## Footy Tipping

March 20, 2016

With one week to go to the start of the footy season, I’ve decided to have a go at the Monash footy tipping competition for the first time.

This is not your ordinary footy tipping competition where you simply get one point per correct team tipped. There are in face three tipping competitions. There is the probablilistic, where you enter a team and the probability you think they have of winning, the normal, where you enter a team and a margin, and the Gaussian, where you enter a margin and a standard deviation. Points are scored according to formulae on their website which I believe reward (over the long run) being as precise as possible in your estimation of the probability/standard deviation.

February 27, 2016

Is it a bug or a feature?

Everything is Yours, Everything is not Yours. First person account of being a refugee.

Tchaikovsky’s Dance of the Sugar Plum Fairy set to the music of Indila’s Dernière Dance.

Chaitanya has a blog.

Tomato parable. (This is the guy responsible for the squiggle).

## Why post here when I can get a much bigger audience on Reddit?

February 14, 2016

September 21, 2015

PhD Comics is coming out with a sequel to their movie.

Untrusted is a cool game where you have to modify the javascript which creates each level in order to pass it. (progress is saved via a cookie in your browser).

Catches win matches. And Z-score’s Cricket Stats Blog is the only place I’ve seen to provide any statistics on the matter.

Spooky Inference and the Axiom of Choice by Matt Baker. Don’t forget to click through all the links he provides. Infinite hat problems are weird!

The AFL ladder. Yes I know the home and away season is behind us for another year. But this clean site looks like it may be my go-to for 2016.

## Review: WeatherWoman (Movie)

September 20, 2015

Those of us above a certain age in Australia will remember a time when SBS did not have advertisments. These days, you even see English language movies on the national multicultural broadcaster, presumably as a result of increased commercial pressures. In ye olden times, however:

Movies were not in English. Often European, sometimes Asian (but never from Bollywood).

Ratings often contained the advisories: (s,n,a) (sex, nudity, adult themes). In practice: you see breasts.

The movies could be anywhere on the spectrum from arthouse classic to plain weird.

Where does WeatherWoman fit in this spectrum?

It is in Japanese.

You see breasts.

And it is squarely located in the weird end of the spectrum.

So what’s it about, you ask? Let me try to describe it without giving away too many spoilers.

There is a woman, who is presenting the weather on TV. While performing this job, she flashes her panties, live on TV.

Understood it so far? Well, that is the plot. And yes, it is somehow perfectly possible to make a feature length film with this plotline. OK sure, there are a few other scenes, such as the scene where you see breasts that I alluded to before, as well as an epic battle between the two alpha females at the end. But it’s the panties that drive the storyline.

It’s something that will go down in the annals of Japanese weather history.

I didn’t make up that last sentence by the way. This is a direct quote from the film.

One and a half stars. Because it will go down in the annals of Japanese weather history.

## Review: YJ MoYu YuSu 4x4x4 for Speed Cubing Stickerless (with pink) (X-cube 4 Mechanism)

September 19, 2015

My old 4x4x4 cube from Mefferts (which will always have a special place in my heart as the first thing I ever bought online) no longer turns very well, and after recently experiencing the difference between my 4x4x4 and a high quality cube, I was motivated to score myself a replacement.

Hence, This cube was procured from the HKnow store.

Let me first be clear about what this cube is not:

It is not a cube for the serious speed-cubist. If you’re going to be playing with your cube a lot and/or want speed, then you want to get yourself a higher end cube.

The turning mechanism is perfectly adaquete for the purposes of recreationally solving the cube. As advertised there are no stickers so you don’t have to worry about the colours falling off. For me, the yellow and green colours are a little close for comfort but your colour perception may be different. Each side of the cube is 6cm long.

So if you are looking for a cube to recreationally solve a few times. Or to put on your mantlepiece to show off. And you’re a tightarse who doesn’t want to spend the extra money on a higher end model. Then this is the cube for you.

Would recommend.

## tar.lrz

June 1, 2015

If presented with a tarball with a tar.lrz extension (e.g. after waiting many hours for one of these torrents to download), proceed as in the following example:

lrzuntar Ubuntu_14.04_LTS_sage-6.7-x86_64-Linux.tar.lrz

## The Prime Number Theorem (up to a constant factor)

April 14, 2015

It is suprisingly easy and pretty to give an elementary proof that the prime number theorem (that the number $\pi(x)$ of primes less than $x$ is asymptotic to $x/\log x$) is true up to a constant factor. (I will address only the part where we show that there are many (i.e. at least $~cx/\log x$) primes less than $x$.)

Consider a binomial coefficient ${n \choose k}$. Let $p$ be a prime. We first want to know what the largest power of $p$ is which divides ${n \choose k}$. There is more than one way to express the answer, the most elegant one I know of is as follows:

Add the numbers $k$ and $n-k$ in base $p$ (by the usual primary school algorithm). Then the number of carries that occur in this addition is equal to the greatest power of $p$ dividing ${n \choose k}$.

What is most important for us is the fact that this number is no more than $\log_p n$.

We immediately get

$\displaystyle \prod_{p\leq n}p^{\log_pn}\geq {n\choose k}$

which is of course equivalent to

$\displaystyle n^{\pi(n)}\geq {n\choose k}.$

Make a good choice of $k$ and we are within a constant factor of the prime number theorem!

## The Butterfly Theorem

March 1, 2015

Let $M$ be the midpoint of the chord $PQ$ of a circle. Let $AB$ and $CD$ be two other chords of the circle passing through $M$ and let $X$ and $Y$ be the intersection points of $PQ$ with $AD$ and $BC$ respectively. Then $M$ is the midpoint of the segment $XY$. Proof: The space of all degree two polynomials vanishing at the four points $A, B, C$ and $D$ is of dimension 2*. Thus it is spanned by the equation of the circle and the equation of the union of the lines $AB$ and $CD$. Choose coordinates such that the line $PQ$ is the $x$-axis and the point $M$ is the origin. Then the coefficient of $x$ in both our spanning polynomials is equal to zero, hence this coefficient is also zero in the equation of the union of $AD$ and $BC$. Therefore $M$ is the midpoint of the segment $XY$, as required.

*To see this there is a six dimensional space of degree two polynomials and we are imposing one linear condition each time we require the polynomial to vanish at a point. These four conditions are linearly independent since it is easy to find degree two curves passing through three of these points and not the fourth (e.g. a union of two lines).