Math is weird

[forsyth]

So now I'm studying engineering, which means I'm studying more advanced math, like linear algebra and differential equations. Which are hard, or at least Diff EQ is. But then, math is a game for the young;.

But that's not the thing I'm noticing.  I'm noticing things where the different math I've learned mets and intersects, and works together.  And because this is engineering, how it works to predict and calculate the real world. Which sometimes seems really damn weird.& I can sit here with a pencil and paper and predict all sorts of physical things to decent degrees of accuracy. Why should it be that we can figure things like acceleration and stress out by putting numbers in columns and then messing with them? Take numbers and just mess with them and the answers fall out.

Now, the obvious answer to this is that math works to describe our physical universe, because it was created by people living in the physical universe, so naturally enough the rules we develop for mathematics are going to match up to the way the universe works, since we're using it to describe the universe. At least if the universe is broadly comprehensible and follows rules of cause and effect and repeatability. If it doesn't, then all our effort at trying to find rules is just us finding patterns that don't exist in chaos.

The problem with that is what about mathematics that doesn't describe things we can currently observe? Nth dimensional algebra, fractal spaces, and the most rarefied bits of math that don't seem like they have any relation to the universe? Do they represent things like strings and exotic matter bubbles? Or what?And if they represent those, how freaking weird is it we can figure out the rules before we find the things? And what about the N dimensional universes we can describe that may or may not be correct? Do they describe the non-spaces where other entities exist, which we would describe as squamous and rumose?

(Don't mind me. I've been reading Charlie Stross. But this kind of feeling does hit me every so often, it's just so WEIRD sometimes to do these complicated math to numbers and find out that yes, this reflects something that really happens)

Comments

[jokermage.livejournal.com]

You are confusing math with science. While the two are linked, they are not the same. Math is axiom-based logic system. Science is a system for describing the universe based on observations and testing.

[forsythferret.livejournal.com]

That's certainly possible, but math in its incarnation as something useful is created in and dependent on our three-dimensional universe. You could in theory create a mathematical logic set that's internally consistent where 2+2=5, and therefore wouldn't reflect the actual universe we inhabit (probably). Just as you can create a largely internally consistent narrative of a world that's not ours. Both subject to Godel's Incompleteness theorem.

But even at that, it's STILL fucking weird, limiting myself just to the mathematics used by various kinds of science.

But also as I've said, I'm reading the Atrocity Archives, by Charlie Stross, and that's helped put my brain in a weird place.

[the-s-guy.livejournal.com]

I'm not surprised. Math started as a way to describe the physical world. Whatever else it has grown into along the way, it still has fingers firmly in the pie of rocks and sticks. This means that no matter what bit of mathematics you start out with, it can be linked to something in the real world, with sufficient time.

Almost by definition, some parts of math are going to have what we perceive as 'closer' links to reality than others. And every time we discover one of those areas where we can see the shorter path, we jump up and down and proclaim OMG Math/Reality OTP!

Of course, we don't do it for those areas where we can't find a short path, but those areas don't sell magazine articles :)

[forsythferret.livejournal.com]

That's part of the point I was trying to make, that of course math has ties to reality, since it's made by us, living in reality. Which is why math works. But it's really strange sometimes to see things that represent reality fall out of seemingly arbitrary logic. Even though that logic, like everything else we do, has a base in reality, because that's the experiences we have to work with.

[moshchyk.livejournal.com]

[forsythferret.livejournal.com]