Since antiquity humans have tried to describe things and ideas. The caves of Lascaux in France contain remarkable, awesome images of animal paintings dated to about 40,000 years ago. Plato tried to describe the essence of things and ideas in his construct of ideals, and Da Vinci tried to understand the essence of things through his drawings and physical models.
It seems to me that all these constructs could be classified as Models.
Examples of Models:
Newton’s Theory of Gravity.
Differential Geometry’s models of non-Euclidean Geometry.
Fractals - A model in search of a something to represent - At least until recently.
Mathematical Model Theory.
Douglas Hoffstadtler’s comments about meaning:
(from “Godel, Escher, Bach: an Eternal Golden Braid”).
Comments about Equivalency Classes.
Relational Data Bases.
Artificial intelligence.
I plan to structure this in such a way that each Model will have it’s own original post and the series of posts will probably extend over the next 3 months or so. Part of the extended length of time is due to the fact that I will be frequently out of town with business or social obligations during this time.
I will try to keep my posts readable, but my post on Differential Geometry will contain material requiring at least a passing knowledge of Calculus. The rest of my posts will be pretty straight forward.
If I state that the new corvette Z06 has 4 - 3.5" exhausts instead of 4" exhausts or forget the runcible spoon in the Owl and the Pussy cat’s great adventure, just jump in a make a correction. Sometimes, I just completely screw up - please help.
Feel free to add your own models if you like.
Ultimately, my goal will be to see if any relationships can be determined to exist among the various models
How models (patterns) relate to one another or how they imitate each others structures is something I’m interested in.
I suspect that like with the Mandelbrot Set, simple things can produce vastly complicated outcomes that repeat themselves infinitely.
We construct models in imitation of how the natural model has constructed our brains.
The Mandelbrot set has been said to be a model of every physical structure - it’s boundary is infinitely detailed, and never repeats itself - meaning that it inevitably includes every possible structure.
I'm interested to read about some of those - I've never heard many of them discussed with regards to this particular concept.
Go for it!
I’m afraid that SIATD might be right about models in general, but I think Satyr’s comment has some merit: “We construct models in imitation of how the natural model has constructed our brains”.
As far as the Mandelbrot set goes, I intend to let the little hair left in my head down for a while and indulge some fantasies.
If this were so then we’d need some supplementary ‘brain structure’ that would allow us to see that we were simply seeing the world as resembling the structure of the brain. And then we’d need another supplementary brain structure to be able to see that brain structure. And so on…