Wednesday, August 03, 2005

Bayesian superminds

Esto es bastante pedante pero igualmente divertido:

How To Be Much Cleverer Than All Your Friends (so they really hate you)

If you want to, you can learn Bayesian probability theory. Start with
Jaynes, it shouldn't take more than about ten years to finish the book,
assuming you don't waste time on anything else, making it excellent value
for money. If you do, you will be acquiring the skill of thinking in a
non-Aristotelian Logic, just as advertised. This will make it possible for
you to solve problems that are currently beyond your powers to even state
let alone solve. People who can reason in such a way about the world are
readily employable and useful members of society: we call them

I claimed that mastering a non-Aristotelian logic makes you smarter and able
to see things lesser mortals cannot. An example would help at this point;
you can see a small problem though: if you are still a lesser mortal, how
will you see it? Still, I shall give one anyway; it deals with the expected
lifetime of the human species. Papers have been written explaining that it
is very likely that the human race will be extinct within a few thousand
years. The argument is one which the simple minded non-Bayesian might find
convincing, but which the Bayesian super-mind can penetrate easily and
dispose of as a pile of dingo-droppings. Naturally, since you are not, as
yet, a Bayesian super-mind, you won't follow this - but you may get the
flavour of it.

Imagine that you are given a box which is fixed on a desk top and has a
button on top.

You are told that the box may contain either ten balls or a thousand balls.
All the balls are the same except that one and only one has your name
printed on it. You are asked to decide which box you have here, the thousand
ball box or the ten ball box. All you can do is to press the button, and you
are told that when you do, a ball will fall out of the box.

You reason that you have to press the button eleven times. If the eleventh
button press produces a ball, then it must have been the thousand ball box,
since the ten ball box wouldn't have anything to produce. So far we have
conventional Aristotelian type reasoning.

You press the button once and a ball comes out. You press it again and
another ball comes out. You press it again and a third ball comes out - and
this one has your name on it.

You can now make a pretty good guess as to which box you have. It is one
hundred times as likely to be the ten ball box as the thousand ball box.
This result should agree with your intuitions if you have any. The Bayesian
can provide a justification for this very quickly - but this is easy and
understandable only for superbeings and you aren't one yet. You should,
however, be able to see that getting your name up in the first three goes is
not too improbable if there are only ten balls in the box but is awfully
unlikely if there are a thousand. And if it is a hundred times as unlikely,
then the ten ball explanation ought to be about a hundred times as
believable. This is the intuitive, common sense approach. To a Bayesian, it
is not just plausible it is blindingly obvious - although it requires some
additional assumptions, which he or she can state precisely and you can't.
This is because as a result of using a powerful non-Aristotelian Logic, they
are smarter than you. Annoying, isn't it?

Now we come to the life of species...

(read the rest at the link!)

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