Good Math, Bad Math

I managed to trash yet another laptop – the city commute through the subways seems to be pretty hard on computers! – so while I’m sitting and slowly restoring my backups, I was looking through the folder where I keep links to crankpots that I’d like to mock someday. I noticed one that I found quite a long time ago – and to my surprise, I realized that I never wrote about it! And given that I’ve been mocking relativity-haters lately, it’s particularly appropriate to cover it now.

The site is called “The Nasty Little Truth About Spacetime Physics”. It takes quite a different approach to criticizing relativity. As we’ve seen in past posts, most anti-relativity rants dislike relativity because it implies that there is no fixed reference frame – that there’s no such thing as an absolute velocity, no distinguished point at the unmoving center of the universe. That’s not this guys tack; no, he’s much smarter than that. His argument is that if you accept the idea of spacetime as defined by relativity, that
it logically implies that motion is impossible – and since we can clearly move, than means
that relativity is wrong!

Some of the most famous physicists in the world are not telling the truth about one of the most taken for granted concepts in scientific history. They are not telling us how they can come up with their fanciful time travel theories (wormholes, advanced and retarded waves traveling in spacetime, etc…) using a model of the universe that precludes the possibility of motion. Nothing can move in spacetime or in a time dimension-axis by definition. This is because motion in time is self-referential. It is for this reason that Sir Karl Popper compared Einstein’s spacetime to Parmenide’s unchanging block universe[*], in which nothing ever happens.

Before I continue, less I be immediately branded as an anti-relativity crank, let me make it perfectly clear that I agree with the mathematical and predictive correctness of both the Special and the General Theory of Relativity.

Now that is some primo crackpottery! You’ve got to love it when the crackpot starts off his argument by both denying that he’s a crackpot, and refuting his own argument!


After that, he goes into a long rant in which he insults every physicist or mathematician who’s ever said anything nice about relativity. As a computer scientist who (like many CS people) is deeply fascinated by Gödel, I’ve got to quote his attack on Gödel:

Kurt Gödel (how did I forget him?) is one of the gods of the voodoo science pantheon. Gödel is
probably one of the most often quoted inconsequential mathematicians of the world. He is known
for his incompleteness theorem, the most obfuscated, non-scientific, chicken feather voodoo
nonsense ever penned by a member of the human species. In 1949, Gödel announced that
Einstein’s General Theory of Relativity allows time travel to the past via “closed time-like
curves.” The only thing Gödel proved, in my opinion, was the incompleteness of his frontal
lobe.

That’s pretty typical of his mode of attack: it’s all personal insults about how stupid and obnoxious all of these people are, without ever being able to address anything that any of them said.

But on to his main point. Why does relativity imply that motion is impossible?

Well, you see, relativity says that time is a dimension. And that means that,
by definition, you can’t move. How does that work? Well, let’s look at his explanation.

Why is motion in spacetime impossible? It has to do with the definitions of space and time and the equation of velocity v = dx/dt. What the equation is saying is that, if an object moves over any distance x, there is an elapsed time t. Since time is defined in physics as a parameter for denoting change (evolution), the equation for velocity along the time axis must be given as v = dt/dt which is self-referential. The self-reference comes from having to divide dt by itself. dt/dt always equals 1 because the units cancel out. This is of course meaningless as far as velocity is concerned.

To emphasize, it is logically impossible for the t coordinate of an object to change because such a change is self-referential. Et voilà! It is that simple. No time travel, no motion in spacetime, no spacetime and no time dimension. They are all abstract mathematical constructs without any counterpart in nature.

So, if you define a “velocity” of motion in the time dimension as distance in the time dimension per distance in the time dimension, then you’ve got something self-referential, which doesn’t make any sense. Since you can’t have a meaningless measure of “velocity” in the time dimension using motion/time, that means that motion in the time dimension is impossible. And if motion in time is impossible, then since motion in space is defined by “distance traversed in space per unit time”, that means that you can’t move in space, either.

This is, of course, rubbish.

First – let me refresh your memory about what a dimension is. The easiest (although not
necessarily completely accurate) definition of a dimension is an independent direction. So,
for example, if you take a plane, and you put two points on it, you can draw a line between
them, which describes the distance between the two points. With one line which you use for
measurement, that’s all you can do – just distance between them. You’ve only got one dimension
that you can use for measurement. If you have a third point, and it’s not on the same line as
the other two points, then you can’t really describe its position relative to the two points:
you can move back and forth along your line, but you’ll never reach the third point: it’s not
on the line. To get to the third point, you need something else: you need to be able to move
in another direction. So you add a perpendicular line – now you’ve got two
dimensions, and you can describe the position of the third point, in two steps: “You
move left three steps, and north two”. You can’t describe the position of all three relative to one another without invoking two different directions, where moving in one of them – say north/south – doesn’t change your position in the other – east/west. You can add a third dimension: add another point, not on the same plane as the first three. Now to be able to describe its position, you’ll need to use east/west, north/south, and up/down.

When we say time is a dimension, that’s roughly what we mean. It’s another direction, or axis of change, which is completely independent of the other directions that we call space. When we define a velocity as Δx/Δt, what we really mean is that every time we move “Δt” units in time, we move Δx units in space.

Think of simple line drawn on graph paper: y=3x+2. Can we ask how fast y changes relative to x? According to the argument of our crackpot, the answer is no. Because how can we define motion in x? The line is already drawn on the page. x doesn’t move. Any motion in x must be defined in one of three ways. It could be motion in x relative to something outside of the system that we’re measuring, but that doesn’t make sense: we’re talking about measurement inside the system – we can’t define that in terms of something that has nothing to do with the system we’re looking at. We could define motion in x in terms of motion in y – but since motion in y is defined in terms of motion in x, that’s circular – and that’s clearly no good. And finally, we could define motion in x in terms of motion in x. But that’s circular. So you can’t look at the rate of change along that line, because “change” is meaningless on the line – any definition of it is nonsensical.

That’s exactly the game that he’s playing. What he’s really doing is invoking a sort of meta-time, and then saying that it’s really the same thing as the time dimension. So to move along the time dimension, you need to move through meta-time; and since he defines meta-time as being the same thing as time, that means that motion through time makes no sense.

Now you can start to see why it is that I quoted his critique of Gödel. He’s created a self-reference loop – exactly the kind of thing that Gödel studied. But his self-reference loop isn’t nearly as interesting as the ones that Gödel studied. It’s more along the lines of Russell’s paradox: an artifact of a poorly designed model. He’s building his argument on unstated axioms which aren’t valid – and as a result, he’s able to create non-sensical statements derived from them.

You can’t introduce “meta-time” into a discussion of relativity, without somehow defining what meta-time is. You most certainly can’t require the existence of this meta-time thing, and then implicitly assert that it’s the same thing as (non-meta) time. Since that’s what he did, his whole argument collapses, and reveals itself as a giant heap of foolish nonsense.

For all the scorn that he heaps on every major 20th century physicist or mathematician that he can think of, he’s the one who’s actually the idiot: he can’t understand the simple concept of “dimension”.

Comments

  1. #1 Eamon Knight
    January 17, 2008

    Louis Savain? He’s hit t.o a couple times in the past few years. See Google Groups for the fun ;-).

  2. #2 Charles
    January 17, 2008

    He also must have failed calculus. From a strictly symbolic point of view, he’s declaring that relativity say that your time coordinate is constant, but has nonzero derivative. The other part of the bad logic is more pressing, but can’t sell him short when he fails to understand both dimension and derivatives.

  3. #3 Sharkey
    January 17, 2008

    Ah, Louis Savain, thought so. I’ve seen him show up on Slashdot to trash Erlang, of all things. Says the world is trapped in “the curse of the algorithm”, and attempting to solve all our computer security woes _by removing functions_. Erlang apparently is the worst offender, attempting to be parallel and stable, but without cool drag-and-drop design tools.

    You’ve just seen the tip of the iceberg, my friend.

  4. #4 SO1OS
    January 17, 2008

    First off, this dude is just one of a great number of angry pseudo-intellectuals to cry “conspiracy” as soon as they confront something they don’t understand. I get the impression this guy might have a repressed inner child trying to get out.

    Anyway, there is a real contention in the philosophy of science whether Einstein’s invocation of the ‘time’ axis in spacetime has any deep ontological implications about the meta-time this guy is trying to describe. I recommend Palle Yourgrau’s “Godel Meets Einstein” for a thoroughgoing treatment on this esoteric subject.

  5. #5 Davis
    January 17, 2008

    Gödel is probably one of the most often quoted inconsequential mathematicians of the world.

    I would have stopped reading there. Your intestinal fortitude impresses me, Mark.

    Since time is defined in physics as a parameter for denoting change (evolution), the equation for velocity along the time axis must be given as v = dt/dt which is self-referential.

    This reminds me of a fallacious argument we read in a philosophy paper, back in my undergrad Metaphysics class (I’ll have to dig up the reference). The author’s basic argument was that things never change because, if we lay out events on a timeline, the location of the events and states on that timeline never changes. His fallacy lies in equivocation: when viewed this way, “change” simply means the state at time A differs from the state at time B. He is redefining “change” to mean something different (a “change in a change”, using the standard definition of ‘change’).

    At a cursory glance, it looks as though this crank is making the same mistake. He’s equivocating in his use of the word “change” (which is where “meta-time” comes in — meta-time appears to be a repackaging of the “change in a change” problem).

  6. #6 Pierre
    January 17, 2008

    Louis Savain was mentioned on PZ’s blog too, just three days ago in fact. If you think his ramblings on relativity are bad, read what it says there about his idea of using the bible to build an Christian Artificial Intelligence!

  7. #7 Randy
    January 17, 2008

    OMG!!!11111. Zeno proved that motion was impossible over 2 thousand years ago. I’d type a link to show you but I’d first have to type half of it….

  8. #8 Tyler DiPietro
    January 17, 2008

    “It has to do with the definitions of space and time and the equation of velocity v = dx/dt. What the equation is saying is that, if an object moves over any distance x, there is an elapsed time t. Since time is defined in physics as a parameter for denoting change (evolution), the equation for velocity along the time axis must be given as v = dt/dt which is self-referential.”

    I’m pretty sure time-derivatives describe a change in motion of f(x) with respect to t. It would seem that he didn’t even get the first part right.

  9. #9 gg
    January 17, 2008

    Ah, another crackpot who uses semantics to dismiss an experimentally verified theory, without any real attempt to address the mathematical structure of said theory.

    If he had any idea of what he was talking about, he would understand that the ‘time derivative of time’ in relativity theory, in the four-vector of velocity, does not equal 1, as he states. But that would require him to understand the concept of ‘proper time’, and he’d actually have to understand the theory and not just copy symbols from a book. Crazy Louis even notices that his ‘time’ component of the four-vector is dimensionless, but considers this a flaw in the theory of relativity, instead of a mistake in his own (crap) calculations! Sad.

  10. #10 Thomas
    January 18, 2008

    Mark, you haven’t seen anything yet. May I recommend Savain’s article titled “The Seven Deadly Sins of Erlang” – the crowning achievement of stupidity.

    Get it from http://rebelscience.blogspot.com/2007/08/seven-deadly-sins-of-erlang.html. Enjoy.

    A quote to whet your appetite:
    “It is a computer language (based on English). Why English? Why not Mandarin, Swahili, Romansh or Latin for that matter? Programming a computer should have absolutely nothing to do with one’s mother tongue. Written code is notoriously hard to understand, even when it is your own code. Only programming nerds are enamored with cryptic code. It’s a badge of honor to them. Truth is, the very fact that programming has to rely on a specific natural language is a sure sign that something is wrong with the linguistic approach. Not to mention the nasty little fact that languages are inherently sequential, which makes them ill-suited to parallel programming.”

  11. #11 Frank Q
    January 18, 2008

    Woa!
    Are you sure that this Savain guy is not simply a troll who likes to get your blood pressure up? I mean, there is no way he is actually serious about what he says…

  12. #12 Tyler DiPietro
    January 18, 2008

    In light of the dreck the Thomas linked to above, I have offered a friendly letter to Louis Savian at my blog.

  13. #13 Donalbain
    January 18, 2008

    Errr.. if dt/dt=1, then doesnt that just show that we travel through time at a speed of exactly 1s per s? Which matches exactly what we record? Yay! Relativity is saved!

  14. #14 Stephen Wells
    January 18, 2008

    More specifically, your proper 4-velocity is your worldline differentiated wrt your proper time tau. In your own rest frame, t = tau, your own clock runs with dt/d(tau) = d(tau)/d(tau) = 1 second per second, as you note, and all is well. An observer in another frame will see your clock running slower, as in that frame t isn’t the same as tau.

  15. #15 Ambitwistor
    January 18, 2008

    Ah, Louis Savain. Mark, the same error that you pointed out today, people have been pointing out to him FOR OVER 10 YEARS on Usenet.

    See here for the historical genesis of “Nothing Moves in Spacetime” — in 1996! He’s truly ineducable.

    It’s amazing how he still confuses semantics with physics, and how abusive he is. (His mantra is “chickenshit voodoo physics”.)

  16. #16 KeithB
    January 18, 2008

    Is it the hard disk that is failing?

    If you are putting the computer on the floor it may be getting erased by the magnetic field from the electric motor.

  17. #17 SteveM
    January 18, 2008

    KeithB @ 16:

    non sequiter much?

  18. #18 Torbjörn Larsson, OM
    January 18, 2008

    1 second per second, as you note, and all is well.

    Besides the nuttery there is a point in the observation that it can sloppily be interpreted as self-reference though. We don’t really know what makes time tick, we have to settle with making clocks tick-tock. :-P

  19. #19 SteveM
    January 18, 2008

    “Time is nature’s way of keeping everything from happening all at once.”

    while glib, it seems to really be all that physics can really say about time. More recently in an article about NIST and their reference clocks, it was said that all we can really say about time is that “time is what clocks measure”, nothing more, nothing less.

  20. #20 SteveM
    January 18, 2008

    KeithB, sorry, please excuse me for taking so long to figure out that you were referring to Mark’s dead laptop. I work in disk drive industry and I doubt that the stray fields from the traction motors is enough to wipe a hard drive. Most likely it is the mechanical vibrations causing a head crash. Although, if is powered down the heads should be “parked”, i.e. physically lifted off the disk and mechanically locked in place.

  21. #21 Mark C. Chu-Carroll
    January 18, 2008

    KeithB:

    I don’t put my computer on the floor in the subway. This is NYC – you hold on to things if you want to keep them. :-)

    I think it’s much more to do with the constant jolting and banging about. I don’t actually know if it’s the disk or something else – all I get to see is a frustrating intermittent lockup.

    Given that I’ve been able to backup all of my data without seeing any disk problems, I doubt it’s the disk. I suspect it’s more likely something like a hairline fracture of a circuitboard. Riding the subway during the rush-hour often makes me feel like a ball in a pinball machine; I’ve often wound up a bit bruised as a result of people bumping into me when the subway brakes unexpectedly – if it’s enough of a jolt to bruise me, I think it’s enough to hurt the poor computer. I’ve gotten a better shielding bag for it, but still, the poor thing is getting banged around an awful lot.

  22. #22 Cyan
    January 18, 2008

    I hereby adopt this fine fellow’s philosophy, and deduce the following syllogism:

    “I agree with the mathematical and predictive correctness of both the Special and the General Theory of Relativity.”

    “…no motion in spacetime…”

    Therefore, you can’t blame me for not getting out of bed this morning.

  23. #23 Davis
    January 18, 2008

    “”Time is nature’s way of keeping everything from happening all at once.”

    I can’t resist adding “Space is nature’s way of keeping everything from happening to me.”

  24. #24 nik
    January 18, 2008

    I must say that I take issue with comparing some quacks rubbish to Russell’s paradox. Russell’s paradox was important because many people did not realize the possible limitations of a naive set theory and, importantly, it was relatively simple to explain and understand. This is important for any sort “paradox” or proof by contradiction, because any kind of convoluted mess may seem to lead to a paradox if it is confusing enough. Anachronistically, one might term “Russell’s paradox” as “Russell’s proof of the non-existence of certain sets.” Of course, the latter is probably too much a mouthful.

  25. #25 hexatron
    January 19, 2008

    A day late and a dollar short:

    I (and a co-worker) once spent a few hours vainly trying to convince an artist we worked with that “3-dimensional” did not mean “has another side”.

    His peculiar definition worked for him (if something is 3-dimensional, it has a backside. Otherwise, you can only see it from the front.)

    He was a quite excellent artist. Flexible too–he adapted easily to painting on a computer in the 1970s (when all this occured). But he denied that “3-dimensional” computer graphics was actually 3-dimensional, because it was still flat art on a monitor (it had no “other side”).

  26. #26 Jonathan Vos Post
    January 20, 2008

    Re: #25: “‘3-dimensional’ did not mean ‘has another side’.”

    How many dimensions does a rainbow have?

    By the way, Isaac Newton did write about there being two different measures of time, a global T and a local t, noted that Dt/dT = 1, said there was something here worth getting back to, but never got back to it.

    Sorry I can’t give you a citation. I’m spoken with top Newton Hisorians, and top Physicists about Newton, but don’t claim such expertise myself.

    On a personal note, prefer not to go into details:

    I’ve just returned from 9 days in hospital for emergency major surgery and complication thereafter. 4 inches of small intestine with necrosis had to be removed in surgery, and the shortened healthy
    intestine stitched back together — BOWL RESECTION — two incisions, now closed with 40 staples.

    The pain level was far, far higher than my previous experience (motorcycle accident with two fractured wrists). Takes a professional torturer to go higher, as this is the threshold of pain-induced loss of consciousness.

    Then came the postsurgical complications.

    I was on Dilaudid, a narcotic, for the extreme pain. Problem is, narcotics and surgical handling both push the intestine into a condition called “ileus” — paralysis of the bowel.

    One’s perception of time is altered by unbearable agony, and the immanent possibility of death. I could have started to slide to death immediately had gangrenous tissue not been timely removed; I could also have begun a gradual descent into being too weak, through non-nutrition, to risk follow-up surgery.

    The literature on ileus (now that I’m home, after 9 days without internet, the longest gap by far in 15 years) I’ve been reading PDFs like crazy found by GoogleScholar, is that there is no true consensus on causes diagnosis nor treatment of ileus. I am a scientist. I publish Mathematical Biology and Complex Systems theory. So, officially, I am now coauthoring a peper with the surgeon who saved my life. I prefer not to go into detail on that either, in this venue.

    Bottom line:
    (1) psychology of perception and state of consciousness strongly linked to psychology of time.
    (2) The unexamined life is not worth living; which, to a Mathematician, Physicist, or Biologist, means applying everything you have including science to one’s own circumstances.

    Thank you for allowing me this personal intrusion. Please understand if I am limited in reply, as there is a lot to catch up on after such an interruption to an already-overloaded schedule. Had to un-register for a graduate school quarter (my night classes towards full-time public school teaching credentials). Literally lost my job over this emergency : I was almost done with my first full day on a full-time High school teaching gig when I had to have another teacher cover the last 2 of 8 classes, rush to school nurse (though was appendicitis), the primary care physician (same mis-diagnosis, then hideously wrong treatment), then emergency room. Next day, I was replaced. Financial emergency now ensues, before the bill arrives for 10% co-pay on Blue Cross for 9 days at major hospital with surgical team and all. No assets to tap. No seconday supplemental insurance (i.e. AFLAC). Oh, wait a minute, the insurance crisis was another thread.

    Great to be back! * returns to lurking *

  27. #27 Louis Savain
    January 21, 2008

    ahahaha… Yo, Mark. Someone just told me that you were having a party at my expense. Nice party. Look, man. All I’m saying is that nothing can move in spacetime. Let’s be clear on this. Are you saying for the record that it’s not true, and that things can indeed move in spacetime? Are you also calling Karl Popper a crackpot for saying (like me) that nothing can move in spacetime which he compares to a block universe? Or do you just like it when all the usual suspects jump out of the woodwork to kiss your ass? ahahaha… AHAHAHA… ahahaha…

  28. #28 SO1OS
    January 21, 2008

    @Louis,

    Are you implying that Einstein’s conception of time, as in a block universe, was so obtuse as to overlook simple motion? If so, you’re wildly offbase.

    If anything, the block universe would re-enforce a Kantian rubric that time we humans experience with certain properties such as an indeterminate future, unchangeable past and a single present are a matter of perspectival fiction. In a block universe, it’s all the same time. It is very much as if we are watching a movie; the reel is set but we are left to only guess what happens next, as in predicting the next plot twist.

    So, rather than assuming Popper was dogmatically saying something perverse like, “spacetime doesn’t describe time/change/Heraclitean flux/whatever” … no, what he was saying is that the block universe doesn’t describe time as we humans experience it. Which, in the grand scheme of things, is entirely acceptable, as Einstein was not putting forth anyting remotely resembling a theory of mind.

  29. #29 Mark C. Chu-Carroll
    January 21, 2008

    Louis:

    Yes, I am saying that things can move in spacetime. And further, I’m saying that your argument about why things can’t is a pathetic construction of ignorance and stupidity.

  30. #30 Jonathan Vos Post
    January 21, 2008

    I guess my #26 was too off-topic, and interrupted what Mark correctly calls “a pathetic construction of ignorance and stupidity.”

    I’ve taught the Block Universe theory, the physics and the metaphysics of time, to several hundred adult students in an Elderhostel class (a week of lectures) from the superb book, with so much on science fiction, and such lovely 19th century illustrations available in paperback as:

    Time Travel: A Writer’s Guide to the Real Science of Plausible Time Travel (Science Fiction Writing Series) (Paperback)
    by Paul J. Nahin
    # Paperback: 200 pages
    # Publisher: Writer’s Digest Books (March 1997)
    # Language: English
    # ISBN-10: 0898797489
    # ISBN-13: 978-0898797480
    # Product Dimensions: 8.9 x 5.9 x 0.6 inches
    # Shipping Weight: 10.6 ounces

    I used the hardcover:

    Time Machines: Time Travel In Physics, Metaphysics, And Science Fiction. Second Edition. Paul J. Nahin. AIP Press, Springer-Verlag, 1999.

    It is no punishment to tell readers of this blog to read this book.

    It will also save Mark and myself and other enormous effort in reinventing wheel, with explanations for the ignorant.

  31. #31 Louis Savain
    January 21, 2008

    ahahaha… Yo Mark, thanks for that honest and heartfelt answer. See you around. ahahaha… AHAHAHA… ahahaha…

  32. #32 Thony C.
    January 22, 2008

    ahahaha… AHAHAHA… ahahaha…

    It would appear that Mr Savain fancies himself as the deranged villain in a 1930’s Hollywood B-movie.

  33. #33 Stephen Wells
    January 22, 2008

    I think I can see the aetiology of this little delusion. If you’re working in a Newtonian model you’d often parametrise the trajectory of a particle as three spatial variables (x,y,z) which are all functions of a time (t). In Newtonian models there’s just one universal time variable. Now we move to a 4D spacetime model, where a particle trajectory is in (3+1) dimensions. Louis tries to parametrise all four variables (x,y,z,t) in terms of t, declares that parametrising t in terms of t is wrong (which is true), and decides that all of SR and GR is a massive fraud and conspiracy (which is false).

    Meanwhile, back in the land of the sane, we parametrise a worldline (x,y,z,t) in terms of the proper time tau of the particle along that worldline. So we don’t parametrise t in terms of t anyway.

    Louis will never grasp this- he can’t allow himself to, after decades spent ranting on the subject. Sad, really.

  34. #34 Louis Savain
    February 4, 2008

    ahahaha… Yo, Stephen Wells. I just posted a rebuttal to your nonsense above on my blog. Don’t bother responding. I’m really geting tired of you crackpots and ass kissers. What you people need is not smarts but backbones. ahahaha… AHAHAHA… ahahaha…

  35. #35 Stewart
    June 11, 2010

    While roughly on topic, I would appreciate your opinion of Wubbo Ockels talk! http://www.tedxamsterdam.com/2009/video-wubbo-ockels-on-time-and-gravity/

The site is currently under maintenance and will be back shortly. New comments have been disabled during this time, please check back soon.