Lazy Line Painter Jane

It's been quite a long day - it has definitely been more than the usual score and 4 hours, yet at the same time I seem to have ran out of day in my hours. Next essay: On the paradoxes of time and study.

In between studying what I should study, my mind wondered onto thinking about numbers and I thought I should write an innumerate persons thoughts on maths. I scribbled a paragraph, then got back to what I was supposed to be doing...

For some reason, the more abstract the mathematical idea the more intuitive it has seemed to me. I have found discussing set theory or fractal geometry less intimidating than multiplication tables and long division. There is something unspeakably beautiful about mathematics, or it seems unspeakable given our conceptual language - as if there is something ineffable about it, which our natural languages can't quite touch yet, and maybe only mathematics itself can touch - or some other, higher-order language - in which case, we better all get fluent. It's not just in mathematics that this is the case though, the abstract in general has always been comforting to me, it has always seemed closer to the truth. It gives us a way to talk about systems, rather than just atomistic phenomena and it allows us to move up beyond dislocated disparate facts into something that coheres and ushers in the next round of facts. It gives a framework, or a frame of reference, from which to ask the right questions. Without it, we flail around in empirical space and every now and then we will hit upon something, just like molecules, every now and then we'll bump into a binding site, and just like molecules, the more frantically we work, the more often this will happen. But also just like molecules, kinetics dictates that eventually there will be diminishing returns - eventually all of the facts (the substrate) will be bound up into a network and the only way forward will be a more fundamental shift. Normal science works well like this within a given frame once the ground has been laid, the day to day, 9 to 5, business-as-usual science (as if any scientist only works 9 to 5) gets along just fine this way. It reminds us that every negative result is still a result and continues on its apparently random motion, gathering up facts, snowballing as it goes, but every now and again, once we reach the plateau, the only way forward is stepping back and thinking more slowly - stepping into the conceptual, the (from that perspective) totally abstract. This all reminds me of Russell's thoughts on mathematics... "I like mathematics because it is not human and has nothing particular to do with this planet or with the whole accidental universe - because, like Spinoza's God, it won't love us in return."