"My own suspicion is that the universe is not only queerer than we suppose, but queerer than we can suppose."
~ J.B.S. Haldane
(1) If it is the case, as some suppose, that mathematics is somehow fundamental to the universe, then the above quote is necessarily true. Simply think of all the weirdness of the Reals. For example:
~ J.B.S. Haldane
(1) If it is the case, as some suppose, that mathematics is somehow fundamental to the universe, then the above quote is necessarily true. Simply think of all the weirdness of the Reals. For example:
"You can hit a random Real number with a dart and we don't even know how to look at the result, how to differentiate it from all the other ones around it" (see 6:41 in the video below). And note that almost surely (probability = 1) we will hit a number of this sort.
Also consider Gödel's Incompleteness Theorem: "Informally, Gödel's incompleteness theorem states that all consistent axiomatic formulations of number theory include undecidable propositions (Hofstadter 1989)." In other words, there are statements that can be made within mathematics that can neither be proven nor disproven: things queerer than we can suppose.
(2) Further, if it is the case that mathematics represents only some part of the universe and there are things within the universe not expressible in mathematics, then Haldane's suspicion is also necessarily true simply because it would entail the conjunction of all those things within the domain of mathematics, which we know contains things queerer than we can suppose, with all those things not expressible in mathematics; thus, it doesn't even matter if the things not expressible in mathematics are queerer than we suppose because we already have that.
(3) Finally, we can suppose that mathematics has nothing at all to do with universe, but if this is the case, then throw out all contemporary science (and, as a result, all the wonders of modern technology) that is intrinsically dependent upon mathematics for its expression. And this seems a result that is queerer than we can suppose.
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(4) Therefore, not only is the universe queerer than we suppose, but it is necessarily queerer than we can suppose.
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