Re: Opinions on mathematics.


Michael Press wrote:
Folks have talked about the how mathematics is
practiced and the nature of mathematical objects. It is
difficult to address these matters without saying
'mathematical objects' and expecting to be understood.
It looks like we are stuck with the notion of
mathematical objects.

From time to time someone tells me that mathematics is
not science. I disagree with this assertion. The reason
is that a mathematical object is a structure that we
construct in our mind with the aid of writings and
diagrams. When doing mathematics we are mapping our
minds, and changing our minds. This is my outlook in a
nutshell. Mathematics is a science. Our minds are real.

manipulation of symbols
(mathematics)
is as much a science as manipulation of flywheels or masers

but this doesn't give you much

you can manipulate symbols many ways
including writing them atop each other
changing their size in pretty fluctuations
branching them in complicated graphs

just as you can place flywheel on top of a maser
inside a bowl of spaghetti

if you have an idea what will happen

it becomes science

and symbols
static as they are
tend to be fairly predictable...
----------------------------------

where symbology becomes useful
though
is through the process of "meaning"

where symbological metaphor
associates a symbol or string
with a referent in experience

this is the fundamental lie of language
one of the most useful tools homo sapiens have discovered

we build games to expect agreement on these meanings
and learn to abstract these meanings over instances

this is how all science becomes technology
and why masers become more useful when in a physics laboratory
and less so in an automotive shop or restaurant

but mathematicians sometimes dislike pointing out meanings

and try to pass some of their agreed-upon-games
their assumptions about a set foundations
or a classical logic of deduction
as having absolutely no technological content

it is a hubris of some mathematicians
that their chosen symbologies could possibly be shown
to be less useful than other ones

fortunately the nature of the game
the ease with which one can manipulate symbols

causes mathematics to regularly change anyways
(as any science will)

-=-==-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-=-
galathaea: prankster, fablist, magician, liar

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