Math and Reality

[Violet]

Thanx for your reaction Sae in these slums of the forums avoided by the great mathematical minds of AF.

I was intrigued by your statements in the shoutbox, especially this one :

"The concepts do not require the human mind to exist. Only in identifying is the mind required. They are helpful in describing reality because they are reality (or at least the pattern[s] by which it follows)."

That first sentence strongly suggest that mathematical concepts exist independently of a mind that thinks 'm. But what follows suggests that you think that math is a conceptual implementation of what the human mind sees in reality.

That would necessarily have to mean that math 'follows' reality i.e., the pattern you speak of is first somehow observed in nature and then abstracted into mathematics. But that imo is not the case with many mathematical concepts. Complex numbers come to mind, infinities too, Minkovski space was there before Einstein made use of it, and a whole lot of contemporary math has no known correlate in reality whatsoever. So this poses a real problem for the view that mathematical concepts are derived somehow from reality. In fact it looks just the other way around. Many mathematical concepts probably will never have known correlates in reality.

To use the color of blue as an example... it is just a hue, but upon perceiving it we turned that hue into a concept, and later into a word. Logic (upon which math is based) has been continually observed in nature... that we can use that base to consider things we haven't even seen yet is due to our trust in logic. If logic is how reality "follows" (at least "here"), then what is based off of it is probably true. However, if math is wrong at a point, it would only be because logic does not apply to the scenario. Mathematical concepts are derived from logic, which is an unprovable assumption we've made to reality. It may not be the "true" reality, but it is the reality as we can see it.

So this is a strong argument for mathematical idealists, which in fact is a form of dualism.

Furthermore in contemporary physics the situation has even 'deteriorated' much more, in the sense that where physical intuition has lead the way to new breakthroughs it has been replaced by math itself. The Nobel Prize winning physicist and one of the fathers of quantum mechanics Paul Dirac was famous for his insightful advice, “follow the math.” Indeed, following the math and leaving our physical intuitions behind has become a necessary and revealing trend in physics, string theory being a exceptionally strong case for that.

If math is ultimately a representation of reality, then following the math would be following the reality. For all we know, infinites might be real (see singularities?). Logic itself is an assumption made... but it remains that it could all be one outlandishly ridiculous coincidence. Following the math would be entirely logical given that it hasn't really let us down yet when describing, and we can see no reason for it to do so. But all of math blows up if the illogical starts occurring. Logic is simply an observation we've made of 'reality'... and there is no way we can test it's validity without using itself.