The Pleasure Of Proliferating Perspectives | Thought Catalog

I could have written almost every word of this article. Sure I’d be less flowery and I’d substitute a selection of other authors in place of the continental philosophers, but this post is basically why I do the subject. I started reading through, got a bit excited, saw the word ‘philosophers’ and got even more excited.

Posted Wed 01 Jun 2011 15:44:00 UTC

Lecturer and textbooks tell me that this theorem is certainly the most important theorem in Number Theory and (therefore?) also probably the most important theorem in all of Mathematics. There are hundreds of proofs; first one was by Gauss at the age of 19. Lecturer: “if Number Theory is the queen of Mathematics, then this theorem is its jewel.”

I do not yet fully grasp what the theorem even says (because I haven’t looked at the proof properly) and I certainly don’t see why it’s so important yet, but I’m posting it here because I rather like the idea that the deepest stuff in Maths lies in ℤ.

Definition. Let p > 2 be prime and let a ∈ ℤ be s.t. $p \nmid a$; a is a unit mod p. Then a is a quadratic residue of p if ∃x ∈ ℤ s.t. x2 ≡ a (mod p) and a is a quadratic non-residue if not.

Notation. For any a ∈ ℤ we define the Legendre symbol: $$\left(\frac{a}{p}\right) \mathrel{\mathop:}= \left\{\begin{array}{cl} +1 &p\nmid a \text{ and } a \text{ is a QR of } p, \ -1 &p\nmid a \text{ and } a \text{ is a QNR of } p, \ 0 &p|a.\end{array}\right.$$

Theorem. (The Law of Quadratic Reciprocity, Gauss, 1796) For p, q distinct odd primes,

$$\left(\frac{p}{q}\right) = \left(\frac{q}{p}\right)(-1)^{\left(\frac{p-1}{2}\right)\left(\frac{q-1}{2}\right)}.$$

Posted Thu 02 Jun 2011 09:47:00 UTC
Posted Thu 02 Jun 2011 11:50:00 UTC

once witnessed a company try to deploy a hot code fix in response to a DDOS attack, only to have their code repository — their only code repository — go down and refuse to come back up.

Scale Fail, part 1 | LWN.net

Scale Fail, part 2 | LWN.net

Really interesting articles on how companies with web applications fail to scale up to high demand. Been waiting for it to stop being subscribers-only for a week or so to post it here.

Posted Thu 02 Jun 2011 12:42:00 UTC

I’ve just finished the most recent episode of Game of Thrones, which means I’m fully up-to-date with the series as it airs live in the US. What a show! The factional infighting is so brilliant, and has me on the edge of my seat. The way in which they are all so unsafe, within the castle walls in the capital city. And then all this is child’s play compared to the storm that’s coming from the north—and from the east! Enjoying it much more than Doctor Who.

The comic that made me aware of the series:

http://chainsawsuit.com/comics/20110525.png

Posted Thu 02 Jun 2011 13:21:00 UTC

How much GNU is there in GNU/Linux? | Split Perspective

This is really interesting. The most important GNU-made part of GNU/Linux is the GPL, of course.

Remove the GNU C library and then report how much of that software runs. —mikankun

Remove the kernel and then report how much of that software runs.

Points scored based on who can hold who to ransom, anybody? —ldo

remove gcc and see how much of that kernel compiles…

wait clang actually compiles the linux kernel http://lwn.net/Articles/411654/pranith

It goes on.

Posted Fri 03 Jun 2011 13:43:00 UTC

These thoughts have led me to the belief that I should scrap all the pages I have on my website that just concern myself (this is all of one very short page, really, but I’ve never felt so against it as I do now) because this view that computers can’t capture people is compelling, and my site is no better than Facebook if it’s a list of top tens or whatever. I contend that there is something fundamentally different about this blog compared with social networking. What I’m doing here is sharing things I’ve written, or interesting things I’ve found elsewhere. The latter is non-problematic, because it’s an example of the web at its best: sharing things over long distances. But what I want to do with those things is chatter to my friends about them in real life, or, if that’s not possible, something real like instant messaging—that is, I want to converse. This is not what happens with things like comments or ‘like’ buttons, where commenting is out of boredom. Essentially I have this idea that writing things is only for things that matter, and talking is for things that matter and things that don’t matter, because our non-serious relationships with others are degraded when we try and do it online whereas our intellectual relationships are not. This is why I don’t have much of a problem with social media—such as a site like reddit—because the engagement there is intellectual, and that’s what the Internet does really, really well.[1] But it doesn’t do personal relationships well, a component of which is laughing over something interesting online together; that fails to be captured in a comment or a ‘like’, even if the incisive comment on how this or that meme has developed is.

In this vein do I defend writing this blog. Here I share things of interest, but the personal discussion happens elsewhere, but on matters of some weight on which I try to write something, the Internet allows the best of engagement. Why do academics, teachers etc. of older generations write e-mails and share pieces of writing on thoughtful topics, but have no interest in chatting online? Because they recognise what the Internet is best at—a step forward from the journal and the book—rather than any kind of replacement for actual social interaction. SMS, phones, and—gosh—meeting for coffee or just to chat, have never yet been superseded.

In addition to the response that Facebook is damn useful, there is the thought that these extra relationships of which I speak are valuable. It keeps us more connected with those around us in our communities; this can be no bad thing, it is said. But it is important to distinguish the value of respect and interest in those around you from the false value of a superficial connection. It’s the kind of connection a certain group of Facebook overlords think is useful, but it’s not related at all to a general spirit of community one can choose to hold towards others in, say, one’s university. I’m interested in the latter, and I’m interested in actual relationships with people. The reduced relationships of Facebook are bad for us, and detract from our investment in the former two things.

It’s good to have written out something more concrete against our Facebook culture. The problem is that this can leave me very isolated at times, because I’m in such a small minority on this one. While I am lucky that most things go out on e-mail around here, I still miss things that only go up on Facebook. Ironically a fellow no-Facebook friend of mine recently got someone else to publicise an event she was organising, via Facebook on her behalf, so I ended up missing out. But what I do know is that I continue to have quality relationships with those around me without it, and I’m not going to risk anything about those by going back.

[1] I appreciate that I glorify social media way beyond what most of it consists of here!

Posted Sat 04 Jun 2011 10:30:00 UTC

New university to rival Oxbridge will charge £18 000 a year | The Telegraph

This was my biggest worry for the education cuts: the humanities of our generation will be defined by the rich. Gargh this is really terrible.

Posted Sun 05 Jun 2011 10:38:00 UTC

A few other points worth mentioning here. Firstly I do not think that my defensive reaction is in any way inappropriate or something negative about my personality; it was an expression of my fierce desire for freedom and individuality and I have no desire to alienate myself from that. And secondly I do recognise that this new way of looking at things is just one theory, and the combination of my judgement with the authority of the counsellor who cemented it is far from infallible. But I have a sceptical disposition and I feel that I am applying the theory critically and finding that it all fits together, so I’m accepting the conclusions and ending up a lot better off for it.

So what are these things that I’m now linking up? Here’s a description of the biggest. Here, the only thing that I have openly lied about, outside of stealing biscuits from the kitchen, for as long as I can remember, gets thrown open to honesty: the topic of my attitude towards love, infatuation, crushes, relationships, the lot (not sex, because I’m still working on that one. Let’s say we’ll consider things up to second base, according to the xkcd specification, in this post). So the official public message up to now is that I am anti-relationships. The reasons I gave for this was that the idea of dependence on one individual was really bad—I didn’t think it was good for people—and also I hated the idea of people lusting after each other. This latter thought remains to a lesser degree, and I reckon that for most people, casual sex based on physical attraction is a bad idea—some can do it, go them, but most people end up hurting themselves, especially if they require alcohol in order to make it happen. Another thing that remains is that I dislike the idea of flirting as it seems rather disrespectful and objectifying (consciously, anyway). However my mistake was to morph this into “sex and relationships are evil and must be preached against with the same ferocity as I preach against everything else”. As will be visible here, I ended up mashing together the worst parts of sex, and the worst parts of relationships, into one amorphous, detestable whole. How ridiculous.

Why did this happen? Well, this is where my recent stuff comes in. The thought is that my reaction is defensive of my unusual stance against the rest of the world trying to convert me, because they think I’m mentally ill/socially inept/whatever. Into adulthood, I maintained the pretence because I would blame any changing opinions on hormones, thinking that I must not allow my father to win this one. But again I’m fooling myself. Hormones have precious little to do with this, because it’s instead a question of correcting my former opinion by understanding people and what they do better, which is just an innocent question of social experience. I am aware of the physical changes that happened to me somewhere between 11 and 17 but I was wrong to link that to my anti-relationships attitude as strongly as I did (further I should note that based on talking to others I am pretty confident that I am far less affected by such chemicals and the associated lustful desires than most are). I do not want to sound as if I’m now claiming “platonic relationships are now great and romantic/sexual ones aren’t” because that’s not what I’m aiming for; my problem was having individual components out of perspective, and refusing to allow myself to correct that perspective, defensively.

But now I can just drop it. That’s the point. I now know that it’s not about me, but about my father and goodness know what else, and so I can let it go and any other neuroses are just bad habits to be corrected. I am no longer anti-relationships and I am no longer conflicted on the question, in fact I am pro-relationships, though this does not mean that I’m going to go out and try to get one!

I said I was only going to discuss one hangover from my father but I actually have another to deal with, the next hurdle on from this one in fact, and that is the thought that no-one would ever like me; no-one would ever want to have a relationship with me. The idea lodged very firmly into my psyche is that I am different in a negative way, in fact, I am mentally ill, disabled, I have ‘issues’, problems that put me in a write-off group by everyone else as little more than a curiosity. I’m not someone to ever consider having a relationship with because I’m not weird in a good way, but weird in a incapacitated way. This I am now trying to drop too. “We accept the love we think we deserve” etc., but it’s hard, because I’ve been convinced of this for a long time. We all suffer from a fear of rejection at all social levels (i.e. including friendship) but while I have so little of it in normal social contexts (to the embarrassment of my friends at how I bulldoze through…), I have the ultimate degree of it romantically. Again a confidence issue I guess.

I am now imagining people from university reading that previous paragraph and wondering why I’m listing things like that. Please ignore it; it’s for others. Well there we go.

Posted Tue 07 Jun 2011 15:09:00 UTC

Finished A Very Short Introduction to Continental Philosophy by Simon Critchley tonight. I got it out of the library because I wanted to know a little more about something certain fellow philosophy students like to talk about a lot, and found it to be a book about the analytic/continental divide. For those who don’t know there is a split in philosophy since (chronologically since, that is) Kant; in the English-speaking world we do analytic philosophy, elsewhere they do continental. It’s not really a geographic distinction any more but philosophy departments do tend to identify themselves fiercely with one or the other, and a student not aware of the divide going to a department studying the other discipline would find themselves wondering if they weren’t in the philosophy department.

The book itself is great when it’s talking about the conflict, because it’s about people defending their meta-philosophy on the academic stage which is always great to learn about, but it falls short when it comes to the author’s defence of his own thesis. He contrasts the excesses of both movements, scientism on the analytic side, and obscurantism on the continental (interesting, obscurantism is in my spell checker’s dictionary but scientism isn’t). These are both derogatory terms. The former is when philosophers start implicitly equating knowledge with scientifically acquired knowledge and brush what we might term wisdom under the carpet, and the latter is when philosophers are willing to hand-wave, to be vague and to try to hide this by saying that they’re talking about ideas and the language isn’t important, without providing an argument why this might be so. I have a friend who doesn’t aim for clarity in his argumentation, and this makes it impossible to actually engage with his thoughts. You can have clarity even if lots of things remain mysterious and unknown. Critchley wants us to steer a course between these two extremes, which is probably right, but I didn’t feel he was presenting it very well.

It has been interesting to discover that lots of the metaphilosophy that I have come to myself in recent months seems to fit the description of the continental approach as described by Critchley. My view that philosophy is about worldviews and it’s useless to say one is better than another because they’re all embedded into historical context and so are we is reflected there; there was something else too that I can’t remember. However I generally tend towards the analytic approach in actually doing the subject. Rigour, clarity and elegance. And the better I get at it the more I get pulled in. And even if analytic philosophers are looking at the wrong problems, the tools of the trade are the best ones available to subject more sweeping continental claims to, as my tutor puts it, “proper intellectual scrutiny”.

Posted Wed 08 Jun 2011 22:04:00 UTC

Revision situation isn’t looking too rosy; I don’t feel like I have very much more in my head for two weeks of about five hours a day. I guess I actually do, though. Also, five hours a day is pretty pathetic. Well, I’m about to go into the second half (tomorrow morning) which would seem like an appropriate time to ramp it up, if any. I am finding that something is hard and I spend half an hour basically just sitting there thinking about other things or looking out of the window, which is a really bad habit because it just destroys time. So I have a new thought which is that if I’m on one thing for 10 minutes and can’t seem to concentrate, I’ll switch over to something else, such as writing out some proofs, rather than, say, doing a computation—and vice-versa. Got to remember to actually do this though.

The big worry is that these second year maths exams will hold me back from graduate philosophy, which is a very real problem. And it all feels overwhelming. So past papers, past papers, and hope the same stuff comes up.

The thought is that I want to be reading rather than (a) computer tweaking (b) computer gaming. Now, this imports a big thick bias that certain activities are worth more than others, and that I should be beating myself into some particular shape rather than doing what I enjoy. There’s more to it than this. I do not wish to throw away the mildly obsessive immersion into a particular tech project or game; this is also a social thing as when a bunch of us got excited by Braid or something. However I can’t help thinking that I would be better off if I became immersed in other things. The point is that these things are easy, and they’re about short term gratification: if I’ve written a script that automates something I used to spend five minutes typing commands to do, I’ve achieved something that wasn’t challenging at all, and similarly with game-immersion. Not so with other things. Can I have both this powerful immersion back for what I see as being more valuable? I hope so, but it’s not a balance one can immediately attain for oneself.

One might also say, why the demand for productivity? Well, my view is increasingly that I’m not going to be at this stage of life for long and I should make the best use of it I can. And that isn’t messing about on the Internet. Maybe saying things like this means I’ve moved into a different phase, though.

Another project is learning to touch-type properly; looking at the reflection of my fingers in the screen now shows how inefficiently I use my fingers.

Finally there are the habits I wish to embed deep into my psychology. For example let’s take getting up. I’m pretty decent at this, but I do fail maybe once or twice a fortnight and I will definitely fail if my alarm clock can be silenced without getting out of bed. I don’t know why I don’t have this willpower, but I do know that periods of life in which I have had a very fixed sleep pattern have been a lot better for that, than otherwise. There are other habits too. I am trying to decide to what extent I can ‘rise above’ certain family member’s ridiculosity. On the one hand it is one of my most important intellectual principles that one must always engage with another person because otherwise you assume your own infallibility. Further, the lack of regard for me and my belongings I get from particularly my mother seems like an injustice that it would be wrong to just ignore. That’s the thing: keeping silent for pragmatic purposes isn’t right to me, because we must do things with energy and passion and a full sense of self behind them; this includes the way we live with people. The only way for me to avoid this is to disengage and be dismissive of them all, which is not warranted and not much fun.

That was a lot more than I intended to write on that subject so now, the things that are bad about the summer. I’ll be leaving Oxford. I’ll have to return to motivating myself entirely rather than attempting to combine my own willpower with my tutors’, I’ll be away from many people I love to have around and to see from day-to-day and they’ll be the thought that ZOMG I’m halfway through my degree. And the thing is, I expect zero contact from people I know in Oxford aside from maybe, if I’m lucky, a few e-mails. I don’t actually consider that to be hugely problematic on a more detached level. Our relationships are weak and are 20% college loyalty and 50% dependent on seeing each other a lot through doing the same subject or whatever, but that doesn’t stop it from being pleasant to have them around.

Michaelmas term will be pretty epic I imagine. They’ll be freshers’ week to help run again, I’ll be living in college again, doing exciting new work, and exams will still be a way off. I wonder what the atmosphere will be like: my year will be the third year, but my year is even cliquier than most and probably less mature. People hanging around in the fourth year, working in the college offices etc. who I knew when I first arrived will be properly gone. The current freshers will be in houses and in Jowett and I’ll see far less of them. And of course they’ll be about a hundred newbies. Looking forward to it in any case. Second year goes really fast compared to first year and I don’t know why, and it wasn’t great for me anyway, so I’m looking forward to the next one. It’ll feel like less maths because there will be fewer courses to learn from, and they’ll be all that philosophy and my romanticisation of philosophy exams will come crashing down. Michaelmas’ll be good though. And I shall make good use of the summer, and come back ready to make more of things than I did this year.

Posted Sun 12 Jun 2011 17:08:00 UTC

Why isn’t there more philosophy in Doctor Who? There is a lot of science—obviously not actual science since by definition it’s not science we’re capable of doing—so, there’s the consequences of having that kind of science and how it means we are to interact. But there is no philosophy going on. The Doctor’s ethics are very ordinary, but he’s lived for 900 years; he must surely have something more interesting to say. Something controversial to get people thinking. And he knows more than any human has ever known; surely he must have some thoughts on epistemology too.

Posted Mon 13 Jun 2011 13:55:00 UTC

Just spend an hour and three quarters refiling paper. Not like me to let it get this disorganised, but I was starting to feel the effect because I was put off looking things up during revision due to having to leaf through lots of stuff. Now it’s all sorted and like a true modern finalist I have everything in lever arch files with labels on them with paper names written in thick black marker (this is the in way to do it, it seems).

Stuff on the floor is stuff to recycle; trying to reduce the amount I keep.

?tt11refiling.jpg

Posted Mon 13 Jun 2011 16:45:00 UTC

I’ve been putting off revising the Rings & Arithmetic course since I didn’t follow the lectures or really do the problems back in Michaelmas, but people keep telling me it’s nice and actually quite easy, so I’m finally doing some—it’s a compulsory course, but I only have to answer one question so I thought I might just skip it and try and put more time into the others. I think that having done some Number Theory helps a great deal. Fellow Hungarian mathematician who did most of the second year number theory course at school says this helped a lot; they did this while we were wasting our time with calculus.

So I’m starting to like algebra more—especially now that quotient spaces don’t scare me quite so much—but this is the usual thing that I really like Maths when I can do it, but I can’t do it often enough in this degree course that I stop enjoying it. I wish I’d had a better year so I could have a better grasp of courses like this; I should have persevered with Fields, too. Also for any maths undergrads reading, Abstract Algebra by I.N. Herstein (Chichester: Wiley 1999) is definitely worth checking out; doesn’t quite do enough for my second year rings course, but shows you what’s important about the topics.

Here’s the coolest thing I’ve found so far, where we use quotients of rings to construct ℂ, rather than just saying that there’s an element i that squares to  − 1, which appeals to my constructivist leanings.

We have the ring of polynomials with real coefficients, ℝ[X], no problem, and now write ⟨X2 + 1⟩ for the multiples of the polynomial X2 + 1.[1] It’s easy to show that $\langle X2+1\rangle \vartriangleleft \mathbb{R}[X]$. So we can form the quotient ring ℝ[X]/⟨X2 + 1⟩, and this is essentially ℂ. So what’s our imaginary unit? Well write $\mathrm{i} \mathrel{\mathop:}= \overline{X} \mathrel{\mathop:}= X + \langle X2+1\rangle$ and then using the division algorithm we can get that every element can be written a + b**i: every polynomial may be written as a + b**X + g(X)(X2 + 1)). And indeed

$$\mathrm{i}^2 = \overline{X}^2 = \overline{X2} = \overline{X2 + 1 - 1} = \overline{X2 + 1} - \overline{1} = 0 - 1 = -1$$

as we require.

[1] The reason we use X rather than x here is to emphasise that polynomials are not functions, just formal expressions of coefficients and a few X. x would traditionally denote a variable in a function rather than just a component of an expression.

Posted Mon 13 Jun 2011 21:05:00 UTC

On Thursday we had a talk at Balliol Left Caucus from Paul Sagar of Bad Conscience fame, on his pessimistic view of the position of the left and where we can possibly go from here. His point that I found most interesting referred to his dphil work on Hume, who in his political writings said that we should assume everyone in society is a knave—selfish, non-virtuous—and design institutions to prevent them from damaging others, as a kind of failsafe: that way we’ve covered the worst case scenario, even if we don’t (and shouldn’t) actually think that everyone is like this. Seems fairly sensible.

The thought from Paul was then that what seems to have happened now is that we want and expect people to be knaves, consumers in the capitalist system, and this forces the left continually onto the defensive. Why has this happened; why have we become so, well, knavish?

Posted Sat 18 Jun 2011 11:55:00 UTC

My college-wife and I just wrote our letter to our children; here it is. It’s pretty scary to think that in three months time I’ll be introducing myself to someone as my college mother did—first person I met in Oxford—two years ago, telling me in her thick welsh accent that she was an “ancient third year”. I’m going to be an ancient third year!

parentingletter.pdf (3.1M pdf)

Posted Sat 18 Jun 2011 15:05:00 UTC

I am finding that not having access to Facebook at all, by not having an account, is a pain because I have to beg people to e-mail me the details of events that I just can’t see. Secondly I’m just not aware of stuff: recently a friend who is anti-Facebook said, you should come to the Balliol Poetry Society that I run, and I said well I didn’t hear about it—and it turned out that she’d got a friend to organise it via Facebook for her. Yeah.

Can I do read-only Facebook? I would delete my account completely (it is presently suspended), recreate it and just add people I actually have contact with. I would stamp a massive “DO NOT POST HERE I DO NOT CHECK THIS PLEASE E-MAIL ME KTHX” somewhere, and then use a web service to have my news feed e-mailed to me. Is this realistic?

This makes me feel so terrible, but I guess it’s no different to buying things while being anti-capitalism to use Facebook for the ‘necessary’ stuff while remaining anti-Facebook.

Posted Sat 18 Jun 2011 15:20:00 UTC

Revision getting a bit better; I am able to write out a lot of standard proofs now, but still got a lot of past papers to get through. Last year come this point I lagged and barely did any work because I’d worked for three weeks, didn’t know enough and knew the exams didn’t matter. But this time they do matter so I seem to be capable of stepping up the number of hours; I’ll probably do eight today. Still lots of stuff I don’t know but every question does actually teach me something more and raise my possible mark, so that’s good.

Been watching my way through the second season of Legend of the Seeker; I don’t get why it got renewed for a second season but then cancelled because the second season is a lot better: they’ve managed to merge each-episode-has-distinct-plot and overall-story much better than the first series where the latter was just “guy trying to take over world”. Shame there aren’t many episodes left and then it’ll be over. Just like, on that note, Game of Thrones which finishes its first season tonight; gotta wait a whole year for the next one

It’s also improved by the addition of a fourth main character, and a lot more offensive magic on the part of Zedd, even to the point of gratuitous fight scenes.

Art by tenshi-rising

Posted Sun 19 Jun 2011 13:51:00 UTC

I’m doing what I said I would, and I’ve deleted my Twitter and Identi.ca accounts today. I’ve backed up my list of followers and following, and as many tweets as I could download: Twitter only lets you have 3200 apparently and I can only get about 1600 with the tool I used,[1] and it seems a shame to lose that data but it’s gone anyway.

I’ve also finally nuked my Facebook account, in preparation for recreating it. It’s been deactivated for a year and a half so not a big deal. It’ll take two weeks to be fully deleted apparently.

Read this piece today; really good, totally agree and nicely stated.

Here are the stats:

Facebook account created 2008-08-01 (this is later than I expected)

Twitter account created 2008-04-20, 113 following, 294 followers, 19 listed, 7545 tweets

Identi.ca account created 2008-11-16, user id 29609, 32 following, 42 followers, 6 groups, 3910 dents

That should satisfy my nerd “I was there ages ago” desires.

Now I have to subscribe to all the people I still want to follow via RSS; this means I shall lose access to the ~2 protected feeds I used to follow but I can live with that (sorry Joe :().

[1] The authors of that tool should add \usepackage&#91;utf8&#93;{inputenc} to their preamble to fix some encoding errors I noticed…

Posted Sun 19 Jun 2011 18:52:00 UTC

Examiners’ reports are very amusing. Here’s a paragraph from the 2010 Part A Mathematics:

Presentation skills were very mixed. Some candidates wrote to the standard of professional mathematicians, and their scripts were a pleasure to read. Others wrote as if grammar and style were far too costly to be lavished on mere examiners. Many scripts were unreasonably illiterate. Misuse of the symbol ⇒ to mean ‘then’ rather than ‘implies that’ was rampant, leading in a number of cases to assertions that could (and perhaps should) have been marked wrong. Too often crucial quantifiers, especially ‘there exists’, were missing (that is, left to the reader to supply).

And from 2009:

It also gave candidates the opportunity to show that they didn’t know what “singular” or “nonsingular” meant. Unfortunately, far too many candidates assumed that if the multiplicity of a root of the characteristic polynomial is r then there are r linearly independent eigenvectors. But then, somewhat surprisingly, those candidates did not deduce in one line that every linear transformation over ℂ is diagonalisable! Of course, if this should have been the case, then the problem, which leads to a proof of the Cayley-Hamilton theorem, would have been trivial (as would the whole of algebra…), but this didn’t stop those candidates from getting into even deeper water. …

This question, unwittingly, gave many candidates the opportunity to show lack of basic understanding. Leaving aside those who define W = {w ∈ W : ……} or worse … [f]or the next part, the few who realised that some geometry was going on fared best …

One candidate bravely wrote “in the lectures we were told that [if W is infinite dimensional, then] W⊥⊥ = W″ – unfortunately, this is not universally true, for example when W = V !

On a computer screen yesterday I read this from a physics past paper (paraphrased): “This equation wasn’t done well. Perhaps we should have provided the auxiliary equation or shown the answer to be worked to? I didn’t think it was very difficult.”

Edit 28/vi/2011: Another someone quoted at me: “it would be an understatement to say that this question was badly answered: indeed, it caused utter carnage.” The report goes on for a page about how this happened.

Posted Mon 20 Jun 2011 15:52:00 UTC

Since I now have no Twitter account and would still like to follow some friends, I’ve written a script which, combined with newspipe, means that I get a daily e-mail with all the tweets of those I’m following. The reason this is non-trivial is that it’s combining multiple RSS feeds into one e-mail—maybe there are other tools that Just Do This, but I wanted to integrate with my existing newspipe setup so I wrote a python script to merge the feeds.

Most of script from here, and Jonathan helped me debug because I was tired and have forgotten most of my Python.

This script grabs the feeds and merges them together:

#+INCLUDE: /home/swhitton/bin/twitterget.py


Here is the newspipe config:

<outline text="Twitter" digest="1" titles="0" ownerEmail="hidden_address">
description="Microblogging"
</outline>


And the cron jobs:

0 18 * * * /home/swhitton/src/newspipe/newspipe.py -i /home/swhitton/etc/newspipe.ini
30 17 * * * /home/swhitton/bin/twitterget.py


Edit 11/vii/2011: Script now excludes @-replies to people you don’t follow.

Posted Tue 21 Jun 2011 11:50:00 UTC

I have learnt from experience that saying “I’ll just have a week off at the beginning of the vac and then get down to it” always fails, so as soon as I’ve moved back in I’ll be getting down to it. However I will be rewarding myself somewhat by starting right away with my switch-to-CRUX project which I keep fervently writing about.

Throughout the vac I’ll be doing academic work from 8 until 12, but that’s a very loose description because that’ll vary from hardcore study to just reading ahead for next term (more of the former towards the beginning of the vac).

For the first week or so in the afternoons I’ll first work on my new CRUX setup (initially on my laptop, so I can still do stuff on PC, then I can redo PC too), and then after that I’ll do solid cleaning up. This is fixing bugs with things like my blog, fixing Emacs annoyances, and clearing out Org-mode. This might take, in total, up to two weeks but by the end I will have already done a fair amount of work (more than many will do the entire vac), I’ll have nothing hanging over my head and I’ll have decided what projects/books/whatever are interesting enough to me and feasible to be completed within the summer.

There’s a fair amount of discipline involved in this because the first two weeks are going to be really rather boring, aside from CRUX, and considering that I will have just finished an incredibly boring four weeks of revision and then a fifth of exams, but it’s going to mean that I don’t feel guilty for not doing things I should have done for the rest of the vac, because they’ll all be done.

And the reason for doing this amount of work? Well, if I am to stand any chance at a first after this set of exams, I will need to get a first in all my philosophy papers so I want to get better at them. More importantly I want to continue my development in philosophy because this is my whole life; others are thinking about their careers and developing their employability, so I should be developing mine in the field of philosophy.

Posted Tue 21 Jun 2011 12:24:00 UTC

College this evening reflected the pitifulness of our situation. It’s the last weeknight of term, so everyone has finished their work and there is a bop on to celebrate this fact—the last bop many the third year will be at and they will be there in force, and of course we’re to miss it. The denizens of the library have been whittled down to a handful of freshers with exams next week, one fourth year with a final exam tomorrow morning and of course the second year mathematicians, doggedly quotienting rings and solving partial differential equations or whatever it is the applied mathematicians do. We’ve essentially spent four weeks feeling like our knowledge of the material is dropping or, at best, staying roughly the same with the minor addition of a few memorised proofs, and watching people finish their exams. Yes, people from all four year groups have been finishing around us, and yet we’re still slogging away at it. And of course all our friends at other universities finished for the summer weeks ago. Oxford second year Maths.

Of course we do actually know rather a lot more than we did a few weeks ago, and there are a few who have really knuckled down and are managing to take things more seriously than the rest of us—but it never feels like that when revising and that’s what makes it so unpleasant. For my part if you average out the days I haven’t made six hours, I’ve basically done four weeks of six hours a day with one day off per week, so I’ve done a perfectly respectable amount of revision. But I feel like I could have done more—say, eight—and I know that that if I could have manged those extra productive hours that my mark would have risen, putting a first a little more in reach. Today is a good example. This week we’re all dejected and worn out, and by 3:30pm I’d only done one hour of revision (11:15–12:15) and of course I get up at 7, so this is quite a lot of wasted hours (although some used usefully in getting vac reading from a library). I then worked in All Souls 3:30–6:30 and then went to Hall and then worked in Balliol 7:20–9:20 so a did a total of six hours, but I could have done so much more! One between midday and 3:30 and, say, 10:15–12:15 would have been so easy. Then on the other hand maybe the hours I did do would have been less useful had this been the case; I don’t know.

My six hours today were on the Rings course and I reckon that my work today is more hours than I’ve spent on this course in the entire rest of the year, since I paid almost no attention to the lectures (despite, of course, attending every one…). Why didn’t I do more before; this is really cool. The first isomorphism theorem which was examinable in first year actually makes sense in this context, and I get how if you quotient a ring R by a maximal ideal I then x, y ∈ R are in the same coset iff x − y ∈ I because this means that their ‘difference’ is small enough to be in the ideal so when you divide they’ve got the same remainder, gargh, I had this in the library earlier but I think it’s gone again; the analogy with division of integers was very clear to me for a moment back there. If I’d actually done this compulsory course—i.e. listened in the lectures and done the work set, which I didn’t really—I think I’d be laughing.

Second year algebra at Oxford, both linear and abstract, is pretty weird. It’s not actually that hard—linear algebra never is, and the abstract courses don’t go far enough in how much content they have to be too problematic—but we’re all rubbish at it, so presumably something is wrong with the teaching or the course structure or whatever. Examiners’ reports reflect this, and the fact they keep re-arranging the course every few years shows it’s a problem they’re trying (yet failing) to solve. There is also the problem that there are some really oddball examiners about who set stupidly hard questions every few years. We had one on a past paper which our tutor said was part of/leading up/in the style of the proof of the classification of simple Lie groups or something terrifically advanced. Chatting about the Gram–Schmidt process and dual spaces is mostly just crunching out definitions, yet we’re quite a lot worse at doing questions in it compared to, say, the Complex Analysis course, which is really quite deep. The integral of a holomorphic function round a closed contour containing singularities is 2π**i times the sum of the residues of the function at those singularities; wow, why the heck is this the case. And Liouville’s Theorem is pretty baffling too.

I was pleased to learn this evening that the prodigy in our year at Balliol, who was either first or second in first year exams across the whole university—and don’t forget this is Oxford so we have some Very Clever People—and mastered a eight hour lecture course in fields this week in two hours to avoid doing a question in probability, is doing all the options that I’ve chosen to do. Third year Maths teaching is in inter-collegiate classes so while it just so happens that one of my courses is being lectured in by my college tutor (hence we’re all doing it), which will mean we can get a little help in-college, it’s going to be detached and more like a real university where we actually have to do the work. Despite failing so hard at algebra, somehow I am doing lots of algebra next year:

• B1a Logic—have to do this as a Math/Phil, it’s a third year Maths course remarkably similar to our first year logic course taught by philosophers, so no problems expected here aside from getting conventions mixed up.
• B1b Set Theory—again have to do this as Math/Phil, this should be pretty fun, lots of induction and curly brackets and axioms.
• B9a Galois Theory—this is the one our tutor lectures. Apparently very elegant, and not too hard.
• B3.1a Topology and Groups—I like topological arguments, I don’t really know much about groups but apparently this is alright too.

I’m actually pretty limited because the second year options I chose, which are sort of like primer courses for third year with some exams in them too, were a stupid combination and so I’m going to have to do a fair amount of algebra over the summer to get myself ready for these. That’s okay though because I’m liking it as I, er, learn it from scratch four days before the exam; the main source of pain will be the continual thought of “if only I’d actually done this in second year.” I realised today just how much Maths I am allowed to forget after these exams. I don’t need any linear algebra, any analysis at all, not even any calculus aside from stuff with polynomials which’ll probably be used to generate examples. I just need abstract algebra, and the ability to mess around with symbols in B1 which we were trained well in in first year. Third year is gonna be gooooood.

I’ve also picked my philosophy options all the way until the end of my degree now which has a note of finality to it; up until now, the rest of the degree—and I have exactly half of it remaining after tomorrow, technically the last day of my second year—seemed fairly indeterminate and distant and not to be worried about, but suddenly by a process of elimination from the massive list of ‘papers’ (philosophy) and ‘units’ (maths) I’ve mapped it all out. I’ve got:

• Philosophy of Maths—unsurprisingly I have to do this as a Math/Phil. Looking forward to it as I enjoyed the taster we did in first year. However learnt today that tutor I was expecting to get will be on sabbatical next year :(
• History of Philosophy from Descartes to Kant—already done this this year, will be putting a lot of work into it over the summer so that I’m on top of it since maths took priority during this year. Excellent paper.
• Ethics—this is really worthwhile but I almost did it solely because I feel a philosophy degree really ought to have some ethics in it. Have done half of this and the other half will be next Hilary; stupid joint honours timetabling.
• Plato’s Republic—this is my wildcard paper; it doesn’t fit with the other things I’m doing except Ethics, some say it’s a bit easier as a paper, and it’s Ancient Philosophy so since I don’t have any Greek I can’t take it any further. But I really want to take the opportunity I have here to study the most influential text of Western thought with an expert.

And in fourth year (no Maths):

• Philosophy of Kant—probably the hardest paper you can do here. Kant is hard hard hard but so important. I want to continue the story told in the History paper above, and see if I can figure out why we get the analytic/continental split with such different interpretations of what Kant is really trying to say.
• Philosophy of Logic and Language—this is a traditional Math/Phil option, and most who do it do it when I did Ethics. I think it’s important stuff so I’ve put my more classic papers in third year and the modern analytic-tinged things like this into fourth year, where I can make more of them. I’m more interested in the Philosophy of Language than of Logic, but of course they are intertwined. I want to know just how much we actually should be worrying about language and how much we should heed those who tell us to deal in ideas instead of words.
• Either Knowledge and Reality or Philosophy of Mind. I had to choose either the History paper or K&R at the beginning of second year; K&R along with Ethics is one of the two “base” papers, if you like, that the rest build upon. So it would be unusual to do it as a fourth year paper and unusual to do it along with the History paper but we could take things a lot further. On the other hand Philosophy of Mind is another core topic of modern philosophy, and could take this sort of stuff further like K&R could as I understand it. Can decide this later though.

Timetabling this is going to be a pain. There are two terms to do all the third year stuff in. Michaelmas is going to be Logic, Galois Theory, Topology and Groups and Philosophy of Maths, so that’s three problem sheets and an essay a week. This is going to be a ridiculous amount of work. I’m aware of this so I can work harder from the very beginning to try to stay on top of things but I am worried about falling behind on particular courses since there is going to be just so much. I am tempted to just do most of the logic problem sheets over the summer, but am not sure this is such a great idea. Hilary will then be the other half of Ethics, the Republic and Set Theory. Hilary will be a beautiful term; it is frustrating that I can’t move Logic into it too.

Lots of stuff about third year there and about revision; hope it wasn’t too dull for those outside of the Oxford bubble.

Posted Fri 24 Jun 2011 21:26:00 UTC

Fire alarm went off about 45m ago; I was just about to go to bed so this was annoying but it turned out it was an actual fire. Someone left some incense burning. While the resolution was just the fire brigade spending ages getting rid of all the smoke, apparently it was a closer run thing than that and we could have had an entire tower up in flames. Instead we just had 45m standing in the rain.

Poor, poor people who have exams tomorrow morning. I only have revision and I was frustrated enough.

Posted Fri 24 Jun 2011 22:13:00 UTC

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Conveniently, for I shall be using cartridges in exams and don’t want to transport nearly-empty bottles of ink home with me, I’ve come to the end of two of my bottles of ink this week. I’ve been writing with ink from a bottle for about a year and a half now, something that isn’t that unusual in Oxford. The primary reason for this is that it’s much cheaper and much more environmentally friendly: a bottle of ink is a fiver or less, and by my calculations the equivalent amount in cartridge-form is about £12 at the price I used to buy cartridges in Sheffield, and £20 at the nearest shop here in Oxford. Substantial for anyone, not just students like me. And think of all the plastic you’re saving.

The secondary reason is that it’s nice to try out different colours. With these bottles I had a nice deep purple and a pleasantly different blue-black, though Waterman Blue–Black is very different depending on the pen, and I still have half a bottle of Diamine Evergreen which is beautifully rich dark green.

However I think that I’m at a point where I’m happy just to have one colour and be consistent, and that colour is Waterman Blue–Black. I’ve never stopped liking it and it doesn’t draw attention away from what you’re writing to the fact you’re writing in an unusual colour. I’ll keep my Evergreen around of course, but I don’t think I’ll fill up with it very often anymore.

Waterman bottles are substantially more practical than Diamine, as they’re shaped to be filled from with a nib whereas the Diamine bottle is just a bottle. The Internet thinks, I recall, that Lamy bottles are even better at getting the last bits out of so I would love to come across an empty one. Fountain pen ink is very simple and you can use ink from any manufacturer in any pen, no matter what the pen manufacturers might like to tell you.

Another bottle of purple I bought, Diamine Imperial Purple, I gave away as I wasn’t too keen.

I really have no interest in fountain pens themselves; I like the way mine writes, but don’t understand why anyone would have more than two and spend loads of money on them. I write a lot and like writing with one, simple as that.

Posted Sun 26 Jun 2011 12:01:00 UTC

First exam was a reasonable paper I suppose but there was a part of a question not on the syllabus, so hopefully once that is communicated to the examiners they’ll bump us all up a few marks. After this non-examinable theorem there was a question about guests at a party and seating arrangements, and apparently it could be done with A-level-style reasoning, but I did what I often do and ignored it because I assumed it relied on usage of the theorem I didn’t know. Shouldn’t have done that.

It’s quite impressive just how much you can fit into your head at this stage of revision. I am about to make a list of all the things that didn’t come up that might well, therefore, come up in the paper tomorrow, and learn them, and I know that if I sit down for half an hour I can master the memorised parts of the topic, and be in a much better stead to answer a question on it. Should have done some more of this last night. The humid weather, and tiredness from so many weeks of revision, has left me headachey almost all the time which is definitely sapping what I’m able to do.

If things keep going like this I should get close to 60, which is recoverable from if I get a first on every paper next year. To get a first overall, since I am joint schools, I have to get an average of 70 in philosophy and an average of 67 overall. Philosophy never give higher than 73 (as a matter of policy), but I have got Maths papers like Logic and Set Theory which are pretty easy so assuming I work hard I should be able to get lots of marks (say, 8) above 67 there to pull me up.

I reckon that if I want a first I have to work extremely hard next year and consistently through the year. A positive aspect of not doing very well at these exams is that I will be able to motivate myself next year by saying, “you have to do this NOW or you won’t get a first”, because they’ll basically be zero room for manoeuvre. Why do I want a first? Well I need one if I want to do graduate philosophy here. A 2:1 would be fine for other universities.

So the next thought is: is the suggestion that I didn’t work hard this year? I didn’t work very well. I put lots of hours into Philosophy, very very few into Maths and didn’t get very much out of those hours that I did put in. I need to make degree work my habitual activity again, like in first year. Then if I consistently work efficiently throughout the year I can still do it.

Of course my predictions could be wildly wrong. If I get substantially less than 60, then I should concentrate on getting firsts across Philosophy since that’s what I’ll be applying for.

Posted Mon 27 Jun 2011 14:28:00 UTC

You make a stupid mistake in every exam I suppose; today mine was forgetting that a matrix over a complex inner product space is Hermitian exactly when it induces a self-adjoint linear transformation, duh, but it wasn’t as bad as a fellow Balliol Math/Phil who answered three Algebra questions when a maximum of two from each section of the paper count; he came out really happy with how well he’d answered those questions too. The exam was a good end to core for me as there was a great Rings question, lots of Algebra bookwork (== proofs from memory) but there wasn’t any classic Analysis bookwork. We reckon this is because the questions were set by our college tutor who is hardcore.

It’s quite something that I’ve now finished what has been the mainstay of my degree for the past two years: Analysis and Linear Algebra. I’m sad to be leaving Analysis behind because I like the proofs, and it was just starting to get interesting with things like Contour Integration (again, Cauchy’s Residue Theorem, wth), but third year analysis is apparently pretty tough so I’m avoiding it. I’m not at all sad to be leaving Linear Algebra. You define something fairly simple, that doesn’t do anything exciting and for which most of your intuitions are correct, and then you laboriously churn out all those consequences. Sure it’s easy marks to prove something is linearly independent or that something is a linear map (did one of those today and the other yesterday) but it’s so dull to study.

Instead I have Abstract Algebra open before me. I know so little of this, interestingly I seem to know so much less than my friend just finishing his first year at Cambridge. Presumably he’s done less Analysis and Linear Algebra than me, I don’t know; it feels like I’m almost starting afresh, though, because of how much I am now leaving behind, only to be used for the occasional example.

No more flippin’ matrices!

Posted Tue 28 Jun 2011 14:15:00 UTC

I reinstalled Minecraft yesterday and hopped into my minecart system, only to learn that minecart boosters have been fixed. Boat elevators have been fixed too. A lot of the fun of Minecraft was exploiting cool, if buggy, Physics mechanics. I no longer have any interest in spending ages mining materials in order to build cool stuff if this element is removed, so I’ve decided that I’m going to play with mods that give you unlimited items and just try to build interesting things. I might even install a mod to replace boosters.

The upcoming creative mode is not quite what I want as I would still like monsters and the possibility of dying, but I’m not interested in spending hours strip mining just so that I can build things.

So normal Minecraft has become boring for me, but I’m still interested in sandboxing.

Posted Wed 29 Jun 2011 11:13:00 UTC
Posted Wed 29 Jun 2011 21:47:00 UTC
Posted Thu 30 Jun 2011 14:06:00 UTC

While waiting for yesterday’s exam to start I read through the unopened front cover the question “What is a prime?”, and no that wasn’t some crazy abstract concept but it was actually asking me to write down what a prime number is. This was swiftly followed by “prove that there are infinitely many primes”, possibly the most famous proof there is, that we got in our first week of first year, followed by “state the fundamental theorem of arithmetic”, again not really degree-level stuff. There were then a couple more prime number things to prove, both of which were fairly standard—very frustratingly I couldn’t prove that there are infinitely many primes of the form 6k + 5 despite doing such a proof by myself before and liking it; I just couldn’t get it to come out in exam conditions, ah well.

This was yesterday’s paper which was fine, but today’s was disastrous for me. Hopefully with moderating/scaling I should get 50%, but this basically means that “I’ve definitely got 60% average this year” has gone to “hopefully I’ve got 60% average” which is rather unsettling. And today’s paper was supposed to be my best: the first year probability question I was expecting to answer was entirely impenetrable and so I wrote down a few number theory definitions and theorems and did most of a topology question, so that’s not very many marks really. Can’t believe I forgot what sequential compactness is!

It really is bad how Maths tutors are so incapable of writing questions. It seems that while results get scaled separately by subject, to take into account the fact that Math/Phils are famously good at Topology and Maths/Stats people beat everyone else on probability, they are not in fact, as I thought, scaled by question. On these options papers, there are questions for different courses and not only are these courses wildly different in actual difficulty but each question is set by a different person, that is the course lecturer for that year, so the chances of getting a consistent difficulty level even within a single year is pretty low. When you add to this that the lecturer’s conception of how hard a question is is so wildly different to how hard an undergraduate thinks it is (reflected in examiners’ reports), and you have a pretty stupid situation. When, like me, you only revise the minimum number of options, you meet disaster when the questions you want to answer are too hard to let you do very much at all.

An example of this is that fellow Math/Phil Sophie who had poured her time into the Fields option which I’d dropped a long time ago had a dreadful time yesterday, writing pretty much nothing, whereas today she owned it and came out very happy. We’ve both done similarish amounts of work and have similar levels of ability and interest so that shouldn’t be happening.

I’ve been reflecting on revision and how I’m going to do it better next year. It seems that actually learning everything is probably a good idea, rather than trying to strategise based on past papers, and you’d think that’d be doable next year when we have something like two and a half months of revision. The problem is that the first week of revision is worth less than the last two days, I suspect: proofs don’t stay in long enough. The best I can come up with is: make sure you have understood all the lecture notes as early as possible and have a good set of summary notes inc. sketch proofs, and then spend the middle period doing all the past papers, and then doing them again, and then at the end force bookwork into your head. But then there is too much bookwork. I can’t figure out how to make this work better.

Now it’s all over for the summer and despite the fact that there’s not been anyone around for the better part of a week already, I’ve been left sad now that the year is over. I have to leave Oxford, a place where we say, we’re going to do everything we can, we’re not going to take the easy way out, we’re not going to let up because once one thing finishes, be that academic, social, political or whatever, we’re going to hit the next one equally as hard. It’s exhausting but I fear nothing else will ever be enough. It’s an exhilarating intensity that actually does work, we do come out rather better thinkers. More importantly we’re all that we can be, realistically, on every level. I have to make as much as I can out of the final half of my degree, and out of my time in the unique position of being an Oxbridge undergrad; staying here for graduate study does not mean extending this which you only get three or four years at, and then that has to be it.

Edit 1/vii/2011: I’ve since confirmed that the question on Monday that wasn’t on the syllabus wasn’t, but they won’t do anything, which is fair enough because some people answered it. The question yesterday that was impossible to me was impossible because it was on stuff I’d never done before i.e. it was completely off the syllabus, not just an unexaminable proof. So carelessness on the part of the examiner has turned my best paper into my worst :\

The time of this post is inaccurate; forgot to fill it in at the time.

Posted Thu 30 Jun 2011 17:00:00 UTC