Welcome dear reader.
This blog is meant to be a brain dump of my thoughts on math, physics and computer science. Nevertheless, I’ll try to make these ideas as approachable as possible, so that you can share them with your grandparents and/or grandchildren (if you have neither feel free to talk about the post with yourself).
But let’s not dwell on idle chatter and jump instead straight into the deep end. There is a certain branch of mathematics known as category theory that deals with pictures such as this one.
It turns out that one can describe most of the objects that one encounters in mathematics and science with similar pictures. I will not dwell on this fundamental fact here, since I mean to describe such objects extensively in future installments. Just take my word for it that pink bubbles and arrows are important.
A consequence of this observation is that mathematics contains an implicit notion of direction that one might not have a priori expected to find there. In the picture above, A is the producer, B is the consumer, and not the other way around. In this post I’d like to discuss precisely this kind of asymmetry and point out that it is not found just in mathematics but also all around us and is perfectly natural.
I — and I suspect many other people — consider myself a consumer. I eagerly read my twitter and RSS feeds. But I do not tweet that much and since this is my very first post, it’s obvious that neither do I blog that much. You can often see me with my nose deep in some mathematical book or other. But I do not write books. I listen to music all the time but I do not compose it nor even interpret it. Why is that? And is it all right or should I change something about it?
I’d like to argue that being a consumer is perfectly natural. For one thing, suppose everybody was a composer and nobody would go to concerts. If a virtuosic piece is played and no one is around to hear it, does it make a sound? Okay, I do not want to push it with my paraphrases but you get the point.
Obviously, I do not claim that everybody is either a composer or a listener and nothing else. We get this relationship for every single product, be it art, science, or a piece of furniture and a single person can and does participate in dozens of them. And the world kind of likes to balance these relationships out so that there is a steady flow of products from producers to consumers. Yes, I am talking about the (in)famous (in)visible hand of the free market. But that’s not quite what I wanted to talk about.
I know you hoped I’ve forgotten already, but let’s get back to those feelings of guilt you get when you have done anything at all all weekend beyond downloading images of kittens, tucking in nachos and dribbling over Khaleesi. That is you producer instinct kicking in. In mathematics there is a fundamental principle of duality. I remarked above that everyone being a composer would not be very useful. But neither would be everybody being a listener — we would have nothing to listen to (well, technically, nature itself does make some interesting sounds too but who cares).
The point is that while it’s fine being a consumer in many areas, one should also produce something from time to time. That’s why I’m starting this blog — duh!
P.S.: I hope you did not expect to find here some grand life-changing ideas — it is my first post after all. Here, have a picture of kitten and fare well, dear reader!