Because minus signs indicate a negative entropy change and hence negative energy. It's like antimatter basically and when antimatter collides (multiplication) you get matter (positive energy). This is basically why.
Because minus signs indicate a negative entropy change and hence negative energy. It's like antimatter basically and when antimatter collides (multiplication) you get matter (positive energy). This is basically why.
Because minus signs indicate a negative entropy change and hence negative energy. It's like antimatter basically and when antimatter collides (multiplication) you get matter (positive energy). This is basically why.
Because minus signs indicate a negative entropy change and hence negative energy. It's like antimatter basically and when antimatter collides (multiplication) you get matter (positive energy). This is basically why.
Essentially to define negative numbers you use ordered pairs (x,y) which translate into an integer x-y. That means each integer is represented by an infinite set of ordered pairs, e.g. -1 is the set {(0,1), (1,2), (2,3), ...}.
So to calculate -1 x -1 you first translate it into (0,1) x (0,1), and use the definition of multiplication for ordered pairs (that's a mouthful - the Wiki page has the formula for this) to find the result is (1,0), which then translates back into 1.
It can be understood with complex numbers; On a diagram which lists the real part of a complex number on the x axis, and its imaginary part on the y axis (called an Argand diagram), a complex number is a point on this diagram, which is often described by the length of the line joining this point to origin (called its magnitude or modulus), and the angle that this line is at compared to the x axis, called the argument.
Now, when we multiply two complex numbers together, it can be shown that the result has a modulus that is the product of the first two moduli, but more importantly, the argument or angle of the two numbers are added. So -1 has an angle of 180 degrees compared to the positive part of the x axis, so if we multiply -1 by -1, we add the two angles, 180 + 180 giving us 360 degrees, which takes us back around to positive one.
Ok that may have been long winded and confusing, but it's at least one explanation. As I understand it there's another, more fundamental reason that can be shown through set theory, but I don't know it.