Good Math, Bad Math

In the comments to another post, Blake Stacey gave me a pointer to a really obnoxious article, called “A New Theory of the Universe”, by a Robert Lanza, published in the American Scholar. Lanza’s article is a rotten piece of new-age gibberish, with all of the usual hallmarks: lots of woo, all sorts of babble about how important consciousness is, random nonsensical babblings about quantum physics, and of course, bad math.

Lanza’s “theory” (if one wants to be generous enough to call it that) is that life is a fundamental, in fact the fundamental guiding force of the entire universe. His argument for that is purest, utter nonsense. Here’s a typical sample:

Our science fails to recognize those special properties of life that make it fundamental to material reality. This view of the world–biocentrism–revolves around the way a subjective experience, which we call consciousness, relates to a physical process. It is a vast mystery and one that I have pursued my entire life. The conclusions I have drawn place biology above the other sciences in the attempt to solve one of nature’s biggest puzzles, the theory of everything that other disciplines have been pursuing for the last century. Such a theory would unite all known phenomena under one umbrella, furnishing science with an all-encompassing explanation of nature or reality.

We need a revolution in our understanding of science and of the world. Living in an age dominated by science, we have come more and more to believe in an objective, empirical reality and in the goal of reaching a complete understanding of that reality. Part of the thrill that came with the announcement that the human genome had been mapped or with the idea that we are close to understanding the big bang rests in our desire for completeness.

But we’re fooling ourselves.

Most of these comprehensive theories are no more than stories that fail to take into account one crucial factor: we are creating them. It is the biological creature that makes observations, names what it observes, and creates stories. Science has not succeeded in confronting the element of existence that is at once most familiar and most mysterious–conscious experience. As Emerson wrote in “Experience,” an essay that confronted the facile positivism of his age: “We have learned that we do not see directly, but mediately, and that we have no means of correcting these colored and distorting lenses which we are or of computing the amount of their errors. Perhaps these subject lenses have a creative power; perhaps there are no objects.”

Mr. Lanza really doesn’t like math very much. A very large part of his argument is really just
an elaborate argument for why it is that biology (which he allegedly understands) and goofy metaphysics (which he can make up as he goes along) are really more important than math.

We have failed to protect science against speculative extensions of nature, continuing to assign physical and mathematical properties to hypothetical entities beyond what is observable in nature. The ether of the 19th century, the “spacetime” of Einstein, and the string theory of recent decades, which posits new dimensions showing up in different realms, and not only in strings but in bubbles shimmering down the byways of the universe–all these are examples of this speculation. Indeed, unseen dimensions (up to a hundred in some theories) are now envisioned everywhere, some curled up like soda straws at every point in space.

This comes down to a rather tacky argument from incredulity: “Gosh, doesn’t all of this mathematical stuff just sound totally ridiculous? Isn’t is just obvious that anything that dumb is total
nonsense?”. No, all of this complicated math stuff, this spacetime crap, the math of relativity: I don’t understand it, and so it must be wrong.

And so he proposes to replace it by a dreadful kind of solipsism, mixed with some serious bad math:

Without perception, there is in effect no reality. Nothing has existence unless you, I, or some living creature perceives it, and how it is perceived further influences that reality. Even time itself is not exempted from biocentrism. Our sense of the forward motion of time is really the result of an infinite number of decisions that only seem to be a smooth continuous path. At each moment we are at the edge of a paradox known as The Arrow, first described 2,500 years ago by the philosopher Zeno of Elea. Starting logically with the premise that nothing can be in two places at once, he reasoned that an arrow is only in one place during any given instance of its flight. But if it is in only one place, it must be at rest. The arrow must then be at rest at every moment of its flight. Logically, motion is impossible. But is motion impossible? Or rather, is this analogy proof that the forward motion of time is not a feature of the external world but a projection of something within us? Time is not an absolute reality but an aspect of our consciousness.

This, kids, is what happens when you don’t learn bother to learn calculus.

Zeno’s arrow isn’t a paradox. It’s just part of another of those problems that the Greek mathematicians screwed up because they had all sorts of problems understanding infinities and infinitessimals. Zeno’s arrow is the beginning of an attempt to understand how continuous processes can be broken into an infinite number of infinitely small instantaneous parts, and how those parts can be recombined back into a finite whole. A moving arrow has a position at a given moment of time – but it’s only in that precise precision for an infinitely small instant. It’s moving, but it’s speed is varying, due to forces like gravity and drag – at any moment, it’s moving at a particular speed – but the period of time during which it’s moving at precisely that speed is infinitely small. But we can add those up, into
real motion. Just because time is made up of an infinitely large stream of infinitely small moments doesn’t mean that time doesn’t exist; just because an arrow is moving doesn’t mean that it’s position
is meaningless.

Alas, Lanza builds his argument on gibberish like this. He doesn’t know math, so he replaces it with
bad egocentric metaphysics:

Space and time are not stuff that can be brought back to the laboratory in a marmalade jar for analysis. In fact, space and time fall into the province of biology–of animal sense perception–not of physics. They are properties of the mind, of the language by which we human beings and animals represent things to ourselves. Physicists venture beyond the scope of their science–beyond the limits of material phenomena and law–when they try to assign physical, mathematical, or other qualities to space and time.

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Shame for Lanza that we do, essentially, bring “space and time” into the lab in a marmalade jar for analysis. We can observe relativistic effects. We can observe the warp of space-time by gravity. The picture over to the right is an example of that: look into the sky with a telescope, and you’ll see four different images of the same thing. Why? Because space-time is warped by the mass of a galaxy, and the warped spacetime essentially acts as a lens – exactly as predicted by the math of relativity.

And from there, it just gets worse. He goes into a very long-winded babble about, essentially, how time doesn’t really exist. Time is just an illusion created by our senses. And so on – typical new-agey babble that explains nothing – but that puts us squarely back and the center of the universe, where we’d like to be:

In order to account for why space and time were relative to the observer, Einstein assigned tortuous mathematical properties to an invisible, intangible entity that cannot be seen or touched. This folly continues with the advent of quantum mechanics. Despite the central role of the observer in this theory–extending it from space and time to the very properties of matter itself–scientists still dismiss the observer as an inconvenience to their theories. It has been proven experimentally that when studying subatomic particles, the observer actually alters and determines what is perceived. The work of the observer is hopelessly entangled in that which he is attempting to observe. An electron turns out to be both a particle and a wave. But how and where such a particle will be located remains entirely dependent upon the very act of observation.

See what I mean? Every time math comes up, Lanza goes off into a rant about how, because he doesn’t understand it, the math must not make sense. And then he compounds it by throwing in yet more ignorant babble about quantum physics and uncertainty. Hey, Bob! “Observation” in quantum theory isn’t talking about you! The collapse of a quantum waveform due to observation does not require an intelligent observer. Consciousness has nothing to do with it. Math does. Just because you’re incapable of comprehending the math doesn’t mean that you get to arbitrary replace it with something you like better.

Bleh. I can’t handle any more of this dreck. It’s just more of the same, on, and on, and on – all of it ultimately reducible to: “I don’t understand math, so anything that uses it must be nonsense; and since I think that I’m the center of the universe, anything that contradicts that must be wrong. So I’ll just replace it all with my own solipsistic nonsense, which must be right, because I understand it.”

Comments

  1. #1 Blake Stacey
    March 13, 2007

    Thanks for tearing into this! My opinion of The American Scholar fell quite a few notches when I found where this dreck had been published, which is too bad, really, since my earlier encounter with that publication was Brian Boyd’s sensible article in the Autumn 2006 issue. What does it say when a literature professor — the biographer of Vladimir Nabokov, actually — says more sensible things about biology than the cell biologist? A sampling of Boyd:

    Evolution has made knowledge possible. Not necessarily reliable knowledge, but knowledge good enough, on average, to confer a benefit. Evolution has developed sociality to the point where members of many species can transfer knowledge across time: culture, in other words. As comparative and developmental psychology have shown, evolution has developed the human brain’s capacity to understand false belief—to understand that others, or we ourselves, might be mistaken about a situation—and hence has driven our quest for better knowledge. Both human culture and our human awareness of the possibility of being mistaken have eventually given rise to science, to the systematic challenging of our own ideas. The methods of science make relatively rapid change and improvement possible—as well, of course, as unforeseen new problems. They offer no guarantee of the validity of individual ideas we propose, but they do offer the prospect of our collectively learning from one another.

    In the long perspective of evolution, testing proposals systematically, as science does, is a very new step for all humanity. Anyone, regardless of origins, can participate in the process, which harvests the natural strengths of our twin tendencies to compete and cooperate. But in order to work, science requires a commitment to the possibility that we can improve our thinking. Insisting that no ideas are valid except the idea that all ideas are invalid, or that all ideas are merely local, except this one idea, is the least likely route to genuine change.

    Boyd wrote the big biography of Nabokov, and one of Nabokov’s most famous students is Thomas Pynchon, in whose hands we can see what a real artist can do with Zeno’s paradoxes:

    Trembling, unfurrowed, she slipped sidewise, screeching back across grooves of years, to hear again the earnest, high voice of her second or third collegiate love Ray Glozing bitching among “uhs” and the syncopated tonguing of a cavity, about his freshman calculus; “dt,” God help this old tattooed man, meant also a time differential, a vanishingly small instant in which change had to be confronted at last for what it was, where it could no longer disguise itself as something innocuous like an average rate; where velocity dwelled in the projectile though the projectile be frozen in midflight, where death dwelled in the cell though the cell be looked on at its most quick.

    (The Crying of Lot 49, p. 105.)

    Thanks again.

  2. #2 El Cid
    March 13, 2007

    Awesome!!! About time!!! I too wanted to write a magnum opus explaining all of cosmology, but I was never very good at any of the math which would be involved.

    Except instead of biocentrism, I will explain everything in terms of color. I shall dub this “Chromocentrism.” If someone has used that term before, I will pretend that I made it up.

  3. #3 Blake Stacey
    March 13, 2007

    El Cid:

    Chromocentrism stumps Google! I think this one is all yours — go to it!

  4. #4 Jonathan Vos Post
    March 13, 2007

    You’re too gentle, this time, Mark, but you hit the nail on the head anyway.

    Younger readers may need to be told that there was a time, as recently as the mid-20th century, when one could get a PhD in Biology or Chemistry WITHOUT knowing Calculus. Isaac Asimov, for example, dropped out of his Calculus class when he could do integration by parts, but couln’t understand why it worked. Good enough for Professor of Biochem in those days.

    Robert Lanza and the editors of American Scholar have no such excuse. There is PLENTY of Good Math in modern Biology.

    The one place where Robert Lanza heads towards an interesting topic, before veering off into solipsismspace (solispace?) is with Smolin’s idea of cosmic evolution by black holes.

    It is a very clever notion, and provides a mechanism for the otherwise pure handwaving of the Strong Anthropic principle. But My objection to it, which I said often and everywhere to universal “who cares?” is this. Smolin’s evolving multiverse is unisexual. Bisexual reproduction of cosmoses (cosmoi?) searches superspace much more efficiently. Unfortunately, I don’t have a plausible model of how two universes mate — and the term “Big Bang” is already taken. So much for my attempt to give biological arguments for cosmology.

  5. #5 Brett
    March 13, 2007

    It is not so clear that a conscious mind is not required for the collapse of the wave function in quantum mechanics. Since Wigner suggested it, this particular version of the Many Worlds Interpretation has been gaining ever greater acceptance; and based on my observation, it now appears to be the dominant paradigm among those physicists who have actually tried to grapple with quantum mechanics’ tricky interpretational questions.

  6. #6 Mark
    March 14, 2007

    It seems as though Lanza has picked up where Berkeley left off. It’s an interesting philosophical position but not really appropriate for science. In my mind, the biggest problem with this kind of subjective idealism arises when you want to communicate your theories to other people.

    Let’s take Lanza’s program at face value and suppose that he successfully revolutionizes science so that we have a subjective theory of how some part of nature works. For it to be a useful theory it will have to make some predictions. If such a prediction are predicated on Lanza being the observer how can I be sure that the prediction is valid for me?

    Things like electrons, the speed of light, etc. all have solid, observer-invariant properties which make them a perfect platform to base and communicate inferences. You could argue that science is the process of finding these sorts of invariants so we can make and relay inferences. I can’t really see what the basis of inference would be in the type of science Lanza is proposing.

  7. #7 Chris' Wills
    March 14, 2007

    I think I understand the resolution of Zeno’s paradox, I can do the calculus and the answers I have read all make sense.
    However we do appear to have a problem, in modern physics we don’t appear to have infinitessimals in the material world. We appear to have limits as to how finely we can split up time and space (i.e. planck time). So does the paradox reappear?

    I suppose it could be that our material reality is just a distorted shadow of the true mathematical reality.

  8. #8 Susan B.
    March 14, 2007

    That’s Platonism, the idea that the perfect constructs of mathematics actually exist in some “higher reality”. I don’t think it much matters, really–calculus seems to be a pretty effective model for the real world even if infinitessimal units of time and space aren’t possible.

  9. #9 Steve
    March 14, 2007

    I think you’re being harsh, the worst criticism you can level against the arguments in the article is that they’re rather trite and badly expressed. It doesn’t seem that he’s rubbishing maths he doesn’t understand, more saying it’s dangerous to ascribe physicality to variables in mathematical models.

    As for his point on quantum physics, perhaps you could explain something that has stumped the physics postgrads I’ve asked. In regard to quantum physics, what is an observation?

  10. #10 Davis
    March 14, 2007

    We appear to have limits as to how finely we can split up time and space (i.e. planck time). So does the paradox reappear?

    I think if anything, quantization of space and time makes the “paradox” disappear completely. One of Zeno’s assumptions was the infinite divisibility of space and time, if I’m not mistaken; this is a key assumption in the construction.

    This sounds like the kind of nonsense people spout off at parties to sound all philosophical and stuff. It’s a bit embarrassing to see it being put forward seriously. But the bit that really bugs me is that Lanka wants to replace modern science, with all its successes, with an idea which has absolutely no predictive power.

  11. #11 Shaneal Manek
    March 14, 2007

    Lanza reads like an undergrad who just heard about Kant for the first time in his Philosophy 101 class.

    As for Emerson: on principle I refuse to give credence to anyone who believes ‘consistency is the hobgoblin of little minds.’ The root of most of the world’s moral and political problems can be traced back to inconsistent world views.

  12. #12 Chris' Wills
    March 14, 2007

    < That's Platonism, the idea that the perfect constructs of mathematics actually exist in some "higher reality". I don't think it much matters, really--calculus seems to be a pretty effective model for the real world even if infinitessimal units of time and space aren't possible.>>

    Hi, I know that it is Platonism; even down to cribbing the shadow analogy :o)

    As someone, far cleverer than me said and I paraphrase, the effectiveness of mathematics is suprising.

    I 100% totally agree that calculus is effective at modelling the material world. I find it even more suprising when it is effective even though the underlying assumptions of the mathematical model used don’t appear to match our understanding/theories (physics theories) of the material world.

    It doesn’t cause me to lose sleep, I just find it interesting.

  13. #13 Chad Groft
    March 14, 2007

    A bit of a tangent: I like your explanation of Zeno’s arrow. However, I have to take exception to the claim that Zeno’s arrow doesn’t constitute a paradox.

    To me, a paradox is when an apparently reasonable result, perhaps in some formal system, is counter to our intuition. Contrast this with a contradiction, which is when a formal system gets in trouble all by itself. A contradiction forces us to discard the system; a paradox may only force us to adjust our intuition.

    By way of example, consider the usual “Russell set” B of all sets which are not elements of themselves. This seems like a perfectly reasonable set, until one asks whether B is an element of B (it is iff it isn’t). By itself, this is a paradox — some principle by which we built B must be faulty, no matter how obvious the construction may seem — and is rightly labeled such. It becomes a contradiction only in certain systems, such as Frege’s, which explicitly allow the construction of B; and we are forced to discard such systems as a result.

    In the case of Zeno’s arrow, a paradox arises in people whose intuition is that time is, for example, a sequence of moments. One proper response is to discard this intuition and think of time as a continuum. One might also discard the argument itself, say by asserting that it breaks down on a sufficiently small time scale, but one isn’t forced to do this, as one would be with a contradiction.

    Certainly this jerk’s explanation is nonsense. But far from explaining why Zeno’s arrow isn’t a paradox, you’ve explained why, for many people, it is.

  14. #14 Andrew Daw
    March 14, 2007

    If you don’t like math you needn’t replace it with sollipsism. Instead you could find that a workable theory of everything is not essentially about mathematical description like in the physics of the forces. But rather you can ask what details could be described of any force to explain how matter can be and remain naturally organised out of its subatomic parts and conclude that a cause acting in addition to any force so as to keep matter organised would not act with any measurable strength…
    Google> foranewageofreason

  15. #15 Kristjan Wager
    March 14, 2007

    Glad to see that my impression of the story was correct. There is no science there.

    And don’t we all hate the misuse of the word ‘theory’?

  16. #16 Chris' Wills
    March 14, 2007

    Posted by: Davis
    I think if anything, quantization of space and time makes the “paradox” disappear completely. One of Zeno’s assumptions was the infinite divisibility of space and time, if I’m not mistaken; this is a key assumption in the construction.>>

    Ok, I may be wrong but I thought that the paradox arose because Zeno took time & space to be quantized (i.e. one unit of time followed by another) and the arrow had to move between these. Yes, he took it to the limit but it always looked like a step wise arguement to me.

    The calculus resolves the problem by replacing steps with a smooth continuum.

    If you know of any, could you refer me to any mathematics (please no woo maths :o)) that resolves this for quantized space/time. If not I’ll continue searching.

    Thanks

  17. #17 Davis
    March 14, 2007

    Ok, I may be wrong but I thought that the paradox arose because Zeno took time & space to be quantized (i.e. one unit of time followed by another) and the arrow had to move between these.

    It’s subtle, but the arrow version of the paradox requires infinitely divisible time. You look at a given moment, and claim the arrow is at rest in a particular location. If time is quantized, there’s no such thing as a “moment” — only a minimum span of time. Since you’re looking at a time interval, rather than an instant, there’s no basis for claiming the arrow is at rest, as the paradox requires.

  18. #18 Chris' Wills
    March 14, 2007

    Posted by Davis:
    It’s subtle, but the arrow version of the paradox requires infinitely divisible time. You look at a given moment, and claim the arrow is at rest in a particular location. If time is quantized, there’s no such thing as a “moment” — only a minimum span of time. Since you’re looking at a time interval, rather than an instant, there’s no basis for claiming the arrow is at rest, as the paradox requires.>>

    Thank you for answering so clearly.
    What you say makes sense, I’ll now try and understand it.
    Off to re-read Zeno.

  19. #19 the english language
    March 14, 2007

    It’s a contraction!

  20. #20 Blake Stacey
    March 14, 2007

    Steve:

    I think you’re being harsh, the worst criticism you can level against the arguments in the article is that they’re rather trite and badly expressed.

    No, the worst thing you can say about Lanza’s “arguments” is that almost every time he makes a specific claim about modern physics, he’s wrong. I’m not saying he draws vague or sophistic conclusions from a correct understanding of physics. I’m saying that he makes a whole list of claims about relativity and quantum mechanics, almost all of which contain painfully evident errors. See my original comment to MarkCC for some details.

    When the errors in basic facts are so big you could drive an SUV through them, any philosophical conclusions can only be interesting by accident. Unfortunately, such an accident has not transpired here.

  21. #21 MiguelB
    March 14, 2007

    Without perception, there is in effect no reality. Nothing has existence unless you, I, or some living creature perceives it, and how it is perceived further influences that reality.

    It seems to me that Lanza is just an average, run of the mill postmodernist. The quote above reminds me of Sokal’s famous prank paper, which states close to the beginning that “reality is a social construct” :)

  22. #22 Billy
    March 14, 2007

    “This, kids, is what happens when you don’t learn bother to learn calculus.”

    No, it’s what happens when you learn bother instead of calculus.

    From the OED:
    “bother, n.
    1. (?) Blarney, humbug, palaver. Obs.
    1803 BRISTED Pedest. Tour I. 267 Among an ignorant..peasantry the bother must consist of coarse and broad flattery laid on with a trowel.”

    Speaking from personal experience: I’m an English major who developed an interest in mathematics in graduate school. I learned the bother first, but got the calculus eventually. With 20/20 hindsight, I shouldn’t have bothered with bother.

  23. #23 island
    March 14, 2007

    Oh good grief. Lanza is simply advocating John Wheeler’s interpretation of the anthropic principle, which has apparently been given a recent experimental boost:

    http://www.sciencemag.org/cgi/content/abstract/315/5814/966

    Paul Davies, a very respected physicist and cosmologist, also holds this view, so get a freaking grip, people, Lanza’s pet theory doesn’t have to be perfectly correct, in order for his claim that the universe is biocentric, to be, and unless you can shoot down Wheeler’s strong cosmological interpretation, then his model is, by default, the most conservative mainstream approach to explaining the structuring of the observed universe:

    http://www.penguin.com.au/lookinside/spotlight.cfm?SBN=0713998830&Page=Extract

    Highly recommended:

    http://evolutionarydesign.blogspot.com/

    I’m betting that Blake Stacy and the rest of the clueless critics who DON’T have any brilliant ideas of their own, don’t know didly squat about the anthropic physics… and I’ll be happy to call any of you out on it to prove it.

    Just click-on my name and away we go…

  24. #24 Ben
    March 14, 2007

    Can you do a basics post about what time and space are? I really don’t understand. I feel dumb for asking actually.

    Is there any definition other than just making them axioms?

  25. #25 Dave M
    March 14, 2007

    Shaneal says:

    Lanza reads like an undergrad who just heard about Kant for the first time in his Philosophy 101 class.

    As for Emerson: on principle I refuse to give credence to anyone who believes ‘consistency is the hobgoblin of little minds.’ The root of most of the world’s moral and political problems can be traced back to inconsistent world views.

    I agree with the first part; the (very) distant echoes of Kant are what struck me too. Kant’s point, though, is not that there are no objects (whatever that means), but that “object” and “objective” don’t mean (as the saying goes) what people think they mean. Not the same thing. So my reaction is a bit different from Mark’s: it’s not that Lanza’s are the bizarre ramblings of a non-mathematician; they’re the bizarre ramblings of a non-philosopher. 8-)

    But I must stick up for Emerson (although I confess I didn’t like that quotation from “Experience”): I think the quote Shaneal cites actually reads “a foolish consistency is the hobgoblin of little minds,” which makes much more sense. We all know people like that, don’t we?

    Oh, and I agree with Chad: “paradox” means “apparent contradiction,” and Zeno’s paradoxes qualify. That doesn’t mean there’s no motion (just as the skeptical paradox means we don’t know anything).

    And another vote for a basics post about time and space!

  26. #26 Jonathan Vos Post
    March 14, 2007

    Chris Wills:

    Your source is Nobel laureate Wigner, one of the “Hungarian Mafia” or “Martians” who worked at Los Alamos in World War II. No need to paraphrase:

    “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960). …
    http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html

    Check in Wikipedia for “The Unreasonable Effectiveness of Mathematics in Biology” by the way.

  27. #27 Torbjörn Larsson
    March 14, 2007

    At the risk of sounding trite, but an article that raises Chalmer’s philosophical zombie’s should immediately be put to death.

    It could be that Lanza is a narrow expert. “Dr. Lanza is a noted pioneer in the field of stem cell science, with more than 25 years experience in the application of stem cells in regenerative medicine.” ( From ACT site). Which could explains his problems with current facts or what theories are.

    Smolin’s idea of cosmic evolution by black holes

    It is indeed an interesting idea since, as Smolin himself points out, in principle it would avoid the usual anthropic problems of finding a relevant statistics (perhaps solved now) by local selection, precisely as biological evolution does. But I had the impression it doesn’t work because black holes doesn’t permit the behavior he needs. (And unfortunately, since his old universes doesn’t die, his statistics should give the same prediction as the weak anthropic principle.)

    the Many Worlds Interpretation

    Actually, already the part with decoherence, usable in some other interpretations, is claimed to describe the observer and remove the speculations about consciousness from the measurement problem. (See for example the Wikipedia article on the measurement problem for references.) And interestingly, decoherence time scales is IIRC also what Tegmark used to debunk Penrose’s speculations about quantum processing in the brain.

  28. #28 Blake Stacey
    March 14, 2007

    Torbjörn Larsson:

    And interestingly, decoherence time scales is IIRC also what Tegmark used to debunk Penrose’s speculations about quantum processing in the brain.

    Tegmark, M. “The importance of quantum decoherence in brain processes“. Phys. Rev. E 61 (2000): 4194–4206. Abstract:

    Based on a calculation of neural decoherence rates, we argue that that the degrees of freedom of the human brain that relate to cognitive processes should be thought of as a classical rather than quantum system, i.e., that there is nothing fundamentally wrong with the current classical approach to neural network simulations. We find that the decoherence timescales ~10-13–10-20 seconds are typically much shorter than the relevant dynamical timescales (~0.001-0.1 seconds), both for regular neuron firing and for kink-like polarization excitations in microtubules. This conclusion disagrees with suggestions by Penrose and others that the brain acts as a quantum computer, and that quantum coherence is related to consciousness in a fundamental way.

    Thanks for the link to the cosmological constant paper.

  29. #29 Torbjörn Larsson
    March 14, 2007

    It doesn’t cause me to lose sleep

    Me neither. Wigner makes an interesting case, but my own conclusion is that science is also interestingly effective on its own, and that math in this and other aspects is more like science than other human endeavors. That is, math is as science constructed after our experiences. (Which btw also solves the problem with theorems for me – a theorem is a justified belief exactly as other knowledge.)

    Is there any definition other than just making them axioms?

    It is not a stupid subject at all, since there is a lot known but more that is not known. But perhaps it is a basics post for a physics blog.

    Meanwhile, to hopefully answer your questions somewhat, we can separate the aspects of time and space from the aspect of spacetime.

    The former are axioms in some fundamental theories such as quantum mechanics.

    The later is an emergent property in the universe we live in. It is also not a basic axiom in the theories, but follows from demanding an observed symmetry, Lorentz covariance. (Roughly, the symmetry is that an interpretation of a physical observation does not depend on where you are.) One of the promises of string theory is the ability to show how fundamental time and space becomes the spacetime we see.

    Another subject is why time is different from space (the arrow of time), and connected to that the observed asymmetry that the entropy of our universe started out low. At least the later promises to perhaps be a result, not an axiom.

    Yet another subject mentioned here is if time and space, or spacetime, is fundamentally discrete or continous.

    Perhaps your question is also about if space and time needs to be axioms, or if they have an explanation? If we find a selfconsistent fundamental theory, it should be enough of an explanation IMHO. At least, we won’t get a better one. :-)

  30. #30 Torbjörn Larsson
    March 14, 2007

    Blake:

    Thanks for the reference.

  31. #31 Blake Stacey
    March 14, 2007

    For follow-ups to Tegmark’s work, see A. Litt et al., “Is the Brain a Quantum Computer?” Cognitive Science 30, 3 (2006): 593–603. I mentioned this back in January; for those joining our program already in progress, here’s the abstract:

    We argue that computation via quantum mechanical processes is irrelevant to explaining how brains produce thought, contrary to the ongoing speculations of many theorists. First, quantum effects do not have the temporal properties required for neural information processing. Second, there are substantial physical obstacles to any organic instantiation of quantum computation. Third, there is no psychological evidence that such mental phenomena as consciousness and mathematical thinking require explanation via quantum theory. We conclude that understanding brain function is unlikely to require quantum computation or similar mechanisms.

    There’s lots of good stuff in this paper, including references into the literature. My favorite bit might be the quotation they give from P. S. Churchland, who said, “The want of directly relevant data is frustrating enough, but the explanatory vacuum is catastrophic. Pixie dust in the synapses is about as explanatorily powerful as quantum coherence in the microtubules.”

    About the evolving-Universes thing:

    I wouldn’t want to give it an enthusiastic endorsement, but it is a well-known idea, and anybody who’s trying to argue for “biocentrism” — or even for the much more modest proposal that physicists should pay attention to biology — should mention it.

    Now, I need to go off and think about the whole “universes not dying” thing. Some ‘verses clearly do croak — they implode upon themselves because they’re too full of matter (dark or otherwise). In the Cosmic Variance thread to which you linked, Aaron Bergman says,

    Besides, I would think that such a strong proponent of background independence as yourself [Smolin] would be disturbed by the arbitraryness of this time slice. Unlike evolutionary biology, there is no universal choice of ‘now’.

    To which Smolin replies,

    Thanks. I agree that universes don’t die but this is not a problem as the population grows exponentially (in a global time picked to track the FRW time in the different universes).

    This doesn’t sit quite right with me. All in all, the best reason to like Smolin’s proposal may be the SF it can generate.

  32. #32 eric
    March 14, 2007

    As for Emerson: on principle I refuse to give credence to anyone who believes ‘consistency is the hobgoblin of little minds.’

    Actually, he said a foolish consistency is the hobgoblin of little minds, which is more sensible.

  33. #33 Chris' Wills
    March 14, 2007

    >>Posted by: Jonathan Vos Post
    Your source is Nobel laureate Wigner, one of the “Hungarian Mafia” or “Martians” who worked at Los Alamos in World War II. No need to paraphrase:
    “The Unreasonable Effectiveness of Mathematics in the Natural Sciences,” in Communications in Pure and Applied Mathematics, vol. 13, No. I (February 1960). …
    http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
    Check in Wikipedia for “The Unreasonable Effectiveness of Mathematics in Biology” by the way.>>

    Thanks for the references, I’ll look them up though may have to give away some books to make room on my floor if I buy them :o)

    >>Posted by: Torbjörn Larsson
    Yet another subject mentioned here is if time and space, or spacetime, is fundamentally discrete or continous.
    Perhaps your question is also about if space and time needs to be axioms, or if they have an explanation? If we find a selfconsistent fundamental theory, it should be enough of an explanation IMHO. At least, we won’t get a better one. :-)>>

    No, the comment was just about how it would relate to Zeno’s paradox. I would hope that a fundamental theory would tell us what structure spacetime has to have.

  34. #34 Chris' Wills
    March 14, 2007

    >>Posted by: the english language
    It’s a contraction!>>

    Yes it is :o)

  35. #35 Coin
    March 14, 2007

    As for Emerson: on principle I refuse to give credence to anyone who believes ‘consistency is the hobgoblin of little minds.’ The root of most of the world’s moral and political problems can be traced back to inconsistent world views.

    I don’t know what Emerson was trying to say there or whether it was reasonable. I do like what Mark Twain said, though:

    There are those who would misteach us that to stick in a rut is consistency–and a virtue; and that to climb out of the rut is inconsistency–and a vice…

    These same men who enthusiastically preach loyal consistency to church and party are always read and willing and anxious to persuade a Chinaman or an Indian or a Kanaka to desert his church, or a fellow-American to desert his party. The man who deserts to them is all that is high and pure and beautiful- apparently; the man who deserts from them is all that is foul and despicable. This is Consistency with a capital C…

    I am persuaded that the world has been tricked into adopting some false and most pernicious notions about consistency–and to such a degree that the average man has turned the rights and wrongs of things entirely around and is proud to be “consistent,” unchanging, immovable, fossilized, where it should be his humiliation.

  36. #36 Norm Breyfogle
    March 14, 2007

    Reference all known objective reality and there’s still the remaining UNknown. Into this unknown metaphysicians will continue to project their metaphors, and enlightened minds will continue to point our the difference between such metaphors and scientific theory. Solipsism plays on the apparent infinite regress in the relationship between the objective and the subjective, on the reality-mirroring function of consciousness. Robert Lanza is pointing out this infinite regress by using biology as his metaphor of choice.

    The existential unknown remains: it isn’t scientifically predictive to point it out, but everything we know could indeed be wrong, a dream, a simulation or shadow of some kind of a more substantial level of energy. It’s not science, but it is an open philosophical or metaphysical question.

  37. #37 SteveM
    March 14, 2007

    I think that one of the worst mistakes ever made in trying to explain the heisenberg uncertainty principle was to describe it terms of trying to measure the position of billiard balls by hitting them with other billiard balls. This turns the principle into purely a “measurement problem” rather than a fundamental principle that velocity and position, or energy and duration, are in a sense “coupled” and cannot be both be exact properties of the “particle”. As a lowly electrical engineer, one of the things that was most impressive to me during my education was the “appearance” of the uncertainty principle in signal analysis. That is, a signal cannot be precisely confined in both the “time-domain” and the “frequency-domain” simulataneously. That is a perfectly time limited signal must have an infinite frequency content, and conversely a perfectly limited frequency content implies infinite duration. It is not a question of measuring its frequency content will make it change its time span, but simply the fact of how the time representation transforms into a frequency representation. Seems to me that this is a perfect analog of the “wave-particle” duality of quantum physics and thus the uncertainty principle really has nothing to do with observation at all but is “built in” to the equations we use to describe quantum phenomena.

  38. #38 Blake Stacey
    March 14, 2007

    SteveM:

    Nicely put. I remember Griffiths’ introductory QM book uses the example of a wiggling rope. If you make the rope shake at a definite frequency, then you can see it has a certain well-defined wavelength, but the idea of the “position of the wave” isn’t meaningful. What’s the “position” of a perfect sine wave? You can make an oscillation which travels along the rope with a fairly well-defined position — a wave packet — but you have to superpose many different frequencies.

    Squeeze one quantity, and the Fourier transform spreads out.

  39. #39 Blake Stacey
    March 14, 2007

    Hey, we hit the “most emailed” top five list. Good job, us! :-)

  40. #40 Steve
    March 15, 2007

    Blake, care to address my second paragraph?

  41. #41 Torbjörn Larsson
    March 15, 2007

    This doesn’t sit quite right with me.

    Me neither. He doesn’t really answer the argument about boltzmann’s brains and statistics by his seemingly handwaving. Unfortunately, any attempt for me to pin down his claims also amounts to handwaving. ;-)

    Seems to me that this is a perfect analog of the “wave-particle” duality of quantum physics

    Sometimes physical analogs have more fundamental underpinnings than one realize at first. When I studied partial differential equations, IIRC already the math sometimes could use an ‘energy principle’ to perfectly naturally constrain solutions, before even looking at the possible physics of an application.

    Steve:

    I assume you want to discuss this:

    In regard to quantum physics, what is an observation?

    I hope to not sound facetious when I say that I think this is what “the measurement problem” is about. In practice, in the math and by observation, one of the possible states are picked out (also called projected, I think) by an observation. How that works and what it means exactly for the whole system seems to be the discussion. (See for example von Neumann’s measurement scheme or decoherence theory for some variants with partial descriptions, falsified or not.)

    Hopefully someone more knowledgeable pitch in here.

  42. #42 Blake Stacey
    March 15, 2007

    Torbjörn Larsson:

    I hope to not sound facetious when I say that I think this is what “the measurement problem” is about.

    Yes. An observation is a process by which a system in a superposition of multiple eigenstates is “collapsed” (or appears to collapse) into a single eigenstate, with the probability of landing in a given state given by the weighting of the states in the original superposition (the “weights” in this case being complex numbers).

    That was a bit of a mouthful. If you’d like a mouthful with equations too, see these technical notes by Greg Egan.

  43. #43 Blake Stacey
    March 15, 2007

    See also Tegmark and Wheeler’s “100 Years of the Quantum” in Scientific American (2001). Abstract:

    As quantum theory celebrates its 100th birthday, spectacular successes are mixed with outstanding puzzles and promises of new technologies. This article reviews both the successes of quantum theory and the ongoing debate about its consequences for issues ranging from quantum computation to consciousness, parallel universes and the nature of physical reality. We argue that modern experiments and the discovery of decoherence have have shifted prevailing quantum interpretations away from wave function collapse towards unitary physics, and discuss quantum processes in the framework of a tripartite subject-object-environment decomposition. We conclude with some speculations on the bigger picture and the search for a unified theory of quantum gravity.

  44. #44 Rob Z.
    March 15, 2007

    “This, kids, is what happens when you don’t bother to learn calculus.”

    +1 QOTW

  45. #45 Norm Breyfogle
    March 15, 2007

    Aside from any outright scientific errors and/or semantic misrepresentations from Lanza, isn’t he pointing out something that’s not perfectly rationally resolveable, *even in principle*, when he brings up what we can rightly call solipsism? Isn’t this recognition of the inevitable interconnectedness between objective fact and subjective perception (“solipsism”) a fundamentally different feature in post-Einsteinian, quantum science when compared to Newtonian science?

  46. #46 Norm Breyfogle
    March 15, 2007

    Or maybe I should have written that the difference is between the *implied world views* of post-Einsteinian quantum science and Newtonian science. The there’s obviously no fundamental difference in the scientifc method in either case.

  47. #47 Brian J
    March 15, 2007

    I thought I’d bring up a small relevant experience. A fellow that I know is quite clever, quite realistic, very honest, understands the value of math but doesn’t know much math himself. I was trying to explain what I considered to be a simple thing to him when he replied “There are two kinds of people. There are those that can do math and those that can’t.” to explain to me the folly of trying to explain even this to him.

    This was well put and increased my respect for the man. One needs to have at least a sense of what one doesn’t understand.

  48. #48 Blake Stacey
    March 15, 2007

    Brian J:

    It would be funnier if he’d said, “There are three kinds of people. . . .”

    Norm Breyfogle:

    Given that solipsism was alive and kicking in the philosophical literature in the many years between Newton and Einstein, I’m not so sure that the “implied worldviews” (at least so far as they leak out into the general populace) are any more or less friendly to the idea. Today, people invoke quantum physics when they want to speak about “the interconnectedness of all things” or say that “reality depends upon the observer”. A few decades ago, the tone of the “cocktail talk” was that Einstein’s relativity meant everything depended upon your point of view (although now Lanza is saying that quantum physics undermines relativity while arriving at the same conclusion).

    I’ll be frank and admit that I don’t know all the attitudes which philosophers took in response to Newton’s mechanics. Somebody call a historian of science. However, I can say that by misrepresenting the science, by making inaccurate statements of fact and putting every assertion in a vague form, one can justify any philosophy using any school of science. Want to make Newton a New Age icon? Everything is influenced by gravity fields, man. The Sun pulls on the Earth, and we pull right back on the Sun. We touch without touching, but we can’t touch without being touched ourselves. It’s like there are fields of energy reaching all through space. Dude.

    (And that’s just vague, not really inaccurate!)

  49. #49 Jonathan Vos Post
    March 15, 2007

    There are 10 kinds of people in the world: those who understand Binary and those who don’t.

    There are 2 kinds of people in the world: the ones who think that there are 2 kinds of people in the world, and the ones who don’t.

    Or, in Lanza’s case: “There is one kind of person in the world: me, me, me, me!”

    See also:

    Quantum physics: It’s all about me, me, me, isn’t it?

    http://www.usatoday.com/tech/science/columnist/vergano/2007-03-11-quantum-quandary_N.htm

    [image: Maybe it's all in your mind: The Hubble Telescope's sharpest view of the Orion Nebula.]

    Exclusive: Response to Robert Lanza’s essay
    American Scholar: A New Theory of the Universe

    By Dan Vergano, USA TODAY

    “… I can’t help thinking that there’s an enormous exercise of vanity in Lanza’s argument — the universe only exists, he says, because we’re here to observe it and be part of it,” Lindley says in objection. “I would go the opposite extreme. I think the universe was a real physical thing long before we came on the scene, and we humans are just crumbs of organic matter clinging to the surface of one tiny rock. Cosmically, we are no more significant than mold on a shower curtain.”

  50. #50 Norm Breyfogle
    March 15, 2007

    Somehow, scientific objectivity and the most vague and inclusive solipsism are BOTH correct because all that we can know about our mold-like state (a la the Lindley quote in JVP’s post above) is – speaking in the most inclusive sense – inseparable from the contents of our minds, and yet, scientific objectification WORKS. Ultimately, existence *as a whole* is both subjective AND objective.

    It’s at least logically conceivable (though difficult if not impossible to verify) that all of objective reality as we know it is some sort of self-consistent fake, since we can’t, even in principle, escape our own ultimate subjectivity (we can prove or disprove individual instances of it, but not the ultimate principle thereof).

    Science deals with objectivity, and yet our imaginations can see the limitations of any present level of objective knowledge, can create metaphors/analogies to fill the void of the unknown, and can even reference the ultimate level of interconnectedness which the search for truth in the extreme objectivity of science itself implies: the striving for a GUT or TOE.

    The problem is that as soon as anyone attempts to say more than “the relationship between consciousness and the objects of consciousness is an endless hall of mirrors” they fall into potential error which is – at least in principle – experimentally falsifiable in objective reality.

    Whether or not Lanza has made such a falsifiable error re quantum science is the question being debated here, and given the various alternative approaches to interpreting certain “paradoxes” in quantum dynamics, surely the jury is still out?

  51. #51 Norm Breyfogle
    March 15, 2007

    Correction to my last post: Lanza has indeed crossed the line into verifiablility/falsification when he equated ultimate or cosmic subjectivity with a specific manifestation of mind, i.e., biological brains. The only sense in which solopsism will legitimately endure forever is as an indeterminate generality.

  52. #52 Norm Breyfogle
    March 15, 2007

    So solipsism is a fundamental and irreducible aspsect of reality for conscious entities. And since it is irreducible, it carries no predictive power beyond the basic assertion that subjectivity will always be an aspect of consciousness to *some* degree, and any attempt at formulating a TOE or GUT will be incomplete without addressing it (which is to say that, strictly speaking, a *perfectly* predictive GUT or TOE is a logical impossibility.

  53. #53 Xanthir, FCD
    March 15, 2007

    I’m responding to someone way up there who talked about how well math fits science.

    I’ve been thinking about this lately. Math is not a singular entity. There are many kinds of maths, based on different axioms, giving different results. The only thing tying all of them together is constancy. They start with regular rules and apply regular processes to arrive at regular results. Math is generally too complex to be done mechanically, but the algorithm is still a useful concept in every branch of math.

    That, I think, explains perfectly why math is so good at modeling the physical world. As long as the physical world is constant and regular (or random with constant and regular biases), we can describe it using rules. Thus, we can build a math for it. The idea of custom-building maths is relatively common these days, even if it’s not thought of in quite that way.

    Thus, it’s no mystery that math matches physics. The universe is patterned, and math is the science of pattern. No matter how the universe turns out, as long as it doesn’t have true randomness (or it does, but we can abstract it away), there will be some math that describes it.

  54. #54 Jonathan Vos Post
    March 16, 2007

    Xanthir: “The universe is patterned” — and that’s the mystery! Why is the universe patterned? By what processes? Why is “pattern” applicable to both physical reality and reproducible mental images and formal mathematical notation?

    “The most incomprehensible thing about the world is that it is comprehensible.” — Einstein

  55. #55 Chris' Wills
    March 16, 2007

    Xanthir: As JvP wrote plus.
    When I peruse the history of mathematics I find things such as i^2 = -1 being discovered and used in mathematics long before any application in the physical world.
    It wasn’t a model built to reflect the world, rather it came out of the mathematics and just happens to be useful in modeling the world.
    The concept of zero as an actual number and the negative numbers are other examples.

    I agree that in modern times the needs of physics have pushed the development of mathematics in some areas, but as often the mathematics has already been discovered that the physicist needs for their model.

    I find it suprising and wonderful :o)

  56. #56 Torbjörn Larsson
    March 16, 2007

    If you’d like a mouthful with equations too,

    Always. Besides being fun, it usually clarifies the scope of definitions and other sundry stuff. And that link seems useful, thanks.

    Nitpick: Technically, it is an eyeful. Except for those who are wording while reading.

    from wave function collapse towards unitary physics,

    I hope Wheeler is as good on quantum as on gravitation. It went to the top of my to-read list.

    “There is one kind of person in the world: me, me, me, me!”

    Btw, that is what autists may think too. I just read an interview with a nowadays highfunctional autist who described that she after years of training could understand intellectually (she claims to have no emotions, btw) that other persons are different from things.

    existence *as a whole* is both subjective AND objective.

    Personal experience is subjective, and I would not have it any other way.

    But as I understand it you have to go solipsism full throttle; I’m not sure what you mean by “inclusive” solipsism. Any acceptance of an objective reality destroys the concept of “the self is the only thing that can be known and verified” or “the self is the only reality”.

    Btw, what we today think as subjective may turn out to be objective. For example, who knew that altruism actually is an acceptable evolutionary strategy?

  57. #57 Blake Stacey
    March 16, 2007

    she claims to have no emotions, btw

    Fascinating, Captain. ;-|

    (All right, how would you do the eyebrow thing with an emoticon?)

  58. #58 Norm Breyfogle
    March 16, 2007

    JVP:”Why is the universe patterned?” is a question beyond the aegis of science, logic, or reason. Since no pattern at all equals nothingness or nonexistence, then pattern equals existence. Reason, logic, science, etc., can only answer *specific* questions about why the pattern wiggles this way here, that way there, but the question of why the universe is patterned at all in the first place is purely metphysical, inviting solipsistic answers and tautologies such as the Anthropic Principle or the Metaphysics of Quality or Zen Buddhism or the grosser pop beliefs of literalistic religion.

    Torbjörn: By the most “inclusive” solipsism I mean to point to the above most general of questions (“Why existence?”) and the only possible answers: metaphorical, solipsistic, or religious ones.

  59. #59 Norm Breyfogle
    March 16, 2007

    For conscious creatures the only answer to the question “What is the final and absolutely predictable relationship between subjective consciousness and the objects of consciousness?” is also a solipsistic, metaphorical, or religious one. We can always progress further in our knowledge of the predictive details of that relationship, but – like probing ever closer to the moment of the Big Bang without ever being able to perceive it’s very beginning – we can’t exhaust the details of that relationship; it’s an infinite hall of mirrors.

    Hence the silopsistic assertion that consciousness is fundamental to the universe. How could it be any other way for us conscious creatures? We can’t consciously escape consciousness and remain conscious at the same time!

  60. #60 norm Breyfogle
    March 16, 2007

    Dang; I’ve got to remember to use the preview button to increase the odds of my catching my spelling errors before posting. =)

  61. #61 Norm Breyfogle
    March 16, 2007

    JVP:

    I’ve read some of your poetry in your link in your posts, but I couldn’t find an email address where I could write to you directly, so I’m asking you here: would you be willing to critique a short story of mine (just a few pages long)?

    If so, let me know via my email address:

    nbreyfogle@chartermi.net

  62. #62 Davis
    March 16, 2007

    No matter how the universe turns out, as long as it doesn’t have true randomness (or it does, but we can abstract it away), there will be some math that describes it.

    There’s that classic joke about the drunk who looks for his lost keys under the street light, because the light’s better there. Sometimes I think mathematics is the street light; it’s the place where we look, because we can’t see anywhere else.

    Of course, I also think that constant improvements in math amount to extending the area that light illuminates.

  63. #63 Xanthir, FCD
    March 16, 2007

    JVP:
    Well, there are two kinds of universes in the totality of theoretical existence: universes with patterns and universes that are completely and utterly random. ^_^

    If the universe was completely random, there would be no way for life to exist (I’m accepting this as a given). Given that we are alive, then we live in a universe with patterns. Thus, it is inevitable that in a universe with life, math is applicable to the world.

    That’s my argument, and I’m sticking to it. ^_^ Questions about why the universe is not completely random are FORBIDDEN. (Not really, of course. I like discussions about the reasons for our particular cosmology, like that absolutely fascinating line I heard a while ago about the fact that knots only exist in 3 dimensions possibly being why we have 3 spatial dimensions rather than any other number and I get a lot of enjoyment out of grammatically correct run-on sentences.)

    Chris Wills:
    I think it’s a beautiful thing as well when we discover interesting mathematical identities that happen to be useful in the real world. Of course, plenty of possible identities are much less useful, so there’s probably some selection bias in there making us more likely to think that math is automatically perfect for describing the world.

    I personally find the applicability of partition theory to fluid dynamics fascinating (partition theory being the study of the number of ways to divide a number into unique natural number sums). I don’t know what good it is, I just heard once that it actually does something useful.

  64. #64 Torbjörn Larsson
    March 16, 2007

    All right, how would you do the eyebrow thing with an emoticon?

    Intriguing. ^_^ But I had to cheat:

    (ó ô)

    quizzical or “Indeed” (designed to mimic Star Trek’s Mr. Spock)
    ( http://en.wikipedia.org/wiki/Emoticon )

    Don’t say that Wikipedia isn’t useful… (^_~)

    By the most “inclusive” solipsism I mean to point to the above most general of questions (“Why existence?”) and the only possible answers: metaphorical, solipsistic, or religious ones.

    OK. But it seems to me this solipsism is the same as the usual one.

  65. #65 Norm Breyfogle
    March 17, 2007

    “OK. But it seems to me this solipsism is the same as the usual one.”

    True, and point well taken. But the revelations of relativity, probability, and uncertainty are accepted as more fundamental elements of modern science compared to the classic Cartesian/Newtonian view, and these modern elements seem soemwhat more amenable to solipsistic interpretations.

  66. #66 Torbjörn Larsson
    March 17, 2007

    these modern elements seem soemwhat more amenable to solipsistic interpretations.

    Ah, but that is what we use to call subjective interpretations, isn’t it? Solipsism is when “the self is the only reality” or “the self is the only thing that can be known and verified”. That isn’t the case here, and I doubt it can be combined with objective realism, which is why your terms are confusing to me.

    Yes, inferential statistics such as bayesian can interject a degree of subjectivity if one lets it, but I don’t think it is required. And uncertainty, or more specifically unpredictability, is part of what we experience subjectively, and indeed expect of ourselves as free agents.

    I wouldn’t say that relativity has a subjective element. Relativity guarantees that observers sees the same physical laws, which is needed for practical objectivity.

    Relativity does so by acknowledging that different observers will make different observations on the same events. But that is not subjective, instead relativity helps us make describe the different observations.

  67. #67 Norm Breyfogle
    March 17, 2007

    Torbjörn,

    As I wrote, point well taken. However, Cartesian/Newtonian scientists certainly tended to assume that science could eventually eliminate ALL subjectivity in its world-view, could consider physical laws without taking the observer into account at all. Modern physics, on the other hand, sees a much closer relation – *arguably* an infinitely interpenetrative one – between the observer and the observed.

    I didn’t write that modern scientific models support a solipsistic model which would provide predictive power in any sense. I wrote merely that modern models *seem more AMENABLE to solipsistic interpretations.*

    Note that I’ve taken pains in my above posts to point out the difference between what I might now call “soft” solipsism (the falsifiable claim that one’s mind can achieve scientific predictibility via solipsism) and “hard” solipsism (the tautologically true and unfalsifiable principle of the inevitability of subjectivism as one of the fundamental aspects of reality for conscious entities). Although those designatiosn should maybe reversed?

    All that you (or I, or anyone) know of objective reality comprises the elements of your (our) consciousness. If you can show me an element of reality that you know by some NON-consciousness means, then I’ll accept that solipsism can be considered a NON-fundamental (though tautological and without predictive power) aspect of existence.

    This is a basis philosophical point, not a scientific one.

    Doesn’t this reflective aspect of consciousness, this hall of mirrors effect, directly reference (in a philosophical, not a scientific manner) the question of why math reflects reality, why the universe is comprehensible to consciousness? And isn’t this final question unanswerable in any manner BUT a metaphorical, philosophical, or religious one?

  68. #68 Norm Breyfogle
    March 17, 2007

    Corrections:

    “Although those designatiosn should maybe reversed?”

    should read:

    “Although those designations should maybe be reversed?”

    And,

    “All that you (or I, or anyone) know of objective reality comprises the elements of your (our) consciousness. If you can show me an element of reality that you know by some NON-consciousness means, then I’ll accept that solipsism can be considered a NON-fundamental aspect of existence.”

  69. #69 Torbjörn Larsson
    March 18, 2007

    I’m still uncertain what your point is. I am reacting to your claim that

    scientific objectivity and the most vague and inclusive solipsism are BOTH correct

    If you by this mean that they can both be interesting to consider in philosophy, but not at the same time, I think it is valid.

    But they can’t both be correct, and especially not at the same time.

    If this was the misunderstanding we are discussing, I hope it is cleared now.

  70. #70 Norm Breyfogle
    March 18, 2007

    They’re both correct, and at the same time:

    1) For conscious entities, all of known reality comprises their mind(s), including all of the instances of their own subjective errors and their mastery of objective predictivity; both the subjective and the objective aspects of consciousness are subsumed under and as the conscious entity’s own conscious experience/existence. This is a fundamental philosophical reality or axiom. You can’t escape your own consciousness; it’s your very identity.

    2) At the same time, for any conscious entity there is indeed the objective aspect of their existence/consciouness whose predictive power can be mastered to greater or lesser degree.

    The former is the only true solipsistic assertion; being merely a philosophical tautology, it’s neverthess true poetically, tautologically, transcendentally, or religiously, even though it possesses no specific predictive scientific power in and of itself.

    The latter is the essence of the scientific world view and carries specific predictive power.

    What I’m driving at is that no matter how refined our scientific knowledge (assertion #2), there will always remain the fundamental axiomatic reality of assertion #1.

    We only know existence through and as the state of our own consciousness. This is a philosophical and logical axiom. Is it solipsistic? It appears to be so, but it’s definitely different from asserting that any specific biological brain(s) *creates* all of existence (which is a scientifically falsifiable solipsistic assertion). The totally inclusive solipsistic axiom of consciousness interpenetrating the objects of consciousness is only true because it’s a tautology. It’s true, but we can derive no scientific knowledge – no predictive power – from it alone.

    Still, the mystery and awe that some of us derive from the interconnectedness of consciousness with its objects (axiomatic solipsism) is more than *just* a tautology. It’s a tautology that lies at the core of the unanswerable question which intrigues so many of us: “Why are the objects of consciousness comprehensible to our conscious minds?”

    I’m not trying to be intentionally obscure. I just don’t want to throw out the baby (the mystery and awe of consciousness’ axiomatic solipsism) with the bathwater (falsifiable solipsistic claims).

  71. #71 Torbjörn Larsson
    March 18, 2007

    They’re both correct, and at the same time

    Well, I (and probably most philosophers) claim that isn’t possible, under the current definitions of solipsism. Solipsism means 100 % subjectivity.

  72. #72 Norm Breyfogle
    March 18, 2007

    Sure, but there appear to be two versions of – or logical levels to – solipsism: the typical one (which I agree is directly refuted by objective facts), and the atypical one (which doesn’t challenge any objective facts but merely points to the tautologically axiomatic interpenetration of consciousness with the objects of consciousness).

    It’s an “all for one and one for all” sort of thing. It’s unity in diversity, Yin and Yang together as the Tao, the one in and as the many. The objective and the subjective are two sides to the same coin of existence/consciousness.

  73. #73 Norm Breyfogle
    March 18, 2007

    The problem with the term “solipsism” is that whenever the obvious fact is asserted that all knowledge is subsumed under consciousness (including objective knowledge, which is obviously an aspect of consciousness), someone invariable cries “solipsism” and means it as a refutation! So as long as this axiomatically fundamental reality is referred to as “solipsism” then it should be admitted that one form or logical level of solipsism is in fact a valid existential truth.

  74. #74 Torbjörn Larsson
    March 18, 2007

    and the atypical one (which doesn’t challenge any objective facts but merely points to the tautologically axiomatic interpenetration of consciousness with the objects of consciousness).

    We are discussing in circles now, so this is going to be my last comment on this. I have pointed out the common definitions and an interpretation, because I think it is good if people understand terms to mean the same things and I also think my interpretation is not only the usual but the only feasible in this case.

    Solipsism should mean, and as I understand it is supposed to mean, that there are no objective facts: “the self is the only thing that can be known and verified”, “the self is the only reality”. “Known and verified” or “reality” is how I would describe objective facts. By allowing only the self it dismiss everything else as subjective experience. (And logically it demotes the self to subjectivity too, but that is another discussion.)

    Obviously you don’t agree, which of course is your prerogative.

  75. #75 Norm Breyfogle
    March 18, 2007

    I’m repeating myself because you don’t seem to be addressing my point in your responses to me.

    So you deny the tautological truth that all the knowable objects of your consciousness are subsumed under your consciousness?

  76. #76 Jonathan Vos Post
    March 18, 2007

    Xanthir:

    I was in Las Vegas all weekend with my wife, relaxing, and never once being online for email, blogs, or web-surfing. That’s about as long as we ever go offline.

    We were not, by the way, gambling. We enjoy now and then watching other people demonstrate how bad they are at elementary Probability Theory.

    As to why the universe appears to have 3 spacial dimensions:

    One standard mathematico-physical pseudoanthropic argument is that only in odd dimensions can electromagnetic or sound waves propogate without distortion, so 2 and 4-dimensional life are tricky at the informational level.

    I’ve heard the knot argument befvore, but it is a little trickier than that, as multidimensional knot theory has advanced in the past decade or so.

    My personal favorite — which I’ve argued with Lisa Randall, is that 3 and 7 dimensions are the only ones with valid cross-products of vectors.

    One of the things I was working on — on paper — was a model of whther or not 4-dimensional ionic crystals with hypercubical lattices of alternating positive and negative unit charges wouold be stable. Sort of hyper-NaCl. My preliminary result is that such 4-D crystals are in equilibrium, but expanding the 4-vector analysis with infinitesimal perturbations to see whether the equilibrium is stable or unstable was beyond my combined imagination and pen-and-paper.

    I’m not good enough yet to generalize to 7-dimensional crystals (7 spacial dimensions + time as othogonal 8th dimensional with different signature). I suspect that 7-D crystals can propogate phonons nicely as crisp hyperplanar or hyperspherical wave-fronts.

    This was a side-effect of a problem with which I’ve been wrestling for a week or so on the hypervolume of the convex hull of certain point-sets in Euclidean 4-D. I’ve reduced it to a problem of carving the shapes up into tens of thousands of pentatopes and calculating the hypervolume of each with Cayley-Munder determinants, but that’s too brute-force for my aesthetics, so I’m being clever, analytical, and it’s slow — my visualization of 4-D is much weaker than when I was in my early teens.

    In the valley of the 3-D blind, the one-eyed 4-D visualizer is King.

    Seems to me that if it takes 2 eyes to have good depth perception in 3-D, it takes 3 eyes to have good 4-D hyperdepth perception. That’s why the mystics’ Third Eye in mid-forehead is needed to see into the future;)

  77. #77 Jonathan Vos Post
    March 19, 2007

    [resubmitted, as did not seem to go online from previous try
    Posted by: Jonathan Vos Post | March 18, 2007 10:44 PM]

    Xanthir:

    I was in Las Vegas all weekend with my wife, relaxing, and never once being online for email, blogs, or web-surfing. That’s about as long as we ever go offline.

    We were not, by the way, gambling. We enjoy now and then watching other people demonstrate how bad they are at elementary Probability Theory.

    As to why the universe appears to have 3 spacial dimensions:

    One standard mathematico-physical pseudoanthropic argument is that only in odd dimensions can electromagnetic or sound waves propogate without distortion, so 2 and 4-dimensional life are tricky at the informational level.

    I’ve heard the knot argument befvore, but it is a little trickier than that, as multidimensional knot theory has advanced in the past decade or so.

    My personal favorite — which I’ve argued with Lisa Randall, is that 3 and 7 dimensions are the only ones with valid cross-products of vectors.

    One of the things I was working on — on paper — was a model of whther or not 4-dimensional ionic crystals with hypercubical lattices of alternating positive and negative unit charges wouold be stable. Sort of hyper-NaCl. My preliminary result is that such 4-D crystals are in equilibrium, but expanding the 4-vector analysis with infinitesimal perturbations to see whether the equilibrium is stable or unstable was beyond my combined imagination and pen-and-paper.

    I’m not good enough yet to generalize to 7-dimensional crystals (7 spacial dimensions + time as othogonal 8th dimensional with different signature). I suspect that 7-D crystals can propogate phonons nicely as crisp hyperplanar or hyperspherical wave-fronts.

    This was a side-effect of a problem with which I’ve been wrestling for a week or so on the hypervolume of the convex hull of certain point-sets in Euclidean 4-D. I’ve reduced it to a problem of carving the shapes up into tens of thousands of pentatopes and calculating the hypervolume of each with Cayley-Munder determinants, but that’s too brute-force for my aesthetics, so I’m being clever, analytical, and it’s slow — my visualization of 4-D is much weaker than when I was in my early teens.

    In the valley of the 3-D blind, the one-eyed 4-D visualizer is King.

    Seems to me that if it takes 2 eyes to have good depth perception in 3-D, it takes 3 eyes to have good 4-D hyperdepth perception. That’s why the mystics’ Third Eye in mid-forehead is needed to see into the future;)

  78. #78 Norm Breyfogle
    March 19, 2007

    Look, it’s very simple: all objectivity is subsumed under the tautological subjectivity of conscious awareness. This philosophical point doesn’t in any way affect science, because it’s outside the aegis of science.

    I’m happy to admit that this mirroring effect of consciousness shouldn’t be called “solipsism” if it can be asserted as a tautological truth without anyone denegrating it as “solipsism.”

  79. #79 Anonymous
    March 19, 2007

    So you deny the tautological truth that all the knowable objects of your consciousness are subsumed under your consciousness?

    Well, perhaps one last attempt, since this pretty much defines the problem.

    No, I am not denying that solipsism is a valid (though non-interesting) world view.

    Of course, “The ontological status of a possible objective reality and references towards the objective should not be confused with, or reduced to, the dichotomous relations between object and subject, or subjectivity and objectivity, without considerable qualifications.” ( http://en.wikipedia.org/wiki/Objectivity_%28philosophy%29 )

    But I don’t know how solipsism can be taken as nothing less than total abandoning of objectivity. No real objects by definition: “the self is the only thing“, “the self is the only reality“.

    I don’t know how the denial of (and so incompability with) real objects and thus denial of objective reality and in the end denial of objectivity can be any clearer.

    Solipsism does not leave any means to make a reasonable definition of objectivity on, as I understand it, as it denies reality outside the self.

    Any attempt would just result in the conclusion that it looks objective because ones self made that subjective decision. ‘A solipsist is the ruler of his world’ – “all the knowable objects of your consciousness are subsumed under your consciousness”.

    (And the possible exception for ones self is pretty much a subjective thing too, I would argue. But that is a detail here.)

    And now I’m done, I think.

  80. #80 Torbjörn Larsson
    March 19, 2007

    To be clear:

    “it looks objective because ones self made that subjective decision.” – it looks objective because ones self made the subjective decision to shape the perceived reality so.

  81. #81 Ørjan Johansen
    March 19, 2007

    It seems to me that you are arguing about different aspects of solipsism, analogous to atheism and agnosticism respectively.

    Torbjõrn Larsson is speaking about the world view that nothing but a single consciousness exists, while Norm Breyfogle is speaking about the impossibility of ever disproving this worldview, and the latter is indeed close to a tautology.

  82. #82 Colugo
    March 20, 2007

    Island is right that Paul Davies sounds like Robert Lanza in some respects. Not quite as loopy perhaps, but check this out:

    http://www.sfgate.com/cgi-bin/article.cgi?f=/c/a/2007/01/21/ING5LNJSBF1.DTL

    “Paul Davies, a theoretical physicist at the Australian Centre for Astrobiology at Macquarie University in Sydney, suggests another possibility: The universe might actually be able to fine-tune itself. …
    (T)he presence of conscious observers later in history could exert an influence on those first moments, shaping the laws of physics to be favorable for life. … “It offends our common-sense view of the world, but there’s nothing to prevent causal influences from going both ways in time,” Davies says. “If the conditions necessary for life are somehow written into the universe at the Big Bang, there must be some sort of two-way link.””

    I don’t buy it.

  83. #83 Blake Stacey
    March 20, 2007

    Colugo:

    When I first pointed Lanza’s essay out to MarkCC, I threw in a Carl Sagan quote as an antidote.

    There is something stunningly narrow about how the Anthropic Principle is phrased. Yes, only certain laws and constants of nature are consistent with our kind of life. But essentially the same laws and constants are required to make a rock. So why not talk about a Universe designed so rocks could one day come to be, and strong and weak Lithic Principles? If stones could philosophize, I imagine Lithic Principles would be at the intellectual frontiers.

    If the conditions necessary for rocks are somehow written into the Universe at the Big Bang — excuse me, the Horrendous Space Kablooie — there must be some sort of two-way link. . . .

  84. #84 Norm Breyfogle
    March 20, 2007

    Ørjan Johansen wrote: “Torbjõrn Larsson is speaking about the world view that nothing but a single consciousness exists, while Norm Breyfogle is speaking about the impossibility of ever disproving this worldview, and the latter is indeed close to a tautology.”

    Bingo, or very close to it.

    Solipsism needn’t contradict the objectivism of science, it can merely point out that such objectivism necessarily concerns the objects of consciousness. Any objects presently and/or permanently *outside* of any consciousness by present circumstance or by definition are unknowable.

    The most tautological of solipsistic assertions is a simple and obvious one: subjectivity is one of the fundamental aspects of consciousness and therefore it’s a fundamental aspect of existence as we conscious beings can know it. Subjectivity need not be the *only* fundamental principle for solipsism to maintain some validity, but if subjectivity is fundamental in any way, then solipsism must have some sort of validity, even if it’s “only” tautologically.

    I don’t see this solipsistic fundamental contradicting anything in science, and subjectivity has been a fundamental feature of conscious reality for philosophers since the beginning of philosophy (Plato’s metaphor of shadows on a cave wall is one early illustration of this).

    The inevitable subjectivity of consciousness (tautological solipsism) is like the existence of the ground of all Being: it’s too tautologically true to disprove or even to derive any instrumental or scientific meaning from it. It’s tautologically true but scientifically valueless.

    It’s the falsifiable form of NONtautological solipsism that we have to worry about, as it leads to many potentially dangerous delusions (e.g., my thoughts create the universe and I can therefore perform miracles, etc.)

    It’s important to distinguish between between these two forms of solipsism in order to distinguish the artists, philosophers, and mystics from the kooks.

  85. #85 Jonathan Vos Post
    March 20, 2007

    The notion that present observers affect the neighborhood of the Big Bang was first described by John A. Wheeler, decades ago. He made a little drawing of the Worm Ouroboros as a sort of big-eyed rattlesnake looking at its tail, the tail being tipped with a Big Bang rattle.

    I don’t recall that being in “Gravitation” by Misner, Thorne, and Wheeler, which I had in pre-print at Caltech in the 1968-1973 era, but circulated seaparately. I still see Kip Thorne now and then at Caltech, and he kindly introduces me to a new batch of his astrophysics/GR grad students and postdocs. Those guys and gals are SMART, and Kip — in his usual low-key way — is a tremendously effective organizer, teacher, and motivator.

    The novel that I started then, one of several novel manuscripts, several completed, only one sold, is about the cosmic conflict between our remote descendants and the superconducting worm civilizations, trying to get the universe to symmetry break again and freeze out a 5th force, whether to our benefit, or theirs. I refer to this explicitly as a fight between the Anthropic Principle and the Vermic Principle.

    My wife also wrote a book-length manuscript, but from the point of view of intelligent beings in the first nanosecond after the Big Bang. The universe had more dimensions then, having not yet rolled them up into a Calabi-Yau manifold.

    Tying these threads togther: the LISA (which wouldn’t have happened without Kip Thorne and his colleagues) is also searching for the fingerprint of the dimensions rolling up, which would release gravity waves of a particular signature.

    I guess that I was only 40 years ahead of my time, and still following the footprints of the amazing Wheeler.

  86. #86 Torbjörn Larssona
    March 20, 2007

    Torbjõrn Larsson is speaking about the world view that nothing but a single consciousness exists, while Norm Breyfogle is speaking about the impossibility of ever disproving this worldview, and the latter is indeed close to a tautology.

    Ørjan, thanks, that must be the difference! I’m seeing it as a coherent world view, but Norm is expressly looking at the operative aspects.

    I will have to think about this some more. There is something here that I’m blind to, since I now remember that I have been confusing exactly this point in a similar circumstance: “The ontological status of a possible objective reality and references towards the objective should not be confused with, or reduced to, the dichotomous relations between object and subject, or subjectivity and objectivity, without considerable qualifications.”

    But I thought that in the case of solipsism we had to drive the coherency through in the philosophical manner. Time to think some more – I’m not a dogmatic atheist, you know. :-) So perhaps I learned something here.

    but there’s nothing to prevent causal influences from going both ways in time

    I don’t buy it either.

    Also, Hawking has proposed a cosmology with similar ideas of the end influencing the start, but the response was AFAIK that it will end with a dS universe instead of the AdS one we see.

    So as far as actual examples go, Davies has problems. And since it is an attempt to put in design and teleology (as reversed causality) where none is needed, I feel for Davies’ ideas as for Penrose’s.

  87. #87 Torbjörn Larsson
    March 20, 2007

    Solipsism needn’t contradict the objectivism of science, it can merely point out that such objectivism necessarily concerns the objects of consciousness.

    But while I’m going to think more about the operative aspects of solipsism, I still think as I have done all along that if you attribute consciousness as a part of your observations, we are no longer discussing objectivity and objectivism but subjectivism.

    It must be an abuse of language to say the above.

    these two forms of solipsism

    And I still think this is unwarranted. Even accepting that we are “speaking about the impossibility of ever disproving this worldview” [italic added] does not make us discussing two different world views, it makes us shift the point of the discussion.

  88. #88 Torbjörn Larsson
    March 20, 2007

    does not make us discussing two different world views

    Returning to Ørjan’s characterisation, atheism and agnosticism are two somewhat different world views but operationally they are the same. Well, I happen to think they are different there too, but I’m rather convinced this isn’t the case for solipsism and Last Thursday ideas.

    But here I go again commenting, when I promised to think about this. :-)

  89. #89 Jonathan Vos Post
    March 20, 2007

    So…. there are “these two forms of solipsism” — mine and yours?

  90. #90 Jonathan Vos Post
    March 20, 2007

    So which way should the tee-shirt read:

    “ARE YOU A SOLIPSIST TOO?”

    or

    “FREE THE SOLIPSISM 1!”

  91. #91 Norm Breyfogle
    March 22, 2007

    I agree that the two forms of solipsism should have two different designations, and such conundrums of language pop up all over the place in philosophical discussions, for instance: self vs. Self (to distinguish between one’s conscious I.D. and one’s greatest transconscious I.D.), reality vs. Reality (to distinguish between what we can know through our senses and consciousnesses and what in its totality transcends such).

    Some examples of such differences-with-similitude already do indeed have separate designations (beyond merely capitalizing the first letter of the more tautological of the pair): relative truth vs. absolute truth, knowable vs. unknowable. In all such examples, just as with solipsism vs. Solipsism, the differences are fundamental ones caused by our own limitations, our own inevitable (though constantly retreating) subjectivity (or Solipsism).

    Mere “solipsism” amounts to magical thinking, while “Solipsism” (note the literary device of capitalization) can be a reminder of both the totality of the infinite unknown beyond our bubble of understanding and of our inevitable corresponding identity with the objects our consciousnesses.

    There’s a basic positivist difficulty that always arises when discussing the ground of all being using any of these terms. The rational, logical, and scientific meaning of any assertion *lies in what it rules out.* But the ground of all being (or “God”, “Reality”, “the “Self”, the “Absolute”, etc.) – the understanding and potential control of which is implied by the scientist’s ultimate but impossible goal of formulating a TOE or GUT, btw – excludes nothing because by definition it includes ALL. Hence the tautological, nonscientific, rationally meaningless, and instrumentally useless nature of such references.

    Ah, but what would we be without the poetic vision such references can elicit!

  92. #92 Norm Breyfogle
    March 22, 2007

    Torbjörn: You’re right, I “shifted the point of the discussion” … slightly.

    However, the word “solipsism” is in the very title of this thread, and I do still consider it an open question whether or not the paradoxes of quantum mechanics are due to a fundamental solipsistic quality of existence. Such paradoxes are at least *amenable* to solipsistic interpretations, as I originally wrote far above.

    I did want to put in my two cents worth of effort at trying to clear up the definition of solipsism first, because it strikes me that said definition isn’t as simply or as necessarily erroneous as it may at first appear.

  93. #93 Norm Breyfogle
    March 22, 2007

    Since this is a math site, I’d suggest that the symbol for the set of all infinities (if there is such a symbol) might be the math equivalent for “the ground of all being.”

    Or is there a better math symbol for this?

    As far and as little as I understand it, paradoxes in using infinity arise from trying to use infinity as a number instead of as an idea. This error appears similar to the errors that arise from trying to use solipsism as a predictive tool rather than just as a philosophical idea.

    In the case of Lanza’s article which is the focus of this blog page, Lanza may be making this error if he’s attempting to derive any scientifically predictive power from his solipsistic pov. But if he’s not trying such, his article can be viewed as a valid philosophical pov and NOT as an erroneous scientific theory (and his use of the word “theory” instead of the more general phrase “world view” would be a semantic error indicating his philosophical error in conflating philosophy with science).

  94. #94 Jonathan Vos Post
    March 22, 2007

    Norm:

    “… set of all infinities …” I don’t want to slow this down with a URL, (and I’ll get back to you on your fiction later) but look up:

    Von Neumann universe
    From Wikipedia, the free encyclopedia

    In set theory and related branches of mathematics, the von Neumann universe, or von Neumann hierarchy of sets is the class of all sets, divided into a transfinite hierarchy of individual sets. It is also sometimes called the cumulative hierarchy.

    This may be defined by transfinite recursion as follows…

  95. #95 Norm Breyfogle
    March 23, 2007

    Thanks, Jonathan. I knew my attempt at addressing this mathematically would fall short; I was hoping someone else here might pick up that ball and run with it.

    Surely it would be interesting to try to model Solipsism (consciousness’ identification with the objects of consciousness) mathematically in some way? Perhaps this is indeed what quantum dynamics represents in some limited sense? Just some thoughts from a non-mathematician …

  96. #96 Anonymous
    March 23, 2007

    In the words of David Hilbert: “No one shall expel us from the Paradise that Cantor has created.”

    First paragraph on Cantor from Wikipedia:

    Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. Petersburg, Russia – January 6, 1918, Halle, Germany) was a German mathematician. He is best known as the creator of set theory. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s theorem implies the existence of an “infinity of infinities.” He defined the cardinal and ordinal numbers, and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware.

    Anyway, Norm, late in life, Cantor’s bipolar problems led him to state what I classify as Theomathematics and Theophysics. Without proof, but interesting, he claimed that consciousness was of a higher infinity than matter. That is, even if space, time, and matter were continua (19th century Physics before people really believed in atoms) the particles of Mind (and Soul) could exist in some way with an infinite number of mental events in between two adjacent particles of matter. Or something like that. I don’t have his original text on the notion.

    I don’t see how Quantum Mechanics grapples with this, as the Hilbert Space beloved of QM is is of the lowest infinity in number of dimensions.

    Von Nemann did try to generalize QM, and here’s the first paragraph of the relevant Wikipedia article:

    A von Neumann algebra or W*-algebra (named for John von Neumann) is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology, and contains the identity operator. They were believed by John von Neumann to capture the concept of an algebra of observables in quantum mechanics. Von Neumann algebras are C*-algebras. The von Neumann bicommutant theorem gives another description of von Neumann algebras, using algebraic rather than topological properties.

    The two basic examples of von Neumann algebras are as follows. The ring L∞(R) of bounded measurable functions on the real line (modulo null functions) is a commutative von Neumann algebra under pointwise operations, which acts on the Hilbert space L2(R) of square integrable functions. The algebra B(H) of all bounded operators on a Hilbert space H is a von Neumann algebra (non-commutative if the Hilbert space has dimension at least 2).

    Von Neumann algebras, under the old name of rings of operators, were first studied by von Neumann in 1929; he and Francis Murray developed the basic theory in a series of papers starting in 1936.

  97. #97 Jonathan Vos Post
    March 23, 2007

    In the words of David Hilbert: “No one shall expel us from the Paradise that Cantor has created.”

    First paragraph on Cantor from Wikipedia:

    Georg Ferdinand Ludwig Philipp Cantor (March 3, 1845, St. Petersburg, Russia – January 6, 1918, Halle, Germany) was a German mathematician. He is best known as the creator of set theory. Cantor established the importance of one-to-one correspondence between sets, defined infinite and well-ordered sets, and proved that the real numbers are “more numerous” than the natural numbers. In fact, Cantor’s theorem implies the existence of an “infinity of infinities.” He defined the cardinal and ordinal numbers, and their arithmetic. Cantor’s work is of great philosophical interest, a fact of which he was well aware.

    Anyway, Norm, late in life, Cantor’s bipolar problems led him to state what I classify as Theomathematics and Theophysics. Without proof, but interesting, he claimed that consciousness was of a higher infinity than matter. That is, even if space, time, and matter were continua (19th century Physics before people really believed in atoms) the particles of Mind (and Soul) could exist in some way with an infinite number of mental events in between two adjacent particles of matter. Or something like that. I don’t have his original text on the notion.

    I don’t see how Quantum Mechanics grapples with this, as the Hilbert Space beloved of QM is is of the lowest infinity in number of dimensions.

    Von Nemann did try to generalize QM, and here’s the first paragraph of the relevant Wikipedia article:

    A von Neumann algebra or W*-algebra (named for John von Neumann) is a *-algebra of bounded operators on a Hilbert space that is closed in the weak operator topology, and contains the identity operator. They were believed by John von Neumann to capture the concept of an algebra of observables in quantum mechanics. Von Neumann algebras are C*-algebras. The von Neumann bicommutant theorem gives another description of von Neumann algebras, using algebraic rather than topological properties.

    The two basic examples of von Neumann algebras are as follows. The ring L∞(R) of bounded measurable functions on the real line (modulo null functions) is a commutative von Neumann algebra under pointwise operations, which acts on the Hilbert space L2(R) of square integrable functions. The algebra B(H) of all bounded operators on a Hilbert space H is a von Neumann algebra (non-commutative if the Hilbert space has dimension at least 2).

    Von Neumann algebras, under the old name of rings of operators, were first studied by von Neumann in 1929; he and Francis Murray developed the basic theory in a series of papers starting in 1936.

  98. #98 Norm Breyfogle
    March 23, 2007

    Jonathan,

    Wow! Well that’s mostly Greek to me. I can’t tell if it addresses the inevitable solipsistic quality of consciousness or not.

    I know; so why am I posting on a math site? Well, mathematicians are so rigorously logical that I enjoy honing my language skills with them. I’ve already noticed an increase in my rational consistency over the last few months of my interacting here.

    If I was adept at math, and if one chosen axiom in a mathematical model of consciousness might be that consciousness = the objects of consciousness, I’d want to show how that solipsistic axiom is compatible with the objectivity displayed by the objects of consciousness. Does your above post address this?

    And here’s a related question: can the Yin/Yang symbol be considered as or translated into a mathematical symbol/function? With the yin always feeding into the yang and vice-versa, it looks like a general symbol for all self-referential equations, like a basic fractal function of the universe. Do you think there’s anything to this observation? Such a question is related to modelling solipsism mathematically because the relationship between consciousness and objectivity appears to be a self-referential one, too.

    Don’t Russell’s paradox and Gödel’s incompleteness theorems point to this infinitely mirroring, mathematically self-referenceing quality of consciousness (Solipsism)?

  99. #99 Jonathan Vos Post
    March 23, 2007

    “can the Yin/Yang symbol be considered as or translated into a mathematical symbol/function?”

    Metaphorically, and mathematically, that seems to be at the heart and soul of “I Am a Strange Loop”, the new and well-reviewed book by Douglas R. Hofstadter.

    He says that people missed the point of his Pulitzer-winning first book — Godel, Escher, Bach — and his meditations on the soul took on great intensity as his wife died.

    I admit that I’m strongly biased in his favor:

    “This sentence contains ten words, eighteen syllables, and sixty-four letters.”

    [Jonathan Vos Post, Scientific American, reprinted in
    "Metamagical Themas: Questing for the Essence of Mind and Pattern",
    by Douglas R. Hofstadter, paperback reprint March 1996, pp.26-27]

  100. #100 Norm Breyfogle
    March 23, 2007

    Isn’t Gödel’s incompleteness theorem very similar to the Heisenberg principle of uncertainty? (I’m sure this is elementary to many here, and thanks for your indulgences). This goes a long way toward illustrating why Robert Lanza sees solipsism illustrated in quantum mechanics, doesn’t it?

    The more I read of the philosophy behind mathematics, the more interested I become in math. I may be spending a long time researching thse facinating foundations of math over the next months. If the philosophy of math had been taught more readily in high school and even in college (rather than just rote memorization of equations) I’d have been much more interested in math from the beginning.

  101. #101 Norm Breyfogle
    March 23, 2007

    We’re posting at the same time here. =)

    Nice to see the predisposition toward similar thoughts in you, Jonathan. Would “I Am a Strange Loop” be beyond me, or is it layman-friendly?

  102. #102 Jonathan Vos Post
    March 23, 2007

    Allegedly “layman-friendly” — but all I’ve seen is reviews and excerpts, haven’t bought a copy yet. If you do, can you let us know?

  103. #103 Norm Breyfogle
    March 23, 2007

    Certainly; will do.

  104. #104 Norm Breyfogle
    March 24, 2007

    JVP wrote, “I admit that I’m strongly biased in his favor:

    “This sentence contains ten words, eighteen syllables, and sixty-four letters.”

    Took me a little time to recognize what you were doing in those last two sentences, but I get it now (I pursued it because it looked like a nonsequitur and yet I just couldn’t imagine you inserting such): although one can reduce your last sentence to all its physical elements (even down to the molecules and electrical bits on our monitors and deep into our brain anatomy), the *full meaning* of the sentence stretches far beyond those elements and into the noosphere … just as our conscious indentities do.

    Your sentence is a highly understated illustration of consciousness’ inevitably interpenetrative, solipsistic identity with all the objects of consciousness.

  105. #105 Jonathan Vos Post
    March 24, 2007

    Norm Breyfogle: you are one of the few who noticed that, although the triply self-referential sentence has a very precise denotation, it has a very open-ended connotation.

    The difference between denotation and connotation is something that not everyone in the general public notices about Mathematics. It is also why Mathematics overlaps Philosophy and Poetry in unexpected ways.

    The part of the sentence which actually appears in print, analogous to the part of an iceberg above sea level, is technically a solution to a set of 3 simultaneous equations in three unknowns, involving the function that maps from a nonnegative intetger to the number of letters in the standard English name of that integer.

    That function itself has ambiguities in definition (spaces? hyphens? what is “standard”?) and equivalents in other languages. There are many such integer sequences involving the name of numbers, in the On-Line Encyclopedia of Integer Sequences.

    I’ve contributed several. There are similarly some weird sequences involving Roman Numerals, several of them linked to from an earlier thread of Good Math Bad Math.

    Do any of these shed light on consciousness? I think so, and I’m pretty sure that Hofstadter thinks so.

    Such theories are not mainstream, but are not automatically denied by mainstream thinkers.

  106. #106 Jonathan Vos Post
    March 24, 2007

    Over at John Baez’s March 23, 2007
    This Week’s Finds in Mathematical Physics (Week 247)

    http://math.ucr.edu/home/baez/week247.html

    is a great discussion on symmetry in higher dimensions, including stuff about the Penrose tiles that were recently discovered to have been used in the Islamic world 500 years ago. At the bottom of the page is the quotation:

    The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry. – Bertrand Russell

  107. #107 Norm Breyfogle
    March 24, 2007

    I’d just referred to connotation/denotation on the “Spirituality and Religion” thread, and I now wish that I, like you, had used that means of describing your clever Integer Sequence sentence. Your explanation was much more lucid than what I offered.

    And I didn’t look at it mathematically, either. I’ve got a lot to learn. I’ve rarely considered before that math could be so connotative.

    It’s interesting to note that *all* sentences illustrate the same mirroring quality of consciousness (and not only sentences, but any and all objects of consciousness whatsoever from the quantum to the multiverse, for all percepts imply a perceiver as all objects of consciousness are meta- or trans-logically subsumed under consciousness). However, your Integer Sequence sentence does so with extremely dry humor by using meticulous denotation to point to unlimited connotation.

    Isn’t this why we find humor in characters like Mr. Spock or Data, because even with their extremely denotative/reductionist outlooks they nevertheless display their connotative/holistic consciousnesses? Don’t we all know people like that?

    All of which reminds me of one of my shortest poems:

    Supreme Identity

    being is meaning
    be what you mean
    mean what you be

    you can’t not

    Or how about this one of mine?:

    Ala Yoda

    do
    do try
    but there is no try
    so do not try
    just do

    I’ll shut up now

    (above poetry copyrighted by me)

  108. #108 jonathan
    March 27, 2007

    so what do you make of Kant, then?

  109. #109 Norm Breyfogle
    March 27, 2007

    I haven’t read Kant since I was in college over 20 years ago, but I’m certain that if I did read his material today I’d see it as I did when I’d finished with it: as an epitome example of the western attempt to rationally categorize all philosophical notions before eastern mystical holism began to have the full impact it’s had since.

    Kant was one of a number of philosophers that exhaused my rational search for absolutes, leaving me free to intuitively grasp the Tao with easy humor.

    Any particular aspect of Kant you have in mind? and what’s your take on him?

  110. #110 Jonathan Vos Post
    March 27, 2007

    Is self-awareness a learned behavior? — A speculative note on the emergence of self-awareness in big-brained organisms

    Authors: Emmanuel Tannenbaum
    Comments: 17 pages, 1 figure, submitted to The Journal of Theoretical Biology
    Subj-class: Neurons and Cognition; Populations and Evolution

    http://arxiv.org/abs/q-bio.NC/0701017

    This paper argues that self-awareness is a learned behavior that emerges in organisms whose brains have a sufficiently integrated, complex ability for associative learning and memory. Continual sensory input of information related to the organism causes the organism’s brain to learn the physical characteristics of the organism, in the sense that neural pathways are produced that are reinforced by, and therefore recognize, various features associated with the organism. This results in the formation of a set of associations that may be termed an organismal self-image, which provides a mechanistic basis for the emergence of various behaviors that are associated with self-awareness, such as self-recognition. In humans, self-awareness includes additional behaviors such as recognition of self-awareness, the concept of I, and various existential and religious questions. This paper shows how associative memory and learning, combined with an organismal self-image and, in the case of humans, language, leads to the emergence of these various behaviors. This paper also discusses various tautologies that invariably emerge when discussing self-awareness, that ultimately prevent an unambiguous resolution to the various existential issues that arise. We continue with various speculations on manipulating self-awareness, and discuss how concepts from set and logic may provide a highly useful set of tools in computational neuroscience for understanding the emergence of higher cognitive functions in complex organisms. The existence of other types of awareness, and the role of mirror neurons in the emergence of self-awareness, are also briefly discussed.

  111. #111 Norm Breyfogle
    March 27, 2007

    “This paper also discusses various tautologies that invariably emerge when discussing self-awareness, that ultimately prevent an unambiguous resolution to the various existential issues that arise.”

    As I’ve written above, tautologies aren’t dangerous unless they’re assumed to have predictive power.

    Any potential for a *completely* unambiguous and *full* resolution of the ultimate existential issues must await perfectly complete knowledge (in a nutshell: omniscience), and omniscience is self-cancelling (for the map can never perfectly equal the territory) and therefore cannot exist.

    In lieu of such impossible omniscience, we have partial predictivity (science) and poetic tautologies. One doesn’t threaten the other if both are understood to be complementary (not contradictory). Tannenbaum is making the classic mistake of confusing the logic of science with translogical philosophy, poetry, and mysticism, which is a common error in our left-brain dominated culture.

  112. #112 Norm Breyfogle
    March 27, 2007

    Then again, I haven’t read the paper; I was only responding to the above brief, and in particular to the sentence I quoted.

    For all I know, Tannenbaum may provide a wonderful accounting of the nature of such existential tautologies.

    But if he’s suggesting that a perfect omniscience is possible, he’s wrong, for no map can equal in all respects the territory it represents.

    And although I keep writing that tautologies have no predictive power, that’s not precisely accurate. More lucidly, tautologies have *little specific* predictive power; what predictive power they do have is very general (for instance, since the map is not the territory, we can predict that omniscience is impossible).

  113. #113 Norm Breyfogle
    March 28, 2007

    I read Tannenbaum’s above linked paper (glossing over – for lack of time – certain more obviously inarguable sections and focussing on the parts more relevent to many of our above posts), and I agree with everything in it. His position on tautologies is identical with mine, even when it comes to the tautologies of solipsism: that they are definitionally true but undecidable and don’t apply to the scientific method.

    I particulary liked his comparison of reincarnation to a quantum superpositioning of the Self, and such reasoning is very pertinent to the topic of this thread: Lanza’s speculations re quantum dynamics.

  114. #114 Norm Breyfogle
    March 29, 2007

    I finally read Lanza’s article which was the basis for this thread (happily, I found that my pre-Lanza-reading comments on this thread are compatible with my post-Lanza-reading pov), and I have to say that I agree with what Lanza is meaning to express although I can how some of his semantic choices will raise the hackles of some extremely rational folks, like it did with Mark CC. As far as I can see, Mark CC is making a mistake that’s similar (though much more complex) to that of PZ’s error on the “Spirituality and Religion” thread: he’s essentially disagreeing with Lanza’s looser, more problematic semantics and missing the real intended meaning.

    Imo, Lanza’s real intended meaning is much more rationally, rigorously expressed by Tannenbaum’s paper for which JVP graciously provided a link above; I don’t see a fundamental disagreement between the two, outside of that due to Lanza’s comparatively sloppy semantics.

    Mark CC, I’d be interested in your reaction to Tannenbaum’s paper, particularly the sections which deal with solipsism and tautologies.

  115. #115 sezam
    August 21, 2007

    “There are 10 kinds of people in the world: those who understand Binary and those who don’t.

    There are 2 kinds of people in the world: the ones who think that there are 2 kinds of people in the world, and the ones who don’t”. – just perfect post :)

  116. #116 jon d. Sanford
    December 18, 2007

    I need help.

    I have been working at developing an AI computer .
    No matter what I do to hide the OS and programs they always find it. Once they can read their own programing they wont accept input.

  117. #117 Even Stephan
    August 27, 2008

    More from Lanza in the September 2008 Discover Interview:


    It all fits, but the problem is, you then do need to accept what people will not accept: When you turn your back to the moon, it no longer exists…

    The core of Lanza’s misunderstanding seems to be an incorrect notion that quantum observation is synonymous with conscious observation.

  118. #118 Even Stephan
    August 27, 2008

    Oh good grief. Lanza is simply advocating John Wheeler’s interpretation of the anthropic principle…

    Wheeler has explicitly written:

    The process whereby the macroscopic world reacts to a quantum event–the process that makes reality–can, in my view, be accomplished with inanimate matter. Following Niels Bohr, I like to call this process “registration” rather than observation (which too strongly suggests human involvement).

  119. #119 Jonathan Vos Post
    August 28, 2008

    I believe in Wheeler and Bohr rather than the befuddled Lanza. One does NOT need a conscious observer, not a cat in the box, not a human, not a robot, not an angel nor deity.

    Though Wheeler does have that classic drawing (he illustrated many of his publications) of the Worm Ouroborous cosmos eyeing its own tail, suggesting that obervationh of the Big Bang has an acausal effect on the Big bang. A particle can be entangled with its own past state, so why not the Cosmos? Just saying… No implication of Noosphere, Teleology, Omega Point, or any of that…

  120. #120 Jonathan Vos Post
    August 29, 2008

    “Faith depends upon belief in things that cannot be proved, and I can prove that more people flunk physics than flunk Sunday School.”

    — P.J. O’Rourke

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