If you make two or more throws, the probability is cumulative, so for two throws the probability of not getting a six is (5/6)*(5/6), or 25/36, or 0.69444... (etc.). Lower, but still significant.

So clearly, over a sufficiently large number of throws, the probability of not getting a six will get very small, though never hit zero. Still, the probability for each single throw is still 5/6. It's confusing, and counterintuitive, but though our everyday experience suggests a six will come up eventually, it may not. Or at least it may take a damn long time.

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List of possible explanations. One: I'm willing it. Inside where nothing shows, I am the essence of a man spinning double-headed coins, and betting against himself in private atonement for an unremembered past. Two: time has stopped dead, and the single experience of one coin being spun once has been repeated ninety-times. On the whole, doubtful. Three: divine intervention. Four: a spectacular vindication of the principle that each individual coin spun individually is as likely to come down heads as tails and therefore should cause no surprise each individual time it does.

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[ 15 May 2003: Message edited by: Sisyphus ]

quote:

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In probability theory, is it possible to calculate a number in which, say, you guaranteed to roll six on a dice?

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I took math in school, a lot of it (hell, I was at U or Waterloo under the mathematics department) but probability was never something I actually took officially. So it's all a grey area for me (not that algebra and calculus comes easy, but I've had formal training and the concepts come easier).

The reason I bring up probability theory is that I was talking to my friend about this Scientific American article. We both read it but I didn't think much of it at the time. However, he said, and I quote, "I read this article and it almost made me believe in God". Now, I think I read more on quantum mechanics than he does, and I've read a lot of whacked out things being theorized, so maybe I'm just used to screwy quantum mechanic claims and they no longer faze me as much (don't get me wrong, I don't claim to understand what I read but if I can't look at a cat and I can say with certainty that the cat is neither dead or alive and yet, if I look at the cat…)

In particular, I'll quote from the start of the article at length:

quote:

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Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on.
The idea of such an alter ego seems strange and implausible, but it looks as if we will just have to live with it, because it is supported by astronomical observations. The simplest and most popular cosmological model today predicts that you have a twin in a galaxy about 10 to the 1028 meters from here. This distance is so large that it is beyond astronomical, but that does not make your doppelgänger any less real. The estimate is derived from elementary probability and does not even assume speculative modern physics, merely that space is infinite (or at least sufficiently large) in size and almost uniformly filled with matter, as observations indicate. In infinite space, even the most unlikely events must take place somewhere. There are infinitely many other inhabited planets, including not just one but infinitely many that have people with the same appearance, name and memories as you, who play out every possible permutation of your life choices.

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The author argues that I have numerous doppelgangers in this universe, with certainty, and one of these doppelgangers actually posts to Free Dominion and thinks all you babblers have a mental defect. And he bases this not on, as he says, the whacky physics but on simple probability.

My friend couldn't accept this. He said that these multiple universes with multiple me's is so screwy that you might as well say, "I believe in a God". That got me wondering and that got us arguing. Now, granted, I'm a factory worker, he designs rivers for a living (yes, you can design rivers) and neither one of us has had a paper published in Scientific American. We are questioning a guy that thinks about this as his job…

But now that my friend brought it up, I'm questioning it, too. What brings up my probability question is that you can't for certainty whether something happens. Even if p=0.999999, it's still not guaranteed even if it's highly likely. The author later uses probability in the number of protons in existence to further back his points and sorta argues along the lines of a million monkeys writing for a million years writes a Shakespearian play. Not only do they write Shakespeare, but they improve on Shakespeare.

But in trying to wrap our heads around this proof based on simple probability, we were playing darts and I had what might be a eureka moment (for me). I can throw darts, and my friend can throw them as well. There is a certain amount probability about us hitting anywhere on the board. But I'm wondering if the multiple, Free Dominion posting, me isn't looking at existence as analogous to saying that it's random where I hit the dart board on a throw, and each throw represents the different me. But if I'm a good dart thrower (and, I admit, I'm okay), it's no longer as random. I can usually cluster my throws around the bull's eye, so the Free Dominion poster me, as represented by the double twenty, never comes into existence.

And, as I'm rambling, I wondering if that's true. It's one thing to think of things as a roll of the dice, as probability, but there is a certain amount of determinism in the way the world (physics on the macro level) works. So, I guess, I'm suspicious of the claim about the multiple me's in this universe. Just because it's possible, and there is enough matter, and the distances are large enough, doesn't mean the multiple me's really exist.

Does that make any sense?

I tried to argue that the nutcase things physicists predicted 70 years ago are slowly being proved true in relation to quantum mechanics. Apparently, as a model, it's very accurate.

But, still… do these interpretations cross a line? Is the Scientific American article sound? Will, in fifty years, the multiple me sya that all this is self evident just as time, distance and mass distort based on it's velocity?

[edited: I think my friend is invoking Occam's Razor, it's just that we have yet to find the simpler explanation of the universe]

[ 15 May 2003: Message edited by: clockwork ]

I don't know as much as I should about probability theory, so I'll just in passing point out that part of the fuzziness about it is that grasping the precise distinction between "per event" and "overall" probabilities can be a challenge at times.

As to the Scientific American example and quantum mechanics, I know they say anyone who understands QM doesn't, but it is true that as with anything, one gets used to the bizarrity of something with repeated exposure, and so wacky ideas in QM aren't really a problem for me - such as the many-worlds interpretation or the more familar Copenhagen interpretation. It isn't that strange to suggest that the quantum state of anything you don't witness is indeterminate until you witness it and collapse the state. It's just that macroscopically, the different virtual states are impossible to differentiate from each other so just because you collapse a state one way and then another way doesn't mean there's a perceptible difference in what you see. However, there is always the finite but very low probability that the virtual state you collapse into a real state will be some totally whacked-out oddball variant that differs from a lot of other peoples' observations of the same object.

I think I'm digressing, but I don't see it as all that strange that in some other universe there is a me who is an arts major, or a me who is some mad scientist world-dictator type, as that satisfies the multiverse interpretation.

But in the same universe? Now there's a whole new ballpark to play in.

Now the idea that there is a me, in this universe that happens to be, say, straight instead of gay, or a physics major instead of a chemistry major, or hell, a right-wing neo-conservative instead of a left-wing populist stretches into the definite "bizarro world" area.

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Another possibility is that space is infinite but matter is confined to a finite region around us--the historically popular "island universe" model. In a variant on this model, matter thins out on large scales in a fractal pattern. In both cases, almost all universes in the Level I multiverse would be empty and dead.

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I know a guy who's just nuts about fractals. Everything was bloody related to fractals to him. I eventually had to tell him to shut the fuck up about the fractals because it was annoying me.

But even so, he was probably onto something there.

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Is there a copy of you reading this article? A person who is not you but who lives on a planet called Earth, with misty mountains, fertile fields and sprawling cities, in a solar system with eight other planets? The life of this person has been identical to yours in every respect. But perhaps he or she now decides to put down this article without finishing it, while you read on.

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(to the tune of "Makin' Whoopie")

Another world
In which you're not
Contains someone
Whose name you've got
And who's that person?
It only worsens
By readin' Kripke!

(I know it isn't quite the same problem as the one you've defined, clockwork, but it sort of fit. )

[ 16 May 2003: Message edited by: Michelle ]

"In infinite space, even the most unlikely events must take place somewhere."

There are infinities and infinites.

Suppose we put each recognizable event into one-to-one correspondence with the natural numbers, N (i.e "count" them). N is infinite, so we won't run out of numbers. Coin tosses, for example can be counted this way. Problem comes if we decide that "events" are not always discernable as discrete units -hence the use of continuous distributions to represent "event probablilities, e.g Bell (Normal Curve). Between each natural number we have an infinity of real numbers, and what's worse between any two real numbers, we have another infinity of real numbers...

Thus, even if we had a completely random real number generator, generating real numbers at any rate for an infinite amount of tome, there is no reason to expect that any number would ever be generated twice.

Any description of the inflationary universe that I've encountered, describes space as being "created" at the edge of the expanding universe-the idead of curved sapcetime helps me visualize this.

Point is, the Universe is probably not infinite, and even if it were, there is no reason to expect doppelgangers to occupy it ( ultimately, this is also true even if the set of all events is "countable").

What this means is :

just cause I've got all the time and space in the world, doesn't automatically mean everything is possible, let alone probable.

I'm not even going to touch the issue of how "different" or "similar" to a person a "double" has to be in order to be considered a "double" rather than just "someone else".

Edited to add: If you'd've put a smiley after your post, ArtJ, I would have responded "Not bloody likely."

[ 16 May 2003: Message edited by: Sisyphus ]

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As a factory worker that who's expertise involves making plastic bags, I'm hesitant to raise my hand and ask a question. Max Tegmark's article, "Parallel Universes" (May 2003) lead me to a rather stark conclusion. Although he wasn't talking about consciousness and free thought, I have to ask: if there was another clockwork that put down the Scientific American article, and yours truly that continued reading, and given that these two clockworks were completely identical in every possible way up until that point, does this mean Mr. Tegmark is saying every action I do is completely, and utterly, random?

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I actually got a response from an editor:

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Many thanks for your note. The article did not discuss the conditions under which you or your alter egos might decide either to read or to stop reading. If this decision is the result of a quantum event -- for instance, a particle decay in one of your neutrons -- then it is indeed random. If it is the result of a very slight difference in the initial conditions of the universe, it is not truly random, although it certainly looks that way to you.

I should point out that the multiverse scenario is not unique in this regard. Standard quantum mechanics postulates that random events occur, and chaos theory talks about pseudorandom events. What the multiverse scenario does is to *interpret* this randomness or pseudorandomness in terms of a collection of other universes.

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I'm also a bit bemused too. Another thing chaos theory talks about is sensitive dependence to initial conditions. So if the universe was chaotic, slight variations at the beginning would result in a lot more than me reading or putting down the article (unless my decision to read the article is an event that makes the beginning of each universe diverging… in which I might gain an even bigger sense of my own importance).