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If Infinite Monkey Were Typing On A Computer…

Author
Akita T
Caldari Navy Volunteer Task Force
#41 - 2012-04-22 11:07:38 UTC
Whitehound wrote:
You will be surprised when you realize how close we are to reaching infinity. When you consider how gravity fields influence time might the discovery of the Higgs boson not only lead to a better understanding of gravity, but of time as well. Once we do might it only be a small step to creating something, which knows no time - infinity.

I will not debate that perceived time can get heavily distorted in certain conditions.
I will not debate that in case the Higgs boson mechanism hypothesis is correct, we might eventually be able to manipulate mass, and in a roundabout way, possibly also time.
What I will debate however is something different - even if we do manage to achieve a pretty damn good mastery over mass and time (and maybe even space itself), the more you try to alter either one, the more energy you require, and the harder it gets to push it further. So even if we eventually might be able to manipulate time itself, I strongly doubt we will ever manage to actually "stop" it altogether.
Whitehound
#42 - 2012-04-22 11:12:25 UTC
Akita T wrote:
Whitehound wrote:
You will be surprised when you realize how close we are to reaching infinity. When you consider how gravity fields influence time might the discovery of the Higgs boson not only lead to a better understanding of gravity, but of time as well. Once we do might it only be a small step to creating something, which knows no time - infinity.

I will not debate that perceived time can get heavily distorted in certain conditions.
I will not debate that in case the Higgs boson mechanism hypothesis is correct, we might eventually be able to manipulate mass, and in a roundabout way, possibly also time.
What I will debate however is something different - even if we do manage to achieve a pretty damn good mastery over mass and time (and maybe even space itself), the more you try to alter either one, the more energy you require, and the harder it gets to push it further. So even if we eventually might be able to manipulate time itself, I strongly doubt we will ever manage to actually "stop" it altogether.

I agree. I am pretty sure that we cannot alter who we are, but only create a tiny bit of infinity if it is possible at all. Just like recreating the conditions of the Big Bang with particle accelerators is not going to recreate the Big Bang itself. This would be hilarious if it was possible.

Loss is meaningful. Therefore is the loss of meaning likewise meaningful. It is the source of all trolling.

Eternum Praetorian
Doomheim
#43 - 2012-04-22 14:46:30 UTC  |  Edited by: Eternum Praetorian
VKhaun Vex wrote:
Eternum Praetorian wrote:
It is not that it won't occur...
It is that it does not HAVE TO EVER happen, even if you typed on and on forever.


This is not correct and I don't know why you would think it is.

You would never make the same argument for a coin and say it's 'possible' to flip it an infinite number of times and get heads every single time. You seem to think because it's unlikely it may never happen, but infinity has no bias. You WILL get heads 50% of the time, and you WILL (heads=0, tails=1) spit out the entire binary code of EVE online and the two do not contradict in the slightest.

If you have a one in twenty trillion chance for your molecules to line up and slide your head through a brick wall, you WILL put your head through it given infinite tries.



I assure you that you will not, because true randomness does not mean all possible variations will be met. What one should expect is the occurrence of extremely simple patterns over and over again forever. Not the emergence of immensely complex reoccurring patterns.


A coin only has two sides as stated previously, and for the reasons previously stated it does not apply to larger patterns and larger variables. Ironically, I am now wonder if a binary code is actually composed of 50% 1's and 50% 0's. I wonder if this information can be found somewhere?

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Eternum Praetorian
Doomheim
#44 - 2012-04-22 15:31:23 UTC  |  Edited by: Eternum Praetorian
Ok so, from a little googling...




The alphabet in binary consists of two sets of 26, capital letters and standard (this does not include numbers atm) There appears to be 208 0's and 210 1's. That seems pretty close until you start multiplying.

208 * 50 = 10,400
210 * 50 = 10,500

That's 100 more 1's then 0's





208 * 50,000 = 10,400,000
210 * 50,000 = 10,500,000

That's 100,000 more one's then zeros (and so on and so for into infinity)


As you progress you will start to get FAR more ones then zeros in this binary language. Meaning that your 50/50 heads or tails analogy regarding coins cannot apply here, because your simple statistical reference is not taking into account all variables involved, like say... the format of a digital language. As the value gets bigger and bigger, you end up with a massively disproportional amount of 1's vs 0's, what that means is if chaos and statistics truly do create a perfect 50/50 as is assumed with the coin, the output of a random number generator would always be encoding more zeros per unit of time then was necessary to generate a perfectly even sequence of letters, or, functioning computer code.




Or Put In Another Way

50% heads and 50% tails applied to a Binary language that is not 50% balances between 1 and 0, means that you will always be generating more 0's then 1's per block of time. This, by definition, means that you cannot generate a perfectly balanced computer code, because the binary language of the code itself becomes a limiting factor. Where as the affects of chaos and statistics stays fixed.


See?

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Taedrin
Federal Navy Academy
Gallente Federation
#45 - 2012-04-22 18:06:19 UTC  |  Edited by: Taedrin
Eternum Praetorian wrote:
Ok so, from a little googling...




The alphabet in binary consists of two sets of 26, capital letters and standard (this does not include numbers atm) There appears to be 208 0's and 210 1's. That seems pretty close until you start multiplying.

208 * 50 = 10,40
210 * 50 = 10,50

That's 100 more 1's then 0'





208 * 50,000 = 10,400,00
210 * 50,000 = 10,500,00

That's 100,000 more one's then zeros (and so on and so for into infinity


As you progress you will start to get FAR more ones then zeros in this binary language. Meaning that your 50/50 heads or tails analogy regarding coins cannot apply here, because your simple statistical reference is not taking into account all variables involved, like say... the format of a digital language. As the value gets bigger and bigger, you end up with a massively disproportional amount of 1's vs 0's, what that means is if chaos and statistics truly do create a perfect 50/50 as is assumed with the coin, [b]the output of a random number generator would always be encoding more zeros per unit of time then was necessary to generate a perfectly even sequence of letters, or, functioning computer code. [/b




Or Put In Another Way

50% heads and 50% tails applied to a Binary language that is not 50% balances between 1 and 0, means that you will always be generating more 0's then 1's per block of time. This, by definition, means that you cannot generate a perfectly balanced computer code, because the binary language of the code itself becomes a limiting factor. Where as the affects of chaos and statistics stays fixed


See?



You are going about this the wrong way. We are dealing with the mathematical concept of "almost surely". This concept is simple: If you have an event which has non-zero probability, then this event will occur at least once with 100% probability given an infinite number of trials

Here's an example: Let's say you are rolling a 6-sided dice

What is the probability that you will NOT roll a 1 a single time when you roll the dice once? How about twice? 5 times? 10 times? 20 times? 1000 times?

You have a 5/6 ~ 83% chance to not roll a 1 with 1 trial
You have a 25/36 ~ 69% chance to not roll a 1 with 2 trials (5/6 * 5/6)
You have a 3,125/ 7,776 ~ 40% chance to not roll a 1 with 5 trials ( (5/6) ^ 5)
You have only a 2% chance to not roll a 1 with 20 trials
You have only a 6.6 * 10 ^ -80 chance to not roll a 1 at least once after 1000 trials

But we're not talking about 1000 trials, or even a large, finite number of trials. We're talking about an INFINITE number of trials. The Last Integer number of trials. An Aleph Null number of trials. We're dealing with infinite cardinal numbers here, and infinite cardinal numbers over power *ANY* non-zero finite number

Or in other words - as you increase the number of trials without bounds, the probability that an even with non-zero probability will NOT occur approaches zero. Because the probability that an event will not occur after infinite trials is zero, we say that the event will "almost surely" occur

Now the OP is dealing with an event with a much lower probability. However, the probability is STILL greater than zero so the probability that the event will NOT occur approaches zero as you increase the number of trials without bounds. It approaches zero very slowly - but it approaches it all the same
Ayla Hanaya
Imperial Academy
Amarr Empire
#46 - 2012-04-22 19:02:16 UTC  |  Edited by: Ayla Hanaya
FloppieTheBanjoClown wrote:
Micheal Dietrich wrote:
My main concern is that, according to the theory, 1000 monkeys punching wildly at keyboards will eventually make a masterpiece, but getting one eve forum user to create a coherent semi-thought out post is impossible.

So what you're saying is that monkeys are superior to Goons?

Because everyone in Eve is a goon alt these days. It's true, I heard it in the recruitment channel and nobody lies there.


At least goons enforce grammar and goodpoasting on the SA forums, thus eve forum user =/= SA poster.

E: And also, in answer to OP, the answer is yes. Simply yes.
Eternum Praetorian
Doomheim
#47 - 2012-04-22 19:16:40 UTC
Quote:
If you have an event which has non-zero probability, then this event will occur at least once with 100% probability given an infinite number of trials



Then you are also claiming that you can flip a coin and get heads 10,000 times consecutively if you flipped it infinite times. That will not happen either. Simply... no.

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Taedrin
Federal Navy Academy
Gallente Federation
#48 - 2012-04-22 21:33:27 UTC
Eternum Praetorian wrote:
Quote:
If you have an event which has non-zero probability, then this event will occur at least once with 100% probability given an infinite number of trials



Then you are also claiming that you can flip a coin and get heads 10,000 times consecutively if you flipped it infinite times. That will not happen either. Simply... no.


Yes it will. The chance of getting 10,000 heads in a row is 1/2^10,000. This is a very small number, but it is still finite and it is still greater than zero. The *only* way to prevent the event from happening after an infinite number of trials is if the event has probability of success of EXACTLY zero. And last time I checked, 1/2^10,000 > 0 is a tautology.

OK, since we are starting to deal with large numbers now, we can't use a calculator. Instead we'll do this generally:

The chance of getting n heads in a row with n coin tosses is 1/2^n. The chances of this NOT happening is 1 - 1/2^n. We can rewrite this as (2^n - 1) / 2^n.

If we consider the possibility that we won't get n heads in n coin tosses in two separate trials (I.e. two sets of n coin tosses), then the probability of NOT getting n coin tosses in EITHER of these two separate trials is:

((2^n - 1)/ (2^n)) * ((2^n - 1) / 2^n))
or
((2^n - 1)/(2^n)) ^ 2

Let us consider the general case of m separate sets of n coin tosses:
The probability of NEVER getting n heads in a row with n coin tosses in m separate sets of n coin tosses is:
((2^n - 1)/(2^n)) ^ m where m is some positive integer.

Take the limit as m goes to infinity:

lim (m->inf) ((2^n - 1)/(2^n)) ^m = lim(m->inf) ((2^n - 1) ^ m) / ((2^n) ^ m)

Let a = 2^n and b = 2^n - 1

Because a > b, we also have a^m > b^m. Therefore, the fraction b^m / a^m converges to zero as m goes to infinity by the ratio test.

Or in other words, the chances that we will NOT see n heads in a row in n coin tosses after an infinite number of n coin tosses approaches zero - meaning that we have a 100% chance of seeing at least one set of n coin tosses landing heads n times in a row.
Eternum Praetorian
Doomheim
#49 - 2012-04-22 21:39:09 UTC
Math it all you want, the coin toss thing is the best example so far. No way, no how... will you ever get 10,000 heads in a row.

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Akita T
Caldari Navy Volunteer Task Force
#50 - 2012-04-22 21:42:36 UTC  |  Edited by: Akita T
Eternum Praetorian wrote:
Then you are also claiming that you can flip a coin and get heads 10,000 times consecutively if you flipped it infinite times. That will not happen either. Simply... no.

If by "infinite times" you really mean whatever almost everybody else means, then yes, we are also claiming that you CAN flip a coin and get "heads" X times consecutively, where X is any arbitrarily large finite positive integer, be it 1, 10, 100, 1000, 10k, 100k or even 10 billion.

We even know the chance of that happening, it's 1/(2^X).
Sure, it very rapidly decreases as X increases, but it never quite reaches zero when X is a finite number.
Yes, 1/(2^10000) ~= 0.501 * 10^(-3010), which in case anybody else wonders, it's 0.000000000....0000000501 with a total of 3010 zeroes between the decimal point and the "5".
Yes, ACTUALLY flipping all coins that ever existed and will ever exist constantly, as fast as possible to still be able to determine order, and until the universe ceases supporting life, THAT will indeed have practically a zero chance of accidentally landing on heads 10000 times consecutively, so in PRACTICAL terms, we can say that "it will never happen", because we already assume a finite time, even if it sounds like we'd want it to mean "at infinity".

You still seem to have the same problem with the concept of infinity, that you could possibly use "at infinity" and not be inaccurate.
Let me put it another way : your arguments mostly live or die depending on your apparent belief that you could actually reach "step number infinity", and once that step is reached, there is no "step number infinity +1".
That's sadly not how infinity works. That's not "infinity", that's just a very, very, VERY large finite number. Again, that's NOT "infinity", I can't possibly stress that enough.

In much simpler and vastly inaccurate terms, "at infinity" (which will "never" be reached), ANYTHING that has a non-zero chance of happening WILL have had "almost surely" happened already at least once.
Sorry, but that's just how "INFINITY" (as opposed to a staggeringly large but still finite amount) "works".

Eternum Praetorian wrote:
Math it all you want, the coin toss thing is the best example so far. No way, no how... will you ever get 10,000 heads in a row.

Again, given some REALISTIC and obvious constraints (like the size of the universe, the numbers of coins that can be flipped in it, and the estimated total lifetime of the universe), yes, you are correct, you can say with enough confidence that "it will never happen" and be mostly correct.
A more accurate way of putting it would be that "the chance of it happening at all before you run out of time is extremely small".
But once you break out the concept of "infinity" and you really, really mean chance of it happening=0% (not 0.000000....00001 with an arbitrarily large amount of zeroes) when you say "it will never happen", then stuff all of a sudden changes, and you are incorrect.

P.S. Replace the word "infinity" when used in the context of time with the phrase "at a point in time in the distant future that can never be actually reached no matter how much time passes" and see how ludicrous everything starts to sound...
Eternum Praetorian
Doomheim
#51 - 2012-04-22 22:10:32 UTC  |  Edited by: Eternum Praetorian
It's not about any of those thing Akita, it's about the plan and simple realty of coin tossing. It does not matter how much time passes, there will never be 10,000 consecutive heads or tails because that is just not the way it works in practice and regardless of what the math says. If you were to flip coins forever, it would look remarkably like flipping coins for a year, repeated forever. You will never get the latter.



All these nerdy-math-wiz-collage graduates, and this fundamental concept of our surrounding reality cannot be grasped?


A word to the wise, math is a language and like any language created by human beings it can tell both factual and fictitious stories. Only our experience and cognitive senses can tell us which is which, and not even with a great deal of accuracy mind you.

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Akita T
Caldari Navy Volunteer Task Force
#52 - 2012-04-22 23:02:10 UTC  |  Edited by: Akita T
Eternum Praetorian wrote:
[...]It does not matter how much time passes, there will never be 10,000 consecutive heads or tails because that is just not the way it works in practice and regardless of what the math says. [...]

You just said almost the same thing I have said but made it sound as if you were disagreeing.

The math says that the chance of 10000 consecutive heads happening if everybody on earth flipped coins for their entire lifetime would be so close to zero that it's even hard to think of a joke for it.
In fact, in practice, the chance for even 100 consecutive heads (not 10000, not 1000, just 100) under the above conditions would also be pretty damn close to zero.
Heck, all 7 billion people in the world today flipping one coin per second for 70 years from now without sleeping or taking a break (and obviously, not dying, heh), but the chance of just 50 consecutive heads would still be under 4%.

So, yes, IN PRACTICE, given a reasonable amount of time, you will almost certainly NOT see it happening.

But you are not claiming a reasonable (finite) amount of time, or are you ?!?
You specifically say "no matter how much time passes".
That means I could take 100 trillion times the entire lifetime of the universe so far if I wanted and call that "a start", then keep on going another similarly-timed round if I didn't yet manage to get that flip yet, and so on, and so on, and so on, until it happens.
And eventually, somewhere, at some time close to "never", you WILL see that 10000th consecutive "heads" flip.
Eternum Praetorian
Doomheim
#53 - 2012-04-22 23:20:51 UTC
No, infinity is infinity. The pattern of heads to tails would continue on and on into infinity. You might get 10 heads in a row, 20 heads, but never ever 10,000. Not ever, ever and ever.



Because like a fractal image descending into infinity, the seeming pattern repeats.

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Akita T
Caldari Navy Volunteer Task Force
#54 - 2012-04-22 23:37:09 UTC  |  Edited by: Akita T
Eternum Praetorian wrote:
No, infinity is infinity. The pattern of heads to tails would continue on and on into infinity. You might get 10 heads in a row, 20 heads, but never ever 10,000. Not ever, ever and ever.
Because like a fractal image descending into infinity, the seeming pattern repeats.

There's no fractal image. There's no pattern. There's just flips, random heads or tails, random 1s and 0s, with equal chances.

Flipping 10 "heads" in a row is equally likely to flipping "heads, heads, tails, heads, tails, heads, tails, tails, tails, heads" in that EXACT order, or any other SPECIFIC combination of flips.
There are 1024 possible combinations of flips, each of them having exactly a 0.09765625% chance of happening.

Same story for 20 throws.
There's 1,048,576 possible combinations of 20 flips, and each of them has exactly a 0.000095367431640625% chance of happening.

Same for 100.
You have 1,267,650,600,228,229,401,496,703,205,376 possible combinations of 100 flips, and each of them has a roughly 0.7888609 * 10^(-26) % chance of happening.

Same for 1000.
You get 1.0715 * 10^301 combinations, each with the exact same 0.9332636 * 10^(-301) % chance of happening.

Same for 10000.
You get 1.995 * 10^3010 combinations, each with the exact same 0.50123727 * 10^(-3010)% chance of happening.

Same for ANY finite number.


Flipping 10000 heads in a row is equally likely to flipping any ARBITRARY pre-chosen combination of flips, and you can't deny that you DO get a certain combination of 10000 flips when you flip a coin 10000 times.
The CHANCE of it being the one you have pre-chosen is infinitesimally small, but it's the exact same chance of 10000 heads in a row or 10000 tails in a row, or any other possible combination.
Again : there's no fractal image, there's no pattern.
Eternum Praetorian
Doomheim
#55 - 2012-04-22 23:38:22 UTC  |  Edited by: Eternum Praetorian
You're taking the fractal representation to literally. It's just a metaphor.

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Akita T
Caldari Navy Volunteer Task Force
#56 - 2012-04-22 23:40:38 UTC  |  Edited by: Akita T
Eternum Praetorian wrote:
You're taking the fractal representation too literally. It's just a metaphor.

Just like your "no matter how much time passes" seems to also be just a metaphor.

If you say "very long amount of time that is still realistically achievable" instead of "infinite time", we can stop any disagreements.
Deal ? Lol
Eternum Praetorian
Doomheim
#57 - 2012-04-22 23:55:45 UTC
You might think that Big smile


Since infinity cannot be reached, sure why not lol Same difference though in the end. The random sequence will repeat indefinitely, and your not going to ever roll 10,000 heads.

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Taedrin
Federal Navy Academy
Gallente Federation
#58 - 2012-04-23 00:12:44 UTC
Eternum Praetorian wrote:
Math it all you want, the coin toss thing is the best example so far. No way, no how... will you ever get 10,000 heads in a row.


Answer me 2 important questions then:

1) What is the upper limit on the number of times you can get a run of "heads" on a fair coin toss? When does a particular permutation's probability cross this magical boundary from "not likely" to "impossible"?
2) What makes other specific permutations more likely than a run of "heads"? After all, each permutation is unique within the entire problem space. So why do other permutations occur but not the run of all "heads"?

Akita T
Caldari Navy Volunteer Task Force
#59 - 2012-04-23 00:55:05 UTC  |  Edited by: Akita T
Eternum Praetorian wrote:
You might think that Big smile Since infinity cannot be reached, sure why not lol Same difference though in the end. The random sequence will repeat indefinitely, and your not going to ever roll 10,000 heads.

Ok, we just established that each sequence of any finite number of tosses has the exact same chance of happening as any other sequence of tosses.

Let's take an arbitrary sequence of 10 tosses, like, say, 10 heads, for simplicity's sake.
We know there are 1024 possible combinations of tosses, and each of them is equally likely to happen.
After 10240 total tosses grouped 10 at a time, there's a fair chance that we have experienced a rather large number of those possible combinations of 10 tosses (with some of them not happening at all, some happening once, some twice and so on).
After 102400 total tosses (10 times more than all possible combinations strung together), there's a very good chance that every possible combination of 10 tosses has come up at least once, some of them came up many times (on average, close to 10 times each) with very few of them not having shown up at all yet.
We can safely say that after 1024000 tosses, we can be almost certain that each and every specific possible combination has almost certainly shown up at least once (on average about 100 times each), and that includes our "10 heads in a row" initial choice. The chance of any particular sequence NOT showing up is the one bordering near zero this time.

If we go with a single person with the full-time-job of tossing the coin once every second for 8 hours a day, 5 days a week, 50 weeks per year, 1024000 tosses would require only a bit over 7 weeks to complete.
So, in about 7 weeks, we have almost certainly managed to flip 10 consecutive heads at least once, and on average, we have flipped 10 consecutive heads about 100 times.
Ok, in fact, on average, we would have been flipping even more than 100 times the 10-heads string, so it would happen even sooner than 7 weeks, because we would reset the sequence every time we would get a tail, but let's assume for the sake of argument for this entire post that we don't do that, because "the error" is in your favour anyway.

Let's go for 20 tosses.
1,048,576 combinations, so in order to get on average about 100 times a 20 consecutive heads toss and almost guarantee at least one, we'd be needing 1,048,576,000 throws, which would require the same "full time job coin tosser" to keep doing it for about 145 years.
He might not get to live that long, but you never know, on average it would only need about 14.5 years for one of those to happen, so he might get lucky.

How about 30 tosses ?
1,073,741,824 combinations, tossing about 1,073,741,824,000 times to almost guarantee one 30-consecutive-heads toss (and on average about 100 of them), or 149,130 years.
Well, I guess ONE single person is unlikely to be able to do it, but he might still get lucky while he's still alive. But take 150k people and in one year, you're almost guaranteed to have at least one of them make it (in fact, probably about 100 of them will make it within a year).

Hmm, let's go a bit faster and try 100 tosses.
1,267,650,600,228,229,401,496,703,205,376 combinations, ouch, now that's a number.
Going by similar rules, 1,267,650,600,228,229,401,496,703,205,376,000 total tosses to almost guarantee at least one 100-heads toss streak.
Uh-oh, the poor person we're talking about would be needing about 176,062,583,365,031,861,318,986,550 to make that many tosses... hmm, guess that's about 12,804,551,517,456,860 times the current estimated age of the universe, oh my !
Even if we take the approximate 7bil population of the planet Earth and make them full-time coin-tossers, that's still about 1,829,221,640 times the age of the universe until we can safely say at least one of them has managed to make a 100-heads coin toss (and about 100 of those have happened on average).
Or, to put it another way, we need about 18,292,210 times the age of the universe for all the people in the world today working full-time (assuming they could maintain their numbers for that long) as coin tossers to have a reasonable chance of one of them having tosses a 100-heads streak.
We can all agree that practically speaking, that is what you would already call "impossible".
But it's still not "infinite time".

What about 10000 consecutive heads tosses ?
1.995*10^3010 combinations, we want 1.995*10^3013 tosses, that's about 2.77*10^3006 years, divided by 7bil people that's around 3.958*10^2999 years, divided by the age of the universe (13.75bil years) that's still 2.8788*10^2989 times the age of the universe.
And after THAT much time has passed, we can be ALMOST certain that AT LEAST one 10000-heads streak has happened, and that on average, chances are about 100 sets of 10000-consecutive-heads tosses have happened.
That's an awful truckload of time, and far, far, far past anything anybody halfway sane would even begin to consider calling possible. But it's quite calculable, and quite finite, thankyouverymuch, so certainly not "infinity" just yet.


Hey, what about 1 billion consecutive heads tosses ?
My calculator croaks if I try to calculate that (it can't even handle calculations for 100k consecutive heads), as it has way too many digits, but you can be fairly sure that it's still a finite number.
Hilariously large, I agree, but still nevertheless finite.

...

Yes, some things have a very low chance of ever happening in a realistic timeframe, but to say that "it would never ever happen" is downright wrong. Anything with even the slightest chance of happening will eventually almost certainly happen. It just takes a ludicrous amount of time (even more than could practically exist in some cases). But always less than "infinity". That's kind of infinity's thing, you know, anything finite, no matter how large, is always smaller than infinity.
Akita T
Caldari Navy Volunteer Task Force
#60 - 2012-04-23 01:48:28 UTC  |  Edited by: Akita T
Let's put it another way. NOT statistically correct (quite wrong in fact, but, eh, it sort of drives the point across more clearly).

Say you know the chance of something happening, and you say that it's NOT quite zero.
This means you can write it down as a number of the form 0.00000000000....0000001 or somesuch.

Do it once. Has it happened ? Almost certainly no.

Do it 10 times more than you've done it before.
Has it happened ? Probably not yet. But the chance of it happening has gone up, not quite 10 times, but close to that.
Approximate that by cutting one of those many zeroes from its chance of happening.

Do it again 10 times more than you've done it before (so 100 times).
So, did it happen ? Again, probably not.
But the chance of it happening has gone up by very roughly the factor of 10 again, so cut one extra zero out.

Keep doing it 10 times more than you have done it previously (so keep adding a zero to the number of times you do it total).
Every time you do that, cut another zero out of the probability.
EVENTUALLY, you will run out of zeroes to cut out of the probability.
So, has it happened yet ? You know, it kind of could have happened already.
Keep adding zeroes to the numbers of times you try.
Has it happened yet ? Well, what do you know, it's first quite likely it already happened at least once, then it's almost certain it happened at least once and there's a good chance it happened many times, and eventually, it's nearly impossible for it NOT to happen at all !!!
So, how many times did you have to try it ? Well, it's a number with many digits for sure, but it's always lower than infinity.

So, yes, anything that has a chance that's NOT EXACTLY ZERO of happening, given a very large amount of time approaching but not quite reaching infinity WILL eventually ALMOST CERTAINLY have to happen at least once, then happen many times if you keep trying.

Assuming you can try it that many times. But hey, it's always less than infinity either way.

...

For something with a known clear and fixed chance of happening, no matter how small the chance (as long as it's not zero), the question is always "DO YOU HAVE ENOUGH TIME FOR IT TO HAVE A DECENT CHANCE OF HAPPENING?" to which the answer could be yes or no depending on available time and what you mean by "decent".
The question is never "Given infinite time, will it happen?" in this case, because the answer to that particular question is always YES, which renders the question kind of meaningless.