The Cantor

An alternate history with small touches of data and humor. Do you think it would work?

The asylum is cold and its walls are damp.

Parvati sits in the cantor’s office. She is a tall, straight-backed woman with brilliant eyes. He is a well-respected cantor, with many degrees in the various sciences of mental health.

“Do you hear voices?” the cantor asks.

Parvati shakes her head.

“Smell things that maybe people around you can’t smell?”

“No,” Parvati says. “Except when their olfactory senses are not acute.”

“Have you ever felt,” inquires the cantor, “that the underlying mathematical reality of your mind was ill-defined?”

Now Parvati is suspicious. She recognizes this question as part of most standard mental health evaluations.

“I am not unduly concerned,” she hedges, “with the existence of thoughts that I possess but cannot prove that I possess.”

The cantor leans forward. He lifts his bushy eyebrows.

“Ms. Himavan, there’s no need to indulge in higher theory, here.”

“No,” Parvati says. “I feel adequately defined. It’s just . . . life is hard, sometimes.”

“Additively or multiplicatively?”


The cantor leans back. He picks up his cup of coffee. He sips. He thinks. “I mean, do the problems you’re having seem to accumulate linearly or geometrically?”


Parvati laughs wryly. Then she holds up a hand when she sees the look in the cantor’s eyes.

“Just linearly,” Parvati says. “Sub-linear, really. I mean, the incremental gain seems to decrease each new day. It’s just that the limit function of the sum doesn’t seem to converge.”

“Is that why you chose to starve yourself? Because the limit function of your accumulated suffering might not converge?”

Parvati says, austerely, “I am starving myself to attract the favorable attention of a god.”

The cantor sighs.

“You know that’s not mathematically sound,” the cantor says.

“There are higher planes of mathematics,” Parvati says, primly.

The cantor opens his mouth to protest.

Parvati’s primness dissolves into an impish grin. “No, no, no,” she says. “It’s okay. I’m here. Prescribe your mathematics. I shall integrate it into my underlying worldview and see what transpires.”

The cantor smiles at her. “Well, it’s good that you’re willing to give it a try. Have you ever had ring therapy before?”

Parvati tilts her head. “Freud? Organizing sexual feelings into matrices and so forth?”

The cantor laughs.

“Oh, my,” he says. “No. Freud’s underlying analysis relied entirely on |R| being the second-largest infinite cardinal. We’re—”

Parvati interrupts him. “How did you say that?”

“|R|,” the cantor pronounces, carefully. “It’s the cardinality of the reals.”

“R,” Parvati says. “r. /R/. ?R?”

The cantor laughs. “|R|.”


“In any case,” the cantor says, “Basic ring therapy consists of organizing your thoughts so that they perform predictably under addition and multiplication. For example, the thought ‘I am a person’ plus ‘I like apples’ sums to ‘boat’.”

“Boat,” says Parvati.

“Do you see how they add?”

“Boat!” says Parvati, despite the fact that this is not so much the sum of the the two thoughts as the third point of a right triangle formed by them in the plane of her transient epistemological context.

“Similarly, you can multiply ‘I am a person’ times ‘I like apples’ to get . . .”

Parvati attempts to think the first thought a number of times equal to the cardinality of the second.

“‘I like apples’ is a really big thought,” Parvati says.

The cantor considers.

“Perhaps you could multiply it by the singular sensation of waking up?”

Parvati’s hands spread reflexively.

“Wow,” she says. “It multiplies to form a somatic thought!”

“Very good!” says the cantor. He scribbles out a prescription for a book on basic ring theory.

“The nurse will come around and make sure you do your reading,” the cantor says.

Parvati hesitates.

“Does the fundamental undercomputability of the mathematics of thought,” she says, uncomfortably, “ever bother you?”

The cantor snorts, lightly.

“My dear,” he says, “if we let it bother us, there wouldn’t be any mathematicians, and people like you would still be getting ‘help’ from the engineers.”

8 thoughts on “The Cantor

  1. accursed engineers!

    then again, without math, what would us physicists do?

    alas, there is a large body of accumulated work done by physicists who didn’t have math.

  2. Now this is my kind of bizarre.

    Shouldn’t that be “second-smallest” transfinite cardinal, though?

  3. *Sigh*

    I suppose this would be as good an excuse as any to knuckle-down and try to get a grip on set theory…

    The piece works very well as a satire, but “would it work,” as an alternate history? Seems unlikely, at best. Even were the human mind capable of arranging its thoughts into a spatial array of that nature (without greatly distorting the contextual associations of its constituent concepts), of which I am doubtful, the proposition that “I am a person” and “I like apples” should sum to “boat” assumes that the subjective meaning of ‘person’, ‘apples’ and ‘boat,’ is identical for all human beings posessing those concepts. Even if this were feasible, this method of treatment seems to demand a higher degree of mathematical sophistication than is posessed by the general population of those needing the attention of mental health professionals.

    Oddly, this reminds me of C.P. Snow’s “The Two Cultures,” inasmuch as it seems to transfer psychiatric care from the context of one intellectual culture to another.

  4. The various thoughts could be assigned a one-to-one correspondance to a given set of numbers, in a way not unlike Gödel numbering.

  5. This is deeply, deeply silly.

    I will point out, however, that if the process of thought is contained entirely in the body and nervous system, the cardinality of the set of all possible thoughts would appear to be at most ℵ2 (if a thought is defined as a mapping from current state to successor state), and possibly only ℵ0 (if a thought is defined as a single state and states can be discretized).

    [size=9:3ac395ed8b”>Stupid phpBB. I can get it to do HTML entities, but not tags, even when I uncheck “Disable HTML in this post.” Thus the lack of subscripts above.[/size:3ac395ed8b”>

  6. Yay, and I was just reading about how to add two points on an elliptic curve! I guess the zero thought is nothing at all. What’s the unit thought?

    There has to be an injection φ: (Thoughts / Silent Thoughts) → English. So thoughts can’t necessarily be given a ring structure compatible with the ring structure of the English language; it requires more proof.

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