Maximum number of possilities?

[GENIERE]

My math is limited to that taken in an engineering curriculum many years ago.

I hope someone might help me on this:

A statement I'm not sure is correct, followed by a question I’m not sure is properly posed.

It must always be possible to add another imaginary coin to an imaginary pile. If one tosses this pile into the air there is a possibility that all coins will land “heads up”. It follows that there is always less than an infinite number of possibilities.

If above is true, is there some maximum number of all possible outcomes?

This question arises due to an article I read recently, wherein the author stated something like “in a given Hubbell volume…. 10^118 is the maximum number of possibilities”. I can’t recall where I read it, nor the exact statement.

Regards

 

[mathman]

For coin tossing (assuming all coins are the same), when there are n coins, there are n+1 possibilities (no. heads from 0 to n). The probabilities are given by the binomial distribution.

If there are n different coins then the number of possibilities is 2ⁿ.

In either case, the number of possibilities is finite.

 

[HallsofIvy]

All integers (indeed all real numbers) are finite but there are an infinite number of them: in addition they have no upper bound.

As to “in a given Hubbell volume…. 10^118 is the maximum number of possibilities", I can't help you because I don't know what a Hubble volume is nor what "possibilities are being enumerated.

 

[Daminc]

http://www.floatingplanet.net/planetp2/archives/000225.html is one of the few references I can find that may have some bearing.

I think he mean's Hubble Volume.

 

[ahrkron]

There was a Scientific American article regarding something of this sort (by Max Tegmark).

I think the point of the number of possibilities was that, if each Hubble volume contains fields that cannot escape from it (hence are confined and quantized) and if spacetime itself is quantized, then there is a countable number of configurations you can have for all the fields contained in a Hubble volume. Then, assuming that all Hubble volumes have a random selection of values for these fields, he computed the distance at which we would be able to find another universe (hubble volume) with the exact same state as ours.

 

[GENIERE]

Thanks for the responses!

Ahrkron - Yes that was the article I was trying to read while everyone was grabbing their luggage. I misread it and inferred 10^118 as a mathematical restraint on possibilities rather than a physical restraint.

It was bugging me ever since.

Regards