I must say I was wrong. I cannot explain to you the functioning of a
computer without doing math. Orally, drawing on a black board, I would
have been able to explain a big part of it, and simultaneously hiding
the mathematics. But I realize now that even this would have been a
bad idea and would have made things more difficult in the longer run,
given the ambition of the project.
After all, I am supposed to explain to you how, when we assume the
comp hypothesis, the ultimate realities become mathematical in nature,
even arithmetical or number theoretical. But how could I explain this
to you without doing a bit of mathematics.
Mathematics is a curious music that only the musicians can hear.
Mathematicians play with instruments that only them can hear.
To listen to a mathematician, you have to be a mathematician and play
the instrument. Fortunately, all universal machine like you, are a
mathematician, and when a human seems to feel he is not a
mathematician, it just means the mathematician living within is a bit
sleepy, for a reason or another.
Especially that I am realizing that some people confuse a computation
with a description of a computation, which are two very different
mathematical objects (albeit relative one) existing in Platonia. This
plays a key role in the articulation of the step seven with the step
eight. It plays a key role to understand the computationalist
supervenience thesis, and thus where the laws of physics come from,
and of course it is strictly needed when ultimately we interview the
universal Lobian machine.
So, the time has come I cure your math anxiety, if you or some others
are still interested. I can awake the mathematician in you (like I can
awake the mathematician living in any universal entity, btw :).
I propose we begin with the numbers, and, to keep our motivation
straight, I propose we meditate a little bit on the distinction
between numbers and descriptions of numbers, and notations for
numbers. It is a bit like the difference between a symphony and a
symphony's partition ....
Given the importance of such distinction in the whole drama, it is
worth to get those conceptual nuances clear right at the beginning.
I really propose to you to begin math at zero.
But now I am already stuck: should I explain first the number 1,
or ... the number zero?
A tricky one that number zero ... :)
PS I now you are busy. I propose we go at the minimum of your rhythm
and mine. But I tell you that "the poem is long".
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