Sound and Fury

Today is the official launch of my website! It took a looming essay deadline to motivate me into the epic procrastination that was this weekend. The links section isn’t working, I haven’t configured the stats things yet, and I haven’t migrated this blog over to its new home, but all that is stuff that I haven’t got time to do at the moment; I actually need to get back to writing my essay now…

Please notice the random quote generator in the footer – it took quite a while to get right… I’m afraid it’s a little too subtle and people might not notice it.

In my LaTeX files, I leave myself notes about bits I still need to write. Sometimes they are fairly mundane: “Weyl/Klein on locally Euclidean.” But ocasionally I leave myself a note that makes me laugh when I go back to find out what I still need to do. The note in question was “Giaquinto pacman triangle.” For a good few minutes this meant as little to me as it probably does to you now. I flicked through the book in question (Marcus Giaquinto’s Visual thinking in mathematics) and found what I was talking about. They do indeed look like Pacmans (Pacmen?)…

Pacmen eating an invisible triangle

Just below this is another note which just says “triangles vs space… asteroids?” I still haven’t worked out what I meant by that one. Perhaps I was thinking of having my whole essay structure based around different classic arcade games. It must have been a long day…

I like fruit yoghurts. But I object to buying “healthy option” type foods, because they are preying on this culture of health as lifestyle and it’s all wrapped up with fad-diets and trendy ways to exercise. But I can’t find yoghurts that aren’t promoting themselves as “low fat” or as being packed with “good bacteria” or some such nonsense. It’s all Ski and Activia… Whether or not those claims are true, I object to buying them on principle. I don’t care about low fat, good bacteria or anything like that. I want my yoghurt to taste of fruit and be a yoghurty consistency. Or maybe they should have little bits of cherry or peach or whatever in. I don’t like to think I am paying more for someone to remove fat from my snack, or pump my summer fruits dessert full of “good” bacteria. My only option is to go for the organic fairtrade tree-hugging smiley faces on the packet ones. And they are significantly more expensive. I don’t actually have anything against organic food or the fairtrade movement, it’s just that those labels come at a premium I don’t want to pay. I actually went for some Activia strawberry ones today, because I was feeling cheap and my principles were at low ebb. Also, I bought “be good to yourself” tuna mayonaise sandwish filler because I couldn’t find Sainsbury’s “look out it’s bad for you” range of products anywhere.

I have been ranting a lot recently. I promise I shall post something goodnatured and happy-go-lucky in the next few days…

Since Bristol University philosophy department lists, as one of its principal research areas, the philosophy of science, you would expect the unviersity to have access to the journal entitled “Philosophy of Science.” Not so. I have spent some time trying to get at two articles from that journal with no luck. They are listed on Jstor, but the actual article isn’t on there and it directs me back to the Chicago Journals website, which asks me to log on. All in all rather frustrating. In desperation I just tried searching Google for “Psillos structure” and lo! I was directed to the PhilSci Archive which contained a version of the paper I wanted. In fact, the other article I wanted was also available through that archive. So God bless you Pittsburgh! I can’t believe I haven’t come across this resource before. The papers I got were from conference proceedings, but there are also some articles that are forthcoming in various journals. It would be nice to see the PhilSci archive grow into a repository of preprints, much like arXiv has for physics papers.

Rather than actually working on the fundamentals of my dissertation, I have been borrowing books and downloading papers tangentially related to my topic. I have a core idea for my dissertation, and then many sattelite projects. Hopefully I can somehow glue it all into a cohesive whole. More for my benefit than anyone else’s I shall summarise the myriad directions my current project is taking. The main nexus of the dissertation is about geometry and structuralism. So a detailed look at Shapiro’s and Resnik’s accounts of ontology and epistemology in the context of geometry. Often when they are discussing the struturalist’s stock example “the natural number structure” they say things which are supposed to be true of all mathematical structures. In the case of geometry, it isn’t apparent that this is as straightforward as they imagine. My main aim is to look at whether structural interpretations of geometry will work. Some of the intellectual meanderings that I might also write about are:

• The history of geometry, particularly 19th century. Interpreted as a move toward structuralism? (Shapiro argues as much in his 1997 book)
• Bourbaki-type set theoretic structure and Klein’s Erlangen Programme as kinds of structuralism
• Genetic Epistemology. Can how we learn geometry be interpreted structurally? (Piaget wrote a book on the child’s conception of geometry which would be my main source for this.)
• Structural realism about spacetime. How this squares with structuralism about mathematical/axiomatic geometry.
• Shapiro talks of “linguistic resources” limiting what we can do. In the case of geometry, it might be better to discuss “conceptual or imaginative resources” instead.
• Our limits as a benefit. Why it is good for structuralism that we aren’t aware that any circle isn’t perfect and that any line we draw actually has a thickness. These defects in our perception make pattern recognition and abstraction easier.

So that should keep me going. All I need to do now is read all this stuff and then write loads. Pff. Easy.

Today’s Guardian had a cool little special section about CERN. It is available here. I now have a false colour bubble chamber image as my desktop background. So the LHC hasn’t blown us all up yet, which is nice. If it ever does, I might feel the tiniest bit responsible, since I’m signed up to the LHC BOINC project…

In other news, the nine-point circle is my favourite fact about triangles. I will try and mention it and its relation to incircles and excircles in my dissertation. Hopefully with gratuitous use of diagrams drawn in Kig. If I can be bothered to learn how to get pictures to work in LaTeX… Another thing I’d like to do is learn how to write chapters as separate files and include them in some master file. For 15,000 words it’s hardly worth it, but it’ll be useful for next year. I’d also like to change the default font to Gentium, for no other reason than to make a move away from default LaTeX formatting…

So I looked into it and Topology and sigma-algebra are distinct things. Apparently a sigma-algebra need only be closed under countable intersection, whereas a topology requires arbitrary intersections to be included. Also topologies won’t necessarily be closed under complement, whereas sigma-algebras will be. But the smallest sigma-algebra containing some topolgy is called the “Borel sigma-algebra.” So that’s that all cleared up…

I took out a book on Euclidean geometry today written by none other than Charles L. Dodgson; better known as Lewis Carroll. Cool huh? And what is more, it’s written as a dialogue! I also recently managed to find Alfred Renyi’s Dialogues on Mathematics. So I’m pleased with both of them.

What with various talks and my being quite lazy I haven’t really managed to get a whole lot done today. And I’m to a conference tomorrow. So this week has been a bit of a write-off really. The real proper work on my dissertation kicks off on Monday. Hoorah!

From now on, if I can’t think of a title for my posts, they will all be Futurama references. Until I run out of them (in, like, 400,000 posts time) when I shall move on to Kung Pow, then Commando and so on, in that fashion.

So I went to Rock am Ring at the weekend. I got rained on and sunburned. I also saw lots of bands and so on.

My new favourite thing is the Burnt Pancake Problem because bacteria are better than computers at solving it. Also because both Bill Gates and David X. Cohen have written about it. Incidentally, if computing the nth digit of pi P or NP hard? Apparently there is an algorithm which allows you to compute digit n without having computed all lower digits. That is pretty cool.

Given a circle, what’s the best way to find it’s centre? Is it true that the midpoint of every chord of a circle goes through the centre of that circle? How would you prove that? I’m sure it would only take a minute to show if I could be bothered (and if it is true, obviously).

I’m glad to see that none of the restrictive amendments to the Human Fertilisation and Embryology Bill got through the free votes over the past few days.

I just found a great way to end my essay on Galileo. It’s a shame I still need to write another 1000 words, because coming up with such a great conclusion makes me feel I’ve finished. I really am running low on stuff to say now. Essay fatigue has really set in.

Also I am physically exhausted because I went to the gym yesterday and foolishly agreed to go through my friend’s gym routine. It was a bit much for me. However, it was good to do some exercise.

8 days to go until essay deadline frees me from this niggling feeling I should be working harder. At least for a while. Until I begin to feel I should start working on my dissertation.

I have now officially applied for my PhD at LSE. That’s rather exciting. I’m sure my research proposal thing could have been better, but I need to concentrate on getting my essays finished and the application had been a distraction. So that’s a weight off my mind. My essays are going well too. And I got my iPod working properly. AND I managed to get a birthday present for the ladyfriend. All in all, one super successful day. But it’s now twenty to six and already I can’t be arsed doing any more work. Sigh. I’ve run out of relevant stuff to read for the part of the essay I’ve been working on today and I don’t want to start the next thing now. (That’s a lie. There is another article I should read. But it’s crap…) I really should work more…

In other news, it’s a shame to see Mark Selby out of the Masters already… Other big names out in the first round: Graeme Dott, Steve Davis, Stephen Lee, Matthew Stevens. I wish I could watch more of the snooker this year. But I don’t have a TV. I wonder if I can catch the highlights on BBC’s iPlayer thingy… I have been using that quite a bit recently. I wonder if I should be using it. I mean, I couldn’t see anything in the conditions about it only being available to people with TV licenses…

Writing down my thoughts about my research proposal was such a good idea that I’ve decided to write a little something about all the other things I’m up to at the moment. If nothing else, it will help me work out what I’m doing. First things first: I’m writing three essays for the three courses I’m taking this term. I shall say a little about each in turn.

History of Science. The course is focussed on the Copernican revolution, so I thought I’d look at the influence of progress in mathematics on the progress in astronomy. I’m aware that Ptolemy and Aristotle probably had a better knowledge of conics than did anyone afterwards in Europe up until the Eighteeth century. The works of Apollonius were translated from Arabic into Latin only in the 1700s. So Copernicus and Galileo didn’t have that stuff available. This might go some way to explaining why it took so long to get over the idea of orbits being circles… So that’s what I want to look at there.

Philosophy of Biology. This is the one I am least sure about. I don’t really know what I want to do. Possibly something about levels of explanation and abuses of language. I feel strongly that people use the idea of “fitness” where they really shouldn’t. As a statistical tool to assess differential population growth based on certain traits or genes, it’s fine. But when people start talking about a gene or trait “conferring a selective advantage” or “increasing fitness” then I start to feel uncomfortable. They seem to be creating an extra level of explanation that is vacuous and possibly misleading. I don’t know if this vague unease can be stretched out to five thousand words, though…

Scientific Epistemology and Methodology. This course is really very broad, and I have managed to pick an essay topic that is kind of outside of the scope of the course. I’m writing about robot scientists and what they can teach us about science. There isn’t really much written on this so I’m sort of a bit all over the place at the moment. I’m looking at robot science from lots of different philosophical perspectives.

The other thing I have going on at the moment is much more on the back-burner until I get these essays out of the way. That is my dissertation topic. I’m looking at structuralism and geometry. A lot of talk about structuralism in philosophy of maths is centred on discussing the natural number structure. I want to look at to what extent can we think of geometry as being structural. I’d also like to look at the relationship between structuralism and axiomatics.

So… that is what I’m currently pondering. That was useful to get it all written down at least in a cursory way…