TakenItSeriously

According to worldometers.info on 03-22-2020 @12:30 afternoon which is the top site from a google search of “coronavirus numbers” Total Cases: 321,278 Active cases: 211,573 Recovered: 96,006 Deaths:13,629 First of all, I am not a doctor nor am I mathematician. However, I was tested as profoundly gifted at logic in college which means that I have a knack for problem solving. These numbers are based on only what we know as reported by governments around the world. Of course the numbers may not be accurate due to political fudging and of course testing is not anywhere close to 100%. However, it seems to me that the odds of dying after testing positive is not really around 4% as reported by most media outlets. This number seems to be a best possible spin of the numbers i.e. # of deaths divided by total cases: 13,629/321,278 = 4.264% I believe this is the wrong way to calculate the numbers because it includes the 211,573 of active cases which are uncertain as to whether they will result in a recovery or a death. If you test positive and you ask the question: what are the odds of coming out alive when all is said and done then a more accurate prediction should be the number of deaths divided by (the number recovered plus the number of deaths). 13,629/(96,006+13,629) = 13,629/109,705 = 12.49% Now to be fair, there is quite a large lag-time between the number dead to the number recovered because it’s early in a growth dynamic scenario where death generally occurs much more quickly than recovery so we can probably assume the recovery number should be much higher but still, I think the most accurate number should be something like somewhere between 4.3% and 12.5%. Thoughts?

Given that the vast majority of the population share the same incorrect illusion, I would hardly think its something unique to my mind and finding a solution would be of particular value for being able to judge the validity of future axioms. Also, I dont think anyone who actually read the solution disputes its correctness. Never the less I gave a method for proving the solution to yourself which would take deck of cards and about 20 seconds to verify.

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No it doesn't. Why do you think it does?

That doesn't explain why people who fully understand why the trade is 1/3:2/3 still see the 50:50 trade as intuitively correct.

Thread is drifting out of context. What makes the incorrect 50:50 answer intuitive is how our intuition reads the MHP. The broken link in this case is in how the reveal is interpreted. Reveals are interpreted by our intuition as a dealer dealing a card. However we also know that Monty always reveals a goat. We have no experiences with dealers who always deal the same card and intuition is only dependent on experiences. Since our intuition sees Monty always revealing a goat as a null experience, we are only left with interpreting it to the experience of dealing a random card, or monty opening a random door. I'm not saying Monty actually reveals a random door, your intuition is interpreting it that way if the 50:50 solution seems intuitively correct to you. To test this, use three cards to simulate the problem. For example: Usr Ax,2x,2x dealt face down. You must take the role of Monty and note the position of the Ace. The contestant can just be a player who always picks door 1 and always sticks. Run the game for a few orbits and the 50:50 answer will no longer seem intuitively correct. Why this happens is that you now have relevant experiences with what happens when Monty always reveals a goat.

No the intuitive error is a result of having no experiences with a dealer who always deals the same card. Without the correct experiences we instead rely on the experiences of dealing random cards as the intuitive model. If Monty reveals a random door: we end up with a 50:50 trade

For a detailed look at the Monty Hall problem, click the Wikipedia link. https://en.m.wikipedia.org/wiki/Monty_Hall_problem I would propose the following hypothesis: The Monty Hall Problem creates a false intuitive result as a consequence of our lack of not having any actual experiences of always revealing the same thing in a game or similar situation. Therefore a logical chain of failures that results in our intuitive experience changing from that of always revealing a goat to create a 1/3:2/3 trade to the false experience of Monty making random reveals that results in an incorrect 50:50 trade that is as real to us as actually experiencing random reveals. Amazingly we can correct this common intuitive failure by modeling the events of Monty always picking a goat using a simple analog of three cards playing cards As, 2c, 2s placed face down and simulate 5-7 hands should be more than enough to correct our own perceptions of reality. The Monty Hall Problem There are three doors, behind one of those doors is a new car, behind the other two are goats eating hey. A contestant is allowed to pick one of the three doors to will win whatever is behind that door. Before the contestant can see what they've won, Monty opens one of the other two doors to show a goat which you already knew was going to be the case. Monty then asks the contestant if he would like to swap what's behind third remaining door for what is behind the contestants door. Should you: A) make the trade B) stick with your first choice C) It doesn't matter (coin-flip) Veridical Paradox The Monty Hall problem is an example of a Veridical Paradox, which could be viewed as: A Correct result from Reason does not agree with a seemingly intuitively obvious result. The Correct Answer from reason: (1/3:2/3) If ignoring our intuition and calculate the odds for the car behind each door using math, logic, or game theory, we would find that the correct answer is a 1/3:2/3 trade. The Intuitive Answer: (50:50) Upon first hearing the problem few would get as far as trying to calculate the odds because the 50:50 trade was already axiomatic and there didnt seem to be a need to look further. The common assumption as to what was duping our sense of intuition is that their are only two doors left and therefore it should be a 50:50 trade. Surprisingly, however, even when people know and fully understand that the correct answer is a 1/3:2/3 trade. They still feel like the 50:50 trade is intuitively true. My intorduction to the Monty Hall Riddle: In my first experience with the problem, I found my own perspective of the intuitive answer to be a rather unique experience which demonstrated that our intuition isn't linked to the simple 2 doors for a 50:50 trade assumption.. When i was in the 9th grade some 40 years ago. The MHP was presented to me as a logic riddle, I had just enough experience with solving logic riddles to have the beginnings of a standard strategy going into a problem. I would take mental notes on key variables as I would hear them in the riddle. I would always look at the least obvious answers first while completely ignoring the other options. If needed, i would move down to the next least obvious answers while ignoring all others, and so on. When I heard that Monty deliberately picked a goat based upon knowing where the car was, I didn't recognize the mathematical form. I did note that picking only goats was an asymmetrical relationship between doors. Therefore I could see that the odds of the doors should diverge though I didn't know much beyond that. Despite that assumption the most obvious answer was still seemed to be 50:50 so I completely ignored the 50:50 case and solved for the trade to see if it was consistent. Goat Reveal: D1. D2. D3 Car Goat Goat Goat Car Goat Goat Goat Car We assume the contestant picks D1 Monty reveals goats in the assymetricle pattern below: Monty Reveals a goat D1. D2. D3 Car xxxx Goat Goat Car xxxx Goat xxxx Car D1 = Car, Goat, Goat = 1/3 Dx = Goat, Car, Car = 2/3 Correct trade at odds of 1/3:2/3 I first assumed that two doors would have diverging odds before knowing about the intuitive trade. Following through with that assumption and my strategy to ignore the obvious. I arrived at the 1/3:2/3 trade directly having never noticed the 50:50 intuitive trade. The problem got very interesting when asked about why I ignored the 50:50 trade. I explained it to him while looking at it for the first time and saw a 50:50 trade that appeared to be intuitively true!!! Instead of an intuitive trade 50:50 trade between two doors which support each other before any other considerations are taken into account. My take on the intuitive 50:50 trade was more surreal. Before I ever considered the intuitive trade, the two doors were already assumed to be asymmetricle and solved at 1/3:2/3 so the state of the problem before I first looked at the intuitive 50:50 solution was known and complete contradiction to the 50:50 trade. Yet even in complete contradiction to all known facts it still seemed intuitively correct!!!? So I knew something much deeper was going on with how our intuition must work. Over the years, I mostly paid the MHP no attention other than to offer up improved intuitive and elegant proofs when it came up now and then. They helped to sell the 1/3:2/3 trade but still did nothing to remove the intuitive illusion which I assumed would never go away. It wasnt like the magician who revealed his secret, and the intuitive illusion of his trick would never work on us again. Finally, some three decades later, when didnt have a pen and paper to help me explain the true answer. i decided to just simulate the problem in front of her with 3 cups and a quarter. She flipped almost instantly to the 1/3:2/3 solution. I finally got the illusion to turn off! But I wasnt sure what that meant yet. Epiphanic Moment Finally, forty years after first expeeiencing the odd intuitive 50:50 that went against everything I knew to be correct. I noticed a post about the Monty Hall problem in a poker forum where the OP had asked if the Monty Hall Problem related to poker like it related to BJ in the movie 21. It turns out it doesnt relate to poker or even to BJ for that matter. Even the movie 21 got it wrong. In fact the MHP doesnt relate to anything in real life. But why would it? No one is ever going to invent a game where we reveal a known constant every time. It would be completely pointless. Much like the game show was. Other that giving away stuff. This explained how gaining the relavent experience would fix the problem. But what was creating the fale intuitive answer? The clue was to find experience resulted in the 50:50 trade. For a random reveal, the odds fit just right: Random reveal Assume D1 was picked initially And D2 was eliminated randomly. D1 D2. D3 Car Goat Goat Goat Car Goat Goat Goat Car D1. D2. D3 Car xxxx Goat Goat xxxx Goat Goat xxxx Car Then D3 = Goat, Goat, Car D1 = Car, Goat, Goat D1 = D3 (50:50) Is the missing deliberate goat reveal experience logically consistent with results of a random reveal?. We have no experience to match with Monty deliberately showing a goat every time. Therefore we remove the context of Monty's always showing a goat. Without the context of always removing a Goat we are left with only an image of revealing a single on purpose revealing a goat on purpose matches revealing a random goat. Therefore the random goat reveal is consistent with results. Is adding the experience revealing only goats consistent with the results normalizing for the 1/3:2/3 trade? We have new experience to match with Monty deliberately showing a goat every time. Therefore we keep the context of Monty's always showing a goat. Making the 1/3:2/3 trade the new intuitive answer. experience of revealing With the visceral experience of always removing a Goat added through a quick simulation using cards our intuitive expectations become normalized. (Intuitive answer changes from 50:50 to 1/3:2/3.) So the hypothesis seems to be logically consistent with results and expectations therefore it is self consistent. But is it consistent with what we know about intuition: Human Intuition: Its widely accepted that Human intuition is based upon the sum of our experiences. It could also be said that human intuition is the ability to recognize patterns in our experiences. For any given event such as dropping a baseball which falls to the ground, the more experienceswe have with consistent results, the more those experiences represent our take on reality. Speaking only for myslef, this was why the odds seemed so bizarrely surreal to me. I had four years experience with playing poker with friends by the time I experienced the intuitive 50:50 problem and it was a powerful illusion. We also know that Human intuition predates human reasoning, or conscious thought. Therefore, it is probably safe to assume that intuition is not a conscious process and it does not rely on reasoning. Experience without the benefit of reason certainly explains the similar yet invalid experienc model. It seems to be consistent with common ideas about intuition. Can we test the hypothesis? If the 50:50 answer still seems intuitive to you regardless of what you choose to believe about the true odds. Or what proofs you have seen to deny the 50:50 result. You can prove it to yourself very easily. If you don't see it as being intuitive, you will need to test someone else who did find the 50:50 trade to be intuitive. All you need to do is provide the missing experience that is missing by simulating the game to yourself. You can use 3 cards such as: As, 2c, 2s dealt face down to represent the doors and prizes. If running the experiment on yourself, you can play Monty Hall and assume the player always picks the same card and sticks with it. After surprisingly few hands you will feel your intuitive perception will flipflop from the 50:50 trade to the 1/3:2/3 trade. Note, that this is by no means a scientificly valid experiment. But it wouldnt be that difficult to create a valid experiment. Only don't expect me to pay for it, I'm just a broke retired engineer.

For a detailed look at the Monty Hall problem, click the Wikipedia link. https://en.m.wikipedia.org/wiki/Monty_Hall_problem The Monty Hall Problem There are three doors, behind one of those doors is a new car, behind the other two are goats eating hey. A contestant is allowed to pick one of the three doors to will win whatever is behind that door. Before the contestant can see what they've won, Monty opens one of the other two doors to show a goat which you already knew was going to be the case. Monty then asks the contestant if he would like to swap what's behind third remaining door for what is behind the contestants door. Should you: A) make the trade B) stick with your first choice C) It doesn't matter (coin-flip) Veridical Paradox The Monty Hall problem is an example of a Veridical Paradox, which could be viewed as: A Correct result from Reason does not agree with a seemingly intuitively obvious result. The Correct Answer from reason: (1/3:2/3) If ignoring our intuition and calculate the odds for the car behind each door using math, logic, or game theory, we would find that the correct answer is a 1/3:2/3 trade. The Intuitive Answer: (50:50) Upon first hearing the problem few would get as far as trying to calculate the odds because the 50:50 trade was already axiomatic and there didnt seem to be a mpneed to look further. The common assumption as to what was duping our sense of intuition is that their are only two doors left and therefore it should be 50:50 Surprisingly, however, even when people know and fully understand that the correct answer is a 1/3:2/3 trade. They still feel like the 50:50 trade is intuitively true. My intorduction to the Monty Hall Riddle: In my first experience with the problem, I found my own perspective of the intuitive answer a rather unique one. When i was in the 9th grade some 40 years ago. The MHP was presented to me as a logic riddle, I had just enough experience with solving logic riddles to have the beginnings of a standard strategy going into a problem. I would take mental notes on key variables as I would hear them in the riddle. I would always look at the least obvious answers first while completely ignoring the other options. solutions. If needed, i would move down to the next least obvious answers while ignoring all others, and so on. When I heard that Monty deliberately picked a goat based upon knowing where the car was, I didnt recognize the mathematical form but, I did note that it was asymmetricle. Therefore I could see that the odds of the doors should diverge. Despite that assumption the most obvious answer was still 50:50 so I completely ignored the 50:50 case and solved for the trade to see if it was consistent. Goat Reveal: D1. D2. D3 Car Goat Goat Goat Car Goat Goat Goat Car We assume the contestant picks D1 Monty reveals goats in the assymetricle pattern below: Monty Reveals a goat D1. D2. D3 Car xxxx Goat Goat Car xxxx Goat xxxx Car D1 = Car, Goat, Goat = 1/3 Dx = Goat, Car, Car = 2/3 Correct trade at odds of 1/3:2/3 So notice how I first assumed that two doors would have diverging odds before half way through the problem. Following through with that assumption and my strategy to ignore the obvious. I arrived at the answer more quickly. The problem got very interesting when asked about why I ignored the 50:50 trade. I explained it to him while looking at it for the first time and saw a 50:50 trade that appeared to be intuitively true!!! Instead of an intuitive trade 50:50 trade between two doors which support each other before any other considerations are taken into account. My take on the intuitive 50:50 trade was more surreal. Before I ever considered the intuitive trade, the two doors were already assumed to be asymmetricle and solved at 1/3:2/3 so the state of the problem before I first looked at the intuitive 50:50 solution was known and complete contradiction to the 50:50 trade. Yet even in complete contradiction to all known facts it still seemed intuitively correct!!!? So I knew something much deeper was going on with how our intuition must work. Over the years, I mostly paid the MHP no attention other than to offer up improved intuitive and elegant proofs when it came up now and then. They helped to sell the 1/3:2/3 trade but still did nothing to remove the intuitive illusion which I assumed would never go away. It wasnt like the magician who revealed his secret, and the intuitive illusion of his trick would never work on us again. Finally, some three decades later, when didnt have a pen and paper to help me explain the true answer. i decided to just simulate the problem in front of her with 3 cups and a quarter. She flipped almost instantly to the 1/3:2/3 solution. I finally got the illusion to turn off! But I wasnt sure what that meant yet. Epiphanic Moment Finally, forty years after first expeeiencing the odd intuitive 50:50 that went against everything I knew to be correct. I noticed a post about the Monty Hall problem in a poker forum where the OP had asked if the Monty Hall Problem related to poker like it related to BJ in the movie 21. It turns out it doesnt relate to poker or even to BJ for that matter. Even the movie 21 got it wrong. In fact the MHP doesnt relate to anything in real life. But why would it? No one is ever going to invent a game where we reveal a known constant every time. It would be completely pointless. Much like the game show was. Other that giving away stuff. This explained how gaining the relavent experience would fix the problem. But what was creating the fale intuitive answer? The clue was to find experience resulted in the 50:50 trade. For a random reveal, the odds fit just right: Random reveal Assume D1 was picked initially And D2 was eliminated randomly. D1 D2. D3 Car Goat Goat Goat Car Goat Goat Goat Car Then D3 = Goat, Goat, Car D1 = Car, Goat, Goat D1 = D3 (50:50) So if the valid experience is missing, the brain substitutes an invalid experience so long as it is a close enough match based upon experience alone. And the image of revealing a random door with a goat behind is not different from revealing a goat on purpose. However it only works once, after a few trials the experience is completely replaced with the correct version. So the hypothesis seems to make sense and is self consistent, but is it consistent with what we know about intuition. How consistent is the hypothesis? Human Intuition: Its widely accepted that Human intuition is based upon the sum of our experiences. It could also be said that human intuition is the ability to recognize patterns in our experiences. For any given event such as dropping a baseball which falls to the ground, the more experienceswe have with consistent results, the more those experiences represent our take on reality. Speaking only for myslef, this was why the odds seemed so bizarrely surreal to me. I had four years experience with playing poker with friends by the time I experienced the intuitive 50:50 problem and it was a powerful illusion. We also know that Human intuition predates human reasoning, or conscious thought. Therefore, it is probably safe to assume that intuition is not a conscious process and it does not rely on reasoning. Experience without the benefit of reason certainly explains the similar yet invalid experienc model and it seems to be consistent with common ideas about intuition. Can we test the hypothesis? If the 50:50 answer still seems intuitive to you regardless of what you choose to believe about the true odds. Or what proofs you have seen to deny the 50:50 result. You can prove it to yourself very easily. If you don't see it as being intuitive, you will need to test someone else who did find the 50:50 trade to be intuitive. All you need to do is provide the missing experience that is missing by simulating the game to yourself. You can use 3 cards such as: As, 2c, 2s dealt face down to represent the doors and prizes. If running the experiment on yourself, you can play Monty Hall and assume the player always picks the same card and sticks with it. After surprisingly few hands you will feel your intuitive perception will flipflop from the 50:50 trade to the 1/3:2/3 trade. Note, that this is by no means a scientificly valid experiment. But it wouldnt be that difficult to create a valid experiment. Only don't expect me to pay for it, I'm just a broke retired engineer.

I was referring to the unintuitive nature of physics outside of the human scale of experience

Well, I'm pretty sure my answer is correct and I've tested it on a limited basis among friends, but I don't have the resources to run a scientific study. I stumbled on the solution because I happened to have the right combination of interests which made it effectively luck. I believe the solution could identify when a false axiom was incorrectly assumed in the future but to be safe, I was also hoping someone else could discover a more reliable method for solving these types of problems before I gave the final solution and method for proving the hypothesis which might bias an original line of thinking. The conflict is between a correct answer arrived at using reason vs a seemingly intuitively correct (but wrong) answer. Therefore the conflict is a function of how intuition works vs reason. Spoiler tags are used incase someone finds a potential line to solve the problem at some point without reading all of the hints. Hint update: I will post the solution tomorrow evening, if you are working on a solution and would like more time please let me know before that time.

Close, but not quite correct IMHO. I think the key to understanding this is that our human intuition is not linked to our ability to reason. Intuition is nothing more than learning through pattern recognition. It was around long before reason or even consciousness existed so it simply does not rely on reason and in fact it works despite our using reason. That is not to say that we have no control over intuition, clearly we can choose to ignore it which many people have finally succumbed to the sheer brute-force of it where too many people shared the opposing opinion and they may have conceded the point but they still would have felt the opposite. However, there are far easier ways to dispel false intuition which I promise to explain after the reveal. Don't worry its not soft science, it's simply correcting a misperception. But the only way to do that is to be able to identify the source of the misperception. Which is the point of this exercise. BTW, I've recently updated the hints in the post above if anyone is interested.

Hint update: Warning, there is no easy method (yet) to solve this problem. Therefore, I will leave it open a little longer than normal and post more hints then your probably accustomed to. Hint 1 Hint 2 Hint 3 Hint 4

You are correct, in that the reason the overwhelming majority of people thought 50:50 was correct is based upon human nature. But, that is the point of the question. Why does the 50:50 choice seem so intuitively correct? It is a varidian paradox. Or a result that differs from what seems to be obvious. I put that in one of the hints, after you had read the OP. Unfortunately, I couldn't think of a way to notify everyone as to when hints would get updated. I generally update hints when peoples responses in the thread were touching on correct points that were on the right track. So look for more hint updates after this post. You are also correct in that math is not the proper tool for finding the source of an incorrect solution. At least, not for a comprehensive proof (beyond a reasonable doubt). It's the tool for finding correct solutions. When looking for the source of an incorrect response, you need to start at that response and work backwards through induction, at least initially. But that is not how most logic problems are approached. Only real world problems are approached that way. For example, when solving a crime, it is always an induction process at the beginning to follow the clues that will produce all of the facts. At that point you can reassess the problem from the perspective of the past moving forward through a deduction process. I had intended the following to be a separate post, unfortunately the forum structure prevents that from happening. Hint update:

Correct. But why is the 50:50 answer wrong and why does it seem intuitively correct. No proofs for the 1/3:2/3 answer please. Only direct proofs for why the 50:50 answer is wrong. Actually, even prominent mathematicians were fooled by this problem. Studies have shown that for those who initially got the answer wrong it seemed to be independent of intelligence or education. Thats, all true but it doesn't address the 50:50 answer directly or why most people think 50:50 is correct. Trust me the answer tells us important information about how the subconscious perceives reality. Actually, they didn't dismiss the additional information, since they thought their odds changed from 1/3 to 50:50. So they were wrong despite changing their odds to what they thought they knew was correct. Your definitely on the right track though.

I was afraid this would happen, Im not asking for the solution or proof. The challenge is to figure out why the incorrect intuitive answer is intuitive. Ive cleaned up the op to hopefully clarify this point. Sorry, it was a mess. My editor is acting up again and it starts becoming a chore to edit posts properly.

I assume everyone here is familiar with the Monty Hall problem. I'm not looking for the solution. I'm not looking for another proof for the solution. I'm not even looking for a full game solution which might incidentally show how the 50:50 solution couldn't be correct.. The challenge is to directly figure out why the 50:50 answer is wrong but more importantly why it seems so axiomatically correct. I've had the solution for some time, but wasn't sure how to present it. Since it's become a classic logic riddle, I realized this was probably the best forum. At least I hope so, Im still pretty new here. I'll give it some time and provide a new hint every now and then, before giving the solution. Hint: If you find the 50:50 answer axiomatic, than you will flip over the solution. Hint: The answer about why we perceive the 50:50 solution as correct will tell us something about how the subconscious perceives reality. Hint: Don't think of this as a logic problem,its more like a human nature problem. PS, I'm posting from an iPad and don't have an editor toolbox. I'd appreciate it if someone could post a hidden text box or spoiler alert box so I can clip the proper formatting elements. Thanks.