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Good catch. I have never thought of this. Thanks. the "common misconception" you mention is common probably because it is normally one's first intuition. So, i

Good catch. I have never thought of this. Thanks. the "common misconception" you mention is common probably because it is normally one's first intuition. So, if I understand well, (sorry to say that but the number 3 analogy didn't help), the probability of something not happening with infinite chances or opportunities to happen can be small, but the chance of it never happening exists (so if we flip a coin infinite times, we may get infinite Heads and never get a single Tail(?)) Now that you said that in your comment, it feels intuitive. And this shows that there is a common misconception about the theorem of the infinite monkey[1]. And changes some intuitions about the chances of intelligent life existing out of Earth... 1- https://en.wikipedia.org/wiki/Infinite_monkey_theorem https://en.wikipedia.org/wiki/Infinite_monkey_theorem

bambax 8y ago
If you flip a coin an infinite number of times, you will get a certain number of heads and a certain number of tails (0 for either, being a possibility), but you will never get something that is neither head nor tails. "Infinite" doesn't mean other constraints cease to exist.
- paradoxparalax 8y ago
  Yes , sure, thanks for adding this point too. It will be infinite only inside the limitations that were set when formulating the problem. It can not extrapolate out of the limitations only because something inside it is infinite. But this I knew before, it is pretty obvious, off course, at least for me, and what you say explain the number 3 analogy in the parent comment I was replying to, I see now, and the reason I found the analogy weak is that this was already obvious. And thanks for confirming that "...(0 for either, being a possibility).." That was the important bit for me. Also, the chances of getting a Head in 10 flips is bigger then the chances of getting a Head with only 2 flips. So if we got 10 Heads already, every time we get another Head, it may decrease in some way the chance of getting another Head next flip, But the Curve of Decrease in the chances of getting a head again will approaching zero forever... ...(no, this may be wrong, theoretically, every time you flip the coin the chance is always 50%) , but the overall(infinite) curve's line will never touch the zero line. this probably wrong somewhere, that is why people go broke trying to do the "double the bet" by playing always on the black or always on the red on the roulette at the casino, always doubling the bet when they loose some shot. This is paradoxal and confusing for me and is the reason I stopped jumping from 15, 20 meter high rocks into the sea. I thought the chances of something going wrong (solely because of the Law of Probabilities, not counting ageing and other factors) will Increase overall, and someday I was going to get hurt.
  - adrianN 8y ago
    Every sequence of coin flips has the same probability. The coin doesn't know that you have seen ten heads already.
    - paradoxparalax 8y ago
      Yes, thats what I thought...but also the chances of getting a head in 10 shots is bigger then getting a head in 2 shots, otherwise playing only once in your life at lottery would be the same as playing everyday, but the financial cost is measured by unit, I mean, the price is by single ticket. Or I am wrong here all again and this is where I was wrong? Sorry you maybe you made your comment before some edit I made, But I am grateful you have pointed out this, Thank You.
      - paradoxparalax 8y ago
        So, the Coin doesn't know that the last shot was a Head, Or the last 10 shots were all Head, and 0 Tails sofa, but....... Someone knows...call it Math, call it God, call it The Universe, my friend, someone knows.
    - hutzlibu 8y ago
      (except that in real life your hand flipping the coin knows that and can and will act differently. With practice you can influence consciously the outcome of the flip)
- PhasmaFelis 8y ago
  Hmmm. What are the constraints on universal possibility, though? My understanding is that it's possible (albeit staggeringly unlikely) for any possible structure, including living beings, to spontaneously form via quantum fluctuation, and given infinite time and space every possible structure will spontaneously generate. If the many-worlds theory is true, then there's a universe where you were just crushed by a hippo that randomly materialized above your head. The odds of any given person tripping (possibly on a spontaneously-generated rock) and breaking his ankle on the day he would have been killed by a mortar shell seem pretty high, relative to that.
  - paradoxparalax 8y ago
    "My understanding is that it's possible (albeit staggeringly unlikely) for any possible structure, including living beings, to spontaneously form via quantum fluctuation, and given infinite time and space every possible structure will spontaneously generate." That was exactly my perception, specially given infinite time, not to mention space, so here is Infinite squared, or Infinite x Infinite, because there are two Infinite fields of possibilities. Off course I didn't have any Idea about the existence of Quantum Fluctuation, just was my intuitive perception. And thank you for teaching me about It's existence. "If the many-worlds theory is true..." This is already too complex for my Simple Mortal Mind to understand, at this moment of my lifetime.
- baxtr 8y ago
  Wait a second... other possibilities are very unlikely but not impossible! It could end up on the side for example
mikorym 8y ago
Normally, one also thinks that Achilles will reach the tortoise. Number 3 is the world in which said chosen author does not die. The set of (both positive or all) real numbers less than 2 or the set of rational numbers less than 2 would be the set of uncountable and countable worlds that exist, respectively. These are two examples of overarching multiverses in which one has infinite possible worlds, but said chosen author always dies anyway.
- paradoxparalax 8y ago
  I had never thought He would reach the Tortoise, even when I was a kid and heard this Zenon's Paradox for the first time. But that is interesting and funny and you made me smile.
nyc111 8y ago
> (so if we flip a coin infinite times, we may get infinite Heads and never get a single Tail(?)) But flipping a coin follows strict rules. A robot who is programmed to flip with same variables will always make the coin land on the same side.
- paradoxparalax 8y ago
  Eureka!!! Thank You nyc111, you are the Genius One! what you said is obviously true, but in our Mental Experiment we assume priorly that we are talking about a imagined perfectly Random 50/50 % chances of Heads or Tails. Reality is more complex then mental experiments, of course... ...So your point is very good!!! Reality is the point...Yes...So the life existing in other planets is still good, no mind the misconceived infinite monkey theorem being wrong or right. And okonomiyaki3000 may have made a good point too, so we don't worry and ... </ Warning: some humor coming in the next words, if you don't like humor you can just stop reading this comment here... </begin humor > ...envy our parallel life where I am the Emperor of the far-eastern Asian Empire and have more then 1 wife. </end of humour>

bambax 8y ago

If you flip a coin an infinite number of times, you will get a certain number of heads and a certain number of tails (0 for either, being a possibility), but you will never get something that is neither head nor tails. "Infinite" doesn't mean other constraints cease to exist.

paradoxparalax 8y ago
Yes , sure, thanks for adding this point too. It will be infinite only inside the limitations that were set when formulating the problem. It can not extrapolate out of the limitations only because something inside it is infinite. But this I knew before, it is pretty obvious, off course, at least for me, and what you say explain the number 3 analogy in the parent comment I was replying to, I see now, and the reason I found the analogy weak is that this was already obvious. And thanks for confirming that "...(0 for either, being a possibility).." That was the important bit for me. Also, the chances of getting a Head in 10 flips is bigger then the chances of getting a Head with only 2 flips. So if we got 10 Heads already, every time we get another Head, it may decrease in some way the chance of getting another Head next flip, But the Curve of Decrease in the chances of getting a head again will approaching zero forever... ...(no, this may be wrong, theoretically, every time you flip the coin the chance is always 50%) , but the overall(infinite) curve's line will never touch the zero line. this probably wrong somewhere, that is why people go broke trying to do the "double the bet" by playing always on the black or always on the red on the roulette at the casino, always doubling the bet when they loose some shot. This is paradoxal and confusing for me and is the reason I stopped jumping from 15, 20 meter high rocks into the sea. I thought the chances of something going wrong (solely because of the Law of Probabilities, not counting ageing and other factors) will Increase overall, and someday I was going to get hurt.
- adrianN 8y ago
  Every sequence of coin flips has the same probability. The coin doesn't know that you have seen ten heads already.
  - paradoxparalax 8y ago
    Yes, thats what I thought...but also the chances of getting a head in 10 shots is bigger then getting a head in 2 shots, otherwise playing only once in your life at lottery would be the same as playing everyday, but the financial cost is measured by unit, I mean, the price is by single ticket. Or I am wrong here all again and this is where I was wrong? Sorry you maybe you made your comment before some edit I made, But I am grateful you have pointed out this, Thank You.
    - paradoxparalax 8y ago
      So, the Coin doesn't know that the last shot was a Head, Or the last 10 shots were all Head, and 0 Tails sofa, but....... Someone knows...call it Math, call it God, call it The Universe, my friend, someone knows.
  - hutzlibu 8y ago
    (except that in real life your hand flipping the coin knows that and can and will act differently. With practice you can influence consciously the outcome of the flip)
PhasmaFelis 8y ago
Hmmm. What are the constraints on universal possibility, though? My understanding is that it's possible (albeit staggeringly unlikely) for any possible structure, including living beings, to spontaneously form via quantum fluctuation, and given infinite time and space every possible structure will spontaneously generate. If the many-worlds theory is true, then there's a universe where you were just crushed by a hippo that randomly materialized above your head. The odds of any given person tripping (possibly on a spontaneously-generated rock) and breaking his ankle on the day he would have been killed by a mortar shell seem pretty high, relative to that.
- paradoxparalax 8y ago
  "My understanding is that it's possible (albeit staggeringly unlikely) for any possible structure, including living beings, to spontaneously form via quantum fluctuation, and given infinite time and space every possible structure will spontaneously generate." That was exactly my perception, specially given infinite time, not to mention space, so here is Infinite squared, or Infinite x Infinite, because there are two Infinite fields of possibilities. Off course I didn't have any Idea about the existence of Quantum Fluctuation, just was my intuitive perception. And thank you for teaching me about It's existence. "If the many-worlds theory is true..." This is already too complex for my Simple Mortal Mind to understand, at this moment of my lifetime.
baxtr 8y ago
Wait a second... other possibilities are very unlikely but not impossible! It could end up on the side for example

mikorym 8y ago

Normally, one also thinks that Achilles will reach the tortoise. Number 3 is the world in which said chosen author does not die. The set of (both positive or all) real numbers less than 2 or the set of rational numbers less than 2 would be the set of uncountable and countable worlds that exist, respectively. These are two examples of overarching multiverses in which one has infinite possible worlds, but said chosen author always dies anyway.

paradoxparalax 8y ago
I had never thought He would reach the Tortoise, even when I was a kid and heard this Zenon's Paradox for the first time. But that is interesting and funny and you made me smile.

nyc111 8y ago

> (so if we flip a coin infinite times, we may get infinite Heads and never get a single Tail(?)) But flipping a coin follows strict rules. A robot who is programmed to flip with same variables will always make the coin land on the same side.

paradoxparalax 8y ago
Eureka!!! Thank You nyc111, you are the Genius One! what you said is obviously true, but in our Mental Experiment we assume priorly that we are talking about a imagined perfectly Random 50/50 % chances of Heads or Tails. Reality is more complex then mental experiments, of course... ...So your point is very good!!! Reality is the point...Yes...So the life existing in other planets is still good, no mind the misconceived infinite monkey theorem being wrong or right. And okonomiyaki3000 may have made a good point too, so we don't worry and ... </ Warning: some humor coming in the next words, if you don't like humor you can just stop reading this comment here... </begin humor > ...envy our parallel life where I am the Emperor of the far-eastern Asian Empire and have more then 1 wife. </end of humour>