### Writing essays

The aim of this post is twofold: to find out whether a certain mental habit of mine is common, and to draw parallels between that habit and the writing of essays. I don’t know whether this is common or not, but when I’m feeling particularly not-alert (for instance, when I’m nearly asleep, or while I’m doing routine tasks like cooking), I sometimes accidentally latch onto a topic and mentally explain it to myself, as if I were teaching it to the Ancient Greeks (who, naturally, speak English).

### Introduction to functional programming syntax of Mathematica

Recently, I was browsing the Wolfram Community forum, and I came across the following question: What are the symbols @, #, / in Mathematica? I remember that grasping the basics of functional programming took me quite a lot of mental effort (well worth it, I think!) so here is my attempt at a guide to the process. In Mathematica, there are only two things you can work with: the Symbol and the Atom.

### Denouement of Myst III: Exile

A long time ago, in a galaxy far far away, I completed Myst III: Exile. It’s a stupendously good puzzle game. For some reason, it popped into my mind again a couple of days ago. This post contains very hefty spoilers for that game (it will completely ruin the ending - I will be discussing information-exchange protocols which are key to completing it), so if you’re ever going to play it, don’t read this post yet.

### The Creation

Once upon a time, before this bountiful age of Matter and Light, there was only the Fell. A single being, surrounded by Chaos, content to remain alone forever (for it did not know what a “friend” was). It had not the power to shape the Chaos; neither had it the inclination, for it needed nothing and had no desires. For seething unchanging aeons, it persisted. Then Chaos bore new fruit. A single electron, a point source of charge.

### Smartphone Charter

I am shortly to receive a new Nexus 5. I am determined not to become a smartphone zombie, and so I hereby commit to the following Charter. I will keep my phone free of social networking apps, and I will ensure that I do not know the passwords to access their web interfaces. While they can be really quite handy, they are usually simply a distraction. People are used to the fact that I am present on the Internet only when I have my computer with me; there’s no need for that to change.

### Three explanations of the Monty Hall Problem

Earlier today, I had a rather depressing conversation with several people, in which it was revealed to me that many people will attempt to argue against the dictates of mathematical and empirical fact in the instance of the Monty Hall Problem. I present a version of the problem which is slightly simpler than the usual statement (I have replaced goats with empty rooms). Monty Hall is a game show presenter.

### The Training Game

The book Don’t Shoot the Dog, by Karen Pryor, contains a simple exercise in demonstrating clicker training. This is a very successful technique used to produce behaviour in animals: having first associated the sound of a click with the reward of attention or food, one can then use the click as an immediate substitute for the reward (so that one can train more complicated, time-critical actions through positive reinforcement; a click is instant, but food or attention requires the trainer approaching the trainee).

### The Jean-Paul Sartre Cookbook

Many thanks to the Guru Bursill-Hall for bringing this tract to my attention through his weekly History of Maths bulletins. It was originally written in 1987 by Marty Smith, according to the Internet. The Jean-Paul Sartre Cookbook October 3. Spoke with Camus today about my cookbook. Though he has never actually eaten, he gave me much encouragement. I rushed home immediately to begin work. How excited I am! I have begun my formula for a Denver omelet.

### Markov Chain card trick

In my latest lecture on Markov Chains in Part IB of the Mathematical Tripos, our lecturer showed us a very nice little application of the theorem that “if a discrete-time chain is aperiodic, irreducible and positive-recurrent, then there is an invariant distribution to which the chain tends as time increases”. In particular, let $$X$$ be a Markov chain on a state space consisting of “the value of a card revealed from a deck of cards”, where aces count 1 and picture cards count 10.

### My quest for a new phone

*This post is unfinished, and may never be finished - I have decided that the Nexus 5 is sufficiently cheap, nice-looking and future-proof to outweigh the boredom of continuing the research here, especially given that such research by necessity has a very short lifespan. I am one of those people who hates shopping with a fiery passion. * My current phone is a five-year-old Nokia 1680. It has recently developed a disturbing tendency to turn off when I’m not watching it.

### How to do Analysis questions

This post is for posterity, made shortly after Dr Paul Russell lectured Analysis II in Part IB of the Maths Tripos at Cambridge. In particular, he demonstrated a way of doing certain basic questions. It may be useful to people who are only just starting the study of analysis and/or who are doing example sheets in it. The first example sheet of an Analysis course will usually be full of questions designed to get you up and running with the basic definitions.

### The Ravenous

Once upon a midnight dreary, while I pondered, weak and weary, I required a snack to feed me. Reaching in the kitchen drawer - With the scissors, cut the wrapping, I revealed a jar of tapen- Ade of olives. Gently snapping, snapping off the lid, I saw: Lines of mouldy olive scored the tapenade. The lid I saw Speckled with each mocking spore. How the pangs of hunger rumbled while I cursed the jar I’d fumbled;

### Training away mental bias

In which I recount an experiment I have been performing. Please be aware that in this article I am in “[meaning what I say][1]” mode. For the past year or so, I have been consciously trying to identify and counteract places in the “natural”, everyday use of language in which gender bias is implicitly assumed to be correct. The kind of thing I mean is: A: I called the plumber.

### Meaning what you say

In conversation with (say, for the purposes of propagating a sterotype) humanities students, I am often struck by how imprecisely language is used, and how much confusion arises therefrom. A case in point: A: I think that froogles should be sprogged! B: Sprogging froogles would make the bimmers go plog. A: But I use froogles all the time - I don’t care about the bimmers! Why are you so caught up on the plogging of bimmers?

### Plot Armour

Wherein I dabble in parodic fiction. The title refers to the TV Tropes page on Plot Armour, but don’t follow that link unless you first resolve not to click on any links on that page. TV Tropes is the hardest extant website from which to escape. Jim, third-in-command of the Watchers, ducked behind the Warlord’s force-field, desperately trying to catch his breath in the face of an inexorable onslaught. His attackers, the hundred-strong members of the Hourglass Collective, had never been defeated in pitched battle.

### How to prove that you are a god

I came across an interesting question while reading the blog of Scott Aaronson today. The question was as follows: In the world of the colour-blind, how could I prove that I could see colour? I’m presuming, to make the discussion more life-like and less cheaty, that this civilisation hasn’t discovered that light comes in wavelengths, or that it has but it can’t distinguish very well between wavelengths (so that all coloured light falls into the same bucket of 100nm to 1000nm, for instance).

### Stumbled across 14th September 2013

On the merits of silence (I wholeheartedly agree): http://www.nytimes.com/2013/08/25/opinion/sunday/im-thinking-please-be-quiet.html Given the previous results on humans' sense of physical location, I’m not particularly surprised that you can make yourself identify your body as being somewhere other than where it really is: http://www.psychologicalscience.org/index.php/news/releases/visualized-heartbeat-can-trigger-out-of-body-experience.html Aaand the future arrives: http://www.washington.edu/news/2013/08/27/researcher-controls-colleagues-motions-in-1st-human-brain-to-brain-interface Another reason why Finland is amazing: http://neomam.com/blog/there-is-no-homework-in-finland A thought-provoking story: WebCite version On the “mundane magics” kind of lines: http://i.

### Slightly silly Sylow pseudo-sonnets

This is a collection of poems which together prove the Sylow theorems. Notes on pronunciation Pronounce $$\vert P \vert$$ as “mod P”, $$a/b$$ or $$\dfrac{a}{b}$$ as “a on b”, and $$=$$ as “equals”. $$a^b$$ for positive integer $$b$$ is pronounced “a to the b”. $$g^{-1}$$ is pronounced “gee inverse”. “Sylow” is pronounced “see-lov”, for the purposes of these poems. $$p$$ and $$P$$ and $$n_p$$ are different entities, so they’re allowed to rhyme.

I’ve been learning some basic topology over the last couple of months, and it strikes me that there are some very confusing names for things. Here I present an approach that hopefully avoids confusing terminology. We define a topology $$\tau$$ on a set $$X$$ to be a collection of sets such that: for every pair of sets $$x,y \in \tau$$, we have that $$x \cap y \in \tau$$; $$\phi$$ the empty set and $$X$$ are both in $$\tau$$; for every $$x \in \tau$$ we have that $$x \subset X$$; and that $$\displaystyle \cup_{\alpha} x_{\alpha}$$ is in $$\tau$$ if all the $$x_{\alpha}$$ are in $$\tau$$.