Saturday, July 14, 2012

Our BFFs the Integers

(That should probably be BFsF, on the model of attorneys-general;  but let it pass.)

Richard Dedekind wrote a book with the delightful title Was Sind und Was Sollen die Zahlen
He proved that “the natural numbers are uniquely characterized by their induction properties.” (Wiki).


Elementary arithmetic -- the times table, long division -- you might find fun or you might find rebarbative, depending on the way you’re wired.  But every child loves learning to count.  It’s like the alphabet song only better;  because, unlike with the alphabet, you can keep going if you like.
Our pleasure in integers  traces back to our time in the nursery, playing with blocks.
My approach to the integers  is that of the milkmaid to the udder.  (Saying a blessing before she begins.)
Notice that the word integer is related to the word integrityIntegers are our friends!


ONE little TWO little
THREE little Indians;
FOUR little FIVE little
SIX little Indians;
SEVEN little EIGHT little   NINE
little Indians:
TEN  little   In-di-an
Boys !!!

To chant that ditty
is like telling-over worry-beads --
soothed by their satisfying
click - click - click …


Certain integers have fan-clubs, like “23”.  That is idolatry.
One integer is much like another.   Each has various combinatorial/arithmetical properties,
but apart from primality,  it is not clear that any of these are of particular significance.
(“Perfect” numbers.  “Taxicab” numbers.)
They amuse us, is all.
They have no hidden meaning, neither individually nor collectively.
God does not speak in riddles;  gematria is false.


I bought some coleus the other day, each in its little pot.    I didn’t plant them right away, but set them here and tried them there, to see how they’d do.  Coleus are quite finicky about how much sunlight they’ll tolerate.  In fact, when the heat wave hit, I was glad I hadn’t planted them yet, for I brought them indoors for the cool and the shade.  But eventually I had to plant them, lest they become root-bound:  finally deciding on some spots beneath the skirts of a bushy shrub, where they are hard to see but at least won’t bake.  It took some doing.  That, and they are thirsty plants, clamoring to be watered.   Taking on coleus is a responsibility;  it’s like tending to a pet.

You can say this for the integers:  They don’t need much maintenance.

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