Some Contributions to the Sociology of Numbers by Robert Dawson

The ones you notice first are the natural  numbers.
Everybody knows their names; they are the anchors,
the stars, the alphas, the reference points. And of course
the rational numbers, who hang out with them,
sit next to them in arithmetic class.
It must be admitted that some are sidekicks,
spear carriers;  11/17  for instance
is never likely to make headlines.
But the Grade Eight teacher makes sure they all fit in.
Then in high school you start to notice the others, the misfits.
They have weird names, refuse to conform,
are the subjects of sinister rumors:
Did you hear about that Pythagorean ritual murder?
Yeah, creepy: something like that happens,
you bet there’s an irrational mixed up in it. You want
to watch yourself around them. One numerator,
one denominator, that’s what I say.

But not all irrational numbers are the same.
Consider  e : poster child for “It Gets Better”.
Awkward and poorly approximated for the first few terms,
but  ¹⁄_n!  gets small so fast
that soon  e  is accepted among the rationals
almost as one of their own. They privately feel
that e ’s exotic air of the transcendental
indicates their own cosmopolitan taste.
Good marks in calculus, outstanding in Theory of Interest.
Ambition:  to get an MBA.

And π :  happy-go-lucky, Whole-Earth-Catalog spirit,
equally at home in Stats or Industrial Arts.
No one can really explain why  π  gets on
so flirtingly well with some denominators,
the sevenths, say, or the hundredandthirteenths.
and not with others. That’s just how things are.
But the fit’s never perfect, and some day you’ll see  π  
leaning against a signpost,  thumb-out by the side of the highway,
living in the moment, destination anywhere,
waiting for the wind to change.

φ , long-haired, dressed in black, with a pentacle pendant,
and ill-fitting T-shirt depicting Stonehenge or the Pyramids.
Talks about sunflowers, crystals, numerology,
doesn’t get on with any fractions at all.
It’s hard to be sure if they avoid  φ  or  φ  them; but every chance
for approximation misses by the largest possible margin.
1 + ¹⁄_{(1 + ¹⁄(1 + ¹⁄(1 + ...)))}    is the loneliest number.