet maintain their connection.

Not just connection but — in the cat's cradle configuration — distance.

"Despite my accomplishments, if I were a young person today, I would have difficulty graduating from high school because I could not pass algebra."

"It was too abstract, with no visual correlations. This is true for many of today’s students who get labeled as bad at math, students who might otherwise pass alternative math courses such as statistics that would also apply to real-life work situations. There is too much emphasis in school on testing and not enough on career outcomes. The fact that I failed the SAT in math prohibited me from getting into veterinary school, but today I am a university professor in animal sciences and I am invited to speak to groups of veterinarians to advise them on their work.... [W]e need a neurodiverse work force. Complementary skills are the key to successful teams.... In Italy and the Netherlands, for instance, a student at about age 14 decides whether to go the university route or the vocational route. The vocational route is not looked down on or regarded as a lesser form of intelligence. And that’s how it should be everywhere...."

Writes Temple Grandin in "Society Is Failing Visual Thinkers, and That Hurts Us All" (NYT).

"The most intrusive animation is a train that twice interrupts the mathematician Moon Duchin, who is reflecting on what it would mean for a mathematical object like infinity to 'exist.'"

"The second appearance of the train blocks her entirely from view and rumbles over her thoughts, as though the underlying ideas aren’t interesting enough on their own. As a mathematician, I may be biased, but I think that they are. Is the universe as infinite as we might imagine it to be?"

Writes Dan Rockmore, in "'A Trip to Infinity' and the Delicate Art of the Math Documentary/One of the most captivating concepts in mathematics is now on Netflix" (The New Yorker).

We watched that documentary last night. That is, we watched half of it. Tonight, we might watch the other half. But if we only watch half of what's left, and we keep doing that, night after night, we will never get to the end of it.

Here's the trailer — which will help you decide if you want your math enlivened/tarted up with graphics:

"William Heard Kilpatrick, one of the most influential pedagogical figures of the early twentieth century, would have felt right at home in today’s educational culture wars."

"Back then, as now, the traditionalist defense of math education came from the idea that the subject created order and discipline in the minds of young students. The child who could solve a geometric proof, for example, would carry that logic and work ethic into his professional life, even if it did not entail any numbers at all. Kilpatrick, a popular reformer... dismissed that idea. Algebra and geometry, he believed, should not be widely taught in high schools because they were an 'intellectual luxury,' and 'harmful rather than helpful to the kind of thinking necessary for ordinary living.' Not everyone was going to need or even have the intelligence to complete an algebra course, Kilpatrick reasoned. Why bother teaching it to them? In 1915, Kilpatrick chaired an influential National Education Association committee tasked with looking into the reform of math instruction in high school. He amplified his attack on the place of math in schools, as the committee’s report declared that nothing in mathematics should be taught unless 'its (probable) value can be shown,' and recommended the traditional high-school-mathematics curriculum for only a select few...."

From "How Math Became an Object of the Culture Wars/As was true in the nineties, today’s fights about math are not entirely about what kids actually learn in their classrooms" by Jay Caspian Kang (The New Yorker).

Here's a line from the newest episode of "Survivor" that I'm not seeing quoted anywhere.

I took the trouble to transcribe it:

"We're all trying to gauge not only what is best for our individual game but what is every other individual thinking is best for their game, and that's just I don't even know what factorial that is, but 13 to the 12th? — like that's just so many different permutations of people working together and thinking different things."

That was said by the cast-member Jeanine Zheng at tribal council, so, in front of all the other contestants, whose faces read to me as though they were thinking things like "Factorial?! I was told there would be no math" and "Too smart, she's got to go."

Anyway... Zheng is 24-year-old UX designer. I had to look up "UX."

"Supermarket shoppers have been left baffled and annoyed by changes to store layouts that have made it harder to find their groceries."

"Chains have been hastily reorganising their aisles to meet the rules.... The regulations restrict the areas in which supermarkets may place products deemed to be high in fat, salt or sugar. Arguably the simplest rule is that no unhealthy food or drink can be displayed within two metres of a checkout or queueing area. But similar restrictions have been imposed on 'gondola displays' at the end of shopping aisles, island bin displays and other easy-to-reach spots. A formula based on floor size dictates unhealthy products’ proximity to the entrance, meaning there are different rules for each shop. The minimum distance is calculated by the square root of the area of the store multiplied by 0.03...."

The London Times reports.

The square root of the area of the store multiplied by 0.03?! They'd never try that in America — not just fat-shaming us by requiring math. Even just bringing up the concept of square roots is unthinkable in the land of the free. 

I've got 5 TikToks to amuse you on this Saturday midday. No corn, just animals, hair, Mahler, and physics. Let me know what you like.

1. Geese are weird and terrifying (and I think it's real, and not some sort of animation). 

2. Name that animal.

3. When is long hair a rebellion?

4. A harmonic reduction of Mahler's Symphony #2.

5. What is the formula for momentum?

"I have many kind friends with wonderful attributes, but one horrible thing they all have in common is a compulsion to come up and talk to me when they see me arrive on my bike."

"There, they find me at my worst, both physically and emotionally. I am damp from the ride and must now take off my helmet and redo my oddly compressed hair. It is possible that the breeze, once a source of my power, blew something gross — an insect, the torn corner of a Snapple label — onto my face. Using only the two hands that the Lord gave me, I must rearrange myself, smooth my rough edges, and prepare to rejoin society. All while also securing my bike to one of the city’s O-racks, or, more likely, a street-sign post with another bike already chained to it. This takes time and focus; I am essentially completing a physical equivalent of a Kumon worksheet. Inevitably, something drops to the ground. This is both embarrassing and part of my process."

From "Never Look at Someone While They’re Locking Their Bike" by Clio Chang (NY Magazine).

Things I spent time doing this morning: 

"What did I learn?... That mathematics is both real and not real. Like novelists and musicians, mathematicians produce thought objects..."

"... that have no presence in the physical world. (Anna Karenina is no more actual than a thought about Anna Karenina.) Like other artists, mathematicians also have the run of a world that others hardly or only rarely visit. For mathematicians, though, this territory has more rules than it does for others. Also, what is different for mathematicians is that all of them agree about the contents of that world, so far as they are acquainted with them, and all mathematicians see the same objects within it, even though the objects are notional. No one’s version, so long as it is accurate, is more correct than someone else’s. Parts of this world are densely inhabited, and parts are hardly settled. Parts have been visited by only a few people, and parts are unknown, like the dark places on a medieval map. The known parts are ephemeral, but also concrete for being true, and more reliable and everlasting than any object in the physical world.... An imaginary world’s being infallible is very strange. This spectral quality is bewildering, even to mathematicians. The mathematician John Conway once said, 'It’s quite astonishing, and I still don’t understand it, despite having been a mathematician all my life. How can things be there without actually being there?'"

From "Teaching Myself Calculus at Sixty-Five/I was never a good math student, but I was determined to penetrate the mysteries of mathematics" by Alec Wilkinson, who got a book out of this project — “A Divine Language: Learning Algebra, Geometry, and Calculus at the Edge of Old Age.”

"One rejected textbook, Florida Reveal Math Grade 1, includes a series of questions under the heading 'Math is… Mindset.'"

"These questions include: 'How can you show that you value the ideas of others?' and 'What helps you understand your partner’s ideas?' The book also encourages students to learn how to 'work together' when doing math and to 'listen to our friends and teachers.' Florida Reveal Math Grade 5, which was also rejected, uses similar prompts to encourage students to think critically about how they work with others in the classroom setting. 'When we do math, we listen to the arguments of others and think about what makes sense and what doesn’t,' the book states in the introduction. Other prompts encourage critical thinking and highlight relationship skills, such as: 'What can I learn from others’ thinking about the problem?' and 'What can you do to help all classmates feel comfortable in math class?' The textbook encourages students to think about how they can 'recognize and respond to the emotions of others' and practice building 'relationship[s]' with classmates."

From "Inside the 'dangerous' math textbooks DeSantis claims would 'indoctrinate students'" (Popular Information).

Is dangerousness really the problem? Shouldn't the state reject the math books because they're not sufficiently about math?

Math is about getting the right answer, not about feelings or ideologies.

In Florida, we will be educating our children, not indoctrinating them. pic.twitter.com/BmhBXEljYM

— Ron DeSantis (@GovRonDeSantis) April 18, 2022

I watch TikTok for you — and here are my 9 new selections.

1. An accurate miniature of a heavily graffiti'd ice storage box.

2. The way someone talks when he wants to get you to volunteer to wall-mount his TV.

3. The charitable work of detangling someone's hair.

4. A cat sings the blues.

5. Reacting to the news that someone's tested positive for Covid — in 2020 and in 2022.

6. Seeing if the dog likes celery.

7. A quick animation of Joe Biden, telling about when he was a little boy.

8. Discovering just how introverted you are.

9. A famous fractal — the Sierpinski triangle.

"My own view is that the biggest brains wouldn't be in the legal profession to start with."

Writes Balfegor, in the comments to the previous post, where I'd said, "But what if we could find the 9 biggest brains in the law field and make a Supreme Court out of them? We might discover they make terrible Justices."

I wrote "biggest brains in the law field" because I thought being in the law field would be a basic qualification to get started on the job, but I wrote that thinking these are not the biggest of the big brains.

That made me think about Laurence Tribe, the noted Harvard professor:

"... Simon and Garfunkel also played a high-profile gig at Gerde’s Folk City in the Village, and a couple of shows at the Gaslight Cafe. The audiences there, though, regarded them as a complete joke..."

"... Dave Van Ronk would later relate that for weeks afterwards, all anyone had to do was sing 'Hello darkness, my old friend,' for everyone around to break into laughter. Bob Dylan was one of those who laughed at the performance — though Robert Shelton later said that Dylan hadn’t been laughing at them, specifically, he’d just had a fit of the giggles — and this had led to a certain amount of anger from Simon towards Dylan."

That's from the podcast "A History of Rock Music in 500 Songs," "Episode 135: 'The Sound of Silence' by Simon and Garfunkel." 

I've never been much of a Simon and Garfunkel fan, though, of course, I've often enjoyed listening to their songs. They did seem self-absorbedly gloomy, and I completely identify with the people who thought it was funny to intone — out of the blue — "Hello darkness, my old friend." I have a vivid memory from 1965, when "I Am a Rock" was a hit, and I was 14. I was with some of my girlfriends and a boy from our class, walking by, suddenly and, I think sincerely, sang out "I Am a Rock." Oh, how we laughed at him! It still makes me laugh. You're a rock, are you? That's so interesting. I guess if he was a rock, our derision didn't hurt him.

Knowing little of S&G's background, I learned a lot from that episode:

"An earlier version of this article incorrectly reported the rate of decline of the non-Hispanic white population since 2010. It was 2.6 percent, not 8.6 percent."

A correction posted at "Census Live Updates: U.S. Grew More Diverse in Past Decade; Most Counties Lost Population/The government released data from the 2020 census showing large increases in the populations of people who identify as Hispanic, Asian and more than one race" (NYT).

How do you make a mistake like that — confusing percent and percentage points?

What's the fastest growing group? Mixed race. That group doubled. Anyone who goes into the group takes away from one of the other groups.

“We are in a weird time demographically,” said Tomás Jiménez, a sociologist at Stanford who writes about immigrants, assimilation and social mobility. “There’s more choice about our individual identities and how we present them than there has ever been. We can presume far less about who somebody is based on the boxes they check compared to previous periods.”

Do the math.

Subheadline in the NYT: "Each additional daily cup of coffee was associated with a 1 percent decrease in the risk of prostate cancer." 

Top-rated comment: "Based on the NYT's excellent reporting, I will immediately begin drinking 100 cups per day and reduce my prostate cancer risk to 0%. What could go wrong?" 

The subheadline is ridiculous for reasons expressed in the comment, but the commenter is doing the math wrong. After each additional cup of coffee — in the mad logic of the subheadline — you have 99% of what you had before. Drink a million cups of coffee, and you still won't get to zero, just 99% of what you had before that last cup.

It's the Zeno's paradox of prostate cancer.

"The state isn’t exactly scrupulous in the evidence it musters. It contends that Biden had less than a one in a quadrillion chance..."

"... of winning any one of these battleground states after Trump established a lead on election night. The chance of winning all four, per the suit, was less than one in a quadrillion to the fourth power. But the calculation assumed that every batch of ballots would have roughly the same partisan breakdown, despite there never having been any real-world expectation of this. It was predicted that Trump would establish an early lead in states that counted in-person ballots first, and then Biden would gain as the states began to count mail-in ballots, which were heavily Democratic. The last-counted ballots were universally understood to be the Democrats’ turn at bat, given who they were and where they came from...."

From "Texas Unleashes an Absurd Kraken" by the Editors of The National Review.

Also in The National Review, "Texas’s Frivolous Lawsuit Seeks to Overturn Election in Four Other States" by Andrew McCarthy. Excerpt:

To say "deviation from Benford’s Law does not prove election fraud took place" is not to say that it isn't relevant evidence.

Reuters does a fact check that begins by stating the proposition in an ultra-strong way:

Social media users have been sharing posts that say a mathematical rule called Benford’s Law provides clear proof of fraud in the U.S. presidential election. 

Here's how the proposition to be fact-checked could have been stated: Benford's Law is of some use in determining whether or not there there was fraud or error in the U.S. presidential election. Lawyers will recognize the test for whether evidence is relevant. 

Reuter's is asking whether this evidence, standing alone, will meet a burden of proof, which is a tricky shortcut through factchecking. In real life, we don't depend on one piece of evidence. We look at whatever might be useful as we make decisions about how much more to investigate. Does Benford's Law raise suspicions that would make a fair-minded person want to look more closely and to gather more evidence? 

But we don't really have fair-minded people! We have highly partisan people on one side who are eager to cast doubt on the election and on the other side who want to say Stop right now! Reuter's strikes me — the closest thing you're going to get to a fair-minded person — as falling in the second group. Why? Because of the way they stated the fact to be checked! 

Now, let's look at the experts consulted (and go to the article for a statement about what Benford's Law is):