Question Hi, I'm a German student in physics. something i noticed is that in every theory we start with a few postulates and conclude predictions about the behaviour of uninlevend objects. Even in quantum- mechanics we can make declarations about things our mind can't even imagine (like electrons). We do all this with math or let's say logic. and here is my question. Why does the universe behave in a logical way? is logic something humans have learned from the universe and only exists in this universe or is logic something that would exist even if this universe wouldn 't exist? Greetings Tobias D. and excuse my bad grammar

Accepted:
June 5, 2011

Comments

There are several questions in what you've asked, all of them interesting. I'm going to single out one of them. If I read you correctly, one thing you're asking is why we can describe the universe using math and logic -- why the universe "fits" our rules of math and logic. We can begin our stab at an answer by noticing that this fact -- that the universe can be described using math and logic -- is weaker than it might seem.

Imagine a computer screen of 1024 by 768 pixels, for a total of 786,432 pixels. For simplicity, imagine that each pixel is simply ether off or on; ignore color. Then there are 2786,432 possible patterns that could show up on the screen. Most of those are a jumble -- not "logical" or orderly in any interesting way. However, each can, in principle, be described. An exhaustive list stating for each pixel whether it's off or on would do. So the fact that the screen can be described using math/logic doesn't really constrain things much at all. Some number of pixels will be on, and the ones that are on will be located at some locations or other. One might say something similar about the universe at large. It could be a real hodge-podge, and yet whatever it's like, that could still be describable using math and principles of logic. (Whether we could come up with the descriptions is another matter.)

I hope that sheds at least some light. However, you might want more. First, we could ask why the universe is describable using relatively tidy math -- elegant laws of physics and such. Second, we could ask why it's describable using math at all, elegant or not. After all, our computer-screen example assumed a lot of order before we got to the details about arrangement of pixels.

On the first question: darned if I know! The universe does seem a lot less messy than it might have been, but whether there's any ultimately satisfying explanation for that fact is pretty unclear, not least because it's unclear what would count as an explanation. We might say, for example, that it's because the universe was designed by a rational deity. Perhaps that's true, but it raises the obvious question why this deity is disposed to make orderly arrangements and why it has an orderly mind. Perhaps the theologians have something to offer here, but I'll admit that I don't. And so one might feel a kind of blank wonder that the universe, God-made or not, isn't a mere mess. Einstein seems to have felt something like this, and I won't quarrel.

This may seem to provide a segue to the second question: why is the universe describable using math and logic at all? The trouble here is that it's not clear what we're asking. The theorems of math and logic seem to be necessary truths, and if so, they apply to any world whatsoever. In particular, they're not up tp us, and they don't depend on the details of this world. No matter what the world was like, nothing would count as having two contradictory properties. If one collection has 2 members and another non-overlapping collection has 3, then the total number of things in the two collections is 5. And so on. We have no idea (or at least I don't) what it would mean for the world not to fit principles of this sort.

Still, one might say that the principles of logic and, especially, math represent abstract forms that needn't be exemplified in the concrete world. Perhaps there's some dim hint of this in the Biblical verse about the world being without form and void before God acted on it. Perhaps it's possible that things could be so chaotic as to resist any coherent description at all. If that's so, however, then we seem doomed not to be able to think about it in any useful way, since it's not clear what it would mean to think coherently in a way that floated free of all logic. However, since this answer itself threatens to disintegrate into incoherence, we've probably reached a good place to stop.