5 ms·

To be fair, for Plato mathematics is but one example of the processes of abstraction, differentiation, and integration, which demonstrate a constancy of princip

by w10-1 3y ago

To be fair, for Plato mathematics is but one example of the processes of abstraction, differentiation, and integration, which demonstrate a constancy of principles at work in both tangible and intangible products. Reducing Plato to Pythagorus is missing quite a bit. (It's Nietzsche who points out that the "eternal return of the same" is the only basis for an individual ethics that doesn't resort to a greater surrounding context.) But Tegmark seems to be saying the same thing logicians have always said: if it doesn't abide by the rules, we can ignore it: "I hypothesize that only computable and decidable (in Godel's sense) structures exist"

mjburgess 3y ago
Well that's a bad principle. Geometry isnt computable, and hence neither physics.
- naasking 3y ago
  Real and complex numbers of arbitrary precision aren't computable. Physics doesn't need such arbitrary precision as precision is always limited by the uncertainty principle [1], which is why physics is computable. [1] Peter Shor, "Because of quantum mechanics and the uncertainty principle, the value of a physical constant can't be defined to more than 60 or 70 digits. And any finite-precision number by definition is computable.", https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput...
  - mjburgess 3y ago
    1) ordinary classical physics is non-deterministic without infinite precision; this isnt observed 2) these "60 or 70" digit -type reasoning omit iterative problems, such as the number of digits required to specify the behaviour of a gas of 10^{big} particles over 10^{big} nanoseconds 3) QM is the most dependent on infinite precision out of all the theories of physics, requiring infinite-dim hilbert space to be linear. QM is linear, so we have infinite dimensions. Reality aint computable. This seems fairly obvious if you're not a csci zealot. QM only limits conjugate precision in conjugate varaiables. The Un-P' says absolutey nothing about whether reality is computable; and as far as QM weighs in, it is overwhelmingly against a computable universe. The formalism uses hilbert spaces indispensibly. ie., whilst expectations of conjugates may, via UP, have a "conjugate precision" the underlying wavefn requires infinite
    - naasking 3y ago
      Only an HNer would so boldly and unironically contradict Peter Shor. Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, and the precision of any real measurement is itself necessarily bounded, ergo infinite Hilbert spaces simply aren't relevant for any actual measurement. They are as unreal as a Turing machine's infinite tape, which is why quantum computers provide only polynomial speedup over Turing machines.
      - mjburgess 3y ago
        > Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, The number of particles in an interaction is irrelevant to the property of linearity requiring infinite dimensions. It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. The question, "are real numbers eliminable in physics?" is an extremely well-discussed on by more people than Mr Shor. There is overwhelming evidence they are not, and no evidence they are. All these local arguments do is show approximations work in some cases. They don't deal with the big issues. The UP does not constrain the value of physical constants, this is just a misunderstanding on Shor's part. It's only relevant to pairs of conjugates; not even to singles, since a single is not constrained by the UP at all. Many physicists are not well-positioned to answer questions in the philosophy of physics.
        naasking 3y ago
        > It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. Even if this were strictly true, which it's not for any real purpose, it's completely irrelevant because reality is non-linear. This non-linearity is how we get probabilities out of QM. Unless of course you're merely assuming a particular interpretation of QM that says otherwise, like MWI, but then I have no reason to accept this premise so your argument is still unconvincing. > There is overwhelming evidence they are not, and no evidence they are. In fact, the opposite is the case, and we don't even need any fancy arguments to demonstrate this: if what you say were true then a trivial proof refuting the Mathematical Universe hypothesis would have been published years ago. No such proof exists.
A_D_E_P_T 3y ago
> Reducing Plato to Pythagorus is missing quite a bit. The Pythagoreans would say just the opposite: That Plato took Pythagorean notions of a mathematical universe and twisted them out of bounds. Plato's notion of the abstract "intelligible world" or "world of forms" is especially a violation. Consider the writings of the Neopythagorean Plotinus, in a treatise titled "On the Question of Whether There are Ideas of Individuals": "If, though, the soul of each contains the expressed principles of all those it will successively enter, then, again, all will be in the intelligible world. And we do say that such expressed principles as the cosmos contains, each soul also contains. If, then, the cosmos contains the expressed principles not only of human beings but also of individual animals, so, too, does the soul. There will be, then, an unlimited number of expressed principles, unless the cosmos is recycled periodically, in which case the unlimitedness will reach a limit when the identical things recur." Here Plotinus quite correctly notes that eventually all things will wind up in the abstract intelligible world, each with their own form, until they recur. For there can be no unlimited number of expressed principles, the number of combinations of matter in space and time being finite, and in the end everything is its own irreducible form of ideal. In not understanding this, Plato arguably didn't understand Pythagoras at all. And of course Pythagorean sayings like "all is number," "things are the same again in number," etc. suggest an entirely classical understanding of a mathematical universe hypothesis. What's more, the Pythagorean abhorrence of irrational numbers hints at the distinction that Tegmark and others later draw: That they had two classes of mathematics -- a "realist" mathematics, and an "irrational" mathematics. > (It's Nietzsche who points out that the "eternal return of the same" is the only basis for an individual ethics that doesn't resort to a greater surrounding context.) The Eternal Return is another Ancient/Pythagorean concept that has been hotly debated over the past 2600 years. Short of popularizing the concept, Nietzsche has not contributed much to the debate, and his words on the topic are far from definitive.
- division_by_0 3y ago
  > The Eternal Return is another Ancient/Pythagorean concept that has been hotly debated over the past 2600 years. Short of popularizing the concept, Nietzsche has not contributed much to the debate, and his words on the topic are far from definitive. I think what Nietzsche is doing beyond popularizing the concept is establishing its strange relationship to nihilism ("Das ist die extremste Form des Nihilismus: das Nichts (das „Sinnlose“) ewig!"[0]) and its life-enhancing qualities: It is life-enhancing because it is impossible to live with it. This may sound strange, but this is the essence of Nietzsche's "pessimism of strength" concept. [0] NF-1886,5[71]
cscurmudgeon 3y ago
> logicians have always said: if it doesn't abide by the rules, we can ignore it: "I hypothesize that only computable and decidable (in Godel's sense) structures exist" No, thats far from what they say. Gödel's theorems (based on the first incompleteness theorem) are famous for saying the opposite of your last sentence.
- Sharlin 3y ago
  How so? Certainly Gödel doesn't say anything about the ontological status of any kind of structures, not in the Tegmark sense! Or, more accurately, Gödel forbids the existence (in both logical and Tegmarkian senses) mathematical structures that are (a) powerful enough, (b) complete, and (c) self-consistent. But Tegmark here seems to make a much stronger claim, namely that, in his ontology, structures that are (a) do not exist and thus everything ontologically real is both (b) and (c) – finite in the sense that neither undecidable nor semidecidable problems exist.
  - cscurmudgeon 3y ago
    > hypothesize that only computable and decidable (in Godel's sense) structures exist The arithmetic hierarchy is a study of non-computable/decidable sets. https://en.wikipedia.org/wiki/Arithmetical_hierarchy https://en.wikipedia.org/wiki/Arithmetical_hierarchy > Or, more accurately, Gödel forbids the existence (in both logical and Tegmarkian senses) mathematical structures that are (a) powerful enough, (b) complete, and (c) self-consistent. But Tegmark here seems to make a much stronger claim, namely that, in his ontology, structures that are (a) do not exist and thus everything ontologically real is both (b) and (c) – finite in the sense that neither undecidable nor semidecidable problems exist. Ys, but is different from claiming that "only computable and decidable exist"

by w10-1 3y ago

mjburgess 3y ago

Well that's a bad principle. Geometry isnt computable, and hence neither physics.

naasking 3y ago
Real and complex numbers of arbitrary precision aren't computable. Physics doesn't need such arbitrary precision as precision is always limited by the uncertainty principle [1], which is why physics is computable. [1] Peter Shor, "Because of quantum mechanics and the uncertainty principle, the value of a physical constant can't be defined to more than 60 or 70 digits. And any finite-precision number by definition is computable.", https://physics.stackexchange.com/questions/16889/non-computable-numbers-in-physics#comment40236_16893 https://physics.stackexchange.com/questions/16889/non-comput...
- mjburgess 3y ago
  1) ordinary classical physics is non-deterministic without infinite precision; this isnt observed 2) these "60 or 70" digit -type reasoning omit iterative problems, such as the number of digits required to specify the behaviour of a gas of 10^{big} particles over 10^{big} nanoseconds 3) QM is the most dependent on infinite precision out of all the theories of physics, requiring infinite-dim hilbert space to be linear. QM is linear, so we have infinite dimensions. Reality aint computable. This seems fairly obvious if you're not a csci zealot. QM only limits conjugate precision in conjugate varaiables. The Un-P' says absolutey nothing about whether reality is computable; and as far as QM weighs in, it is overwhelmingly against a computable universe. The formalism uses hilbert spaces indispensibly. ie., whilst expectations of conjugates may, via UP, have a "conjugate precision" the underlying wavefn requires infinite
  - naasking 3y ago
    Only an HNer would so boldly and unironically contradict Peter Shor. Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, and the precision of any real measurement is itself necessarily bounded, ergo infinite Hilbert spaces simply aren't relevant for any actual measurement. They are as unreal as a Turing machine's infinite tape, which is why quantum computers provide only polynomial speedup over Turing machines.
    - mjburgess 3y ago
      > Infinite dimensions aren't needed for any real interaction because the number of particles are bounded, The number of particles in an interaction is irrelevant to the property of linearity requiring infinite dimensions. It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. The question, "are real numbers eliminable in physics?" is an extremely well-discussed on by more people than Mr Shor. There is overwhelming evidence they are not, and no evidence they are. All these local arguments do is show approximations work in some cases. They don't deal with the big issues. The UP does not constrain the value of physical constants, this is just a misunderstanding on Shor's part. It's only relevant to pairs of conjugates; not even to singles, since a single is not constrained by the UP at all. Many physicists are not well-positioned to answer questions in the philosophy of physics.
      - naasking 3y ago
        > It is straightforward to show QM isnt a linear theory in anything other than an inf-dim space. Even if this were strictly true, which it's not for any real purpose, it's completely irrelevant because reality is non-linear. This non-linearity is how we get probabilities out of QM. Unless of course you're merely assuming a particular interpretation of QM that says otherwise, like MWI, but then I have no reason to accept this premise so your argument is still unconvincing. > There is overwhelming evidence they are not, and no evidence they are. In fact, the opposite is the case, and we don't even need any fancy arguments to demonstrate this: if what you say were true then a trivial proof refuting the Mathematical Universe hypothesis would have been published years ago. No such proof exists.

A_D_E_P_T 3y ago

> Reducing Plato to Pythagorus is missing quite a bit. The Pythagoreans would say just the opposite: That Plato took Pythagorean notions of a mathematical universe and twisted them out of bounds. Plato's notion of the abstract "intelligible world" or "world of forms" is especially a violation. Consider the writings of the Neopythagorean Plotinus, in a treatise titled "On the Question of Whether There are Ideas of Individuals": "If, though, the soul of each contains the expressed principles of all those it will successively enter, then, again, all will be in the intelligible world. And we do say that such expressed principles as the cosmos contains, each soul also contains. If, then, the cosmos contains the expressed principles not only of human beings but also of individual animals, so, too, does the soul. There will be, then, an unlimited number of expressed principles, unless the cosmos is recycled periodically, in which case the unlimitedness will reach a limit when the identical things recur." Here Plotinus quite correctly notes that eventually all things will wind up in the abstract intelligible world, each with their own form, until they recur. For there can be no unlimited number of expressed principles, the number of combinations of matter in space and time being finite, and in the end everything is its own irreducible form of ideal. In not understanding this, Plato arguably didn't understand Pythagoras at all. And of course Pythagorean sayings like "all is number," "things are the same again in number," etc. suggest an entirely classical understanding of a mathematical universe hypothesis. What's more, the Pythagorean abhorrence of irrational numbers hints at the distinction that Tegmark and others later draw: That they had two classes of mathematics -- a "realist" mathematics, and an "irrational" mathematics. > (It's Nietzsche who points out that the "eternal return of the same" is the only basis for an individual ethics that doesn't resort to a greater surrounding context.) The Eternal Return is another Ancient/Pythagorean concept that has been hotly debated over the past 2600 years. Short of popularizing the concept, Nietzsche has not contributed much to the debate, and his words on the topic are far from definitive.

division_by_0 3y ago
> The Eternal Return is another Ancient/Pythagorean concept that has been hotly debated over the past 2600 years. Short of popularizing the concept, Nietzsche has not contributed much to the debate, and his words on the topic are far from definitive. I think what Nietzsche is doing beyond popularizing the concept is establishing its strange relationship to nihilism ("Das ist die extremste Form des Nihilismus: das Nichts (das „Sinnlose“) ewig!"[0]) and its life-enhancing qualities: It is life-enhancing because it is impossible to live with it. This may sound strange, but this is the essence of Nietzsche's "pessimism of strength" concept. [0] NF-1886,5[71]

cscurmudgeon 3y ago

> logicians have always said: if it doesn't abide by the rules, we can ignore it: "I hypothesize that only computable and decidable (in Godel's sense) structures exist" No, thats far from what they say. Gödel's theorems (based on the first incompleteness theorem) are famous for saying the opposite of your last sentence.

Sharlin 3y ago
How so? Certainly Gödel doesn't say anything about the ontological status of any kind of structures, not in the Tegmark sense! Or, more accurately, Gödel forbids the existence (in both logical and Tegmarkian senses) mathematical structures that are (a) powerful enough, (b) complete, and (c) self-consistent. But Tegmark here seems to make a much stronger claim, namely that, in his ontology, structures that are (a) do not exist and thus everything ontologically real is both (b) and (c) – finite in the sense that neither undecidable nor semidecidable problems exist.
- cscurmudgeon 3y ago
  > hypothesize that only computable and decidable (in Godel's sense) structures exist The arithmetic hierarchy is a study of non-computable/decidable sets. https://en.wikipedia.org/wiki/Arithmetical_hierarchy https://en.wikipedia.org/wiki/Arithmetical_hierarchy > Or, more accurately, Gödel forbids the existence (in both logical and Tegmarkian senses) mathematical structures that are (a) powerful enough, (b) complete, and (c) self-consistent. But Tegmark here seems to make a much stronger claim, namely that, in his ontology, structures that are (a) do not exist and thus everything ontologically real is both (b) and (c) – finite in the sense that neither undecidable nor semidecidable problems exist. Ys, but is different from claiming that "only computable and decidable exist"