Rhett Butler
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Registered User
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May 15 |
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Google question: In a country in which people only want boys @Steven Landsburg: DZ calculated the difference for 10 couples: 47.5 grils and 52.5 boys. Here comes my receipe for your gambling: Put everytime 1 million bucks on black. If black comes don't stand up but start your next series. During 10 series there will be less reds than blacks. It is really ridiculous that nobody ever thought about this simple method of making money! But what happens, if another player will bet on red everytime also always stopping a series, when red comes (not standing up then but starting the nexts series)? 52.5% red and simultaneously 52.5 % black? Overflow??? |
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May 14 |
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Google question: In a country in which people only want boys @Douglas Zare: What you say is true: you get paid B-G. When playing ten rounds, always stopping if boy/black shows up, then according to your prediction you win in 52 % and lose in 48 % of all cases. Or would you like to revise your prediction? |
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May 14 |
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Google question: In a country in which people only want boys @Jon Peterson: $\frac{G_n}{B_n + G_n}$ is not a martingale. But it is completely irrelvant to calculate it. $\frac{E(G)}{E(B + G)}$ is asked for. The latter is 1/2 for every country and every number of families. |
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May 14 |
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Google question: In a country in which people only want boys @Jon Peterson: If for 10 rounds/families always stopping at b (for black or boy) will supply 47 % red/girl and 53 % black/boy, then you have a winning strategy. Always bet the same amount of money on black. You will win more frequently than you will lose. |
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May 14 |
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Google question: In a country in which people only want boys @Douglas Zare: What is the difference between sequences of bits in form of boys and girls, interrupted at "boy" and started new at an arbitrary point, and bits of black and red interrupted at "black" and started new at an arbitrary point? If you can find a reasonable explanation, I will not hesitate to apologize. |
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May 14 |
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Google question: In a country in which people only want boys @Douglas Zare: "Showing that E(A)/E(A+B) = 1/2 is not enough. You need another assumption." No, you need nothing else. The original question is: Can the family planning of a set of families result in a set of children such that E(A) differs from E(B)? The answer is no, since probability of 1/2 per girl is a martingale. You have answered another question not relevant in the present context. |
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May 14 |
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Google question: In a country in which people only want boys @Douglas Zare: Whatever you did, you did not correctly answer the question whether family planning can influence the equilibrium beteen boys and girls. The answer is no. But you claim that this answer is correct only for large populations and that your answer is different and the only correct one for smaller populations. Once you will recognize that the sex of a child is in no way dependent on the intentions or history of the mother, you should see your error. Your calculation of the weighted average over the ratios is not what you claim it was, namely an answer to the original question. |
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May 13 |
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Google question: In a country in which people only want boys The question asks about the ratio of boys and girls and not about the mean value of averages in families. My own treatment and my recognition of this fact should show anybody that I am very interested in this question. I attribute your insulting manner to the fact that you recognize to have lost against Lubos Motl (who, as a Harvard string theorist, is certainly not less than you able to understand the simple error made by Douglas and accepted by you). |
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May 13 |
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Google question: In a country in which people only want boys You ask: "But what is the expected fraction of girl-births?" Why should this number interest anyone who cares whether familiy planning can influence the population equilibrium? or "what fraction of the population is female?". Even if it is made crystal clear that average of fractions is not equal to the fraction of average, this does not entitle anybody to chose the wrong number. |
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May 13 |
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Google question: In a country in which people only want boys @:Qiaochu: Douglas' receipe could be used to play roulette, always betting on black and, after stopping (for a while), starting a new sequence. If the chance of red for the current single sequence is less than 31 % in the average, even the sporadic appearance of the zero could not hinder you to get a rich man. |
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May 13 |
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Google question: In a country in which people only want boys @rgrig: But it lets us hope. |
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May 13 |
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Google question: In a country in which people only want boys @Timothy: E[G/(B+G)] is not interesting in order to find "the fraction of female population". For that sake we need E[G]/E(B] and that is 1 because the sex of a child does not depend on the history of the mother. |
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May 13 |
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Google question: In a country in which people only want boys Reading some less upvoted answers below I have to correct me. There are some correct answers. Nevertheless, the overwhelming majority has gone astray. |
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May 13 |
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Google question: In a country in which people only want boys @Kevin: The question is obviously well defined. Steven Landsburg formulated it in the same sense as Douglas Zare and others: "What fraction of the population is female?" And the question is one of the most interesting ones I ever encountered because it shows what is possible in mathematics. Over three years nobody in this elite forum has observed that this big answer is a big mistake as can be proved by a very simple idea. |
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May 13 |
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Google question: In a country in which people only want boys @Federico: Neither monogamay nor immortality nor the opposite will have any influence. Consider the children being taken from a very large conveyor belt. It is of no influence on the sex of the child which mother takes the next one off the belt. |
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May 13 |
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Google question: In a country in which people only want boys @Jon: The probability of a girl to be born is a martingale, completely independent of the number of girls and of the history of their mothers. The expectation value of additional girls within the next 200 births is 100 with an error marge of 10. Same holds for boys. Therefore the population will never deviate by more than the statistical fluctuations from the 50:50 equipartition. |
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May 13 |
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Google question: In a country in which people only want boys @Jon: The answer calculated the average of the percentage of girls. But the question asks for the percentage of all girls. Further what is an expectation value? It has no meaning for a single case but only for a big number of cases. If 31 % girl expectation for a single family would be correct, then the ensemble of all families of the country would get close to it. If you don't believe in my explanations, then play roulette. Always bet 5 bucks on black and stop a sequence after black has appeared. Within 3000 sequences you should have earned more than 1000 bucks. Good luck! |
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May 13 |
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Google question: In a country in which people only want boys @Douglas: You have found a roulette winning strategy without raising the stakes. No doubts? |
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May 12 |
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Google question: In a country in which people only want boys @Douglas: You answered the false question. The ratio B/G of boys to girls in a population is (nearly) 1. And by a birth that has same probabilities b = 0.5, g = 0.5, b/g = 1, it is impossible to change this ratio. It has been asked whether the ratio B/G can be subject to manipulations. It can not. And as Thorny says and as I also few minutes ago found myself: It is completely irrelevant which couple decides to cease fire and which will continue. Therefore the independent variables will remain equal within the statistical margin. |
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May 12 |
awarded | ● Fanatic |
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May 11 |
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Sum of odd number is a square, whos theorem is this? deleted 2 characters in body |
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May 11 |
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The Angel Problem - was the bet paid? @aorq: Any news? |
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May 11 |
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Did any new mathematics arise from Ruffini’s work on the quintic equation? name corrected |
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May 9 |
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Who first cared about singular points? @Paul: Well, Hermann used this word. l'Hospital would have had far better a reason, but according to my research he did not use that word. By the way, as far as I have looked through some of Newton's writings, neither does he. |
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May 9 |
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Prove that the sum of a certain infinite series is 1 Is this a cry for help or an invitation to a contest? |
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May 9 |
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Who first cared about singular points? Additional remarks |
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May 6 |
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Can different bicycles leave the same tracks? In every point you can calculate the radius of curvature, using the well-known formula. And in every point you have a certain front angle. Both force the rearwheel to follow according to the Pythagorean formula. |
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May 6 |
awarded | ● Nice Answer |
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May 6 |
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What is the history of $\sqrt{}$ added 842 characters in body |
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May 6 |
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What is the oldest known evidence of application of mathematics? @fedja: If every shaping counts as an application of geometry then every birth counts as an application of arithmetic. I think that is exaggerating a bit, a matter of opinion though. |
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May 6 |
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Can different bicycles leave the same tracks? @Douglas: Every piece of the tracks can be considered to be a piece of a circle (depending only on the momentary angle of the frontwheel). |
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May 5 |
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Can different bicycles leave the same tracks? @Yoav: I don't think so. You are right, it is possible, for instance, to have a circle with radius $r_2 = 0$ But as soon as $r_1$ is changed also $r_2$ will follow by the given Pythagorean equation such that never limit- or start-effects can take pace. |
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May 5 |
answered | Can different bicycles leave the same tracks? |
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May 5 |
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What is the oldest known evidence of application of mathematics? @fedja: I have heard that pigeons can count up to seven (so they can apply the pigeon-hole-principle so far). And Pythagoras' theorem has been known long before himself in Egypt, Babylon and other places. But my question concerns artefacts of arithmetic or geometry that are really older than 30 KY. |
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May 5 |
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What is the oldest known evidence of application of mathematics? @unknown: Thank you very much for that interesting source. |
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May 5 |
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What is the oldest known evidence of application of mathematics? @Carlo: Thank you, but I saw it already some time ago (and upvoted your answer). According to Wikipedia there could be prime numbers involved in the interpretation of the Ishango text. But I think that is not very probable. Anyhow would like to know more about these earliest origins of mathematics. |
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May 5 |
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The eliminant of a system of differential equations deleted 1 characters in body |
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May 5 |
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What is the oldest known evidence of application of mathematics? deleted 2 characters in body; edited tags |
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May 5 |
asked | What is the oldest known evidence of application of mathematics? |
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May 4 |
answered | What does ! above = mean |
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May 4 |
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What is the best *general triangle*? @Mark: I see. I overlooked the not-obtuse condition. Personally, in a 270° triangle I would admit an obtuse angle. |
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May 4 |
answered | The eliminant of a system of differential equations |
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May 4 |
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Large numbers in small systems added 1 characters in body |
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May 4 |
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Large numbers in small systems added 243 characters in body; edited body; added 4 characters in body; added 2 characters in body |
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Apr 30 |
awarded | ● Nice Answer |
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Apr 30 |
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Math History Question about the exponential function edited body |
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Apr 29 |
answered | Periods and commas in mathematical writing |
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Apr 28 |
awarded | ● Necromancer |
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Apr 28 |
answered | Math History Question about the exponential function |
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Apr 26 |
answered | What is about J. v. Neumann’s “continuous geometry”? |
