I’m confused. Why do you bring up matter? I was working within your metaphore: computer generated pixels – under the assumption that the computer will randomly generate pixels for an infinite amount of time. It could theoretically randomly repeat itself to the point of never producing a picture.
Sorry, I just felt like being a gadfly, showing that even though this seems like an almost perfect deduction, it isn’t.
You’re right. I used the analogy as a simplistic arena for a model of reality. I see your point better now.
Somebody tell me why this is impossible? I’d prefer a gadfly over someone that just agreed. I’d like to say that this is where my model fails, but not sure why. Maybe the lack of thermodynamics in randomness?
If there was an infinite amount of time, an infinite number of pixels would conglomerate an infinite number of times. Everything whould show up on the screen, because there is no end. There is no probibility that the same pitcure would be on the screen for an infinite amount of time.
Where did you get the idea that a screen has an infinite amount of pixels? The screen has a finite amount of pixels. This very factor requires infinite repetition. An infinite quantity of pixels would not require repetition.
Can somebody who is good at probability prove this mathematically? I know I’m right but have yet to dig into statistics.
Is there a simple equation you can use to prove this?
This is easy enough but it doesn’t follow a probability equation. This very well may be enough evidence but I want to see it in the form of a probability equation. Somebody has to know a bit of simple statistics?
It’s easy to say, easy to intuit. But how do you know? You’re assuming with infinite time that everything will occur; you don’t know this, you simply assume it. I can assume that only a banana will pop up on the screen, and though intuitively, I find my assumption to be a lot less probable than yours, it is still possible. Which is why I’m unwilling to claim any knowledge that we know, with infinite time, every single possible variation will play out–for, what if it doesn’t?
Check this out. There is an old hustle that goes: “I bet I can show you a man who wins every coin flip he plays.” You say, based on your knowledge of probability, “I’ll take that bet!” Well, I simply need to get a few thousand people together in a room, have them all flip coins in a single elimination process, and then present you with the winner: the man who has won every single consecutive coin flip.
Such is the nature of chance. On every spin of the roulette, it is no more likely to be 00 than 39, possibly, 00 every single time. Perhaps our computer, by some odd chance, produces a banana for an infinite number of times. Well, that’s Chance! Not everything that can occur, must occur, even with an infinite amount of time. Nevertheless, it was interesting to make infinity concrete in the way it was described. For the time being, I’m done with this subject, thanks for posting.
Richard Dawkins did this same bit in a lecture I saw recently. However this does not prove your point either. This is just a simple game of elimination: one half the room beats the other half of the room until there are only two players left in the winning category. When the two play each other one is bound to win. This, again, does not break down the 1:2 probability. Sorry. . .
I guess if no one here knows statistics, I will have to learn it, and return with an answer.
As for a banana repeatedly occurring on the screen, it is a failure of my model. The first failure was the use of the word random. I should know better than to suggest randomness in a deterministic world, so there must be order.
This order is based on Thermodynamics. The Zeroth law of thermodynamics states that the thermodynamic equilibrium is an equivalence relation. In simpler terms, assuming the monitor’s output is not static, this means that the output is in motion and cannot stay the same.
As for the necessary infinite recurrence of sequenced events, I will get back to you once I understand probability equations.
Herein lies the sum and substance of what I think you are saying:
I disagree. My definition of “infinity” makes it mandatory that everything that can occur must occur. Indeed, it has already occured, is occuring and will occur. And, of course, to be truly infinite, it must never have occured at all. Finally, every possible combination of occurances and non-occurances will also be accounted for. Otherwise, how could it be “infinite”?
The idea that infinity is linear necessarily incorporates the concept of eternity, or time; which also includes space (that’s the linear nature of some people’s definitions of it). But that is all relative. That is all coin flipping and computers running screen changes over time. Infinity is bigger than that. It has no spacial or chronological restrictions.
I think what this all boils down to is this:
“My infinity is bigger than your infinity; so there!” CharlieGadfly
I don’t know if it’s probability or not, but I would use it to say this: Take 1,000 computers of the type you came up with, given infinite time, maybe 999 of them will come up, at one point or another, with a picture of you. Seems probable. But that one computer that doesn’t, also possible, demonstrates that there is a chance–a small room, for doubt.
So, I take it, reality must conform to your definitions? I see no reason for must, only can.
Flip a coin 100 times and odds are you’ll get 50 heads, 50 tails. If you’ve gotten 75 heads and 15 tails in 90 flips, there is no greater chance that the 91st flip will result in tails. Now, flip that coin an infinite amount of times, and every flip will still have the same odds, 1:2. The same is true with every pixel generation at any given point in time, one never knows if the computer will ever generate that precise picture of oneself, even a single time.
TUM, I have that same intuition as well, but you can’t say that is true until you can prove it mathematically. Although, I feel how you come to that conclusion, mathematically, I am almost positive probability will show us that it is necessary that all that can, will occur an infinite amount of times.
Above you mentioned 1000 computers of the type in question. However, there could be an infinite number of the type of computers in question and they are no more likely to come up with anything other than that which is arrived at by a single one of those computers running infinite times. The only distinguishing character is that of time, since 1000 computers or an infinite number of computers would seemingly get the result sooner. However, that is relative because of the time factor which means nothing in infinity.
In otherwords, in your coin flip example to me, odds matter naught. It all happens an infinite number of times, one result no more than another. Including the coin landing on it’s edge, not landing at all, not getting flipped, never bring struck, and etc, ad infinitem.
Here’s some clarification about the potential/actual infinite distinction.
Potential infinite: a quantity (more precisely, function) Q = Q(t) that varies with time t is potentially infinite if Q grows without bound as t becomes larger and larger. Q will always break any bound you set on it if you wait for a big enough t. Thus we say Q has the “potential” to become “infinite” if only one could wait an infinite amount of time for it to do so.
Actual infinite: a quantity that is “actually infinite” already, as opposed to one you have to wait forever for it to become infinite. An example would be the set of positive numbers. This set has an actually infinite size, as it has an infinite number of members all at once. We don’t have to wait for the set to get bigger and bigger, as in the potential infinite case. It’s already infinitely big.
