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Hierarchy Mathematical Systems


Dean Mullen
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Mixing maths with science, many scientists are convinced there is other Universes and that they have varying laws of physics, I realize that this may effect mathematics in a real way. Mathematics may work differently in different universes, although it sounds uncomprehendbale that there could be a universe in which 1+1 = 3, it maybe possible, for if you lived in a universe were 1+1 always equalsed 3, and it was natural for if you put an apple beside another apple, there is three apples, you would not question 1+1 = 3, yet in our universe, maybe 1+1=2 just seems natrual and normal, for we grew up with it, and no nothing else than it.

 

There may also be multi-multiverses, where +, -, x and divsion come into existence and whom knows if you climb the hierarchy ladder of existence far enough, you reach a point were maths is created, if not then were does maths come from? you could pressume it doesn't come from anywhere and is just the natrual concept of reality, yet we cannot pressume this if the laws of physics vary per universe, and thus you can conclude that you must throwaway the assumptions that the way things work in this universe is the same for everywhere else. I call this theory the Hierarchy Mathematical Systematic Theory.

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Mixing maths with science, many scientists are convinced there is other Universes and that they have varying laws of physics, I realize that this may effect mathematics in a real way.

 

This I don't understand. Mathematics "lives in a world of its own".

 

Mathematics may work differently in different universes, although it sounds uncomprehendbale that there could be a universe in which 1+1 = 3, it maybe possible, for if you lived in a universe were 1+1 always equalsed 3, and it was natural for if you put an apple beside another apple, there is three apples, you would not question 1+1 = 3, yet in our universe, maybe 1+1=2 just seems natrual and normal, for we grew up with it, and no nothing else than it.

 

We can build up without reference to the real world the system of integers. Up to issues of notation, 1+1 =2.

 

There may also be multi-multiverses, where +, -, x and divsion come into existence and whom knows if you climb the hierarchy ladder of existence far enough, you reach a point were maths is created, if not then were does maths come from?

 

This sounds like a question of metamathematics and philosophy. I am not very familiar with the different philosophical ideas of the origin of mathematics. Wikipeadia has a nice article on the philosophy of mathematics here.

 

you could pressume it doesn't come from anywhere and is just the natrual concept of reality, yet we cannot pressume this if the laws of physics vary per universe, and thus you can conclude that you must throwaway the assumptions that the way things work in this universe is the same for everywhere else. I call this theory the Hierarchy Mathematical Systematic Theory.

 

This sounds a bit like the mathematical universe hypothesis, as laid down by Tegmark in The Mathematical Universe. Found.Phys.38:101-150,2008 (arXiv:0704.0646v2 [gr-qc]). In short, all structures that mathematically exist also physically exist.

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I think even if some other dimension with its own set of rules did exist the concept of 1 + 1 = 2 would hold. When creating the counting system and assigning Ordinals to such devices I do believe the quark would become apparent and the reasoning would have its own law explaining the logic of the event transpiring. I could see this sort of thing happening in a system where quanta are forced to exist in odd and not even whole numbered states, but I don't see how it would eliminate the set of whole even numbers. Mathematics extends to all dimensions and is not localized so even if the rules were different in the one universe from another the rules would still be a subset of the powerset known as the 'Universal Set' which extends to all of everything.

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For a sufficiently useless metric, it'd be perfectly reasonable to say that 1+1=3 (mod 1) and for that to apply to real spaces.

 

I've never been keen on the mathematical universe, it sounds awfully similar to the 'the universe can be, and so it is' type of ToEs - although the question is entirely philosophical in nature I tend to hold on to the idea that there are ways things could have been but they turned out not be.

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I've never been keen on the mathematical universe, it sounds awfully similar to the 'the universe can be, and so it is' type of ToEs - although the question is entirely philosophical in nature I tend to hold on to the idea that there are ways things could have been but they turned out not be.

 

I have not thought too deeply about the mathematical universe hypothesis. It does seem to be an extreme interpretation of Eugene Wigner "unreasonable effectiveness" [1].

 

To me it is interesting that very abstract mathematics can often find application in physics. The question is can all mathematics find application in physics?

 

This is then also tied to Hilbert's philosophy that mathematics is a game in which you can set any initial rules. If the mathematical universe hypothesis is correct then mathematics may be more constrained that initially thought, constrained by reality!(???). To some extent this is the case anyway, in order to get non-trivial and interesting structures you are not really free to do whatever you want. This is certainly true at a practical level, mathematics departments usually have researchers working in relatively well defined branches. It is not a complete "free for all".

 

 

This all gets very philosophical very quickly...

 

References

[1] Eugene Wigner (1960). "The Unreasonable Effectiveness of Mathematics in the Natural Sciences". Communications on Pure and Applied Mathematics13 (1): 1–14.

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