There are transparent contradictions inherent in all current mathematical systems for reasoning about real numbers, but no human mathematician/physicist can notice them because they rely heavily on visuospacial reasoning to construct real analysis proofs.
I thought about this once, but I discovered that there are in fact people who have little or no visual or spatial reasoning capabilities. I personally tested one of my colleagues in undergrad with a variant of the Mental Rotation Task (as part of a philosophy essay I was writing at the time) and found to my surprise he was barely capable of doing it.
According to him, he passed both semesters of undergraduate real analysis with A’s.
Of course, this doesn’t count as science....
EDIT: In the interest of full disclosure, I should point out that I make something of an Internet Cottage Industry out of trolling people who believe the real numbers are countable, or that 0.9999… != 1, and so on. So obviously I have a great stake in there being no transparent contradictions in the theory of real numbers.
I thought about this once, but I discovered that there are in fact people who have little or no visual or spatial reasoning capabilities. I personally tested one of my colleagues in undergrad with a variant of the Mental Rotation Task (as part of a philosophy essay I was writing at the time) and found to my surprise he was barely capable of doing it.
According to him, he passed both semesters of undergraduate real analysis with A’s.
Of course, this doesn’t count as science....
EDIT: In the interest of full disclosure, I should point out that I make something of an Internet Cottage Industry out of trolling people who believe the real numbers are countable, or that 0.9999… != 1, and so on. So obviously I have a great stake in there being no transparent contradictions in the theory of real numbers.