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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.18 15:43:00 -
[151]
Originally by: Sitara Akita - I'm developing a theory here that Whitehound is CCP's revenge for the 'discussions' on the new forums - a bot designed to post words in an *almost* meaningful manner pitched to keep you busy thinking if you just get the right explanation he'll finally see it
You are the blind fool here. You are making every attempt you can think of to win some attention. --
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2011.04.18 15:45:00 -
[152]
Again...
HOW EXACTLY do YOU define "the probability to return to the origin" ?
You know, since you already rejected the idea that the correct answer might be "amount of walks that did return divided by total number of possible walks" (or at least, limit of that when number of steps goes towards infinity). _
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.18 16:02:00 -
[153]
Originally by: Akita T x is a positive real number. Is 2x > x ? I think so. If x goes towards infinity, does that inequality change ? ...
It only goes towards infinity, Akita. You should really understand this by now (and I am sure that somewhere you do.)
I have proven your statements to be wrong a couple times now and you are still only guessing what it was you have done wrong. It is a problem you have to deal with or you can ignore it, but it is not my issue. I told you several times that you are mixing finite with infinite mediations. Seeing how you keep doing this do I doubt you will ever get it right.
...
A tiny quiz for those not as stupid as Akita. Which is the proper one:
a) R = (-inf, +inf) b) R = [-inf, +inf]
if you want to define R to be the set of real numbers? --
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2011.04.18 16:14:00 -
[154]
Edited by: Akita T on 18/04/2011 16:19:04
So let me recap your entire argument for you, insults stripped out...
:ahem: paraphrasing begins...
Infinity does not exist and can not exist, it is purely a mathematical abstraction. However, if you do say "given an infinite amount of steps, what is the probability of X", I will never automatically convert it into the only mathematically meaningful alternative wording to me, namely "as number of steps approaches infinity, what does the probability of X approach to", because that's just how I roll. Also, even if infinity is just abstract and can not possibly exist, I will still claim that "at infinity" anything and everything is possible, so the possibility of ANYTHING "at infinity" is always P = 1, but the possibility of NOT(ANYTHING) is also P = 1, since everything and anything is possible at infinity, and I somehow see absolutely no contradiction between those two statements, that's just how the impossible, non-existing infinity works. In closing, I will always chastize anybody who ever assumes that I should ever make that verbal conversion automatically like almost every other human on the planet and I will keep arguing semantics until the cows come home. Also, insults are a nice bonus.
:ahem: paraphrasing ends...
ACCURATE ? C/D.
Second part.
Assuming that the initial wording of the problem WOULD have said "As the number of steps approaches infinity, what does the probability you will have landed on the origin point at least once more approach to, for each of the three cases ?", you DO agree that the correct answers would have been P = 1, P = 1 and P ~= 0.34 ?
_
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.18 16:34:00 -
[155]
Originally by: Akita T Assuming that the initial wording of the problem WOULD have said "as the number of steps approaches infinity, what does the probability you will have landed on the origin point at least once more approach to, for each of the three cases ?", you DO agree that the correct answers would have been P_1D = 1, P_2D = 1 and P_3D ~= 0.34 ?
And again do you strip Polya's proof down to an unrecognisable gibberish for your own personal amusement. How sad. --
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Akita T
Caldari Navy Volunteer Task Force
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Posted - 2011.04.18 16:44:00 -
[156]
Edited by: Akita T on 18/04/2011 16:55:55
EDIT : I notice you are not denying the accuracy of the first part at all. ARE YOU ?
Originally by: Whitehound
Originally by: Akita T Assuming that the initial wording of the problem WOULD have said "as the number of steps approaches infinity, what does the probability you will have landed on the origin point at least once more approach to, for each of the three cases ?", you DO agree that the correct answers would have been P_1D = 1, P_2D = 1 and P_3D ~= 0.34 ?
And again do you strip Polya's proof down to an unrecognisable gibberish for your own personal amusement. How sad.
Then give us your personal interpretation of what Polya's proof AND THE OTHER STUFF MENTIONED IN THE LINKED WEBPAGES actually means, for us unwashed mathematically challenged masses, oh mighty wizzard ! What DOES the probability approach to as number of steps approaches infinity, and if it is P = 1 in your view, what exactly does P = 0.3405... mean ?
Also, your interpretation on HOW EXACTLY do YOU define "the probability to return to the origin". You know, since you already rejected the idea that the correct answer might be (limit of) "amount of walks that did return in x steps divided by total number of possible walks for x steps" (as x approaches infinity).
_
Make ISK||Build||React||1k papercuts |
Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.18 17:14:00 -
[157]
Originally by: Akita T Then give us your personal interpretation of what Polya's proof AND THE OTHER STUFF MENTIONED IN THE LINKED WEBPAGES actually means, for us unwashed mathematically challenged masses, oh mighty wizzard !
Would you not rather want me to get my unwashed, magic wand out for you? --
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Pr1ncess Alia
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Posted - 2011.04.18 17:15:00 -
[158]
Originally by: Akita T
Quote: Despite the mathematical proofs, can you not see the difficulty in stating you are most certainly a 1 in the first two scenarios but not in the last? -Why doesn't the math proofs display an answer such as: 'scenario 1 and 2, odds are .999999/infinitely approaching 1 but never reaching it?' What makes it impossible for our moves to extend away from the origin into infinity without ever returning in 1-d, 2-d scenarios but somehow perfectly reasonable with the added third dimension.
That's actually not impossible to explain.
In case of 1D and 2D, as the number of possible paths increases with number of steps, the number of paths that did not yet return to the origin continually shrinks as a proportion of the total possible paths, ever approaching zero, and it shrinks fast enough that the limit (probability(step_x)) when step_x trends to infinity will be 0.
However, for the 3D case, as the number of possible paths increase with number of steps, the number of those paths that have not yet returned to the origin does not shrink fast enough like it happens for 1D and 2D... in fact, the more steps you take, the closer to almost 66% the number of paths that have not yet returned to the origin goes... so for 3D, limit (probability(step_x)) when step_x trends to infinity will be ~0.66, not 0 like for 1D and 2D.
My brain hurts so dumb it down for me. If I read that correctly, the numerical answer is "approaches 1" for the first two scenarios not "exactly 1" ?
That I can live with and it does make sense.
My problem with the answers wasn't that the third isn't a 1. It was the certainty and specificity that the first two WERE =1. I didn't read the whole thread so it may have already been discussed.
--- Players are losing faith and loyalty in CCP due previous expansions not living up to player expectations. The CSM and CCP agreed that expectation management can be improved |
Akita T
Caldari Navy Volunteer Task Force
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Posted - 2011.04.18 17:42:00 -
[159]
Edited by: Akita T on 18/04/2011 17:49:13
Originally by: Pr1ncess Alia [...]dumb it down for me[...]My problem with the answers wasn't that the third isn't a 1. It was the certainty and specificity that the first two WERE =1. I didn't read the whole thread so it may have already been discussed.
Basically, in a very simplified manner of speaking (which is not perfectly accurate and Whitehound would certainly flip after he reads it, quoting and ridiculing it for its inaccurate terminology, etc)
In case of 1D (where it's easiest to understand), while the NUMBER of paths that do not lead back to the origin never actually goes to zero (it most likely keeps increasing with each step, in fact), the PERCENTAGE of those paths keeps decreasing, approaching zero. For 2D, since you can rearrange an entire infinite 2D grid into an infinite 1D grid, the same logic you used for 1D can apply. But you can not rearrange an entire infinite 3D grid into an infinite 1D grid, so the same logic no longer applies. For the 3D case, with each additional step, while more of the possible paths do end up back where they started, even more of the possible paths don't (almost twice as many).
Originally by: Whitehound same old, same old
Yes, the high and mighty "I am right, you are wrong, and I do not care enough to even bother explaining why until you are convinced, but I do care enough to read what you write and conclude that you are still wrong" approach.
I am growing tired of it, and now *I* have something better to do with my time for the next couple of days or so than keep arguing with you (or anybody else for that matter). Meanwhile, I shall play a similar game : while I agree that the initial wording could have been better, even after a pretty clear rewording which should have no longer bothered you, you still persist in your view, so *I* am right, *you* are wrong, I have already said everything that I could possibly say without repeating myself too much, so I do not need to say anything at all extra until you come up with a detailed argument, and if you fail to do so, you really are worth ignoring from now on.
_
Make ISK||Build||React||1k papercuts |
Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.18 22:17:00 -
[160]
Edited by: Whitehound on 18/04/2011 22:19:32
Originally by: Akita T One LAST attempt at mitigation before I (mostly) go AFK for two days: Do you at least agree that "In the case of a random 3D walk, as numbers of steps increase (ignoring the limit to infinity), the percentage of walks that do return to the origin approaches ~34.05%, not 100%" ?!?
One last attempt, huh? You will not give up failing...
Do I agree? No. Let us assume for a moment the probability was not 34% nor 100%, but 0%! Meaning no such walk would ever return...
I can take each of these infinite, never-returning walks and insert a finite walk into them to make them return. For each infinite, never-returning walk would I get an infinite, returning walk. So it cannot be 100% but it has to be at least 50%. How are you going to beat that? --
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Jill Xelitras
Xeltec services
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Posted - 2011.04.18 22:34:00 -
[161]
Edited by: Jill Xelitras on 18/04/2011 22:36:15 Edited by: Jill Xelitras on 18/04/2011 22:34:23
Originally by: Akita T "In the case of a random 3D walk, as numbers of steps increase (ignoring the limit to infinity), the percentage of walks that do return to the origin approaches ~34.05%, not 100%"
So ... THAT'S what Buzz Lightyear meant with: "To infinity and beyond !"
Hmm. Though I am absolutely incapable of following the mathematical proof posted earlier in the topic, I found this quite interesting.
I wonder what happens to the probabilities if you change the condition on passing through the origin into:
1) crossing a predetermined line of infinite length that crosses them origin. 2) crossing a plane that intesects with the origin and stretches out to infinity.
Jill.
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Scorpyn
Caldari Warp Ghosts Omega Spectres of the Deep
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Posted - 2011.04.18 22:44:00 -
[162]
Edited by: Scorpyn on 18/04/2011 22:47:11
Originally by: Whitehound ...I can take each of these infinite, never-returning walks and insert a finite walk into them to make them return. For each infinite, never-returning walk would I get an infinite, returning walk...
That doesn't seem to be relevant.
If you list all possible walks, and compare the ratio of the ones that do return to the origin vs the ones that don't, it doesn't make sense to add a returning path from the ones that don't return, since those are already included in the sum of the ones that do return.
It's like adding 50 to one side of the equation while not doing so on the other side.
Originally by: Akita T ...For 2D, since you can rearrange an entire infinite 2D grid into an infinite 1D grid...
No you can't. See my previous post about the exceptions to the rule about the 50% chance of any move to get closer to or further away from the origin when using >1D.
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 06:37:00 -
[163]
Edited by: Whitehound on 19/04/2011 06:46:14
Originally by: Scorpyn
Originally by: Whitehound ...I can take each of these infinite, never-returning walks and insert a finite walk into them to make them return. For each infinite, never-returning walk would I get an infinite, returning walk...
That isn't relevant.
Of course it is. There is nothing limiting infinity, because that is what it is - limitless. I can add many more walks to infinity and it stays infinity. It shows that one can always return to the origin. Are you now telling me that no walk ever returns to its origin?
Only when you assume that every walk can return to its origin could I not add another walk to it, because it would already have to be part of the set. --
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Scorpyn
Caldari Warp Ghosts Omega Spectres of the Deep
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Posted - 2011.04.19 07:41:00 -
[164]
Originally by: Whitehound Edited by: Whitehound on 19/04/2011 06:53:17
Originally by: Scorpyn
Originally by: Whitehound ...I can take each of these infinite, never-returning walks and insert a finite walk into them to make them return. For each infinite, never-returning walk would I get an infinite, returning walk...
That isn't relevant.
Of course it is. There is nothing limiting infinity, because that is what it is - limitless. I can add many more walks to infinity and it stays infinity.
Didn't you read the rest of my post? If you want to add paths then you must add all possible paths that take that many steps.
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 09:49:00 -
[165]
Originally by: Scorpyn Didn't you read the rest of my post? If you want to add paths then you must add all possible paths that take that many steps.
I do not need to add all possible walks. It is enough to only look at the walks that do not return to show that one can have an equal amount of walks that do return. If I added more then I would only add more returning walks, because I already include all non-returning walks. --
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Sitara
Minmatar Solar Flare Trade and Production
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Posted - 2011.04.19 10:48:00 -
[166]
Originally by: Whitehound Edited by: Whitehound on 19/04/2011 06:53:17
Originally by: Scorpyn
Originally by: Whitehound ...I can take each of these infinite, never-returning walks and insert a finite walk into them to make them return. For each infinite, never-returning walk would I get an infinite, returning walk...
That isn't relevant.
Of course it is. There is nothing limiting infinity, because that is what it is - limitless. I can add many more walks to infinity and it stays infinity.
I suggest you study the concepts of cardinality of infinite sets and the aleph numbers :
Pretty good basic explanation
Quote: Can one possibly say, then, that the number of aleph-one numbers are greater than aleph-null numbers? Not exactly. They are both infinity. One can be considered greater than the other, however, and that is what makes this idea of cardinality of infinite sets so mathematically interesting. The cardinality of infinities does not end here, of course. This is just one example of a conclusion that might be drawn from this idea. It should be able, at the very least, to allow one to realize that perhaps not all infinities are equal, and that mathematicians have their work cut out for them in making sense of these things
Linkage
Linkage
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Scorpyn
Caldari Warp Ghosts Omega Spectres of the Deep
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Posted - 2011.04.19 10:54:00 -
[167]
Edited by: Scorpyn on 19/04/2011 10:57:20
Originally by: Whitehound
Originally by: Scorpyn Didn't you read the rest of my post? If you want to add paths then you must add all possible paths that take that many steps.
I do not need to add all possible walks. It is enough to only look at the walks that do not return to show that one can have an equal amount of walks that do return. If I added more then I would only add more returning walks, because I already include all non-returning walks.
You can't determine the ratio of returning walks vs non-returning walks while only adding steps to one of the sides, because by adding steps you also create more non-returning walks.
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 11:48:00 -
[168]
Edited by: Whitehound on 19/04/2011 11:55:12
Originally by: Scorpyn You can't determine the ratio of returning walks vs non-returning walks while only adding steps to one of the sides, because by adding steps you also create more non-returning walks.
Yes, and I did. I am also not creating new non-returning walks, but I am creating returning walks. I cannot create new non-returning walks, because then I would create duplicates of the non-returning walks that are already in the set. --
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Scorpyn
Caldari Warp Ghosts Omega Spectres of the Deep
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Posted - 2011.04.19 13:13:00 -
[169]
Originally by: Whitehound Edited by: Whitehound on 19/04/2011 11:55:12
Originally by: Scorpyn You can't determine the ratio of returning walks vs non-returning walks while only adding steps to one of the sides, because by adding steps you also create more non-returning walks.
Yes, and I did. I am also not creating new non-returning walks, but I am creating returning walks. I cannot create new non-returning walks, because then I would create duplicates of the non-returning walks that are already in the set.
Do you actually believe that or do you simply like to argue? Because right now it's a bit like discussing with a wall.
For every step you take on your journey back towards the origin, the same amount of steps could just as well have been taken in the opposite direction, which is why you can't just add steps in one direction.
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 14:25:00 -
[170]
Originally by: Scorpyn Do you actually believe that or do you simply like to argue? Because right now it's a bit like discussing with a wall.
You only have no further argument. Good.
Originally by: Scorpyn For every step you take on your journey back towards the origin, the same amount of steps could just as well have been taken in the opposite direction, which is why you can't just add steps in one direction.
Oh yes, I cannot create new non-returning walks because I already have all of them in the set. I can only create returning walks and for each non-returning walk do I create one returning walk.
Do you now believe that 10% or 34% or 90% of infinity is actually less than infinity when you said yourself that infinity cannot be more or less infinity?!
Your mistake is to read something into those 0.34 that is not there. It is simply a number as the result of a formula and it brings the number of dimensions into an order. These values are as abstract as the idea of infinite drunks taking infinite steps while trying to find their way home. --
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Lallante
Reikoku Cascade Imminent
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Posted - 2011.04.19 14:51:00 -
[171]
Edited by: Lallante on 19/04/2011 14:51:33 Whitehound you basically dont seem to get orders of infinity.
Lall - THE Vocal Minority - Reikoku
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 15:33:00 -
[172]
Edited by: Whitehound on 19/04/2011 15:36:23
Originally by: Lallante Whitehound you basically dont seem to get orders of infinity.
Sure... And the next thing you want to tell me is that you can have infinite drunks in 7 dimensions and their chance to get home is something like 8.5%. --
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Lallante
Reikoku Cascade Imminent
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Posted - 2011.04.19 15:35:00 -
[173]
Originally by: Whitehound Edited by: Whitehound on 19/04/2011 15:33:55
Originally by: Lallante Whitehound you basically dont seem to get orders of infinity.
Sure... And the next thing you want to tell me is that you can have infinite drunks in 7 dimensions and their chance to get home is something like 8.5%.
You are trolling aren't you.
If not, here's a childs explanation that might be closer to your level: http://www.ccs3.lanl.gov/mega-math/workbk/infinity/inbkgd.html
Lall - THE Vocal Minority - Reikoku
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 15:40:00 -
[174]
Originally by: Lallante You are trolling aren't you.
If not, here's a childs explanation that might be closer to your level: http://www.ccs3.lanl.gov/mega-math/workbk/infinity/inbkgd.html
You are a bit too late. Had you followed the thread would you know that I already mentioned Cantor and the different infinities. --
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Kazuo Ishiguro
House of Marbles
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Posted - 2011.04.19 17:50:00 -
[175]
Edited by: Kazuo Ishiguro on 19/04/2011 17:50:51 Some observations on infinities, random walks, probabilities and percentages:
1. One cannot make valid statements about percentages of infinite sets. 2. The set [0,1] is such a set. 3. As such it makes no sense to say something like '34% of the real numbers in [0,1] are less than 0.34'. 4. However, it is nevertheless valid to say something like 'for a uniform random variable x on [0,1], P(x < 0.34) = 0.34' 5. There's a trivial bijection between the interval [0,1] and the set of all unbounded 3-dimensional random lattice walks:- At each step in your walk, you can move in any of 6 directions.
- Map these directions to the digits 0 to 5.
- For each walk, construct a number by setting the nth base-6 digit equal to the number that the nth step was mapped to.
6. On this basis, I think it might be reasonable to talk about the probability of a random walk possessing a particular property. --- 34.4:1 mineral compression |
Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.19 18:48:00 -
[176]
Edited by: Whitehound on 19/04/2011 18:49:41
Originally by: Kazuo Ishiguro 5. There's a trivial bijection between the interval [0,1] and the set of all unbounded 3-dimensional random lattice walks:- At each step in your walk, you can move in any of 6 directions.
- Map these directions to the digits 0 to 5.
- For each walk, construct a number by setting the nth base-6 digit equal to the number that the nth step was mapped to.
No. The real numbers are uncountable infinite whereas walks are only countable infinite. So you can find a relationship between the numbers [0,1] and an infinite walk, but it cannot be a bijective relationship.
The probability function of a random walk does only need to have one particular characteristic and that is of being a metric. The numerical value you get from it is of little meaning.
You really just end up with something like "every family has got 2.3 children," but for a problem of infinite walks of infinite movements, while you already cannot answer a question as simple as: "what is a 0.3 child?"
So you end up with a brain teaser. It is however just foolish. --
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Kazuo Ishiguro
House of Marbles
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Posted - 2011.04.19 23:16:00 -
[177]
Originally by: Whitehound No. The real numbers are uncountable infinite whereas walks are only countable infinite. So you can find a relationship between the numbers [0,1] and an infinite walk, but it cannot be a bijective relationship.
I would agree that the set of all random walks of finite lengths is countable (via a process of induction), but not the set of random walks of infinite length. By a similar line of reasoning: the set of integers Z is countable, and so is Z^n for any finite n, but Z raised to an unbounded power is not countable. --- 34.4:1 mineral compression |
Dhaikin Lharoud
Caldari Antares Technology
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Posted - 2011.04.20 00:03:00 -
[178]
Hmmmmmmmm
"GIVEN AN INFINITE AMOUNT OF TIME, what is the probability you will EVENTUALLY land on the origin point at least once again for each of the three cases ?"
I take a step to the left, then I take a step to the right and I don't land where I started 66% of the time?
Maybe that is why 66% of my alts can't find Jita
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Scorpyn
Caldari Warp Ghosts Omega Spectres of the Deep
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Posted - 2011.04.20 07:37:00 -
[179]
Originally by: Dhaikin Lharoud Hmmmmmmmm
"GIVEN AN INFINITE AMOUNT OF TIME, what is the probability you will EVENTUALLY land on the origin point at least once again for each of the three cases ?"
I take a step to the left, then I take a step to the right and I don't land where I started 66% of the time?
Maybe that is why 66% of my alts can't find Jita
Jita is on the avoid list by default.
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Whitehound
The Whitehound Corporation Frontline Assembly Point
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Posted - 2011.04.20 09:06:00 -
[180]
Edited by: Whitehound on 20/04/2011 09:08:09
Originally by: Scorpyn What I don't get is why this doesn't apply to 2D, since sometimes only 1 of 4 options take you closer to the starting point (when directly above, below, left or right of the starting point).
It applies for 2D, too. Towards infinity are these cases only being ignored, because they become negligibly small and you end up with having (at least) 2 out of 4 directions to lead you back.
You then need to fulfil the requirement of all chosen directions to have an equal probability. The further away you get from the origin the more steps you need to make into the reverse direction to satisfy this requirement. So when you approach infinity are you left with at most 2 out of 4 directions to get away and you are forced to choose the ones leading back, or the probabilities for each direction will not be equal. --
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