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?
http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principl... describes nature's limit to precision of measurement of position and speed vector of objects. In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision.
> In physics, it does not make sense to discuss position (nor boundaries) of object with infinite or absolute precision.
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.
Actually, it's you who is doing the over interpreting. The Heisenberg uncertainty principle is a physical constraint that wave functions obey. If you define a state with an infinitely precise location, then the range of momentums is infinite. This result is fairly easy to reproduce, so it would probably be instructive to try it.
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.
Just to be sure: the wave function is still a distribution of complex amplitude over a configuration space, right ? If I understand, you are saying is that if we have a Dirac peak at some point, then the momentum spread everywhere (the infinite momentum). I don't dispute that.
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'm not sure what your argument really is here. Your very invocation of "the wave function" implies continuity in the evolution of the state vectors, described by the wave equation - it matters not that results of macroscopic measurements will only produce quantized results. You still used continuity of the more abstract (but no less "real") state vector evolution.
The quote is not hogwash, in fact it looks to me like you do not oppose the thesis of the quote.
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
-----------
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.
This is not mathematics though, nor science, it's just the meta-mathematical philosophical opinion of a guy (mostly self-taught, by the way, and know for his cool inventions and ideas, not for his deep mathematical insights).
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.
Yes, it's "only" philosophy, but that doesn't mean it's utter BS.
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."
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.
Austin doesn't say performatives aren't propositions. Note that there are still truth-evaluable performatives, and that as Austin and others continued down the il/perlocutionary rabbit hole, they came to regard all language as essentially performative.
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.
I never said it refutes our ability to model nature. I said it seems to refute the idea that nature itself runs on mathematics. Because what is the super system of nature?
