On 17 May 2002, at 12:16, Morgan L. Owens wrote:
At 18:35 16/05/2002, David Jones wrote:
On 15 May 2002, at 10:49, Jim Muth wrote:
am indulging in fantasy,
No, just not that good at it.
but none can dispute that the
Mandelbrot set and its associated Julia sets comprise a single four-dimensional object that in a sense most certainly does exist, yet cannot be comprehended by the human mind. This 4-dimensional object is sometimes called the Julibrot figure.
Hmm, I disagree. I believe the 4D Julibrot can be *comprehended* by the human mind - it just cannot be *visualized* by the human mind.
David gnome@hawaii.rr.com
No, Jim finds he can't comprehend it,
Personally, I suspect he comprehends it better than I do. I just poke around and see how they look. Jim actually has some idea of what a formula will give him.
and tends to mistake his own abilities and opinions for universal constants. What's so impossible about comprehending a two-dimensional stack of two-dimensional structures? It's like comprehending the graph of y=x^3+ax+b as a and b are varied independently. It could take more or less work, but comprehension always does. How much work depends in part on how much practice and thought is undertaken. Remember the hassles involved in learning to read?
Nope, did it too long ago. ;-)
Besides, the Julibrot itself can be treated as a slice of and index to an uncoubtable infinity of other higher-dimensional structures.
That could be true, beyond my knowing. David gnome@hawaii.rr.com