Can Math Help Answer Philosophical Questions?

[metatr2n]

Warning: I know very little math.

I have these two questions on my mind and felt this was a good place to ask if math, logic, etc. could be used to provide some measure of objectivity to these questions of a more philosophical nature. Like I said, the last time I looked at a quadratic equation was almost 20 years ago so read at your own risk...

1. I heard someone claiming that the outcomes of sports events were random. Not to say no skill or strategy at all involved, but that ultimately the outcome was random. This caused me to wonder how/if you could determine this with any degree of mathematical correctness. Is there any way to logically, statistically, mathematically- whatever- determine if the results of a sport event are random or else? Or is this knowledge beyond the ability of men to determine with any degree?

2. You and a friend are watching a man flip a coin. He flips the coin once and the result is heads. No surprise. He flips a second time; heads again. A third time; heads. This continues until the 20th straight heads and your friend states, "The coin is biased."

Is there any logical, statistical, mathematical way to determine that it is more likely that the coin is biased than it is not? Meaning, upon which flip does one reasonably move from, "It is as equally likely that the coin is biased than that it is not, to, it is more likely that the coin is biased than it is not?

I know that at some point- arguably far before the 1000th straight heads result- that we will intuit that the coin is biased; but that's just intuition of some sort. Is there any way to reasonably determine when an improbable result is more likely the outcome of chance and when it is more likely to be the outcome of interference? Not to say one or the other must be known with certainty- but when "<likely or =likely becomes >likely"?

 

[honestrosewater]

It sounds like you would find http://en.wikipedia.org/wiki/Law_of_large_numbers" helpful. If the two teams are evenly matched, as is often the case in highly-competitive leagues, it does make sense to me that chance plays a large role in the outcomes as far as being evenly matched means being equally likely to win. (Though their chances can change as the game progresses.)

As for your question about what math can do in these situations, I think you'll want http://en.wikipedia.org/wiki/Statistical_inference" .

I give links because they're somewhat large topics and wikipedia does a better job than I can at introducing and surveying them.