Cleverbeans wrote:On the contrary. We only have a few pages worth of phenomenon that can be described mathematically, that's strong evidence of it's limitations.
Huh? What the **** are you talking about?
Einstein's General Relativity describes the behavior of ANY gravitational system. The Standard Model describes the three other fundamental forces - completely.
There are countless physical systems which are simple enough to be directly calculated by the above. And countless more which can be described in decent accuracy (like that baseball example we've discussed earlier).
You call that "a few pages worth of phenomenon"? Really? If what you said were true, that we need a few pages of math to describe a few pages worth of phanomena, then math would have been completely and utterly useless.
True, however it often coincides with the development of additional mathematical tools.
Not as often as you think.
The math for Einstein's General Relativity was invented by Riemann 50 years earlier.
Group Theory, which revolutionized quantum mechanics in the 1960's, was invented over 100 years earlier (at least as early as Galois in the 1830's).
Of-course, sometimes it does
happen the other way around. Newton inventing calculus, for example. But considering that calculus has so many diverse uses (most of which Newton never dreamed of), this is hardly supportive of your argument.
It works because we developed the language to intentionally describe it the way we perceive it. That doesn't seem particularly profound to me.
Think about it for a moment:
We look at the world around us, make up descriptions of what we see as we go along, and this gives us models which remain relevant for decades of new obseravations.
That doesn't seem profound to you? Boy, you're a very hard person to satisfy...
(and as I've already stated, even this miraculous description cuts mathematics short, because in most cases we've developed the mathematical language decades before it was relevant in any way to physics)
We invented the language specifically to describe the cosmos I don't see that as any more miraculous than painting a picture or building a scale model. If we build something to do a specific task, should we be surprised when it does that task?
When it works so well for 400 years, even after our view of the universe was revolutionized half a dozen times in the process: Yes, we should be surprised.
Especially when no other human language even comes close
to having this kind of power.
You want to compare our model of the universe to a scale model? Fine. It is an animated scale model of the entire universe. A model which is run by a computer program shorter than a modest chess program, yet it is so detailed that it describes... everything. And while it is not perfect, it is good enough to give us correct results in 99.99999% of the cases.
Oh, and in that once-in-a-blue-moon occurence where the model needs updating? We somehow have all the needed new parts waiting at bay to be installed. These new parts weren't even built for this purpose. They were built by the kids next door who just love to play with stuff and build beautiful complex structures.
Most of these kids actually regard our litte scale model with scorn. "The stuff we build doesn't have to be useful!" is their cry. Yet somehow, whenever we need a new part of our scale model, one of their toys fits the bill perfectly.
But other than that, yeah. It's just a scale model. Nothing too impressive
The intractability of the three body problem has absolutely nothing to do with math. It has to do with the simple fact that the position of the bodies after a very long time is incredibly sensitive to their starting positions.
Another way to say this is that because of the instability mathematics is useless for making predictions here. It simply can't describe what's happening because it requires specific information we have no access to.
Oh come on...
Mathematics can easily describe what's happening in the three body problem. It even tells you - exactly - how accurate your initial measurements need to be in order to be able to predict the future up to time t with the desired precision.
We can't actually do that? Well, that's too bad. But it isn't math's fault. Don't kill the messenger just because you don't like the message.
You're essentially saying the universe is too complex to be described mathematically.
I'm essentially saying that the universe is too complex for us to know everything, let alone predict the future.
So yes, if you expect mathematics to be some kind of lamp genie that can grant you any wish, you'll be sorely disappointed. Math is a language and a tool, not some kind of voodoo magic.
We already have a mathematical model which reconciles the two: String Theory.
Not one supported by evidence. It's very easy to describe the universe if we just assume it's a certain way but it's not meaningful.
Easy? In your last post you've claimed that this very task of mathematically unifying QM and GR is "impossible". You've made a huge deal of the claim that "math breaks down" when we try to do that.
So I'm telling you that it doesn't. Math, as a language, can handle it.
As for the evidence: We don't have the technology to look for it. We have zero experimental data, so we are forced to make a guess. What does this have to do with the limits of mathematics as a language?
Nobody here claims that math has no limits.
Then it's a question of how good those limits are.
That's exactly right. This question is at the crux of this entire discussion.
...So far it only describes a few pages of information...
Already refuted that at length. The real situation is exactly the opposite.
Information theory here to show our knowledge must be a form of lossy compression. In some sense have to blur reality to contain it in out tiny minds.
As gmalivuk already hinted, actual compression algorithms serve as a nice example of the things we've talked about here.
A typical photograph can be compressed by at least a factor of 2 WITHOUT ANY LOSS of information. English text can usually be compressed by at least a factor of 5, because of the patterns of the language.
The more pattern and order there is in a file, the better it compresses.
So, what does this have to do with our universe? Well, it seems to be full of patterns and repetition. There are about 10^90 particles in the universe, but only a few dozen different types of them, and only 4 basic types of possible interactions between them. The physical laws and the building blocks are the same everywhere. And this is exactly why our mathematical models work so well.
At this point I think we're working with different definitions of universal. In one sense it's universal since anyone could arrive at these conclusions by noticing the logical nature of causation and building from there. In another sense it's not universal in that most of the universe can't be described this way. Can we both agree on this or am I missing something?
I agree with your distinction of the two types of "universal".
But I can't agree with your claim that "most" of the universe can't be described mathematically. I grant you that SOME things seem to defy mathematical description, but these things are the exceptions and not the other way around.
And you know the really weird thing? It didn't have to be that way. I can't think of any a-priori reason to believe math would describe the world so well. Yet it does. So at least in our own universe, saying that "math is the universal language" seems like a reasonable thing to say.