Maths Meets Music

Mum *sings a note* I’m guessing either a C or a D.
*goes to piano* Oh, it’s a C sharp.
Dad Well, it’s the average of your guesses.
Me Only if it’s a linear relationship.
Dad Of course it is. The C above a middle C has twice the frequency.
Me Then it wouldn’t be linear. It would increase by powers of two.
Dad
Me *consults Wikipedia* Yep, powers of two. Twelve semitones, so to get the frequency of the next semitone, multiply by the twelfth root of two. Middle C is roughly 262 hertz; Tenor C is 523 or so and Soprano C is 1047.
Dad *does the maths* And the fifth, the seventh semitone, is roughly halfway. Maybe that’s why it’s the perfect cadence.
Me *gets calculator* *nearly blasphemes*   2(12√2)7 ≡ 2(2) ∕ (12√2)5!!!! Modelling 2 as n hertz. And the best thing is that the answer is 2.996614154…which rounds to 3, which is halfway between 2 and 4. Aaaaghhh *the romance of logic overwhelms*
Dad So our brains aren’t adding a fixed value between each semitone. They’re actually making a complex geometric calculation.
Me What do you think, Mum?
Mum I stopped listening when you mentioned averages.
Me Yet you’re the only one of us who can sing in tune.
Dad and I *return to calculations* *major excitement*musicalnotes
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God is Maths!

1 + 1 = 2

Right?

Prove it.

What does true matter consist of? What is the real component of matter?

Atoms.

Prove it.

And don’t get microscopic on me, because who’s to say the stuff you can see under a microscope is really what’s there? You rely on your sensory experience. But how can you be assured of anything, anything except the contents of your own mind at the present moment? Maybe you just popped into existence a few seconds ago, complete with memories, knowledge and theories.

Surely I couldn’t dream all this up myself, you say.

Well, prove you didn’t. And don’t try using your senses to do that. That would be working upon the very assumption you’re attempting to prove. Total nonsense!

Atoms, again. It’s logical, you say.

Logical, eh? And tell me exactly why the things you observe correspond to your own ideas of theoretical explanations for those very observations.

1 + 1 = 2

I won’t ask you to prove it. Numbers are abstract. And if you held up one finger on one hand and one on the other, and counted two, I’d ask you how you knew your fingers existed, how you knew you were holding up two of them.

1 + 1 = 2

Everyone in their sane mind agrees. Not because they see it, but because it’s the assumption they must make in order to believe in every mathematical process in ‘existence’. Maths is there. You can’t prove it, but it doesn’t go away. It always has been, and always will be.

We say 1 + 1 = 2, and if we didn’t, everything we’d built upon that one assumption would fall through.

God is an axiom, should you choose to believe it.

I am a mathematician. I build my future on earth upon 1 + 1 = 2, and my future in Heaven upon my belief in God.