I’ve long been fascinated by the phenomenon of imaginary numbers. Mandelbrot fractals depend on them entirely, at least when they’re used in the form of complex numbers.
And subsequently, they’ve been discovered to be at work in several real-world situations, especially in chaos theory as well as quantum field theory.
One problem with them is the problem physicists imagine because the notion of an imaginary number is so profoundly, well, unimaginable. But whereas some physicists have been horrified by their use, I’ve been endlessly intrigued by them.
An imaginary number is founded upon the square root of -1 which they indicate with the letter i. The problem is there is no such thing as the square root of -1. But, so what? The entire universe is unimaginable!
Benoit Mandelbrot is the guy who made complex numbers famous. He used i in complex numbers from which he plotted graphs where an x-axis is a real number and a y-axis is an imaginary number. The result is what has been famously called Mandelbrot Fractals, derived from complex number math.
If we apply them in an iterated formula Z=Z^2 + C and iterate it billions of times (with a computer of course) we get blossoming images that look like this, called a Mandelbrot zoom:
Thanks, Ben this is great… Julian M.Galvez says that the reason we don’t have an irreducible fraction for Pi and the diagonal of an oblong is that we present geometric ideas as if they are flat when the world is curved. His indication is that when we deal with the idea of a different idea of the world we will find many ideas that we can’t truly imagine now. There is a book I just received (not read yet) The Number Sense by S, Dahaenes. I understand he talks about how our brain deals with numbers. Thank you for your continued look at life.
Thanks, Suzanne