The Mathematical Universe Hypothesis (2007)(arxiv.org)
arxiv.org
The Mathematical Universe Hypothesis (2007)
https://arxiv.org/abs/0704.0646
118 comments
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/
2. 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)
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/
2. 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)
Read “Pythagoras Revived” for Neoplatonist views on the mathematical universe
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.
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.
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"
(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"
> 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.
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.
> 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]
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]
> 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.
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.
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.
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.
> 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
> 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"
The arithmetic hierarchy is a study of non-computable/decidable sets.
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"
Well that's a bad principle. Geometry isnt computable, and hence neither physics.
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-comput...
[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-comput...
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
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
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.
> 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.
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.
> 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.
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.
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.
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.
I appreciate Sabine Hossenfelder's take on MUH[1]:
"...the justification that we have for calling some mathematical structures real is that they describe what we observe. This means we have no rationale for talking about the reality of mathematics that does not describe what we observe, therefore the Mathematical Universe Hypothesis isn't scientific."
"...this is a belief-based statement, not supported by evidence."
[1] https://www.youtube.com/watch?v=CTpp0EChDbI
"...the justification that we have for calling some mathematical structures real is that they describe what we observe. This means we have no rationale for talking about the reality of mathematics that does not describe what we observe, therefore the Mathematical Universe Hypothesis isn't scientific."
"...this is a belief-based statement, not supported by evidence."
[1] https://www.youtube.com/watch?v=CTpp0EChDbI
Sabine is either straw manning or didn't read the actual paper, because the whole point of Max's paper is that there's no substrate or quintessence beyond just the mathematical properties.
If her counter is that "No there isn't just mathematical properties", then what is there? What is a quark if not its mathematical properties?
If her counter is that "No there isn't just mathematical properties", then what is there? What is a quark if not its mathematical properties?
One thing this hypothesis has going for it, from a purely armchair metaphysics perspective, is that it gives some kind of answer to the question 'why does anything exist'. If mathematics (or the underlying 'thing' that math describes) is objectively true or real, then it could have a platonic existence by power of its own self reference.
It also explains why all physical laws are mathematical and all physical properties are quantifiable ('mathematics is the language of the universe' as Galileo said).
I still don't believe in it for several reasons. But I believe that it is the only logical conclusion of a purely materialist worldview.
It also explains why all physical laws are mathematical and all physical properties are quantifiable ('mathematics is the language of the universe' as Galileo said).
I still don't believe in it for several reasons. But I believe that it is the only logical conclusion of a purely materialist worldview.
> If mathematics (or the underlying 'thing' that math describes) is objectively true or real, then it could have a platonic existence by power of its own self reference.
Indeed; I managed to independently arrive at this part of the idea, I think even before the Mathematical Universe Hypothesis was published.
It's even more cognitively unstable than Boltzmann brains, but maths is also the only thing I can think of that doesn't need to be caused in order to exist.
https://kitsunesoftware.wordpress.com/2018/08/26/mathematica...
Indeed; I managed to independently arrive at this part of the idea, I think even before the Mathematical Universe Hypothesis was published.
It's even more cognitively unstable than Boltzmann brains, but maths is also the only thing I can think of that doesn't need to be caused in order to exist.
https://kitsunesoftware.wordpress.com/2018/08/26/mathematica...
> maths is also the only thing I can think of that doesn't need to be caused in order to exist
I never understood this line of argument. Plainly, there is something at the beginning of the universe (or an eternal existence in some other way) which doesn't need to be caused in order to exist. So then, why do we take this notion that everything needs to have a cause to exist as some kind of rule, when it is self-evidently broken?
I never understood this line of argument. Plainly, there is something at the beginning of the universe (or an eternal existence in some other way) which doesn't need to be caused in order to exist. So then, why do we take this notion that everything needs to have a cause to exist as some kind of rule, when it is self-evidently broken?
The argument is "only X has property Y, therefore this other thing of unknown nature with property Y must also be an X".
Well, except for the bit where X is cognitively unstable, and also for the other bit where I don't seriously believe the fact that I personally can't imagine alternatives means they don't exist.
Well, except for the bit where X is cognitively unstable, and also for the other bit where I don't seriously believe the fact that I personally can't imagine alternatives means they don't exist.
If mathematics (or the underlying 'thing' that math describes) is objectively true or real, then it could have a platonic existence by power of its own self reference.
My response would be, that math is not true. It is build on top of logic, which is not universally true. x && !x == false, sounds right, doesn't it? In one place at one time it either rains or it does not rain. But this is, I would argue, an observed fact about our universe, not some universal truth. Imagine a different universe, something like the Everett multiverse where all possibilities actually happen and where the inhabitants of that universe experience all the different branches. For them it could be raining and not raining at the same time in the same place, their logic might say x && !x == true.
My response would be, that math is not true. It is build on top of logic, which is not universally true. x && !x == false, sounds right, doesn't it? In one place at one time it either rains or it does not rain. But this is, I would argue, an observed fact about our universe, not some universal truth. Imagine a different universe, something like the Everett multiverse where all possibilities actually happen and where the inhabitants of that universe experience all the different branches. For them it could be raining and not raining at the same time in the same place, their logic might say x && !x == true.
Would you agree that an alien civilization completely separate from humans but equally intelligent would also be likely to discover Pythagoras theorem (with a different name and different symbolics)? To me that would imply that its truth is independent of human perception.
Math and logic are fundamentally some kind of game, you make up some rules and axioms and then you figure out the consequences. So the interesting question is which rules and axioms you pick and I would guess aliens in our universe would pick similar rules and axioms as we did because they will want to describe the same universe. And they would probably discover the Pythagorean theorem.
But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best.
So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?
But in a different universe without space dimensions or multiple time dimensions or discrete space dimensions or something completely incomprehensible to us for which we do not even have concepts and words, there I am not sure that they would certainly come up with the axioms of Euclidean space and discover the Pythagorean theorem, or it might be a very esoteric mathematical structure to them at best.
So it seems there is still something universal in there, the idea of inventing rules and axioms and figuring out the consequences, which could maybe essentially boil down to computations or something like that. But even there I am not so sure that it is truly universal, the original idea of a Turing machine is an abstraction of repeatedly modifying some state over time, and can we not imagine a universe where updating state over time makes no sense?
i don't find this argument convincing. it depends, at minimum, on bounding 'aliens' to mean something reasonably close to humans. if we allow aliens to be arbitrarily different, than i don't see a reason to bound their abstract symbolic technical development any more than arbitrarily distant to human development. otoh, if we assume that aliens are significantly similar to humans in some specific respects, then it seems likely to me that their technical development will also have substantial similarities, including but not limited to their abstract symbolic development. the space of abstractions seems large, and our particular path through it is historically contingent in both obvious and likely non-obvious ways; likewise for the formal inferential constructs which we use to parameterize this space
If you look carefully at Frege’s original notations you’ll see that all logical connectives are simply if-then statements with the exception of ‘not’. Logic is just formalized cause and effect, partly inspired by Hume. Cause and effect seems to reflect some deep truth about the universe.
How can that even make sense without any axioms. You can’t say logic doesn’t work because i proved a true statement is false.
You mean how can I do any kind of reasoning if I think the logic I use for reasoning does work or at the very least is kind of an arbitrary choice? I have no answer for that. And that is very similar to something else that always bothered me. I think there is no free will, everything in the universe just mindlessly follows the laws of physics. But if that is the case, how can anyone do any meaningful reasoning? If you just think, write and say what the laws of physics make you think, write or say, what guarantees that your thoughts or words follow any logic?
I have no good answer, at best some extremely vague idea of consistency, that the laws of physics in our universe have some logic to them or maybe better that they imply some logic that is useful to reason about them and that this implied logic gets imprinted onto composit systems in the universe. But even if that was true, you would end up with new questions, why is it true and does it have to be true?
And I can think of at least one more instance of a similar problem, namely what guarantees that your perception of the the world is in any way linked to an actually existing world that you inhabit? How do you know that you are not just hallucinating the universe into existence? There the usual answer is, I think, to just assume it, otherwise any reasoning would be doomed right from the beginning as you can never know whether there is any real universe or whether you are just making it up.
The lesson is probably that reasoning from the inside - from your mind about your mind, from inside the universe about the universe, with logic about logic - is really hard, in the same way that Gödel's incompleteness theorems tell us about the limits of reasoning with math about math.
I have no good answer, at best some extremely vague idea of consistency, that the laws of physics in our universe have some logic to them or maybe better that they imply some logic that is useful to reason about them and that this implied logic gets imprinted onto composit systems in the universe. But even if that was true, you would end up with new questions, why is it true and does it have to be true?
And I can think of at least one more instance of a similar problem, namely what guarantees that your perception of the the world is in any way linked to an actually existing world that you inhabit? How do you know that you are not just hallucinating the universe into existence? There the usual answer is, I think, to just assume it, otherwise any reasoning would be doomed right from the beginning as you can never know whether there is any real universe or whether you are just making it up.
The lesson is probably that reasoning from the inside - from your mind about your mind, from inside the universe about the universe, with logic about logic - is really hard, in the same way that Gödel's incompleteness theorems tell us about the limits of reasoning with math about math.
You're way over thinking it. You either have causality/time component, and can derive some basic axioms that get you existence or not existence (boolean) or you don't. If you have the former, we have turing completeness, and there we go.
If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.
If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.
You either have causality/time component [...]
I don't understand what you mean.
If you get distracted by a message on your phone and hit a tree with your car, the person sending you the message caused you to be distracted which caused you to hit the tree. But did not also your driving teacher cause this because he did not get you to understand to not use your phone while driving well enough? And your parents because without them you would not exist and be driving a car? And the phone designers and manufactures because without them there would be no phone to distract you. And no car without the car manufacturer. And no tree without the person planting it exactly where you hit it?
Causality is at the very least a really tricky concept, we usually just pick something pretty arbitrarily and declare it the cause. And what about the relationships between time, space, change, events, correlation, cause, and effect - what comes first, what depends on what? Does time enable change or does change define time? Does causality cause change or does change define causality? Does causality even exist fundamentally, after all cause and effect are no where to be found in the fundamental laws of physics? Is it just a human abstraction to talk about the world? What does the theory of relativity tell us as the ordering of events is observer dependent?
[...] and can derive some basic axioms that get you existence or not existence (boolean) or you don't.
Derive axioms from what, causality and time? And does deriving axioms even make sense, are they not the things that you just postulate as true without further justification? And who said that existence - or anything for that matter - has to be binary? From the law of excluded middle which is an axiom and not even universally accepted in our universe? And what does existence even mean? Is there only one kind of existence or are there several? Does wetness exist in the same way as the keyboard I am just typing on?
If you have the former, we have turing completeness, and there we go.
What is the former and how on earth did we get from whatever the former is to Turing completeness and why does it matter?
If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.
I don't think it really matters whether it interesting or not, but this sounds a bit like you are just dismissing my main point in a single sentence - if there could be universe where our logic does not apply or is even wrong, how can we call our logic and the math on top of it true and assign some kind of Platonic existence or whatnot to it, if it is at best true relative to our universe?
Maybe I am overthinking it but I would counter that you are underthinking it.
I don't understand what you mean.
1. causality and time component
2. causality or time component
3. causality and time component are two words for the same thing
4. causality and time component are deeply connected, maybe depend on each other or imply each other
5. something else
If you get distracted by a message on your phone and hit a tree with your car, the person sending you the message caused you to be distracted which caused you to hit the tree. But did not also your driving teacher cause this because he did not get you to understand to not use your phone while driving well enough? And your parents because without them you would not exist and be driving a car? And the phone designers and manufactures because without them there would be no phone to distract you. And no car without the car manufacturer. And no tree without the person planting it exactly where you hit it?
Causality is at the very least a really tricky concept, we usually just pick something pretty arbitrarily and declare it the cause. And what about the relationships between time, space, change, events, correlation, cause, and effect - what comes first, what depends on what? Does time enable change or does change define time? Does causality cause change or does change define causality? Does causality even exist fundamentally, after all cause and effect are no where to be found in the fundamental laws of physics? Is it just a human abstraction to talk about the world? What does the theory of relativity tell us as the ordering of events is observer dependent?
[...] and can derive some basic axioms that get you existence or not existence (boolean) or you don't.
Derive axioms from what, causality and time? And does deriving axioms even make sense, are they not the things that you just postulate as true without further justification? And who said that existence - or anything for that matter - has to be binary? From the law of excluded middle which is an axiom and not even universally accepted in our universe? And what does existence even mean? Is there only one kind of existence or are there several? Does wetness exist in the same way as the keyboard I am just typing on?
If you have the former, we have turing completeness, and there we go.
What is the former and how on earth did we get from whatever the former is to Turing completeness and why does it matter?
If you don't, well, sure, whose to say there isn't a universe where you can't have both presence, absence, and a time component but it's not all that interesting.
I don't think it really matters whether it interesting or not, but this sounds a bit like you are just dismissing my main point in a single sentence - if there could be universe where our logic does not apply or is even wrong, how can we call our logic and the math on top of it true and assign some kind of Platonic existence or whatnot to it, if it is at best true relative to our universe?
Maybe I am overthinking it but I would counter that you are underthinking it.
To be honest, I'm not even particularly impressed by the claim that the only mathematical universes that can exist are the self-consistent ones. I think that is mostly stipulated in these theories for post hoc reasons. So some of them aren't consistent... so what? Do the consistency police come along and strip you of your "existence"? How? Why? We humans use inconsistent logics all the time. When confronted by inconsistencies we often just fix them up, either with some other logic or just plain ad hoc new rules. Inconsistent universes can similarly each be rescued by an infinite number of "fixups", up to and including uncountably infinite functions that simply brute force resolve the inconsistencies. This renders the term "inconsistent" meaningless in this context because rather than an inconsistent universe not being able to "exist" it instead represents some infinite class of existing universes with some fixups applied.
The main problem I have with this line of argumentation is that in its zeal to explain why anything exists, it actually goes all the way to the other end of the spectrum and can't explain why anything doesn't exist. But clearly there are things that don't exist, by virtue of the fact that the subjective experience of being in a universe where literally everything exists would be one of total chaos; in any given moment, the countably-infinite possible futures where the next subjective instant is "reasonable" to you is dwarfed by the uncountably infinite possible futures that contain an embedding of "you" and your next subjective instant is not reasonable to you. (And if you're objecting to my casual assertion that your next instant is at best countably infinite, I'm already erring on the side of giving grace to the argument; I'd personally characterize them as straight-up finite.)
Things exist; some things also don't exist. The mathematical universe hypothesis covers the first at the cost of failing the second. Math isn't parabolas and conic sections and tiny integers getting added together; math is uncountably infinite functions of uncountably infinite structures being mapped to other uncountably infinite structures with no pattern, out of which we carve our little niches that are useful and comprehensible and mistake them as being the rule, rather than than the vanishingly tiny exception. Something isn't just causing things to exist, it is also holding back the incomprehensible chaos of total, undifferentiated existence.
(The fine tuning of the physical universe is a nearly insignificant mystery next to this. How is reality reasonable to any degree at all? Forget the question of life, how does there exist any structure that has a reasonable subjective existence rather than total, utter chaos beyond any capability we have to imagine?)
The main problem I have with this line of argumentation is that in its zeal to explain why anything exists, it actually goes all the way to the other end of the spectrum and can't explain why anything doesn't exist. But clearly there are things that don't exist, by virtue of the fact that the subjective experience of being in a universe where literally everything exists would be one of total chaos; in any given moment, the countably-infinite possible futures where the next subjective instant is "reasonable" to you is dwarfed by the uncountably infinite possible futures that contain an embedding of "you" and your next subjective instant is not reasonable to you. (And if you're objecting to my casual assertion that your next instant is at best countably infinite, I'm already erring on the side of giving grace to the argument; I'd personally characterize them as straight-up finite.)
Things exist; some things also don't exist. The mathematical universe hypothesis covers the first at the cost of failing the second. Math isn't parabolas and conic sections and tiny integers getting added together; math is uncountably infinite functions of uncountably infinite structures being mapped to other uncountably infinite structures with no pattern, out of which we carve our little niches that are useful and comprehensible and mistake them as being the rule, rather than than the vanishingly tiny exception. Something isn't just causing things to exist, it is also holding back the incomprehensible chaos of total, undifferentiated existence.
(The fine tuning of the physical universe is a nearly insignificant mystery next to this. How is reality reasonable to any degree at all? Forget the question of life, how does there exist any structure that has a reasonable subjective existence rather than total, utter chaos beyond any capability we have to imagine?)
From [0]:
"Something like this view is defended by philosophers such as James Ladyman and Don Ross in their book 'Every Thing Must Go: Metaphysics Naturalized', and by the physicist Max Tegmark. I have a lot to say about Ladyman and Ross’s project in the forthcoming 'Aristotle’s Revenge'[1], all of it critical. Suffice it for present purposes to note that this sort of view essentially identifies the physical world with a kind of Platonic abstract object. Ladyman and Ross try to deal with this problem by denying that there is a clear distinction between abstract and concrete. As I argue in the book, this position is incoherent and the arguments for it are entirely question-begging. Moreover, even apart from that it doesn’t really solve the problem at all, because (as the Aristotelian would argue) Platonism itself essentially blurs the distinction between the abstract and the concrete. For a Platonic Form is characterized both as a universal (and hence as abstract) and as a substance (and hence as concrete). To blur the abstract/concrete distinction is to fall deeper into Platonism, rather than to avoid it."
[0] https://edwardfeser.blogspot.com/2019/01/materialism-subvert...
[1] https://a.co/d/6JNDiCH
"Something like this view is defended by philosophers such as James Ladyman and Don Ross in their book 'Every Thing Must Go: Metaphysics Naturalized', and by the physicist Max Tegmark. I have a lot to say about Ladyman and Ross’s project in the forthcoming 'Aristotle’s Revenge'[1], all of it critical. Suffice it for present purposes to note that this sort of view essentially identifies the physical world with a kind of Platonic abstract object. Ladyman and Ross try to deal with this problem by denying that there is a clear distinction between abstract and concrete. As I argue in the book, this position is incoherent and the arguments for it are entirely question-begging. Moreover, even apart from that it doesn’t really solve the problem at all, because (as the Aristotelian would argue) Platonism itself essentially blurs the distinction between the abstract and the concrete. For a Platonic Form is characterized both as a universal (and hence as abstract) and as a substance (and hence as concrete). To blur the abstract/concrete distinction is to fall deeper into Platonism, rather than to avoid it."
[0] https://edwardfeser.blogspot.com/2019/01/materialism-subvert...
[1] https://a.co/d/6JNDiCH
Also PBS Spacetime: https://www.pbs.org/video/what-if-the-universe-is-math-mysv4...
Mathematical universe is obviously true yet uselessly ahead of its time in the same way as Schrodinger asserting heredity was controlled by an "aperiodic crystal" a decade before DNA was discovered.
> Ahead of its time.
> First posited by Pythagoreans 2600 years ago, and by various other people in the centuries since.
> Centuries older than Christianity, Islam, and Rabbinic Judaism.
It's not ahead of its time. Instead, it's a very old concept that is manifestly disfavored because it doesn't work as a folk metaphysics. (i.e. as something that the common man can understand with ease, which provides him with an explanation of the world.) It also doesn't work, within reasonable bounds, as the foundation of an ethical system.
> First posited by Pythagoreans 2600 years ago, and by various other people in the centuries since.
> Centuries older than Christianity, Islam, and Rabbinic Judaism.
It's not ahead of its time. Instead, it's a very old concept that is manifestly disfavored because it doesn't work as a folk metaphysics. (i.e. as something that the common man can understand with ease, which provides him with an explanation of the world.) It also doesn't work, within reasonable bounds, as the foundation of an ethical system.
I find it interesting that we can think about [simple and complex] mathematical structures. How did we get the ability to do so and why we can do so?
I distinguish between mathematical structures and "reality". From my perspective, mathematical structures are being used provide succinct description of the perceptible portion of "reality", the Universe as we say. Need all mathematical structures exist?
What can we say about [biological, AI, or even theoretical] systems that can deal with abstract mathematical structures: to be able to construct, modify, specialise or generalise such structures in a extra-computable manner?
I distinguish between mathematical structures and "reality". From my perspective, mathematical structures are being used provide succinct description of the perceptible portion of "reality", the Universe as we say. Need all mathematical structures exist?
What can we say about [biological, AI, or even theoretical] systems that can deal with abstract mathematical structures: to be able to construct, modify, specialise or generalise such structures in a extra-computable manner?
>How did we get the ability to do so and why we can do so?
By having to predict or own futures?
When we're deciding which tree to climb for the most fruit and balancing our choice against the one that attracts the least predators we are taking a lot of complex concepts in a very fuzzy manner. The threat we imagine may not be real. The rewards we imagine may not pan out.
This reality simulator we made to survive happened to also work very well when we extend it into maths, which if math is reality would make sense.
By having to predict or own futures?
When we're deciding which tree to climb for the most fruit and balancing our choice against the one that attracts the least predators we are taking a lot of complex concepts in a very fuzzy manner. The threat we imagine may not be real. The rewards we imagine may not pan out.
This reality simulator we made to survive happened to also work very well when we extend it into maths, which if math is reality would make sense.
Relevant discussion https://www.lesswrong.com/posts/HBHsFCeAMSqMD7Td7/does-the-s...
I wondered aren't the structures where there's more randomness than what we see more likely since there are a lot of different ways for it to be random.
The discussion helped me realise it's a measure problem, and a measure can be constructed according to the complexity of the mathematical structure.
Makes sense, but why should the measure be constructed like that?
I wondered aren't the structures where there's more randomness than what we see more likely since there are a lot of different ways for it to be random.
The discussion helped me realise it's a measure problem, and a measure can be constructed according to the complexity of the mathematical structure.
Makes sense, but why should the measure be constructed like that?
In section II.D:
> If one rejects the ERH, one could argue that our universe is somehow made of stuff perfectly described by a mathematical structure, but which also has other properties that are not described by it, and cannot be described in an abstract baggage-free way. This viewpoint [...] would make Karl Popper turn in his grave, since those additional bells and whistles that make the universe non-mathematical by definition have no observable effects whatsoever.
I don't think that follows. It could be that the universe is asymptotically mathematical, in the sense that any mathematical structure falls short of perfectly describing the universe, but there is always a more sophisticated mathematical structure that is a closer approximation. The problem of course is that a mathematical description is made of a finite number of symbols. It could be that the external reality hypothesis holds, but the universe can only be described in a baggage-free way with an infinite number of symbols.
> If one rejects the ERH, one could argue that our universe is somehow made of stuff perfectly described by a mathematical structure, but which also has other properties that are not described by it, and cannot be described in an abstract baggage-free way. This viewpoint [...] would make Karl Popper turn in his grave, since those additional bells and whistles that make the universe non-mathematical by definition have no observable effects whatsoever.
I don't think that follows. It could be that the universe is asymptotically mathematical, in the sense that any mathematical structure falls short of perfectly describing the universe, but there is always a more sophisticated mathematical structure that is a closer approximation. The problem of course is that a mathematical description is made of a finite number of symbols. It could be that the external reality hypothesis holds, but the universe can only be described in a baggage-free way with an infinite number of symbols.
This fits in nicely with Woflram's theories about computational irreducibility.[0]
[0]https://writings.stephenwolfram.com/2020/04/finally-we-may-h...
[0]https://writings.stephenwolfram.com/2020/04/finally-we-may-h...
To grasp these arguments, one has to have done enough self-reflection to perceive the workings of the mind, where thoughts arise. If a person has not done this, then many of these arguments fall on deaf ears, and they cling to their illusions.
Then what is consciousness?
People keep telling me that consciousness is just some illusion which happens inside brain neural network.
However, in case of mathematical universe hypothesis, nothing really happens. If you have a mathematical universe with seed 42, which you spend a lot of effort actually simulating, it is not in any way different from a mathematical universe with seed 43, which you don't. Neural networks have exactly the same zero amount of consciousness in both cases.
Why do we feel that we exist? Who does the feeling part?
People keep telling me that consciousness is just some illusion which happens inside brain neural network.
However, in case of mathematical universe hypothesis, nothing really happens. If you have a mathematical universe with seed 42, which you spend a lot of effort actually simulating, it is not in any way different from a mathematical universe with seed 43, which you don't. Neural networks have exactly the same zero amount of consciousness in both cases.
Why do we feel that we exist? Who does the feeling part?
> People keep telling me that consciousness is just some illusion
In my view, consciousness is the only thing that can not be an illusion. If it's an illusion, who is being fooled? Consciousness isn't the illusion, it's the audience.
> If you have a mathematical universe with seed 42, which you spend a lot of effort actually simulating, it is not in any way different from a mathematical universe with seed 43
Yes, this is the key point of the mathematical universe (for me). No simulation has to occur.
There is no way to tell, from within the mathematical universe, whether or not anyone is running the simulation. The simulation helps someone outside find out what happens in the universe, but the stuff that happens in the universe happens whether you simulate it or not.
All of the possible mathematical universes "exist" and are equally valid.
"Existence" and "the passage of time" are things that only make sense within the mathematical universe. There is nothing outside.
In my view, consciousness is the only thing that can not be an illusion. If it's an illusion, who is being fooled? Consciousness isn't the illusion, it's the audience.
> If you have a mathematical universe with seed 42, which you spend a lot of effort actually simulating, it is not in any way different from a mathematical universe with seed 43
Yes, this is the key point of the mathematical universe (for me). No simulation has to occur.
There is no way to tell, from within the mathematical universe, whether or not anyone is running the simulation. The simulation helps someone outside find out what happens in the universe, but the stuff that happens in the universe happens whether you simulate it or not.
All of the possible mathematical universes "exist" and are equally valid.
"Existence" and "the passage of time" are things that only make sense within the mathematical universe. There is nothing outside.
Why do I have this long term feeling that I exist in a specific mathematical universe and is absent from all others, or at least represent an unique path distinct from all other paths which I am not?
Who does the feeling part? Who is the audience? When you run simulation there's at least some audience, but in case of math universe there is only archeology, by definition. Mathematical object has no original, only replicas.
Who does the feeling part? Who is the audience? When you run simulation there's at least some audience, but in case of math universe there is only archeology, by definition. Mathematical object has no original, only replicas.
I think for humans our memory is why we only feel connected to a particular causal timeline of consciousness. For myself I am conscious of the present moment and of my memories and of my imagination.
For us to be conscious of our experiences in other universes or timelines we would need a way to know what those experiences are like. In our universe memory is a cheap way of recording what the causal past was like vs. needing to compute/simulate what happens in other timelines with enough accuracy to be as fully conscious of it as we are of our memories.
For us to be conscious of our experiences in other universes or timelines we would need a way to know what those experiences are like. In our universe memory is a cheap way of recording what the causal past was like vs. needing to compute/simulate what happens in other timelines with enough accuracy to be as fully conscious of it as we are of our memories.
> In my view, consciousness is the only thing that can not be an illusion. If it's an illusion, who is being fooled? Consciousness isn't the illusion, it's the audience.
I don't why people keep being taken by this silly argument. You've merely assumed that "illusion" requires a subject. Here's a definition of illusion that doesn't require a subject: a perception that entails a false conclusion if taken at face value. There, now "consciousness is an illusion" is simply, "consciousness is a perception from which we falsely infer the existence of subjective qualities".
I don't why people keep being taken by this silly argument. You've merely assumed that "illusion" requires a subject. Here's a definition of illusion that doesn't require a subject: a perception that entails a false conclusion if taken at face value. There, now "consciousness is an illusion" is simply, "consciousness is a perception from which we falsely infer the existence of subjective qualities".
Subjective qualities like color and pain? What about dreams and imagination? Illusions are misleading conscious experiences, usually perceptual. That's why it doesn't make much sense to say consciousness is itself an illusion.
> Subjective qualities like color and pain?
Colour is perceived. The "what is it like" to see colour is the qualitative illusion. Ditto for pain.
> What about dreams and imagination?
What about them? Does Midjourney plausibly imagine the scenes it generates?
> Illusions are misleading conscious experiences, usually perceptual
Illusions are misleading perceptions. There's no reason to throw "conscious" in there at all, it just muddies an otherwise simple concept.
Colour is perceived. The "what is it like" to see colour is the qualitative illusion. Ditto for pain.
> What about dreams and imagination?
What about them? Does Midjourney plausibly imagine the scenes it generates?
> Illusions are misleading conscious experiences, usually perceptual
Illusions are misleading perceptions. There's no reason to throw "conscious" in there at all, it just muddies an otherwise simple concept.
> Who does the feeling part?
An even more intriguing question is if there are meta-consciousnesses on humans.
Let's assume humans have consciousness, and we are all just a bunch of cells.
Does a cell feel conscious? Maybe, maybe not. A bacteria doing gradient descent perhaps doesn't make that many decisions. But perhaps this hunt has something similar to our hormones, and they can feel happiness.
An arm? A brain? The neurons of just an eye? They can't really affect their survivability on their own, so perhaps there was no evolutionary advantage in being conscious.
For something with arms, feet and brain and two eyes? They can compare the world now, to what used to be, and reason about what should be. This awareness of time and the space I effect, I'd argue is a huge part of consciousness.
But what about some group of people, or the species as a whole? I'm fairly sure my cells don't understand that together they are "conscious." The same way, how could I tell if some meta-organism that includes me is considering itself conscious? Surely, if I'm capable of consciousness, anything that includes me would inherit that property?
If consciousness is transitive, that would be a huge result. Then the "who" is no longer of relevance, because it's all relative: a single consciousness could be a meta-part of multiple other consciousnesses at the same time.
And then we go all the way up to galaxy clusters. Are they conscious? I'm part of one. The slowness of information travel alone would make it incomprehensible for me to even observe it. If they are conscious, I would die long before I could even communicate the question.
I think this time scale problem will limit our understanding of consciousness for a long time. Even just looking at groups of humans, how would we recognize if they feel themselves? We can study biological systems on our scale, but anything beyond that... Well, it just sucks. Because I'd really, really, love to know the answer.
An even more intriguing question is if there are meta-consciousnesses on humans.
Let's assume humans have consciousness, and we are all just a bunch of cells.
Does a cell feel conscious? Maybe, maybe not. A bacteria doing gradient descent perhaps doesn't make that many decisions. But perhaps this hunt has something similar to our hormones, and they can feel happiness.
An arm? A brain? The neurons of just an eye? They can't really affect their survivability on their own, so perhaps there was no evolutionary advantage in being conscious.
For something with arms, feet and brain and two eyes? They can compare the world now, to what used to be, and reason about what should be. This awareness of time and the space I effect, I'd argue is a huge part of consciousness.
But what about some group of people, or the species as a whole? I'm fairly sure my cells don't understand that together they are "conscious." The same way, how could I tell if some meta-organism that includes me is considering itself conscious? Surely, if I'm capable of consciousness, anything that includes me would inherit that property?
If consciousness is transitive, that would be a huge result. Then the "who" is no longer of relevance, because it's all relative: a single consciousness could be a meta-part of multiple other consciousnesses at the same time.
And then we go all the way up to galaxy clusters. Are they conscious? I'm part of one. The slowness of information travel alone would make it incomprehensible for me to even observe it. If they are conscious, I would die long before I could even communicate the question.
I think this time scale problem will limit our understanding of consciousness for a long time. Even just looking at groups of humans, how would we recognize if they feel themselves? We can study biological systems on our scale, but anything beyond that... Well, it just sucks. Because I'd really, really, love to know the answer.
If you were an alien and showed up on earth, then hurt a human, you'd likely think we work at least like a semi-collective consciousness. Much like a cell that is injured starts chemically communicating problems, we'd start communicating at a meta organism against the new threat.
This is one thing that's always given me the 'concern of the unknown' when it comes to AI. The potential meta consciousness abilities of AI could vastly exceeded human capabilities.
This is one thing that's always given me the 'concern of the unknown' when it comes to AI. The potential meta consciousness abilities of AI could vastly exceeded human capabilities.
Good point, though the reaction doesn't necessarily mean consciousness is required. It could be akin to a simple spasm.
> meta consciousness abilities of AI
Yeah. The more we create order out of chaos, the more likely something incomprehensible emerges.
> meta consciousness abilities of AI
Yeah. The more we create order out of chaos, the more likely something incomprehensible emerges.
> People keep telling me that consciousness is just some illusion which happens inside brain neural network.
Ask those people what is experiencing the illusion, and whether we can program a computer to have conscious experience using the same illusion generation.
It's like answering the question of "what created the universe" by saying "a god did it." It just pushes the question back.
If something can experience an illusion - i.e. to use the philosophical language, "there is something it is like" to have that illusion - then it has consciousness, and the illusion has nothing to do with it.
Ask those people what is experiencing the illusion, and whether we can program a computer to have conscious experience using the same illusion generation.
It's like answering the question of "what created the universe" by saying "a god did it." It just pushes the question back.
If something can experience an illusion - i.e. to use the philosophical language, "there is something it is like" to have that illusion - then it has consciousness, and the illusion has nothing to do with it.
At high doses of psilocybin you experience the loss of ego. It's a weird feeling, where "you" are not there anymore. There is no "I". So it's definitely possible to be conscious but feel like "you" or whatever the idea you have of a self just isn't there anymore.
Beyond the ego, what is this conscious stuff providing awareness qualia? It seems we must assert one of these options:
a) consciousness is an emergent system of matter (materialism).
b) matter contains elements of consciousness (panpsychism).
c) matter/energy is consciousness with varying levels of complexity (monism).
a) consciousness is an emergent system of matter (materialism).
b) matter contains elements of consciousness (panpsychism).
c) matter/energy is consciousness with varying levels of complexity (monism).
Your option (c) is idealistic monism specifically, since physical monism corresponds to materialism.
And then there's:
d) matter, energy, and consciousness all arise from or are different aspects of some single "substance" (neutral monism)
e) consciousness and matter are "radically different kinds of things" (dualism)
f) the question is unanswerable and/or incomprehensible to us (mysterianism)
And then there's:
d) matter, energy, and consciousness all arise from or are different aspects of some single "substance" (neutral monism)
e) consciousness and matter are "radically different kinds of things" (dualism)
f) the question is unanswerable and/or incomprehensible to us (mysterianism)
Thank you for that catch, yes, idealistic monism. Oh, I should have added E for as I already mentioned monism. D & F are also interesting positions.
Neutral-monism sounds like an hegelian dialectic [the gap]:
Many neutral monists hold that the terms “physical” and “mental” apply only to groups of neutral entities, not individual ones, "The stuff of which the world of our experience is composed is, in my belief, neither mind nor matter, but something more primitive than either. Both mind and matter seem to be composite, and the stuff of which they are compounded lies in a sense between the two, in a sense above them both, like a common ancestor". (Russell 1921: 10–11)
Neutral-monism sounds like an hegelian dialectic [the gap]:
Many neutral monists hold that the terms “physical” and “mental” apply only to groups of neutral entities, not individual ones, "The stuff of which the world of our experience is composed is, in my belief, neither mind nor matter, but something more primitive than either. Both mind and matter seem to be composite, and the stuff of which they are compounded lies in a sense between the two, in a sense above them both, like a common ancestor". (Russell 1921: 10–11)
Is c really a workable hypothesis? It doesn't seem it could account for most of what we observe, at least not if we don't start believing in new sun gods or something like that.
Ultimately, if the world has a constant shape that looks the same to most people, it resembles what we call matter more than what we call consciousness.
Ultimately, if the world has a constant shape that looks the same to most people, it resembles what we call matter more than what we call consciousness.
Who knows?
https://en.wikipedia.org/wiki/Hard_problem_of_consciousness provides some interesting reading though.
Maybe we have it backwards, and consciousness is the underlying firmament of reality and the material world emerges from that (if it even exists, of course).
https://en.wikipedia.org/wiki/Hard_problem_of_consciousness provides some interesting reading though.
Maybe we have it backwards, and consciousness is the underlying firmament of reality and the material world emerges from that (if it even exists, of course).
> Maybe we have it backwards, and consciousness is the underlying firmament of reality and the material world emerges from that (if it even exists, of course).
This is unsupportable, even in principle, and reduces very quickly to solipsism. There's no way to account for an objective world with this (bad) philosophy.
This is unsupportable, even in principle, and reduces very quickly to solipsism. There's no way to account for an objective world with this (bad) philosophy.
> reduces very quickly to solipsism
Not necessarily. Solipsism generally is the idea that only one's own mind exists (or at least, it's the only mind whose existence one can supposedly be certain of.) But the gp description seems to encompass something like idealistic monism, where consciousness is fundamental, but it's not necessarily that of one person's mind. This is not equivalent to solipsism in general.
Not necessarily. Solipsism generally is the idea that only one's own mind exists (or at least, it's the only mind whose existence one can supposedly be certain of.) But the gp description seems to encompass something like idealistic monism, where consciousness is fundamental, but it's not necessarily that of one person's mind. This is not equivalent to solipsism in general.
I wasn't even trying to account for an objective world so much as to consider one possible explanation for the subjective experience of being. Though it is, admittedly, a bit of a cop out ("consciousness exists because it is existence").
I don't think it reduces to solipsism, though. I don't think anything I said precludes the existence of multiple minds?
I don't think it reduces to solipsism, though. I don't think anything I said precludes the existence of multiple minds?
Not if you can think of some predictions from that theory that would later be proven true.
In the mathematical universe consciousness is equivalent to a proper class (the sets that feel like something from the inside) and the intersection of that class with the possible states of our physical universe yields the possible consciousnesses in our universe.
How are some sets conscious? Probably some encoded self-reference or other self-similarity. E.g. there are infinitely many integers that under Gödel numbering refer to logical statements about the same integer. If anything, that should feel like some sense of self with reference to the choice of numbering and logic. Human consciousness is possibly many layers of parallel self-references that yield additional and comparative qualia. There are almost certainly other mechanisms of achieving consciousness as well.
How are some sets conscious? Probably some encoded self-reference or other self-similarity. E.g. there are infinitely many integers that under Gödel numbering refer to logical statements about the same integer. If anything, that should feel like some sense of self with reference to the choice of numbering and logic. Human consciousness is possibly many layers of parallel self-references that yield additional and comparative qualia. There are almost certainly other mechanisms of achieving consciousness as well.
But who does that achieving of consciousness?
A random seed written on a piece of paper?
The "who" is the set that is conscious. Just like a prime number is prime without having any external force make it so or requiring anything to embody the primeness. Primality is in the nature of the natural numbers. The claim is that consciousness is in the nature of sets. The latter does not yet have experimental evidence. It seems as reasonable to me as other possibilities like electrons are conscious or quantum fields are conscious mostly because both of those are well-described by mathematics.
Why do I feel like I am living in time if I am actually not in a simulation, not a Boltzmann brain, but just a random seed that is not written on a piece of paper anywhere? What is the meaning of all this, then?
You are reiterating cheezy stuff about "nature" and quantum fields, ignoring the random seed part.
You are reiterating cheezy stuff about "nature" and quantum fields, ignoring the random seed part.
You are your brain.
Your mind is a part of your brain; a part that combines a spatial-temporal sense with a future-oriented simulating function.
Your brain is modelable – not only is it "a structure" in an abstract sense, it is an ordered physical structure made of molecules, and, both in whole and in part, it is reducible to a mathematical structure of highly limited complexity. "Qualia" consist of your mind's representations of external things, immediately derived from sensory input, wedded to that sense of being in space and time and the associations raised by that sense.
As your brain exists within a logical system -- a structure with a mathematical model which includes an evolution function -- your brain is also a logical system which evolves through time.
As for "nothing actually happens" -- the block universe hypothesis, which is strongly implied by relativity, fully accounts for this.
As an aside: I think that Tegmark is basically correct, but his hypothesis is not well defined and could use further explanation.
Your mind is a part of your brain; a part that combines a spatial-temporal sense with a future-oriented simulating function.
Your brain is modelable – not only is it "a structure" in an abstract sense, it is an ordered physical structure made of molecules, and, both in whole and in part, it is reducible to a mathematical structure of highly limited complexity. "Qualia" consist of your mind's representations of external things, immediately derived from sensory input, wedded to that sense of being in space and time and the associations raised by that sense.
As your brain exists within a logical system -- a structure with a mathematical model which includes an evolution function -- your brain is also a logical system which evolves through time.
As for "nothing actually happens" -- the block universe hypothesis, which is strongly implied by relativity, fully accounts for this.
As an aside: I think that Tegmark is basically correct, but his hypothesis is not well defined and could use further explanation.
It must feel really, really good when everything is so perfectly crystal clear and easily explainable; when there are only answers, and no questions. How it is possible, is a mystery in itself.
Unfortunately these questions may not be answerable. For example, let's imagine a universe where all these questions are answerable,how it started and why it works can be explained. Then that universe has a vacuum meta instability and collapses into a new form. In the previous universe it was completely predictable that it would happen, but the singularity effect of the state change left a low entropy universe. Information was lost, and new physics takes over.
An observer in the new universe would see a blank piece of paper and would have no idea why this paper existed and why it was blank. And could know how we got there.
This universe would be a very unsatisfactory place for the inquisitive to exist.
An observer in the new universe would see a blank piece of paper and would have no idea why this paper existed and why it was blank. And could know how we got there.
This universe would be a very unsatisfactory place for the inquisitive to exist.
That was irony.
Inability to model a basic worm with 100 neurons and fully mapped out connections defeats this simplistic worldview.
I wouldn't go that far.
I don't know if we can model any biological structure with complete fidelity. There's a lot that modern science doesn't know about the cell. The Golgi apparatus, for instance, is still a mystery; there are models, but nobody really knows how it works, and all of the models are apparently incomplete. You'll note that the Golgi apparatus is one of the very largest cell structures.
Our cognitive processes rest upon an extremely complex biological substrate. That we're not able to simulate a nematode's brain, however, absolutely does not imply that it's not simulatable in principle.
...I'd say that it's made of fermions, which in a coordinate space approximate bits of information. Those fermions are mostly arranged into atoms, which are grouped together in molecules. As, contra Penrose, quantum effects don't seem important for cognition, if you have an absolutely complete molecular picture of the brain and an evolution function, you'll have a model of the brain.
You need more than "mapped out connections," but it's eminently possible in principle, which is to say that it's not infinitely complex or somehow ineffable. It's just decades beyond us, by my estimate.
I don't know if we can model any biological structure with complete fidelity. There's a lot that modern science doesn't know about the cell. The Golgi apparatus, for instance, is still a mystery; there are models, but nobody really knows how it works, and all of the models are apparently incomplete. You'll note that the Golgi apparatus is one of the very largest cell structures.
Our cognitive processes rest upon an extremely complex biological substrate. That we're not able to simulate a nematode's brain, however, absolutely does not imply that it's not simulatable in principle.
...I'd say that it's made of fermions, which in a coordinate space approximate bits of information. Those fermions are mostly arranged into atoms, which are grouped together in molecules. As, contra Penrose, quantum effects don't seem important for cognition, if you have an absolutely complete molecular picture of the brain and an evolution function, you'll have a model of the brain.
You need more than "mapped out connections," but it's eminently possible in principle, which is to say that it's not infinitely complex or somehow ineffable. It's just decades beyond us, by my estimate.
Before we can rule out quantum effects, we need to understand that nematode at least. It's quite possible that the discrete computing model is completely unfit for simulating intelligence - a possibility that many scientists are afraid to consider.
As I say, we might not be able to "understand" the nematode's brain before we're able to understand its constituent parts. We don't really understand the neuron itself. Nor do we understand glial cells and their function.
...Nor, indeed, do we fully understand _any_ cell. Case in point: Both neurons and glial cells feature Golgi apparatuses, which remain mysterious...
As we neither understand nor can simulate a brain made up of neurons and glia, what makes you think that our lack of a nematode simulation is a big deal? Seems to me that it is rather to be expected. But when our biological models improve, simulating a nematode brain -- or _any_ brain -- will not be beyond us.
...Nor, indeed, do we fully understand _any_ cell. Case in point: Both neurons and glial cells feature Golgi apparatuses, which remain mysterious...
As we neither understand nor can simulate a brain made up of neurons and glia, what makes you think that our lack of a nematode simulation is a big deal? Seems to me that it is rather to be expected. But when our biological models improve, simulating a nematode brain -- or _any_ brain -- will not be beyond us.
Not saying I agree with a mathematical universe hypothesis, however I have given it some thought. I'd argue that any 'operator' is consciousness in that setting.
There's some quote out there by some famous mathematician or hpyscisist along the lines of "it appears the operations themselves act as if they were conscious"
Even then, how we think of operations symbolically is just an emanation of a universal that we can't see in that sense; but in another sense, we are also emanations of that thing too in the sense that we (humans) are extensions of measurement and operations.
There's some quote out there by some famous mathematician or hpyscisist along the lines of "it appears the operations themselves act as if they were conscious"
Even then, how we think of operations symbolically is just an emanation of a universal that we can't see in that sense; but in another sense, we are also emanations of that thing too in the sense that we (humans) are extensions of measurement and operations.
Another problem (which Tegmark writes about) is math will have to change. Some of the math we study will have to be part of illusion - there is no “one” math currently, and how could something exist in MUH which isn’t computable. His vision pairs down math, much to the ire of many mathematicians. But it is not unviable, we don’t need much of math for physics.
I think the view that mathematics and logic are static is incorrect. Computers are mathematical as well.
I think viewing mathematics as the study of structure, and structures can be transformed into other structures via a mathematical procedure we know of as computation resolves the difficulties.
I think viewing mathematics as the study of structure, and structures can be transformed into other structures via a mathematical procedure we know of as computation resolves the difficulties.
You cannot transform a mathematical structure. The only thing you can do is find another structure with linked properties. But both structures are immutable.
It is not possible to transform a sphere so that it turns into a cube and no spheres can be reasoned about anymore.
It is not possible to transform a sphere so that it turns into a cube and no spheres can be reasoned about anymore.
> You cannot transform a mathematical structure. The only thing you can do is find another structure with linked properties. But both structures are immutable.
I think you're conflating the structures that describes mathematical structure with the structure itself. Like I said, mathematics is the study of structure, so the syntactic elements you're used to interacting with are themselves structures that describe other structures. These syntactic descriptions have isomorphisms to the underlying structures they're describing, but they are not the structures themselves (map is not the territory, etc.).
Mathematics is larger than this immutable descriptive layer IMO.
Edit: as a more concrete example, consider how we model mutable data structures and stateful session protocols in programming languages. One way is to project these into an immutable trace, as an immutable description of the object's state changes, but that trace is not the underlying structure. The underlying structure itself is still mathematical, but mutable, eg. cellular automata.
I think you're conflating the structures that describes mathematical structure with the structure itself. Like I said, mathematics is the study of structure, so the syntactic elements you're used to interacting with are themselves structures that describe other structures. These syntactic descriptions have isomorphisms to the underlying structures they're describing, but they are not the structures themselves (map is not the territory, etc.).
Mathematics is larger than this immutable descriptive layer IMO.
Edit: as a more concrete example, consider how we model mutable data structures and stateful session protocols in programming languages. One way is to project these into an immutable trace, as an immutable description of the object's state changes, but that trace is not the underlying structure. The underlying structure itself is still mathematical, but mutable, eg. cellular automata.
The idea here is that deterministic computations neither exist nor don't; regardless of whether they are being simulated. A Life pattern does not xare whether you simulate it or not. It will not become conscious in any way after your decision to simulate it.
> A Life pattern does not xare whether you simulate it or not. It will not become conscious in any way after your decision to simulate it.
Where's the proof of this? The game of Life is Turing complete. We have every indication that human beings can be modelled by Turing machines.
Where's the proof of this? The game of Life is Turing complete. We have every indication that human beings can be modelled by Turing machines.
Then you arrive at questions such as "Why do we exist?", even "Why anything exists at all, what was the need for all of this?"
> Why do we feel that we exist? Who does the feeling part?
There’s the non-helpful answer “I think, therefore I am.” I don’t think there’s any good answer to these questions. We can think about ourselves, we can think about existence, so we feel we exist? Let us imagine a person can not receive any external stimuli, can not send any instruction to control the movement of body, [e.g. a brain with blood circulation to keep it alive, but no input/output], in awakened state, now what should they feel? [Such a horrible state!] It seems they should feel their existence only on the basis of the functioning of their brain.
> Why do we feel that we exist? Who does the feeling part?
There’s the non-helpful answer “I think, therefore I am.” I don’t think there’s any good answer to these questions. We can think about ourselves, we can think about existence, so we feel we exist? Let us imagine a person can not receive any external stimuli, can not send any instruction to control the movement of body, [e.g. a brain with blood circulation to keep it alive, but no input/output], in awakened state, now what should they feel? [Such a horrible state!] It seems they should feel their existence only on the basis of the functioning of their brain.
consciousness is just a real-time continuous representation of time/space, i.e. of the parts of the universe in front of us (and some of it already within us, i.e. memory and imagination).
No, it's not. I feel that I exist. I can represent time/space in a computer program. Nothing would feel that it exists there.
Overall, I feel I'm trying to push against another philosophical maxim that I know: "If somebody tells you that consciousness does not exist, it's all just measurement and neuron signals - believe them"
Overall, I feel I'm trying to push against another philosophical maxim that I know: "If somebody tells you that consciousness does not exist, it's all just measurement and neuron signals - believe them"
What is that maxim supposed to mean?
My first interpretation is that it's saying that people who say that might be philosophical zombies, lacking consciousness.
My first interpretation is that it's saying that people who say that might be philosophical zombies, lacking consciousness.
| I can represent time/space in a computer program. Nothing would feel that it exists there.
That's why I said real-time and continuous. All digital systems, at the lowest level of computations are discrete, not continuous (i.e. analog). And the changes happening in real-time, i.e. the transistors values changing in processing units are very far removed from a representation of reality. What I mean by that is that if you are watching a video of a desert on a computer screen and took a snapshot of the transistor values in a GPU/CPU happening at the same time, they is no good mapping from one to the other (Since that one screenshot may be computed by thousands of computation cycles in the GPU/CPU).
That's why I said real-time and continuous. All digital systems, at the lowest level of computations are discrete, not continuous (i.e. analog). And the changes happening in real-time, i.e. the transistors values changing in processing units are very far removed from a representation of reality. What I mean by that is that if you are watching a video of a desert on a computer screen and took a snapshot of the transistor values in a GPU/CPU happening at the same time, they is no good mapping from one to the other (Since that one screenshot may be computed by thousands of computation cycles in the GPU/CPU).
Memory is the current spacetime location's fuzzy view when looking towards the past. Imagination is the fuzzy view when looking forwards to the future or with the many-worlds view, imagination is the looking out(?) towards multiple outcomes.
Consciousness is the step towards the next point in the many world multiverse.
Without the ability to be blind to the future, life as we know it wouldn't exist. Nothing conscious would take risks and so complexity couldn't evolve.
If you could glance to the future and see all of the laid out spacetime, there wouldn't be any interesting exploration of it.
So we have to be blinkered just to exist with this level of insight into the complexities of the universe.
Consciousness is the step towards the next point in the many world multiverse.
Without the ability to be blind to the future, life as we know it wouldn't exist. Nothing conscious would take risks and so complexity couldn't evolve.
If you could glance to the future and see all of the laid out spacetime, there wouldn't be any interesting exploration of it.
So we have to be blinkered just to exist with this level of insight into the complexities of the universe.
You are a body. Consciousness is your UI to the world that you generate and you use. Don't over-complicate this shit.
Are computers conscious? If not, why not, and can they be programmed to be conscious?
> Don't over-complicate this shit.
One big issue that makes this difficult is that we have no understanding of how it's possible for physical matter to possess consciousness. Absolutely none, just lots of conjecture with no evidence or well-developed theory to support it.
If you have a non-complicated answer to all this, you will be world-famous for solving the hard problem of consciousness (https://consc.net/papers/facing.html).
> Don't over-complicate this shit.
One big issue that makes this difficult is that we have no understanding of how it's possible for physical matter to possess consciousness. Absolutely none, just lots of conjecture with no evidence or well-developed theory to support it.
If you have a non-complicated answer to all this, you will be world-famous for solving the hard problem of consciousness (https://consc.net/papers/facing.html).
I don't need to answer any of those questions to state what I did as facts. They aren't grounded in the same evidence.
Ok, but in that case what you wrote has no relevance to the questions asked in the comment you responded to: "What is consciousness? ... Why do we feel that we exist? Who does the feeling part?"
All you're talking about is its role, and making an unsupported assertion about it at that.
All you're talking about is its role, and making an unsupported assertion about it at that.
That's one viewpoint, but it's not "over-complicated" to consider others.
You are a consciousness. Your body is your UI to the world.
You are a consciousness. Your body is your UI to the world.
That reduces to solipsism or idealism, which have been explored extensively. Defenses of them are definitely over-complicated, which is why they aren't considered serious positions in philosophy anymore. Your questions are orthogonal to my answers.
> they aren't considered serious positions in philosophy anymore.
Statements like this say more about your biases than about anything happening in philosophy. As recently as 2019, Chalmers published "Idealism and the Mind-Body Problem" (https://philpapers.org/archive/CHAIAT-11.pdf), a survey of some current positions in idealism.
Statements like this say more about your biases than about anything happening in philosophy. As recently as 2019, Chalmers published "Idealism and the Mind-Body Problem" (https://philpapers.org/archive/CHAIAT-11.pdf), a survey of some current positions in idealism.
It's nice to see this treated as an hypothesis rather than an assumption. Too many smart people I talk to take it for granted that the universe is made out of math.
Of all assumptions to make, assuming the universe is made of math is likely the least harmful.
Related discussion from 2017:
https://news.ycombinator.com/item?id=15637074
https://news.ycombinator.com/item?id=15637074
If anyone is interested in some further reading on Pythagorean Number, I’d recommend ‘The Theology of Arithmetic’ attributed to Iamblichus.
What is the difference between a universe partially governed by chaos and singularities, vs one not totally ruled by maths?
Should add (2007) for the publication date, or even (13.8 bya) if referring to when that took place.
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Fancy words to say there is a grand designer.
I don’t buy it.
Always at the edge of human understanding we say “well we don’t understand that, so there must be a man behind the curtain”.
I don’t buy it.
Always at the edge of human understanding we say “well we don’t understand that, so there must be a man behind the curtain”.
Tegmark proposes no such thing; indeed, he may as well be proposing the exact opposite of what you claimed. He is essentially suggesting that all mathematical structures are "real", which would explain why the universe exists at all -- presumably because it is also a mathematical structure.
Then it would be the "grand designer" hypothesis, wouldn't it?
I notice that the big unspoken resistance to metaphysics these days is the fear that it is somehow a trick to smuggle God back into our understanding of reality. This fear can become excessive, and carry the unsavory and perhaps ironic side-effect of turning physicalism into a God that cannot be questioned.
I notice that the big unspoken resistance to metaphysics these days is the fear that it is somehow a trick to smuggle God back into our understanding of reality. This fear can become excessive, and carry the unsavory and perhaps ironic side-effect of turning physicalism into a God that cannot be questioned.
I've noticed that as well. I do think it tends to compromise thinking on the subject of consciousness, because it basically creates a space of questions one must not ask, taboo topics.
Homo sapiens is the most arrogant little pile of carbon this side of the Tanhausser gate.
While every scientific advance has pushed us further and further away from the center of the universe, we just cant let go of our existential angst of being utterly irrelevant and keep our megalomaniac posturing totaly infatuated with our "specialness".
There is no doubt that there something extraordinary profound in the ability of our brains to create coherent representations of reality. But there is an abyss to cross before we can assert that these imperfect, evolving and malleable mental models are actually "all there is".
In fact our exciting and beneficial journey of "uncovering" the mathematical fabric of the universe may have ended already. Our mental tools (causality, initial value problems, fields etc.) are powerful but they are rather like hammers looking for nails.
We have now almost a century of stagnation around any really new mathematical concepts that would help us push further into "in your face" empirical manifestations, e.g. around complex phenomena.
There is no obligation that the Universe is made of nails.
While every scientific advance has pushed us further and further away from the center of the universe, we just cant let go of our existential angst of being utterly irrelevant and keep our megalomaniac posturing totaly infatuated with our "specialness".
There is no doubt that there something extraordinary profound in the ability of our brains to create coherent representations of reality. But there is an abyss to cross before we can assert that these imperfect, evolving and malleable mental models are actually "all there is".
In fact our exciting and beneficial journey of "uncovering" the mathematical fabric of the universe may have ended already. Our mental tools (causality, initial value problems, fields etc.) are powerful but they are rather like hammers looking for nails.
We have now almost a century of stagnation around any really new mathematical concepts that would help us push further into "in your face" empirical manifestations, e.g. around complex phenomena.
There is no obligation that the Universe is made of nails.
> We have now almost a century of stagnation around any really new mathematical concepts that would help us push further into "in your face" empirical manifestations, e.g. around complex phenomena.
Could you substantiate this rather outrageous claim with some sources?
Could you substantiate this rather outrageous claim with some sources?
Me thinks the burden is on you to "easily" invalidate my claim with a single example.
Our core explanatory framework (underpining eg quantum or relativity) is essentially still serviced by 19th century mathematics.
NB: Actually I would be thrilled if we had such a new tool to explain the universe.
Our core explanatory framework (underpining eg quantum or relativity) is essentially still serviced by 19th century mathematics.
NB: Actually I would be thrilled if we had such a new tool to explain the universe.
No offense but you made a very broad and rather surprising (= anything but well-established) claim, so the burden of proof is on you I'd say.
> Our core explanatory framework (underpining eg quantum or relativity) is essentially still serviced by 19th century mathematics.
Eh what? Quantum mechanics and high-energy physics largely build upon functional analysis and representation theory which were largely developed in the 20th century because of quantum mechanics.
General Relativity did pick up some concepts which were already developed in the 19th century already but today's formulation is quite a bit more modern (and rigorous) I'd say and there have also been lots of advances on the mathematical side since then.
Generally speaking, the issue in fundamental physics is not that we lack the mathematical tools; the issue is that we lack physical insights (from experiments).
> Our core explanatory framework (underpining eg quantum or relativity) is essentially still serviced by 19th century mathematics.
Eh what? Quantum mechanics and high-energy physics largely build upon functional analysis and representation theory which were largely developed in the 20th century because of quantum mechanics.
General Relativity did pick up some concepts which were already developed in the 19th century already but today's formulation is quite a bit more modern (and rigorous) I'd say and there have also been lots of advances on the mathematical side since then.
Generally speaking, the issue in fundamental physics is not that we lack the mathematical tools; the issue is that we lack physical insights (from experiments).
We are drifting into specifics (eg Hilbert spaces were already a first decade of the 20th century thing) that are really not relevant for my argument.
The core question is whether the Universe is somehow mathematical (which I would say is the really extraordinary and clickbaity claim of attention seeking physicists with no more serious stuff to work on).
The empirical data point that I am trying to derive (so that we don't talk metaphysically) is focusing on the historical development of mathematical physics. The fact that it had spectacular success up to a point but then it stagnated. Does this suggest something about "maths is in our brains" versus "maths is running the universe"? Maybe it does, maybe it doesnt (keep reading).
Please note that my asserted stagnation does not concern fundamental physics (where indeed experimental barriers have become the limiting factor). More telling imho is that we have no real mathematical tools to understand complex systems, even of fairly benign nature (non-equilibrium thermodynamics), let alone extraordinary phenomena like biology. We have become comfortable that all complexity can "in principle" be explained, but that is not exactly actually grasping the mathematics of it. Pressumably a mathematical universe is mathematical at all scales, so where is the math?
So to recap, my question/challenge is essentially: if the universe is mathematical and we managed to explain quite a bit of it, why not more? There are now more living scientists than ever before. Discoveries are made continuously, but not of the type that counts as a mathematical understanding breakthrough.
The answer might be:
its just a matter of time (it takes cultural evolution, resources and trial and error for brains to "reconnect" with the underlying math universe) and a near century-long hiatus is part of how this works
OR
we had a lucky run in the last two/three centuries (some aspects of brain function can do a good job emulating certain aspects of the underlying "non-math" universe) but there is no reason to expect that this will be an ongoing process of "ever closer union".
I obviously dont know the answer.
The core question is whether the Universe is somehow mathematical (which I would say is the really extraordinary and clickbaity claim of attention seeking physicists with no more serious stuff to work on).
The empirical data point that I am trying to derive (so that we don't talk metaphysically) is focusing on the historical development of mathematical physics. The fact that it had spectacular success up to a point but then it stagnated. Does this suggest something about "maths is in our brains" versus "maths is running the universe"? Maybe it does, maybe it doesnt (keep reading).
Please note that my asserted stagnation does not concern fundamental physics (where indeed experimental barriers have become the limiting factor). More telling imho is that we have no real mathematical tools to understand complex systems, even of fairly benign nature (non-equilibrium thermodynamics), let alone extraordinary phenomena like biology. We have become comfortable that all complexity can "in principle" be explained, but that is not exactly actually grasping the mathematics of it. Pressumably a mathematical universe is mathematical at all scales, so where is the math?
So to recap, my question/challenge is essentially: if the universe is mathematical and we managed to explain quite a bit of it, why not more? There are now more living scientists than ever before. Discoveries are made continuously, but not of the type that counts as a mathematical understanding breakthrough.
The answer might be:
its just a matter of time (it takes cultural evolution, resources and trial and error for brains to "reconnect" with the underlying math universe) and a near century-long hiatus is part of how this works
OR
we had a lucky run in the last two/three centuries (some aspects of brain function can do a good job emulating certain aspects of the underlying "non-math" universe) but there is no reason to expect that this will be an ongoing process of "ever closer union".
I obviously dont know the answer.
I would argue it's both: Yes, there are more scientists than ever but the scientific landscape has also become considerably larger. Everyone is doing research in a different niche and every niche occupies maybe 5-10 people. Also, no one knows all fields or research anymore. So any sort of breakthrough will take time.
And we probably did have a lucky run in the sense that the phenomena in fundamental physics are comparatively simple – at some point you will have solved them. They are not nearly as complex as phenomena in condensed matter, for example, where there might be some overarching patterns & schemes, but ultimately every material is still going to be slightly different and come with unexpected (or at least very material-specific) properties. (The recent discovery of the room-temperature superconductor might be a prime example here.)
The thing with complexity is, well, that it's complex. Why are you expecting any general breakthroughs?
And we probably did have a lucky run in the sense that the phenomena in fundamental physics are comparatively simple – at some point you will have solved them. They are not nearly as complex as phenomena in condensed matter, for example, where there might be some overarching patterns & schemes, but ultimately every material is still going to be slightly different and come with unexpected (or at least very material-specific) properties. (The recent discovery of the room-temperature superconductor might be a prime example here.)
The thing with complexity is, well, that it's complex. Why are you expecting any general breakthroughs?
"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.