71–80 of 81 posts
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0 and 1 are really extreme probabilities. It's often better to think of a probability of 0.001 being closer to 0.5 than to 0. As odds ratios it's easy to see that 999:1 is closer to 1:1 than to infinity:1. 0 probability means that even infinitely many pieces of evidence will not change your assessment: no matter how many heads you see restored from cryogenic storage, you will still believe that the probability is 0,…
> 0 probability means that even infinitely many pieces of evidence will not change your assessment Well no, this isn’t really what probability 0 means. An event is not impossible if it has a probability of 0. More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. In the Bayesian view, your probability…
Earlier quoted context omitted.
0 and 1 are really extreme probabilities. It's often better to think of a probability of 0.001 being closer to 0.5 than to 0. As odds ratios it's easy to see that 999:1 is closer to 1:1 than to infinity:1. 0 probability means that even infinitely many pieces of evidence will not change your assessment: no matter how many heads you see restored from cryogenic storage, you will still believe that the probability is 0,…
> 0 probability means that even infinitely many pieces of evidence will not change your assessment Well no, this isn’t really what probability 0 means. An event is not impossible if it has a probability of 0. More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. In the Bayesian view, your probability…
Bayesian probability absolutely tells you what to do when evidence of an event arises: Bayes' theorem precisely tells you how to update your certainty when evidence arises (and "seeing" an event is only fairly strong but not certain evidence of its occurrence).
To me fear of death is a sign of not really having been born yet. If you can't make 50 years worthwhile, you can't make 50000 years worthwhile, and if you can't cope with being limited to 80 years or so, you will not be able to cope with the heat death of the universe. It also stands to reason that if you feel it's impossible to give up 100 years of grown personality and memories, it will be even harder and more pain…
If we reverse this logic, if 50 years are enough, then so are 5 years or 5 months or 5 days. Or is "50 years" a magical number where the rules of the game change, so that the fourty-nineth year can make a difference but the fifty-first can't?
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0.001 is closer to 0 than 0.003 ;) All probability's have error bars, so 0 +/ 10e-20 is still very much 0.
Thanks, I can count :) Of course 0.001 is closer to 0 than 0.003, but my point is that linear distance is not a very good way of comparing probabilities-as-degrees-of-certainties: rather than differences of probabilities one should consider the ratios of odds ratios (or differences of log-odds-ratios) because these better represent how we update our certainty in the light of evidence. Frequentist probabilities can ha…
Anyway, my point is not that you should interpret probability functions in a linear fashion just that non linear interpretations are not nessisarily more accurate.
Suppose I am playing a chess I have non zero odds for a 2 win streak, but the odds of winning 1 googleplex games in a row is 0. Not becase it’s some probability ^ a googleplex but rather I am not going to play that many games. Sure, you might say their are some error bars on that zero, and error bars on those error bars etc, but still the direct estimate is still a 0 probability.
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Thanks, I can count :) Of course 0.001 is closer to 0 than 0.003, but my point is that linear distance is not a very good way of comparing probabilities-as-degrees-of-certainties: rather than differences of probabilities one should consider the ratios of odds ratios (or differences of log-odds-ratios) because these better represent how we update our certainty in the light of evidence. Frequentist probabilities can ha…
Bayesian has direct error bars and error bars on your error bars, and error bars on the ... It’s however generally ignored. Edit: I believe I preformed this experiment which updates my prior probability. Anyway, my point is not that you should interpret probability functions in a linear fashion just that non linear interpretations are not nessisarily more accurate. Suppose I am playing a chess I have non zero odds fo…
Was I supposed to understand that from your previous comment? I didn't, and I don't see how I could have.
> their are some error bars on that zero
There'd better be, because the true probability is somewhere within those error bars: I'd be very confident (but not certain!) that the true probability is not zero. What if you turn out to have been imagining all your life up till now, a googleplex is much less than you think, and you're actually an immortal chess-playing machine? That's unlikely, but I'm fairly sure the probability is not zero.
Zero is a probability (unlike the title of the page I linked to) but it's a very special one, mostly of theoretical interest.
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Bayesian has direct error bars and error bars on your error bars, and error bars on the ... It’s however generally ignored. Edit: I believe I preformed this experiment which updates my prior probability. Anyway, my point is not that you should interpret probability functions in a linear fashion just that non linear interpretations are not nessisarily more accurate. Suppose I am playing a chess I have non zero odds fo…
> Anyway, my point is not that you should interpret probability functions in a linear fashion just that non linear interpretations are not nessisarily more accurate. Was I supposed to understand that from your previous comment? I didn't, and I don't see how I could have. > their are some error bars on that zero There'd better be, because the true probability is somewhere within those error bars: I'd be very confident…
You are welcome to try and come up with a possibility, but really it's 0 with error bars on something not conceivable.
Edit, by which I mean if my understanding if the game is flawed then the estimate is less accurate, but that does not directly improve the odds. Thus that’s an error bar as again it does not directly change the actual probability.
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> Thought experiments of this kind are dissimilar to say Einstein fantasizing about elevators in that they do not yield insight over and beyond that which is already readily apparent. They do. That's why you don't want to partake in them, because it's pretty obvious that you would say cryo-preserved brain has more chance of being restored. And of course you would judge cryo-restoration to be more probable than a seat…
> They do. That's why you don't want to partake in them [...] No, this thought experiment does not yield new insights. This conversation went roughly as follows: jacquesm: "I assume that action A is impossible as far as we know, therefore the probabilities of A1 respectively A2 happening are both 0." ALittleLight: "Assumimg A were not impossible, would A1 or A2 be more probable?" (where A= "restoring a dead brain" ,…
You're correct that thought experiment I posed cannot offer analytic insight - it doesn't tell us anything about the mechanism for restoring life to frozen people or allow us to update our beliefs as to the likelihood of this being possible. The thought experiment does offer an introspective insight into beliefs that you already hold though - specifically that you believe there is a non-zero possibility of cryogenic enabled resurrection occurring.
Let's work through the thought experiment with my answer (M) and the answer of an imaginary interlocutor (I).
Experiment: In 100 years someone long dead is restored to life. Is this person a mummy or a cryogenics patient?
I: Could be either with equal probability. I believe that both are impossible and therefore I'm ambivalent about the choice.
M: I'd guess the cryogenic patient. While I think the odds of both are low, the odds of the cryogenic patient are better in my estimation. Because I believe that the odds of the cryogenics patient are greater than the odds of the mummy, I logically cannot believe that both are zero.
In other words, if you aren't ambivalent about the choice, you cannot logically hold the belief that both are impossible. If you are ambivalent, then you are free to think that both are impossible. Because I suspect you have an intuitive reluctance to claim ambivalence, I doubt you really think that the odds of cryogenic resurrection are zero.
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Brother Cavil. I really feel like that - stuck in a body of flesh: limited in its sensory capability, very fragile, almost impossible to repair.
I don't know man, the human body is an incredible machine... I think it's more six of one, half dozen of the other. The one truth you can count on is: there's gonna be tradeoffs.
Earlier quoted context omitted.
> 0 probability means that even infinitely many pieces of evidence will not change your assessment Well no, this isn’t really what probability 0 means. An event is not impossible if it has a probability of 0. More importantly probability informs you about how many times you should expect an event to occur, not what to do with this information if the event does or does not arise. In the Bayesian view, your probability…
I think there's a legitimate question as to whether every real number is actually physically real. [1] It seems credible that our universe can only actually present us with a finite number of possible sensory experiences, in which case an event with probability 0 actually couldn't ever happen. That said, even if the universe can present you with an infinity of observations you can certainly only consider a finite num…