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If our toes were our fingers, if Pyongyang was Tehran

[ by Charles Cameron — metaphors, mathematics, and a question for you all ]
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There’s a toe ointment ad for Kerasil that begins:

If our toes were our fingers, everyone would instantly notice the difference..

— accompanied by various shortt clips of feet serving various functions of hands, see above.

I’ll talk about fingers and toes, okay, if you’ll tell me about Pyongyang and Tehran, deal?

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This is the first ad — or for that matter, mass media mention — I’ve seen of the hands / feet comparison, and that’s significant in itself because, along with day / night, sun / moon, fingers / toes must be one of the earlier comparisons on which we base all future comparisons / parallelisms / oppositions, and thus analogies, and by extension, metaphors.

Fingers and toes, then, are an early matrix for us, but that matrix gets abstracted into the decimal counting system, no small matter in our culture and many others. And from decimals we can go to the Dewey Decimal System used in, Wiki informs us, 200,000 libraries in at least 135 countries — and that’s just one of the branches of the tree whose roots are in fingers and toes — our fingers and toes, not the toes of a three-toed sloth or woodpecker…

And of course, the day / night, sun / moon and other dual contrasts arguably derive some of their power from the duality hands / feet, which also gives us left / right, sinister / right, right / wrong and the entire range of moral judgments, based on the two sides of the body and extrapolated from there. We seldom think of these things, unless perhaps in early education, but as Jung and others have noted, they hold great significance for psychology and cultural anthropology.


image: the Nassau County Mathletes

Using decimals, we can represent irrational numbers — impossible to represent as fractions, pi and the square root of minus one foremost among them — a notion so disturbing tto the purist Pythagoreans that Tobias Dantzig, in Number: the Language of Science, quotes Proclus as saying:

It is told that those who first brought out the irrationals from concealment into the open perished in shipwreck, to a man. For the unutterable and the formless must needs be concealed. And those who uncovered and touched this image of life were instantly destroyed and shall remain forever exposed to the play of the eternal waves.

Irrational, or just plain crazy? And those waves — a metaphor for randomness, chaos, or for the universality (via Fourier transforms) of the sine wave?

Oh. And when a zen master wants to set a student a problem that cannot be solved by our binarily inclined minds, he gives them the koan “what’s the sound of one hand clapping?”

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Okay, that’s enough about about hands / feet — now let’s hear about the Pyongyang summit and the Iranian nuclear deal — the Joint Comprehensive Plan of Action. I’m sure you have plenty of thoughts on the matter — your turn, please..

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