On 19 Oct 99, at 1:01, Steinar H. Gunderson wrote:
> >you can compare this to something like the value of Pi, relation of the
> >radius to the circumference, which human mind tries to instantly
> >rationalize as a "real" number, demonstrated clearly by the actual attempt
> >to _legalize_ Pi as 3.
I thought the legal value of pi was 4, in Indiana. Actually the
timber trade still calculates the volume of logs in an absurd way
which implies that pi = 4.
> >In fact, ask anyone what Pi is, and majority of
> >them will instantly reply to you "3.14".
In my experience, most of them will think of something sitting on a
plate, probably stuffed with apple & destined to be served
"schlagobers".
>
> >The square of two is another good
> >example of how "irrational" and counter-intuitive mathemathics really is.
>
> You made a slight typo there -- you did mean the square _root_ of two, did
> you?
In base phi, 2^2 seems to be irrational ;-)
> >To really claim that primes are either "random" or "non-random"
> >in nature would give you a ranom chance of being right ;)
Prime numbers clearly _aren't_ random in themselves, since they can
be constructed in a wholly deterministic way. Their distribution may
approximate to some defined trend with apparently random deviations
from that trend, but that's a different assertion altogether.
>
> But then, define random! If I toss a (`fair') coin, I'd say that it's
> random. However, a very quick viewer (or a computer) might see the moment
> before the coin hits the ground (and stays there), what it will turn up
> as. In other words, then the randomness is _not present_ at that time.
> Now, if you go backwards, you can probably calculate (if you're VERY
> quick -- remember this is all theoretical) this earlier on, perhaps all
> the way back to when the coin leaves your hand. Who knows, perhaps even
> further? :-)
I used to know someone who could shuffle a deck of cards so
accurately that he still knew what order they are in with about 95%
accuracy, even after eight or nine runs through. Needless to say, it
wasn't wise to play for money against him too often!
The point about the coin tossing is that I would expect that it's
_very_ rare for a human to have sufficiently accurate control to
consciously remove the "randomness" from the act of tossing a fair
coin. I wouldn't bet on the outcome of a coin tossed by a robot,
though.
Regards
Brian Beesley
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