Reply
Fri 27 Nov, 2009 03:17 pm
When a statistically unlikely event occurs, we need to decide whether it is more likely to be due to pure chance or to some other factor. To do this, we calculate the respective probabilities. For example, if successive throws of a die continue to result entirely in sixes, there comes a point at which we start to believe that the run is not due entirely to chance, and that there are other factors involved, e.g. a weighted die or some kind of sleight-of-hand. The tipping point in our belief may vary from one person to another, but I think everyone would agree that, if the run of consecutive sixes is long enough, pure chance ceases to be a serious possibility, and it becomes overwhelmingly probable that some other factor is in play.
The point at which we cease to believe in pure chance as a plausible explanation will depend on the statistical probability of the sequence of events. Now, this probability will vary vastly according to whether we adopt a third-person or a first-person perspective. Given a world population of six billion, it is millions (perhaps hundreds of millions) of times less likely that I will witness an improbable event (e.g. a person throwing 20 consecutive sixes) than that someone somewhere will witness it. The question is therefore: When calculating whether pure chance is the best explanation, should I adopt a 3rd-person or a 1st-person perspective? At first sight, the obvious answer would seem to be that the objective, 3rd-person perspective must be the right one. But I am not so sure....
Imagine, as a thought experiment, that the universe, and its population, were many orders of magnitude larger. Imagine that you entered a vast lottery in which an astronomical number of people participated (let's make it a really spectacular figure - say 10 to the power 100), and that you won first prize on the first occasion it was held. From a 3rd-person perspective, there would be nothing at all remarkable about this; someone would have to win. But from your 1st-person perspective, it would be amazing beyond words!
In such circumstances, could you honestly accept the 'objective' 3rd-person view, or would you look at it from your own perspective and believe that (to put it crudely) "something strange is going on"? In other words, would you consider, as a better explanation, the possibility of some (perhaps unknowable) metaphysical reason why you had been "favoured"? Or is there some other, more prosaic, alternative? I cannot think of one; any conceivable explanation from the 3rd-person view (e.g. "the lottery was rigged in your favour") runs up against the problem of why you should have been singled out from such a vast number of people.
So is this an argument for some kind of solipsism? Maybe not 'strong' solipsism (i.e. "only I exist") but a 'weak' variety (something like "other people do exist, but I exist in a unique way")? It is easy to caricature any kind of solipsism as a form of vanity, but I hope I have demonstrated that there is a serious point at issue here, even if you disagree with my argument.
Any comments and/or refutations?
@ACB,
hi acb
yeh very interesting.
i think with regard to the universe lottery numbers then you have the background knowledge that the lottery was set up. This automatically gives the winner a third person perspective in addition to the first person perspective. It then becomes a personal contest between the two perspectives for the winner.
But what if something extraordinary happened to you and you had no knowledge that it was a set up? eg. a secret ruling universe elite constructed the 'extraordinary lottery experience', played it out ....... then handed you the winner the extraordinary event without any knowledge as to why you recieved it?
This is much more difficult because the 'winner' is in the dark with regard to the secret lottery. From an earth based perspective the person could quite reasonably believe that something very strange had happened to them for which there is no rational explanation. OR the person could still believe that extraordinary things happen by chance on a universal scale, and dismiss the whole thing as coincidence when it wasn't.
Probability theory is extremely tricky as i am sure you are aware. Especially the contribution of prior knowledge. At the heart of it is the concept of randomness. Is it inherent or is it apparent or is it contrived?
I don't think we can ever expect to answer that question in our lifetime. eg in the above scenario it is still possible that randomness is apparent, and therefore the universal elite who thought they created the 'extraordinary lottery experience' were actually deluding themselves in thinking that they had created it, when in fact it was predetermined behaviour on their part in a deterministic universe. Thus a lack of knowledge with regard to the universe being deterministic impinges now upon them. On the other hand ...... maybe they were manipulated by another secret elite such that although they thought that the winner was chosen randomly in fact it was fixed by some other very clever secret elite with a hidden agenda as to who won.
This sort of thing is at the heart of 'spiritual' experience of course as i think you are pointing out? The fact is we don't know if the universe is deterministic or not, let alone have 3rd person objective evidence for spiritual phenomena. Its a dilemma..... but is it a dilemma with meaning?
@ACB,
ACB;106437 wrote:When a statistically unlikely event occurs, we need to decide whether it is more likely to be due to pure chance or to some other factor. To do this, we calculate the respective probabilities. For example, if successive throws of a die continue to result entirely in sixes, there comes a point at which we start to believe that the run is not due entirely to chance, and that there are other factors involved, e.g. a weighted die or some kind of sleight-of-hand. The tipping point in our belief may vary from one person to another, but I think everyone would agree that, if the run of consecutive sixes is long enough, pure chance ceases to be a serious possibility, and it becomes overwhelmingly probable that some other factor is in play.
The point at which we cease to believe in pure chance as a plausible explanation will depend on the statistical probability of the sequence of events. Now, this probability will vary vastly according to whether we adopt a third-person or a first-person perspective. Given a world population of six billion, it is millions (perhaps hundreds of millions) of times less likely that I will witness an improbable event (e.g. a person throwing 20 consecutive sixes) than that someone somewhere will witness it. The question is therefore: When calculating whether pure chance is the best explanation, should I adopt a 3rd-person or a 1st-person perspective? At first sight, the obvious answer would seem to be that the objective, 3rd-person perspective must be the right one. But I am not so sure....
Imagine, as a thought experiment, that the universe, and its population, were many orders of magnitude larger. Imagine that you entered a vast lottery in which an astronomical number of people participated (let's make it a really spectacular figure - say 10 to the power 100), and that you won first prize on the first occasion it was held. From a 3rd-person perspective, there would be nothing at all remarkable about this; someone would have to win. But from your 1st-person perspective, it would be amazing beyond words!
In such circumstances, could you honestly accept the 'objective' 3rd-person view, or would you look at it from your own perspective and believe that (to put it crudely) "something strange is going on"? In other words, would you consider, as a better explanation, the possibility of some (perhaps unknowable) metaphysical reason why you had been "favoured"? Or is there some other, more prosaic, alternative? I cannot think of one; any conceivable explanation from the 3rd-person view (e.g. "the lottery was rigged in your favour") runs up against the problem of why you should have been singled out from such a vast number of people.
So is this an argument for some kind of solipsism? Maybe not 'strong' solipsism (i.e. "only I exist") but a 'weak' variety (something like "other people do exist, but I exist in a unique way")? It is easy to caricature any kind of solipsism as a form of vanity, but I hope I have demonstrated that there is a serious point at issue here, even if you disagree with my argument.
Any comments and/or refutations?
Interesting. I doubt there is a problem with perspectives here. What there is a difference between the probability of in your example are these two propositions:
[INDENT]1. Someone won the lottery.
(∃x)(Wx)
2. ACB won the lottery.
Wa
[/INDENT](1) is not very improbable. In fact if we stipulate that someone won, it has a probability of 1.
(2) is very unlikely and it would be wise to consider alternative explanations such as a "they are trying to trick me" theories.
It seems to me that mathematically speaking (2) is just as unlikely seen from some 3rd person perspective (whatever that means) as seen from a 1st person perspective. The chance is (simplifying) 1/10^100.
There may be evidence for a "the lottery was rigged in your favour" theory. Suppose that your good friend works for the lottery company in the technical section. He may have been able to influence the choice of the winner. But did not choose himself because that would look suspicious.
@Emil,
Emil;106684 wrote:It seems to me that mathematically speaking (2) is just as unlikely seen from some 3rd person perspective (whatever that means) as seen from a 1st person perspective. The chance is (simplifying) 1/10^100.
It would be 1/10^100 from another person's point of view if they had somehow "specified" me beforehand (e.g. by mentioning my name, or maybe just by thinking about me). But if they had not "specified" me in any way, I would merely be "someone", and the probability of "someone" winning is 1. (Strange how just
thinking about me alters the probability so greatly!)
Emil;106684 wrote:There may be evidence for a "the lottery was rigged in your favour" theory. Suppose that your good friend works for the lottery company in the technical section. He may have been able to influence the choice of the winner. But did not choose himself because that would look suspicious.
But the fact that
I, out of all the entrants, have such an influential friend is itself extremely improbable and requires explanation. Even if it supposed that a significant proportion of the entrants have friends in the technical section, and each such entrant is favoured by his own friend, it needs to be explained why it is I who just happen to have the
most influential one.
@ACB,
ACB;106698 wrote:It would be 1/10^100 from another person's point of view if they had somehow "specified" me beforehand (e.g. by mentioning my name, or maybe just by thinking about me). But if they had not "specified" me in any way, I would merely be "someone", and the probability of "someone" winning is 1. (Strange how just thinking about me alters the probability so greatly!)
I don't understand. I don't see how the perspective change changes anything.
ACB;106698 wrote:But the fact that I, out of all the entrants, have such an influential friend is itself extremely improbable and requires explanation. Even if it supposed that a significant proportion of the entrants have friends in the technical section, and each such entrant is favoured by his own friend, it needs to be explained why it is I who just happen to have the most influential one.
Lots of things require explanations. So what?
@Emil,
Emil;106703 wrote:I don't understand. I don't see how the perspective change changes anything.
From someone else's point of view I am not of special significance, whereas from my point of view I am. For someone else, my win is not a 'coincidence', as it does not 'coincide' with anything. For me, however, it does coincide with something, namely my viewpoint.
Emil;106703 wrote:Lots of things require explanations. So what?
Yes, but the purpose of this thread is to decide what explanation is appropriate. Pure chance or not?
@ACB,
ACB;106728 wrote:From someone else's point of view I am not of special significance, whereas from my point of view I am. For someone else, my win is not a 'coincidence', as it does not 'coincide' with anything. For me, however, it does coincide with something, namely my viewpoint.
Just that? That does not seem interesting to me. What is the problem?
@Emil,
Emil;106731 wrote:Just that? That does not seem interesting to me. What is the problem?
I don't know - maybe I am just confused. I don't think this thread is worth continuing any further. :surrender:
@ACB,
ACB wrote:It would be 1/10^100 from another person's point of view if they had somehow "specified" me beforehand (e.g. by mentioning my name, or maybe just by thinking about me). But if they had not "specified" me in any way, I would merely be "someone", and the probability of "someone" winning is 1. (Strange how just thinking about me alters the probability so greatly!)
Perspective does not change probability.
Assuming in your thought experiment everyone had equal chance of winning, and the lottery could be won, the probability that each person individually may win
does not change with perspective, nor does the probability that the lottery will be won. These are two distinct things and perspective is not changing anything - perspective merely
reveals another way of looking at the lottery.
Quote:Imagine, as a thought experiment, that the universe, and its population, were many orders of magnitude larger. Imagine that you entered a vast lottery in which an astronomical number of people participated (let's make it a really spectacular figure - say 10 to the power 100), and that you won first prize on the first occasion it was held. From a 3rd-person perspective, there would be nothing at all remarkable about this; someone would have to win. But from your 1st-person perspective, it would be amazing beyond words!
Your feelings have nothing to do with probability.
Quote:In such circumstances, could you honestly accept the 'objective' 3rd-person view, or would you look at it from your own perspective and believe that (to put it crudely) "something strange is going on"? In other words, would you consider, as a better explanation, the possibility of some (perhaps unknowable) metaphysical reason why you had been "favoured"? Or is there some other, more prosaic, alternative? I cannot think of one; any conceivable explanation from the 3rd-person view (e.g. "the lottery was rigged in your favour") runs up against the problem of why you should have been singled out from such a vast number of people.
The fact that something may have altered the lottery does not change the fact that the flat probability of someone winning the lottery is 1/10^100. If this changes, because of whatever reason (perhaps because someone only in the state of Arkansas would be picked, for instance), it is not the probability, but neither feeling nor perspective have any influence on this. It is a matter of asking the right questions, finding out the truth, and then calculating the probability accordingly.
@ACB,
Perhaps it only appears to be different from the 1st and 3rd party perspective because from the first person perspective, it
matters to you whether it is you or someone else who wins.
If you were perfectly disinterested in winning, in other words, it was of no consequence to you whether you won, or someone else won, there would be no difference whether it was you or another.
So the difference in perspectives is due to your attachment to the outcome.
@jeeprs,
jeeprs;106924 wrote:Perhaps it only appears to be different from the 1st and 3rd party perspective because from the first person perspective, it matters to you whether it is you or someone else who wins.
If you were perfectly disinterested in winning, in other words, it was of no consequence to you whether you won, or someone else won, there would be no difference whether it was you or another.
So the difference in perspectives is due to your attachment to the outcome.
Exactly. Whether you're interested in winning or not does not
change probability - it simply
reveals a new way to consider the same lottery.
@ACB,
But it is illuminating in that it makes you reflect on how ubiquitious the effect of
expectation is on your perception. I imagine we are making judgements of this nature at almost every moment.
@jeeprs,
jeeprs;106928 wrote:But it is illuminating in that it makes you reflect on how ubiquitious the effect of expectation is on your perception. I imagine we are making judgements of this nature at almost every moment.
It is most definitely interesting, I just don't think that was the point of ACB's initial post - he thought perspective actually altered probability in some way.
But yeah, there's definitely much to be said on perspective, if we want to take the discussion in that direction. I think that would be ACB's decision.
@Emil,
Are you implying that in order for one to fully understand an argument, they must formalize it? If so, why would you think this?
@Zetherin,
Zetherin;106940 wrote:Are you implying that in order for one to fully understand an argument, they must formalize it? If so, why would you think this?
That's not what I wrote. I wrote must be able to formalize it. If you can formalize it, that's a very good reason to believe that you understand it fully. Though it's possible that you may understand it fully without being able to formalize it. I prefer to be certain.
@Emil,
Emil;106943 wrote:That's not what I wrote. I wrote must be able to formalize it. If you can formalize it, that's a very good reason to believe that you understand it fully. Though it's possible that you may understand it fully without being able to formalize it. I prefer to be certain.
Sorry if you thought that I was implying that's what you wrote, I wasn't. I was very conscious of how I phrased my question, and I was just asking if the aforementioned implication was present or not. It wasn't, thanks.
(I was just wanted to be clear as to what you meant)
@Zetherin,
Zetherin;106947 wrote:Sorry if you thought that I was implying that's what you wrote, I wasn't. I was very conscious of how I phrased my question, and I was just asking if the aforementioned implication was present or not. It wasn't, thanks.
(I was just wanted to be clear as to what you meant)
Though I have been thinking about some writing style that allows me to write arguments in 'plain english' and keep the formalization around for people who are interested in that. I haven't found a good way yet. One hypothetical way is to have some box with the formalization pop up when the cursor is above the argument. That seems like a good idea but I cannot do it technically yet.
@jeeprs,
This may be a related in some way.
How about this - it's a variation of another puzzle;
If you entered a draw type of game, where you were given your number according to the order in which tickets were purchased...50th ticket is "number 50", and so on...and after all the tickets are sold, the winning number is secretly given by machine, and then
1/ the person calling the numbers knows the winning number, and he always chooses to call a losing number, eliminating that person.
2/ you are repeatedly allowed to change your number, choosing any of the available numbers, IOW, you can choose to take someone else's number, after every call - solely at your discretion
Is it ever an advantage to switch numbers ?
Stumble It!
Tweet This
Bookmark on Delicious
Share on Facebook
Share on MySpace