# Visualization And Re-presentation

Visualization is a main characteristic of Greek culture. You could
easily see it if you visit an orthodox church. It is a tradition
since ancient Greece. They were especially good at architecture,
sculpture, pottery, stage play, &c. Also Buddha was originally
symbolic. But Greeks in Gandhara had made statues for the first
time.

Similarily "Music" means the sounds. Or maybe only the sheets. But
the Greek term "Mousike" means the overall performances including
the sounds. Then is music inherently better than mousike?

Is arithmetic inherently better than geometry?



If you actually have read Euclid's Elements, you will know that it
is not just geometry. The number 1 and the line segment with the
length 1 mean the same thing. If x is a factor of n, then it says
that x measures n. It does arithmetic and geometry at the same
time.

For example, since 6 = 2*3 you can say that 6 is 2 times "the
measure 3" which also means the line segment with the length 3.
Then 3 measures 6.

Also Pythagoreans studied arithmetic geometrically. They used
pebbles to present numbers. Especially they were interested in
polygonal numbers. Some Pythagorean concepts came from it. For
example, why odd numbers are stable and even numbers are unstable
is because of square vs rectangular. 1+3+5+... vs 2+4+6+... .

. . .        . . . .
. . .        . . . .
. . .        . . . .

Arithmetic and geometry are strongly intertwined. In fact number
theory is abstract algebraic geometry.



Visualization is a re-presentation. What does it present again?
NUMBERS. And forms which reduce to numbers in the end.

Numbers are immanent. You can experientially discover it. Numbers
in that world and numbers in this world are not different things.
Numbers in arithmetic, music, geometry, astronomy are all the same
things.

Therefore music is not inherently better than mousike. If numbers
in music and numbers in its representation make an unison or a
harmony, mousike is better. If not, music is better. Though it is
true that there are tons of poor representations.