Here's a thought: the way mathematicians use numbers is fantasy.
Example: mathematicians claim 1 + 1 = 2.
'= (equals)'? Impossible in absolute terms. They can only mean that 1 and another 1 have something in common; and that common feature, there are two of.
But 1 + 1 actually means 'this 1' plus 'that 1'.
If it didn't, there would be no difference between the 1's; such that you couldn't even talk of another 1. If one 1 is absolutely the same as the other 1; there is in fact only one 1.
So to have 1 plus 1; you must be really talking about different 1s. So everyday math is a fantasy of imaginary numbers and generalisations.
Ironically; the numbers that mathematicians call "imaginary" are the REAL ONES.
Why? Because 'i' incorporates within it the fact that each '1' IS DIFFERENT. The square root of -1 represents a vector which 'multiplied by itself' gives a vector of one unit in a 'negative' direction. "Multiplied by ITSELF"? Impossible: can only multiply 'this' by 'that'. Actually there is a superposition of vector operations: the pattern that results gives you -1.
If you look closely at vector multiplication; you find there is a difference in the two vectors and their application relative to each other.
Now any difference at all, is as good as saying well 'this' by 'that' gives -1; and you could just call 'this' '+' and 'that '-' and you have the regular result say -1 times 1 = -1.
Relativity, superposition, and quantum jumping are all tied up in this whole business, it seems.
Nature reads its book by complex numbers, they say at www.emmynoether.com. Of course; because with complex numbers you get nature's numbers ('i') mixed with man's pattern-recognition (natural numbers etc.), thus gives you complex numbers.
-dolphin |