5 ms·

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 mus

by lutorm 15y ago

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?

m_for_monkey 15y ago
"Hogwash" 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.
- backprojection 15y ago
  "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
  - sev 15y ago
    Agreed. Forget Pi, maybe the way we count is flawed!
    - nodemaker 15y ago
      I think any way of counting will have the same basic axioms (http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms) Also See What are numbers, and what is their meaning?: Dedekind http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/dedek.html http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/ded...
- batista 15y ago
  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.
  - m_for_monkey 15y ago
    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." http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_and_worldview http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_a...
    - batista 15y ago
      Look we either talk about the exact pi, or not pi at all. In my computer there's no pi. You'd be surprised to hear about the wonderful concept of approximation. As for the "alternative", sounds like bogus science to me...
brudgers 15y ago
The description of a thing is not the thing itself.
- FreakLegion 15y ago
  Except in the case of performatives! http://en.wikipedia.org/wiki/Performative_utterance http://en.wikipedia.org/wiki/Performative_utterance
  - brudgers 15y ago
    Not exactly. 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.
    - batista 15y ago
      Wait, what? "I promise" is as much a description as "You promised". A description can be made in the first person.
      - brudgers 15y ago
        Austin's argument is that "I promise" is unique because saying "I promise" is the act of promising. "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/0674411528/ref=sr_1_1?ie=UTF8&qid=1327701128&sr=8-1 http://www.amazon.com/How-Do-Things-Words-Lectures/dp/067441... ]
        FreakLegion 15y ago
        He didn't say "You promised" is also a promise. Rather, he said "I promise" is also a description.
    - 15y ago
dexen 15y ago
http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle 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. There are suggestions that http://en.wikipedia.org/wiki/Planck_distance 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.
- loup-vaillant 15y ago
  > 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.
  - mattheww 15y ago
    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.
    - sixbrx 15y ago
      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.
keithnoizu 15y ago
My understanding of Godels is that it only implies that a super system will always be required to explain certain results in a base system. Which does not refute out ability to model nature.
- lutorm 15y ago
  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?
arctangent 15y ago
> Mathematics is a way of describing nature, not the other way around. I think this comes down to whether you are of the "realist" or the "Platonist" school of thought: [1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics http://en.wikipedia.org/wiki/Philosophy_of_mathematics
Dn_Ab 15y ago
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 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.

by lutorm 15y ago

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?

m_for_monkey 15y ago

"Hogwash" 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.

backprojection 15y ago
"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
- sev 15y ago
  Agreed. Forget Pi, maybe the way we count is flawed!
  - nodemaker 15y ago
    I think any way of counting will have the same basic axioms (http://en.wikipedia.org/wiki/Peano_axioms http://en.wikipedia.org/wiki/Peano_axioms) Also See What are numbers, and what is their meaning?: Dedekind http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/dedek.html http://www.math.uwaterloo.ca/~snburris/htdocs/scav/dedek/ded...
batista 15y ago
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.
- m_for_monkey 15y ago
  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." http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_and_worldview http://en.wikipedia.org/wiki/Buckminster_Fuller#Philosophy_a...
  - batista 15y ago
    Look we either talk about the exact pi, or not pi at all. In my computer there's no pi. You'd be surprised to hear about the wonderful concept of approximation. As for the "alternative", sounds like bogus science to me...

brudgers 15y ago

The description of a thing is not the thing itself.

FreakLegion 15y ago
Except in the case of performatives! http://en.wikipedia.org/wiki/Performative_utterance http://en.wikipedia.org/wiki/Performative_utterance
- brudgers 15y ago
  Not exactly. 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.
  - batista 15y ago
    Wait, what? "I promise" is as much a description as "You promised". A description can be made in the first person.
    - brudgers 15y ago
      Austin's argument is that "I promise" is unique because saying "I promise" is the act of promising. "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/0674411528/ref=sr_1_1?ie=UTF8&qid=1327701128&sr=8-1 http://www.amazon.com/How-Do-Things-Words-Lectures/dp/067441... ]
      - FreakLegion 15y ago
        He didn't say "You promised" is also a promise. Rather, he said "I promise" is also a description.
  - 15y ago

dexen 15y ago

http://en.wikipedia.org/wiki/Heisenberg_uncertainty_principle 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. There are suggestions that http://en.wikipedia.org/wiki/Planck_distance 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.

loup-vaillant 15y ago
> 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.
- mattheww 15y ago
  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.
  - sixbrx 15y ago
    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.

keithnoizu 15y ago

My understanding of Godels is that it only implies that a super system will always be required to explain certain results in a base system. Which does not refute out ability to model nature.

lutorm 15y ago
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?

arctangent 15y ago

> Mathematics is a way of describing nature, not the other way around. I think this comes down to whether you are of the "realist" or the "Platonist" school of thought: [1] http://en.wikipedia.org/wiki/Philosophy_of_mathematics http://en.wikipedia.org/wiki/Philosophy_of_mathematics

Dn_Ab 15y ago

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 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.