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Saturday, April 12, 2008

The Brian Wilson Paradox

"Happy times together we've been spending
I wish that every kiss was never-ending
Wouldn't it be nice?"

My daughter Emma, upon hearing those lines, asked, "But Dad, if every kiss was never-ending, wouldn't that mean there could only be one kiss?"

"Hey, that's right," I responded.

To which my son Eamon replied, "No, there'd be zero kisses."

"Huh?"

"Well, he'd never finish a kiss. And what's more, he'd never even really get any fraction of the way into a kiss."

(His point here being, by the way, different than the Zeno paradox -- he wasn't saying you could never cover any finite time of kissing, but that no finite amount is ever more than 0% of an infinite kiss. Similar problem: Throwing a dart at the real number line from 0 to 1, what is the probability you'll hit 2/3? Answer: 0!)

Discussing this with Wabulon, he noted that there are (theoretical) super-Turing machines that can do x amount of processing in time t, then x more in time t/2, then x more in t/4, and so on, thus completing and infinite amount of time.

"Good point," I said, "but given that Brian Wilson couldn't even get out of bed for around 20 years, I don't think he is an instantiation of one of those machines.

But, thinking it over a bit more, we figured out a way that Wilson could make his kiss never-ending for the rest of us, while it would end for him.

What did we come up with?

28 comments:

  1. Kiss while falling into a black hole.

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  2. You cover your lips with cyanide (to which you've built up immunity) and then kiss him forever.

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  3. BTW I'm not sure I would let Wabulon discuss long kisses with young children.

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  4. Shonk wins the prize again!

    I liked the idea that what Wilson really wanted was to impose the image of him kissing X forever on the rest of us.

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  5. Bob, you have a good point. Now, he was discussing long kisses with an adult, but I'm not even sure that's a good idea.

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  6. Are you serious about the black hole? If so please elaborate.

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  7. P.S. I assume Shonk is thinking that Brian Wilson experiences a finite kiss, but that we never actually see it end because we see him and his lover getting slower and slower as they fall deeper into the black hole.

    But I think we would see them get turned into (reddish?) spaghetti before they crossed the event horizon.

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  8. Hey, we didn't say there were no practical problems with the idea. We're doing high theory here, Bob. Think LSE and Cambridge in the 30s!

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  9. Anonymous12:59 AM

    Discussing this with Wabulon, he noted that there are (theoretical) super-Turing machines that can do x amount of processing in time t, then x more in time t/2, then x more in t/4, and so on, thus completing and infinite amount of time.

    This is a misuse of the words "there are". It's a bit like saying "there are (theoretical) demons and angels" simply because they are conceivable ... except that some notions of demons and angels are at least theoretically realizable in this physical universe, whereas such "super-turing machines" aren't. It's not even clear that ordinary quantum computers are physically realizable, and they have an infinitesimal fraction of the computational power of these supposed super-turing machines.

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  10. Are you going for most nit-picky blog comment of 2008? These things exist in theory, only. That's what theoretical meant! These theories have been written up. That means "there are" them theories!

    Try the opposite: There aren't theoretical super-Turing machines. Obviously false.

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  11. Anonymous1:09 AM

    Shonk wins the prize again!

    I can understand why you would give a prize to someone who has just enough surface knowledge about a subject to accept common mythologies about it.

    http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/fall_in.html


    Won't it take forever for you to fall in? Won't it take forever for the black hole to even form?


    Not in any useful sense. The time I experience before I hit the event horizon, and even until I hit the singularity-- the "proper time" calculated by using Schwarzschild's metric on my worldline-- is finite.

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  12. Oh, yeah, and a Turing machine itself is only a theoretical concept that can''t be implemented in the real world -- remember that infinitely long tape?!

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  13. Anonymous1:10 AM

    Are you going for "too stupid to comprehend what I wrote"? Apparently so.

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  14. Anonymous1:14 AM

    Oh, yeah, and a Turing machine itself is only a theoretical concept that can''t be implemented in the real world -- remember that infinitely long tape?!

    Which makes my point, moron. You apparently don't even understand what "in theory" means; it does not simply mean that someone wrote a theory about something, it applies to a realization.

    Oh well, you're just another ignorant but arrogant net philosopher who has no grasp of how little you know. Not really worth my time ... ta ta.

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  15. Anonymous1:17 AM

    There aren't theoretical super-Turing machines. Obviously false.

    No, you moronic git, it is not obviously false. That there are all sorts of mathematical models does not mean "there are" the things modeled.

    Ok, now I'm really out of here.

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  16. No, anusymous, I got it -- they don't exist in the real world. Uh, yeah, that's why I wrote "theoretical."

    And since you've decided to come here and call people stupid and shallow, may I point out that Shonk, Bob, Wabulon and I all KNEW that Brian Wilson falling into the black hole would not take forever! That was stated quite explicitly. What we were all talking about, which someone was too stupid to figure out, was that FOR AN OBSERVER Wilson would seem to take forever falling in.

    As it it says ON THE VERY SITE you just pointed me too:
    "So if you, watching from a safe distance, attempt to witness my fall into the hole, you'll see me fall more and more slowly as the light delay increases. You'll never see me actually get to the event horizon."

    Doh!

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  17. "Ok, now I'm really out of here."

    Oh, please come back, please! Your sparkling wit, your charming Brit manners, and your wonderfully incisive commentary positively made this blog for the five minutes you were around!

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  18. Bob, by the way, the site our guest of last night cited claims you can get past the event horizon alive if the hole is large enough:
    "So for black holes larger than about 1000 solar masses I could probably fall in alive, and for still larger ones I might not even notice the tidal forces until I'm through the horizon and doomed."

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  19. Gene,

    Oh, we were talking about black holes larger than 1000 solar masses? Why didn't you say so, you bloody fool?

    (OK I don't know how to sound British. I didn't even realize your tormentor was British till you said so.)

    All joking aside, that really surprises me. I had always assumed something strong enough to hold in light would rip you apart, but in retrospect the tidal forces are due to the accelerational gradient, not the acceleration itself. Hmm, I must ponder.

    Finally, in theory does there exist a more annoying comment poster?

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  20. "Finally, in theory does there exist a more annoying comment poster?"

    Yes.

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  21. You know, this guy followed me across two blogs and several comment threads insulting me. I later found him first calling me "an arrogant twit" on a thread at Unqualified Offerings about 1/2 hour before he got here.

    Brit: It's the "ta-ta," "twi," and so forth that leads me to make that guess.

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  22. Brian N.8:07 AM

    If'n I remember my Copleston right (I have the damn book right here) then Zeno's paradoxes were primarily meant as refutations of Pythagoreans' conception of reality. He didn't actually agree with the argument.

    Though there is that famous story about the philosopher who wanted to prove to Diogenes that motion was impossible.

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  23. Gene, apropos the "infinitely long tape"--it isn't. It's just that you are allowed to paste an additional space onto either end of the tape if otherwise you'd run off the end. Perfectly doable.

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  24. Oops -- good thing anonymous had bid us "ta-ta" before you posted that!

    I know I've seen the tape described as infinite, but of course you are right -- the writer must have confused "unbounded" with "infinite."

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