Well I second you on that. Even stronger:
All of (theoretical) science is a leaky abstraction. When an area is new, people are doing the spherical-cow-approximation willy nilly. After it gets established, corner cases start to surface.
Incidentally, theoretical physicists are the masters of creating spherical-cow-approximations and leaky-abstractions. They're always going for the next big unexplored territory. E.g., once QM got established as a theory, they moved on to high-energy, while there is about 1000x more work to be done picking up the pieces of QM in the areas of solid-state-physics and molecular-chemistry. (largely speaking that is; not everyone is like that).
http://euclid.trentu.ca/math/sb/misc/mathsci.html
> The natural sciences investigate the physical universe but mathematics does not,
> so mathematics is not really a natural science. This leaves open the subtler
> question of whether mathematics is essentially similar in method to the natural
> sciences in spite of the difference in subject matter. I do not think it is.
I'm not even including that famous Einstein quote about math.Example: When you are doing math in economics you are not doing something that is even more foundational than physics.
> if all that exists follows mathematical law
As a thought experiment, try the opposite direction: Math mirrors reality, not reality mirrors math. I don't see electrons solving quantum equations - equations describe an electron. The cannonball follows a trajectory that we can describe using math - but it doesn't do math. Sure, you can say that it does, implicitly, but IMHO that's stretching it a bit, I don't see the value in such a metaphor.From a certain level such questions become completely arbitrary and useless: Remember, it's your brain that interprets everything and you can just say whatever you want when there are no consequences.
If this was true, it would severely limit the usefulness of math. We'd see our predictability break down much sooner than we do actually. Read up on it here:
http://dilbert.com/strip/2015-06-07
I said - and I have no idea why I have to paraphrase my one sentence - to try a thought experiment, to see what happens when you reverse the direction.
Not to mention that you didn't really say anything? I have no idea what your point even is.
In any case, I should have read more carefully, because
> reality is a subset of what's mathematically possible
does not mean anything. It's a grammatically correct sentence, sure, and that's all. The number of (grammatically) correct sentences is definitely larger than the number of useful ones though :)I probably replied to the wrong post, but I wanted to say that math is in fact a tool for science - instead of being the most fundamental science itself. I've met some people, including mathematicians, who think that because everything can be described with math, it means that math is all that's needed to find the truth about reality. My point is that the process of appying math to find the model that best fits our own world is something that's outside of math itself.
EDIT: After skimming the Wikipedia article, both articles agree that it is a possible but not yet confirmed mechanism.
OTOH, we have a theory that classical computation adequately accounts for intelligence. Finding an unavoidable quantum route that nature has picked would certainly be interesting, despite that quantum Turing machines are also classically computable (I think).
I don't think we have a foundation for classical computation without thermodynamics, which is a classical theory whose ultimate foundations probably require quantum information theory.
Evolution contradicts this, because it is a genuinely new idea. Some may say it is the ONLY new idea in biology, but that's good enough.
It's often quoted here that "Computer Science is no more about computers than astronomy is about telescopes." You could extend this to "Biological science is no more about chemistry..."
There has never been "classical" theory for chemistry like there has been classical mechanics that works reasonably well within limits, just weird heuristic rules. Chemistry is quantum chemistry is quantum electrodynamics.