Tag Archives: geeky

Gratuitously stolen from Marcus Honeysett (see this post), word clouds are a handy way of analysing content and so I created one for recent blog posts just to see what would show up.

If I can be bothered I might look for a sidebar gadget to create up to date word clouds, because they’re nifty and it’s nice to have an indication of just what it is I’ve been writing about. Anyway, here is the result:

On the 16th of May 2006 a man named Ze Frank who ran a popular daily video blog challenged his viewers to do something global. His challenge was to turn the Earth into a sandwich by placing two slices of bread on the ground at precisely opposite sides of the Earth.

At the time I was amused by the idea and excited by the challenge of uniting people from opposite sides of the planet by something really rather pointless and fun. It didn’t take very long for the challenge to be completed, using fancy internet tools like Google Earth and neat GPS thingies a couple of British guys took a detour on the way to Portugal to hit up Spain and complete the sandwich. The scary thing is that the managed to do it by April 12th, it took less than a month to turn the whole earth into a tasty sandwich!

Anyway, the reason I mention this is because of todays XKCD comic which contains a neat algorithm based on the DOW opening value for determining a specific location. The way it works is that the world is split into 1 degree square blocks (known as graticules), and within this block the algorithm uses the DOW opening value to determine the precise latitude and longitude of the location. The result is that every location is precisely 1 degree away from the next location, the result is that at the location within your graticule is always going to be within 100 miles or so (usually much closer).

Why is this interesting in any way? Well that I suppose is up to you. If for some reason you feel like going on an adventure, but don’t know where to go, then something like this makes the decision easy for you. Assuming todays location is reachable then why not go there and have a picnic or something. Even more exciting is the fact that Randall (xkcd author) has determined that 4pm on Saturday should be the standard meet up time, and so in theory if the location is reachable and there are enough xkcd readers in your location, heading there on a Saturday afternoon will result in meeting other random people who read xkcd.

As an aside, this comic also lead me to discover the game GeoDashing, which is a similar idea except that it’s implementation is that at the beginning on the month a few thousand random points are created globally, and then “players” are challenged to visit as many of those points as possible in the month to earn points.

I’m pretty sure internet based real world entertainment (usually in the form of random adventures) is on the increase. At some point in the future I will probably embark on one of these adventures myself.

I stopped posting in my LJ almost 2 years ago now. I stopped because I got my website up and running again and wanted to use that for blogging so that I could have a little more flexibility in what I did with the blog.

Since then I have kept on visiting LJ for the sake of my friends page, which has been a great way to keep track of a select few people who I know on LJ, and it’s been neat for maintaining a steady flow of comic strips throughout my week.

I’ve found myself using LJ more and more recently to comment on other peoples blogs and generally have a bit of fun regarding a few comics, and I figured it would be nice for those people who mainly keep in touch with me through LJ to actually have something on my LJ to read!

As such, I’ve just set my blog up to crosspost everything to LJ when it is written. This has included backdated entries as well, so there is no longer a gaping hole in my LJ, it just carries on from when I transferred to my personal blog!

I am writing a dissertation currently. This is not a bad thing in itself, I actually rather enjoy writing, however there is a small problem with the subject, and general system for writing. I am a mathematician, and thus my dissertation contains a not insubstantial quantity of mathematics, furthermore, I am a pure mathematician, which means the maths is obscure and abstract, and is therefore represented in obscure and abstract ways.

As such, I have to make use of a typing system called LaTeX, which is extremely good in that it formats documents in a very standardised way, and is able to handle mathematical symbols very well, spacing them accurately and generally doing a good job of making things look correct. However the nature of the program is that instead of type a/b for a fraction, you have to type something like: $frac{a}{b}$, for it to show up correctly. Then you compile the stuff and it makes a nice pdf file which looks as it should.

This sounds like a good idea, and indeed it is. However the result of this approach to typing is that what I write looks like pure evil. Here is a short excerpt from what I have written so far in it’s raw pre-compilation format.

begin{ttt}
Let $i:K to K’$ be an isomorphism of fields, and let $Sigma$ be a splitting field for some $f$ over $K$, and $Sigma’$ be a splitting field for $i(f)$ over $K’$. Then there exists an isomorphism $j:Sigma to Sigma’$ such that $j|_k=i$. That is to say, the extensions $Sigma:K$ and $Sigma’:K’$ are isomorphic.
end{ttt}

begin{pf}
We have the following situation:$$xymatrix{
Kar[r]ar[d]_i & Sigmaar[d]^j \
K’ar[r] & Sigma’
}$$
and we must show first that $j$ exists, and then that it is in fact an isomorphism.

To begin with we will show by induction on the degree of $f$ that there exists a monomorphism $j:Sigma to Sigma’$ such that $j|_K = i$. $Sigma$ is a splitting field for $f$, so $f$ can be written as a polynomial over $Sigma$,
[ f(x) = (x – alpha_1) hdots (x – alpha_n), ]

with $alpha_1, hdots , alpha_n in Sigma$ being the zeros of $f$ in $Sigma$. There will then be a minimum polynomial, $m_{alpha_{1}}$ of $alpha_1$, and this $m_{alpha_{1}}$ will be and irreducible factor of $f$. This $i(m_{alpha_{1}})$ will also divide $i(f)$, and hence will split over $Sigma’$, so it can be written;
[ i(m_{alpha_{1}}) = (x – beta_{alpha_{1}1}) hdots (x – beta_{alpha_{1}r}), ]

with $beta_{alpha_{1}1}, hdots , beta_{alpha_{1}r} in Sigma’$. We also know that $i(m_{alpha_{1}})$ is irreducible over $K’$, so it is a minimum polynomial of $beta_{alpha_{1}1}$ over $K’$. Hence by ref{th3.9}, we have an isomorphism
[ j_1 : K(alpha_1) to K'(beta_{alpha_{1}1}) ]

such that $j_1|_K = i$ and $j_1(alpha_1) = beta_{alpha_{1}1}$. It is clear that $Sigma$ is also a splitting field of $g = f/(x-alpha_1)$ over $K(alpha_1)$, and so by induction we can form an isomorphism
[ j:K(alpha_1, hdots, alpha_n) to K'(beta_{alpha_{1}1}, hdots , beta_{alpha_{n}1}). ]

As we saw in Definition 1.3, $K(alpha_1, hdots, alpha_n)$ is precisely the splitting field for $f$ over $K$, $Sigma$. And since each $beta_{alpha_{1}1}, hdots, beta_{alpha_{n}1}$ is a zero of $i(f)$, $K'(beta_{alpha_{1}1}, hdots, beta_{alpha_{n}1}) subseteq Sigma’$. Hence $j:Sigma to Sigma’$ is a monomorphism, and by construction $j|_{K(alpha_{1})} = j_1$. So we now have that $j|_K = i$.

All that remains to be shown is that this $j$ is in fact an isomorphism. This follows easily, since $j(Sigma)$ is a splitting field for $i(f)$ over $K’$, and is contained in $Sigma’$, and $Sigma’$ is also a splitting field for $i(f)$ over $K’$. So we have that $j(Sigma) = Sigma’$, so $j$ is surjective, and hence is an isomorphism.
end{pf}

Internet holidays are brilliant things. There are some fairly well known ones, like talk like a pirate day, which are actually celebrated by a lot of people. I’ve seen some fantastic pictures of silliness due to such events.

There is a rather neat website which has been set up to track some of the more obscure holidays, and I discovered that May 25th, today, is Towel Day. It’s a tribute to the legend that is Douglas Adams, and the idea is quite simply that you carry a towel around with you all day. If you don’t understand, then I suggest you seriously need to read the hitchikers guide to the galaxy.

For more information, and some pictures and stuff, check out the website:
http://www.towelday.kojv.net/

I am embarking on a new and exciting adventure. I’m not entirely sure where it will lead. Heck, I don’t even know if it’ll get started at the moment!

I have spent some of my spare time over the past week or so building a website called “Daily Choice”. The design for the site is complete and I’ve put some forums up, although I still have quite a bit of coding to do in order to make it functional.

The concept for the site is a very simple one. Each day members will be given a choice of two things which they can do that day. The two options could be pretty much anything, from the somewhat mundane like doing some housework, to the slightly extroverted like greeting a complete stranger loudly, to the rather odd such as wearing at least 3 different outfits in public in one day.

My plan is to launch the website at Easter, by which time I hope to have all the coding complete and the site running properly. I also rather hope to have a large collection of options by then, so that the choices don’t run dry too quickly.

The inspiration for this little adventure came from a Lent experiment which was initiated on facebook, which was much the same idea, although restricted to “doing nice things” (not that that’s very restricting!).

If you’re at all interested, I would love for you to sign up, even if you don’t take part when the site starts it would be nice to hear your opinions on the idea!

You can check it out here:
http://dailychoice.net/

I had a little play around with a rather neat tool today. It’s called last.fm, and it basically sends what music you’re listening to to the last.fm website, where the information is stored and made available to the general public. It’s pretty neat, as you can look up who has been listening to what and there are weekly, monthly and even yearly charts of what people have been listening to.

There’s also a rather neat feature which allows you to do this:

This makes me smile so much that I will be running last.fm on my computer forevermore!