Those other things are still up (plotter, graphics, recursion) and this is an Excel spreadsheet which I used to do a bunch of simultaneous equations to determine that the sum from r=1 to n of r⁴ is n⁵/5 + n⁴/2 + n³/3 - n/30. I’ll simplify that later I suppose.

The idea was that the sum of r^p can be expressed as a polynomial of order p + 1, so I just got 5 simultaneous equations involving the 5 coefficients of the quintic expression and got Excel to solve them in an “algorithmic” way similar to the triangular form thing we have to do.

I was revising FP1 and the sections on triangular form and summations of r^p “inspired” me to do this.

Pax

I’ve begun wondering if there’s anything special I can find with recursion, or if it’s just a fun way of expressing things. Is there anything new in there?

Pax

If my muddled understanding of cellular automata and neural networks (and indeed the human brain itself), logic gates and the internet has taught me anything, it’s that the networking of nodes (simple[r] systems) can yield impressive, unpredictable or lulzworthy results. For me at least, pieces of fiction (films, books and such… not like, rubbish stuff) have an effect because I pick up on certain connections within the material to other parts of itself as well as to other things I don’t fully understand and stuff I already know etc.. This generates a kind of feel which I struggle to capture with my poor photography and endless blogging.

Maybe these complex network “feels” are also what govern sociology, love and anti-lulz! I think of this “feel” as a generalisation of the term zeitgeist, removing it from time. Geist, then? It already has a definition; I like mine better. How about nGeist? For network Geist? WordPress seems content with it… yes, that’s fine. Maybe The Node was just one Geist. Or the Universal nGeist. The uGeist! I MAKE WORDS UP.

Usually when I’m not fully acquainted with someone - or something - I get a more attractive “feel” than I will when I get more familiar.

Occasionally though, it just gets better and better until I get lost completely. Very occasionally. But when it does, it increases O(x^x!). These cases have been computing, maths and a few other special cases which maybe I’ll write about later.

Ha ha! Later!

Pax

I’ll standardise CPT1 and CPT2 to 3.7. Core 2 was 3.8ish? Have all three physics papers on Thursday, Stats 1 on Friday and then a break for a week. Then Core 3 and FP1 on Monday, all three chemistry papers on that Wednesday and Mechanics 1 on that Friday - AND I’M DONE!

Pax

Yes, I forgot a lot of stuff.

I went to the CERN open day on Sunday April 6^th - I’ll put up videos (of the Computer Center) and general photos if someone reminds me. For now, here and here.

I saw Muse and The Futureheads on April 12^th (Teenage Cancer Trust) thing with Oliver Jones (I don’t think I give that guy enough credit for his sociopolitical intelligence. A good guy. One to watch.) and it was awesome.

With Bryant Tan and Charlie Patterson being prodigiously good informaticians and Vivan somewhere in Princeton talking to legends of computing, it actually seems like maybe some of the interesting things that are going to happen in computer science could, you know, be initiated by some of us. That’s cool. We’re not bad. As Mr Rokison despairs over our computing set, I can’t help thinking that actually we’ve come a long way - and are, for the most part, totally awesome.

Also, I’m going to buy this. It is an almost-perfect proxy for the experience of old computer stuff. Which I missed. Because of time.

I saw Iron Man. I didn’t think it was a masterpiece… but I thought it was very good, actually. The thing I liked about Fantastic Four was the characterisation (especially The Thing and The Human Torch) - but the rest of it was crap. Iron Man, however, had Mr Downey Jr. (who I thought was really good in this - REALLY!) as well as other general awesomeness. I don’t know about the Stane guy - I don’t think he had the villainous undercurrent these superhero bad guys usually do. I think a subtle hint of what a character will develop into isn’t actually that unrealistic and can be an elegant storytelling device, even if people pan things like that as making the plot too obvious etc.. Done properly, it would have added weight. Anyway, yeah. That was good. Yeah.

Good things coming up: The Dark Knight, Watchmen, The Incredible Hulk
Horrifying things: A-levels

Crippling self-doubt, not helped by genius of peers, can be remedied, I found out, with guitar practise*. Just practise. Seriously. You’ll be a better guitarist and worry less. Coping mechanisms: fun, fun, fun! I don’t even let the self-doubt thing percolate properly anymore. I just refresh my whole brain whenever it starts. It’s pretty good.

Pax

* lulz commas

I like exams. I will revise for them.

I very quickly read Counterknowledge (the book, not the blog). I kept thinking about Baudrillard and his simulations - probably to do with hysteria and mass media stuff. The book is acerbic. I think I like it, although I haven’t really considered it in great detail. It’s very angry. As in most cases, a balance (here of “credulous thinking” and assumption of good faith) is probably necessary.

I’m going to do the Turing Omnibus exercises in more detail and then read Algorithmics, and if I have time (…), The Pleasures of Counting.

Must be ready!

Pax

Method 1

Method 2

If we consider that the largest square that has to be looked up in method 1 is ((a+b)/2)² and in method 2, a² (if a is the larger of the two), it’s clear that method 1 will require a smaller square table but more operations per run, so there’s some tradeoff involved there.

I’m making an assumption here as I don’t know about general cases for binary subtraction but I think that addition or subtraction of 2 n-digit numbers is O(n·k) while multiplication is definitely O(n²).

Considering binary numbers, 11111111·10101010 will take n² + 2n - 1 operations (New Turing Omnibus p168).

Substituting into method 2:

If each lookup is one operation (and there is a fixed number of lookups and subtractions for the general case) and subtraction is O(n·k), and division by 10 (i.e. by 2) is also O(n·k) (another assumption - I suppose that since we’re dealing with a fixed denominator unlike the multiplication case where it seemed logical for it to be O(n²)) then I think the function increases as n·k.

But it requires a square table. A LARGE ONE. However, this may be okay because you can reuse the squares in many calculations so perhaps in the long run it somehow balances out the initial deficit?

Or maybe the table can be populated as you go so there’s no initial deficit but a general inefficiency which soon disappears as the table values start getting filled in?

I really don’t know though.

It’s a nice thought.

Hmm?

Pax

I’m quite glad that I’m going to have a chance to talk to a real psychologist about this now. I noticed some years ago that my self esteem (should it be hyphenated?) seemed to be influenced by the outside world but also comprised some other more random elements. It wasn’t really reflected in my mood - I would always feel kind of confrontational and angry as I’d never really felt I’d totally excelled in any respect and would thus feel like I had a fight to pick with everyone. The thing was, I would sometimes feel like I was a rubbish, untalented person and want to one-up the arrogant and unfairly successful people I met and would sometimes feel immensely proud of myself and want to maintain some phantom “good reputation” that I never really had. I was never in the middle - it was a little extreme. I think this is what made me work so hard.

My surviving grandparents are now both declining rapidly, my maternal grandmother’s death remains an interesting event and my general angst about the world is at an all time high, but I now feel stable and, really, quite good. Windmill Lodge told me I had a period of depression between September and sometime in January, which seems to make sense. It feels so much better now - to be able to categorise it and seal it off is a tremendous relief.

It’s a surreal situation - consistently failing to perform well in Mr Motion’s tests and generally failing at Dr Zetie’s top set exercises should really be killing me but actually, I find myself beginning to change in a more fundamental way than any of these surface fluctuations that have plagued me for so long.

Computer Science with AI at Imperial - where my dad went for Mechanical Engineering - looks awesome, but then again everyone I’ve talked to wants me to apply for Cambridge. It’s a nice thought but I wonder what the course is really like. I’m fascinated by problems of optimisation, logic and semantics… but I also like programming. Erroll Wood (probably the only person in our computing class who comes close to really understanding computing as a discipline - James and Vivan program well but I don’t really know what their views on actual computer science are) has expressed concern over the level of practical stuff in the Cambridge course… meh, open days will resolve these quibbles (hopefully).

On that note, Mr Brewis, Dominic Yeo and Mr Motion all gave me blank looks when I mentioned the Simplex algorithm. I mentioned it to Mr Brewis when we were discussing optimising the equilibrium in the Haber Process, Dominic Yeo for fun and Mr Motion to see if he could properly explain it to us (we’re doing matrices right now, so it might’ve been possible).

I feel like I’m the only one in the whole school apart from Dr Zetie who takes any sort of computer science seriously! Vivan confused the bogosort with the bucket sort as Will played with Mr Fry’s sorting demo app in computing. For a few hopeful minutes I really thought he know what the bucket sort was but I soon realised that NO-ONE CARES ABOUT ANY REAL COMPUTER SCIENCE. ALL THEY CARE ABOUT IS SHOWING OFF HOW THEY CAN CHEAT AT GAMES AND PROGRAM STUFF IN VB, ONE OF THE WORST LANGUAGES IN THE UNIVERSE.

It doesn’t matter how much you know about iPods or how authoritative you can sound while quoting Wikipedia! AUGH! Don’t mistake this for a rant, however, as I’m not really complaining about a sudden retardation - more like getting emotional while stating the forgotten situation in all its stupidity.

Oh, I’m also very optimistic about the Public Schools this year. I somehow did well last year and I feel like I’m becoming a much better fencer anyway. Yeah. Optimistic.

I’m reading Brainwashing. Its cover is so tacky that I almost didn’t buy it but I’m so glad I did. It’s RIDICULOUSLY good. It is now among my top books (Simulacra and Simulation, The Psychology of Interpersonal Behaviour, Surely You’re Joking, Mr Feynman? et al [ask Facebook]). Afterwards I need to read The Theory of the Leisure Class. I think The New Turing Omnibus, which is a little textbooky but incidentally contains Conway’s Game of Life as well as Simplex and a load of other pretty great stuff, will probably be up there once I understand it fully. I’m plodding through it. Like a retard on muscle relaxants. Seriously.

Mr Smith alerted me to the correct pronunciation of Proust (”proost”, for phonetically [is this the right word?] retarded people such as myself). I had mentioned it because of (you won’t see this coming) Lain (his madeleines in In Search of Lost Time were used as a metaphor for involuntary memory).

I’ll finish this with a conspicuous ego-boost. I feel immensely happy when I see someone I know giving someone else the finger or calling them fat or even a chode. Elliot and I, in our social ineptness, broke down barriers and behaved oddly until people began to realise that arbitrarily criticising us or trying to be funny to our detriment didn’t work as well as it should and adopted our crap. Even Michael B, someone very, very critical of odd behaviour - someone who would often mock me for trying to be funny in a perceived-to-be-OTT way - was recently seen giving the one finger salute across the atrium.

Poor Mr Rokison still mutters “You’re all so weird/strange” every time he puts his head down in a desperate attempt to renew his self esteem (aha, we’ve come full circle) in front of a class that is no longer captivated by his paradoxical energy or random lapses into making repeated Pingu sounds. It’s refreshing that he mercilessly mocks Will (I’m sure Will finds it funny or he’d assert himself and throw Ollie - sorry, Rokison… sorry, Mr Rokison - to the ground or something). This isn’t a joke, by the way - I’m growing tired of his attitude. Condescension - especially at such a similar age to us - do not help his position at all. I suspect the way this ends will be hilarious.

Imagine turning down a place at Cambridge. My parents and siblings were horrified. That gives me hope - it means they thought I had a real chance of getting a place there.

Pax

Well, would you look at that?

Pax

Yes, I’m finally doing what people have been telling me to do since the 4th form: learning Python! …that’s all.

We had the senior club sabre today - the winner was Adam, who fenced really, really well (obviously) and trumped the top sabre-only fencers (Adam fences all three weapons). Unfortunately for ME, my first fight was against him and so the final score was 15-11. I’m sure I didn’t deserve most of the points I got. Now I have to think about how to explain a first round exit to my club when I won the junior sabre last year… oh well. There’s always club computing!

Just while discussing fencing, I’ll reiterate that the Camden International Cadet Sabre is on Saturday the 9th. Last time Elliot and I did it - we washed out completely (both came sixtysomethingth, Elliot a few places above me [yeah, yeah… laugh it up, fatboy!]). I don’t think we’d ever been in such an intense situation (although the BYC 2007 was pretty close). We’ll try to do better this time.

I love counterattacks so much. You have no idea.

Pax