Sound and Fury

I don’t intend of making a habit of posting webcomics, but this was just so relevant to that post I made a while ago about watching water boil that I thought I should include it.

I’ve spent a lot of today watching stuff from the Everett@50 conference and messing with bibliography styles for bibtex. I now have it all working how  I want it. What this really means is that I’ve made very little progress on actual work work. I seem to do that a lot. Tomorrow I intend to print off a whole bunch of articles and update my bibliography bibtex files.

But once I’ve got a few more papers under my belt, I think my physics essay will come into focus and I will be able to just reel off a couple of thousand words a day. Easy. The maths essay  has been put on the back burner a little bit, since it’s bloody hard. I have to read a few books before I can write much of any use for that. So I think I’ll get something substantial done on the physics one and that will allay my fears that I’m spiralling towards a massive 72-hour essay writing panic marathon come late January…

Here’s a cool thing; In Structure of Mathematics and Logic Steve Awodey shows how you can characterise logical structure in terms of a Topos. The idea of topos arose first in Algebraic geometry in the study of topological spaces. So maybe my crazy geometrical logic thing isn’t as crazy as it seems.

The trouble is is that all this stuff is really hard. So I am not really getting anywhere very fast. I’m revising how much talk of Category Theory I can realistically put into my essay. I’m revising it right down to `not very much at all.’

Tomorrow is all about reading about structuralism, which is something I hope isn’t going to turn out to be too hard to fit into my essay. Because otherwise I won’t have an essay…

I’m such a crazy fun-lovin’ guy that I’m thinking about how to formalise Euclidean geometry. By this I mean affine geometry. Without a measuring function. So all you have is an infinite 2D plane, a compass and a straight edge. How would one rewrite the Elements in a symbolic language? Perhaps taking a,b,c… to be points and having operators like being equidistant and stuff. I don’t know enough about algebraic geometry to know this isn’t what they’re doing, but it is different from the group theory stuff one can do with symmetry groups and such. There is something to geometry over and above what can be done with group theory. For example, one can prove that a pentagon is constructible with a compass and straight edge. But that is a non-constructive proof. So the construction procedure for a pentagon is outside the realm of groups.

Why would you want to do this? Firstly to explore the relationship between geometry and logic. When you are doing number theory or set theory or other branches of mathematics, there is a kind of presupposed foundation of logical consequence required to do anything useful. I wonder if the same is true of geometry. Since all we are doing is constructing geometrical objects from other geometrical objects, it isn’t obvious how logic gets involved. A formalised system might make the link clearer. Or maybe you’d want to go the other way and say such a system doesn’t presuppose any logic. Either way it should be an interesting exercise. The other reason for doing this is related. I’m interested in Category Theory and I wonder if the formalisation of geometry in this way might make it easier to deal with in Category Theoretic terms.

I don’t know enough about Euclid’s Elements, Logic or Category theory to know whether this is a worthwhile endeavour, but that’s not going to stop me trying it out!

What problems are there with this approach? I don’t want to import more logic or set theory than I need to into the system. In fact, I want to absolutely minimise my commitments in that area. Now obviously a point will have to be a primitive notion here. One way to proceed is to say a line is a defined term; it is a set of points. But what if there were a way to avoid using the idea of a set here? The only interesting lines are straight lines and circles. So perhaps we can treat them separately. But I also want to limit myself to finitary procedures. In other words, every construction  must only consist of a finite number of steps. This means that say we have a line going through two points. Then there is no general way to construct a point a third of the way along the line. We still want to be able to say that point is on the line, otherwise the parallel postulate becomes a little awkward (since it rests on the fact that the point is not on the line…)

I’m sure there are many other difficulties. But I’m off to read the first part of the Elements and see if I cant come up with something fun.

You know what we need? More excuses to go a-drinking! Well here is another one! The day the US repealed prohibition. Hoorah! Fuel the binge-drink economy! Punish your liver! Pump money into the coffers of Diageo and InBev.

I can’t decide which is worse; the government’s oddly draconian proposals on making criminals of parents who allow their children to drink the safety of their own homes or the coagulation of most of the brands sold in Britain into fewer and fewer soulless multinational conglomerates.

Whoah, mood kill. Anway… Mine’s a Guinness. Cheers.

I saw this week’s Epigram headline ”Taxi Terror as Cabbie Kidnaps First Year” and thought that the alliteration detracted from the seriousness of the story. So I amused myself on the way to Sainsbury’s by concocting another headline that had even more alliteration in it. It got a bit out of hand…

Sensationalist Story ”Taxi Terror as Cabbie Kidnaps Frightened Fresher” Earns Epigram Prestigious Prize.

The Awful Alliteration Award was Presented by President Pete Powell of the Association for the Amelioration of Articles Authored by Amateurs to Epigram’s Editor Edward Ellis.

Oh, the ways I find to amuse myself…

The English language needs some new words. I would like to propose the word ‘’schlurple” to mean the way you sip tea or coffee when it is too hot to drink normally. Another drinking related action that needs a word is the gulp you take off the top of a drink so you don’t spill it when carrying it to somewhere else. (Maybe ‘’sklep”?) This is distinct from the sip you take from a drink on a table without lifting it up because it is full to the brim.

Another thing that needs a word will take a little more explaining. When you have a certain number of somethings that need a name (be they harddrives, potted plants, whatever else you feel like naming) and you name them each after one of something else that had that number of things. An example or two will illuminate;

• When you have 2 of something and call them ”Bonnie” and ”Clyde” or ”Bill” and ”Ben” or ”Bert” and ”Ernie”
• When you have three of something and name them ”Athos, Porthos and Aramis”
• Four of something could be named ”John, Paul, George and Ringo”, ”North, South, East and West” and so on

There’s the seven deadly sins, four horsemen of the apocalypse… Countless examples of sets of names associated with a number. Surely there should be a word to describe the act of naming things after a set of things like this? A more exhaustive list of sets like this will probably follow, as I think of more ways to avoid work…

And what about ”Yoko Ono” or ”D’Artagnan”? Associated with, but not part of the set… These kinds of outsiders deserve a word too.

I will single handedly change the face of the English language! Watch this space.