Continued from:
4. How the leopard got its spots
Turing himself turned toward this most intriguing topic towards the end of his research career. It’s a little-known fact that his most cited research paper is not for his eponymous Turing Machine, but for his contribution to developmental biology
Turing showed that one could provide insight into questions like ‘how the leopard got its spots’ and ‘how the zebra got its stripes’ by solving a set of ‘Differential equations’. These equations, assuming only cells and propagating waves of chemical reactions, produce solutions that are eerily similar to the patterns of stripes and spots we see in nature.
‘Differential equations’ are prolific throughout physics, but we don’t find them much in computer science, the field Turing helped found.
That’s because differential equations imagine that we can change ‘functions’ through infinitely small means. We imagine functions that change gradually, which are smooth, like sine waves or circles. This branch of mathematics is called ‘analysis’ in modern literature*
The functions of computer science are not like this, however. If we imagine a physical switch, the basis of transistors, they can only be ‘on’ or ‘off’. 0 or 1.
Computer science is founded on discrete mathematics. This digital, or boolean logic powers our digital world.
One thing we do know about biology though is that it is not completely digital.
Our neurons at the lowest physical level do not signal one another digitally like computer switches do. They are analogue, as are our cells and organs.
Curiously though, the foundation and likely origin of all life… our DNA and RNA is digital. DNA is fully described by 4 digits, ‘A’, ‘C’, ‘G’ and ‘T’
How can digital DNA give rise to complex, analogue cells and organs?
It’s an open-question which we’re only beginning to unravel.
[* Most often this is called ‘calculus’. However, referring to ‘calculus’ and ‘lambda calculus’ in the same context is confusing to an unfamiliar reader. The two branches are unrelated in their regular formalism]