psyche

You may remember Approval and Optimisation, in which I minimised the error between a function and a candidate function, linearly parameterised in one variable.

By linearly parameterised, I mean the function would be something like y = mx^n or mx + sinx or something with m the parameter. If it were non-linearly done, like y = nx^m or x + sin(mx), then my quadratics ‘n’ completing the square approach wouldn’t work (although you could just use derivative = zero stuff).

I’ll just summarise the general process before writing up the obvious extension which Bryant and I both considered. The parameter in your candidate function is m.

1. Get expression (candidate function - target function)^2 in integrable form
2. Let E be the integral of that expression between whatever limits you want
3. Find m such that E is a minimum (the most robust way is to solve dE/dm = 0 but I used a completing-the-square shortcut last time as I was only using a linearly parameterised thing)

For a candidate function that is a polynomial, remember that it must approach some kind of infinity as x goes to ±infinity, so there is no maximum error, so dE/dm can be rigorously shown to give the minimum.

Ok, now the important stuff. As I understand it, partial differentiation is just treating everything except the thing you’re differentiating with respect to as a constant. To illustrate, consider z = x^2 + xy + y^2

Implicit differentiation: dz/dx = 2x + (x dy/dx + y) + 2y dy/dx (having y as a function of x and chaining/producting it as necessary - the bracket in the middle is just the product rule)

Partial differentiation: ?z/?x = 2x + y (as if y was a constant)

A quick scout online showed that this business of finding “critical points” i.e. maxima and minima of multivariable functions simply involves setting all the partial derivatives to zero.

The extended method is pretty similar, but here’s an example. I can’t be bothered to type up all the working - it won’t look nice anyway - so I’ve skipped all the simplification/algebra. Note to self: use The Integrator more often…

Candidate function: ax + b
Target function: x^2 on [0, t]

E = integral from 0 to t of ( (ax+b) - x^2 )^2 dx
= (a^2)/3t^3 + abt^2 + tb^2 - (at^4/2) - (2bt^3)/3 + (t^5)/5

Thus ?E/?a = (2/3)at^3 + bt^2 - (t^4)/2
Setting this equal to zero leads to 4at + 6b = 3t^2 (EQ 1)

and ?E/?b = at^2 + 2bt - (2/3)t^3
Setting this equal to zero leads to 3at + 6b = 2t^2 (EQ 2)

Solving EQs 1 and 2 simultaneously gives a = t, b = -(t^2)/6, so y = t(x - t/6). Oddish but niceish result I guess. Someone please confirm.

I sanity checked this with ax + b and mx + c and thankfully a = m and b = c dropped out fairly easily despite some difficult-looking but actually tolerable multiplying-out.

Infinitely more promising is the fact that your function doesn’t have to be linearly parameterised or just a straight line or any of that batshit insane stuff. You can do an arbitrarily high-order polynomial approximation… or something. Cool. Going to do that for some badass functions and see how they compare with Taylor/Maclaurin expansions.

Pax

I have come up with a number of heuristics that have helped me become happy and appreciate good things and act on challenges while being unreactive to meaningless things that I would previously have interpreted as “negative”. The net effect of these (which I am about to explain) is to cut out the type of self-talk that needlessly slows down (or even ruins) social interactions and problem-solving while maintaining the level of introspection necessary for looking beyond the superficial. The principles I started with - or, in some cases, later reconciled the heuristics with - were “belief in oneself” and “not caring what other people think of you”. More on this later.

YES!/oh hellz yeah

Directly inspired by the “YES!” that Captain Falcon shouts while performing his (amazing) Falcon Dive, YES! is an expression of active rather than passive compliance. Before, if someone asked me to play Tank Trouble (a great game), I offered similar weird token resistance/inertia as if they’d asked me to copulate with their toilet and then eat one of my own eyes. YES! forced me to acknowledge my own intent and break free from the complete passivity I was in before. It builds a sense of identity and each YES! sums towards having a better day. I take responsibility for my actions now.

oh hellz yeah is a funny one, but it’s not quite as concise or snappy as YES!. However, it remains a good method for keeping such positivity varied and the pace controlled.

nah dude/bad news

Originally met with some resistance, nah dude is similar to saying “chill” and “no thanks” at the same time. Bad news is an acknowledgement of something dumb happening without getting all “OH MAN MY DAY IS SO BAD AND THEN EVERY DAY IS RUBBISH LIFE IS HARD”. They unambiguously asserting your rejection of whatever it is, but both of these WAY better with a smile than “no” or “not too good” or whatever other buzzkillers I could think of.

’sko

A contraction of “let’s go”, for moving people. Reduces subconscious token resistance and interestingly effective for eliminating personal procrastination for me.

smile

I think I read somewhere that physically smiling actually makes you happier (i.e. the link between “being happy” and “smiling” isn’t one way). I’m constantly smiling and/or pulling ridiculous faces (even in lessons, although sometimes teachers try to stop me… guitar lessons are the best).

chill

When in danger of jumping onto something and smashing it or throwing my brother out of a window, I just remember this and the others follow.

lulz

What more can I say on this? It’s just… epic win.

raw

This doesn’t mean anything… raw.

good plan

A multi-tool. If something is literally a good plan, say it. If something is a funny, insane plan, say it (and maybe do it unless it would incur extreme carnage of the bad news variety).

How to use the heuristics

Either say them in your head or say them out loud. Self-amusement and a sense of humour is necessary. By taking these things so mock-seriously, I give myself permission to make them 100% effective. A lot of this kind of stuff seems to be “giving yourself permission” to do stuff, which requires humour when you’re starting out.

I read that some studies indicate that the mania aspect of bipolar disorder could be caused by phases of deep denial of depression, and other sources concur that blanket repressing “negativity” can be just as disastrous as wallowing in self-pity. This is why a chill aspect is definitely necessary, to sort of “ground” lulz. In fact, I saw a brilliant infomercial which I will now show you so you don’t do cannabis:

The different aspects of his personality are “exploded” (yes, like an Excel pie chart) and we can see that while some of the individual components aren’t “bad” by themselves, some are (and note Dr Chill sitting there… amazing).

What was I saying? Oh yeah: don’t go for extremes. Just chill out. Allow yourself to experience the full range of your conscious existence, but train yourself to be controlled. Always feel yourself pulling back to state of serenity. Some people advocate a total lack of emotion, and while this is theoretically viable, I find that in practice as I get to know these people they seem to reach a maximum of being “in the moment” and then slowly disown all their human aspects and become deeply conflicted. They feel guilty about being human. It’s better to accept your humanity - even your mortality - and then just chill with it. In my experience, this works. Literally, you can just start doing it right now and it will work. TRIED AND TESTED!

If you think other people are mean, it’s one of a few things:

1. Low level: they’re casually insulting you etc. in a way that is just socially acceptable. You must learn not to care. It mystifies me when I see an otherwise cool person fall to pieces when someone questions them. Really, really believe in yourself. Be happy, do things you want to, accept responsibility for your life, lose your victim complex, blah blah blah. It’s possible… and necessary, unless you want to realise at the end of your life that you could’ve done better. If you’re fun, confident etc. this problem will just disappear, or you’ll realise it was just “banter” all along.
2. Mid level: people turn away from you when you try to talk to them, people throw your pencilcase into a woodchipper etc. … you’re not presenting yourself properly, probably because you’re still internally messed up. You’re being alternately irrationally spineless and then irrationally angry/insane (this is “nice guy syndrome”… you don’t have to be nice to be a “nice guy”, one of the mediocre people that we can now easily be socially conditioned to be).
3. High level: people beat you up, attempt to wage war on you, attack you with submarines - try to bring in law enforcement or national guard. Take responsibility for your survival - this is what evolution designed you for. Learn to operate vehicles. Escape. Do not take lives. Conquer your fear. Try not to get into life-or-death situations. This may be beyond the scope of this guide.
4. Ultra-high level: you seem to suffer from personal environmental disasters. You are the last human on Earth, etc. I cannot help you. Just use the heuristics and chill, lulz. Play some games or something.

Try to take steps to do what you want. Try not to derive your self-esteem from others - this is bad. Sometimes people are socially successful with a particular group or by some particular merit (a talent or physical attractiveness etc.) … this leads to addiction to validation, which can work but is UNSUSTAINABLE. You will not have people to derive comfort from all the time. Sometimes you will have to take responsibility for this. The sooner you honestly come to terms with this, the better.

Here is a list of experiences that have helped me be happier despite no significant change in external life:

• Having photosensitive sunglasses/dancing or singing badly wherever you want: I learned that whether someone thinks I look stupid or not doesn’t affect me ;-] unless I make it. It’s like The Matrix - other people’s feelings towards you only affect you when your mind makes them real
• Tank Trouble: how you can have fun without really moving
• The tuck shop: how talking with good friends about nothing while arranged in a circle is amazing
• Randomly talking to people: how friendships start from nothing
• Depression: how you control your own mind - it’s sometimes tricky, but never as hard as, say, fighting a Jedi Master or something… or like defusing a really hard-to-defuse bomb…. not that hard
• Trying to explain why I haven’t done my homework: the benefits of honesty, humour, smiling, clarity and concision in work-corrupted interpersonal relationships
• Boxing: putting stuff into immediate perspective, believing in oneself, GETTING EXERCISE (GOOD PLAN)
• Attending family functions: learning that “dancing” means “lulz” for non-professionals
• The common room: clique boundaries are in your head
• The guitar: how music can change your mood if you let it… how “technical excellence is the antecedent of … creativity”
• Insane friends: how normal interactions can wear you down if you never learn to approach them properly

That last one is worth remembering. Sometimes people feel guilty about consciously trying to make themselves happier… they feel like life shouldn’t require these hokey self-helpish tricks. Eventually they become subconscious so you don’t have to worry about them, but people who think they should naturally be happy stay in denial. If you’re unhappy, just accept that by random chance you didn’t integrate into society. Civilisation lays down a lot of well-defined and easy-to-access rules - it’s the norm for procedures in human life to be well-defined. After all, people have been there before, right? Well, maybe so, but I promise you, to truly enjoy life and do what you want, you do have to accept that not everything will come naturally to you. There’s nothing “natural” about a lot of life, and a lot of what we consider “science” like lightning bolts and stars is NNNNNature. So chill and take responsibility. Don’t expect it to be handed to you. This approach definitely worked for me.

Cynicism

Remember the difference between choosing to be a lulzorific parody of humanity and becoming a dark, twisted mofo.

If you get these aspects of your life handled, the rest seems to fall into place - sometimes in a way you didn’t imagine possible. Performance anxiety, schoolwork, proficiency at your hobbies, relationships of all kinds… they flow if you’re more confident. You allocate time to doing what you want to do. You don’t feel resentment for no reason. But you’re still human, you’re happy without being insane, but it wouldn’t even matter if you are, and wait, maybe you are, but you know, CHILL!

Belief in yourself and not caring what other people think, when combined with the intellectual base you have probably already cultivated (while letting your emotional/mental [same thing] health go without realising it). It’s just the best way to be. It’s YES!

A last thing. This concept seems so universal that it must have already been defined somewhere, but here I go anyway - macro and micro stuff.

Macro: I want to be great at … roundhouse kicks.
Micro: I want to eat. I want to watch TV. I’ll do my homework… oh, she’s hot… I want to ja–go to the toilet. I want to eat. BLAH BLAH BLAH

It’s easy to sabotage yourself. You’re not automagically equipped to learn skills over a long time period, with indistinct and sometimes abstract results. You have to really believe in what you want and commit to it. It’s possible… and necessary.

Beware: don’t develop an ego about this. Chill out. It’s ridiculous but I have felt this - and people I know have independently documented this. You can actually become arrogant about being happy. You can get a self-righteous sense of pity. This indicates that you are still a bit of a social chameleon, getting your identity from others. Everyone is adaptive to some extent, but it can become stupid… you don’t want to let your values slosh around. You’re not a zombie who can be turned directed by anyone who acts like they know what they’re doing … are you? You can lose direction in your life by not being in the moment - you don’t really participate in life, you let it “slide”. You have your reality dictated to you; you do not dictate reality. You are like a cloud of reflective particles… you are defined by who you are and what you are doing. This is not correct. You want to be dynamic but stable. Controlled but flexible. It is not an oxymoron. Think of a great martial artist. It is cool. The ego can sneak back in. You have to really let it go. Do things for yourself, not to “please” people you don’t know (and don’t break your back to please your friends - you’re a human, not a tool [well...]) - this ends up annoying the people you should care about and the randomers you’re trying to impress will only notice that you’re a CHODE. Being too ego-centred promotes deriving your self-esteem from comparing yourself to others, which is unsustainable (and there are moral problems with this as well, but this is a practical post, not a theory one) - you might one day acquire a flaw that you have learned to hate, thanks to your ego, and that will mess you up. You can have healthy self-esteem without being an egomaniac. It just takes time to learn control, as with all these things.

Now, it’s time for lulz, so I will report back later.

Pax

My A2 computing project involves downloading stock prices and related news and showing it in a VB6-made executable. Most of the work is actually getting VB to co-operate with filetypes and graphing modules and whatnot, but it does raise some questions (or maybe I just randomly raised them). Mr Barker explained that Charlie Paterson’s algorithm for predicting trends involved inspecting the last five (or some similar number) changes in price and then looking back for a bunch of five similarly-sized consecutive changes and seeing what the sixth change was and then predicting that that sixth change would happen this time around. It sounded quite interesting to me but apparently it was rather unsuccessful. My dad mentioned “trend-following” ones that predict the price will go down if it’s gone down the last n times. The smaller n is, the more “sensitive” the thing is - obviously if n is 1, it’ll just predict the last change which is probably around 50% useful… but the larger n is, the more “behind the trend” you’ll be when you pick it up.

I kind of dream of fitting polynomials to the last 100 data points or something - maybe this would help predict minima and maxima as well? I think someone once mentioned Fourier analysis of the stock market to me, years and years ago… … … I don’t know. Sounds very interesting.

Then I started thinking in very general terms - think about the deterministic universe idea that if you know its initial state, you can predict its whole future. Obviously you wouldn’t expect to be able to predict the entire progress of the stock market from its initial state (!) because not only is it externally-influenced, it’s completely controlled by external forces. Now, if we could model the behaviour of lots and lots of investors… :)

I’m going to try to have a look at some stats/compsci mashups when I have the change.

The second part of this high-variance post is about some probably useless things that I’ve been thinking about. In a culture of mass consumption (blah blah) perhaps we slide towards defining ourselves through what we buy etc. … perhaps this is unavoidable, but I hope it’s understandable (in some sense). What I’ve been worrying about is the idea of being not just emotionally invested in endeavours and inanimate items (or even other people) but really, really relying on external things for validation. Maybe it’s insane to think you can fuel yourself - maybe that’s a microneurosis of my own, the belief that someone can function alone - but sometimes it seems insane to think that your environment totally controls you and you are just living “in reaction” to the world. I chanced upon the print version of this article, possibly exaggeratedly (I’m not very good at reading between lines etc.) mocking Twitter users’ need for constant attention/validation… its criticisms seem to ring true in some sense… … I suppose everyone who tries to maximise their “connectability” (*cough, shuffle*) is guilty of trying to “feel alive” by connecting to stuff. Is that bad? Possibly.

I think there must be an optimum point between being {selfish, obstinate, unreactive} and {personalityless, fickle, reactive}. Some particularly cool people seem to just settle near this optimum while others like myself flounder in a state of extreme self-consciousness, spewing a narrative of the slightly odd journey as they (I…) go. I’d like to think I’m slowly migrating towards a healthy emotional state - I’m definitely very happy but it feels a little bit fragile, like if I hit my head and was paralysed and couldn’t do any maths or guitar or exercise anymore I would become depressed. I don’t want that kind of mental breakdown to be possible ever.

What of the idea that one’s ego and one’s self-esteem aren’t the same, and that one’s ego is a big rationalisation (”I’m Farhan, I go to a good school, I have {some skills}, I’m a sexy beast” and one’s self-esteem is one’s natural will to survive? In that case, some people will be successful in maintaining their ego and have that at their core and let their self-esteem wither and with good luck will remain happy for their lives and be so confident that they can be happy that they will always somehow manufacture the situation necessary to reinforce their ego and assure them that they are a functioning life-form. I suspect that these people, if confronted by a terrible accident, would “lose it”, so to speak. Because their ego generally works for them and the world has tricked them into believing that “that is the way happiness works”, they never confront the strange damage that has taken place to their self-esteem as a result of the way modern human civilisation plays itself out.

On the other hand, cool mofos who have worked to genuinely improve themselves as people (I don’t mean in a “LOL LERN NEW SKILLZ” but in a “understand what it means to be human and not a robot or an animal or a brick”) and have avoided or got wise to the hidden and never-discussed subtle, indirect and psychological pitfalls of consumerism have their bodies compeltely crippled by fate and respond amazingly well.

I suspect/hope that for the majority of people, this works itself out - as they “mature” they somehow “find themselves”, some later than others. Fun.

So much/many lulz! countable(lulz)?

Pax

EDIT:

The obvious thing of taking the mean change for the last five and extrapolating is probably ill-fated, so I asked my dad about weighting the means so the ones closer are much more important. I thought that was quite nifty. He laughed in my face and suggested that I read up about the tremendous amount of stuff that’s been done and about how complex and, occasionally, effective it was. Interesting…

Slowly detaching myself from the need to gain approval from others and losing the arbitrary restrictions I have placed on myself is an enjoyable process.

Now, optimisation. Initially I wanted something like “What is the optimum quadratic ax² + bx + c to model the cubic px³ + qx² + rx + s on the interval [x₀, x₁]?” but realised that this was rather ambitious.

I tried a crippled version of this, which was kind of fun. Say I have a function f(x) and want to approximate it with a straight line g(x) = mx on [0, t] (mx because I want g(x) to be strictly of the form m*h(x)… you’ll see why later).

The integral of f(x) - g(x) dx from 0 to t will give, in some sense, the “error” between the two - the distance. Unfortunately, the distance of one line below the other cancels out with the distance of that one above the other. In order to skip out integrals of |f(x)| (…), I’ll go for int[0, t]{(f(x)-g(x))²}dx. The integrand is a quadratic in m, as is the integral. If I call this integral sigma e² (”sum of infinitesimal square errors” in a handwavy way), … nothing. That naming was pointless. Anyway, I now rewrite the evaluated definite integral by completing the square with respect to m. From this I can see the value m must take to set the newly-created (m - k)² term to 0 and thus minimise the expression. Thus I have my line y = mx.

I understand that I just botched the explanation, so I’ll give an example with f(x) = sqrt(x).

You can evaluate the integral term by term by multiplying it out (it’s just polynomial in x) but I used The Integrator (I’LL BE BACK!!) to speed this along.

sigma e² = int[0 to t]{(sqrt[x] - mx)²} = (1/30)t²(10tm² - 24m.sqrt(t) + 15)

I don’t even need to fully complete the square… just take that 10t outside the bracket: (10/3)t³(m² - (12/5)m/sqrt(t) + 3/(2t)) and then we know the (m - k)^2 bit is (m - 6/(5sqrt(t)))² so to zero that term, m = 6/(5sqrt(t))…

…so in conclusion, the line y = 6x/(5sqrt(t)) best approximates y = sqrt(x) on [0, t]. Try it in Autograph. Lulz.

Yes, it’s useless, but it… is something that should work and it… does (?). It highlights the interpretation of the integral as an infinitesimal sum rather than “the area under a graph” or whatever. Eh.

Pax

Here’s my guess for the importance of chords in a key, in descending order:

I, V, IV, vi, iii, ii, VII (this is in the key of I major with i meaning I minor)

Little fills like ii V7 I or IVm V IVm I seem to be falling out of favour. There seem to be two types of songs: I IV V vi songs and “minor key” songs which are all like vi III ii (or II) and then V IV I. Lots of songs masquerade as minor key songs while actually being mainly iv IV V. Meh.

Of course, everyone who attempts to write music seriously figures this out pretty quickly and some choose to capitalise on how weird it seems to people who don’t think about it (1,2) while others just keep quiet and write hits and everyone wonders “Wow, so catchy. But how?”… lulz.

Pax

Should people have some kind of responsibility to contribute proportionally to their ability?* Is there some significance behind the discrepancy in the definitions of genius?

Look at the difference between, say, Richard Feynman and George Dantzig. Dantzig didn’t seem to be a prodigy and, although he won prizes, has never really been acclaimed as a genius. However, as a grad student he found high-profile unsolved statistics questions merely “a little harder than usual”. Should people who work hard and, as a result of this, achieve fantastic things be respected more than those who do it with little effort? Should they be respected in a different way?

I’m slowly but surely becoming someone else. I’m not certain it’s who I want to be or who I wanted to be or who I will want to be but it’s like, the only solution (like). It’s all about… something.

I feel like disastrous climate change etc. is going to cut short our progress as a species. I think we should go into space. Maybe we can’t solve problems apparently intrinsic to human society - but if we can, it’d be almost unforgivable to give up. What a dilemma, ha ha ha!

Just concentrate on your breathing and slow it down and don’t think about anything. Initially, your mind will wander as it doesn’t usually get the chance, I guess (unless it does, in which case you’re ahead of me and like, should forget this). After a while you’ll have it, you know, down. You’ll make patterns with your thoughts and then you can be really calm and just sort of forget about the petty things that might ruin you.

Yes - I’m testing my theory.

Pax

*socialism? meritocracy?

Cambridge interview seemed to go well (…) - as my mum and then Dr Eves - and then even a hallucination of Dr Eves - said, fingers crossed. Discussed P =? NP and other such lulz, as well as some memorable maths questions (I have an infinite string of bits, initially all zeroed. I increment this binary number repeatedly for a long time. In the long run, if altering a bit is one operation, what is the mean number of operations per increment?)**.

Algorithmics from now on:

* that’s two grade 1s in STEP
** my guess is two, but… uh…

Pax

The main highlight was Will revealing that he was stalking one of the students who was giving us a tour. However, the interview was also pretty good. We discussed - very informalulzily, sort of how my conversations with friends go if they’re in a good mood - my A-level computing project, the Collatz conjecture (my interviewer’s wife had worked on it) and Last.fm. It turns out that Dr Paul Garatt, the admissions tutor who happened to sit in on my interview, supervised Richard Jones’ third year project - Audioscrobbler. Also, Tim Berners-Lee* lectures at Southampton occasionally and has set up web groups etc. there. There was some pretty awesome-sounding semantic web stuff there.

It made me think: what if universities integrated web science properly with informatics? Wouldn’t that be better? Otherwise, it takes extreme determination on the part of web developers to fashion themselves into experts. While people like Jeremy Keith are testament to how motivated - and as a consequence, skilful - people get with (semantic) web stuff, it’d be nice if people had their eyes opened without having to start from the angle of commercial web design. Also I wonder: if people like me, who are genuinely interested in the semantic web and aren’t either i) ignorant or ii) extremely dismissive, don’t work on it, who will? Perhaps someone will come along with a web messiah complex and fix it for us.

Pretty good!

Pax

* am I omitting the “Sir” as a sign of respect?

Not sure if this is correct, but I thought this was quite good (done while procrastinating about doing Mr Miller’s Cosmology prep):

Consider an object whose initial speed, u or v₀, is zero. A constant force F then acts on it (and continues acting on it). I will (attempt) to find an expression for the speed v(t) of the object. I will use u’ to mean du/dt. Please ignore terrible interchanges between functions of stuff and such like - don’t really know what I’m doing.

Remember, v₀ is zero.

First, use the crunched version Newton’s second law: F = ma, so a = F/m, so v’ = F/m. Integrating both sides with respect to t gives v(t) = Ft/m + k. Since v(0) = 0, k = 0 so v = tv’ (cf. suvat stuff, v = u + at when u = 0… it’s all fine so far).

Now consider the relativistically tweaked version of Newton II: F = ma/sqrt(1-(v/c)^2). Using the same juggling as before, this gives:

v’ = Fsqrt(1-(v/c)^2)/m

Rearrange and use separation of variables/whatever to get:

int(1/sqrt(1-(v/c)^2))dv = int(F/m)dt

which gives (remembering the boundary condition v(0) = 0)

csin^-1(v/c) = Ft/m

sin^-1(v/c) = Ft/mc

v/c = sin(Ft/mc)

finally:

v(t) = csin(Ft/mc)

This looked promising (note the maximum value of v is c)…

To try to convince myself that this was correct, consider the sin small angle approximation: sin(x) is approx. equal to x for small values of x. Well, Ft/mc is certainly small for most F and t when you consider how large c is, so: for values of F that are small compared to c (and small t but not sure what that means physically), we get v(t) is approx. equal to c*Ft/mc = Ft/m (which = at for small v as this means we can ignore the Lorentz factor), which is the Newtonian one… which seems quite interesting. Tell me where I’ve messed up.

I almost did it with a non-zero initial speed but I saw a bunch of sqrt(1-(v₀/c)^2) blah (because of the trig addition formulae and Pythagorean identities) in there so I avoided that and then gave up entirely (good times).

Pax

Met Erroll on tube - he seemed cool and his interview went well. After the general talk (which I’ve now seen three times) there was one for just JMC people (about nine of us). Randomly, maths person pointed to Sierpinski triangle and asked if any of us knew what it was. I said “Sierpinski” in a mid-volume high-pitched whine. The speaker then said “BRILLIANT!”, looked at some admissions guy and shouted “TAKE THAT GUY!”. Wikipedia browsing has its benefits.

Random highlights included a candidate’s unassuming parent who had actually supplied the electromagnets for the LHC (!!), free food, the lulziest tour guide students in the history of lulz and some pretty good talks.

I applied for JMC 4-year but my interviewer didn’t know until I told him. He didn’t seem to have read my personal statement or know my A-levels either, so I spent about two minutes telling him a condensed version of my entire application.

He then gave me a wooden Towers of Hanoi thing, asked me if I knew what it was called (I did) and then told me to find out the number of moves to solve it. He gave me a piece of paper and a pen and for a second I wasn’t sure if he wanted me to just start writing. He didn’t do anything, so I solved it physically (it came out easily). He then asked about the number of moves. I said that since I had gone from a tower of 4 to a base and a sub-tower of 3 during the solution, it might be to do with recursion. He seemed surprised/happy for a moment - I scribbled a bit and got the recurrence relation and then pattern-spotted the closed form thing (it was some obvious thing of O(2ⁿ)). He asked me how I would prove it, to which I replied induction, which he then made me do. He seemed pretty happy after that and implied that that question was meant to take longer.

He then asked me to integrate 1/x² from -1 to 1. I became extremely suspicious because of how easy antidifferentiating it was which led me to realise that the point was that it was undefined at zero. I said this and he just didn’t respond, so I evaluated it (initially making a sign error, but then fixing it to get -2). He asked me what I’d said about undefinedness before and I restated it. He then asked me what the actual value of the integral was, and I non-comittally said it could be infinite but might converge. He didn’t do anything, so I sketched it and then re-said that it could be infinite but might converge. He agreed and then asked how I’d evaluate it, and I said by symmetry, integrating from 0 to 1 and then doubling by using a variable as the limit for the bit near the origin and making it tend to a value. He nodded “OK” and then said I’d be well-suited to the JMC course and shook my hand. The interview was about seven minutes of frantic scribbling and stammering, but I got the questions so I don’t care how crack-addicted I appeared.

They’re going to mail us offers/rejections within three weeks (probably within two).

The JMC course looks really good and it’ll be weird to choose between top universities if I have to. I was thinking that depending on how other people do, I may be able to ditch all of my friends in one fell swoop. Joy. As we (my mother insisted on accompanying me) trudged back down Birch Grove, she told me to “stop taking school and teachers so seriously” and “just coast”. It was strange to hear that type of psycho-social engineering.

It was almost as if she was reading my mind*.

Pax

* blog?