Hogwash. Mathematics is a way of describing nature, not the other way around. And doesn't Gödel's incompleteness theorem make it clear that any such attempt must necessarily be flawed?
Godel's incompleteness theorems are only applicable to a very specific type of mathematical system: formal axiomatic systems of a specific power (allow (+), (-), succ, ( * ), = , and a few more axioms relating these). Gödel says:
a) Within your formal system some statements simply cannot be proven nor disproven. Kinda like junk dna of your formal system. Very, very roughly, imagine a bunch of islands connected by bridges. Some bridges lead nowhere. Getting from A -> B, is a proof of something's truth. The set of bridges and islands is your deductive system. Godel 1st ICT says there are some islands of legend where you cannot show that no bridges lead to them nor can you find a path to get to them. They are effectively unreachable, "independent". You need a boat or plane to prove that the islands are even real instead of just a trick of fog.
b) GIT2 follows from 1 and says you cannot prove the consistency of your full formal system within your formal system.
Notice that our scientific theories thus far have been neither formal, consistent or complete. But what about nature? For Gödel to apply to nature the question basically is, does a sufficiently powerful formal system underlie nature? That is, is the universe a Turing machine? Buckminster Fuller looks to say yes or less. Buckminster Fuller is basically saying that nature does not compute with arbitrary reals (well what he is saying is actually stronger since he disallows computable reals). That is, hypercomputers do not exist in reality. A very reasonable stance I agree with. http://en.wikipedia.org/wiki/Hypercomputation
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The next lines of musing leave the realms of fact and edge into philosophy.
If nature is Turing equivalent and hence axiomatically encodable by a formal system or as a computable function then is it complete and consistent? Is a mind + universe a subset or superset of the universe? A system can be complete and consistent without us having access to a stronger system to prove it. So it is possible that the universe is complete. It could also be incomplete, we may never know. Something interesting is that Heisenberg's original terminology translates to indeterminacy not uncertainty. Work's attempting to bridge to Godel typically do so via leveraging Kolmogorov randomness.
There are suggestions that http://en.wikipedia.org/wiki/Planck_distance is the smallest distance (or size) nature handles.
You could say nature has no concept of real numbers.
No, no, no, you are over interpreting. The fact that you cannot measure with infinite precision doesn't mean it doesn't even makes sense to talk infinitely precisely about positions. You can for instance make thoughts experiments, by imagining an initial state infinitely precisely, then conclude that subsequent measures will give such and such results, this time with finite precision.
According to current models, nature runs on infinitely precise mathematics. (And according to most sensible current models, that math is also deterministic.) The fact that your access to those maths lack infinite precision doesn't mean the math itself is imprecise.
The measurement interpretation of the Heisenberg uncertainty principle is both a useful way to understand it, and historically, a way to ease experimentalists into accepting and believing it.
I only meant that we could describe (in principle) a hypothetical wave function with infinite precision. Meaning, at each exact point in our hypothetical configuration space, we would specify an exact amplitude. (With the usual caveats due to the fact that we're talking about a distribution, not a function.) From then, we could predict the experimental results, which are bound to yield finite precision.
Now, current physics say we will never infinitely accurately measure our wave function. But it also says that this wave function behaves lawfully, with infinite precision, from some (I think?) unknown initial state. Is there a problem left ?
Edit: it just hit me that there is a problem if you don't believe in Many Worlds. Just know that I think the Copenhagen interpretation is crazy (I don't believe in the collapse of the wave function), and that currently, I find some form of Many World Interpretation most likely.
I wouldn't dare to say that about Dr Fuller...
"Mathematics is a way of describing nature, not the other way around."
He doesn't say otherwise, he says that our description of nature (that we are using pi) is flawed.
Every description we'll ever have will probably be flawed to some degree.
I concur that it's hogwash
Also See What are numbers, and what is their meaning?: Dedekind http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/ded...
He also use Pi in computers, e.g to draw circles, and computers (and displays) are even more discrete that nature.
Has he come up with something better to use in Pi's place?
That we don't use "all" of Pi to draw a circle doesn't matter, the "Pi" kind of circle is like the perfect archetype. We don't make the "perfect bridge" or the "perfect car" either, that doesn't mean the concept of bridges and cars is useless.
Look we either talk about the exact pi, or not pi at all. In my computer there's no pi.
As for the alternative, at least he tried something:
"Fuller also claimed that the natural analytic geometry of the universe was based on arrays of tetrahedra. He developed this in several ways, from the close-packing of spheres and the number of compressive or tensile members required to stabilize an object in space. One confirming result was that the strongest possible homogeneous truss is cyclically tetrahedral."
http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_a...
You'd be surprised to hear about the wonderful concept of approximation.
As for the "alternative", sounds like bogus science to me...
I think this comes down to whether you are of the "realist" or the "Platonist" school of thought:
Austin's proposition is that the statement, "I promise," is a promise not a proposition.
But that does not make it a description of a state of affairs [or a picture of reality per Wittgensteinian]. A description would be, "You promised," and that is clearly not a promise.
YMMV.
"You promised" is not a promise, it is a description of the act of promising (carried out by someone else).
[see How to Do Things with Words: http://www.amazon.com/How-Do-Things-Words-Lectures/dp/067441... ]
Don't get me wrong though, I see the point you want to make; but it misses the mark in statements like Rimbaud's "Je est un autre." Writers, poets especially, do this a lot, pushing performativity to some limit where the form accomplishes what the meaning merely asserts.
Which totally reminds me of a line from Marshall McLuhan:
Just before an airplane breaks the sound barrier, sound waves become visible on the wings of the plane. The sudden visibility of sound just as sound ends is an apt instance of that great pattern of being that reveals new and opposite forms just as the earlier forms reach their peak performance.
Which does not refute out ability to model nature.