|
|
Post by general313 on Feb 16, 2020 17:49:48 GMT
I'll try to keep that in mind next time I forget to put in winter window-washer fluid in my car and I lose the ability to clean my windshield. I haven't said that priors aren't important in some cases, and your coin-flip experiment is a good example. Cladistics and other sciences involving DNA matching would fall in this category. But in those others where we throw out the entirety of the old thinking, including the priors, then we are no longer using anything like Bayes's theorem, except perhaps a trivial reduction of it. To capture Einstein's imagination in his relativity thought experiments, you have to look elsewhere than Bayes. QM is different than Maxwell's equations (even when viewing the latter from the perspective of the 19th century) because it's so bizarre and counter-intuitive. It may be urban legend that Feynman said "Anyone who claims to understand quantum theory is either lying or crazy" but I think there's a lot of truth in it regardless of whether it's an accurate quote. Until scientists develop some kind of experiment that can shed light on some of these interpretations it remains beyond the realm of science. I'm a great fan of Occam's Razor but it shouldn't be confused as evidence, rather it's a good guide when we lack actual evidence. The atom has turned out to be much more complicated than Rutherford anticipated, so nature isn't always as simple as we would like it to be (at some particular moment). Meanwhile, that these interpretations remain unresolved isn't stopping semiconductor device engineers from building faster and better chips. The point with temperature is that it doesn't exist on any fundamental level of physics. Rather, it's an estimation of the average kinetic energy within a system. Break that down and all that actually exists is lots of particles moving at certain speeds. The notion of "average" and what's considered a "system" are ways in which our brain categorizes things on larger levels than the fundamental one. They're mental concepts about reality not found in fundamental descriptions of reality: "useful fictions." You do realize that once evidence modifies a prior the old prior essentially "doesn't exist" anymore, yes? All you're doing is using a kind of hindsight bias to say the prior never mattered, and that's just silly. Yeah, once we find an experiment that provides us the "Given E(vidence), the P(robability) of H(ypothesis) is ~100%; Given E, the P of ~H is ~0%." evidence then the old prior doesn't matter because the new evidence overwhelms whatever it is. I'd argue that's neither the situation in the vast majority of science, nor the vast situations in everyday life. Nearly everything you do in your everyday life is not a product of new evidence provided by some definitive experiment, but is a product of priors built from past evidence. If you walk out your door without fearing an airplane will fall on your head, that's because your "prior" experience of planes not falling on your head, not because of some rigorous new experiment you did before you walked out your door to prove a plane won't fall on your head. If you were to come home and find your home ransacked and things gone, your first instinct is "human burglars" not "alien burglars," and that's a product of priors, not some rigorous investigation to rule out aliens. I could come up with a near infinite examples of why our priors are crucially important in everyday life. Besides, even experiments of the kind that proved Relativity are STILL operating on Bayes. That "Given E(vidence), the P(robability) of H(ypothesis) is ~100%; Given E, the P of ~H is ~0%" is still Bayesian in nature. QM is "bizarre and counter-intuitive" when you try to force our intuitions about how the world is onto QM rather than just taking what QM say is happening seriously. It's amazing how science has such a history of shattering human intuitions, yet here are in the 21st century and scientists, the very people using the discipline that's supposed to minimize human biases, are still clinging to those biases and intuitions for no good reason when the math, and what it says about reality, are staring us in the face. Occam's razor is more than just "a guide," it's a mathematically provable notion that simpler hypotheses are more probable than others (look up Solomonoff Induction). The point is, in QM we have a model that perfectly describes how particles behave. We call it the "wavefunction" (or Shrodinger's Wave Equation). If we take that as it is, there are many-worlds. Simple as that. What science has done in the 20th century have added things to that to make the "many-worlds" go away. Not because an experiment says they don't exist (experiments say they do), not because they math says they don't exist (the math says they do), but because they don't like them intuitively. Sorry, but that's stupid, and it's not less stupid because it's fueled by bias and intuition, and it's not less stupid than adding unicorns to electricity. Yes, temperature is an emergent property of collections of particles, and less "fundamental". Deciding that that makes it somehow less real is a philosophical position. You could view human intelligence as a useful fiction if you like, meanwhile I will continue to make sure I stay warm in winter. You didn't address at all my point about Einstein's imagination and the crucial role it played in his breakthrough theories. I suppose you can try to fit Bayes into all sorts of scientific questions but it isn't necessarily the best tool, just like one could participate in the Tour de France on a mountain bike but you're unlikely to win the race with that bicycle, even if you're Lance Armstrong. Thanks for the intro to Schrodinger's Wave Equation. I am quite familiar with it, as I had to solve differential equations with it in college (in physics exercises involving the hydrogen atom). As for interpretations of QM, let's just say that the jury is still out, with many experts in the field in disagreement.
|
|
|
|
Post by gadreel on Feb 16, 2020 18:48:03 GMT
It's amazing you always start running out of "interest" when someone is proving you wrong. You suffered the same sudden "lack of interest" the last time we discussed this at precisely this same point. Your "cursory inspection" is wrong. P(B|~A) is the probability Monty randomly opened every door except D100. Another way to ask that question is "what's the probability Monty randomly leaves ANY door unopened?" The answer is 1/99, or .01. Again, my issue with your 100-door variation, or 52-card variation, isn't that you can't get the right answer and intuitively understand why that is; my problem is that you can't explain why that is. You just keep repeating "it is so" without explaining why. What's so hard/complicated about saying: "Given the right card/door is my original choice (.02/.01, respectively), the probability host eliminated 50 cards/98 doors leaving that card/door is .02/.01, respectively; given the right card/door is the the last choice (.02/.01, respectively), the probability the host eliminated 98 doors/50 cards leaving that door/card is 1." Here's the difference in our views, as I see it. You're wanting to start from a position of saying the probability the prize is behind D1 is 1%, the probability it's in D2-100 is 99%, and when we eliminate D2-99 the 99% just "transfers" to D100. This isn't what happens. What happens is that after D2-99 are eliminated you have a 50/50 shot given no additional information; but the intention (or lack of intention) behind the host's choice IS additional information. That additional information is modeled when we think conditionally: If I chose right, the host randomly opened doors, and the probability of him randomly leaving only D100 is 1/99. If I chose wrong, the host DIDN'T randomly open doors, and the probability of him only leaving D100 closed is 1. You just gloss over this reasoning in your version. I don't know why you're doing this other than that you don't understand it. Have you tried pressing CTRL+ALT+DEL ? I know I have, and still no explanations from you. Be forewarned, improving your English won't help in cases where people do not want to understand what you say. I have a much lower tolerance for needless repetition than most people here. That's all. Try a key or rhythm shift to keep it interesting. Holy shit you love being ignorant.
|
|
|
|
Post by Arlon10 on Feb 16, 2020 20:06:20 GMT
Have you tried pressing CTRL+ALT+DEL ? I know I have, and still no explanations from you. Be forewarned, improving your English won't help in cases where people do not want to understand what you say. I have a much lower tolerance for needless repetition than most people here. That's all. Try a key or rhythm shift to keep it interesting. Holy shit you love being ignorant. Who? Me? Why? Is it because I didn't show you how to solve the Monty Hall problem using Bayes' Theorem? Neither did Eva Yojimbo. Here's his "solution" Nice, but the probability the prize is not behind D3, P(~A), is 2/3 not 1/3. See line 3, P(A). Here is a correct application of Bayes' Theorem A is the probability prize at D3; P(B|A) is the probability Monty reveals D2 given A. Same as above. What is needed is P(B). Obviously the way P(B|~A) and P(~A) were employed above is flawed. The correct probability of B is the combination of the probability of B in three cases The prize is at D1 P(B 1)=1/2 The prize is at D2 P(B 2)=0 The prize is at D3 P(B 3)=1 The probability of B is B 1/3 + B 2/3 + B 3/3 1/6 + 0 + 1/3 = 1/2 P(B) =1/2 Now you can use this formula P(A|B) = (P(B|A) x P(A) ) / P(B) and you will get the correct answer, 2/3 That was easy enough for 3 doors, but when there are more than three doors things can get hairy. Suppose you have a hundred doors. Calculating B becomes a bit more complicated. Choosing "B" now means choosing all of the doors except the door with the prize and the contestant's door of course. Try that.
|
|
|
|
Post by gadreel on Feb 16, 2020 20:18:33 GMT
Holy shit you love being ignorant. Who? Me? Why? Is it because I didn't show you how to solve the Monty Hall problem using Bayes' Theorem? Neither did Eva Yojimbo . Here's his "solution" Nice, but the probability the prize is not behind D3, P(~A), is 2/3 not 1/3. See line 3, P(A). Here is a correct application of Bayes' Theorem A is the probability prize at D3; P(B|A) is the probability Monty reveals D2 given A. Same as above. What is needed is P(B). Obviously the way P(B|~A) and P(~A) were employed above is flawed. The correct probability of B is the combination of the probability of B in three cases The prize is at D1 P(B 1)=1/2 The prize is at D2 P(B 2)=0 The prize is at D3 P(B 3)=1 The probability of B is B 1/3 + B 2/3 + B 3/3 1/6 + 0 + 1/3 = 1/2 P(B) =1/2 Now you can use this formula P(A|B) = (P(B|A) x P(A) ) / P(B) and you will get the correct answer, 2/3 That was easy enough for 3 doors, but when there are more than three doors things can get hairy. Suppose you have a hundred doors. Calculating B becomes a bit more complicated. Choosing "B" now means choosing all of the doors except the door with the prize and the contestant's door of course. Try that. Yes you. Why?? Heaven only knows, I am guessing it is an extreme case of trying to make up for shocking lack of self esteem with trying to sound clever, but I can only go from your internet persona, I am hoping that it is a parody.
|
|
|
|
Post by Arlon10 on Feb 16, 2020 20:27:18 GMT
Who? Me? Why? Is it because I didn't show you how to solve the Monty Hall problem using Bayes' Theorem? Neither did Eva Yojimbo . Here's his "solution" Nice, but the probability the prize is not behind D3, P(~A), is 2/3 not 1/3. See line 3, P(A). Here is a correct application of Bayes' Theorem A is the probability prize at D3; P(B|A) is the probability Monty reveals D2 given A. Same as above. What is needed is P(B). Obviously the way P(B|~A) and P(~A) were employed above is flawed. The correct probability of B is the combination of the probability of B in three cases The prize is at D1 P(B 1)=1/2 The prize is at D2 P(B 2)=0 The prize is at D3 P(B 3)=1 The probability of B is B 1/3 + B 2/3 + B 3/3 1/6 + 0 + 1/3 = 1/2 P(B) =1/2 Now you can use this formula P(A|B) = (P(B|A) x P(A) ) / P(B) and you will get the correct answer, 2/3 That was easy enough for 3 doors, but when there are more than three doors things can get hairy. Suppose you have a hundred doors. Calculating B becomes a bit more complicated. Choosing "B" now means choosing all of the doors except the door with the prize and the contestant's door of course. Try that. Yes you. Why?? Heaven only knows, I am guessing it is an extreme case of trying to make up for shocking lack of self esteem with trying to sound clever, but I can only go from your internet persona, I am hoping that it is a parody. So you're not going to consider the problem with more than 3 doors? I don't blame you. My solution works for any number of doors although I'm sure you're not interested.
|
|
|
|
Post by gadreel on Feb 16, 2020 20:29:54 GMT
Yes you. Why?? Heaven only knows, I am guessing it is an extreme case of trying to make up for shocking lack of self esteem with trying to sound clever, but I can only go from your internet persona, I am hoping that it is a parody. So you're not going to consider the problem with more than 3 doors? I don't blame you. My solution works for any number of doors although I'm sure you're not interested. The problem I am interested in is a grown adult so enamoured with anti-intellectualism, your specific presentation of that condition is not relevant.
|
|
|
|
Post by Arlon10 on Feb 16, 2020 20:35:20 GMT
So you're not going to consider the problem with more than 3 doors? I don't blame you. My solution works for any number of doors although I'm sure you're not interested. The problem I am interested in is a grown adult so enamoured with anti-intellectualism, your specific presentation of that condition is not relevant. Again who? Sorry.
|
|
|
|
Post by gadreel on Feb 16, 2020 20:58:06 GMT
The problem I am interested in is a grown adult so enamoured with anti-intellectualism, your specific presentation of that condition is not relevant. Again who? Sorry. I already answered that, but dont be sorry it's exactly that kind of self hatred that manifests as this
|
|
|
|
Post by Eva Yojimbo on Feb 17, 2020 2:00:03 GMT
Holy shit you love being ignorant. Who? Me? Why? Is it because I didn't show you how to solve the Monty Hall problem using Bayes' Theorem? Neither did Eva Yojimbo . Here's his "solution" Nice, but the probability the prize is not behind D3, P(~A), is 2/3 not 1/3. See line 3, P(A).
Here is a correct application of Bayes' Theorem A is the probability prize at D3; P(B|A) is the probability Monty reveals D2 given A. Same as above. What is needed is P(B). Obviously the way P(B|~A) and P(~A) were employed above is flawed. The correct probability of B is the combination of the probability of B in three cases The prize is at D1 P(B 1)=1/2 The prize is at D2 P(B 2)=0 The prize is at D3 P(B 3)=1 The probability of B is B 1/3 + B 2/3 + B 3/3 1/6 + 0 + 1/3 = 1/2 P(B) =1/2 Now you can use this formula P(A|B) = (P(B|A) x P(A) ) / P(B) and you will get the correct answer, 2/3 No it's not. You're just flat-out, factually wrong about this. P(~A) and P(A) are both either .5 or .33, whichever you prefer to use (you get the same correct answer either way). What's more, your "formula" doesn't get the correct answer if P(~A) is .66. You derive P(B) by adding P(B|A)*P(A) and P(B|~A)*P(~A). If P(~A) was .66, that would make P(B) .66, not .5 as you stated above. Observe: P(B) = P(B|A)*P(A) + P(B|~A)*P(~A) P(B) = 1*.33 + .5*.66 P(B) = .33 + .33 P(B) = .66 Things don't get "hairy" with more than three doors, it's the same damn formula. You calculate B the same way you do above. In the 100-door version P(B) is .0101. I solved for it HERE.
|
|
|
|
Post by Eva Yojimbo on Feb 17, 2020 2:26:00 GMT
The point with temperature is that it doesn't exist on any fundamental level of physics. Rather, it's an estimation of the average kinetic energy within a system. Break that down and all that actually exists is lots of particles moving at certain speeds. The notion of "average" and what's considered a "system" are ways in which our brain categorizes things on larger levels than the fundamental one. They're mental concepts about reality not found in fundamental descriptions of reality: "useful fictions." You do realize that once evidence modifies a prior the old prior essentially "doesn't exist" anymore, yes? All you're doing is using a kind of hindsight bias to say the prior never mattered, and that's just silly. Yeah, once we find an experiment that provides us the "Given E(vidence), the P(robability) of H(ypothesis) is ~100%; Given E, the P of ~H is ~0%." evidence then the old prior doesn't matter because the new evidence overwhelms whatever it is. I'd argue that's neither the situation in the vast majority of science, nor the vast situations in everyday life. Nearly everything you do in your everyday life is not a product of new evidence provided by some definitive experiment, but is a product of priors built from past evidence. If you walk out your door without fearing an airplane will fall on your head, that's because your "prior" experience of planes not falling on your head, not because of some rigorous new experiment you did before you walked out your door to prove a plane won't fall on your head. If you were to come home and find your home ransacked and things gone, your first instinct is "human burglars" not "alien burglars," and that's a product of priors, not some rigorous investigation to rule out aliens. I could come up with a near infinite examples of why our priors are crucially important in everyday life. Besides, even experiments of the kind that proved Relativity are STILL operating on Bayes. That "Given E(vidence), the P(robability) of H(ypothesis) is ~100%; Given E, the P of ~H is ~0%" is still Bayesian in nature. QM is "bizarre and counter-intuitive" when you try to force our intuitions about how the world is onto QM rather than just taking what QM say is happening seriously. It's amazing how science has such a history of shattering human intuitions, yet here are in the 21st century and scientists, the very people using the discipline that's supposed to minimize human biases, are still clinging to those biases and intuitions for no good reason when the math, and what it says about reality, are staring us in the face. Occam's razor is more than just "a guide," it's a mathematically provable notion that simpler hypotheses are more probable than others (look up Solomonoff Induction). The point is, in QM we have a model that perfectly describes how particles behave. We call it the "wavefunction" (or Shrodinger's Wave Equation). If we take that as it is, there are many-worlds. Simple as that. What science has done in the 20th century have added things to that to make the "many-worlds" go away. Not because an experiment says they don't exist (experiments say they do), not because they math says they don't exist (the math says they do), but because they don't like them intuitively. Sorry, but that's stupid, and it's not less stupid because it's fueled by bias and intuition, and it's not less stupid than adding unicorns to electricity. Yes, temperature is an emergent property of collections of particles, and less "fundamental". Deciding that that makes it somehow less real is a philosophical position. You could view human intelligence as a useful fiction if you like, meanwhile I will continue to make sure I stay warm in winter. You didn't address at all my point about Einstein's imagination and the crucial role it played in his breakthrough theories. I suppose you can try to fit Bayes into all sorts of scientific questions but it isn't necessarily the best tool, just like one could participate in the Tour de France on a mountain bike but you're unlikely to win the race with that bicycle, even if you're Lance Armstrong. Thanks for the intro to Schrodinger's Wave Equation. I am quite familiar with it, as I had to solve differential equations with it in college (in physics exercises involving the hydrogen atom). As for interpretations of QM, let's just say that the jury is still out, with many experts in the field in disagreement. I agree it's a philosophical position, but all knowledge is built on some philosophical position (including the scientific method). Of course we stay warm in winter because of our understanding of temperature: that's the "useful" part of the "useful fiction."  Sorry about not addressing Einstein's imagination. Of course the ability to think of alternative hypotheses (and even ways of testing them) requires great imagination, but I'm not sure why that would be an argument against Bayes. Again, I'm not saying we can just use Bayes practically to solve every question/mystery; I'm saying Bayes models the ways in which we do, it models how we get from hypothesis (prior), to evidence (experiment), to, eventually, theory (experiment making a hypothesis very probably true). The reasons "experts in QM" disagree on interpretations is many-fold, often having little to do with careful thought given to the topic. Most physicists are firmly in the "shut-up and calculate" camp. They use the equations to solve problems and don't bother thinking about the underlying reality/philosophy. Sean Carroll has written/lamented about this. It's also a sad fact that the "stupid version" of QM (Copenhagen Interpretation) got proposed first, and is still taught as a kind of "default" in textbooks. Really, QM is not as "mysterious" as it's made out to be. Once you strip away the unproven/unjustified assumptions, it turns out to be local, real, and deterministic like General Relativity. Add stuff to it and weird stuff happens, like violations of the speed-of-light, non-local causality, etc. The obvious answer should be: don't add stupid stuff to it.
|
|
|
|
Post by Arlon10 on Feb 17, 2020 7:15:05 GMT
Things don't get "hairy" with more than three doors, it's the same damn formula. You calculate B the same way you do above. In the 100-door version P(B) is .0101. I solved for it HERE. What is your game? Are you really what you claim to be? No, you plugged numbers, for a result we already knew, into the formula for Bayes' Theorem. That is incredibly easy. You did not show your work in obtaining the numbers, as I did. Remember now? P(B 1 through 3). That would be honest. It's not like we couldn't solve the problem and were crying, "What ever will we do?" Then you came to the rescue with Bayes' Theorem. We already knew the answer. When the host picks the cards they're face up to him. You make a good point though. Bayes' Theorem is not useful most of the time. In some cases when the answer has already been found it might help convince advocates of Bayes' Theorem, who are not very bright, I've noticed. If people understand the problem well enough to use Bayes' Theorem, they don't really need to know that theorem. You can't know your specific scenario will even fit Bayes' till you solve it first. Witness when there are more than three doors. I think the most valuable lesson here is that people who have poor abilities to communicate in English expect to be taken more seriously if they doll it up with mathematical language. That won't work unless you know the English that got you there. Oh wait, it might work on Democrats.
|
|
|
|
Post by dividavi on Feb 17, 2020 11:02:35 GMT
5. science asks how, religion asks why (attributed to UK author Peter James) - Actually, religion doesn't ask anything since every cult or creed already knows the answer. The answer to any question about why things are this way instead of that way is this: Because God wants it this way. Here's a cartoon that succinctly demonstrates the different questions asked by rational people (the scientific approach) and those asked by religious types: 
|
|
fatpaul
Sophomore
@fatpaul
Posts: 502
Likes: 193
 
|
Post by fatpaul on Feb 17, 2020 17:01:30 GMT
Wtf? Even my ex-wives give me A+ for effort! It would have needed to be longer, harder and illustrated in pretty colours for an A+.  You must be praketing richcraft because they're the exact same reasons why they gave me A+!
|
|
fatpaul
Sophomore
@fatpaul
Posts: 502
Likes: 193
|
Post by fatpaul on Feb 17, 2020 17:15:43 GMT
I figured the implication followed pretty obviously: I struggled to follow because I found your explanation complicated. It wasn't pretty obvious to me. I was kind of expecting something on the lines of: I think my probabilistic take is less complicated because it can easily be translated into everyday language and this is how I do x to ease translation which, when compared to a particular of your post, I cannot do x, or I do y instead, to facilitate translation. An argumentum ad populum for a strawman because I didn't sign up for a pissing contest to be verified by the crowd. It's my opinion that you didn't find my original post complicated at all. I'm willing to put this to the test. Below is even less info than I gave in my original post: E = Eva; G = Go. Guess the phrase: ∃x[E(x)&G(x)&F(x, x)]
|
|
|
|
Post by general313 on Feb 17, 2020 18:14:46 GMT
Yes, temperature is an emergent property of collections of particles, and less "fundamental". Deciding that that makes it somehow less real is a philosophical position. You could view human intelligence as a useful fiction if you like, meanwhile I will continue to make sure I stay warm in winter. You didn't address at all my point about Einstein's imagination and the crucial role it played in his breakthrough theories. I suppose you can try to fit Bayes into all sorts of scientific questions but it isn't necessarily the best tool, just like one could participate in the Tour de France on a mountain bike but you're unlikely to win the race with that bicycle, even if you're Lance Armstrong. Thanks for the intro to Schrodinger's Wave Equation. I am quite familiar with it, as I had to solve differential equations with it in college (in physics exercises involving the hydrogen atom). As for interpretations of QM, let's just say that the jury is still out, with many experts in the field in disagreement. I agree it's a philosophical position, but all knowledge is built on some philosophical position (including the scientific method). Of course we stay warm in winter because of our understanding of temperature: that's the "useful" part of the "useful fiction." Sorry about not addressing Einstein's imagination. Of course the ability to think of alternative hypotheses (and even ways of testing them) requires great imagination, but I'm not sure why that would be an argument against Bayes. Again, I'm not saying we can just use Bayes practically to solve every question/mystery; I'm saying Bayes models the ways in which we do, it models how we get from hypothesis (prior), to evidence (experiment), to, eventually, theory (experiment making a hypothesis very probably true). The reasons "experts in QM" disagree on interpretations is many-fold, often having little to do with careful thought given to the topic. Most physicists are firmly in the "shut-up and calculate" camp. They use the equations to solve problems and don't bother thinking about the underlying reality/philosophy. Sean Carroll has written/lamented about this. It's also a sad fact that the "stupid version" of QM (Copenhagen Interpretation) got proposed first, and is still taught as a kind of "default" in textbooks. Really, QM is not as "mysterious" as it's made out to be. Once you strip away the unproven/unjustified assumptions, it turns out to be local, real, and deterministic like General Relativity. Add stuff to it and weird stuff happens, like violations of the speed-of-light, non-local causality, etc. The obvious answer should be: don't add stupid stuff to it. Glad we agree on the "philosophical position" point. The difficulty with philosophy is that it's more slippery than science, in the same way that religion is. At least philosophy is more grounded in rationalism, yet there are multiple schools, again like religion. My point in raising Einstein's imagination is not to dispute Bayes per se, other than to show it's not a universal path to discovery. I think Bayes may be useful to describe how the brain works, but there's a lot more. Deep learning, for instance, is helping us understand how the brain works, and mapping is an important aspect of it. Our brains have the ability to use mapping to not only solve mazes, but also deal with complex social situations. Interestingly enough, Einstein probably shared the view that the "stupid version" (I'll use your terminology here) of QM got interpreted first, much to his lament. I think I share the feeling that there's something wrong about the Copenhagen interpretation, but I'm not enough of an expert to be certain about it, so I think the "shut-up and calculate" camp is a sensible approach until we can devise experiments that shed more light. One reason for my resistance to proclaiming Bayes as the unifying principle of all science is that I never heard it in my university education where I took many classes in theoretical physics, chemistry and electrical engineering, with good coverage of the history of those sciences. Now it's possible that in the 40 years since I took those classes there has been a fundamental change in these sciences, where Bayes has taken a central role, but I doubt it. I read many science journals, none of which have reported anything like that.
|
|
|
|
Post by Arlon10 on Feb 17, 2020 23:23:31 GMT
I disagree with the idea that it's Completely "Junk"... The adage isn't very specific, and can easily be used to prove or disprove any theory... Let's take this popular debate, for Example: "Does GOD Exist?" @graham 's suggestion of: " you didn't search well enough"... comes to the very heart of that debate! Just because GOD didn't leave any evidence of his existence on PLANET EARTH, doesn't mean that he didn't leave evidence of his existence on, let's say: "PLANET VULCAN". Since Humans have NOT been to "PLANET VULCAN" (or anywhere else in the UNIVERSE)... We can NOT be sure that he does NOT exist. In this instance: " The Lack Of Evidence of GOD on PLANET EARTH... IS NOT... Evidence of GOD's Absence in the UNIVERSE!" The adage is not "Junk", it is completely TRUE! However... Yeah, I guess it could depend on how specific a person wishes to use that adage, and how other people chose to interpret it... With the murderer analogy, there may be no evidence of the murderer hiding in the house, though he may exist, but before one searches a house for a murderer, somewhere evidently, a murder took place, so we know there’s a murderer hiding somewhere. But to search for God, one needs a “crime” or evidence of his actions to be searching for. It’s assumed by believers God exists and his creation is the evidence. However, it’s not been established with any proof that any intelligent being created the universe. So, searching for the “murderer” here is one where no murder has been proven to have happened in the first place. What's really funny about that is the same argument can be used about the random assembly of life. Laboratories have been trying to find a random assembly of life, life from matter not alive, especially since Miller-Urey in the 1950s, and it hasn't happened. Now it can be argued just because life doesn't randomly assemble itself here on Earth doesn't mean it can't assemble itself on another planet.
|
|
|
|
Post by Eva Yojimbo on Feb 18, 2020 2:02:50 GMT
Things don't get "hairy" with more than three doors, it's the same damn formula. You calculate B the same way you do above. In the 100-door version P(B) is .0101. I solved for it HERE. What is your game? Are you really what you claim to be? No, you plugged numbers, for a result we already knew, into the formula for Bayes' Theorem. That is incredibly easy. You did not show your work in obtaining the numbers, as I did. Remember now? P(B 1 through 3). That would be honest. It's not like we couldn't solve the problem and were crying, "What ever will we do?" Then you came to the rescue with Bayes' Theorem. We already knew the answer. When the host picks the cards they're face up to him. You make a good point though. Bayes' Theorem is not useful most of the time. In some cases when the answer has already been found it might help convince advocates of Bayes' Theorem, who are not very bright, I've noticed. If people understand the problem well enough to use Bayes' Theorem, they don't really need to know that theorem. You can't know your specific scenario will even fit Bayes' till you solve it first. Witness when there are more than three doors. I think the most valuable lesson here is that people who have poor abilities to communicate in English expect to be taken more seriously if they doll it up with mathematical language. That won't work unless you know the English that got you there. Oh wait, it might work on Democrats. What did I claim to be? Dude, I "showed my work" for both problems. I wrote out the entirety of the theorem and what each number was. I don't know how else I'm supposed to "show my work." Your "shown work" was wrong anyway, as P(B|~A) is either .33 or .5, not .66 as you said. How about you explain what you think is "hairy" about your 100-door version. I mean, there's only 4 numbers, and 3 are the same for both versions. In both, P(A) and P(~A) are 50/50. For "50/50" you can use .33/.33, .01/.01, .66/.66... it doesn't matter, they all get the same result. In both, P(B|A) is 1. The only difference is P(B|~A). In both cases, that number is 1/(doors-1). In the 3-door version it's 1/2, in the 100-door version it's 1/99, in a 3748-door version, it's 1/3747. Pretty simple. Yep, Bayes's Theorem is so useless it was used the crack the Enigma Code and hunt down Russian Submarines in the Cold War... not to mention it's the backbone of most modern AIs and stuff like spam filtering. Yep, totally useless. When we eventually invent AIs running Solomonoff Induction/Bayes's Theorem solving all kinds of problems for us, it'll be useless then too.
|
|
|
|
Post by Eva Yojimbo on Feb 18, 2020 2:13:08 GMT
I figured the implication followed pretty obviously: I struggled to follow because I found your explanation complicated. It wasn't pretty obvious to me. So you're getting thrown by a basic subjective/objective distinction? If I find your explanation complicated and define it to be such, then you made it complicated as defined by that. Those two statements mean the same thing. We can disagree about that definition of "complicated" but that's how it works since nothing is innately "complicated" without our subjective say-so. I was kind of expecting something on the lines of: I think my probabilistic take is less complicated because it can easily be translated into everyday language and this is how I do x to ease translation which, when compared to a particular of your post, I cannot do x, or I do y instead, to facilitate translation. I already translated mine, so if you can translate yours, then feel free to do so. I don't know why you "expected" me to do your work for you. An argumentum ad populum for a strawman because I didn't sign up for a pissing contest to be verified by the crowd. Argumentum ad populum works for definitions because that's how language is defined. I also have no idea what "strawman" you're referring to, and if you didn't sign up to "communicate with people," I have no idea why you're on a public message board. It's my opinion that you didn't find my original post complicated at all. Good job, Kreskin. Tell me another.
|
|
|
|
Post by NJtoTX on Feb 18, 2020 2:25:57 GMT
|
|
|
|
Post by Eva Yojimbo on Feb 18, 2020 2:29:49 GMT
I agree it's a philosophical position, but all knowledge is built on some philosophical position (including the scientific method). Of course we stay warm in winter because of our understanding of temperature: that's the "useful" part of the "useful fiction." Sorry about not addressing Einstein's imagination. Of course the ability to think of alternative hypotheses (and even ways of testing them) requires great imagination, but I'm not sure why that would be an argument against Bayes. Again, I'm not saying we can just use Bayes practically to solve every question/mystery; I'm saying Bayes models the ways in which we do, it models how we get from hypothesis (prior), to evidence (experiment), to, eventually, theory (experiment making a hypothesis very probably true). The reasons "experts in QM" disagree on interpretations is many-fold, often having little to do with careful thought given to the topic. Most physicists are firmly in the "shut-up and calculate" camp. They use the equations to solve problems and don't bother thinking about the underlying reality/philosophy. Sean Carroll has written/lamented about this. It's also a sad fact that the "stupid version" of QM (Copenhagen Interpretation) got proposed first, and is still taught as a kind of "default" in textbooks. Really, QM is not as "mysterious" as it's made out to be. Once you strip away the unproven/unjustified assumptions, it turns out to be local, real, and deterministic like General Relativity. Add stuff to it and weird stuff happens, like violations of the speed-of-light, non-local causality, etc. The obvious answer should be: don't add stupid stuff to it. Glad we agree on the "philosophical position" point. The difficulty with philosophy is that it's more slippery than science, in the same way that religion is. At least philosophy is more grounded in rationalism, yet there are multiple schools, again like religion. My point in raising Einstein's imagination is not to dispute Bayes per se, other than to show it's not a universal path to discovery. I think Bayes may be useful to describe how the brain works, but there's a lot more. Deep learning, for instance, is helping us understand how the brain works, and mapping is an important aspect of it. Our brains have the ability to use mapping to not only solve mazes, but also deal with complex social situations. Interestingly enough, Einstein probably shared the view that the "stupid version" (I'll use your terminology here) of QM got interpreted first, much to his lament. I think I share the feeling that there's something wrong about the Copenhagen interpretation, but I'm not enough of an expert to be certain about it, so I think the "shut-up and calculate" camp is a sensible approach until we can devise experiments that shed more light. One reason for my resistance to proclaiming Bayes as the unifying principle of all science is that I never heard it in my university education where I took many classes in theoretical physics, chemistry and electrical engineering, with good coverage of the history of those sciences. Now it's possible that in the 40 years since I took those classes there has been a fundamental change in these sciences, where Bayes has taken a central role, but I doubt it. I read many science journals, none of which have reported anything like that. I agree about philosophy, which is why we need a rigorously defined epistemology (which I find Bayes/Solomonoff to be) and philosophers informed by science. Science may get along well (for the most part) without philosophy--much better than the reverse--but it would still be better off knowing the fundamentals of rationality. I also agree that Bayes isn't a universal path to discovery. It's very much like logic; logic is only as useful as the truth of the propositions we feed it. Likewise, Bayes is only as useful as the accuracy of our priors and the strength of the evidence. However, it's still important to correctly reason and update our beliefs based on new evidence, and the human brain is not innately good at this. In fact, as Aj_June posted HERE, the deviation from Bayes's Theorem in finance can be used to prove the existence of cognitive biases. I doubt if Bayes is taught as any "unifying principle" in science, because the way I'm talking about it is certainly more philosophical in nature. Again, I'd highly recommend reading through that Jaynes textbook as he offers dozens of examples from science, but also from everyday reasoning. Really, I'd say Bayes is more a fundamental principle of rationality; science works because the rationality of science is, essentially, Bayesian even when it isn't explicitly being used, if that makes sense. Einstein didn't like Copenhagen because he understood it would wreck General Relativity--GR is local, real, deterministic; Copenhagen is none of those. If we're being charitable, we might say Einstein deeply felt General Relativity was an accurate model of reality, so he equally felt Copenhagen couldn't be right; if we're being cynical, we might say Einstein was biased because he didn't WANT General Relativity to be wrong. Einstein devised the EPR experiment in an attempt to show what he thought was an absurdity about non-local causality under Copenhagen (basically, the ability of a measurement to affect another measurement at great distances from each other). He thought this proved there must be hidden variables. Unfortunately, Bell's Theorem later showed that no hidden variable theory could account for all the predictions of QM while maintaining locality, so many theorists have just been happy to abandon locality, either in the form of Copenhagen, or in the form of Bohm (which is a hidden variable interpretation). Hugh Everett didn't propose Many-Worlds until 2 years after Einstein's death. Basically, Everett just eliminated the "collapse" of Copenhagen and the "hidden variables" of Bohm and reduced QM to the wavefunction, making QM local, real, and deterministic (like General Relativity). For whatever reason, people don't like it because accepting it would mean that all the other states of the wavefunction, the "worlds," actually exist. I wonder what Einstein would've thought of MW, but it's too late to know now.
|
|
