Are numbers Real?

I think numbers are a great argument against the spread of the
pernicious intellectual cancer of relativism.
The relativists would say that numbers are a "cultural construct",
basically that we invented them.
I think the evidence is very strong that human beings started using
small numbers 1,2,3, Many, a long time ago.
After the decent into agriculture larger numbers were need for
counting Animals and units of grain to pay to the small number of
people at the non-shit end of the long stick. The "Elite" needed to
be able to Add, Subtract, Multiply and Divide, and handle large
numbers.
Later on numbers are used to measure the dimensions of things,
weights and distances. Along with this comes an increase in
mathematical knowledge.
Then some bright spark discovers Pythagoras's Theorem (well before he
did), and an even brighter spark asks what happens if I want to know
the distance across the diagonal of a unit square and, Oh Dear, the
shit hits the fan, the distance is an "irrational" number and cannot
be written down. If I recall correctly a Greek mathematician got
drowned for letting this secret slip.
It turns out that most numbers are Irrational and the integers a
small sub set (scary).

My point is if numbers were a "cultural construct" why would the
number system end up having properties that we did not design or want
(at the time).
Clearly numbers are real, as every one on this site knows.

All the best

John S

hi John,

> From: "jsnelsonone" <jsnelsonone@yahoo.co.uk>
> To: <tuning@yahoogroups.com>
> Sent: Monday, June 23, 2003 4:54 AM
> Subject: [tuning] Are numbers Real?
>
>
> I think numbers are a great argument against the
> spread of the pernicious intellectual cancer of
> relativism. The relativists would say that numbers
> are a "cultural construct", basically that we
> invented them. I think the evidence is very strong
> that human beings started using small numbers
> 1,2,3, Many, a long time ago. After the descent into
> agriculture larger numbers were need for counting
> Animals and units of grain to pay to the small number
> of people at the non-shit end of the long stick. The
> "Elite" needed to be able to Add, Subtract, Multiply
> and Divide, and handle large numbers.
> Later on numbers are used to measure the dimensions of
> things, weights and distances. Along with this comes
> an increase in mathematical knowledge.

what you say here agrees very well with most interpretations
of the archaeological record.

the Sumerians left the earliest surviving written records
(on baked clay tablets) c. 3500 BC, and they are indeed
simply accounting records, as you descrbe in the first part
of your post.

by c. 3100 BC they had figured out how to write down
full sentences, and thus began both history and literature.

> Then some bright spark discovers Pythagoras's Theorem
> (well before he did), and an even brighter spark asks
> what happens if I want to know the distance across the
> diagonal of a unit square and, Oh Dear, the shit hits
> the fan, the distance is an "irrational" number and
> cannot be written down. If I recall correctly a Greek
> mathematician got drowned for letting this secret slip.
> It turns out that most numbers are Irrational and the
> integers a small sub set (scary).
>
> My point is if numbers were a "cultural construct" why
> would the number system end up having properties that
> we did not design or want (at the time).
> Clearly numbers are real, as every one on this site knows.

you might be interested in the Babylonian evidence
of knowledge of the "Pythagorean theorem", of you
don't know it already:
http://www.maths.uwa.edu.au/~schultz/3M3/L1Babylonianroot2.html
http://it.stlawu.edu/~dmelvill/mesomath/tablets/YBC7289.html
http://www.gap-system.org/~history/HistTopics/Babylonian_Pythagoras.html

which i have (as usual) transmuted into my own wild
speculations -- in this case, that the Sumerians could
have calculated an arbitrarily close approximation
to 12edo.
http://sonic-arts.org/monzo/sumerian/simplified-sumeriantuning.htm

... there, now i've brought this post back on-topic! :)

Kurt, you're getting into philosphical stuff in which
i am indeed very interested, but it goes way off-topic
for this list. (perhaps if i can find the time we
can engage in some offlist banter about it ... and
there's always the metatuning list.)

suffice to say that i'm coming at tuning theory from
the angle that humans strive to comprehend their
environment, and do that primarily by organizing
sensory experiences into repeating and/or similar
*patterns*.

numbers simply describe those patterns, and
prime numbers describe them with the ultimate
simplicity, which, i would argue, makes them
more easily comprehensible.

-monz