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This is one of the oldest concepts in Ancient Philosophy. Not only did the Pythagoreans famously believe it, they also derived a number of other concepts from

This is one of the oldest concepts in Ancient Philosophy. Not only did the Pythagoreans famously believe it, they also derived a number of other concepts from it, including Eternal Return: "The Pythagoreans too used to say that numerically the same things occur again and again. It is worth setting down a passage from the third book of Eudemus' Physics in which he paraphrases their views: > ‘One might wonder-whether or not the same time recurs as some say it does. Now we call things 'the same' in different ways: things the same in kind plainly recur - e.g. summer and winter and the other seasons and periods; again, motions recur the same in kind - for the sun completes the solstices and the equinoxes and the other movements; But if we are to believe the Pythagoreans and hold that things the same in number recur - that you will be sitting here and I shall talk to you, holding this stick, and so on for everything else - then it is plausible that the same time too recurs.’" - Simplicius Commentary on the Physics 732.23-33." The notion of a mathematical universe was also quite famous with Platonists and Neoplatonists, who debated it over centuries. There was a form of Platonic revival -- which might owe something to Spinoza and Newton -- in the Early Modern period. In the 20th century, Konrad Zuse's "Digital Physics" is explicitly a Mathematical Universe Hypothesis. The way people attribute the concept to Tegmark is somewhat laughable, IMO. He just modernized small slices of it, in a rather haphazard way.

zoogeny 3y ago
I just happened to have the SEP article for Parmenides [1] open. It makes the claim that Plato was strongly influenced by Socrates, Pythagoras and Parmenides. It isn't easy to understand Parmenides and there are conflicting interpretations of his arguments. But he seems to be one of the first philosophers to connect that which can be thought (or understood) with that which is real through the abstract concept of "being" (ontology). [2] In some sense, mathematics is just a formalization of the attempt to capture the totality of "what may be conceived of by thought". 1. https://plato.stanford.edu/entries/parmenides/ https://plato.stanford.edu/entries/parmenides/ 2. https://en.wikipedia.org/wiki/Ontology#History https://en.wikipedia.org/wiki/Ontology#History (as an aside, one of the reasons we even have the thought of Parmenides is because Simplicius wrote out a large excerpt of his work in one of his own books)
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
dr_dshiv 3y ago
Read “Pythagoras Revived” for Neoplatonist views on the mathematical universe https://academic.oup.com/book/293 https://academic.oup.com/book/293 And listen to SHWEP.net (secret history of western esotericism) which is one of my favorite podcasts on the internet. The Pythagorean idea still has so much empirical opportunity and investigation left open. I think that math makes possibility which makes matter which makes information processing which make computation which makes math… so eventually computers get powerful enough to make new universes and it’s math all the way down.
kromem 3y ago
What's been a very interesting deep dive over the past few years is that there was almost a simulation theory like rethinking of these ideas attributed to Jesus of all people in the first to fourth centuries CE. Part of the debate on these ideas in antiquity that's often left out of discussions were the naturalists, specifically the Epicureans. Around 50 years before Jesus was born, Lucretius wrote De Rerum Natura, swapping the Greek word for indivisible ('atomos') with the Latin word for seed. And in that work, explicitly describing randomly scattered seeds plus survival of the fittest as the origin of life, even describing failed biological reproduction as "seed falling by the wayside of a path." So around the first century there's this ongoing pre-Neoplatonist debate between whether we are some physical incarnation of a pre-existing 'form' like Plato said (and connected to Judaism's dual creation of man in Genesis such as in Philio) and the idea that there was no design but simply randomness and survival to reproduce. An important nuance to Plato's ideas is in Book 10 of The Republic in the bed analogy, where he lays out the idea of a spiritual 'form' of a bed, then the physical bed, and then the 'image' of the physical bed as rendered by an artist (which he considered least valuable of all). Well this later apocryphal sect of Christianity is all about rejecting the Epicurean surety of final death by building on their own recurrence thinking using Plato's ideas - not of 'forms' (as the Neoplatonist influences on later developments in Gnosticism circle back to), but specifically on 'images.' The later Naassenes allegedly described their belief of an original spontaneous being bringing forth a creator of a non-physical copy of a physical original (with the original likened to a spontaneous tumor). They seemed to regard the first spontaneous being as 'Man'/'Adam' (which in Hebrew/Aramaic can mean the proper named individual or more generally humankind). So you have this rather wild reworking of Plato and Epicurus's ideas into a combined picture where naturalist physical origins can eventually result in non-physical recreation as enacted by a creator itself brought forth by an original mankind. What's particularly wild is their thinking that the proof for all this was in "motion and rest" and their claim that the ability to discover "an indivisible point as if from nothing" (how the Naassenes described their understanding of seeds in the mustard seed and sower parables) would not be possible in the physical. It's a radically different set of beliefs from what modern Christianity is across the board. Nearly the complete opposite. Very negative views of religious obligations and especially payment. Advocated self-discovery and being true to oneself. Saw salvation as a birthright entitlement. That being "born again" was literally being born as a baby into the non-physical copy of the original, not some symbolic ritual. Encouraged the drinking of words to become one with the author, not the consumption of blood and flesh. Overall one of the most interesting things I've ever studied.

zoogeny 3y ago

I just happened to have the SEP article for Parmenides [1] open. It makes the claim that Plato was strongly influenced by Socrates, Pythagoras and Parmenides. It isn't easy to understand Parmenides and there are conflicting interpretations of his arguments. But he seems to be one of the first philosophers to connect that which can be thought (or understood) with that which is real through the abstract concept of "being" (ontology). [2] In some sense, mathematics is just a formalization of the attempt to capture the totality of "what may be conceived of by thought". 1. https://plato.stanford.edu/entries/parmenides/ https://plato.stanford.edu/entries/parmenides/ 2. https://en.wikipedia.org/wiki/Ontology#History https://en.wikipedia.org/wiki/Ontology#History (as an aside, one of the reasons we even have the thought of Parmenides is because Simplicius wrote out a large excerpt of his work in one of his own books)

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

dr_dshiv 3y ago

Read “Pythagoras Revived” for Neoplatonist views on the mathematical universe https://academic.oup.com/book/293 https://academic.oup.com/book/293 And listen to SHWEP.net (secret history of western esotericism) which is one of my favorite podcasts on the internet. The Pythagorean idea still has so much empirical opportunity and investigation left open. I think that math makes possibility which makes matter which makes information processing which make computation which makes math… so eventually computers get powerful enough to make new universes and it’s math all the way down.

kromem 3y ago

What's been a very interesting deep dive over the past few years is that there was almost a simulation theory like rethinking of these ideas attributed to Jesus of all people in the first to fourth centuries CE. Part of the debate on these ideas in antiquity that's often left out of discussions were the naturalists, specifically the Epicureans. Around 50 years before Jesus was born, Lucretius wrote De Rerum Natura, swapping the Greek word for indivisible ('atomos') with the Latin word for seed. And in that work, explicitly describing randomly scattered seeds plus survival of the fittest as the origin of life, even describing failed biological reproduction as "seed falling by the wayside of a path." So around the first century there's this ongoing pre-Neoplatonist debate between whether we are some physical incarnation of a pre-existing 'form' like Plato said (and connected to Judaism's dual creation of man in Genesis such as in Philio) and the idea that there was no design but simply randomness and survival to reproduce. An important nuance to Plato's ideas is in Book 10 of The Republic in the bed analogy, where he lays out the idea of a spiritual 'form' of a bed, then the physical bed, and then the 'image' of the physical bed as rendered by an artist (which he considered least valuable of all). Well this later apocryphal sect of Christianity is all about rejecting the Epicurean surety of final death by building on their own recurrence thinking using Plato's ideas - not of 'forms' (as the Neoplatonist influences on later developments in Gnosticism circle back to), but specifically on 'images.' The later Naassenes allegedly described their belief of an original spontaneous being bringing forth a creator of a non-physical copy of a physical original (with the original likened to a spontaneous tumor). They seemed to regard the first spontaneous being as 'Man'/'Adam' (which in Hebrew/Aramaic can mean the proper named individual or more generally humankind). So you have this rather wild reworking of Plato and Epicurus's ideas into a combined picture where naturalist physical origins can eventually result in non-physical recreation as enacted by a creator itself brought forth by an original mankind. What's particularly wild is their thinking that the proof for all this was in "motion and rest" and their claim that the ability to discover "an indivisible point as if from nothing" (how the Naassenes described their understanding of seeds in the mustard seed and sower parables) would not be possible in the physical. It's a radically different set of beliefs from what modern Christianity is across the board. Nearly the complete opposite. Very negative views of religious obligations and especially payment. Advocated self-discovery and being true to oneself. Saw salvation as a birthright entitlement. That being "born again" was literally being born as a baby into the non-physical copy of the original, not some symbolic ritual. Encouraged the drinking of words to become one with the author, not the consumption of blood and flesh. Overall one of the most interesting things I've ever studied.