Archive for September, 2008

Thoughts about the cogito.

Posted in philosophy on September 21, 2008 by Philonous

In his Meditations on First Philosophy, Descartes coined his most famous phrase

Cogito, ergo sum.

(or ‘I think therefore I am’). I was wandering through a bookshop the other day and noticed a book called The Last Word by Thomas Nagel, an American philosopher based at NYU.

It seems (from the introduction – I’m not so good at the ol’ reading lark yet…) that the idea of this book is essentially an apology for rationalism, the belief that human knowledge can be derived by careful consideration from an armchair. I could well be misinterpreting this, but as far as I can tell, Nagel thinks that subjectivism (that truth and knowledge are subjective notions which may vary from person to person) is a very pernicious influence in society.

The implications are widespread. Take for example issues presented by cosmopolitanism of modern societies. Cultures vary from country to country and although it can be said that many moral issues are agreed upon universally, there are clearly some divergences. In a democratic multicultural society with disparate moral codes, how should one resolve disputes? My own position is one of bewilderment. It seems that taking the subjectivist view and saying, ‘Well, what is morally right for one side may not be the same as what is morally right for the other…’, leads only to shoulder shrugging and a lack of resolution. In my mind therefore that although subjectivism is a convenient position to take logically, it is more than toothless when applied to real life. On the other hand, taking a more authoritarian and moral absolutist view is not satisfactory either – presenting people with moral rules – ‘Drinking soda is wrong!’ – which are to be agreed on universally is impractical.

Nagel’s book then claims to have some ideas about how to justify rationalism and therefore be able to conjure absolute certainty, indubitable truth, from thin air (or at least our minds). So far, he has talked about Descartes cogito with much affection. The cogito is supposed to be a demonstration of our existence. As soon as one tries to doubt one’s existence, one affirms it by thinking. Indeed, Descartes asks proposes ‘So who am I? A thinking thing.’ There are various objections to this, indeed some say that Descartes has rather a circular argument, presupposing the existence of this ‘I’ and endowing it with personal attributes which cannot be justified on purely logical grounds. Nagel’s view is that there is some worth to the cogito, and I agree. Nagel gives this nice example:

After all, if someone responded to every challenge to tea-leaf reading as a method of deciding factual or practical questions by appealing to further consultation of the tea leaves, it would be thought absurd. Why is reasoning about challenges to reason different?

The answer is that the appeal to reason is implicitly authorized by the challenge itself, so this is really a way of showing that the challenge is unintelligible. The charge of begging the question imples that there is an alternative – namely, to examine the reasons for and against the claim being challenged while suspending judgement about it. For the case of reasoning itself, however, no such alternative is available, since any considerations agains the objective validity of a type of reasoning are inevitably attempts to offer reasons against it, and these must be rationally asessed. … In contrast, a challenge to the authority of tea leaves does not itself lead us back to the tea leaves.

This argument makes a lot of sense. It somehow tells us that we cannot doubt our own reasoning since this would involve something self-referential. Nagel goes on to say that reason is something which we just have to take on trust as being sound. That is not to say that one may not make mistakes reasoning, simply that these could be pointed out and corrected. I think he plans to argue from a sort of foundationalist standpoint having established the indubitability of reasoning.

There is some part of me that feels slightly uneasy about this though. It seems that the ‘reason’ Nagel is talking about is the ‘synthetic analytic’ that Kant proposed in the Critique of Pure Reason. Reason, in my view, is part of the apparatus of perception. Thinking long and hard may lead to greater understanding of the apparatus itself, but there is still a fundamental disconnect between what we can derive from sheer brute force logical computation in our heads and the real world outside. Nagel refers to this and claims that his reason is something quite different, but I’m not so sure.

Check out the Google books preview of The Last Word (and tell me what it’s all about). Please also feel free to rant in the comments about how badly I’ve interpreted all of this.


Posted in random on September 19, 2008 by Philonous
  • beat
  • peat
  • boats
  • been
  • pears
  • boast
  • been
  • moats

These are all words for which removing any one letter always produces another word. Someone asked me for a longer one. Any ideas?


Posted in random on September 18, 2008 by Philonous

That’s right. Not Dvořák. Dvorak. If, like me, you grew up a philistine, you’ll probably share with me the experience of discovering that there was a Czech composer called Antonín Dvořák having already seen the option in Windows 3.1 to switch to a Dvorak keyboard layout. Curious, thought I, that he was named after a keyboard layout that I assumed was named, like qwerty, by taking at random a line on the keyboard and heading right.

I turns out that the keyboard layout was named after a distant relative, one August Dvorak, a professor of education and an educational psychologist at the University of Washington, Seattle. The original qwerty keyboard layout was designed in the 1860s having been decided upon by the maker of the first commercially sucessful typewriter. The layout was designed to try, as far as possible, to eliminate typewriter jams rather than for ergonomic purposes. To do this, the keyboard layout tries as far as possible to alternate between the left and right hand, although typing this sentence, I wonder how successfull it was.

The advent of the electric typewriter in the 1930s completely eliminated the need for a layout that eliminated jamming. Moreover, the increased speeds that were now possible started to reveal the inefficiency of the QWERTY layout as typists became fatigued faster. To the rescue August Dvorak who, through careful analysis of letter frequencies in the English language and the application of various a priori principles designed the right-handed Dvorak layout. Apparently of prime importance were

  • Letters should be typed by alternating between hands.
  • For maximum speed and efficiency, the most common letters and digraphs should be the easiest to type. This means that they should be on the home row, which is where the fingers rest, and under the strongest fingers.
  • The least common letters should be on the bottom row, which is the hardest row to reach.
  • The right hand should do more of the typing, because most people are right-handed.
  • Digraphs should not be typed with adjacent fingers.
  • Stroking should generally move from the edges of the board to the middle. An observation of this principle is that, for many people, when tapping fingers on a table, it is easier going from little finger to index than vice versa. This motion on a keyboard is called inboard stroke flow.

As far as I know, Dvorak keyboards hold the speed record at the moment (which I think is Barabara Blackburn 212wpm). It seems rather hard to actually find references to this though.


Posted in nerd pride, xkcd on September 17, 2008 by Philonous

Now that GPS has been around for a little while and the devices and chips come down in price, various games have sprung up around the technology. More well-known are things like GeoCashing (a GPS-based treasure hunt) and many more… I came across a concept called Geohashing today while trawling the internet. The original idea of was to provide, given a location, a short URL which uniquely specified that location. It seems that the algorithm was inteded for use in forums etc.

Geohashing spawned an xkcd comic which gives an algorithm for generating a random location near you each day in terms of latitude and longitude. Here’s the algorithm, as seen on xkcd:

Having read this, apparently, people started to travel to the location given by the algorithm, quickly realising that there were other xkcd readers there too.

Check out the wiki for more details. Or alternatively go here to have Google maps show you where the geohashing algorithm will take you today!

Sporadic Simple Games

Posted in maths, Uncategorized on September 16, 2008 by Philonous

Are you au fait with finite simple groups? Well I know I’m certainly not.

For the uninitiated, a group is a mathematical object which can be thought of as the collection of symmetries of some object. As for simple groups, I guess they can sort of be thought of as the basic buidling blocks of groups (whatever that means…)

There’s a classification of finite simple groups which is one of the great results of the 20th/21st century. It shows that there are four categories (not in the mathematical sense) into which the finite simple groups may be divided, the most romantic of these consisting of the 26 sporadic groups. I say romantic, what I really mean is quirkily named – one of the groups contained therin is the Monster group while another is called the Baby Monster… Ah those finite group theorists.

Anyway, as someone who finds finite simple groups particularly scary, I was rather pleased to see a rather interesting page at Scientific American. There you can find a couple of games that give some idea of the structure of the groups M12, M24 and the Conway group without actually knowing any mathematics whatsoever. Click on the link below to investigate. Happy playing!

The finite simple groups at play

Incidentally, if you’re feeling slightly fobbed off by my lack of a definition of a finite simple group, then check out the articles on group, normal subgroup, quotient group and simple group.

The Power Ballad Conspiracy

Posted in 80s, music on September 15, 2008 by Philonous

Remember the 80s? Don’t answer that. Those ten years made up the best possible tribute to that most hallowed of musical forms – the Power Ballad. I was listening to Bonnie Tyler’s Total eclipse of the heart today and thought it sounded rather like Meatloaf. Indeed, it sounded like a lot of songs I remember from the 80s. I discovered that in fact there was a much more tangible link between all of these; the man, the legend – Jim Steinman. He wrote and produced all of these songs and many more including:

In fact, he wrote the whole of Bat out of Hell (I&II) and a significant proportion of 80s chart music. Amazing eh?

Some Facts About North Korea

Posted in politics on September 13, 2008 by Philonous

(taken from the book ‘A True and Impartial Look at North Korea’, published by the Kim Jong-il Foundation for Truth, Freedom, and Countering the Malicious Lies of the American Imperialist Aggressors; Pyongyang)

  • North Korea won the Korean War.
  • North Korea tolerates all religions. However, the state religion is so magnificent, 100% of all Koreans are converts, rendering all other religions superfluous.
  • North Korea developed the world’s first invisible car, which is why the roads look so empty.
  • Jesus famously fed 5,000 people with 5 loaves and 2 fishes. But during the famine in Korea in the mid ’90s, the Dear Leader Kim Jong-il fed 22 million Koreans without any food at all. In fact, this famine is the first famine in history in which officially nobody died.
  • North Korea does not, contrary to popular belief, suffer from food shortages, but thanks to the magnificence of the Dear Leader Kim Jong-il, produces a massive surplus every year. To give thanks to the beloved Dear Leader, though, many devout Koreans frequently fast themselves as a form of worship. In remote rural areas, people have been known to fast themselves for several months at a time.
  • Koreans consider potholes to be a sign of good luck.
  • The Great Leader Kim Il-Sung is the founder of the all-encompassing Juche idea, a philosophy so complicated only Koreans are intelligent enough to understand it.
  • MASH would be much better if it was set in North Korea.
  • The Dear Leader Kim Jong-Il once beat Chuck Norris at arm wrestling.
  • South Korea is one of the most backward countries in the world, but in an effort to fool tourists, the government orders millions of citizens to walk around Seoul looking prosperous.
  • Lee Myung-Bak, the President of South Korea, lures little boys to his gingerbread house.So does George W. Bush.
  • North Korea is home to the world’s shortest acrobat.
  • The Dear Leader Kim Jong-il has never lost a game of rock, paper, scissors. So far he has 9,683 wins, many of them by knockout.
  • It is not true, as some have suggested, that The Great Leader Kim Il-Sung once raced a cheetah and won. It was in fact a leopard.
  • North Korea won the World Cup in 2006, equalling Brazil’s record of five triumphs. Thanks to the efforts of the Imperialist American Aggressors’ propaganda machine, however, many people mistakenly credit Italy with the victory.
  • In 2003, The Dear Leader Kim Jong-Il entered the Guinness Book of World Records by winning 120% of the vote in that year’s elections; such is the high esteem and reverence with which he is held by the Korean people. His tally beat a record previously held by Robert Mugabe and Saddam Hussein.
  • In 1994 The Great Leader Kim Il-Sung died of a heart attack, and ascended into heaven, where he is seated at the right hand of the Father. He will come again in glory to judge the living and the dead, and His kingdom will have no end.

By Goldengate

[Ed. Check out Kim Jong-il’s official biography]