Math, Science, Reality and Language:

'Every day understandable language' is not reducible to mathematics, and mathematics is not mappable to any every day understandable 'lingua-franca' language. Trying to 'power through' the meaning of mathematical formulae, derivations, functions, etc with linguistically based thought is doomed to failure. And I mean this in the most emphatic way possible. Doomed.

To try to believe that mathematics is a 'stand-in' for some collection of words under some grammar is fundamentally incorrect on the deepest level.

Love is a red red rose. Love is also never having to say you're sorry (snort!). Love is blind, love is a gift. Love burns brightest in the darkest night. But 2, under the standard axioms and operations of arithmetic always equals 2. Nothing else. It is not company, and 3 is not a crowd. An integer, under the axioms of arithmetic closed under a standard system of deduction does not burn brightly in the darkest night, it does not hurt, it is not a red red rose. It is a unique integer, and it means only what it means. It can be described, within a system, in terms of operations on other integers, it can be assigned to a variable after a process of deduction, a product of a funtion on a collection, etc etc. But it is what it is and nothing else.

I am not speaking lunacy here. I'm making a point.

Mathematics is a language, of sorts, but its a very parsimonious language, with an absolutely clear and mechanical grammar. There are no Synonyms, metaphors, etc in mathematics.

This special thing, 'math', meaning only what it means, can be used to describe the universe we see around us, and its properties. Part of any empirical science is to 'reduce' (something now considered a bad word, usually by people who don't know math or logic) observed, repeatable phenomenon to a formal system or language (so-called 'math').

And here is where the beauty is- The little glimpse of the infinite in a finite experience... A peek at god, perhaps. Because a formal system is closed under a grammar, you can derive, using the grammar of the formal system, other statements about other phenomena in the universe we see around us. You can then test that derived statement against the universe around us to see if you were right. If not, you're not the first one to be wrong, you go back and do your homework and see what happens.

This is, of course, an oversimplification of empirical science and its relationship to 'math' (math is in scare quotes because math is not really whats up here, its formal systems that can be thought of as valid, IE truth-preserving, and 'unitary', for lack of a better word). Sometimes empirical science is about coming up with the right system to articulate the known observations of the universe- Newton with his calculus, Einstein with Non-Euclidian Geometry, and Andrew Wiles with Elliptical curves and modular forms (although the last example is from Mathematics itself). As with Newton and Einstein, these discoveries gain empirical strength through unifying and explaining diverse, seemingly different classes of phenomenon with a pure and simple formal system.

The relationship between Math and Science is manifold and rich, and goes on and on in something like relational wholeness. Not because that Math IS science, and not because Math IS the Language of science (although both could be true in common-language metaphorical sort of way), but because Math is the intuition of science. Math is the glue between the scientist and the world he seeks to understand. Math is how the Scientist knows about the universe. Its nothing magical or 'ivory-tower-ish', or elitist. Its a mind-bending trek into a discipline of thought. Its for many one of the greatest and most spiritual adventures accessible in life. A Scientist may day-dream thought experiments, but like dreaming in color, that daydream is contexted/shaped/bound/whatever by math. Chomsky. Grammar shapes thought. Its key to understanding what I'm saying here.

The point of this is that you are on a dead-end mission. I can talk 'about' math all day. I can 'tell' you about a hierarchy of infinities. I can explain to you that not all mathematical statements are computable, or can be proven true. I can try to explain to you what entropy means in communication. I can speak about wave functions (Or rather, SDAI will, ad-nauseum) and observations collapsing probability functions. There are more functions in heaven and earth, my dear horatio, than can be computed by your grammar!

But anything that I tell you won't be the truth of the matter, and anything you are inspired to think of, lingustically driven by these lingustic constructions, won't be science. Nor will it be philosophy. Nor will it be truthful in any way like science is truthful. It will be, at best, speculation. It will have all the logical 'truthfullness' of a day-time soap- at best.

Using a checker board and some checkers, or using a story about two brothers that youe meet at a fork in the road, I can explain to you about the hierarchy of infinities- I might even convince you that there are a hierarchy of infinites or incomputable functions. But unless you LEARN AND DO THE MATH, you ultimately won't understand what these things mean or why they are true, or what these things say about anything!

But, when you do the math (or in this case, properly, logic), you will understand in a way that no words can explain. Its not a bigger truth than what words can convey, its not a more valuable truth to life and existence- but it is a truth that will floor you, change the way you think. It will blow your mind.

Now, I have heard you gripe about Ivory-Tower hubris or arrogance. What you do not understand or refuse to understand is that you do not understand and refuse to understand. You are living in an ivory tower where you think that somehow you can just common-sense it all. That you can grok scientific truth just by leaning back, thinking it through, and posting something on a BBS. What you do not understand is that the truth of science is not found in words. That somehow your unhoned raw intuition is special. Science can explain itself to the rest of the human world in words, but the truth of science is in the math and in the discipline. People far, far more intelligent than you or I have submitted themselves to years of patient study, have learned the math, done the observations. Its not some sort of clique. Anyone can do it, anyone can 'join up'. Science is not about yawning accpetance, but about critical exploration and proof. You have to do the math. You have to open up a dialogue with the universe- not some people on a board in cyberspace.

ER was wrong about something. Newton did not just 'sit and think up' physics. I'll recount a story from Newtons life before he wrote Principia (I think, or one of his later works)- or rather before he published it.

Sitting with a friend in his parlor, discussing Kepler and Newtons calculus, his friend wondered what shape the planets would follow in their path around the sun. Newton said without reflection 'an elipse'. His friend asked if he had observed this and newton replied: 'No, I have proved' it. And proceeded to write out the proof right there, that he had been sititng on as he worked out his ideas for oh so many years.

You see- Newton had engaged for a large part of his life in a mathematical and empirical exploration of the universe that surrounded him. His intuitions shaped by observation and mathematical proof and the new mathematics he discovered as part of this process. He didn't sit there and think about force and mass in common-linguistic terms, but he was seeking out the universe in far more pasimonious, simple way, and when he sat down to communicate with his fellow scientists, he did not write a story or a letter or aint a picture- he derived. He was asking quiet questions and getting quiet answers.

There are truths in language- huge thruths in language. In music, in poetry and art, and even truths in just the sun on your face or your toes in the grass. But these are not the truths of mathematics or science. Don't confuse what you are doing with either mathematics or science. I assure you it is neither.

DL