5 ms·

Tested in the field: Will monkeys type shakespeare?

2 points by huangm 17y ago

RiderOfGiraffes 17y ago
People really, really don't understand the concept of infinity, nor the concept of "with probability 1." The most interesting point about the idea that people actually go out and try these things, is to prove that people just don't understand these things. The conclusion that "the theory is flawed" shows they don't understand the theory. The question I have is - should we care? Should we try to explain these things? Or should we just shrug and give up. How will it actually make their lives better? For some people it might, but then again ...
- pp 17y ago
  While I certainly agree with you, I must admit that it never occurred to me that the whole monkey typist experiment depends on the assumption of the monkey's being able to actually hit each key. :)
- abdulhaq 17y ago
  Yes this small study does not disprove that, given enough monkeys and enough typewriters, a shakespearean play will be produced. However, we need only look to the internet to see that the proposition is indeed false.
  - RiderOfGiraffes 17y ago
    Cute, but wrong (as you probably know). Even the size of the internet and all the drivel on it is infintesimally smaller than infinity. Ron Graham once told me that the problems we have in mathematics are caused in part by the fact that we only ever deal with small numbers, and he's the one who used Graham's Number. http://en.wikipedia.org/wiki/Grahams_number http://en.wikipedia.org/wiki/Grahams_number
- pp 17y ago
  On a serious note, have people been more educated in probability, the economic crisis might not have turned out as bad. Look at Nassim Taleb to see how far some probability consciousness can get you.
- astine 17y ago
  If the probability of producing the desired result in any given attempt is zero, then the probability of producing the desired result given infinite attempts is still zero. If monkeys are incapable of typing, then the probability is zero.
  - RiderOfGiraffes 17y ago
    > If the probability of producing the desired result > in any given attempt is zero, then the probability > of producing the desired result given infinite > attempts is still zero. This is a common misconception. Pick a point uniformly at random in the interval from 0 to 1. The probability of any given point is zero, but the probability of being in the interval [a,b) is b-a (assuming 0<=a<=b<=1). This is a case of infinitely many zeroes giving a non-zero sum, and why you need to deal carefully with infinities. Yes, I know about countable and uncountable infinities. This is a big subject, and small comments here won't cover it. There are rules and exceptions.
    - astine 17y ago
      One over infinity is a different kind of zero than we're talking about. An infinitesimal value is not a nil value.
      - RiderOfGiraffes 17y ago
        One over infinity is not a zero at all, because it's an ill-defined operation. You need to say exactly what you mean, and which number system you're working in. Are you in the surreals? Non-standard analysis? The hyper-reals? If you work with standard analysis, your comment seems to be a non-sequiteur. If not, you need to say which system you're in. Personally, I think the other systems are largely unhelpful, although independently interesting. And of course an infinitesimal is not zero (nil being a different technical term). If I've missed the point(s) you were tying to make, you'll need to be more explicit. Probably further "discussion" here is not going to be fruitful, but I'll be interested to read anything you care to add.

2 points by huangm 17y ago

People really, really don't understand the concept of infinity, nor the concept of "with probability 1." The most interesting point about the idea that people actually go out and try these things, is to prove that people just don't understand these things. The conclusion that "the theory is flawed" shows they don't understand the theory. The question I have is - should we care? Should we try to explain these things? Or should we just shrug and give up. How will it actually make their lives better? For some people it might, but then again ...

pp 17y ago
While I certainly agree with you, I must admit that it never occurred to me that the whole monkey typist experiment depends on the assumption of the monkey's being able to actually hit each key. :)
abdulhaq 17y ago
Yes this small study does not disprove that, given enough monkeys and enough typewriters, a shakespearean play will be produced. However, we need only look to the internet to see that the proposition is indeed false.
- RiderOfGiraffes 17y ago
  Cute, but wrong (as you probably know). Even the size of the internet and all the drivel on it is infintesimally smaller than infinity. Ron Graham once told me that the problems we have in mathematics are caused in part by the fact that we only ever deal with small numbers, and he's the one who used Graham's Number. http://en.wikipedia.org/wiki/Grahams_number http://en.wikipedia.org/wiki/Grahams_number
pp 17y ago
On a serious note, have people been more educated in probability, the economic crisis might not have turned out as bad. Look at Nassim Taleb to see how far some probability consciousness can get you.
astine 17y ago
If the probability of producing the desired result in any given attempt is zero, then the probability of producing the desired result given infinite attempts is still zero. If monkeys are incapable of typing, then the probability is zero.
- RiderOfGiraffes 17y ago
  > If the probability of producing the desired result > in any given attempt is zero, then the probability > of producing the desired result given infinite > attempts is still zero. This is a common misconception. Pick a point uniformly at random in the interval from 0 to 1. The probability of any given point is zero, but the probability of being in the interval [a,b) is b-a (assuming 0<=a<=b<=1). This is a case of infinitely many zeroes giving a non-zero sum, and why you need to deal carefully with infinities. Yes, I know about countable and uncountable infinities. This is a big subject, and small comments here won't cover it. There are rules and exceptions.
  - astine 17y ago
    One over infinity is a different kind of zero than we're talking about. An infinitesimal value is not a nil value.
    - RiderOfGiraffes 17y ago
      One over infinity is not a zero at all, because it's an ill-defined operation. You need to say exactly what you mean, and which number system you're working in. Are you in the surreals? Non-standard analysis? The hyper-reals? If you work with standard analysis, your comment seems to be a non-sequiteur. If not, you need to say which system you're in. Personally, I think the other systems are largely unhelpful, although independently interesting. And of course an infinitesimal is not zero (nil being a different technical term). If I've missed the point(s) you were tying to make, you'll need to be more explicit. Probably further "discussion" here is not going to be fruitful, but I'll be interested to read anything you care to add.