We need more discussion of Tegmark's mathematical universe hypothesis

Discussion in 'Site Feedback' started by James R, Nov 18, 2023.

  1. Halc Registered Senior Member

    Messages:
    350
    You see a distinction between the idea of an apple and an apple, the reference vs. the referent, map vs territory. You seem to accept this for most things, but then decide to treat mathematics differently by equating idea and the thing itself, equating reference to referent. This seems inconsistent to me. The distinction is clear to some of us, and the MUH presumes such a distinction, so I don't think it a valid criticism to be incapable of it.

    What are physical things made of, anyway, in your opinion? What, say, composes an electron? They've never found any actual matter consuming actual volume no matter how close they look. The closer they look, the less it looks physical. That was one of the points Tegmark was trying to make in one of his replies to a suggestion that physical things are made of mathematics. I don't think Tegmark ever said physical things are made of mathematics. He said something else, that the universe is a (one) mathematical structure.

    BIV (the VR hypothesis) does not posit that there is a human brain. It just says mind. Sure, it is fed artificial input to make it believe it is human with a pink brain that sits in its head, but there's absolutely no evidence of that given the BIV scenario.

    I don't think you get it, because in post 98 (quoted just above), you assert that mathematics can only be an idea, denying that the idea is a mere referent to the actual mathematics, which is objective, independent of both mind and of this particular universe.

    Being real is a relation to me. It has nothing to do with perception, but rather to do with cause and effect. Hence only the observable universe being real to me since anything outside that has no more causal effect on me than say some 5-dimensional universe with confused unicorns.

    And no, I never support a simulation hypothesis, which seem a category mistake. It would be a simulation OF something, which doesn't change what the thing being simulated is. For the record, our universe cannot be classically simulated (here's a state, and now we compute the next state some short moment later). That just doesn't work with our physics.

    It's been measured by you, so yes. You can't un-measure something.
    You are actually. It has nothing to do with conscious measurement or 'looking at'. Stuff in Paris has a continuous effect on all particles in the planet, if nothing else, by its mass curving spacetime. It's why I used the water as the thing measuring the duck, something that doesn't do a conscious measurement.
    It cannot cease to be. It can fall down, and be recycled into new stuff. Any of that would have an effect on you in Australia in probably under a second. To stop measuring it, you'd have to put it in a Schrodinger's box, something from which zero information can escape. Even then, the tower would exist, but its exact state (up, fallen say) might be in superposition. The largest object they've ever managed to isolate like that was barely visible to the naked eye, and even then, they only managed to keep it unmeasured for under a microsecond. Long enough to demonstrate the superposition state though.

    Never about that. I'm not an idealist. A rock does not perceive, but it very much is affected by its environment and thus it measures.

    You and I measure each other, and thus cannot have a significantly different list of what is real. If you and I were separated by a trillion light years, then yes, we'd have a completely different list, and neither of us would be real to the other. Again, this would be unrelated to us being conscious things. All this seems somewhat irrelevant to MUH. It's just how I define 'is real' since I find the usual (property) definition somewhat useless. Does a unicorn have a horn? How would you answer that? How might an idealist answer it? I would simply say yes.

    He doesn't talk about the duck of course, but the universe in question has a worldline of you in it, and a worldline of the duck, and these two interact. There is no 'present moment' in such a universe, so a universe that contains your worldline also has the duck worldline, else they could never have interacted. But you speak of after your death, like the universe somehow doesn't contain your worldline in that case, but it does. Only under presentism are you actually no longer part of the universe after your death, and MUH is not a presentist interpretation.

    Maybe he says that. I read the book, a library copy. Don't have it. I don't know if he actually says a particular thing (duck) is mathematics, rather than being simply part of a mathematical structure. If the criticism revolves around that particular wording, I'd have to see the context because I would not have said that the duck is somehow some kind of separate mathematics on its own. Physics for one defines no concept of identity. The grouping of atoms into an 'object' upon which the label 'duck' is applied is strictly a conscious construct. The duck does not operate independently of the mathematics of the universe. Saying it is separate seems wrong.

    Our universe contains both, so without both, it would be a different mathematical structure, a different universe. This is similar to noting that there are other worlds (MWI worlds) that contain neither you nor the duck in question, but contain other people and ducks. There are also worlds where Earth has no life at all. But all those worlds are still part of our particular mathematical structure, and that structure contains you and the duck, in many but not most worlds. And yes, Tegmark is a big MWI fan. I am not due to my issues with realism.
     
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  3. Halc Registered Senior Member

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    You are of course under no obligation to accept MUH. I have problems with it myself. Tegmark was stupid enough to suggest tests, all of which are fallacious. I thought they degraded the impact of his proposal.

    I don't get this comment. Why should other mathematical structures be instantiated in other ones? Why is the lack of that (e.g. there are no circles in a triangle) be a problem for the hypothesis?

    To critique some hypothesis, you can't assume different premises and then find contradiction with your new premise. That's a begging fallacy. If our universe is a mathematical structure, time is part of that structure (block view). The structure does not exist within time (presentist view), which would make time more fundamental than the mathematical structure, a contradiction with the MUH premises.
    So a universe that contains your worldline cannot also not contain your worldline, hence this structure contains you. The phrase 'stops existing after a time' is meaningless outside of presentism. Your worldline is bounded by time, going from year X to Y, but that worldline is part of the block and there is no present time at which that worldline is not meaningfully part of the block.

    Well it is of course. The block view regards time as a dimension. In a view where the structure is contained by time, one is saddled with the additional task of explaining what initiates the evolving mathematical structure, and how time can be meaningful in the absence of that structure, and if other structures are also contained by that same time.

    Dualism asserts that your choices are not the product of physics, so one needs to identify some construct somewhere in the causal chain leading to an action that has no physical cause. A human for instance needs to violate physics for it to work, and yet no such violation has been found, and those suggesting it decline to look for it, despite it being a very solid evidence for their stance.
    Lara Croft raises her arm. Does her brain cause her to do that? No, she doesn't even have a brain. Clearly her action are not the product of internal brain activity, but come from outside. The limbs are controlled directly. Clearly a case of dualism. I hope you get the Lara reference.
    Talk of this concerns the VR hypothesis, and seems pretty irrelevant to this topic.

    Disproving presentism is like proving the afterlife. There's a test, but the results of the test cannot be published. The test is fatal.

    I agree that VR and simulation hypothesis are not important to MUH discussion. Both posit a higher reality, and MUH does not.

    I said 3 was on equal ontology as our universe. I didn't say 3 made a duck. 3 is a trivial mathematical structure, and our universe appears quite complex, sufficient complexity to contain internal states that glean the nature of the structure itself.

    That 3 is only an abstraction without a distinct referent. You were quite explicit about this in several posts. See top of this post.


    I am attracted to MUH, but it has problems which I have pointed out, not in much detail. And no, I don't think a duck is a mathematical structure. It is only part of a much larger structure. A duck being a separate thing seem not emergent from any physics, and is essentially a mental construct. Sure, there is a referent. Other minds perceive and similarly label the same duck as an object, but physics doesn't seem to recognize any system as an object, distinct from 'the state of particles in a given volume' or some such.
    To illustrate what I mean, physics allows the state of location 'x' to change from a missile to a bowl of petunias. All one has to do is consider some inertial frame where that volume is occupied by the missile at time x and the same volume is occupied by petunias a second later. There's no identity in physics, so a protest that the missile still exists elsewhere presumes the state of the EM field to somehow constitute the identity of 'missile', and that the similar state elsewhere is now where 'the missile' is. But physics assigns no such identity, and we defined the identity in this case to be simply the state of a certain volume over time, in a specific frame. Sorry if the example is hard to explain, and only somewhat relevant. I'm just trying to illustrate that 'duck' as an identity isn't part of physics but more of a mental designation.

    Appealing to common sense would have much of the last century of physics abandoned. Is the hypothesis useful? Only from a philosophical standpoint since it solves many of the issues with other explanations for the universe. As for matter and ideas, not all referents of ideas are material, so that is unfair. God is an idea. Is the idea wrong because the referent isn't matter? Is that a valid falsification of a god hypothesis?

    That I very much do claim. When asked what we can know for sure, I immediately balk at 'cogito ergo sum', but I have a hard time denying that the sum of 2 and 3 is 5, even in the absence of a mind to conceive of it.
     
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  5. Yazata Valued Senior Member

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    My guess is that W4U is arguing (perhaps without realizing it) for a currently popular idea in the philosophy of science called Structural Realism.

    https://plato.stanford.edu/entries/structural-realism

    The SEP says,

    "Scientific realism requires belief in the unobservable entities posited by our most successful scientific theories. It is widely held that the most powerful argument in favour of scientific realism is the no-miracles argument, according to which the success of science would be miraculous if scientific theories were not at least approximately true descriptions of the world...

    ...arguably the most powerful arguments against scientific realism are based on the history of radical theory change in science. The best-known of these arguments, although perhaps not the most compelling of them, is the pessimistic meta-induction, according to which reflection on the abandonment of theories in the history of science supports the expectation that our best current scientific theories will themselves be abandoned...

    ...Structural realism was introduced into current philosophy of science by John Worrall in 1989 as a way to break the impasse that results from taking both arguments seriously, and have “the best of both worlds” in the debate about scientific realism. With respect to the case of the transition in nineteenth-century optics from Fresnel’s elastic solid ether theory to Maxwell’s theory of the electromagnetic field, Worrall argues that:

    'There was an important element of continuity in the shift from Fresnel to Maxwell—and this was much more than a simple question of carrying over the successful empirical content into the new theory. At the same time it was rather less than a carrying over of the full theoretical content or full theoretical mechanisms (even in “approximate” form) … There was continuity or accumulation in the shift, but the continuity is one of form or structure, not of content.' (1989: 117)

    According to Worrall, we should not accept standard scientific realism, which asserts that the nature of the unobservable objects that cause the phenomena we observe is correctly described by our best theories. However, neither should we be antirealists about science. Rather, we should adopt structural realism and epistemically commit ourselves to the mathematical or structural content of our theories. Since there is (says Worrall) retention of structure across theory change, structural realism both (a) avoids the force of the pessimistic meta-induction (by not committing us to belief in the theory’s description of the furniture of the world) and (b) does not make the success of science (especially the novel predictions of mature physical theories) seem miraculous..."


    And I take Tegmark as basically publishing a publicly accessable version of a rather Platonic (and Kantian?) sort of idea that is known in the literature as Ontic Structural Realism.

    The SEP again:

    "Some philosophers of physics had already more explicitly signalled a significant departure from traditional realist metaphysics. For example, Howard Stein says:

    '[O]ur science comes closest to comprehending “the real”, not in its account of “substances” and their kinds, but in its account of the “Forms” which phenomena “imitate” (for “Forms” read “theoretical structures”, for “imitate”, “are represented by”).' (1989: 57)

    Michael Redhead (1999: 34) says: “the best candidate for what is ‘true’ about a physical theory is the abstract structural aspect”. Accordingly, Ladyman (1998) argues that structural realism ought to be developed as a metaphysical position according to which, since the continuity in scientific change is of “form or structure”, the success of science should be accounted for in terms of the representation of modal relations among phenomena, not in terms of continuity of reference to objects and properties."


    My own view is that this kind of idea might arguably be a reasonably plausible way of conceptualizing theoretical physics with its penchant for filling chalkboards full of mathematical squiggles describing relationships between variables, but it's less so for sciences like biology who damnedly persist in thinking that the objects of their sciences physically exist and can't be reduced without remainder to mathematical relationships between observations.
     
    Last edited: Nov 28, 2023
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  7. Pinball1970 Registered Senior Member

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    Those objects do exists, DNA, chemical messengers, organelles, cells , tissues organs organism and populations. There is no point learning about organisms or cells in terms of quarks.
     
  8. Write4U Valued Senior Member

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    19,970
    Applied mathematics isn't abstract, is it?
     
  9. Write4U Valued Senior Member

    Messages:
    19,970
    Try learning something without mathematics. It can't be done. Mathematics is pervasive throughout the universe. If you accept the concept of physical patterns, then you are using mathematics.

    So, do you see quarks as mathematical objects? Something that has a mathematical "value"? If fundamental elements are mathematical values, does that make all of physics a mathematical discipline?

    DNA is a mathematical pattern, a mathematical code that guides mitosis and cell growth.

    Let me look at this from another perspective.
    Questions: If something does not have mathematical properties, can it be mathematically described?
    If not, is there anything in physics that cannot be mathematically described?
    If everything can be mathematically described from the very fundamentals, why should it not be a property of the universal geometry?
     
  10. Write4U Valued Senior Member

    Messages:
    19,970
    The term structure refers to a mathematical object.
    The voice of reason....

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    The Structure of Scientific Theories
    .............
    ....
    A table helps summarize general aspects of the three views’ analyses of the structure of scientific theories:

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    https://plato.stanford.edu/entries/structure-scientific-theories/[/quote]

    Note; a structure is a mathematical object.

    Space (mathematics)

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    Fig. 1: Overview of types of abstract spaces. An arrow indicates is also a kind of; for instance, a normed vector space is also a metric space.
    https://en.wikipedia.org/wiki/Space...tical_implication_diagram-alt-large-print.svg

    Note that David Bohm already proposed an abstract "ordering" principle to spacetime.

    He coined it the "Implicate Order".
    The enfolded potential that may become expressed in reality as the Explicate or unfolded order.

    If everyone recognizes some mathematical aspects to spacetime, what is the objection to the notion that spacetime itself is a mathematical object?
     
    Last edited: Nov 29, 2023
  11. James R Just this guy, you know? Staff Member

    Messages:
    39,237
    While much of what Write4U has just posted is as irrelevant as usual, the article from the SEP on the structure of scientific theories is interesting. At a glance, the one that comes closest to my own view is what they call the "Pragmatic View":

    Finally, for the Pragmatic View, scientific theory is internally and externally complex. Mathematical components, while often present, are neither necessary nor sufficient for characterizing the core structure of scientific theories. Theory also consists of a rich variety of nonformal components (e.g., analogies and natural kinds). Thus, the Pragmatic View argues, a proper analysis of the grammar (syntax) and meaning (semantics) of theory must pay heed to scientific theory complexity, as well as to the multifarious assumptions, purposes, values, and practices informing theory.​

    Apparently, all that Write4U took away from that article (which I assume he didn't read or understand) was that "a structure is a mathematical object". There's a bit more in there than that.
     
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  12. James R Just this guy, you know? Staff Member

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    39,237
    I learned to tie my shoelaces. Where was the maths?

    I learned how to speak English. Where was the maths?

    etc.
    Where? I don't see any maths when I look at the universe.
    That's tricky. I see quarks as theoretical entities that (currently) form part of the bedrock of a particular scientific theory (the Standard Model of particle physics). The theoretical model uses mathematics, of course. However, when we say something like "a proton contains quarks", we're really trying to say something about the properties of a material object, rather than only talking about a theoretical model. Nevertheless, it can be hard to separate talk about the theory from talk about the physical things that the theory is describing.

    The bottom line is that, whatever a (physical) proton actually is, it isn't "made of maths".
    Your usage of the word "value" is essentially meaningless. You have never been able to adequately define it.
    Define "mathematical discipline". Is that just a field of study that makes use of mathematics? Is accounting a mathematical discipline, then? Is English Literature a mathematical discipline? Does it matter, if you think that everything is mathematical?
    No. DNA is not maths. It is not a code. It is a molecule.
    Define "mathematical properties". Does English Literature have mathematical properties? Can it be mathematically described?
    The map is not the territory. A description of a thing is not the thing.

    You keep making the same basic category error, along with Tegmark.
    A completely irrelevant cut-and-paste.
    Who cares? Why do you need to name drop Bohm in every second post?
    That doesn't actually mean anything. It's metaphysical gobbledygook.
    I already told you.

    What's wrong with you, man?
     
  13. gmilam Valued Senior Member

    Messages:
    3,500
    From your own link: "In the past, practical applications have motivated the development of mathematical theories, which then became the subject of study in pure mathematics where abstract concepts are studied for their own sake. The activity of applied mathematics is thus intimately connected with research in pure mathematics."
     
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  14. Write4U Valued Senior Member

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    19,970
    Yes indeed, and that article addresses the narrative of theory in general and does not address the mathematical essence of spacetime geometry.

    Category error.
     
  15. James R Just this guy, you know? Staff Member

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    39,237
    How did you manage to miss post #108?

    "Mathematical components, while often present, are neither necessary nor sufficient for characterizing the core structure of scientific theories."

    Tegmark's position is in direct opposition to this, but he goes further, asserting that not only are scientific theories mathematical, but "reality" is mathematical. That is, he believes that mathematics is necessary, indeed fundamental.
     
  16. James R Just this guy, you know? Staff Member

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    39,237
    Sarkus:
    I assumed you knew, if you're telling me that I am wrong.

    It seems that neither you nor I have read Tegmark's book, so we're on an approximately equal footing when it comes to commenting on his claims and reasons. I have been going by what I have read about the specifics of his claims from various sources on the internet. How about you?

    I'm always happy to learn more, and to be corrected if you can demonstrate that I've made a mistake. If you can show me I'm not fairly assessing Tegmark's arguments, fine. Go to it.
    Tegmark's MUH is about the "ultimate nature of reality". He says that if we keep digging down, we'll discover that, at the bottom, our universe is nothing but mathematics.

    The simulation hypothesis is not consistent with the base level of our universe being mathematics because it posits another undiscovered layer - the one which is doing the simulating.

    I do not think the 1s and 0s in the computer in front of me are mathematics. The characters in a video game on my computer are not "made of mathematics". If they can think for themselves, they should not conclude that they are made of mathematics, even though they, in universe A (inside the simulated computer game) can't access universe B (our universe, in which my computer exists). The fact of the matter, in this example, is that the relevant information that makes up those simulated people in my computer, is encoded in a physical substrate that involves silicon chips, electrons and such.
    Don't worry about me. I'll be fine.
    Good of you to allow for my mental deficiency. You're clearly much cleverer than I am, as usual.
    Read his book? No. Understood sufficiently what his argument is? I think so. But I could be wrong. I've heard him talk, so I do have some direct access from the horse's mouth, so to speak.

    How about you?
    I don't know whether he has addressed the issue or not. I hope he is aware of it. It seems like an obvious and important objection.

    Certainly, some of his reviewers, who have read his book, don't think that he has dealt with the matter.
    There's only one way to find out for sure if I'm wrong about what he says. Happy reading, Sarkus!
     
  17. Write4U Valued Senior Member

    Messages:
    19,970
    Oh I showed you the maths of tying shoelaces a long time ago. If you had looked at some of the links I posted then all these question would go away.
    This is what happens when you are prejudiced. It clouds decision making.
    See below.
    ETC doesn't belong in this thread. It belongs in the thread about microtubules.

    Electron Transport Chain - Definition and Steps | Biology Dictionary

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    sciencing.com › electron-transport-chain-etc-definition-location-importance-13717928.html
    Electron Transport Chain (ETC): Definition, Location & Importance
    Yes you do, you are just trying to see symbolized human invented numbers, but that's a category error.
    You mean, the description of the values of your theoretical entities? And of course you can use human-symbolized maths to identify the real generic mathematics you see in the patterns.
    And those properties are the relational "values", that can be described with maths because they are mathematical in essence.

    And no one proposes to drop the narrative that accompanies the fundamental mathematics of the interactive properties.

    This is not an either/or situation. For human communication and understanding, generic maths requires narratives in addition to symbolic representation. A chameleon just uses maths without needing speech or even understanding. Triangulation is the proper method of estimating distance and trajectory. Catching a bug is a mathematical enterprise.

    Which proves the independent existence of the mathematical nature of spacetime and the interactive functions of everything.
    Interestingly, I have already told you that if I understand the scientific narrative, I don't need the maths, which are the proofs of the narrative, no?
    It has a value that can be described with maths proving its mathematical essence.
    And that is a problem for you? Do you understand the definition of "value"?
    Have you ever heard of theoretical mathematics?
    What Is the Benefit of an Accounting Degree Vs a Mathematics Degree?
    https://www.degreequery.com/queries...tween-an-accounting-degree-and-a-math-degree/
    It doesn't matter what you or I think at all. The universe was here before you and me and will be here long after you and I have gone "away". It will not stop without us.
    And what does this molecule do?
    [/quote]Define "mathematical properties". Does English Literature have mathematical properties? Can it be mathematically described?[/quote]
    Yes, quite easily. See below.
    Yes, it is a description of the mathematical properties of a thing.
    Why don't you tell him?
    What's wrong with your prejudicial attitude?
    All I see from you is mud-slinging. Very uncivilized.
    You demand that I provide evidence, yet you refuse to examine the evidence that I produce.

    For once, will you please look at this short lecture by Roger Antonsen? He visually demonstrates the mathematics that answers some of your questions. There is nothing complicated or mystical about his presentation, but he discusses this very subject.

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    The maths of shoe lacing.

     
    Last edited: Nov 30, 2023
  18. James R Just this guy, you know? Staff Member

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    39,237
    Write4U:
    Show me the maths of learning to tie shoelaces. That was your claim. Remember?
    Irrelevant.
    Nothing in your post shows how English Literature is mathematical.
    Other people have already told him. My objections to his hypothesis are already in the public space. He can access them. He can even access this forum.

    If I spent all my time firing off emails telling various public figures why they are wrong about things, I'd have no time left for all the other stuff I have to do.

    I'm not so concerned about the implications of Tegmark's being wrong that I feel like I need to contact him personally to let him know. If I did feel more strongly about it, I suppose I might do that, but I don't.
    Towards what?
    Give one example.
    What are you talking about?
    I watched the video. It was an entertaining talk. It was, however, irrelevant to the question of whether the universe is mathematics and he did not discuss that.
     
  19. James R Just this guy, you know? Staff Member

    Messages:
    39,237
    Write4U:

    You edited your post while I was replying. I will respond to the rest.
    Which categories am I mixing up?
    Yes. The theoretical model of quarks uses mathematics.
    I don't know what "real generic mathematics" is.
    I have no problem with the idea that mathematical descriptions of physical things are a thing.
    I disagree. I don't think a chameleon is really "doing maths" when it catches a bug. What is going on in its brain is complicated, but it isn't something I would describe as "doing maths". I am aware that a lot of nature documentaries use that sort of metaphor in explaining what is going on, but it's a very simplified description of what's actually going on.
    It depends on what you're trying to use the scientific narrative for.

    (How is this relevant to Tegmark's hypothesis?)
    Then tell me, Write4U. What is the mathematical "value" of a proton, that proves its mathematical essence?
    Not as you use it. You seem to be incapable of defining it. Like I said. And you still haven't explained what you mean.
    No. What's that?
    Irrelevant. Why won't you answer the question I asked you?
    So you don't know whether English Literature is a mathematical discipline or not. I thought as much.
    Ask in a different thread. Really, though. You honestly have no idea what DNA molecules do?
     
  20. Write4U Valued Senior Member

    Messages:
    19,970
    It directly answered your question about shoelaces and alphabetical letters.
    Antonsen taught you in the above clip.
    As was your "etc". Antonsen showed you the relevance
    What is the difference between 'form' and 'structure' in poetry?
    Found any reference to mathematical properties in that example of literature?
    I doubt he knows you exist.
    You're spending a lot of time unnecessarily telling me that I am wrong about EVERYTHING!
    Right, so Tegmark is wrong and you could set him straight?

    Well then...this must be you.

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    Last edited: Nov 30, 2023
  21. Write4U Valued Senior Member

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    Generic mathematics (relational values), and human symbolization of the generic relational values.
    And in reality a quark has no value at all? Check this out.

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    http://hyperphysics.phy-astr.gsu.edu/hbase/Particles/quark.html
    The enfolded mathematical potential of a thing (Bohm)
    How about mathematical functions?
    Yes, they are all wrong.
    When I see a chameleon gauging the distance and exact location of the prey, I see it turning both eyes toward the spot, the brain does the rest. And yes the brain is complicated but triangulation isn't and even a chameleon's brain can do triangulation.
    I told you, understanding. What do you use narratives for?
    This? Many animals use mathematics without knowing it.
    The universe uses mathematics and it does not know this either. It just behaves that way.
    If it has any value at all it is mathematical in essence. Are you telling me, a proton has zero relational value?
    A value is an inherent potential to do work, ok?
    You better read up on that then.
    English literature doesn't have to be mathematical, it is not science. However algebra is!

    Algebraic Expressions
    https://byjus.com/maths/algebraic-expressions/
    You insist that I answer in this thread.
    What makes you spill that piece of drivel?
    A DNA molecule is a mathematical object that contains the coded blueprint of the organism that is faithfully copied via the Mitotic spindle, a mathematical copy machine.

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    Simplified diagram
    Properties

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    Chemical structure of DNA; hydrogen bonds shown as dotted lines. Each end of the double helix has an exposed 5' phosphate on one strand and an exposed 3′ hydroxyl group (—OH) on the other.
    more.... https://en.wikipedia.org/wiki/DNA
    Building block (chemistry)

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    https://pubmed.ncbi.nlm.nih.gov/18275887/#

    Sounds pretty mathematical to me.
     

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  22. Write4U Valued Senior Member

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    19,970
    Didn't learn the maths of tying shoelaces, did you?
    You cited shoelacings as not being mathematical. Antonsen showed you they are.

    Antonsen showed you the "image" of the value 4/3

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    I think this is a nice example of an emergent self-organizing mathematical pattern from an abstract value.
     
  23. Write4U Valued Senior Member

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    19,970
    What about displacement? Is the water making an involuntary measurement?
     

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