This is a semi-serious question about the nature of reality

[Nique]

I'm bad at math, so part of me feels like this is a half-baked attempt to justify being bad at math, but my question is this: Is mathematics, even very complicated mathematics, just an approximation of reality? We have a system of study that can, through the processing of numbers, seemingly duplicate natural patterns and systems.

But, just to use an example, we can use an equation to simulate the forming of ice crystals/ snowflakes, but those simulations usually produce a "perfect" or at.least perfectly bi-lateral result. A real snowflakes or crystal forms only basically this way, with lots of little imperfections etc.

I realize you can probably extend your math to encompose the variables to produce a more realistic result, but it seems that this has upper limits? We don't know what happens past lightspeed, or in a black hole partly because the equations stop making sense or seem to contradict our understanding of other areas of study. We have math problems that don't seem to have any basis in reality but are just a quirk of that 'system' (like "Super Tasks", for example). Does this actualy limit us somehow? Is there some more 'advanced' form of physics/mathematics that will solve these problems and I simply lack awareness of them? What does that mean for the future of human learning?

[_mike]

I'm neither a mathmetician nor am I a phsycist, so instead of giving you answers, I'll point you at some neat stuff. Laplace's demon is a theoretical mind (computer if you prefer) that knows the current state of every atom in the universe, which allows it to predict the future perfectly. What you want to read up on are counter arguements for why that wouldn't work. You still won't know exactly how far simulation can go as far as emulating the universe, but you'll know more than you do now.

As far as "more advanced math" goes, google the triangle of power. Similarly to how using arabic numerals lets us do operations like multiplication more easily just by better arranging things on the page, the triangle of power simplifies the relationships between powers and logs by just using different arbitrary symbols than the ones we use now. In other words, it's possible that we're making math more difficult for ourselves because we haven't found the best way to write even basic functions, yet.
Sorry about the lack of links, but this was enough of a pain to type on my phone as is, and I'm mostly just doing this to share cool math stuff and kill time at work.

[Nique]

Originally Posted by _mike

triangle of power.

Managed to escape the rabbit hole this google search sent me into.

Also watched some stuff about 'Hilbert Curves' that showed me how the infinite nature of math is useful for defining rules for finite realities.

[Sithdarth]

Generally speaking a survey of the history of math will turn up a very specific pattern that has repeated over and over again. Some pure mathematician does some work on some really abstract mathematical concept and no one (including the mathematician) thinks it's of any current practical use or that it will ever be of any practical use. Some amount of time later someone (either an applied mathematician or a scientists) stumbles on this supposedly purely abstract math and uses it to model some aspect of reality. Its pretty much the equivalent of a mathematical trope.

For example.

This is a pretty niffty short explination of why pure math is cool and has another example of something applied that came from the abstract.

[shiney]

I imagine that a snowflake that forms in a vacuum from atomic elements that are introduced consistently will always be identical. Like, to the alternate, there's the equation that creates the crystal from its elements, but in our world or universe there's also the equation that introduces those elements to the whole, the equation governing wind and temperature, gravity, light, and whatnot that ends up changing the overall structure of each individual flake.

This is my uneducated input and I will stop typing now.

[dementedmongoose]

My pet philosophy regarding the math/reality relationship is that math is "real," accurate, flawless, what have you, but that the reality we experience is in fact the approximation, and a rather crude and flawed one, at that. Using the snowflake example above, math produces a perfect snowflake every time. The universe, being a flawed approximation of reality, just can't seem to get one right.

It's like how an architect can design a building, and his design is flawless, but when the building is constructed, it has flaws. The architect (math) designed a perfect building (snowflake), but the contractor (reality) flubbed it, and now the building is a burning, crumpled heap on the side of a mountain twenty miles from where it was supposed to be.