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Post by phludowin on Mar 29, 2018 6:25:42 GMT
I got the 0.002% using Bayes where the prior is unknown but the conditionals and posterior is known. You can just plug: 0.95 = 1t/(1t+(1−t)(0.000001)) into HERE. Generally, you use Bayes where the prior and conditionals are known in order to find the posterior, but you can also use a known posterior and conditionals to find the prior. That's what I'm getting at with the OP thought experiment. We know the conditionals P(flips|trick) and P(flips|not trick). If you say that it will take, say, 20 flips to make you 95% sure it's a trick coin, you use .95 as your posterior, and 0.000001 (probability of 20 head flips given fair) as your second conditional to find the prior T. I believe that we don't disagree so much after all; but that we have trouble with communication. In your formula, what does 1t stand for? Is it P(T)? Case in point: I think you need to read Cash's post because now you're just arguing with the scenario of the experiment rather than trying to understand the points I'm trying to illustrate with it. Nobody argues with Copenhagen by saying we don't put cats in poison-filled boxes. I read theoncomingstorm 's post. And I admit that I don't like hypotheticals or multiple-choice questions. Science works with models, and models simplify; but they should still have a relation to reality. Speaking of simplification: Copenhagen is a city in Denmark, not an interpretation of quantum physics. This is another example of you using language that is probably understandable for native speakers of English who went to an English speaking university; but might be challenging for people to whom English is the third language (like me). Bottom line: Maybe I am not well equipped to have these discussions with you; or you could start posting in German.
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Post by Eva Yojimbo on Mar 29, 2018 6:56:48 GMT
I got the 0.002% using Bayes where the prior is unknown but the conditionals and posterior is known. You can just plug: 0.95 = 1t/(1t+(1−t)(0.000001)) into HERE. Generally, you use Bayes where the prior and conditionals are known in order to find the posterior, but you can also use a known posterior and conditionals to find the prior. That's what I'm getting at with the OP thought experiment. We know the conditionals P(flips|trick) and P(flips|not trick). If you say that it will take, say, 20 flips to make you 95% sure it's a trick coin, you use .95 as your posterior, and 0.000001 (probability of 20 head flips given fair) as your second conditional to find the prior T. I believe that we don't disagree so much after all; but that we have trouble with communication. In your formula, what does 1t stand for? Is it P(T)? Case in point: I think you need to read Cash's post because now you're just arguing with the scenario of the experiment rather than trying to understand the points I'm trying to illustrate with it. Nobody argues with Copenhagen by saying we don't put cats in poison-filled boxes. I read theoncomingstorm 's post. And I admit that I don't like hypotheticals or multiple-choice questions. Science works with models, and models simplify; but they should still have a relation to reality. Speaking of simplification: Copenhagen is a city in Denmark, not an interpretation of quantum physics. This is another example of you using language that is probably understandable for native speakers of English who went to an English speaking university; but might be challenging for people to whom English is the third language (like me). Bottom line: Maybe I am not well equipped to have these discussions with you; or you could start posting in German. 1t = t is the prior probability of finding a trick coin; 1 = 100% all heads given trick coin. It's just a simplified, algebraic version of the dividend of Bayes. There are plenty of scientific thought experiments and hypotheticals that have less relation to reality than the one I devised here. Sorry about the confusion RE Copenhagen, but I thought the cat reference (and general science context) would make it clear what I meant. I wish I spoke German... it would make understanding Wagner and Goethe easier.
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Post by phludowin on Mar 29, 2018 7:41:24 GMT
Sorry about the confusion RE Copenhagen, but I thought the cat reference (and general science context) would make it clear what I meant. I wish I spoke German... it would make understanding Wagner and Goethe easier. No problem. I got the reference to Copenhagen because someone started a thread here, which mentions the Copenhagen interpretation. Otherwise I would have googled it. But my point still stands: Not everybody learned to speak English in a science classroom.
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Post by Deleted on Mar 29, 2018 9:28:15 GMT
Mar 29, 2018 2:28:07 GMT 1 Eva Yojimbo said: I'd highly encourage you to read that QM thread I linked to because this is a whole different can of worms. I do not believe the wavefunction is probabilistic. I think we treat it is as probabilistic because that's how we experience it. I used this example in that QM thread: imagine you have a line of gunpowder. The gunpowder forks into three paths. You are the fire, the gunpowder is the wavefunction, the split is the measurement. As the fire, you will experience having gone left, middle, OR right after the split/measurement. You can ask "what's the probability of me going left VS going middle or right?" and produce an answer of "33%," but the truth is that the probability of you going left, right, AND middle is 100%. You will go all three ways, even though the "you" after the split will have experienced only having gone left, middle, OR right. It will seem to you as if the other two "paths" have disappeared. But I have to stress that the probabilistic nature of QM is entirely dependent on interpretation, not science. The equation that models how quantum systems behave (Shrodinger Wave Equation) is deterministic, and you have to interpret it by adding to it a stochastic collapse in order to make it probabilistic. The simplest interpretation is Many-Worlds, which just takes the Shrodinger Wave Equation as a complete description of QM, and like I said above, in such situations it's best to just assume the simplest explanation until unique evidence is produced that favors the more complex explanations. So you can't really turn to QM in order to make the argument that probability is inherent in reality. In my strong opinion, probability only exists in the mind. It expresses various states of ignorance about reality. Any time we're using probability, we're acknowledging there's some facet of reality we don't know or can't account for. Good stuff, I did have a glance at that thread yesterday, I might have a closer look when I get into the right 'head space'. As far as the deterministic or probabilistic nature of the wave function is concerned, I think it really depends on what lens you are looking at it from, which I think that is what you are getting at. Your arguments make sense, but only when we assume all possibilities will happen, and personally, I am a bit wary of introducing new stuff into the model that can't be testable. I'm not saying you are wrong but I'm not saying you are right either. It is a neat way of thinking about it though, and is probably a good way to get one's head around it, but as I say, I have my reservations as I sometimes feel that we've just replaced the 'god of the gaps' with the 'everything of the gaps' with the 'Many Worlds' interpretation. But I know where you are coming from. On a sidenote, I'm curious, it's been a long while since I last played poker, but how would you even work them out afterwards without huge samples of data? Well I guess you must be playing online and datamining? But even then, instinctively the maths feels like it would very quickly get extensive and laborious to say the least, taking all factors and data into account. Well... unless you had a tool to help? Am I answering my own questions here? But if you had a tool and you are playing online, why not just do the maths in real time?
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Post by Eva Yojimbo on Mar 30, 2018 1:56:35 GMT
Mar 29, 2018 2:28:07 GMT 1 Eva Yojimbo said: I'd highly encourage you to read that QM thread I linked to because this is a whole different can of worms. I do not believe the wavefunction is probabilistic. I think we treat it is as probabilistic because that's how we experience it. I used this example in that QM thread: imagine you have a line of gunpowder. The gunpowder forks into three paths. You are the fire, the gunpowder is the wavefunction, the split is the measurement. As the fire, you will experience having gone left, middle, OR right after the split/measurement. You can ask "what's the probability of me going left VS going middle or right?" and produce an answer of "33%," but the truth is that the probability of you going left, right, AND middle is 100%. You will go all three ways, even though the "you" after the split will have experienced only having gone left, middle, OR right. It will seem to you as if the other two "paths" have disappeared. But I have to stress that the probabilistic nature of QM is entirely dependent on interpretation, not science. The equation that models how quantum systems behave (Shrodinger Wave Equation) is deterministic, and you have to interpret it by adding to it a stochastic collapse in order to make it probabilistic. The simplest interpretation is Many-Worlds, which just takes the Shrodinger Wave Equation as a complete description of QM, and like I said above, in such situations it's best to just assume the simplest explanation until unique evidence is produced that favors the more complex explanations. So you can't really turn to QM in order to make the argument that probability is inherent in reality. In my strong opinion, probability only exists in the mind. It expresses various states of ignorance about reality. Any time we're using probability, we're acknowledging there's some facet of reality we don't know or can't account for. Good stuff, I did have a glance at that thread yesterday, I might have a closer look when I get into the right 'head space'. As far as the deterministic or probabilistic nature of the wave function is concerned, I think it really depends on what lens you are looking at it from, which I think that is what you are getting at. Your arguments make sense, but only when we assume all possibilities will happen, and personally, I am a bit wary of introducing new stuff into the model that can't be testable. I'm not saying you are wrong but I'm not saying you are right either. It is a neat way of thinking about it though, and is probably a good way to get one's head around it, but as I say, I have my reservations as I sometimes feel that we've just replaced the 'god of the gaps' with the 'everything of the gaps' with the 'Many Worlds' interpretation. But I know where you are coming from. For the two bolded parts: Yes, I'm saying the determinism/indeterminism of QM is all a matter of interpretation rather than math or empiricism. All of the interpretations are experimentally indistinguishable. To be clear, it's actually most of the OTHER interpretations, not many-worlds, that are "introducing new stuff into the model." Many-worlds is the interpretation that takes the basic model and says "that's it, that's all there is to QM." That's what I mean when I say it's the simplest explanation. The more famous Copenhagen is adding a stochastic wavefunction collapse, and the various hidden variable theories are adding... well, hidden variables. I linked to these in that other thread, but two good laymen's explanations of this is from physicist Sean Carroll: www.preposterousuniverse.com/blog/2014/06/30/why-the-many-worlds-formulation-of-quantum-mechanics-is-probably-correct/ and here: linkOn a sidenote, I'm curious, it's been a long while since I last played poker, but how would you even work them out afterwards without huge samples of data? Well I guess you must be playing online and datamining? But even then, instinctively the maths feels like it would very quickly get extensive and laborious to say the least, taking all factors and data into account. Well... unless you had a tool to help? Am I answering my own questions here? But if you had a tool and you are playing online, why not just do the maths in real time? Afterwards it's just about assigning a range of hands, assigning probabilities to those hands, and then working out my equity, and then figuring my best play given that range and equity. This is mostly educated guesswork; I'm usually not drawing from huge samples of data, though I am good about taking notes on players (that helps me inform the range I give them and the probabilities I assign to hands). The math is laborious if you're very unused to it, but I've developed various short-hands over the years to make it easier. Plus, because similar circumstances crop up a lot after a while stuff like the number of possible overpair/overcard combinations there are becomes pretty automatic. I used to work with data mining tools, but mostly just to keep track of my own play and tendencies. I kinda gave them up over the years as I never could make a ton of use out of them. Perhaps if I hadn't gotten so used to doing it the manual way I might've made more of an effort, as I can see how someone dedicated to learning from them could get better. I guess I was just too lazy.
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Post by general313 on Mar 30, 2018 3:03:41 GMT
I wouldn't go that far. There's some pretty important real world consequences to the second law of thermodynamics, where descriptions of entropy are tied to probability and randomness. I'm not certain why you think this contradicts my post; I didn't imply that probability (in general) doesn't have real-world consequences. If you're suggesting that the probability/randomness of thermodynamics is inherent in reality, then I'd say that like with QM this is actually a matter of interpretation. I don't know as much about thermodynamics (really not much at all) as I do QM, but I do know that Maximum Entropy Thermodynamics interprets thermodynamics in terms of inferences. Yudkowsky has a post explaining this, as interpreting thermodynamics as observer-dependent. Though I haven't read it myself, I usually find myself agreeing with him. I also found with a quick Google search that Sean Carroll (another guy I usually agree with) recently published a paper on this and discussed it on his blog. I'm posting these links as much for myself as for you so I'll remember to read them tomorrow. I’m on vacation for a week so my posting will be very limited until after that.
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Post by Eva Yojimbo on Mar 30, 2018 7:07:18 GMT
I'm not certain why you think this contradicts my post; I didn't imply that probability (in general) doesn't have real-world consequences. If you're suggesting that the probability/randomness of thermodynamics is inherent in reality, then I'd say that like with QM this is actually a matter of interpretation. I don't know as much about thermodynamics (really not much at all) as I do QM, but I do know that Maximum Entropy Thermodynamics interprets thermodynamics in terms of inferences. Yudkowsky has a post explaining this, as interpreting thermodynamics as observer-dependent. Though I haven't read it myself, I usually find myself agreeing with him. I also found with a quick Google search that Sean Carroll (another guy I usually agree with) recently published a paper on this and discussed it on his blog. I'm posting these links as much for myself as for you so I'll remember to read them tomorrow. I’m on vacation for a week so my posting will be very limited until after that. No problem. Enjoy your vacation!
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Post by goz on Mar 30, 2018 22:00:29 GMT
Having read this thread, I have come to the conclusion that Sweet Baby Jesus is in charge of ALL coin flipping ALL around the world for ALL time end even butterside down events.
He is such a trickster!
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Post by general313 on Apr 12, 2018 0:14:31 GMT
I’m on vacation for a week so my posting will be very limited until after that. No problem. Enjoy your vacation! Thanks! I'm back. Pele put on an impressive display of lava fountains. Looking back on the thread, I think I misinterpreted an earlier post of yours, that I took to mean that probability only exists in the mind, hence my saying "I wouldn't go that far". Anyway, we probably don't want to go down a Platonic rabbit hole about perfect spheres and stuff like that.
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Post by Eva Yojimbo on Apr 12, 2018 1:46:38 GMT
No problem. Enjoy your vacation! Thanks! I'm back. Pele put on an impressive display of lava fountains. Looking back on the thread, I think I misinterpreted an earlier post of yours, that I took to mean that probability only exists in the mind, hence my saying "I wouldn't go that far". Anyway, we probably don't want to go down a Platonic rabbit hole about perfect spheres and stuff like that. Nice! Glad to hear you enjoyed it! The "probability is in the mind" statement can be confusing because it seems to suggest we just make up probabilities. I'm not suggesting that, merely that probability seems to be a result of our combined knowledge and ignorance about reality; but without that ignorance, there is no probability.
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