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Posers and Puzzles

Posers and Puzzles

  1. 08 Sep '07 03:43
    We want to predict how long the human species will continue to exist. This seems like a hard thing to predict, but let's try to attack the problem with probability.

    Imagine all the humans who were ever born or ever will be born, stretched out in one long line, in order of their birth. Label the front of the line 0 and the end of the line 100. Where are we on the line? There's no way of telling, as we don't know how many people come after us. We can, however, estimate how many people come before us. There are various estimates of the total number of humans who have ever been up to the present; let's use 100 billion as our number.

    OK, so now imagine picking a random human from our line. On average, where will this human be on the line. The mean value will be 50, the exact center. There's only 10% chance that our random human will be at a point less than 10, that is, in the first 10% of all humans ever born.

    But here's the important part: since we have no way of knowing where we fall on the line, we might as well imagine ourselves as being located in a random point on it. *That means that there is only a 10% that we are among the first 10% of humans born.* There is a 90% chance that we are among the last 90% of humans. So, let's suppose we are at the location on the line numbered 10. That means that, there will be 800 billion humans born, ever. Let's say 100 million babies are born each year until the species dies out. That gives us a mere 7,000 years of future existence, if we're at position "10" on the line.

    But there's a 90% probability that our position comes later than 10! In that case, we even have less than 7,000 years left!

    Basically, we have shown that there is a 90% chance that the human species will die out in the next 7,000 years.
  2. Subscriber sonhouse
    Fast and Curious
    08 Sep '07 04:59
    Originally posted by GregM
    We want to predict how long the human species will continue to exist. This seems like a hard thing to predict, but let's try to attack the problem with probability.

    Imagine all the humans who were ever born or ever will be born, stretched out in one long line, in order of their birth. Label the front of the line 0 and the end of the line 100. Where are we o ...[text shortened]... t there is a 90% chance that the human species will die out in the next 7,000 years.
    You are forgetting the potential of new technological developments like cheap travel to other parts of the Solar System, Mars, moons of Jupiter, Saturn, etc. That could and if we get there very probably would lead to interstellar travel, which spreads us to minimum Alpha Centauri, three stars there for the price of one, must be dozens of planets colonies could start on. I am writing a SciFi about a second start for humanity, the short gist is we get out into the solar system and sometime around 200 years from now, people start thinking about the problem of how to make sure humans survive into the far future so they, having mastered DNA/Nanotech, put seeds of our civilization in the form of Von Neuman machines but seed the outer moons, Jupiter, Saturn, etc., with these seeds that have all the accumulated knowledge of humanity and the seeds just lie dormant for billions of years, meanwhile, the human race goes on for hundreds of thousands of years and has a nice run in the galaxy but eventually dies out, the seeds on the moons forgotten. So billions of years go by, the sun starts into its red giant phase, becoming bigger than the orbit of the Earth so our planet fries but now the moons of Jupiter and Saturn start to warm up which is what the seeds have been waiting for, having been seeded on ice bodies, they start a process of preparing for the return of mankind, first with simple machines, the size of a dot where they come together by the millions and create more complex arrangements till they have enough of a local ecology going to make incubators which grow the first humans in billions of years, they are tended as infants by intelligent robots whose programming is to have the infants grow to adulthood and start a new human race, but this time the genetic material has been improved a lot, humans now a lot smarter, faster, immune systems a thousand times better, no auto-immune diseases and the like, stronger version of old humans, with an added vector of compassion for fellow humans and other life. Now a small city, later building spaceports, launching new vessels into interstellar space, much more mature humans going forth and spreading not only though our galaxy but Andromeda as well, which by this time has come crashing into the milky way so there are literally trillions of new star systems to explore. This time there are no religious wars tearing apart civilizations, no fanatics, everyone equal and expected to pull their own weight. So now humans have only the end of the universe to worry about, which they do, and devise ways to escape even that disaster by making bridges to new universes, young ones which will give them billions of more years of relative peace. Of course not everything goes according to plan but overall the human race goes on basically forever. How's that for a plot?
  3. Standard member wolfgang59
    Infidel
    08 Sep '07 06:15
    "*That means that there is only a 10% that we are among the first 10% of humans born.* There is a 90% chance that we are among the last 90% of ..."

    and a 100% chance we are amongst the last 100%??????
    therefore we die out today!

    methinks there is something wrong with your logic!
  4. 08 Sep '07 06:59
    Originally posted by GregM
    We want to predict how long the human species will continue to exist. This seems like a hard thing to predict, but let's try to attack the problem with probability.

    Imagine all the humans who were ever born or ever will be born, stretched out in one long line, in order of their birth. Label the front of the line 0 and the end of the line 100. Where are we o ...[text shortened]... t there is a 90% chance that the human species will die out in the next 7,000 years.
    I don't think we can do any prediction of the future with this kind of reasoning. Don't rely of extrapolations.

    Do the same kind of reasoning about the existence of the roman empire, the population mammoths, or the use of DDT and you will see at none of this can be predicted.

    If you try to predict the future of humanity you will be wrong in any method you use, and there is no way to confirm the result. You can't just wait and see if you were right.

    When the last man on earth has died, you just can't say "I was right!", nor anyone else can say "You were wrong!".
  5. Standard member agryson
    AGW Hitman
    08 Sep '07 10:50
    Originally posted by GregM
    We want to predict how long the human species will continue to exist. This seems like a hard thing to predict, but let's try to attack the problem with probability.

    Imagine all the humans who were ever born or ever will be born, stretched out in one long line, in order of their birth. Label the front of the line 0 and the end of the line 100. Where are we o ...[text shortened]... t there is a 90% chance that the human species will die out in the next 7,000 years.
    But if we were to think about it the way you are, the most probable "average place" on that line is at 50%. Funnily enough, if we continue to use that logic, we always stay at the 50% mark because it's the most probable. Tomorrow is the day that never comes...
  6. Subscriber AThousandYoung
    It's about respect
    08 Sep '07 23:09
    Originally posted by GregM
    We want to predict how long the human species will continue to exist. This seems like a hard thing to predict, but let's try to attack the problem with probability.

    Imagine all the humans who were ever born or ever will be born, stretched out in one long line, in order of their birth. Label the front of the line 0 and the end of the line 100. Where are we o ...[text shortened]... t there is a 90% chance that the human species will die out in the next 7,000 years.
    According to all the facts, the human species has never died out. Thus the probability of the human species dying out must be zero. Therefore,

    we will never die.
  7. 09 Sep '07 00:48
    Originally posted by wolfgang59
    and a 100% chance we are amongst the last 100%??????
    therefore we die out today!

    methinks there is something wrong with your logic!
    Of course there's a 100% chance that we are among the last 100% of humans ever born. By "ever born," I mean past, present, *and* future.

    It's pretty clear that the argument must be invalid, but that's not the issue.
  8. 09 Sep '07 00:49
    Originally posted by FabianFnas
    I don't think we can do any prediction of the future with this kind of reasoning. Don't rely of extrapolations.

    Do the same kind of reasoning about the existence of the roman empire, the population mammoths, or the use of DDT and you will see at none of this can be predicted.
    Right, the argument can't be correct. But where's the flaw?
  9. 09 Sep '07 00:52 / 1 edit
    Originally posted by agryson
    But if we were to think about it the way you are, the most probable "average place" on that line is at 50%. Funnily enough, if we continue to use that logic, we always stay at the 50% mark because it's the most probable. Tomorrow is the day that never comes...
    No, I don't think so. If we consider a random stretch of consecutive days, on average the first day will be before 50 and the last day after 50. Anyway, consider in light of the revised argument below.
  10. 09 Sep '07 01:14 / 3 edits
    Perhaps a more compelling version of the argument:

    Imagine you are placed in front of a machine with a lever and a small slot. Whenever you pull the lever a ball rolls out of the slot. There is exactly one red ball in the machine and a certain number of black balls. The number of black balls is exactly 10 or exactly 10,000.

    You pull the lever seven times, and on the eighth time the red ball comes out. Is it more likely that there are 10 black balls or 10,000? Obviously 10, because the red ball came up so soon. If there were 10,000 black balls, it would be extremely unlikely that the red ball would come out after only 8 tries.

    So let's apply the same argument to the human species. Suppose that the number of human beings who will ever live is either 1,000 billion or 1,000,000 billion. Only one of these human beings is you: you are like the red ball. Now, we start going through human beings in order of their birth. After only 80 billion people, we come to you. Is it more likely, then, that there are going to be 1,000 billion or 1,000,000 billion people ever born? Obviously 1,000 billion, since it is more likely that you would be so early in that scenario.

    Of course, there aren't only two possibilities for the lifespan of the species. There are an infinite number of possibilities, ranging from 80 billion to infinity. But we can still apply the ball machine argument: suppose you have no idea how many black balls are in the machine, but you get the red ball after 8 tries. It's likely that the number of black balls is of a similar magnitude, probably around 10-30. It's unlikely that there are more than, say, 300. Similarly, if we initially have no idea how long the human race will last but realize that only 80 billion people have come before us, it's unlikely that many thousands of billions of people will come after us.

    --

    Yes, the argument is obviously flawed. It's not so obvious just what the flaw is.
  11. Subscriber AThousandYoung
    It's about respect
    09 Sep '07 04:01
    Originally posted by GregM
    Perhaps a more compelling version of the argument:

    Imagine you are placed in front of a machine with a lever and a small slot. Whenever you pull the lever a ball rolls out of the slot. There is exactly one red ball in the machine and a certain number of black balls. The number of black balls is exactly 10 or exactly 10,000.

    You pull the lever seven time ...[text shortened]...

    --

    Yes, the argument is obviously flawed. It's not so obvious just what the flaw is.
    The flaw is that you need to designate which person is the red ball before you "pull the lever" for the first time.

    What we actually have is a machine with all different color balls, no two alike.
  12. Standard member wolfgang59
    Infidel
    09 Sep '07 09:52
    Originally posted by GregM
    Of course there's a 100% chance that we are among the last 100% of humans ever born. By "ever born," I mean past, present, *and* future.

    It's pretty clear that the argument must be invalid, but that's not the issue.


    Then what is the issue?
  13. Standard member ark13
    Enola Straight
    09 Sep '07 14:40
    http://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Probability-generating_function

    Look at the section on inductive probability. This is similar to what you're doing. And it makes sense with large numbers for the variable "s," but little sense when you have few. For example, the chance of there being another human being born = (100 billion +1)/(100 billion +2) which seems reasonable to me. However, the chances of there being another 100 billion people born = (1+1)/(1+2). Now, this is reduced to pure speculation, as the probability of a failure is entirely unknown without a single one. You must remember that this method only provides a rough estimate, which can hardly even be called an estimate without sufficient trials and failures.
  14. Standard member agryson
    AGW Hitman
    09 Sep '07 21:53
    Originally posted by GregM
    Yes, the argument is obviously flawed. It's not so obvious just what the flaw is.
    Well the flaw seems perfectly clear to me. Whatever logic is applied should be able to come up with the same result if applied to earlier or later generations. Both versions of the logic presented come up with pretty much the same answer no matter which generation we apply it to. In the first version of the logic, the second generation of humans were 50% along the line, just like we are today.
    In the red ball version, since we do not know which number of balls we're dealing with, as well as the very self-centered view that we are the red ball as opposed to some far in the future generation, then the result is the same, since there is any number of permutations from 0 to infinity, there is no useful probability through any means that can give us even a rough estimate.
  15. 10 Sep '07 01:39
    Originally posted by ark13
    http://en.wikipedia.org/wiki/Pierre-Simon_Laplace#Probability-generating_function

    Look at the section on inductive probability. This is similar to what you're doing. And it makes sense with large numbers for the variable "s," but little sense when you have few. For example, the chance of there being another human being born = (100 billion +1)/(100 billio ...[text shortened]... estimate, which can hardly even be called an estimate without sufficient trials and failures.
    That does seem somewhat similar, and if the argument used Laplace's formula I think you would be right to criticize it on that grounds. But as it stands the argument makes no reference to "successes" or "failures."