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According to Max Tegmark the ultimate reality is the Mathematical world. Mathematically possibility also refers to physical possibility. Can there be such a type of universe where mathematical impossibility is a possibility but we humans are limited to know about its existence?

  • Not an easy issue.... There are universe (the physical one: see Relativity) where the geometry is different from our "natural" geometry (the Euclidean one), but this does not mean taht non-Euclidean geometries are "mathematically impossible". – Mauro ALLEGRANZA Mar 15 '20 at 7:53
  • The very idea of “possibility” still follows logic. But it still can be partial or wrong, so I’d answer ‘maybe’. – Francesco D'Isa Mar 15 '20 at 10:21
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    No. There is no scientific evidence of other universes. Period. – J D Mar 15 '20 at 19:00
  • We have been developing our mathematics in such a way that it meets the physical observations of our universe, if there is any other universe it might not follow the same mathematical models. It might even be infinitely complex system for mathematics but as history proves mathematicians find a way to bypass the difficulties to get a model they want! – Baba Yaga Mar 15 '20 at 19:29
  • At the Big Bang and maybe in black holes we have points in time at which neither the laws of physics nor consciousness exist, so I suppose one could call that "mathematical impossibility." But there is a problem with "points" in time or space, so one could argue that "mathematical impossibility" exists at any "point" in time. But I think that discussion of "possible impossibilities" whose existence is unknown to us puts us pretty far adrift in meaninglessness. And since logic constrains possibility, I don't think math it is compatible with "possible impossibilities." – Nelson Alexander Aug 27 '20 at 15:35
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"Impossibility" assumes a fixed logic frame, preceding the possible existence of any universe. Logicians consider Logic itself to be contingent -- IE there are potentially infinite versions of logic. So "impossible" carries its own caveat: "within X logical reference frame". https://math.vanderbilt.edu/schectex/logics/

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The conceptual basis for such a question has some problems.

Our Universe is ruled by irreducible laws of physics.

Mathematics is ruled by irreducible laws of logic.

So the first question must be, on what basis can one suggest that the laws of logic are in any way related to the universe we happen to be noticing them in? Sure they apply here, but on what basis could they not apply in any other unrelated physical universe which might exist?

The irreducible laws of logic comprise certain characteristics of propositions without which one cannot reason. These include things like; "something exists", "something else exists", "the something and the something else are distinct", "If I look at the something tomorrow, it will still be the something and will still be distinct from the something else," and so on.

Mathematics provides a significant subset of such reasoned logic, i.e. all of mathematics is subservient to such laws. For example, what use would it be if we woke up tomorrow to discover that 1+1=3 and after breakfast we found that now 1+1=an elephant? We might suspect that we were in the Heart of Gold Spaceship, but even that would be merely infinitely improbable. Mathematical rigour would have lost al meaning.

A mathematical impossibility by definition breaks one or more foundations of reason. So the second problem this question faces is that one can hardly lay claim to reason when suggesting that such things actually exist.

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Our own universe does not follow the rules of Mathematics. The rules of Mathematics are abstract and unconnected with reality, Mathematics transcend physics. This is because the Axioms of mathematics are based on theory, not on physical reality, for a given set of axioms, mathematics will be the same, regardless of universe.

The value of the fundamental constant pi (as a ratio between the distance is not a constant within our own universe, it is ONLY constant within the abstract, theoretical, featureless plane of Euclidian geometry; someone living in any universe could still invent Euclidian geometry, and if they did, the relationship between the circumference and diameter of a circle would be based on the same value of pi.

Even if in my universe whenever if I have thing, then having added another thing I have 0 things, 1 + 1 still equals 2 in the abstract world of number theory, it's just that in the physics of my universe, bringing two things together causes them both to disappear

We know this to be true, because it's nearly true in some situations in our physical universe too: 1 star with volume A + 1 star with volume A = 1 black hole with volume 0 (ish) for a large enough value of A. (or 1 cat + 1 mouse = 1 cat)

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