"The idea of the continuum seems simple to us. We have somehow lost sight of the difficulties it implies ... We are told such a number as the square root of 2 worried Pythagorus and his school almost to exhaustion. Being used to such queer numbers from early childhood, we must be careful not to form a low idea of the mathematical intuition of these ancient sages; their worry was highly credible." - Erwin Schrödinger

Aleph-0 Metaphors:
originally published in homonumos magazine

Cantor's diagonal proof shows us that the set of rational numbers is larger than the set of integers, even though both sets are infinite.  That there are more fractions than whole numbers can be supported by observation; the world is filled with more partial things than with whole ones.  More slices than pizza, more snow than snowmen, more hair than wigs.  Uncountably many fragments, packed between the spaces of the complete things.

Who doesn't feel it themselves, that for each of us there is an aborted quarter, and a polydactylous twin (1.01), and his brothers, conjoined Chang and Eng at a digit approaching 2.  Each of them rational (a terminating or repeating decimal) standing between yourself, none of you and two of you, waving many fingered hands.

Self is the first set we enumerate, and yet, despite the bushels of people who we are, our imagination remains finite and bound.  Like Pi, its arc passes the horizon, but our mind is only knowable from digit to given digit.  We can browse the number and pick any of it’s round fruit, but it’s no Mormon Heaven, only a human toiling inside time and computation, more than sometimes gleaning another's field.

Numbers are tempting for writers, because writers are desperate for description.  Their job is depicting things which have been described twelve or two million times before.  Numbers have a sexy accuracy if the sums remain small, and are poetically bewildering if the numbers grow large.

"...

da mi basia mille, deinde centum,

dein mille altera, dein secunda centum,

deinde usque altera mille, deinde centum.

..."

Numerical metaphors are dangerous to employ seriously, though.  Scientists(1) are sensitive to levels of accuracy, and literary metaphors are naturally approximate.  Shklovsky identified this inaccuracy as the soul of literature, which appears when the reader is forced to reconcile accounts the writer has intentionally bungled.

"...

dein, cum milia multa fecerimus,

conturbabimus illa, ne sciamus,

aut ne quis malus inuidere possit,

cum tantum sciat esse basiorum."

(Catullus, poem V)

Authors must therefore steel themselves to the patronizing smiles of mathematicians, before both return to their ledgers.  Or they must supply instances for analysis.

Astronauts report that the smell left over when an airlock is exposed to outer space is like burnt gunpowder.  A vacuum is a concrete example, but is that the smell of 0, a number, or of empty set { }, not a number, but the absence of numbers?  Or is it only the smell of { }+{airlock}?

And if odor is reflexive and { }={ }, then outer space is one of many gunpowder smelling voids.  An entry wound {0}, the bullet opens the abdominal airlock, and the gingerbread man taped out at the crime scene.  The hand holding the gun, the index finger curls to the thumb and forms the nothing number, too, with residue left for the detectives.  There are known professions that can report smell of {0}+{body}.  Besides detectives and assassins, there are soldiers and surgeons.  So far, though, there is no space cowboy who knows the fragrance {0}+{body}+{airlock}.

Or the sting of chili peppers, measured on the Scoville scale from bell-pepper zero to pure capcasin 16,000,000.  A finite set subject to Cantor's infinities.  The first obvious thought is the possibility of tasting digits.  In the lab with a shotglass of diluted Tabasco- one, two, fifty.  Imagine the poor scorched and choking Dr. Scoville laboriously making his way into the upper thousands.

Some of the properties of the Scoville set are well known- the hottest pepper grown measures ~998,000, the Dorset Naga, a strain of scotch bonnet.  But the set seems incomplete.  Could we yoke the Scoville negatives- celery, icy Sichuan peppercorn and pure -16,000,000 novacaine- to develop a spice arithmetic?(2)

With sufficient operators, the properties of Scoville primes, squares and irrationals can be derived and analyzed qualitatively, for use in the food industry.  Pringles Potato Chips, already tasty 2-saddle minimal surfaces, could be packaged as an ordered Fibbonaccho Flavor set, each one additively hotter than the last.  Can you Slam the Stack?

Besides being nonsense, math metaphors risk being unliterary, by appealing with cool logic instead of hot fluids.

"My brain is busy with the daily grind. The high point of the day is morning tea.  And that is too bad: some artists shed blood and sperm. Others urinate.  Net weight is all that matters to the buyer." - Victor Sklovsky

It's the rare reader ("fewer than 100 on earth") who will cry to learn that x^n+y^n=z^n has no solution for non-zero integers x, y, and z if n is an integer greater than 2, and know why they cry.  Andrew Wiles' masterpiece remains obscure.  A good writer, like Gregor Mendel, will allow the narrative to usurp the data.  Story is a trend line shot through random graph points, and results must sometimes be falsified.

Scientific metaphors, on the other hand, have to be accurate for their gedanken experiments to properly unspool.  When Einstein rode his lightwave, he didn't mention the tack you would need to harness such a crazy mount.  But Austrian office nebish as Phaeton is the first picture which springs to mind.

Who can resist a dramatic flourish?  If Schrödinger's device halved apples, who would recognize his name today?  Instead, like Nansen, he kills cats, just saying which brings fricative pleasure.  The connection between quantum mechanics and Buddhism may then be purely rhetorical or sadistic.

Ultimately, if mathematics and literature are united in obscurity, their origins conflict.  Math is the strange hand of the universe, kneading the brain's dough.  Prose is the brain's own hand, fingering the world like uncertain fruit.

The scientists imagination is forced out of human shape by the weird universal hand, and free to grasp it with new digits and invaginations.  A scientist has to take his personhood off and see things with the eyes of a cube, a dog stem cell, or a mole of sodium.

The authors imagination is a procrustean bed, where that hand is trimmed of excess fingers and troubling dark spots to fit human motives.  A cat, a flea or a ghost all record themselves in letters.  If the meaning is still private, it's the private meaning of a human, not much different from any other.

"I am so in favor of the actual infinite that instead of admitting that Nature abhors it, as is commonly said, I hold that Nature makes frequent use of it everywhere, in order to show more effectively the perfections of its Author. Thus I believe that there is no part of matter which is not - I do not say divisible - but actually divisible; and consequently the least particle ought to be considered as a world full of an infinity of different creatures." - Georg Cantor

Notes:

1) In this essay, my first deliberate error is to conflate science and mathematics.  Although both are reasoning professions, they are as different as the coffee and the cup.  The difference is chiefly in the role of proof.

In science, proof is just a flavor of data, always subject to reinterpretation and overthrow.  Gravity, evolution by natural selection, and the periodic table of elements are just convenient models describing the surface effects of ever-more complex and refined events.  Scientists approach their mysteries Philip Marlowe style, pushing uncertainty ahead of them.

Mathematics regards proof as inviolate.  A proof (and note the change from collective to singular) might be shown incorrect, or superseded by a more general case, but correct proofs are true, pits inside the soft fruit of computation.  A mathematical proof is as inflexibly real as a deduction of Sherlock Holmes.