Computation vs Mathematics
I’m amazed by how poorly this distinction is understood. The Computer changed everything because it abandoned mathematics and replaced it with algorithms.
The book Complex Adaptive Systems, Chapter 5, Computation as Theory, has two excellent quotes, the first from Robert Hooke, in his Micrographia:
By the addition of such artificial Instruments and methods, there may be, in some manner, a reparation made for the mischiefs, and imperfection, mankind has drawn upon it self, by negligence, and intemperance, and a wilful and superstitious deserting the Prescripts and Rule of Nature, whereby every man, both from a deriv’d corruption, innate and born with him, and from his breeding and converse with men, Is subject to slip into all sorts of errors.
The second is from Stanislaw Ulam in his Adventures of a Mathematician:
The use of computers seems thus not merely convenient, but absolutely essential for such experiments which involve following the games or contests through a very great number of moves or stages. I believe that the experience gained as a result of following the behavior of such processes will have a fundamental influence on whatever may ultimately generalize or perhaps even replace in mathematics our present exclusive immersion in the formal axiomatic method.
You may have to lift up your pants as you wade through that last quote. He is saying the computer is affecting the practice of mathematics itself – a real revolution in Science!
The book goes on to discuss models in housing construction, and the invention of balloon framing in Chicago in the 1830s. This is how most houses are still constructed in America: using 2x4s and nails.
In Costa Rica, prefabricated concrete walls and posts are used with metal rafters and roofing – because of the earthquake hazard, and also to make them fire-proof and termite-proof.
In either case a construction model is used – which makes construction easier. But using a model has its drawbacks – all the houses tend to be the same.