Bill Jefferys wrote:
> At 9:20 AM -0800 3/29/02, Hal Finney wrote:
>
> >That's true, but even so, a coin with a .95 chance of coming up heads
> >and a .05 chance of coming up tails is "simpler" by your definition
> >than a fair coin, right? Even though the parameter is not adjustable,
> >the presence of an ad hoc value like .95 makes it seem intuitively less
> >simple than a fair coin, at least to me.
>
> Suppose it's a computer program that produces 95% 1's and 5% 0's...In
> that case I don't see this.

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I'm sorry, do you mean (A) you don't see that the computer program is
"simpler" by your definition, or (B) you don't see that the computer
program is intuitively more complicated than one that produces even
numbers of 0's and 1's?
In any case, all I was trying to do was to come up with an example of a
case where your definition of "simple" seems to run contrary to what I
think most people's intuitions would be. I agreed earlier that there
were cases where your definition does have a good correspondence with
the intuitive meaning; for example, both would consider a theory complex
if it had many adjustable parameters.
Possibly the computer program does not present as obvious a contrast
between intuition and your definition as a biased coin; I don't know.
The point is that in at least some cases the definition seems to differ
from the intuition.
Hal Finney