### Metathought

I have recently discovered the game of Agricola, a board game involving using resources (family members, stone, etc) to build a thriving farm. The game is turn-based, with the possible actions each turn being severely limited. This makes the game be in large part about optimising under constraint (the foundation of any good game). However, during gameplay I also detected a certain resonance between Agricola and the game of Magic: The Gathering, beyond the usual “constrained optimisation” theme.

### Stumbled across 24th July 2013

This is something I will try at some point, probably when I get back to uni: http://www.bulletproofexec.com/how-to-make-your-coffee-bulletproof-and-your-morning-too/ This was fun: http://www.sporcle.com/games/Government_Agent/true-or-false-logic-quiz Hah - stupid copyright owners: https://torrentfreak.com/hbo-wants-google-to-censor-hbo-com-130203/ The government’s got around to allowing the testing of driverless cars: https://arstechnica.com/tech-policy/2013/07/uk-govt-approves-autonomous-cars-on-public-roads-before-years-end/ An insightful comic about getting to sleep: https://abstrusegoose.com/523 Roll on the cheap and easy satellites: http://www.guardian.co.uk/science/across-the-universe/2013/jul/17/sabre-rocket-engine-reaction-skylon A bunch of interesting sciency things, including a new application of zapping current through the brain: https://arstechnica.

### The Orbit/Stabiliser Theorem

The Orbit/Stabiliser Theorem is a simple theorem in group theory. Thanks to Tim Gowers for the proof I outline here - I find it much more intuitive than the proof that was presented in lectures, and it involves equivalence relations (which I think are wonderful things). Theorem: $$\vert {g(x), g \in G} \vert \times \vert {g \in G: g(x) = x} \vert = \vert G \vert$$. Proof: We fix an element $$x \in G$$, and define two equivalence relations: $$g \sim h$$ iff $$g(x) = h(x)$$, and $$g \cdot h$$ if $$h^{-1} g \in \text{Stab}_G(x)$$, where $$\text{Stab}_G(k) = {g \in G: g(k) = k}$$.

### On Shakespeare

I’ve now seen two Shakespeare plays at the Globe - once in person, to see A Midsummer Night’s Dream, and once with a one-year-and-eighty-mile gap between viewing and performance (through the Globe On Screen project), to see Twelfth Night. Both times the plays were excellent. Both were comedies, and both were laugh-out-loud funny. The performance of Twelfth Night, then, was beamed into a local-ish cinema for our viewing pleasure. (Definitely more comfortable than the seating at the Globe, although I am reliably informed that if you go to the Globe, you really have to be a groundling, standing at the front next to the stage, in order to get the proper experience.

### My objection to the One Logical Leap view

A large chunk of the reason why changing someone’s mind is so difficult is the fact that our deeply-held beliefs seem so obviously true to us, and we find it hard to understand why those beliefs aren’t obvious to others. Example: A: A god exists - look around you; everything you see is so obviously created, not stumbled upon! B: No, that’s rubbish - look around you, everything you see is easily explained by understood processes!

### Prerequisites for hypothetical situations

Usually when I discover (or, more rarely, think up) a thought experiment about a moral point, and discuss it with an arbitrary person whom I will (for convenience) call Kim, the conversation usually goes like this: Me: <Interesting scenario> - what do you think? Kim: I would just <avoids point of scenario by nitpicking> Me: You know what I meant. <applies easy fix to scenario to prevent nitpick> Kim: Well then, I’d <avoids point of scenario by raising unrelated moral issue>

### The Multiple Drafts view of consciousness

I’ve been reading one of Daniel Dennett’s books, Consciousness Explained. Aside from the fact that the author has an incredible beard and is therefore correct on all matters, he can also write a very cogent book. In Consciousness Explained, Dennett outlines what he calls the Multiple Drafts approach to explaining consciousness; this blog post is my attempt to summarise that view in a couple of short analogies. Dennett starts off by providing evidence that our time-perception is somewhat malleable: we can interpret two dots of different colours (appearing separated by a short distance in time and space) as a single moving dot that changes colour abruptly at some point.

### Stumbled across 13th July 2013

This is really quite heartwarming: http://www.reddit.com/r/Random_Acts_Of_Pizza/ Interesting article on current trends in fiction: http://www.locusmag.com/Perspectives/2013/01/david-brin-our-favorite-cliche-a-world-filled-with-idiots-orwhy-films-and-novels-routinely-depict-society-and-its-citizens-as-fools/ A ridiculous reason for a rocket to explode: https://arstechnica.com/science/2013/07/parts-installed-upside-down-caused-last-weeks-russian-rocket-to-explode/ A very information-dense way of storing data long-term: http://phys.org/news/2013-07-5d-optical-memory-glass-evidence.html (compare http://rosettaproject.org/disk/technology/ which is much less information-dense but much more easily decoded in the event of being discovered after the collapse of civilisation) A cool thing to do with a Raspberry Pi and a microwave: http://madebynathan.com/2013/07/10/raspberry-pi-powered-microwave/ I really want one of these - I think I might order one: http://www.

### A framework for discussing "pricelessness"

Sometimes some people argue that certain things are “priceless” - that is, worth an infinite amount of money to them. I posit that what this really means is that it would take work and uncomfortable imagination to evaluate the worth of that thing to them. The example that triggered this framework was my evaluation of how much my sense of smell was worth to me. (It was late at night and I couldn’t get to sleep, so I just let my mind wander around for a bit.

There was once a small website devoted to noting the more interesting quotes from our more idiosyncratic lecturers. It has sadly vanished from the web - although after some detective work, I found a copy floating around on one of Amazon’s servers, and I have cached the whole site using WebCite. The entrance to the retirement home of the Imre Leader Appreciation Society is now this very website.

### Stumbled across 9th July 2013

Being bored over the summer holiday, I decided that I would document the cool things I ran across on the Internet. Over the last week, there have been many of these. If I see anything particularly amazing, it’ll go in one of these aggregation posts. Neurons are surprisingly beautiful: http://blog.eyewire.org/gallery/image-gallery/ A rather neat and very short story: https://qntm.org/timeloop A bit less short but just as good a short story: https://qntm.

### An obvious improvement to tennis

So yesterday the Wimbledon tennis tournament was decided. The system for verifying whether the tennis ball is out or not (and hence whether play for the point stops or continues) on the main courts is as follows: The ball lands. The linesperson keeping charge of the line nearest to the landing point of the ball works out whether the ball landed inside or outside the region demarcated by the line.

### Mundane magics

I have stumbled across a LessWrong post on the importance of seeing what is real for just how cool it is. It lists such examples as: Vibratory Telepathy. By transmitting invisible vibrations through the very air itself, two users of this ability can share thoughts. As a result, Vibratory Telepaths can form emotional bonds much deeper than those possible to other primates. Psychometric Tracery. By tracing small fine lines on a surface, the Psychometric Tracer can leave impressions of emotions, history, knowledge, even the structure of other spells.

### Cambridge vocab - a guide for the mystified

There is an awfully large collection of confusing words you will encounter on first coming to study at Cambridge. You pick them up really quickly in the natural run of things, but I thought perhaps a mini-dictionary might be helpful. The list is alphabetised (if I’m competent enough, anyway) and may, like so many of my writings, grow. Apologies for my crude attempts at pronunciations for the non-obvious words, but it’s very hard to find someone who can read IPA.

I wrote this when I was excessively bored during exam term of my first year. It may grow as I get better at working (I’m something of a revisionist). The advice is entirely Cambridge-based; a lot of it probably applies to other places with minor alterations. Most of this comes from personal experience. During a supervision, your supervisor will be writing all the time. As soon as you leave the supervision, mark the sheets that are particularly important in some obvious way (eg.

### In which I augment the lexicon

A few dubiously-real words which I think should be more widely used.

### CUCaTS Puzzlehunt

At the end of last (that is, Lent 2012-2013) term at Cambridge, I took part in the Cambridge University Computing and Technology Society Puzzlehunt (for some reason, as of this writing, they haven’t yet updated that page for this year’s Puzzlehunt, but last year’s is up there). A short summary: the Puzzlehunt is a treasure hunt around Cambridge, crossed with a whole bunch of online computing-based puzzles. It’s very difficult, and it lasts for twenty-four hours.

### First post

Hello all! In the spirit of shouting into an echoing void, this is my first post, testing whether the setup works. Some content will probably turn up soon.

### Sylow theorems

A fairly long and winding way through a proof of the three Sylow theorems.