Jim Muth wrote:

At 08:07 PM 9/13/05 -1000, David wrote:

...

But fractals are real things, ...

Said in jest, but a true philosophical statement. I don't know about you, but I'm not so sure that fractals are real. They are certainly not as real as the tree outside my window. Actually, I have never seen a real fractal. All I have seen are pictures of fractals. We have pictures of the fractal objects but no objects to take photographs of.

Sure we do. The way trees organize themselves in forests, the ways leaves are positioned on branches, etc, etc, are all fractals, also.

Fractals are made of complex numbers, which are very useful abstractions, but they were created and exist only as mental constructs. By contrast, the tree outside my window is made of atoms, and from the number-filled books I have tried to read about quantum theory, I see that atoms are also apparently made of little more than numbers. The contrast has all but vanished.

Oh, they're made of stuff besides numbers, math is just a very poewrful and successful way to describe them and their relationships.

I am left with the quite philosophical thought that fractals and trees are made of the same stuff. This leads me to suspect that fractals might be more real than they appear, or maybe trees are less real.

Jim (now questionably real) Muth

Maybe we're all just devices fractals use to reproduce themselves???? -- David gnome@hawaii.rr.com authenticity, honesty, community