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Thanks for the explanation. While I have no doubt you're right (because I am completely outside my field of expertise), I have difficulty intuitively accepting

Thanks for the explanation. While I have no doubt you're right (because I am completely outside my field of expertise), I have difficulty intuitively accepting the answer. By way of comparison, the wikipedia entry on the infinite monkey theorem [1] refers to the probability of producing the Shakespeare corpus as "almost sure", a situation that seems broadly analogous to the one you describe. I suspect the difference is that the monkeys are required to produce an output which is merely random rather than evenly distributed. [1] http://en.wikipedia.org/wiki/Infinite_monkey_theorem http://en.wikipedia.org/wiki/Infinite_monkey_theorem

lutusp 14y ago
> I suspect the difference is that the monkeys are required to produce an output which is merely random rather than evenly distributed. Perhaps, or the fact that probability theorists regularly describe a probability of 1.0 as "almost certain", a wording that to me contradicts common sense: http://en.wikipedia.org/wiki/Almost_surely http://en.wikipedia.org/wiki/Almost_surely
- jasomill 14y ago
  Of course it does. It's similarly unreasonable to call a Möbius Strip with a disc attached along the boundary circle a "plane"[1], the surface of Cartesian (x, y) coordinates a "line"[2], and numbers having counterintuitive special features, "normal". [1] http://en.wikipedia.org/wiki/Real_projective_plane http://en.wikipedia.org/wiki/Real_projective_plane [2] http://en.wikipedia.org/wiki/Complex_line http://en.wikipedia.org/wiki/Complex_line
  - JadeNB 14y ago
    > numbers having counterintuitive special features, "normal". I don't think that 'normal' implies 'intuitive', even in normal usage.
- Evbn 14y ago
  Any technical field has to define more concepts than can be distinctly named by casual vocabulary using their plain England meaning, so some words will be jargon. Don't pick on "almost sure". We also have group, ring, field, ideal, prime, countable, closed, ....
tzs 14y ago
> While I have no doubt you're right (because I am completely outside my field of expertise), I have difficulty intuitively accepting the answer. When intuition fails while contemplating something involving infinity, I find it comforting to recall something John von Nuemann said: "Young man, in mathematics you don't understand things. You just get used to them".

lutusp 14y ago

> I suspect the difference is that the monkeys are required to produce an output which is merely random rather than evenly distributed. Perhaps, or the fact that probability theorists regularly describe a probability of 1.0 as "almost certain", a wording that to me contradicts common sense: http://en.wikipedia.org/wiki/Almost_surely http://en.wikipedia.org/wiki/Almost_surely

jasomill 14y ago
Of course it does. It's similarly unreasonable to call a Möbius Strip with a disc attached along the boundary circle a "plane"[1], the surface of Cartesian (x, y) coordinates a "line"[2], and numbers having counterintuitive special features, "normal". [1] http://en.wikipedia.org/wiki/Real_projective_plane http://en.wikipedia.org/wiki/Real_projective_plane [2] http://en.wikipedia.org/wiki/Complex_line http://en.wikipedia.org/wiki/Complex_line
- JadeNB 14y ago
  > numbers having counterintuitive special features, "normal". I don't think that 'normal' implies 'intuitive', even in normal usage.
Evbn 14y ago
Any technical field has to define more concepts than can be distinctly named by casual vocabulary using their plain England meaning, so some words will be jargon. Don't pick on "almost sure". We also have group, ring, field, ideal, prime, countable, closed, ....

tzs 14y ago

> While I have no doubt you're right (because I am completely outside my field of expertise), I have difficulty intuitively accepting the answer. When intuition fails while contemplating something involving infinity, I find it comforting to recall something John von Nuemann said: "Young man, in mathematics you don't understand things. You just get used to them".