[ExI] Belief in maths (was mind body dualism).
msd001 at gmail.com
Wed Jul 7 23:51:33 UTC 2010
2010/7/7 John Clark <jonkc at bellsouth.net>:
> On Jul 6, 2010, at 8:27 AM, Mike Dougherty wrote:
> I feel that even if you have seen a coin flip result in heads 99 times in a
> row, you cannot state with absolute certainty that the 100th toss will also
> be heads.
> Assuming that the coin is fair (and I'd have my doubts after 99 heads) the
> chance it will come up heads again is 50-50. And being absolutely certain is
> the easiest thing in the world; being absolutely certain and also correct is
> much more difficult, and even then you may not know you are absolutely
> certain and correct.
Of course a fair coin is 50/50. How did we learn this?
I'm not trying to make a counterpoint. I would really like to grok
this. Given no prior experience of a fair coin, is the 50/50
probability so obvious? If we start with the understanding that there
are two countable states of coin then it is possible to claim one or
the other will result from 2 choices, therefore 1/2 or 50/50 chance.
Suppose we now try to enumerate the states of a hypercubic golden
dragon (for the sake of an absurdity) What is the probability that it
will be in any of those states upon being discovered?
How do we compute probability on unknown states of objects with
complexity several orders of magnitude beyond a coin or a pair of
dice? It's not an academic exercise where one can start with "assume
a large computronium-based Jupiter brain" or some theoretical
"enumerate the states of the universe and subtract..." We make these
guesses about the likelihood of everyday events... well... everyday.
How do we get from personal/subjective experience to ideal mathematical models?
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