Computer technology vs. partial differential equations
I studied Engineering and graduated with honors, but I must admit that I never liked mathematical analysis, and was never too good at it. I found it as being too abstract and hard to visualize; on the other hand, I loved computer science, it was my second nature, I could naturally visualize it without efforts. My thesis work, when I graduated, was about a simulation of an automatic storage system at a car factory, which I simulated using what are now generically called cellular automata.
After graduation I started working in management related jobs, later became an entrepreneur and last year I sold the latest company; I never really used calculus.
After selling the company, I took sometime off to understand more about neuroscience, cell biology, artificial intelligence and the principles of computer science. I am reading all kinds of different stuff. I find fascinating how observations coming from biology and neuroscience inspire many different fields that have been historically separated (physics, engineering, AI, CS, math, etc).
What I found out, is that there are efforts from engineers to export their modeling skills (mainly based on mathematical analysis) to neuroscience and biology, which is something I instinctively feel is not right.
I am reading a "controversial" book from Stephen Wolfram: A New Kind of Science. Wolfram offers his perspective:
It is in a sense surprising that systems [partial differential equations] which involve such a high level of mathematical abstraction should have become so widely used in practice.
And I suspect that in fact the current predominance of partial differential equations is in many aspects a historical accident - and that had computer technology been developed earlier in the history of mathematics, the situation would now be different.
Maybe Wolfram will come up with the issue of "time" later in the book, but another strong feeling that I have, after reading some cell biology and neural science, is that time should be taken out of the loop, because it does not help much in describing these emergent systems. It actually complicates the whole picture.
Moreover, one should imagine if there is something even more primitive than computer science (which was formalized by Turing, a mathematician, as a way to solve a mathematical problem). The idea that computer science is the primitive to describe the world and not an accident itself should be at least contemplated.
