PigLick on 27/9/2007 at 15:10
yeh fucking monkeysee man, whats up with that.
RocketMan on 27/9/2007 at 16:34
who is this guy anyway?
catbarf on 27/9/2007 at 18:45
Rocketman, every coin toss is independent. You could roll a dozen dice and they all come up sixes, but that doesn't mean the next roll will be a one. Entropy has no bearing here. Probability remains the same. The reason for there not often being 99 heads out of 100 coins is not because of entropy, it's because getting 99 heads is nearly impossible whereas getting 6:4 ratio or better is virtually guaranteed.
I actually once rolled twenty sixes out of twenty dice. Then I rolled six more, and got every number. I think the probability of that is somewhere in the 1:1x10^800 range.
Rug Burn Junky on 27/9/2007 at 18:49
Quote Posted by aguywhoplaysthief
He was my favorite poster.
You have no idea how much that hurts me.
RocketMan on 27/9/2007 at 20:41
Quote Posted by catbarf
Rocketman, every coin toss is independent. You could roll a dozen dice and they all come up sixes, but that doesn't mean the next roll will be a one.
I know :) I posted it at the beginning of this thread
Quote Posted by catbarf
The reason for there not often being 99 heads out of 100 coins is not because of entropy, it's
because getting 99 heads is
nearly impossible whereas getting 6:4 ratio or better is virtually guaranteed.
HOW is it impossible. "Impossible" is not a reason, nor is it a mechanism. If it is nearly impossible (and I agree with you in that there is a low probability of such occurances), then what is the trigger, the precursor, the physical manifestation that is responsible for the affinity towards an even distribution amongst many trials. If you picture a coin spinning in the air and think of all the variables that determine its final resting orientation (strength of flip, trajectory, orientation at impact with floor, blah blah blah,etc, etc), they can all be amalgamated under the heading matter-matter interactions, which of course along with time and energy are all governed by thermodynamics and therefore entropy.
Chade on 27/9/2007 at 21:30
Quote Posted by RocketMan
But you are contradicting yourself.
Rocketman, the first bolded section should have included all the words: "will not tend to change
in any particular direction".
This is to say, even though you don't expect to get exactly the same number of heads and tails, there's no way to predict which side you will get more of.
Now, the absolute magnitude of NoHeads - NoTails will increase over time, but at an increasingly slow rate (I
think it's approximately sqrt(NoTosses), but don't quote me on that! I would have to work it out properly). However, the total number of coins you have tossed will increase at a constant rate.
So over time, (NoTails - NoHeads)/NoTosses will go to 0, even though NoHeads - NoTails will increase (on average).
Therefore, the expected ratio of heads to tails will tend to go to 50/50 as you toss more and more coins. You don't expect to get exactly 50/50, but as you toss more coins, you expect the ratio to get closer and closer to 50/50.
It's the
ratio which approaches a certain value, not the absolute difference between NoHeads and NoTails.
I hope I'm making sense to you ... I'm not all that good at explaining this stuff. :/
catbarf on 27/9/2007 at 22:57
Quote Posted by RocketMan
HOW is it impossible. "Impossible" is not a reason, nor is it a mechanism. If it is nearly impossible (and I agree with you in that there is a low probability of such occurances), then what is the trigger, the precursor, the physical manifestation that is responsible for the affinity towards an even distribution amongst many trials. If you picture a coin spinning in the air and think of all the variables that determine its final resting orientation (strength of flip, trajectory, orientation at impact with floor, blah blah blah,etc, etc), they can all be amalgamated under the heading matter-matter interactions, which of course along with time and energy are all governed by thermodynamics and therefore entropy.
Entropy does not alter probability. That's the key. The 'physical manifestation', as you put it, is simply the vagaries of the way the coin is flipped by any one person. If you flipped 99 heads, entropy is not going to step it and screw it all up- otherwise, how did you get to 99 heads in the first place?
The thing that makes the results tend towards the standard is the exceedingly high probability of such a result. The larger the sample, the more likely such a result is. Getting an improbable result (like 99 heads) doesn't break the system, just shows an exceedingly unlikely event. In fact, the likelihood of getting 99 heads is 1.577e-30.
RocketMan on 27/9/2007 at 23:47
The vagaries of the way the coin is flipped, is what I'm saying is just a facade for particle to particle interactions and these are not goverened by intelligence even though at first blush it seems that way. The universe is just playing itself out and we have no control over it. It plays according to the rules of the game (physics) of which entropy is a big player. If you look at a graph of entropy vs. time vs. space (and assuming time is unidirectional) you do get spikes here and there where entropy locally decreases but always increases globally. This looks very similar to the behaviour of coins as they are flipped over and over again. You will see spikes of unlikely consecutive trials but as n --> infinity the entropy increases to its maximum value and the distribution is 50 50. This part of what I'm saying although it includes entropy, is really nothing more than explaining the law we already believe in, that the outcome of any number of trials tends to 50%. The controvercial part of what i'm saying is that this has direct implications as to the outcome of a single event, having considered its past. Its like watching a graph of the stock market and seeing a fluxuation. You know that a good solid company will tend to behave predictably on the 5 year chart for example but when you zoom in you see fluxuations. You can certainly use the history of the company to predict how these fluctuations will behave in the future. I'm not saying stock = probability/statistics but the graph of a stock company and its predictive power is sort of the way i see trials of any probabilistic event.
Scots Taffer on 28/9/2007 at 00:18
Quote Posted by RocketMan
who is this guy anyway?
NO WHO THE FUCK ARE YOU
sorry
I'm just getting very emotional thinking about him
RocketMan on 28/9/2007 at 00:47
heh i suppose you're right...i never post in com chat
