Friday, July 20, 2012

Does pure math exist?

Sometimes I long to have a profound thought or to encounter one.  When I was doing my education, I encountered them often.  I don't know if you've ever felt the way I used to feel when something would blow my mind. I'm trying to think of an example. One that comes to mind is when I began to think that universals are aggregates of like-minded particulars (at least as we experience them) rather than Platonic absolutes expressed in the material world.

Those moments come less often these days. You get older.  You think you have stuff mostly figured out. I thought of another one, when I had the thought that scientific theories are really just very precise myths expressing the mystery of the world.  Still myths, just a lot more precise in their expression.

Why am I writing this? Because I couldn't think of anything interesting to blog today, let alone profound.  Sometimes when I can't sleep at night I'll google, "something profound."  It's not very consoling.

So here's a stupid question.  I've always tended to think of the kind of math they do in physics and other sciences as an imperfect version of pure math.  So in quantum physics they use "statistical mechanics."  You can't have a precise sense of things so you approximate using statistical methods and probabilities.

So I always viewed this sort of applied math as an inferior version of pure math, where everything is tidy and exact, an imperfect shadow of the Platonic ideal.  But is it possible pure math is only a simplistic shadow of applied math, an abstraction from the real world?

What do you think?  Hey, I had to write something to get us off the topic of health care... ;-)


John Mark said...

The founding fathers did not seem to be interested in math as such, but they did give us forms; not platonic to be sure, but in great number and variety. {Whistling tunelessly] Seems I never have a profound thought......and what does this have to do with health care, anyway ?:)

Angie Van De Merwe said...

If math is a mystery and there is "no pure math" (proving God), then, isn't life about experience? And one's experience equips in a given sphere. A lack of experience is what has been damaging in my opnion with this adminstration, as to military and business. Theory seems to be the all encompassing concern, not the proven, but the probable, in hopes of changing the world (no less!)!

Free societies have many people with various experiences that orient them in a certain way to frame their life, so that it has meaning or "purpose" and is seen as valuable. The value of a life is understood by a sense of liberty in its expression and experience. This is where government's demands, even for "public good" or the "common welfare" can be "felt" as opressive, and sometimes actually is, because it limits choice about how, where and what one will spend one's time and extra monies...

Ken Schenck said...

Very typical... a post about math ends up being about politics and atheism.

Angie Van De Merwe said...

Your comment about the "real world" projecting the "ideal" is how we come to "God". Isn't this Feurbach's understanding? Our natural fathers represent "God" to us as children via child development and educational understandings....

Instead of Meeting the "Ideal" or understanding the "pure", as man is limited within his own context (culture and brain), man creates out of those realms the idea of "God", or "math".

Isn't Kant's view on human knowledge "contextual"? And science's experience as "paradigmic" as Kuhn explained?

Math is a way of explaining the world, just as "God" is another way of explaining the world. The problem is the "God" is often used as an absolute, where math is understood as a theory!

Bob MacDonald said...

Hey Ken - I remember my Physics classes on special relativity and time dilation as being a defining moment of deep thought. Physics continues to have this delight for me - sharing wisdom's delight at play before the foundation of the world. Maybe sometimes I confuse boson with bosom.

I must admit - governance in the human world is a difficult problem - anything but pure. But I love that word pure - (Psalm 2 - kiss, pure lest he be angry - let me throw in the Hebrew for Angie's sake נַשְּׁקוּ בַר פֶּן יֶאֱנַף).

I get deep thoughts from wrestling hard with the Psalms these days - and translating them into awkward poetry.

Martin LaBar said...

Or, to rephrase your question, since I can't answer it: "Is mathematics invented, or discovered (or both)?"

Ken Schenck said...


John Mark said...

Hey, don't accuse me of talking about politics and atheism.....I was just being silly!!! Let's make that clear!! Yes indeed.....:)

Bill Heroman said...

If the origin of existence is the Godhead, then Math might not be Math "there", because 1 + 1 + 1 = 1. Supposing this to be true may just validate your question at the post's bottom.

The perfect eidos of a tree doesn't really exist. Neither does, in any practical sense, the perfect eidos of "1 + 1 = 2".

@InterestInMaths said...

This is a twitter page devoted to the origin of Maths.
Follow and speak your mind there.

Maths A language we observed. It was there before the observation. It was mans observation of the maths and ability to formats it to language is how some understand maths and the complexity's.
Twitter = @InterestInMaths

Come ask questions