Maximum number of possilities?

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Discussion Overview

The discussion revolves around the concept of the maximum number of possibilities in the context of coin tossing and theoretical physics, particularly related to Hubble volumes. Participants explore the implications of finite versus infinite possibilities and the mathematical frameworks that might apply.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant suggests that it is always possible to add another imaginary coin to an imaginary pile, leading to the question of whether there is a maximum number of possible outcomes.
  • Another participant states that for n identical coins, there are n+1 possibilities, while for n different coins, the number of possibilities is 2n, both of which are finite.
  • A different viewpoint is presented, arguing that while integers and real numbers are finite, there are infinitely many of them, raising questions about the nature of possibilities.
  • One participant mentions a reference to a Hubble volume but expresses uncertainty about what possibilities are being enumerated in that context.
  • Another participant refers to a Scientific American article by Max Tegmark, discussing the countable configurations of fields within a Hubble volume and the implications for finding other universes with identical states.
  • A later reply acknowledges a misunderstanding regarding the interpretation of 10^118 as a mathematical versus physical restraint on possibilities.

Areas of Agreement / Disagreement

Participants express differing views on the nature of possibilities, with some asserting that possibilities are finite while others suggest a more complex relationship with infinity. The discussion remains unresolved regarding the implications of Hubble volumes and the specific nature of the possibilities being discussed.

Contextual Notes

There are limitations in the discussion regarding the definitions of terms like "Hubble volume" and the specific configurations being referenced. Some mathematical steps and assumptions about the nature of possibilities are not fully explored.

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
 
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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.
 
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.
 
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.
 
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.
 
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
 

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