[The Huge Entity] New comment on This Discrete Universe: Time Exposed via Computati....
tridentblue has left a new comment on your post "This Discrete Universe: Time Exposed via Computati...":
Here's what bothers me about a continuous universe, transfinite numbers.
A countable numbers has the quality that it can be completely specified with a finite amount of information in a finite period of time. Uncountable numbers don't have this quality. So pi is a part of a countable set (Computable numbers) because a finite computer program can enumerate its infinite digits, and in enumerating all such finite computer programs, we come to pi. ANY number with a finite definition is countable, by enumerating all such definitions. Yet transfinite number theory states that the vast amount of real numbers, even on a finite interval, are uncountable, which is to say that they have infinite decimal places which are so random that they cannot be expressed (or compressed) into any finite expression, unlike numbers like pi and e which have finite definitions. So in other words it takes an infinite amount of information to precisely specify a given point on a real interval in the majority of cases.
So in using this to describe the universe, you have that classical "God doesn't play dice" view where an omniscient viewer (God) could tell you a particles position on its path at any moment of time. However even if an itsy bitsy particle where moving over an itsy bitsy interval, it would probably (2^aleph vs aleph) take an infinite amount of information to tell you where exactly where it is. Furthermore, in addition to having to know an INFINITE amount of information about a single particle at a moment in time, "God" would also have to know an infinite amount of information infinitely many times a second, just for one particle. What a pain in the ass for God!
I can't say for sure that this is not the case, but something about that deeply hints to me that the universe is discrete, call it a gut feeling.
Posted by tridentblue to The Huge Entity at May 03, 2010 10:55 PM
Here's what bothers me about a continuous universe, transfinite numbers.
A countable numbers has the quality that it can be completely specified with a finite amount of information in a finite period of time. Uncountable numbers don't have this quality. So pi is a part of a countable set (Computable numbers) because a finite computer program can enumerate its infinite digits, and in enumerating all such finite computer programs, we come to pi. ANY number with a finite definition is countable, by enumerating all such definitions. Yet transfinite number theory states that the vast amount of real numbers, even on a finite interval, are uncountable, which is to say that they have infinite decimal places which are so random that they cannot be expressed (or compressed) into any finite expression, unlike numbers like pi and e which have finite definitions. So in other words it takes an infinite amount of information to precisely specify a given point on a real interval in the majority of cases.
So in using this to describe the universe, you have that classical "God doesn't play dice" view where an omniscient viewer (God) could tell you a particles position on its path at any moment of time. However even if an itsy bitsy particle where moving over an itsy bitsy interval, it would probably (2^aleph vs aleph) take an infinite amount of information to tell you where exactly where it is. Furthermore, in addition to having to know an INFINITE amount of information about a single particle at a moment in time, "God" would also have to know an infinite amount of information infinitely many times a second, just for one particle. What a pain in the ass for God!
I can't say for sure that this is not the case, but something about that deeply hints to me that the universe is discrete, call it a gut feeling.
Posted by tridentblue to The Huge Entity at May 03, 2010 10:55 PM
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