The Numbers Are Not Enough

from Too Many Robots by Angelastic

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about

Numbers used to be as easy as 1, 2, 3. This song explains why we went and complicated things with negative numbers, fractions, irrational and complex numbers, and ends with a little abstract algebra.

This was written as part of a series called ‘Forms and Formulae‘ in which I write about articles in the Princeton Companion to Mathematics using poetic forms covered by articles in the Princeton Encyclopedia of Poetry and Poetics. This song's mathematics article is entitled ‘Some Fundamental Mathematical Definitions’ and the poetic form is air.

lyrics

[1 2 3]
You can play the Peano axioms.
Your successor will never fail.
But if you ain't got nothing you ain't got enough
so you start lower down the scale

[0 1 2]
Well you've now got zero problems.
You can count on every fact.
You can add without an end but exceed your subtrahend
or you'll find you can't subtract

[-1 0 1]
So you add in the minus integers.
Zero gains another side.
You can add and take away, but not conquer all the way
'cause you can't always divide.

[⅕,⅓, ¼]
Now your system is highly rational,
no division you can't deal.
But no matter what you do, you can't find the root of two
though you know that it must be real.

[ɸ, e, π]
So you fill all the gaps with irrationals.
You have a solid number line.
Solve ab-surd-ities at will but you're out of square roots still
when you start with a minus sign

[1+⅕i]
So you use your imagination.
You take the square of your mind's i.
Your calculations never stall, but you wonder if that's all
that this complex plane can fly.

[triangles, snares, cats]
The operations work on all numbers,
but is that all they can do?
They apply to other things; now you've groups and fields and rings
to apply that structure to.

credits

from Too Many Robots, track released July 12, 2014
Singing by the Mac voices Whisper and Victoria
Wilhelm Scream probably by Sheb Wooley

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Angelastic image

Angelastic Vienna, Austria

A poet, mathematician linguist and coder who built a robot choir to sing for her.

gelastic, adj. relating to or causing laughter

www.facebook.com/thefamousangelabrett

angelastic.com ... more

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