Good Math, Bad Math

I was reading an article on Slashdot the other day about a recent discovery of what might be a MECO. A [MECO][wiki-meco] is a “magnetospheric eternally collapsing object”; if this were true, it would be a big deal because according to relativity, either black holes exist and MECOs don’t, or MECOs exist and black holes don’t.

I have no intention of getting into the MECO vs. black hole argument. But a commenter there put down a link to something that he seemed to think was a [reasonable argument against relativity][nastytruth]. I took a look, and it’s just *hysterically* funny. The author of the site is a total crackpot; not only does he propose a way of totally redefining physics, but he also proposes an explanation for everything that’s wrong with modern software, and exactly how to build a real, proper AI.

One of my mantras for dealing with crackpots is: “The very worst math is no math”. This guy does a spectacular job of demonstrating that.

Just for fun, I’ve got to quote the beginning of his diatribe. There’s nothing more fun than watching a crackpot rant about how it’s the *rest* of the world that are crackpots.

>The Crackpottery
>
>We have all been taught that there is no such thing as absolute motion or
>position or that every motion and position in the universe is relative. This
>unsubstantiated belief, which I have named exclusive relativity, has been
>around for centuries, even before the advent of Albert Einstein and the theory
>of relativity. It was not until early in the twentieth century, however, that
>exclusive relativity became in vogue. Nowadays most physicists consider the
>concept of absolute motion to be no more credible than the flat earth.

>Simple Proof #1 That Exclusive Relativity Is Bogus

>If all positions are relative, then we have a self-referential system in which
>every position is ultimately relative to itself. For example, suppose we have a
>two-body universe. Body A’s position is relative to body B’s position and vice
>versa. Since both positions are relative to the other and there are no other
>bodies, each body’s position is ultimately relative to itself. Of course, it
>does not matter whether there are only two bodies or a billion.
>
>Exclusive relativity amounts to saying things like, “you are as tall as you
>are” or “this sound is as loud as itself” or “pick yourself up by your own
>bootstraps.” Of course this is silly but this is the sort of silliness we have
>to believe in if we accept exclusive relativity.

Nope.

If you have two particles and nothing else, you can define their *positions* relative to each other in terms of their *distance* from each other. It’s not circular. Distance is the important fact. In a relativistic universe, there is no special *distinguished* reference point where the “real” position of objects is defined relative to that reference. Everything is described relative to *a* reference; but that reference can be pretty much any location you choose.

This doesn’t mean that measurements or positions are meaningless. It just means that they’re *relative*.

There’s actually a whole field of mathematics that studies things like this: it’s called metric topology. Speaking *very* loosely, metric topology looks at what kinds of *shapes* a continuous surface can take, and how to measure distance in those different kinds of spaces.

For example, if we lived in a two dimensional world, we could imagine that the world was a flat plane. In that case, the distance between two points is defined in one way. And it doesn’t matter *where* you put your reference point on the plane; the distance between two objects on that surface will be the same. We could also imagine a two dimensional world that was the surface of a torus. The distance between objects would be rather different there; but still, you could measure the distance between two objects on the surface of the torus. And no matter what point of reference you choose, the torus looks the same.

But if you’re a clueless twit who doesn’t understand what “relative position” means, then you can end up with the argument that this guy just presented.

>Simple Proof #2 That Exclusive Relativity Is Bogus
>
>Suppose there is a force acting on a particle so as to accelerate it. The
>particle has as many relative velocities as there are possible frames of
>reference, an infinite number in fact. Which of the myriads of relative
>velocities does the force change? How does the accelerating agent know about
>them so as to change them all? Answer, it does not. Only one velocity is
>changed by the force because it has no access to the others. The others are
>abstract, i.e., non-physical.

Once again, nope.

One of the things that’s beautiful about relativity is that it provides a set of equations that make this all work. From one point of reference, it may appear that an object is accelerating at rate X; from another point of view, it may appear that it’s accelerating at rate Y; work out the relativity equations, and they’re *both* right. Time dilation and relativistic mass shift makes it all work. (If fact, if you were around to read [my series on group theory][groups], you can see [where Blake Stacey explained in a comment][relativity] how relativity describes a lot of things as groups that are symmetric over the kinds of transformations that we’re discussing.)

The problem with the author of this piece is that *he’s not doing math*. Relativity isn’t just a theory with a bunch of words that say “position is relative”, etc. It’s a set of mathematical equations that define in a very precise way what that means, and how it works. Like I said: the worst math is no math. If he’d tried to understand the math, he’d know that there’s no problem here.

>Simple Proof #3 That Exclusive Relativity Is Bogus
>
>Let’s consider the motion of a particle. How does a particle “know” about its
>motion or rest relative to extrinsic frames of references so as to move or be
>at rest relative to them? Are particles psychic? I think not. No particle in
>the universe can make use of the relative because it has no access to it. It
>follows that the universe does not use the relative. The only properties that
>it can use are absolute ones.

Same exact problem as his “simple proof #2″. He didn’t do the math, and so he drew a really stupid invalid conclusion. The math of relativity explains how this works: the apparent velocity and acceleration of a particle in all frames of reference are equally valid; and the reason that they’re equally valid is because if you do the math for shifting the reference frame, you find that the different apparent values are really just different views of the same thing.

[nastytruth]: http://pages.sbcglobal.net/louis.savain/Crackpots/nasty.htm
[groups]: http://goodmath.blogspot.com/2006/06/group-theory-index.html
[relativity]: http://goodmath.blogspot.com/2006/04/some-applications-of-group-theory.html
[wiki-meco]: http://en.wikipedia.org/wiki/Magnetospheric_eternally_collapsing_object
[slashdot-meco]: http://science.slashdot.org/article.pl?sid=06/07/28/0543250

Comments

  1. #1 ericnh
    July 29, 2006

    “Are the particles psychic?”

    Apparently this guy’s never heard of entanglement, or understood it if he has (I’m not a physics or math major but I’m pretty sure I get it). I’m currently reading Brian Greene’s The Fabric of the Cosmos and couldn’t help but laugh at this guy’s “proofs”. This crackpot needs to brush up on his reading so he’ll stop embarassing himself.

  2. #2 Bob Munck
    July 29, 2006

    The software stuff is MUCH funnier. Turns out our main problem in the software business is that we’re using algorithms. Who knew? The COSA main page has a particularily apropos footer:

    These pages are under continual revision. Refresh your browser often.

    Last Update: 08/07/2002

  3. #3 BenE
    July 29, 2006

    The group theory stuff is kindof interesting though I’ll have to read the posts all over again. I first stumbled upon it when reading about the Bayesian stuff but it wasn’t really explained in Jaynes book. Basically, Jaynes uses group theory to select the most uniformative priors for different situations. The most uninformative priors, for example, gives the same result for groups of different scales of the parameter.

  4. #4 Torbjörn Larsson
    July 30, 2006

    It is such a serious disconnect between what we know and the sites claims that it is too hard to sort it all out.

    First, on MECO’s:
    The referenced Wikipedia is inconsistent. Black holes may have mass, charge and spin. There is also the rotating Kerr-Newman black hole solution. QM charged particles with spin or classic charged objects with rotation has magnetic moments. Magnetic moments are a measure of the strength of a magnetic source. So contrary to claims the black hole itself should give magnetic fields IMO.

    They also explain that they base the MECO claim on radiation from the accretion disc. Stars accretion disc, including white stars and neutron stars, may have magnetic moments. There is nothing that preclude a collapsing star accretion disc to continue having its precollapse properties, including magnetic fields.

    MECO’s are crank science, based on denying the existence of black holes.

    Second, on relativity:
    There are degrees of relativity vs groups.

    No relativity – Newton argued for an absolute space.

    Galilean relativity – later it was found that relativity regarding inertial (same velocity) frames was compatible with newtonian physics. This is general galilean invariance, with its own group describing transformations.

    Special relativity – inertial frames gives the same nongravitational physics. (Ie light speed constant.) Generel lorentz invariance, lorentz group. Lightcone causality.

    General relativity – frames gives the same physics. Local lorentz invariance.

    And, BTW:
    Invariance of particles – no observable physical quantity should change after exchanging two identical particles. In QM bosons are identical, fermions are not.

  5. #5 shaker
    July 30, 2006

    From the main page of the site:

    If a scientist claims to have a theory about a natural phenomenon but is unable to explain the theory in a simple language that the average layman can understand, one can be absolutely certain that he is as clueless about the nature of the phenomenon in question as anybody else. Voodoo science is not about understanding nature but about working at being so incomprehensible or so arcane to one’s fellow human beings as to be regarded as brilliant. The weapon of choice of a voodoo scientist is mathematics.

    So basically he suffers from mathphobia and wants all scientific research done without any maths. I can’t decide whether he is for real or it is all very elaborate satire.

  6. #6 Blake Stacey
    July 30, 2006

    MarkCC wrote:

    Relativity isn’t just a theory with a bunch of words that say “position is relative”, etc. It’s a set of mathematical equations that define in a very precise way what that means, and how it works.

    Other people have had problems with this, too, and not just about relativity. Let me quote from Sokal and Bricmont’s Intellectual Impostures (2003), p. 177:

    The natural sciences are not a mere reservoir of metaphors ready to be used in the human sciences. Non-scientists may be tempted to isolate from a scientific theory some general ‘themes’ that can be summarized in few words such as ‘uncertainty’, ‘discontinuity’, ‘chaos’ or ‘nonlinearity’ and then analysed in a purely verbal manner. But scientific theories are not like novels; in a scientific context these words have specific meanings, which differ in subtle but crucial ways from their everyday meanings, and which can only be understood within a complex web of theory and experiment. If one uses them only as metaphors, one is easily led to nonsensical conclusions.

    In a footnote, they continue:

    For example, a sociologist friend asked us, not unreasonably: Isn’t it contradictory for quantum mechanics to exhibit both ‘discontinuity’ and ‘interconnectedness’? Aren’t these properties opposites? The brief answer is that these properties characterize quantum mechanics in very specific senses — which require a mathematical knowledge of the theory to be properly understood — and that, in these senses, the two notions do not contradict one another.

    Note that once you have two contradictory postulates — e.g., “QM says everything is discontinuous” and “QM says everything is interconnected” — you can deduce absolutely anything you want!

    Oh, and thank you for bringing my bit about symmetry back into the limelight! (-:

  7. #7 Xanthir
    July 30, 2006

    Ericnh:
    Entanglement isn’t needed to show that this guy’s argument is retarded. He’s just talking about relative frames. I believe he’s essentially arguing that every relationship that a particle can have is encoded in the particle. If relationships are relative to your reference point, then the particle needs to encode *all* the possible relationships.

    Of course, the second sentence isn’t even necessary for his first sentence to be very, very wrong. Using just that first sentence, one can argue that particles must be psychic even in an absolute reference frame! How else can it know how it should be moving?

    Ooh… I understand now… I don’t know if he realizes it, but the guy is arguing for the existence of a God. If every relationship between particles must be encoded somewhere, then in an absolute reference frame all the relationships are encoded in a single place: God’s mind, the information-center of the universe. Of course he hates relativity, because by his interpretation every particle in existence must have all the properties of God!

  8. #8 Xanthir
    July 30, 2006

    Blarg, I just read his site. His ideas on computers are retarded. Neural networks are just a way of sussing out algorithms automatically. They could be thought of as evolutionary algorithms. ^_^ They search over a fitness space for the correct relationships between input and output. While it could be complicated, you can certainly take the results of a tuned neural network and translate it into a pure algorithm. Unless neural networks (which are implemented on Turing-complete machines) have some magical way of performing operations that a Turing machine can’t, the two are exactly equivalent theoretically.

    While neural networks are certainly cool, he has a total hard-on for them. The reason biological neural networks can do things that our electronic ones have such a difficult time with is because we invented computers, oh, about 50 years ago, while biology has been operating over billions of years on a massively parallel processer (the earth). Of *course* we haven’t figured out all of the secrets yet. It’s very complex stuff. Jeez.

  9. #9 Torbjörn Larsson
    July 31, 2006

    Xanthir:
    “Unless neural networks (which are implemented on Turing-complete machines) have some magical way of performing operations that a Turing machine can’t, the two are exactly equivalent theoretically.”

    I’m not sure I follow this. That the hardware and instruction set of a computer is Turing equivalent (Turing complete), which I think it is basically being von Neumann architectures, doesn’t seem to imply that an implementation is. How could there else be non-Turing complete languages?

    So it seems you are claiming that neural networks are at least as powerful as Turing machines. How do we know that? Algorithmic capability doesn’t seem to be enough, spreadsheets without loops aren’t Turing-complete. So we probably have to assume tuning and feedback.

    “The reason biological neural networks can do things that our electronic ones have such a difficult time with is because we invented computers”

    When we have this model of neuroscience, which claims that some dynamical systems, such as certain analog recurrent neural networks, are super-Turing because they can compute a wider class of functions ( http://www.philosophy.unimelb.edu.au/tgelder/papers/DH.pdf , p 17).

    The reference, Siegelmann & Sontag, “Analog Computation via Neural Networks”, Theoretical Computer Science, 131, 331-360 ( http://citeseer.ist.psu.edu/cache/papers/cs/74/http:zSzzSzwww.math.rutgers.eduzSz~sontagzSzFTP_DIRzSznets-real.pdf/siegelmann94analog.pdf ), makes it clear that it is based on a finite number of nodes.

    The difficulty seems to be if the internal analog operations on the modelled soft binary input/output can be made with realistic precision, since their result depends on assuming infinite precision.

    Are there any general results that shows that realistic analog systems are merely Turing?

  10. #10 Torbjörn Larsson
    July 31, 2006

    Xanthir:

    Sorry, the last citation I wanted to make from your comment was of course meant to be “The reason biological neural networks can do things that our electronic ones have such a difficult time with is because we invented computers, oh, about 50 years ago,”

    I didn’t mean to imply computers aren’t nifty. ;-)

  11. #11 Mark C. Chu-Carroll
    July 31, 2006

    Torbjörn:

    I think that what Xanthir meant is that at best, neural networks could be as powerful as Turing machines; they can’t be *more* powerful, because Turing completeness defines the limit of what’s doable by a mechanical computing device.

  12. #12 Mark C. Chu-Carroll
    July 31, 2006

    Xanthir:

    I hate to come to the defense of a crackpot, but there *is* one important fact that you’re neglecting. Any turing-complete computing system can perform all of the computations that are performable by any other TC system. But a given computational task may be significantly more complex to specify in some systems; and the time and space complexity can be *exponentially* worse on some devices.

    That exponential difference in complexity *can* conceivably be the difference between a computation being possible and effectively impossible.

  13. #13 SteveF
    July 31, 2006

    Mark,

    You might find the following book to be of interest. Produced by one of the guys behind:

    http://www.catholicintl.com/

    it is apparently the new manifesto for geocentrism.

    http://galileowaswrong.com/

    Hmmmmmm

  14. #14 David
    July 31, 2006

    This is similar to arguments I’ve heard others say about relativity. One particular one is that length is undefined because according to special relativity length can be anything depending at what velocity you are travelling. Since objects and points-of-view in the universe are always travelling at different velocities, they measure different lengths for the same object. Therefore, there is no true length.

    What some people forget is the consistency of a rest-length. If I measure the length of a rod while at rest and give it to someone else who takes it on a rocket, I will measure the length to have contracted. However, the person in the rocket will measure the same length I did back on the ground, the rest-length. So all observers will agree on the rest-length. This is the consistency upon which all “relative” measurements are based and agreed upon.

  15. #15 loren king
    July 31, 2006

    This particular crackpot comes across as someone who studied philosophy but stopped reading at Leibnizian metaphysics. But lest anyone think it impossible to make philosophical arguments and speculations about relativity without coming off as a crackpot, I offer this old note in the Journal of Philosophy as evidence that philosophers can find interesting puzzles in well-established scientific theories …

    Robert Weingard, “On the Ontological Status of the Metric in General Relativity,” Journal of Philosophy 72 (August 1975): 426-431.

  16. #16 Torbjörn Larsson
    July 31, 2006

    Mark:

    “I think that what Xanthir meant is that at best, neural networks could be as powerful as Turing machines;”

    I think I got that.

    “they can’t be *more* powerful, because turing completeness defines the limit of what’s doable by a mechanical computing device.”

    Okay. I think I’m doing a pretty good job of confusing digital machines, analog machines and dynamical systems.

    When I look into the Wikipedia definition of a turing machines it handles symbols with infinite precision. If it reads and writes states with infinite precision it seem to be fundamentally analog machines operating with a function on each read state. (So it may be the paper I referenced is wrong.)

    Wikipedia on Computability theory says “The Church-Turing thesis conjectures that there is no reasonable model of computing more powerful than a Turing machine”, which is stronger than the formulations under the thesis itself.

    Perhaps turing machines can model some dynamical systems such as artifical and biological neural networks faithfully due to the function mapping part.

    But does this mean that neuroscientists should work under the assumption that a brain is turing complete?

  17. #17 Torbjörn Larsson
    July 31, 2006

    Perhaps I should mention the reason I’m suspicious is that it is fairly easy to make continuous dynamical systems that doesn’t give functions out from functions in, but such stuff as hysteresis.

    Which is a bad example, because a state machine such as turing machine could probably describe hysteresis it seems to me. But perhaps there are more serious problems.

  18. #18 Xanthir
    July 31, 2006

    MarkCC: I used the word ‘theoretically’ at the end of my first paragraph to indicate exactly that. I glossed over the practical difficulties of implementing some things in certain languages/architectures because I assumed everyone knew it. I mean, we’re already discussing theoretical Turing machines, right? ^_^

    Torbjorn: Mark answered for me partially. I was trying to only use standard wording, rather than inventing stuff like super-Turing or sub-Turing. As for your later post…

    You know, now that I think about it, I can’t recall the specifics of what I’ve read about Turing limits. Essentially, I think it’s been proven that any digital computer can’t be any more powerful than a theoretical Turing machine. That is, a theoretical Turing machine can simulate any digital computer. I am of course defining power in terms of possible functions it can compute, not in terms of speed or similar. This would mean that *anything* you implement on a computer is Turing-equivalent at best. I also know that quantum computing holds the possibility of being super-Turing, but last I had read it was only strongly suggested, and not yet proven.

    Now, it is generally accepted that the real world can be thought of as composed only of digital information. It is more than likely in fact composed of quantum information (which, again, may or may not reduce to being equivalent to digital information, and so may or may not allow the construction of super-Turing machines). If the world is essentially digital, then our minds are Turing-equivalent at best. If the world is essentially quantum (and it can be proven that quantum algorithms can be super-Turing), then it may be possible that our minds (and presumably any other neural network) are super-Turing as well.

    However, that’s a lot of ifs. Until physics and mathematics nails down a bit more of the details, I run with the assumption that the world is digital, and so the Church-Turing thesis applies to *everything*.

    Note that I’m a mathematician by hobby, not practice, only.

  19. #19 wamba
    July 31, 2006

    I’m sure this offer is completely genuine:

    EINSTEIN WAS WRONG
    (SEE THE $10,000 CHALLENGE)
    THE AETHER EXISTS

    All those caps are enticing, yes? This must be a reasonable person.

  20. #20 wamba
    July 31, 2006

    Be sure to check out the rules on that $10,000 CHALLENGE:


    The object is to disprove the above statement to the satisfaction of R F Norgan…
    R F Norgan has the sole right to choose his challengers…
    The decision as to who has won the challenge at the end of the challenge period is made by one of the two participants admitting defeat…

    How could you be any more fair than that?

  21. #21 Blake Stacey
    July 31, 2006

    Xanthir wrote as follows:

    I was trying to only use standard wording, rather than inventing stuff like super-Turing or sub-Turing.

    While I follow your meaning, I feel the duty incumbent upon me to point out that “sub-Turing machine” was used in episode 15 of Ghost in the Shell: Stand Alone Complex, so your coinage is not original. However, in this case, “sub-Turing” refers to an AI which cannot pass the Turing test, so it’s really talking about a different thing.

    Oh dear Moloch, I am such a nerd.

  22. #22 Xanthir
    July 31, 2006

    There is no shame in admitting you’re a nerd. You’re commenting on a math/programming blog. It’s pretty much assumed. ^_^

  23. #23 Torbjörn Larsson
    August 1, 2006

    Xanthir:

    “Essentially, I think it’s been proven that any digital computer can’t be any more powerful than a theoretical Turing machine.”

    Yes, I strolled through Wikipedia, and it claims von Neumann architectures (essentially our computers) are turing. And the Church-Turing theorem makes an (unsupported, except by many examples) hypotheses that are stronger (various forms).

    “that quantum computing holds the possibility of being super-Turing”
    IIRC, I have seen the converse claim.

    “Now, it is generally accepted that the real world can be thought of as composed only of digital information.”

    At infinite resolution, sure. (Or possibly even finite, if we look at entropy formulations.) The problem as I understand it isn’t in the description but in the ability to let algorithms describe nature, either with digital or analog methods. Some philosophers would rather see neuroscience be about superturing problems, so they can avoid discussing algorithmic descriptions of brain mechanisms.

    But now I found a description that superturing means solving the halting problem, ie avoid gödel incompleteness (http://en.wikipedia.org/wiki/Super-Turing_computation ; Wikipedia again, CS naive guy here; BTW, it says “it has been proved that regular quantum computers are Turing reducible”). That doesn’t seem likely, and indeed they say on proposals that “none of these devices seem physically plausible”.

    It feels like superturing would imply denying a lot of important math and CS results. Gödel incompleteness, the halting problem, that randomness can’t be proven, all efficient computing devices equivalent (classical, biological, quantum), IC nonexistent (Mark’s theorem :-). Also stuff like NP-hardness remains welldefined. So I now believe you are correct, and that the paper I found is pathetically wrong.

    The problems and their “near but not quite” solution proposals feels remarkably like some other more or less general and important science problems. For example, the denial of superluminal communication, naked singularities or time machines are also connected and with similar close call overturn ideas that are refuted by most peculiar mechanisms.

    Perhaps Mark will make a post about turing completeness and its relation to all other goodie CS stuff some time.

  24. #24 Xanthir
    August 1, 2006

    Hey, no problem with wikipedia – I’m gathering my information from memories of books that I didn’t full understand in the first place (often because I read them before I had enough math!). So Wikipedia is at least as reliable as me. ^_^

    Yes, I strolled through Wikipedia, and it claims von Neumann architectures (essentially our computers) are turing. And the Church-Turing theorem makes an (unsupported, except by many examples) hypotheses that are stronger (various forms).

    Like I said, I think the similar claim of “A Universal Turing Machine can simulate any digital computer” is what has actually been proven, which does indeed indicate that digital computers cannot exceed Turing limits. And, of course, by “digital” I’m referring simply to the type of information the machine passes around, not anything special about the particular architecture. That is, there’s no difference between digital and analog, as long as the machine can be abstracted to a bit-passer.

    On the Turing stuff – I’d really like to see the proof of quantum computers being Turing-equivalent. As I said, it was still hoped that quantum properties such as superposition and entanglement could solve some classically non-computable functions last I had heard. Of course, even if they do turn out Turing-equivalent, they can still very well be useful. I know that it was hoped that superposition could at the very least transform the solving of NP problems.

    Man, though, a super-Turing machine would be amazing. Stephen Baxter (a favorite hard-scifi author of mine) postulated a super-Turing machine based on superluminal travel. Tiny computer-bots zipped around a small area superluminally, performing calculations and then returning to a point before they left. This cascaded, allowing an infinite number of operations in a finite amount of time. This of course requires all sorts of exotic physics that we don’t yet know about. ^_^ So yeah, any super-Turing machine would be pretty darned exotic.

  25. #25 Mark C. Chu-Carroll
    August 1, 2006

    There aren’t any super-turing machines. One of the things that we study a lot in theoretical computer science is the implications of various differences in how computers and computation could work. The thing is, a “super-turing” machine – that is, a machine that could solve the halting problem – is impossible per Godel. You can’t get around the fundamental Godel limitation no matter what your machine can do: any mechanical system is fundamentally limited by the limits of mathematics itself.

    The big different between a quantum machine and current hardware is performance. Different computing systems can solve all of the same problems; but some can be exponentially faster on some problems than others. Quantum machines, at least theoretically, have the capability to push things that are currently *intractable* into the realm where they become reasonable.

    Quantum computers aren’t super-turing. What they *are* is non-deterministic, in the formal sense. The formal computational meaning of non-deterministic is that all possible paths are followed at the same time; so, for example, a search that required exponential time because of the number of paths that needed to be covered could be done in polynomial time with a quantum computer; it would effectively search all paths and collapse on the successful one.

    A quantum machine would make NP-complete problems tractable. The definition of NP is “nondeterministic polynomial time”: that is, things that can be done in polynomial time given a non-deterministic machine; NP complete problems are problems with no known deterministic polynomial-time solutions, but which are polynomial time on a non-deterministic machine, and which are part of an equivalence class so that if any could be solved in polytime, all could be solved in polytime. But since a quantum machine is non-deterministic, it means that the NP problems are polynomial time on the quantum machine.

  26. #26 Blake Stacey
    August 1, 2006

    I move we have a GM/BM post on quantum computation — what it can in principle do and what it can’t. This topic has the advantage that it lets one cover both good math (P v. NP, etc.) and bad science. As an example of this “quantum flapdoodle”, as Murray Gell-Mann calls the genre, check out this Wikipedia article:

    Wikipedia on Orch-OR

    I don’t recommend this article as a good treatment of the subject, since it is fairly drenched in woo. It’s more an hors d’oeuvre to get the flavor — and to remind us all that Wikipedia is the place to start research, not to stop it! A better introduction is A. Litt et al.‘s paper “Is the Brain a Quantum Computer“, Cognitive Science 30, 3 (2006): 593–603.

  27. #27 Xanthir
    August 1, 2006

    Hmm. I was sidestepping around the Incompleteness thing – I didn’t think it was even theoretically possible to complete such things (except perhaps with time-travel as in the example I gave – ooh, does Incompleteness imply that time travel can’t exist? I’m just wildly hypothesizing on these things and probably don’t know what I’m talking about, but it’s certainly interesting…).

    However, I *assumed* that there are non-computable functions that are possibly computable by a super-Turing machine. Or are all non-computable functions essentially dependent on the halting problem?

    And yeah, transforming the NP-complete problems into something solvable was precisely what I was talking about in the later part of my post. I assumed that this was theoretically possible while still being Turing-equivalent, and it appears I was right. ^_^

  28. #28 Torbjörn Larsson
    August 1, 2006

    “ooh, does Incompleteness imply that time travel can’t exist?”

    I hope you realise that I didn’t mean that these two groups of interconnected phenomena were themselves trivially interconnected.

    Interesting idea, though. But offhand I would say that a fundamental result on formal theories (or computability) shouldn’t be expected to affect physics in such a manner.

    All known tentative timetravel solutions in GR require physics that doesn’t seem to exist. Wormholes for example doesn’t seem to be expandable to large sizes as earlier thought. Ultimately time travel mess with (global) causality, which is the connection to superluminal communication, and IIRC naked singularities.

    On the superturing article wikipedia mentions a speculative connection between computability and relativistic physics that are thought to fail as the other superturing proposals: “A digital computer in a special kind of spacetime, called a Malament-Hogarth spacetime, can perform an infinite number of operations while remaining in the past light cone of a particular spacetime event.” Probably the idea Baxter exploited.

  29. #29 Xanthir
    August 1, 2006

    I hope you realise that I didn’t mean that these two groups of interconnected phenomena were themselves trivially interconnected.

    Nah, I made the connection myself. If time travel would allow one to solve the halting problem, and the halting problem is a retelling of Incompleteness, and Incompleteness *can’t* be defeated, then time travel is impossible. The important part is the third premise, of course.

    Interesting idea, though. But offhand I would say that a fundamental result on formal theories (or computability) shouldn’t be expected to affect physics in such a manner.

    Eh, I think math has very real implications for the world. I’ve never figured out what the proper label is, but I’m one of those who figure that, deep down, the universe is math. Platonic realists? I don’t know.

    On the superturing article wikipedia mentions a speculative connection between computability and relativistic physics that are thought to fail as the other superturing proposals: “A digital computer in a special kind of spacetime, called a Malament-Hogarth spacetime, can perform an infinite number of operations while remaining in the past light cone of a particular spacetime event.” Probably the idea Baxter exploited.

    Eh, I dunno. It’s certainly possible, but I think it might have been as simple as superluminal travel causing backwards time travel. He conjectured that superluminal travel violates causality, allowing you to freely traverse spacetime.

    It’s all crazy talk anyway. ^_^

  30. #30 Torbjörn Larsson
    August 2, 2006

    “I’ve never figured out what the proper label is, but I’m one of those who figure that, deep down, the universe is math. Platonic realists?”

    Here I disagree. To quote myself from another comment here: “My view on math is that it is based on observations and idealisations on the real world. I think real numbers are an excellent model of a dimensional measure. I’m not a “modellist” in extremis, I just don’t see that Platonic cryptodualism is useful, nor compatible with naturalism.”

    And I feel strongly about this since I don’t think any dualism is allowed, based on all earlier and remaining problems with them. But that is my figuring. :-)

  31. #31 Torbjörn Larsson
    August 2, 2006

    Sorry, that was a confusing quote. I mean’t to say:

    “”My view on math is that it is based on observations and idealisations on the real world.”

    “I’m not a “modellist” in extremis, I just don’t see that Platonic cryptodualism is useful, nor compatible with naturalism.”

  32. #32 Xanthir
    August 2, 2006

    Hmm. Unless there are elements to my philosophy that I don’t know about, I’m certainly not a dualist. That’s why I’m not sure that Platonic Realism is the correct word. I think at least part of your disagreement is with the idea that there is an ideal world and a material world. I certainly don’t believe that. I think that the material world is a representation of the math behind it all. A good analogy is with The Sims. If we imagine that a Sim is sentient (play along here…), then presumably he would feel and experience the world as real. He would have no way of knowing that everything is simply code, that all of the world is generated by relationships between bunches of bits.

    This is, in essence, my belief about the real world. There’s nothing mystical about it, it’s just an assumption that math is fundamental to our reality. The universe is an equation. ^_^

  33. #33 Torbjörn Larsson
    August 2, 2006

    Xanthir:

    Okay, now I see. Perhaps Platonic realism is a good term for that, when you don’t apply platonism on math separately but on everything. That is a lot better than dualism, yes.

    Well, I don’t think our most basic theories are only numbers by themselves, and so can’t be enough to be the basic part of reality either. Numbers are human idealisations in math. But I can certainly be wrong.

  34. #34 JOHN R.WAGNER
    October 18, 2006

    Dear Sirs: the following is simply a test to see if transmission occurs. I would like to write some articles but I wondered if this could be done off-line and then simply pasted on the blank sheet that I have now or is it necessary to do all writing while on-line using up valuable phone time? I am an electrical/electronic engineer, not a programmer so I am not exactly sure what you wish for an URL in the blank space above. As a member of AOL, I am not sure I have a distinct URL or are you thinking of the ip address for the dial-up adapter?
    Finally, I am extremely concerned about the grasping qualities of the religious right and others who would bastardize science until it conforms to THEIR particular interpretation of scripture. It is time we band together to FIGHT BACK! I have joined the Michigan Citizens for Science group. Is there also a way to join the Scientists and Engineers for America that Chris Mooney mentions in his latest article for SEED magazine? Any help that you could give me in this area would be deeply appreciated.
    Sincerely,
    John R. Wagner

  35. #35 Xanthir, FCD
    October 18, 2006

    I don’t know about the latter, but as for the former:
    What do you mean, “Write some articles”? For this blog? You can write some *responses* to the articles, but all top-level stuff is done my Mark himself, as it is his blog.

    As long as you’re dealing with a big ol’ text box like this, you can always copy+paste into it from an offline word processor.

    The URL field is for plugging your website. It’ll turn your name into a link to the site.

    Are you on pay-by-the-minute dial-up? I thought that stuff died out years ago. Get DSL, or cable, or *something* modern. Also, dump AOL and use a real browser. I can recommend the standard, Firefox, but I also enjoy Avant browser.

  36. #36 JOHN R. WAGNER
    October 19, 2006

    Dear Xanthir,

    Thank you for the very fast response to my question(s).
    They helped quite a bit. Most of my life has been spent designing the logic for machine control and teaching standard college calculus, so “blogging” is all new to me.
    But I am starting to get the hang of it.
    Sincerely,
    John R.Wagner

  37. #37 JOHN R. WAGNER
    October 20, 2006

    Just in case you have not heard. We have one small victory for science and intellectual integrity. The Michigan State Board of Education ruled UNANIMOUSLY (8-0 decision)on Tuesday, October 10, 2006 that Michigan science educators must teach evolution, not creationism. This makes it clear that “Intelligent Design”, at al, is NOT to be taught in science class; although there may be room for it in courses such as philosophy or the history of science. To the best of my knowledge, this is all that science educators have been asking for in the first place.
    Needless to say to all. Do not let your guard down. To paraphrase a famous quote, the price of this honest science is eternal vigilence.
    Hoping I have made your day a liitle brighter, I remain,
    John R. Wagner

  38. #38 John R. Wagner
    November 10, 2006

    Re: Posting of July 31, 2006 by SteveF.
    If you think the Magnum Opus “Galileo Was Wrong” by Robert Sungenis is an abuse of math and physics, try “FixedEarth.com” by Marshall Hall and see if you can still stop throwing up. Neither of the gents knows beans about physics, but Sungenis is arrogant enough to think that he does. He banters around talk about relativity and quantum physics with an assurance that would make most Ph.D’s in physics blush. Like most creationists he has a fixation on credentials and obtained a “Ph.D” in religious studies from a “non-traditional university”, which is usually a kind way of saying “diploma mill”. The “Fixedearth” is even more pathetic. The sun is really an electric transformer and gravity at outworn concept among other things. I do suggest you have a stiff drink before reading. Both accuse Kepler of murdering Brahe.
    Sincerely,
    John R. Wagner

  39. #39 ItsCoolToBeCrazyAmongCrazies
    May 6, 2007

    One particle looks very attractive when seen from the back but only somewhat attractive when seen from its front side.

    How does the particle know if it is very attractive or somewhat attractive?

    If the particle gets drunk and then pregnant who is the father of the child? (hint:observer looking from the front side may have been more drunk than the observer looking from behind)

  40. #40 ebg
    August 5, 2007

    I understand the theory of special relativity very well, and when I have to make the grade, I give all the correct answers and equations. However, I totally think its incorrect because of one mathamatical flaw I precieve it to have. Yes,Yes, its not good to agrue in the classroom, and its better to keep your mouth shut, pass the test, and get out of there. I, myself, don’t offer any other theories to replace special relativity. Niether, do I profess to have discovered any unknown force and name it after myself (like “the ebg effect”). Nor do I rant on about the injustice of “scientifc truths”. However, I do wish to explain my perceptions on the subject to someone. ANY RESPONSE?

  41. #41 Torbjörn Larsson, OM
    August 5, 2007

    However, I totally think its incorrect because of one mathamatical flaw I precieve it to have. … However, I do wish to explain my perceptions on the subject to someone.

    I honestly doubt there would be a point, from that context. Since Lorentz invariance is a fundamental requirement in physics and so overwhelmingly tested as being the correct description, this is what any antagonist in the discussion would ultimately point to. It isn’t a mathematical formalism based on axioms, it is a physical theory based on observational facts.

    A better context would be to note that you have a point that is unclear to you and would like to clear out. Have you really tried to discuss this with your teachers? I’m sure they would appreciate helping, besides that it is their duty.

  42. #42 Torbjörn Larsson, OM
    August 5, 2007

    Lorentz invariance … a physical theory based on observational facts.

    Ahem. In that context it should be “Lorentz covariance” – but the theory it is based on and what we are discussing is really special relativity.

    Also, “a physical theory based on and tested against observational facts” is better.

  43. #43 Anonymous
    August 6, 2007

    Your right, what would be the point. But remember: If science is the observation of nature, then math is the explanation of that observation.

  44. #44 Jonathan Vos Post
    August 6, 2007

    Well, your teacher might not mention the exotic and ghostly advanced speculations such as those below.

    High Energy Physics – Experiment, abstract
    hep-ex/0703015

    From: Michela Cozzi
    Date: Thu, 8 Mar 2007 16:48:41 GMT (15kb)

    MACRO constraints on violation of Lorentz invariance
    Authors: M. Cozzi (Bologna University and INFN-Bologna)
    Comments: 3 pages, 2 figures. Presented at NOW 2006: Neutrino Oscillation Workshop, Conca Specchiulla, Otranto, Italy, Sep 2006. To be published in Nucl. Phys. B (Proc. Suppl.)

    The energy spectrum of neutrino-induced upward-going muons in MACRO has been analysed in terms of relativity principles violating effects, keeping standard mass-induced atmospheric neutrino oscillations as the dominant source of nu_mu to nu_tau transitions. The data disfavor these exotic possibilities even at a sub-dominant level, and stringent 90% C.L. limits are placed on the Lorentz invariance violation parameter |Delta v| < 6 times 10^-24 at $sin 2 theta}_v = 0 and |Delta v| < 2.5 divided by 5 times 10^-26 at sin 2 theta_v = $1. These limits can also be re-interpreted as upper bounds on the parameters describing violation of the Equivalence Principle.

    ============

    Unphysical Higgs Bosons and Spontaneous Violation of Lorentz Invariance
    Authors: Noboru Nakanishi
    (Submitted on 20 Apr 2007)

    Abstract: The standard theory of elementary particle physics is modified in such a way that the Higgs boson becomes unphysical and Lorentz invariance is slightly violated at the level of the S-matrix. The basic technique of realizing these properties without violating the unitarity of the physical S-matrix is the use of the complex-ghost quantum field theory.

    Comments:
    8 pages
    Subjects:
    High Energy Physics – Theory (hep-th)
    Cite as:
    arXiv:0704.2645v1 [hep-th]

  45. #45 Torbjörn Larsson, OM
    August 7, 2007

    If science is the observation of nature, then math is the explanation of that observation.

    I see that my point that the math, such as it is, is compliant with physics and thus tested didn’t really penetrate.

    But FWIW, the math of SR and GR is pretty self-contained. AFAIK it is when you wander into the esoteric basis for energy principles (GR) or quantization (QM, GR) that the formalism and results loses its groundings in a comprehensive interpretation.

    Also, since both science and math is descriptive on both data and models (theories), I’m not sure exactly what you mean with an explanation. A ToE would be the ultimate description – is that what you mean?

  46. #46 Steve
    October 2, 2009

    So thats what I have been doing wrong for 20 years, “too many algorithms” damn :)

  47. #47 John Ryskamp
    April 18, 2010

    Wow, you are really out of date. Begin by reading A. Garciadiego, BERTRAND RUSSELL AND THE ORIGINS OF THE SET-THEORETIC ‘PARADOXES.’ Then, assuming you have a brain in your silly head, you will be prepared to understand Einstein’s “natural” coincidence–in his formulation of the relativity of simultaneity–as an example of “practical geometry,” which was his term for constructivism.

    You simply don’t know what the hell is going on.

    SSRN-Paradox, Natural Mathematics, Relativity and Twentieth …by J Ryskamp
    Apr 18, 2006 … SSRN-Paradox, Natural Mathematics, Relativity and Twentieth-Century … Ryskamp, John Henry, Paradox, Natural Mathematics, Relativity and …
    ssrn.com/abstract=897085