SUNDAY, SEPTEMBER 25, 2022
As spooned in the New York Times: Almost surely, Alec Wilkinson, age 70, is a thoroughly good, decent person.
According to the leading authority on his life, Wilkinson "has been on the staff of The New Yorker since 1980." According to The Philadelphia Inquirer, he is among the "first rank of" contemporary American "literary journalists."
Also, Wilkinson wrote a guest essay in today's New York Times which helps explain the gloomy last line of that Graceland album:
"That's why we must learn to live alone."
Wilkinson says that he is trying, late in life, to learn mathematics. By total coincidence, he also writing a book about this undertaking.
Needing to fill space, the New York Times decided to give him a chance to publicize his book. Along the way, in his guest essay, Wilkinson offers this assortment of mumbo-jumbo and argle-bargle, causing the later Wittgenstein to roar with pain in his grave:
WILKINSON (9/25/22): The beginner math mystery, available to anyone, concerns the origin of numbers. It’s a simple speculation: Where do numbers come from? No one knows. Were they invented by human beings? Hard to say. They appear to be embedded in the world in ways that we can’t completely comprehend. They began as measurements of quantities and grew into the means for the most precise expressions of the physical world — E = mc², for example.
The second mystery is that of prime numbers, those numbers such as 2, 3, 5, 7, 11 and 13 that can be divided cleanly only by one or by themselves. All numbers not prime are called composite numbers, and all composite numbers are the result of a unique arrangement of primes: 2 x 2 = 4. 2 x 3= 6. 2 x 2 x 2 = 8. 3 x 3= 9. 2 x 3 x 3 x 37 = 666. 29 x 31 = 899. 2 x 2 x 2 x 5 x 5 x 5 = 1,000. If human beings invented numbers and counting, then how is it that there are numbers such as primes that have attributes no one gave them? The grand and enfolding mystery is whether mathematics is created by human beings or exists independently of us in a territory adjacent to the actual world, the location of which no one can specify. Plato called it the non-spatiotemporal realm. It is the timeless nowhere that never has and never will exist anywhere but that nevertheless is.
Mathematics is one of the most efficient means of approaching the great secret, of considering what lies past all that we can see or presently imagine. Mathematics doesn’t describe the secret so much as it implies that there is one.
In that passage, Wilkinson describes the two great mysteries he's come across in this pursuit of old age.
On the one hand, he wants to know "where numbers come from." Also, he wants to know why prime numbers "have attributes no one gave them."
As Wilkinson ponders these puzzlements, he takes us back to Plato's belief in "the timeless nowhere that never has and never will exist anywhere but that nevertheless is." He somehow feels that he is somehow "approaching the great secret!"
In effect, he's asking where the number 2 lives. Simply put, you can't stop humans from saying such things, from revisiting such high bafflegab.
Today, we have instant instruction! Concerning Wilkinson's first question, the correct answer is this:
QUESTION: Where do numbers come from?
CORRECT ANSWER: I don't know what you mean.
In short, the person who presents that fuzzy question must be asked to explain himself. Briefly, let's be fair:
In fairness, that question sounds like a perfectly sensible question, along the lines of such questions these:
Daddy, where do babies come from?
Mommy, where did our ancestors come from?
Did these raspberries come from the store? Or did they come from our garden?
Everyone knows what is being asked when someone asks those questions. But what is Wilkinson talking about when he asks where numbers come from?
Simply put, the point of his question isn't abundantly clear. Assuming he can't get clearer in his own head, we'd offer these reactions:
Our species' use of number words emerged through a laborious process of evolution.
Some collections of objects were seen to be greater; some collections of objects were seen to be lesser. Slowly, our ancestors invented ways to distinguish between the size of such groups.
Beyond that, we can offer no help, until the high-ranking American writer is able to explain what he means.
Concerning Wilkinson's second "mystery," Wittgenstein writhes in his grave.
In all honesty, the later Wittgenstein was hopelessly inarticulate himself. This helps explain why his methods of clarification never caught on with our species.
Wilkinson seems to be saying that prime numbers (the numbers 5 and 7, let's say) have the following attribute: they can only be divided by themselves and one.
That simply means the following:
If you have a collection of seven rocks, you can't split them into two groups of equal size (as you could with a collection of six rocks). Also, you can't split a collection of seven rocks into three groups of equal size!
We're not sure what makes a person want to keep asking why that is, but it's a great deal like the habit, familiar among 5-year-olds, of thinking that saying "Why?" makes sense in every context.
At some point, the question "Why?" stops making sense. At some point in their development, most humans come to understand that fact, leaving only the logicians and the gifted American writers.
Let's explore this matter further:
If you have four cupcakes and two children, you can split the cupcakes evenly among the children. (Each child can get two cupcakes.)
If you have five cupcakes and two children, you'll have to split one of the cupcakes in half! Remarkably, people like Wilkinson, dating to Plato, have found themselves mystified by such basic facts.
In modern times, such people speak to the New York Times. Their work is then rushed into print.
The later Wittgenstein was remarkably inarticulate. He wasn't good at explaining what he was talking about.
Articulating for him, he might have said something like this:
We get tangled up in forms of language which lead us far astray. We take forms of language which make perfect sense in various familiar contexts and export them to other contexts, where they produce a feeling of mystification.
Rather than think those differences through, we start inventing mystical worlds. Numbers and circles now seem to live in one such world, along with their various "attributes." In short, we generate hocus-pocus.
(Wittgenstein, in a different context: "Where our language suggests a body and there is none: there, we should like to say, is a spirit.")
Needless to say, this is all Rebecca Goldstein's fault. It's all her fault, but it's also the fault of the process of evolution which invented our highly imperfect human brain, an organism which rather plainly wasn't designed to handle such puzzles as these.
For the record: For the record, Plato said very few things which made any actual sense.
In his defense, he lived more than a hundred years ago. At the very dawn of the west!