This is one of the oldest concepts in Ancient Philosophy. Not only did the Pythagoreans famously believe it, they also derived a number of other concepts from it, including Eternal Return:<p>"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:<p>> ‘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.’"<p>- Simplicius
Commentary on the Physics 732.23-33."<p>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.<p>In the 20th century, Konrad Zuse's "Digital Physics" is explicitly a Mathematical Universe Hypothesis.<p>The way people attribute the concept to Tegmark is somewhat laughable, IMO. He just modernized small slices of it, in a rather haphazard way.
I appreciate Sabine Hossenfelder's take on MUH[1]:<p>"...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."<p>"...this is a belief-based statement, not supported by evidence."<p>[1] <a href="https://www.youtube.com/watch?v=CTpp0EChDbI">https://www.youtube.com/watch?v=CTpp0EChDbI</a>
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.<p>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).<p>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.
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.
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?<p>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?<p>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?
Relevant discussion <a href="https://www.lesswrong.com/posts/HBHsFCeAMSqMD7Td7/does-the-simulation-argument-even-need-simulations" rel="nofollow noreferrer">https://www.lesswrong.com/posts/HBHsFCeAMSqMD7Td7/does-the-s...</a><p>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.<p>The discussion helped me realise it's a measure problem, and a measure can be constructed according to the complexity of the mathematical structure.<p>Makes sense, but why should the measure be constructed like that?
In section II.D:<p>> 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.<p>I don't think that follows. It could be that the universe is <i>asymptotically</i> mathematical, in the sense that <i>any</i> 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 <i>finite</i> 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]<p>[0]<a href="https://writings.stephenwolfram.com/2020/04/finally-we-may-have-a-path-to-the-fundamental-theory-of-physics-and-its-beautiful/" rel="nofollow noreferrer">https://writings.stephenwolfram.com/2020/04/finally-we-may-h...</a>
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?<p>People keep telling me that consciousness is just some illusion which happens inside brain neural network.<p>However, in case of mathematical universe hypothesis, nothing really <i>happens</i>.
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.<p>Why do we feel that we exist? Who does the feeling part?
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.
Related discussion from 2017:<p><a href="https://news.ycombinator.com/item?id=15637074">https://news.ycombinator.com/item?id=15637074</a>
Fancy words to say there is a grand designer.<p>I don’t buy it.<p>Always at the edge of human understanding we say “well we don’t understand that, so there must be a man behind the curtain”.
Homo sapiens is the most arrogant little pile of carbon this side of the Tanhausser gate.<p>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".<p>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".<p>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.<p>We have now almost a century of stagnation around any really <i>new</i> mathematical concepts that would help us push further into "in your face" empirical manifestations, e.g. around complex phenomena.<p>There is no obligation that the Universe is made of nails.