Re: coin flipping

James Wetterau (
Thu, 28 Oct 1999 12:14:12 -0400

Anders Sandberg says:
> Rob Harris <> writes:
> > And I assert that probability exists only as a fix for uncertainty in
> > systems one wishes to predict that have too many variables of too high a
> > complexity to track. Probability will become obsolete with the arrival of
> > the necessary technology. Or will it? What do you think?
> There are processes that are too complex for any finite system to
> predict. Many of the most interesting and relevant systems in the
> universe are chaotic and highly influenced by weak interactions from
> the environment. In these cases you would still need
> probability. Remember, probability is best viewed as uncertainty (yes,
> I'm a Bayesian too :-), and no matter what our level of technology, we
> will have uncertainty due to limitations in information processing,
> sensing abilities, information storage and complexity.

Assuming that the probability is in fact uncertainty, do we not still have a circularity in the definition? Let's take coin flipping. Let's pretend that we have good historical data showing close to 50% heads / 50% tails, with no apparent correlation to any other factor. So we hypothesize that the state sets that lead to heads or tails are both about equal in size. We've received the 50/50 results *up until now* due to the flip occurring in a world state that leads to heads half the time and tails half the time.

Now consider future flipping. Just because the state sets are roughly equal in size, why do we believe that future flips will be roughly equally divided between those that produce heads and tails? Because the probability of the flipper being in any particular state from among the state space that leads to a particular result is about 50%. So we're back to appealing to probability. We've moved the probability, not explained it.

Help me break this circle.