Date: Apr 1, 2013 3:17 PM Author: dan.ms.chaos@gmail.com Subject: Re: Mathematics and the Roots of Postmodern Thought On Apr 1, 9:58 pm, david petry <david_lawrence_pe...@yahoo.com> wrote:

> On Monday, April 1, 2013 11:38:05 AM UTC-7, Dan wrote:

> > Falsifiability only comes into consideration when you have something

> > apparently 'external' against which to test your mathematical models .

>

> Precisely. The "external" reality underlying mathematics is computation.

>

> A very good way of thinking about this stuff is to think of the computer as the mathematicians' microscope which helps mathematicians peer into the world of computation, and then mathematics itself is the science that studies the phenomena observed in that world of computation. The "science of phenomena observable in the world of computation" includes all of the mathematics that helps us reason about the real world.

>

> > What's so hard to understand?

>

> What's hard to understand is why you ... oh, never mind.

You've never actually seen a "real computer" , nor will you ever do

so . The Turing machine requires an infinite tape . At most , you have

pathetic, finite automata. What about if a "real computer" makes a

floating point error when calculating pi? Does that change pi?

All 'models of computation' are abstract, as 'internal to Mathematics'

as they could be .I build a computer not because I can't think my task

out, but because it helps me execute a 'mechanized part of my

thinking' faster. Historically , computability theory relies and is

intertwined heavily with other mathematics, (beginning with

arithmetic , going recently to the high abstractions of Category

Theory), and could not have developed without the existence of said

mathematics. Was Mathematics before Turing invalid or useless?

"What Turing disregards completely is the fact that mind, in its use,

is not static, but constantly developing" -Godel

"It is perhaps just dawning on five or six minds that physics, too, is

only an interpretation and exegesis of the world (to suit us, if I may

say so!) and not a world-explanation; but insofar as it is based on

belief in the senses, it is regarded as more, and for a long time to

come must be regarded as more - namely, as an explanation. Eyes and

fingers speak in its favor, visual evidence and palpableness do, too:

this strikes an age with fundamentally plebian tastes as fascinating,

persuasive, and convincing - after all, it follows instinctively the

canon of truth of eternally popular sensualism. What is clear, what is

"explained"? Only what can be seen and felt - every problem has to be

pursued to that point. Conversely, the charm of the Platonic way of

thinking, which was a noble way of thinking, consisted precisely in

resistance to obvious sense-evidence - perhaps among men who enjoyed

even stronger and more demanding senses than our contemporaries, but

who knew how to find a higher triumph in remaining masters of their

senses - and this by means of pale, cold, gray concept nets which they

threw over the motley whirl of the senses - the mob of the senses, as

Plato said. In this overcoming of the world and interpreting of the

world in the manner of Plato, there was an enjoyment different from

that which the physicists of today offer us - and also the Darwinists

and anti-teleologists among the workers in physiology, with their

principle of the "smallest possible force" and the greatest possible

stupidity. "Where man cannot find anything to see or to grasp, he has

no further business" - that is certainly an imperative different from

the Platonic one, but it may be the right imperative for a tough,

industrious race of machinists and bridge-builders of the future, who

have nothing but rough work to do." -Friedrich Nietzsche