<div dir="auto"><div><br><br><div class="gmail_quote gmail_quote_container"><div dir="ltr" class="gmail_attr">On Thu, Feb 19, 2026, 3:59 PM Ben Zaiboc via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org">extropy-chat@lists.extropy.org</a>> wrote:<br></div><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">Apologies for not changing the subject line (again!), as this is now so far off the original topic. Probably not worth it now, though, as I think this has run its course.<br>
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On 19/02/2026 18:12, Jason Resch wrote:<br>
> On Thu, Feb 19, 2026, 7:05 AM Ben Zaiboc via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank" rel="noreferrer">extropy-chat@lists.extropy.org</a>> wrote:<br>
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> On 17/02/2026 12:05, Jason Resch wrote:<br>
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> > On Mon, Feb 16, 2026, 1:33 PM Ben Zaiboc via extropy-chat <<a href="mailto:extropy-chat@lists.extropy.org" target="_blank" rel="noreferrer">extropy-chat@lists.extropy.org</a>> wrote:<br>
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> > On 16/02/2026 16:34, Jason Resch wrote:<br>
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> Maths is an expression of the properties of the universe, a consequence of the particular laws this universe uses, or at least a consequence of the way we see them. <br>
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> That is one way to look at it, among many.<br>
> For example see this section:<br>
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> <a href="https://alwaysasking.com/why-does-anything-exist/#Math_Matter_Mind" rel="noreferrer noreferrer" target="_blank">https://alwaysasking.com/why-does-anything-exist/#Math_Matter_Mind</a><br>
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> Which shows even among three physicists, they each hold different positions.<br>
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> For example, you say that "Math is an expression of properties of the universe." But I think it is just as possible that "The universe is an expression of properties of mathematics."<br>
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> We don't have to abandon maths just because it might not be 'true', or might not actually exist in some hypothetical mystical plane of existence.<br>
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> Those who subscribe to mathematical realism hold mathematical objects to exist as concretely as any existing physical universe does. There's nothing mystical about it.<br>
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If someone tells me that the square root of -1 exists as concretely as the monitor sitting in front of me, I'm going to call that mysticism. I don't know what else to call it.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Imaginary numbers are a crucial element of quantum mechanics. Your monitor's LEDs are based on quantum mechanical principles. Before your retina can register a photon emitted from your monitor, quantum mechanics, and it's imaginary numbers, have already been invoked.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> We use maths because it's useful, not because it's true, or actually exists.<br>
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> But note that to be useful, a mathematical theory must accurately differentiate true from false. So when one of our useful mathematical theories says it is true that "$1000 - $995 = $5" also tells us that 9 is non-prime because an integer factor of 9 (besides 1 and 9) exists, are we not right to say "3 exists"? <br>
You've lost me there.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">For the number 9 to be composite (non-prime), the number 3 must exist. So this is an example where truth and existence are intertwined and inseparable: the mathematical truth that "9 isn't prime" implies the existence of a mathematical object (the number 3).</div><div dir="auto"><br></div><div dir="auto">This is my counterpoint to your claim that math only needs to be useful, and doesn't concern itself with what's true or what exists.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> What about when the theory says there are primes so large we will never be able to compute them? This is an inevitable conclusion if we take our mathematical theories seriously.<br>
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Well that's simple enough. The theory says that these prime numbers will never exist. If there can be such a theory.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">This is counter to Euclid's theorem ( <a href="https://en.wikipedia.org/wiki/Euclid%27s_theorem">https://en.wikipedia.org/wiki/Euclid%27s_theorem</a> ) which proved there exist infinite primes.</div><div dir="auto"><br></div><div dir="auto">So our choice is we either abandon everything fundamental to our mathematical theories and try to build some patchwork around the ultrafinitist position you advocate for, or we make peace with and accept the simpler theory, which says there is no largest integer.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> It is no different from the physicists who takes general relativity serious and who concludes, based on the measured curvature of the universe, that there exist regions space far beyond the cosmological horizon. They are so far away that we will never be able to see them. But these regions must exist if our theory of GR is true.<br>
So these regions of space /have/ been calculated. Which is a different thing.<br>
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> In both cases, we are taking established useful theories at their word, and using them to predict the existence of things we may never see.<br>
I think you are confusing things which can be shown to exist and things which can't.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">I thought I was clear that we couldn't see those other positions in space. However, we can infer these things exist indirectly, through our observation of things that confirm GR as a theory.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
We can show that there are regions of space beyond what we can see, but we can't show that there are (or are not) infinitely many primes.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">In both cases, we are simply relying on the assumption that our given theory is true.</div><div dir="auto"><br></div><div dir="auto">If you want to abandon the use of theories for making claims of what does or doesn't exist, then I am afraid you must retreat to solipsism and abandon the belief in anything existing aside from your current instantaneous moment of conscious experience. Everything else we believe exists (the outside world, other people, other minds, the past and future) is based on theories we assume but can never prove.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"><br>
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> Do those certain things exist independently of being worked out? That's kind of a non-question. Does a falling tree make a noise if nobody hears it?<br>
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> Did this physical universe not exist before life arose in it?<br>
Yes, it did. We can figure that out.<br>
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> Would it not then still exist even if no life ever evolved in it?<br>
That's not a question that can be answered.<br>
<br><br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">But that does seems to follow from your agreement that the universe existed before there were conscious observers in it.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> > You believe there are more than 52 Mersenne primes, don't you?<br>
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> I have no beliefs concerning Mersenne primes, mainly because I don't understand what they are. I did look up the definition, but that didn't help.<br>
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> A Mersenne prime is any prime number that's one less than a power of 2. In other words, a prime that when expressed in base 2, consists of all 1s. For example:<br>
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> 3: 11<br>
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> 31: 11111<br>
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> As of today, only 52 Mersenne primes are known. But it is believed more (and possibly infinitely many) exist. Let's assume there are more.<br>
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> Then consider the following statement:<br>
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> "A 53rd Mersenne prime exists."<br>
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> Is such a statement true?<br>
You just said 'it is believed...', so the answer to your question is "some people believe so".<br>
><br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Yes, I said let's assume that there are more left to be found, so we can focus on what we each mean when we say something exists (or doesn't) before any person sees it. Or if it helps, imagine anyone when only 51 Mersenne primes were identified. I would say the 52nd Mersenne prime exists (despite the fact that no one had yet identified it at that time). Would you say that it did not exist until the point in time some human found it?</div><div dir="auto"><br></div><div dir="auto">If you say no, then would your answer change if some alien race on the other side of the galaxy had found it already? If this changes things, that seems to make math into a very subjective thing, whose theorems and truths could vary between each person. I don't know how to make sense of such a view of mathematics.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
> Or does it only become true after someone finds it?<br>
After someone finds it, it is certainly true. As to whether it's true before then, well, "some people believe so" is the most you can say.<br>
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> I don't think that someone in ancient mesopotamia who said "there are no buildings half-a-mile tall" could reasonably be said to have been wrong, despite the fact that, given the right circumstances, it's possible to create buildings half-a-mile tall.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">If he said such buildings were not possible he would be wrong. If he said he was unaware of any such buildings he would be right. I don't see how these statements are meant to show that objective facts change with discovery, the qualifiers of "possible" "exists" and "is known to me" are each very different.</div><div dir="auto"><br></div><div dir="auto">As I see things, there is no mathematical truth that is true for one person, in one time, or in some place, that is false for some other person, in a different time, or in a different place.</div><div dir="auto"><br></div><div dir="auto">We can't even say this much about physical facts, since some believe constants of physics can change over time, or they can be different in different universes. So in this sense, physics is a less objective field than mathematics.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> I am not talking about possibilities which may or may not exist, but rather, conclusions we must accept if the theories we use and rely on happen to reflect the underlying reality.<br>
Which applies to tall buildings as much as to mathematics. We know for a fact that half-mile-tall buildings can exist. Nevertheless, we don't conclude that the mesopotamian was wrong.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">I hope my point above clarified any confusion about this.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> > There are different forms of existence.<br>
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> > There is existence defined by being mutually causally interactive (what we normally think of as physical existence, or existing within this universe). <br>
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> > But then there is also existence for things which are acausal. For example, two bubble universes in eternal inflation that will never interact, or two decohered branches in many worlds, or even just other universes with different laws, which we presume must exist to explain the fine tuning of the laws of our own universe. In what sense do these other universes exist?<br>
In the 'hypothetical' sense, unless they are proven to be factual.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Nothing can be proven. Even 2+2 = 4 cannot be proven, because any proof of such must make assumptions about the axioms, which themselves can never be proven (without making still further unprovable assumptions).</div><div dir="auto"><br></div><div dir="auto">So we are stuck with either falling into solipsism of the worst kind, or living with the understanding that all our beliefs concerning what exists beyond our immediate consciousness is based on theory and assumptions, for which we can have varying degrees of confidence.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> > Are they still worth of the full "concrete physical existence" when we can't see them and can't interact with them? Or should their existence be demoted to inferred/abstract/theoretical?<br>
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> > If the latter, isn't that the same sort of existence that mathematical object have? Other physical universes can be studied via simulation, we can analyze their properties, what structures exist as a result of their different laws, etc.<br>
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> > The abstract sort of existence that other possible universes have seems to be, to be the same sort mathematical objects have.<br>
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> Ok, we can agree on that.<br>
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> It could be called 'imaginary, but with rules'. Which is a subclass of 'imaginary'.<br>
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> I think other physical universes deserve a category slightly higher than imaginary.<br>
Don't think I mean anything derogatory by the word 'Imaginary'. I have a lot of respect for the imaginary. It could even be said to be the key factor that makes us human. And allows us to devise things like maths and science.<br>
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We don't know that there are other physical universes, we only actually know about this one. We can theorise about them, though ('imaginary with rules').<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto">The experiences we point to that justify our belief in the universe we think we see, are the same sorts of experiences we point to to justify our belief in the universes we don't see, or the parts of this universe we don't or can't see.</div><div dir="auto"><br></div><div dir="auto">In the end, there is only immediate conscious experience, and our inferences from those to some greater reality.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> Certainly the physicists who postulate the actual existence of other universes (to explain cosmological fine tuning observed in our universe) are doing something a little more serious than contemplating things in the same category as Santa.<br>
Absolutely, hence my simplified classification system.<br>
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> Likewise, I think mathematicians who devote their lives to thinking about objects in math are doing more than playing imaginary games.<br>
That is exactly what they're doing. We have countless examples showing this, from Einstein through William Hamilton to Kekule (yes, chemistry rather than maths, but it's the same process: playing imaginary games (with the relevant rules)).<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto">For me the word imaginary doesn't work because it conveys a sense of arbitrariness and subjectivity that isn't there. Newtown wasn't free to make up any laws he wanted, reality led him to "F = ma". Likewise mathematicians aren't free to make up whatever axioms they like. They, like Newton, are constrained by reality.</div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex"></blockquote></div></div><div dir="auto"><br></div><div dir="auto"></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> Quite often in history, mathematicians had already laid the groundwork for physical theories not yet conceived.<br>
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> So I'd propose a simple classification system:<br>
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> A) Stuff that physically exists (ducks, people, sofas, stars, magnetic fields, etc.)<br>
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> B) Things that are imaginary (exist as information patterns in minds: Santa, Jealousy, Immoveable objects, Other minds, etc.)<br>
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> B1) Imaginary things that conform to specific rules (Maths, Cricket scores, Cutlery etiquette, etc.)<br>
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> A gold start, but I don't think there is a clear spot for:<br>
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> - Regions of space so far away we can't see them or interact with them?<br>
> - Other branches of the wave function?<br>
> - Actually existing alternate universes with different laws?<br>
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> Are all these things physical?<br>
Ok, to expand it:<br>
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A) Physical stuff<br>
A1) Stuff that can be demonstrated to physically exist (ducks, people, sofas, stars, magnetic fields, etc.)<br>
A2) Stuff that can be shown by theory to physically exist (space-time beyond our light-cone, black holes, quarks, etc.)<br>
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These two categories are closely related, with experiments sometimes proving theories, and sometimes giving birth to new ones<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">What is the significant difference between accepting the existence of something because a physical theory suggests it, can accepting the existence of something because a mathematical theory suggests it? Note that in both cases, we are using empirically derived theories to make inferences about the content of external reality.</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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B) Things that are imaginary (exist as information patterns in minds: Santa, Jealousy, Immoveable objects, Other minds, etc.) <br>
B1) Imaginary things that conform to specific rules (Maths, Cricket scores, Cutlery etiquette, etc.)<br>
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I don't know how to categorise 'other branches of the wave function' because I don't exactly know what it means. Sounds like quantum stuff, though, and might mean the same thing as 'other universes'?<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">You can treat them as functionally other universes, which have theoretical from quantum mechanics. They are other universes that can, in certain circumstances, interact with our own, until they deochere, in which case further interaction is prevented.</div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> If so, consider that string theory suggests there are at least 10^500 different sets of physical laws. All these different universes existing as different laws as a result of one mathematical foundation of string theory equations.<br>
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> According to strong theory, all these universes physically exist.<br>
According to religious theory, so does the holy ghost.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">Just before you said we can use physical theories to justify beliefs in physical things we can't see. Are you now denying this?</div><div dir="auto"><br></div><div dir="auto"><br></div><div dir="auto"><div class="gmail_quote gmail_quote_container"><blockquote class="gmail_quote" style="margin:0 0 0 .8ex;border-left:1px #ccc solid;padding-left:1ex">
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> But what makes the equations of string theory special? Why shouldn't there be universes that follow other equations besides those of strings? If other equations defining other universes, are no less valid than string theory, then the line between physical existence and mathematical existence dissolves.<br>
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> Physical existence is nothing more than mathematical existence. And we are back to Platonism. Or as Tegmark describes it, the mathematical universe hypothesis:<br>
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> <a href="https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis" rel="noreferrer noreferrer" target="_blank">https://en.wikipedia.org/wiki/Mathematical_universe_hypothesis</a><br>
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Well, I think it's the other way around.<br>
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In the end, as John Clark is fond of reminding us, there's no disputing matters of taste.<br></blockquote></div></div><div dir="auto"><br></div><div dir="auto">It would be a matter of taste except for the fact that there is strong empirical evidence that it is as I say, that the physical emerges from the mathematical/computational. Until and unless you can show some alternate explanation or theory for these observations, this is simplest (and so far the only known) answer for these facts:</div><div dir="auto"><br></div><div dir="auto">The logician and computer scientist Bruno Marchal showed that computationalism and arithmetical realism predict a physics with quantum logic, quantum indeterminacy, quantum non-locality, and an ontology of parallel states (Marchal, 2001).</div><div dir="auto"><a href="https://iridia.ulb.ac.be/~marchal/publications/CC&Q.pdf">https://iridia.ulb.ac.be/~marchal/publications/CC&Q.pdf</a></div><div dir="auto"><br></div><div dir="auto">The computer scientist Russell Standish assumed observation within an infinite plenitude and showed he could derive the linearity of physical law, Occam's razor, and the Schrödinger equation (Standish, 2006).</div><div dir="auto"><a href="https://www.hpcoders.com.au/theory-of-nothing.pdf">https://www.hpcoders.com.au/theory-of-nothing.pdf</a></div><div dir="auto"><br></div><div dir="auto">The quantum physicist Markus Müller detailed how algorithmic information theory predicts that most observers will find themselves in universes with time, a beginning, and governed by simple, computable, probabilistic laws (Müller, 2020).</div><div dir="auto"><a href="https://quantum-journal.org/papers/q-2020-07-20-301/">https://quantum-journal.org/papers/q-2020-07-20-301/</a></div><div dir="auto"><br></div><div dir="auto">The computer scientist and physicist Stephen Wolfram details how all computations playing out in all possible ways explain why observers will see a universe with the second law of thermodynamics, general relativity, and quantum mechanics (Wolfram, 2021b).</div><div dir="auto"><a href="https://writings.stephenwolfram.com/2021/03/what-is-consciousness-some-new-perspectives-from-our-physics-project./">https://writings.stephenwolfram.com/2021/03/what-is-consciousness-some-new-perspectives-from-our-physics-project./</a></div><div dir="auto"><br></div><div dir="auto">Jason </div></div>