Of Maths and Science

I was reading Forty Signs of Rain by author Kim Stanley Robinson and came across this passage that really sums up the world of mathematics and science:

Mathematics sometimes seems like a universe of its own. But it comes to us as part of the brain's engagement with the world , its structure or recipe.

Over historical time humanity has explored further and further into the various realms of mathematics, in a cumulative and collective process, an ongoing conversation between the species and reality. The discovery of the calculus. The invention of formal arithmetic and symbolic logic, both mathematicizing the instinctive strategies of human reason, making them distinct and solid as geometric proofs. The attempt to make the entire system contained and self-consistent. The invention of set theory, and finessing the various paradoxes engendered by considering sets as members of themselves. The discovery of incompletability of all systems. The step-by-step mechanics of programming new calculating machines. All this resulted in an amalgam of maths and logic, the symbols and methods drawn from both realms, combining in the often long and complicated operations that we call algorithms.

In the time of the development of the algorithms, we also made discoveries in the real world: the double helix within our cells. DNA. Within half a century the whole genome was read, base pair by base pair. Three billion base pairs, parts of which are called genes, and serve as instruction packets for protein creation.

But despite the fully explicated genome, the details of its expression and growth are still very mysterious. Spiralling pairs of cytosine, guanie, adenosine, and thymine: we know these instructions from growth, for the development of life, all coded in sequences of paired elements. We know the elements; we see the organisms. The code between them remains to be learned.

Mathematics continues to develop under the momentum if its own internal logic, seemingly independent of everything else. But several times in the past, purely mathematical developments have later proved to be powerfully descriptive of operations in nature that were either unknown or unexplainable at the time the math was developed. This is a strange fact, calling into question all that we think we know about the relationship between maths and reality, the mind and the cosmos.

Perhaps no explanation of this mysterious adherence of nature to mathematics of great subtlety will ever be forthcoming. Meanwhile, the operations called algorithms become ever more convoluted and interesting to those devising them. Are they making portraits, recipes, magic spells? Does reality use algorithms, do genes use algorithms? The mathematicians can't say, and many of them don't seem to care. They like the work, whatever it is.