• staticphoton
    121
    As it appears, 13 Billon years ago, space, time, matter, and energy sprung into existence by a process not quite yet understood, and thus began a process of expansion and interaction of its components under a set of boundaries which ensured the results were fairly uniform accoss the expanse as things grew in size and age.

    Eventually, acting within these boundaries, the primordial components formed complex structures which eventually aquired conscience, and a tendency to explore the origins and order of the system that produced them.

    Some might find it easier to believe on the tendency of the components to produce life and that the universe's isomorphism would suggest life is abundant, and some might find the situation on planet earth so unique that life in the universe is a rarity.
    So this knowledge is as of now out of our reach and the above beliefs unprovable.

    All that said... do you find it rather odd and marvelling, regadrless of your existential values, that we are standing here, incessantly peering and probing not just into our origins but into the origins of the very system that phoduced us? And even more so that we are actually making progress in our quest? And that we are able to craft this "mathematics" thing that allows us to model the system that produced us?

    Ok, stepping down from my soapbox now. I know this is a very ancient subject and I promise I did not smoke any weed previous to writing this post.
  • sydell
    4
    Now that you have spoken of thepossible origins of the universe, how does the idea of God come into play? The athiest supposedly claims that the universe has been here forever. I can'tfocus on the universe, because, to me, everything in the world is an idea that has been created. Even an apple tree, seems tome, to be an idea that has been created from a thought. But, I wrestle with not knowng who or what that creator is,or if I am to learn something that would lead me to believe there is none.
  • alcontali
    802
    And that we are able to craft this "mathematics" thing that allows us to model the system that produced us?staticphoton

    Max Tegmark has made an interesting attempt at modeling the "Ultimate Ensemble theory of everything" (ToE):

    ... whose only postulate is that "all structures that exist mathematically exist also physically". This simple theory, with no free parameters at all, suggests that in those structures complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world. This idea is formalized as the mathematical universe hypothesis,[16] described in his book "Our Mathematical Universe".

    Tegmark tries to model us as "self-aware substructures" (SASs). If humanity has free will, then we are a very serious problem for any ToE, which will then necessarily be incomplete.

    In fact, we can even define the term "free will" in that manner: A being has free will, if there does not exist any theory that can correctly predict its behaviour.

    So, Tegmark's self-aware substructures (SASs) are actively sabotaging the completeness of his ToE by their mere existence. If our universe is then a model of Tegmark's ToE, and since it contains true facts that are not provable from his ToE, then there must be other models, i.e. universes, in which these facts are false.

    Tegmark agrees that there must be other universes:

    The MUH is related to Tegmark's categorization of four levels of the multiverse.[6] This categorization posits a nested hierarchy of increasing diversity, with worlds corresponding to different sets of initial conditions (level 1), physical constants (level 2), quantum branches (level 3), and altogether different equations or mathematical structures (level 4).

    I don't see, however, why Tegmark needs four levels in his approach. Gödel's incompleteness theorems are enough to predict that his ToE will have more than one model. It is our very presence, causing true but unprovable facts, that makes it inevitable.

    But then again, Tegmark's detailed interpretation of how it works, goes off in directions that are inconsistent with Gödel's incompleteness theorems:

    In[3] (sec. VII) he gives a more detailed response, proposing as an alternative to MUH the more restricted "Computable Universe Hypothesis" (CUH) which only includes mathematical structures that are simple enough that Gödel's theorem does not require them to contain any undecidable or uncomputable theorems. Tegmark admits that this approach faces "serious challenges", including (a) it excludes much of the mathematical landscape; (b) the measure on the space of allowed theories may itself be uncomputable; and (c) "virtually all historically successful theories of physics violate the CUH".

    I do not believe in Tegmark's "Computable Universe Hypothesis" (CUH).

    I believe that it is exactly the other way around.

    It is the very fact that our universe is not computable, i.e. that it is a model of the ToE which contains true facts but that are unprovable from the ToE, that determines the very nature of our universe. It is rather a multi-world system that very much looks like the religious take on heaven and hell.
  • staticphoton
    121
    Now that you have spoken of thepossible origins of the universe, how does the idea of God come into play?sydell

    I think God very much comes into play.
    To the deeply religious individual, asking "why" is not necessary, since the purpose of existence is defined in scriptures.
    The resolved atheist tends to downplay "why", as it stinks of purpose.

    It is the most important question I have ever pondered and therefore find it impossible to prescribe to religion or atheism.
    But I also find it impossible not to conceive, in the process of asking "why", that the answer points towards a primordial originator, a first cause for the universe, with of course the cascade of possible implications.

    But, I wrestle with not knowng who or what that creator is,or if I am to learn something that would lead me to believe there is none.sydell

    Well, you're not alone. Being part of the unloved middle ground that refuses dogmatic structure from either side makes you an easy target to well established camps. Keeping an open perspective is a struggle because we naturally seek the comfort of a foundation. But here we are.
  • Terrapin Station
    13.8k
    to me, everything in the world is an idea that has been created. Even an apple tree, seems tome, to be an idea that has been created from a thought.sydell

    Hard--and maybe impossible--for me to relate to thinking that everything is an idea or that it would seem to someone like it has been created from a thought.
  • staticphoton
    121
    It is the very fact that our universe is not computable, i.e. that it is a model of the ToE which contains true facts but that are unprovable from the ToE, that determines the very nature of our universe. It is rather a multi-world system that very much looks like the religious take on heaven and hell.alcontali

    I'm not sure how this perspective influences the premise that we have evolved to inquire about our origins, but I will definitely give it some thought and get back with you.
  • Terrapin Station
    13.8k
    Max Tegmark has made an interesting attempt at modeling the "Ultimate Ensemble theory of everything" (ToE):

    ... whose only postulate is that "all structures that exist mathematically exist also physically". This simple theory, with no free parameters at all, suggests that in those structures complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world. This idea is formalized as the mathematical universe hypothesis,[16] described in his book "Our Mathematical Universe".
    alcontali

    I don't see how that's not basically just making up arbitrary SciFi-like crap.
  • staticphoton
    121
    Hard--and maybe impossible--for me to relate to thinking that everything is an idea or that it would seem to someone like it has been created from a thought.Terrapin Station

    Although I also think that the apple tree came from the seed instead of from a thought, the concept that first there was an idea and then there was a universe is not without merit.
    Of course I'm not referring to human thought, which is too limited to create universes.
  • Terrapin Station
    13.8k
    the concept that first there was an idea and then there was a universe is not without merit.staticphoton

    What would be the merit of that? It just seems like an arbitrary fantasy notion.
  • staticphoton
    121
    What would be the merit of that? It just seems like an arbitrary fantasy notion.Terrapin Station

    Well its not completely arbitrary, again I'm not a religious person although I can quote what John wrote in the opening of his gospel "In the beginning was the Word, and the Word was with God, and the Word was God" so there is merit in the sense that it offers an explanation for believers of the gospel, that the idea of the world came before the world.
  • Terrapin Station
    13.8k
    Well its not completely arbitrary, again I'm not a religious person although I can quote what John wrote in the opening of his gospel "In the beginning was the Word, and the Word was with God, and the Word was God" so there is merit in the sense that it offers an explanation for believers of the gospel, that the idea of the world came before the world.staticphoton

    I have no idea why that would seem to be an explanation to them.
  • staticphoton
    121
    I have no idea why that would seem to be an explanation to them.Terrapin Station

    That is ok, you are under no obligation to understand why people believe everything they believe.
  • alcontali
    802
    I don't see how that's not basically just making up arbitrary SciFi-like crap.Terrapin Station

    I may not completely agree with Tegmark's "Ultimate Ensemble theory of everything" (ToE) but if you treat the unknown ToE like a blackbox, there are still quite a few meaningful things that you can say about it.

    Tegmark's approach may have its problems, but the Theory of Everything is actually a very legitimate mathematical and scientific subject:

    Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, David Hilbert,[19] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein intensely searched for, but ultimately failed to find, a unifying theory.[20]:ch 17 (But see:Einstein–Maxwell–Dirac equations.) More than a half a century later, Einstein's dream of discovering a unified theory has become the Holy Grail of modern physics.

    It is in fact the only theory that is both abstract, Platonic (=mathematics) and empirical-scientific. All other theories can only be either.
  • Terrapin Station
    13.8k
    Tegmark's approach may have its problems, but the Theory of Everything is actually a very legitimate mathematical and scientific subject:alcontali

    Just as an instrumental way to try to reconcile quantum mechanics and general relativity without having to retool physics and/or mathematics, sure. But that's a very specific task with a misleading name if one isn't familiar with the specific issues we're trying to solve and why.
  • alcontali
    802
    Just as an instrumental way to try to reconcile quantum mechanics and general relativity without having to retool physics and/or mathematics, sure.Terrapin Station

    We do not need to have a copy of the ToE to actually know quite a few things about it -- even without reconciling QM with GR.

    As a theory, i.e. an axiomatic system, the ToE is subject to the "theory of theories", i.e. metamathematics. That is undoubtedly why Gödel's incompleteness theorems so often pop up in this context.

    I don't think that the goal of ToE research is to retool physics and/or mathematics.
  • Terrapin Station
    13.8k
    I don't think that the goal of ToE research is to retool physics and/or mathematics.alcontali

    Yeah, definitely not. That's why I said "without having to retool . . ."--folks want to avoid that.
  • Gnomon
    237
    All that said... do you find it rather odd and marvelling, regadrless of your existential values, that we are standing here, incessantly peering and probing not just into our origins but into the origins of the very system that phoduced us?staticphoton
    Yes. And all humans of all times have been intrigued by the enigma of existence with no definite cause. Yet, the only solution that makes sense requires Eternity, which is not found in Nature. The Greek First Cause was necessarily eternal. The Hindu Brahman was inherently timeless. The creator in Genesis was assumed to exist forever outside the creation. Tegmark's Mathematical Universe theory assumes that the immaterial laws of Logic & Math pre-existed the origin of it's material manifestation. And even the Materialist Multiverse is defined as existing prior to the beginning of space-time in the Big Bang, and of course un-caused or self-existent.

    So, I think it's undeniable that the only viable explanation for our contingent being is something prior to space-time, hence literally super-natural. I call it G*D. But beyond that Prime Mover axiom we can only speculate. So, without a direct revelation from beyond, the mystery remains. And your guess is as good as mine. :smile:
  • sydell
    4
    Terrpin Station, Just s it is near impossible for you to consider everything in this world is "from an idea," well, it is just as hard for me to think otherwise. I see that everything has a pattern, and comes from a source that has created it. I guess it must be the poet in me. I have very little interest in scientific explanations.
  • sydell
    4
    So, Kierkegaard advocated being an individual, but so did Thoreau. Both of them had a distaste for "sheepdom"...(people following in lockstep with one another). I think that's why both were critical of organized religion. Aside from that, what I find interesting is that Kierkegaard is said to have explored other writings to come up with his philosphical conclusions. I don't trhnk Thoreau did that, as he was more of an independent self experimenter. I guess it makes no difference how one comes up with one's conclusions. However, there are several philosophers who have gotten their conclusions from the bible, Budda, Jesus, and other philosophers. In fact, there is a man, and his name is Dr. Thomas Hora who formed his own method of psychiatry, based on his explorations. (I think Albert Ellis did the same). I am trying to read them all, to discover who I most agree with and /or who makes the most sense to me. It's difficult!!!!
  • alcontali
    802
    So, Kierkegaard advocated being an individual, but so did Thoreau. Both of them had a distaste for "sheepdom"...(people following in lockstep with one another). I think that's why both were critical of organized religion.sydell

    Most people eat breakfast in the morning, but is it "sheepdom"? Lots of people enjoy playing or watching tennis, but is that "sheepdom"? Kierkegaard may have extensively criticized existing systems, but did he propose alternative ones? No, he did not do that either.

    As usual, his atheist morality remains the typical, random collection of single-concern issues, also known as the atheist system-less bullshit.

    Single-concern issues are not innocent.

    For example, look at the women's right issue. Out of context, the rhetoric may sound attractive. However, we are now in the long run of the erstwhile short-term decisions. The long-term result means that the these atheist populations have a very low birth rate and increasingly fail to reproduce. There simply was an entire system to consider geared at keeping families together.

    But then again, now that the system has decided to replace these shrinking atheist populations by immigrants, the problem is actually solving itself. These immigrants are certainly not atheist and seem to reproduce themselves fine. Still, it was a long detour to get there. If getting rid of atheist populations was the original goal, they could have achieved that much faster and much cheaper.

    Kierkegaard would have been proud to see his atheist followers dying out like they are doing now. They can now follow their leader Kierkegaard to hell, where they can collectively burn in the hands of their master, Satan.
  • sydell
    4
    Alcontali,
    Thanks for your comment. Frst of all, I never said that I'm an atheist, and I am not one. I get that you don't like Kierkegaard, but I don't know that he was a proponent of atheism. Organized religion, yes, he was critical of it, but he also said that without a belief in God, we are all doomed. To answer your comment, yes, we eat breakfast, and some of us play the organized game of tennis. But "sheepdom, or being a "sheeple, would be defined, I think, as following and accepting rules or rituals with no meaining..It's a contradiction, I think, because Kierkegaard proposed his famous"leap of faith". Then again, he was a contradiction. Also, if you can please define Satan. I'm interested.
  • noAxioms
    753
    Max Tegmark has made an interesting attempt at modeling the "Ultimate Ensemble theory of everything" (ToE):

    ... whose only postulate is that "all structures that exist mathematically exist also physically". This simple theory, with no free parameters at all, suggests that in those structures complex enough to contain self-aware substructures (SASs), these SASs will subjectively perceive themselves as existing in a physically "real" world."...
    alcontali
    First of all, Tegmarks premise there is not what is usually referred to as the theory of everything. The latter is what you're talking about here:
    Prominent contributors were Gunnar Nordström, Hermann Weyl, Arthur Eddington, David Hilbert,[19] Theodor Kaluza, Oskar Klein (see Kaluza–Klein theory), and most notably, Albert Einstein and his collaborators. Einstein intensely searched for, but ultimately failed to find, a unifying theory.[20]:ch 17 (But see:Einstein–Maxwell–Dirac equations.) More than a half a century later, Einstein's dream of discovering a unified theory has become the Holy Grail of modern physics.alcontali
    That 'holy grail' is a unified theory, and Tegmarks comment paves no way towards unifying gravity with quantum field theory. It's just a philosophical postulate about the question of why existence exists.

    Secondly, if Tegmark says that all such structures exist physically, then the SAS will exist in a physically real wold, and not just perceive themselves to. Not sure who wrote your quote, but it obviously wasn't Tegmark. The comment isn't entirely self consistent.

    I am a big fan of Tegmark, and he has deeply influenced my beliefs. This postulate of his is a sticking point with me though since it makes pretty much everything physically real, making it not distinct from something that isn't physically real. But it points out that there is no distinction between mathematics that exists and mathematics that does not. 2+2=4 is true whether or not something physical performs the sum or not.

    This has led me to a a different approach where being 'real' is not a property of something (like a rock say) but rather a relation. The rock is real to the water it diverts. But such a view is very different now than what Tegmark is proposing.

    I don't see how that's not basically just making up arbitrary SciFi-like crap.Terrapin Station
    How wonderfully well (and typically) argued... You're free to disagree, but if you cannot point out an inconsistency in it without dragging in some strawman assumption of your own, then it is not crap at all.
  • Terrapin Station
    13.8k
    How wonderfully well (and typically) argued... You're free to disagree, but if you cannot point out an inconsistency in it without dragging in some strawman assumption of your own, then it is not crap at all.noAxioms

    The problem isn't inconsistencies. It's that it's just arbitrary crap we're making up. We could make up anything.
  • alcontali
    802
    First of all, Tegmarks premise there is not what is usually referred to as the theory of everything.noAxioms

    I understand Tegmark idea of "Ultimate Ensemble theory of everything" (UE-ToE) as being a fully-fledged "theory of everything". I think that Tegmark really means a ToE with his idea of UE-ToE. What else would he mean to refer to?

    Tegmark's proposal about SASs is rather some kind of detail in his complete idea, which on the whole is, in my impression, a ToE.

    That 'holy grail' is a unified theory, and Tegmarks comment paves no way towards unifying gravity with quantum field theory.noAxioms

    That unification attempt is the concept of ToE as seen through the lens of nuclear physics. They want the real details of the ToE. Tegmark's view is a metamathematical approach in which we are not necessarily interested in the details, and in which we treat the ToE as a black box with emergent properties.

    The ToE is the only subject-matter intersection between mathematics and physics, in a sense that it is the only place where both disciplines study the same subject.

    I am personally not particularly interested in the grand unification attempt in physics. I do not believe that Tegmark is either. Unification is obviously a legitimate research subject in physics, but I consider it to be a subject for physicists.

    But it points out that there is no distinction between mathematics that exists and mathematics that does not.noAxioms

    It only works like that in the context of the ToE. That is what is so special about this theory. If a sentence is provable in the ToE, it is guaranteed to appear as a true fact in the physical universe. This is not the case for any other mathematical theory. It will not work for number theory, set theory, or another partial theory in mathematics, which are merely Platonic abstractions, divorced from the real, physical world.

    2+2=4 is true whether or not something physical performs the sum or not.noAxioms

    The sentence "2+2=4" is true in the abstract, Platonic world of the natural numbers, which is one model (the standard one) of number theory. This model is not the physical universe. That would be impossible because number theory is not the ToE. Hence, "2+2=4" cannot be deemed (physically) true in the physical universe, unless you can argue that it is provable from the ToE. That is not possible without having access to all the details of the ToE. Proving anything from the ToE requires you to have a full copy of it. Hence, you cannot prove anything from the ToE.

    Still, even a black box ToE has emergent system-wide properties, for which we do not need access to its details. We know that the ToE is consistent, because it has a model, i.e. the physical universe. We also know that the physical universe contains true facts that are not provable from the ToE, and therefore, that there must exist other universes in which these facts are false. Hence, we know that the ToE is incomplete. Still, all of that still does not allow us to (inferentially) prove anything from the ToE. We do not know even one single theorem in the ToE. We only understand some of its emergent properties.

    That is the power of metamathematics, in which theories are just objects; just like numbers are objects in number theory. You can actually discover quite a bit about these objects without knowing (all of) their details.

    This has led me to a a different approach where being 'real' is not a property of something (like a rock say) but rather a relation. The rock is real to the water it diverts. But such a view is very different now than what Tegmark is proposing.noAxioms

    We cannot seek to abolish the distinction between mathematics and science.

    Except for the ToE, all mathematics is divorced and deemed unrelated to the real, physical world. Partial theories concerning the real, physical world must first go through the hands of correspondence-seeking scientific bureaucracies, i.e. mostly: experimental testing.
  • noAxioms
    753
    I am personally not particularly interested in the grand unification attempt in physics. I do not believe that Tegmark is either.alcontali
    Well surprise, because Tegmark is a physicist by profession where empirical results count. His dabbling on the side into metaphysics produces no falsification tests and thus is metaphysics, which in turn is philosophy. Not to discredit what he says, since it is mostly those metaphysical positions which interest me.
    Many philosophers only have a weak background (if any) in physics, and thus often produce philosophies that directly contradict physics. I appreciate Tegmark because he's not among these.

    If a sentence is provable in the ToE, it is guaranteed to appear as a true fact in the physical universe. This is not the case for any other mathematical theory.
    Going to have to give me some examples so I can figure out what you mean by this.

    It will not work for number theory, set theory, or another partial theory in mathematics, which are merely Platonic abstractions, divorced from the real, physical world.
    Tegmarks statement, as quoted by whoever authored that quote you posted, says quite the opposite: "all structures that exist mathematically exist also physically". Platonic abstractions are mathematical structures, and thus are posited to exist physically by Tegmark. I will not go so far, for the reasons I posted before. I personally don't give meaning to something 'existing physically' or 'being real'. That means I'm not a realist I guess. Tegmark definitely is one. But I like the rest of what he says.

    The sentence "2+2=4" is true in the abstract, Platonic world of the natural numbers
    It's true in many more worlds that just that one; e.g. it's true in the world of real numbers, and it's true in our world. But that was not my point. My point was about the truth of it not being contingent on instantiation. The world of natural numbers can be real or just abstract, and it is still true for that world in both cases.

    We cannot seek to abolish the distinction between mathematics and science.
    Was proposing no such thing since I am suggesting nothing scientific here. It is a straight philosophical proposition, still entirely distinct from science.
  • alcontali
    802
    Going to have to give me some examples so I can figure out what you mean by this.noAxioms

    Every sentence that is provable in a theory is true in every of its models. The physical universe is a model of the ToE. A true fact in the physical universe will be directly visible to us.

    it's true in our world.noAxioms

    Number theory are rules about numbers, which are language expressions. A theorem provable in number theory will be true in its models (of language expressions). The physical universe cannot be a model of number theory, because it is not a structure that consists exclusively of language expressions. A particular subset of English or French or Chinese could be models of number theory.

    The world of natural numbers can be real or just abstract, and it is still true for that world in both cases.noAxioms

    No. Imagine that you associate natural numbers to successive physical miles in the universe. At some point, you will run out of physical miles, because the universe is deemed finite. You will not run out of natural numbers, though. From there on, you will run into facts that are true in the natural numbers but not true in the physical universe. Hence, there is no one-to-one correspondence between both worlds. They are simply not isomorphic for arithmetic.
  • noAxioms
    753
    Number theory are rules about numbers, which are language expressions.
    ...
    The physical universe cannot be a model of number theory, because it is not a structure that consists exclusively of language expressions.
    alcontali
    Tegmark is not suggesting the universe is a structure of language expressions. You're confusing mathematics with the methods used to convey mathematical concepts. Tegmark's mathematical universe is an ontological proposition, not an epistemological one.

    At some point, you will run out of physical miles, because the universe is deemed finite.
    Is it now? You have some evidence of this?

    From there on, you will run into facts that are true in the natural numbers but not true in the physical universe.
    Nobody said the universe was the set of natural numbers. I can think of plenty of finite sized mathematical structures.
  • alcontali
    802
    Tegmark is not suggesting the universe is a structure of language expressions.noAxioms

    I wasn't discussing Tegmark's views there. The ToE is a theory of which the physical universe -- with its matter, energy, and other physical phenomena -- is a model, while number theory is a theory of which the set of natural numbers -- essentially, language expressions -- is another model. This is not Tegmark's view. It is my own opinion.

    You're confusing mathematics with the methods used to convey mathematical concepts.noAxioms

    Mathematics are language expressions about other language expressions. Both the methods and the objects being manipulated by these methods are language expressions. Certainly the formalist philosophy sees it 100% like that:

    In the philosophy of mathematics, formalism is the view that holds that statements of mathematics and logic can be considered to be statements about the consequences of the manipulation of strings (alphanumeric sequences of symbols, usually as equations) using established manipulation rules.

    Mathematical statements are strings which manipulate other strings. A number is just a string, i.e. a language expression.

    Now, this is not the only aspect of mathematics. This does not mean that I would reject the Platonist, logicist, or structuralist views on mathematics. These are other aspects of the same thing. In this context, however, in my impression, the formalist aspect dominates: Math is language about language.

    Tegmark's mathematical universe is an ontological proposition, not an epistemological one.noAxioms

    When Tegmark talks about the ToE, I actually agree with what he says, but only, because the ToE has special status: its model is the physical universe. I disagree with the idea that it would apply in general. When the model for a mathematical theory is not the physical universe, such as in number theory or set theory, I do not believe that these models physically exist in our universe. They exist in their own abstract, Platonic world.

    Concerning Tegmark's view:

    Mathematical existence equals physical existence, and all structures that exist mathematically exist physically as well.

    I agree when it is about the ToE (Theory of Everything) and I disagree for all other mathematical theories.

    Is it now? You have some evidence of this?noAxioms

    There is no entirely conclusive evidence for the theory of the Big Bang, but the theory is considered quite mainstream. If the universe started expanding from a high-density initial state, i.e. a singularity, it cannot be infinitely large today.

    As I wrote before, if the physical universe has a finite size, it cannot possibly be isomorphic with the natural numbers under arithmetic, because the cardinality of the natural numbers is countable infinity.

    At the same time, I certainly admit that there is no entirely conclusive evidence concerning the size of the physical universe.

    Nobody said the universe was the set of natural numbers. I can think of plenty of finite sized mathematical structures.noAxioms

    Yes, of course. Arithmetic is allowed in finite natural-number calculation fields as long as their size is a prime power ("Galois fields"). You do not even need first-order theories for them, because you can always apply quantifier elimination. But then again, that is only true for natural-number calculation. Real numbers always require -- at minimum -- second-order theories, and therefore, reintroduce the original problem with a vengeance.

    The physical universe is indeed not the set of natural numbers, but it is not even isomorphic with the natural numbers. Except for the ToE, there are no mathematical theories that have models that are isomorphic with the physical universe. That is why, out of the box, mathematics has no connection with the real, physical world.

    Claiming any such connection is epistemically acceptable, only when the theory first goes through a bureaucracy of correspondence-seeking formalisms, such as experimental testing in science. In all other cases, the model fitting a mathematical theory is just a Platonic abstraction that consists of language expressions describing other language expressions that are completely divorced from the physical universe.
  • jorndoe
    735
    A general theory of everything (not just the unification thing) — a model — would have something like a one-to-one mapping with the world.
    If we had such a model, then the model (cf map) would be a proper part of the world (cf territory).
    That is, the model would be a proper part of what it models, and the model would also model itself.
    I think this would lead to a fractal'ish infinite sort of structure, which may not be impossible, just odd.
    (By "proper part" I mean wholly included in the world, and not identical to the whole of the world.)
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