Do you think that probability could operate any differently to how it does or that it is an intrinsic mathematical property of any universe’s reality? I ask because my father who is a philosopher asked my sister who is a mathematician and I think it is an interesting question.
My sister plumbed for, no, probability cannot operate any differently.
I think my dad was interested in a universe for instance containing deities with the power to usurp probability, in which case everything is lawless (or miraculous depending on your outlook) and evolution is anyone’s guess! At this point I get lost in ontology.
My immediate answer was yes, probability could operate differently; it might not function at all. I was thinking of universes that are too chaotic to make observations: there would be no way to formulate any probability, evolution could not occur.
There are probably other ways a universe could operate probability differently if you were allowed to change the values of fundamental constants. This maybe is not a mathematical answer but a different physical manifestation of how the maths would play out. The maths and physics equation might stay the same but have expression differently because of the varied constants.
I tried to think of what would happen if Pi was not the transcendental number 3.142… but was equal to 1! Pi is the ratio of the diameter to the circumference of a circle. It seemed to me the result would be circles would be reduced to a line so that the circumference was equal to just the diameter, but I wasn’t sure and I couldn’t visualise it or any other values. Google to the rescue!
It turned out, to be technical, Pi is only defined in Euclidean space. Other non-Euclidean geometries can and will have a different value for the ratio of the diameter to the circumference (in which case, it is not called Pi).
http://www.daviddarling.info/encyclopedia/N/non-Euclidean_geometry.html includes a nice table for the geometries where the relationship is Pi, less than Pi, and greater than Pi.
So we may well be living in a universe that is “open” and has a hyperbolic geometry but it occurred to me that still won’t change a coin toss probability. Maybe my sister is right and maths is so fundamental that it is abstract from implementation. I will stick by chaotic realms as an alternative though. Likewise, universes which usurp probability by being completely deterministic and tosses are foretold can be imagined by those that want to.
matthew simpson 