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02/16/2011 05:56:32 PM · #326 |
Originally posted by DrAchoo:
Oh man JH, I need to turn that into a t-shirt... |
This whole thing made me cry today Achoo. Today I learned you actually are human, and my heart grew three sizes this day. |
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02/16/2011 06:15:10 PM · #327 |
| If Greene is correct about the infinite universe, I wish I could be there to see the sparrow/quarter/meteor thing. That would be sweet... |
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02/16/2011 06:24:33 PM · #328 |
Originally posted by DrAchoo:
If Greene is correct about the infinite universe, I wish I could be there to see the sparrow/quarter/meteor thing. |
Maybe in some other universe he IS correct. ;-) |
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02/16/2011 07:20:32 PM · #329 |
Originally posted by DrAchoo:
Oh man JH, I need to turn that into a t-shirt... |
I think (one of) you could sell quite a few of those ... ;-)
Anyone have some capital these days ...? |
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02/16/2011 07:22:03 PM · #330 |
Originally posted by scalvert:
Originally posted by DrAchoo:
If Greene is correct about the infinite universe, I wish I could be there to see the sparrow/quarter/meteor thing. |
Maybe in some other universe he IS correct. ;-) |
If there exist an infinite number of universes, he must be correct in at least one of them, right? ;-) |
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02/16/2011 08:24:01 PM · #331 |
Originally posted by GeneralE:
If there exist an infinite number of universes, he must be correct in at least one of them, right? ;-) |
Nope, that one's readily falsifiable. There are an infinite number of possible outcomes to the sparrow scenario, so an infinite number of chances doesn't help mathematically. Same goes for the scenario Raish proposed- evolution doesn't yield a finite number of iterations, so you could never guarantee a specific outcome given infinite chances. Such a result isn't just 99.9999[wholebunchofnumbers]% improbable, it's INFINITELY improbable. One might then "logically" conclude that something infinitely improbable can never occur, but this is a form of the Gambler's Fallacy. Even with infinite scenarios, something will happen with every proverbial roll of the dice... and every single result will have been infinitely improbable. Not only are there a number of such infinite variables standing between you and any possibility of a duplicate you on some distant planet, there are also a tremendous number of variables that aren't random. Regardless, we know from astronomical observations that time itself "began" at some finite point, and since time is not infinite this whole exercise in mental futility goes buh-bye anyway. |
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02/16/2011 09:06:34 PM · #332 |
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02/16/2011 09:14:59 PM · #333 |
You should send the physicists an email Shannon. You'll save them a lot of work.
If you still think the swallow/meteor/quarter scenario doesn't have a probability of 1 in an infinite universe, I think you are in a minority now. (As long as you don't assume that your swallow/meteor/quarter scenario isn't impossible due to some logical contradiction). |
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02/16/2011 09:48:01 PM · #334 |
Originally posted by DrAchoo:
You should send the physicists an email Shannon. You'll save them a lot of work.
If you still think the swallow/meteor/quarter scenario doesn't have a probability of 1 in an infinite universe, I think you are in a minority now. (As long as you don't assume that your swallow/meteor/quarter scenario isn't impossible due to some logical contradiction). |
It's not a physics problem, but one of mathematics, probability and practical limitations. The swallow scenario will never happen. Ever. You're still insisting that every possibility is probable given infinite time, but it simply doesn't work that way. That sparrow sequence is one of an INFINITE number of possible scenarios. Plug that into your equation and see what happens:
Imagine you've found a particular snowflake. Given an infinite number of possible snowflake variations and infinite time, would you ever be able to find a match? Nope, the odds would always be one in infinity against it. And yet you've already found that very pattern. How can this be? Because the odds of finding ANY snowflake pattern are 100%, and you happened to find that one.
However, this exercise is useless even with large finite numbers because time cannot be infinite if events converge at the Big Bang, so in reality you can never have infinite opportunities and the odds will never change from one-in-some-incomprehensible-number against you. Outside of reality, you can believe whatever you want... |
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02/16/2011 10:05:51 PM · #335 |
I'm going to do this mainly as an exercise in articulation. I'm trying to present the generic argument in support of the view. Those who agree can just critique the effort.
For every scenario S which has a probability presented as 1:X there exists a real number N where the probability of that scenario occurring equals 90%. For easy examples we can use a probabilty calculator like this one.
EXAMPLE: The probability of rolling a 3 on a 3-sided die is 1:3. Using the calculator we find that there is a 90% chance of rolling at least one 3 in 6 attempts.
For the same scenario S, we can also find a number N' where the probability of that scenario occurring equals 99%.
EXAMPLE: Using the same 3-sided die, we can use the calculator to find a 99% chance of rolling at least one 3 in 12 attempts.
For the same scenario S, we can continue to find a number N'' or N''' where the probability of that scenario occurring is another order of magnitude more likely. 99.9%. 99.99%. 99.999%. (In our 3-sided die example, roughly 18 attempts, 25 attempts, and 30 attempts)
If we allow the experiment to include an infinite number of attempts, we can see that we can always find a real number N to stretch the decimal one place further. This can be repeated infinitely. In other words, the probability can be expressed as 0.99999999....(repeated forever). (Typed now as 0.9999(9)
Mathematical proofs demonstrate that the number 0.9999(9) is the same as 1. Not almost 1. It is 1.
Therefore, any scenario S with a probability expressible as 1:X, when considering an infinite number of attempts, will occur with a frequency of 1. |
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02/16/2011 10:34:14 PM · #336 |
Originally posted by DrAchoo:
any scenario S with a probability expressible as 1:X, when considering an infinite number of attempts, will occur with a frequency of 1. |
The math is fine, it's the model that fails. The sparrow scenario is NOT a probability expressible as 1:X and the limits of spacetime preclude an infinite number of attempts. Further, what natural process is perfectly random— absolutely free of the influence of other particles or energy (including its own)? Introduce the slightest bias to those monkeys and the probability is no longer expressible as 1:X to the precision that model requires. I submit that the model itself is impossible. |
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02/16/2011 11:18:16 PM · #337 |
Originally posted by scalvert:
The sparrow scenario is NOT a probability expressible as 1:X |
It isn't? Didn't you quote: "If you flip a quarter a bunch of times, what is the probability that one of those times a house sparrow will catch it in midair and then get whacked by a meteorite, dropping the quarter on edge upon the back of an albino box turtle? Extremely low, but not zero."
Are you changing your mind? If it's not zero, then it is expressible as 1:X.
Originally posted by scalvert:
and the limits of spacetime preclude an infinite number of attempts. |
This is an assumption and if we make it, I agree we are not allowed an infinite number of attempts and the answer changes to "it may happen, but doesn't have to". However, if you pick up Greene's book, you will find that , unbelievably, "the big bang model of cosmology includes a detail that will prove essential. The model provides not one but a handful of different cosmological scenarios; all of them involve an expanding universe, but they differ with respect to the overall shape of space--and, in particular, they differ on the question of whether the full extent of space is finite or infinite." Between you and me, I think we both want to believe in a finite universe.
Originally posted by scalvert:
Further, what natural process is perfectly random— absolutely free of the influence of other particles or energy (including its own)? Introduce the slightest bias to those monkeys and the probability is no longer expressible as 1:X to the precision that model requires. |
A red herring. Either we consider the scenario to be possible or impossible. If bias does not allow for a possible result, then that probability is 0. If bias still allows for the possible result, that bias can be accounted for in the 1:X probability and the frequency remains 1. Further, precision is not necessary. If we see that a higher chance event has a frequency of 1 and a lower chance event has a frequency of 1, we can see rationally that all events between also have a frequency of 1 regardless of the exact value. I will grant you, of course, that it is practically impossible to calculate the actual 1:X probability of our swallow/quarter/meteor event. But all we have to do is determine whether it is possible. Can a swallow catch a quarter? Can it land on its edge? Can the bird be hit by a meteor? As long as the answer isn't "no" to any of the details, it is possible and the frequency of occurrence is 1.
Message edited by author 2011-02-16 23:23:06. |
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02/16/2011 11:35:46 PM · #338 |
Originally posted by DrAchoo:
If it's not zero, then it is expressible as 1:X. |
It's one in infinity, which still ruins your equation.
Originally posted by DrAchoo:
If bias still allows for the possible result, that bias can be accounted for in the 1:X probability and the frequency remains 1. |
Not necessarily (uncertainty principle and all that). You can't eliminate infinite variables all the way down to particle spin in nature, and therefore can't actually come up with an accurate probability. That's why you can express the "problem" mathematically, but cannot apply it to the real world.
Message edited by author 2011-02-16 23:36:08. |
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02/16/2011 11:59:20 PM · #339 |
Originally posted by scalvert:
Originally posted by DrAchoo:
If it's not zero, then it is expressible as 1:X. |
It's one in infinity, which still ruins your equation.
Originally posted by DrAchoo:
If bias still allows for the possible result, that bias can be accounted for in the 1:X probability and the frequency remains 1. |
Not necessarily (uncertainty principle and all that). You can't eliminate infinite variables all the way down to particle spin in nature, and therefore can't actually come up with an accurate probability. That's why you can express the "problem" mathematically, but cannot apply it to the real world. |
"One in infinity" is a meaningless mathematical term. You cannot divide something by infinity. It's like dividing by zero. The answer is meaningless. Therefore, you cannot declare it as the odds. It's like saying, the odds of something happening are "cheese".
If I grant you the possibility that you can't eliminate infinite variables all the way down, I can still arive at the conclusion. As we go further and further "down", the effect is smaller and smaller. You can keep adding decimals onto the probability, but you will never radically change the number. Again, you can rationally conclude that if the probability is between two other real probabilities. If so, the frequency is still 1.
Are you saying that we cannot apply mathematical odds to things like die rolls in the real world? That would freak out a lot of people in Vegas! Because the odds of rolling a six on a die isn't exactly 1:6, we can't apply the concept to the real world?
I'll allow you to conclude and then I'll leave you to your own thoughts.
Message edited by author 2011-02-17 00:00:42. |
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02/17/2011 12:57:23 AM · #340 |
Originally posted by DrAchoo:
"One in infinity" is a meaningless mathematical term. You cannot divide something by infinity. |
It's not meaningless. That's exactly how you would express the odds of something happening when the possibilities are infinite: one chance in infinity. You are correct that it royally screws the equation, though. My condolences on your loss.
Originally posted by DrAchoo:
If I grant you the possibility that you can't eliminate infinite variables all the way down, I can still arive at the conclusion. |
Nope. Given infinite possibilities, the probability is one in that infinite range and adding decimals does absolutely nothing as you noted above.
Originally posted by DrAchoo:
Are you saying that we cannot apply mathematical odds to things like die rolls in the real world? Because the odds of rolling a six on a die isn't exactly 1:6, we can't apply the concept to the real world? |
The odds of rolling dice are, for practical purposes, finite. While there may be a ridiculously slim chance of the die landing balanced on a corner on a flat surface, that probability is so slim that Vegas needn't account for it at all. However, when you're talking about calculating the odds of that particular event you DO have to account for it and every variable, from barometric pressure to the pull of the moon's gravity, becomes a factor. The infinite nature of those variables will void the warranty on your favorite calculator.
Message edited by author 2011-02-17 00:57:48. |
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02/17/2011 01:01:28 AM · #341 |
I will actually retract the first part. Infinity divided by infinity is meaningless, but otherwise you can divide a real number by infinity (and get zero for an answer). So in fact you are contradicting yourself. First you said the probability wasn't zero ("Extremely low, but not zero"), then you said it was ("1 in infinity"). Just as 0.9999(9) IS 1. 1-0.9999(9) IS 0. (If you say the odds are 1 in infinity, you are also saying the odds against are 0.9999(9).)
For the rest, I believe my point still stands. (see, I said it nicer that time).
Good night.
Message edited by author 2011-02-17 01:05:51. |
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02/17/2011 01:21:45 AM · #342 |
Let me just say that if one of you (Jason, Shannon) were to argue that the letter A is the first letter of the alphabet, the other (and it matters not which one starts, which refutes) would find a way to argue "That's just not true!"
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02/17/2011 01:34:01 AM · #343 |
Originally posted by Melethia:
Let me just say that if one of you (Jason, Shannon) were to argue that the letter A is the first letter of the alphabet, the other (and it matters not which one starts, which refutes) would find a way to argue "That's just not true!" |
While I hope that you are wrong, I'm afraid that you are right. Although, you could probably say that same thing for a number of the regulars in the rant forum. |
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02/17/2011 01:59:19 AM · #344 |
Originally posted by DrAchoo:
First you said the probability wasn't zero ("Extremely low, but not zero"), then you said it was ("1 in infinity"). Just as 0.9999(9) IS 1. 1-0.9999(9) IS 0. (If you say the odds are 1 in infinity, you are also saying the odds against are 0.9999(9).) |
See earlier snowflake example: any given pattern has a one in infinity chance of occurring, but SOME pattern will always occur. If the odds were truly zero, then you would never get any pattern. So the odds are extremely low, but obviously not zero and your point still fails. The proposed equation simply does not work mathematically with infinite variables. |
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02/17/2011 06:12:03 AM · #345 |
Originally posted by DrAchoo:
For the rest, I believe my point still stands. (see, I said it nicer that time). |
You totally discarded my initial example on the basis that you don't "buy" chaos theory. However, the elephant trap that you are falling into is exactly the one I was trying to explain with the monkeys example.
I'll try again.
If you regard the monkeys as random letter generators of a finite set within the confines of pure maths and statistics, you can come up with the odds of something happening. Given infinite sets of infinite monkeys that will happen at some point in time. I acknowledged this right up front in my clarificatory post. You've finally reached that point.
However, if you try and apply this in the physical universe (and by extension any multiverse) it doesn't work because there are an infinite number of variables.
Simplifying it, if the universe contained just two moving particles, could an infinite number of universes contain every possible direction and speed of travel and every possible relative location of those particles? The answer is no, they cannot because there are an infinite number of possible directions of travel, speeds of travel, and an infinite number of locations. (If you don't believe me, then imagine halving and then rehalving the points of a compass and let me know at what point you have described every possible direction).
If an infinite number of universes cannot contain all of the potential states of just two particles, then how could you suppose that an infinite number of universes could contain every possible combination of particles, directions and locations?
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02/17/2011 06:40:49 AM · #346 |
With all due respect, Matthew, I've a lingering doubt as to whether your example here works.
That's a bit of a laugh, because infinity doesn't exactly 'work' anyway, what with being purely conceptual.
Lots of work has been done in establishing the application of infinity to mathematical models. In other words, I suppose, lots of work has been done in establishing what infinity is. As Bill Clinton might say, that depends what you mean by 'is'.
I guess, then, that that which has been established is to some extent not so much what infinity is, but more a conventional consensus as to how the term and/or concept should be used. I further guess that at some point in the realm of infinity theory there may be some divergence between schools of thought.
Be all that as it may, my lingering doubt is triggered by my understanding that, for the generally accepted mathematical concept of infinity there is, however contra-intuitively, room in infinity for an infinite number of infinities. |
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02/17/2011 11:08:52 AM · #347 |
Originally posted by raish:
I guess, then, that that which has been established is to some extent not so much what infinity is, but more a conventional consensus as to how the term and/or concept should be used. |
Yes, and it's established that the equation in question only works when there's a finite, non-zero probability you can throw against infinite time. If either the possible outcomes are infinite or time is not infinite, then the model goes out the window and you're just navel gazing.
If you could imagine a perfectly balanced die so precise that every edge and surface is also perfect, eliminate external factors all the way down to particle spin and get a perfectly random roll every time, then you'd have an absolutely finite probability of 1 in 6 that a given side will come up. Now imagine doing the same thing with a sphere. The number of possible 'sides' is infinite, so even with infinite time you could never account for all of them. So the first experiment is impossible in practice, the second is impossible even in theory, and time isn't infinite anyway. |
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02/17/2011 11:17:58 AM · #348 |
Just to continue the naval-gazing: Shannon, you keep saying that time isn't infinite because it had a beginning at the big bang. This isn't exactly true. There are different types of infinite series. Consider this:
0,1,2,3,...-> is an infinite series of numbers even though it begins at 0.
<-...-3,-2,-1,0,1,2,3...-> is also an infinite series of numbers without beginning or end. In fact, this series is twice the size of the first series, even though both are infinite.
The fact that infinite series can have scale (one is twice the size of the other) itself should point out that our system of mathematics does not deal well with infinities.
Back to time: if the universe expands forever, then time should be infinite, at least in the positive direction. Whether this is true or not, well, your guess is as good as mine. |
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02/17/2011 11:34:51 AM · #349 |
Originally posted by eqsite:
you keep saying that time isn't infinite because it had a beginning at the big bang. |
It also has an end... either as the total energy of the universe eventually dissipates or as a "big crunch." (Note that this isn't necessary since Matthew already pointed out that you can't reduce the characteristics of even a single particle to an absolutely finite probability.)
Message edited by author 2011-02-17 11:38:42. |
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02/17/2011 11:36:51 AM · #350 |
Originally posted by scalvert:
Originally posted by eqsite:
you keep saying that time isn't infinite because it had a beginning at the big bang. |
It also has an end... either as the total energy of the universe eventually dissipates or as a "big crunch." |
Originally posted by eqsite:
Back to time: if the universe expands forever, then time should be infinite, at least in the positive direction. Whether this is true or not, well, your guess is as good as mine. |
If the universe continues to expand, which is one theory, then time must obviously be infinite. I don't personally like that option, but so far nobody has consulted me on the matter. |
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