On the 1 = -1 “proof”:
Part of it appears chopped off for me bu I can guess how it goes. The problem is clearly in splitting sqrt(-1 * -1) into sqrt(-1) * sqrt(-1). I don’t know why.
But our math system is flawed in its foundations in that it was built based on our perception of the world. First integer numbers (counting finite things), then decimals, then negative numbers (which have no physical meaning), then imaginary numbers (which only go to show that our math system is lacking). Or think about numbers like pi, e, sqrt(2), 10/3 etc which have an infinite number of decimal digits (so their exact value cannot be represented), yet geometry allows you to definitely divide a 10cm piece of paper in 3 exactly equal parts which is a contradiction. Or think of all the ugly constants in physics, that have seemingly arbitrary values.
My theory is that the world is too well structured (in all scales, from galaxies to quarks) to be ruled by such ugly values. There must be a physics/math system, where all these ugly numbers are actually simple and sensible and where calculation don’t come with conditions attached.
On the 1 = -1 “proof”: Part of it appears chopped off for me bu I can guess how it goes. The problem is clearly in splitting sqrt(-1 * -1) into sqrt(-1) * sqrt(-1). I don’t know why.
But our math system is flawed in its foundations in that it was built based on our perception of the world. First integer numbers (counting finite things), then decimals, then negative numbers (which have no physical meaning), then imaginary numbers (which only go to show that our math system is lacking). Or think about numbers like pi, e, sqrt(2), 10/3 etc which have an infinite number of decimal digits (so their exact value cannot be represented), yet geometry allows you to definitely divide a 10cm piece of paper in 3 exactly equal parts which is a contradiction. Or think of all the ugly constants in physics, that have seemingly arbitrary values.
My theory is that the world is too well structured (in all scales, from galaxies to quarks) to be ruled by such ugly values. There must be a physics/math system, where all these ugly numbers are actually simple and sensible and where calculation don’t come with conditions attached.