Wednesday, May 5, 2010

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Running Barefoot

A few months ago, an interesting headline about how we evolved to run made the news:

I've always been a "heel plodder", but my friend Dave has always been a good runner, and once ran a marathon in 4:10 despite only 2 weeks training and otherwise being in pretty poor shape. He always runs "on his toes" - so I decided that if I want to become a better runner, I too need to learn to run "on my toes".

So I decided to start trying to run on my toes, in my normal shoes, so that my calve muscles would get stronger. Initially, my calve muscles would be tight - but I was expecting this and thought they just needed time to get stronger (wrong!).

I got blisters under my big toes from the wear and tear there. But, I thought, "that's also expected - my feet and muscles have to toughen up" (also wrong!).

Then one day in the gym, I tried running on the treadmill wearing just my socks. It was a revelation. My heel was able to reach the ground, whereas in normal running shoes, because of the padded foam underneath the heel, I was always having to run "too much on my toes".

However, about a day later, I could barely walk - because my foot hurt so much! I later learnt that this was because you need to build up slowly, and most importantly, running on the cushioned surface of the treadmill meant that it did not hurt immediately when I was running with poor style - it only hurt a day or so later.

But I really wanted to start running in some shoes that let my heel go all the way to the ground. If you're landing on the ball of your foot, heel cushioning just gets in the way. So I bought a pair of Vibram Five Fingers. I went out for a few runs in these, but would always get quite a big blister under my big toe in a very short amount of time, and the ligaments in my foot would often end up very tight. So I switched back to my normal Asics trainers for a bit. Then, after a particular fast "sprint" in which I really went up on my toes, I found that the base of my left index toe was really tender and sore.

So hopefully you're getting the idea that in my attempts to transition gradually to a more natural running style, I was always injuring my feet.

OK so what's the upshot of all this?

I should have just started running barefoot, completely barefoot, from the very beginning.

If you want to learn to run properly in Vibram Five Fingers, learn to run barefoot first. Preferably on hard ground like pavement (not soft ground like grass). The "rougher" the terrain you try to run barefoot on, the more quickly you will learn how to run properly, in a way that does not damage your feet.

This is actually the established advice on websites such as, founded by legendary barefoot runner Ken Bob Saxton. Above all, it should never hurt. It's not a case of "toughening up" your feet. Even your calve muscles should not get tight (this is caused by your heel not going all the way to the ground). The analogy he gives goes like this: While a deaf person can learn to speak, but generally not very well, people who can actually hear can sing! Running with shoes is like trying to learn how to sing while being deaf. We have to listen to the soles of our feet, which give constant feedback on whether you are running properly or not.

I started going for short runs (5-10 minutes) around Canary Wharf, slowly, completely barefoot. For the first time, the injuries in my feet started to improve (they are fine now!)

I'm still a beginner at this - but yesterday I ran 5.4 km at a pretty fast pace, and it was a turning point because I think I actually ran faster and with less effort than when I was wearing shoes. The movement felt so natural! I felt a sense of joy at the way it felt to run this way. My feet felt alive!

Oh and one other thing - people always ask about broken glass. So far, it hasn't been a problem. I keep my eyes open of course, I certainly don't try to run over broken glass. But if you are running "softly" then it seems you can even run right on top of small particles of glass and they don't get stuck in your feet. I've done enough running that I almost certainly have run over some small bits of glass (unintentionally) but it has not been a problem.

Here's a picture of the sole of my foot now. As you can see, there are no callouses or blisters. I can tell you that the skin actually feels softer - I think this is because there is a layer of subcutaneous fat that is developing giving me additional padding (and the skin seems thicker). My feet in general feel more flexible and supple, but also stronger:

I'm never going back to trainers - although I may wear some Vibram Five Fingers when it gets colder.

If you're interested,  I recommend you read this page and this page for some very good advice from one of the masters - then take off your shoes and give it a try!



Sunday, April 18, 2010

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Zermatt 2010

I've put some pictures up from New Years Eve in Zermatt.


Sunday, November 1, 2009

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Well, I finally got a chance to post my pictures from when I went to California this September.



Monday, August 3, 2009

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Kingsdown: My favourite new golf course

Depending on traffic, it's one or two hours away from central London, but I love this golf course (I'm sure you can understand why! ;) ):



Thursday, July 30, 2009

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OK, this is a drunken post. Apologies in advance.

First, there's a couple new TV programs that I've really enjoyed lately.

1. Bang Goes The Theory

Great program! It's like Mythbusters, but somehow cooler. This week they built a "vortex" gun that essentially sends high powered smoke-rings (powerful enough to knock down a pile of bricks from 30 meters away!)

2. Inside Natures Giants

So far, they've dissected:

  • an Elephant
  • a Whale
  • a Crocodile
  • a Giraffe

It's fascinating, and well done, not insulting your intelligence, but really explaining how their bodies work and explaining things in the context of how they might have evolved.

3. I've come to the conclusion that our biggest problem still remains that we do not share a collective vision of our future.

In fact, it's worse: we block the future out of our thoughts. People don't even think about the world as it will be 1000 years from now.


A profound pessimism has set in.

I have a theory on why this is.

We are constantly being reminded that the future is going to be awful. Day after day we are inundated with stories telling us that the future is going to be terrible, "unless we do X". The proponents of these news stories say all of this to try to induce the general population towards doing "X".

But, this doesn't work.

Their motives are probably sincere - but the effect is anything but what they want. The problem is, everybody realises that they themselves cannot personally change the outcome. Everybody collectively goes through the thought process "anything I might personally do is not going to change anything, and in fact will make me, personally, worse off, unless everyone else also changes their behaviour". A classic "Nash Equilibrium".

Faced with this situation, most people choose a form of irrationality. Subsconciously, think go "If I know that I can't affect things, there's no point being unhappy about it. Better to absolve myself of guilt too then and just deny that the calamity will even happen". Or worse, they'll suspend rationality by thinking that merely performing some sort of penance like turning the TV off instead of letting it go to standby will make a significant difference.

We're still a very young society, with only the most primitive ways of organizing collective action. We're woefully inept at organizing our collective behaviour in the ways that actually accomplish what everyone wants. It must be so frustrating, as an environmental activist, to advertise so widely about the problems we all face and yet see George Bush elected in office twice.

For me, the big picture, the really really big picture, is profoundly optimistic. We've evolved, through billions of years, to where we are now. Life, in some form or another, will go on, no matter what we do. As capable as we are of self destruction, we are still not actually capable of destroying life on earth - only our own civilisation and our own way of life, and only then if we trully fuck things up.

The future exists, and we are most probably still in it.

Well... I wrote a bunch of things after this but realised that I don't really have any answers other than a vague concept that if we could just communicate the awesome facts we already know about our existence to every living person on Earth, this might help build a sense of shared identity and purpose, which is what is required for collective action such as this...

In fact, that's another interesting point, which is that we're brought up to believe that the people in charge have some better idea about what we should be doing than we do ourselves but of course in reality we will always be, metaphorically, the blind leading the blind.

But I digress... Time for bed!


Thursday, March 26, 2009

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Two thoughts

That I had today:

  1. I am constantly reminded of the fact that when you gain a proper perspective of our place in the universe... the concept that a mere human brain is able to discover and understand everything that is trully knowable is... ridiculous. We are just the best that 4 billion years of evolution has managed to come up with in our little speck of the universe. Compare the most stupid person who has eve lived to the most brilliant person who has ever lived: the difference is utterly insignificant compared to how intelligent someone, or some machine, could in theory be.
  2. I was having a discussion with a friend about "big-O" notation... (basically, looking up a name in the phone book by searching sequentially through the pages is much slower than other ways you could adopt given that you know the names are sorted). As hardward has improved, "preferred" programming languages have changed towards what programmers can express against efficiency of execution... Yet, "big-O" notation has still kept dominion over what constructs people invent in programming languages.  Paul Graham wants to design an "idealized" programming language ... a "perfect" programming language, if you will. But... think really big for a moment: Suppose some technological advance (quantum computers or such) made it possible to compute any decidable proposition in constant time? What would programming languages look like then? The most important thing would be how easy it was to express the answer that you wanted. There would never be any point in saying "how" you wanted to calculate something - you would only ever be interested in the sorts of "questions" you could pose...  (what a delicious thought... to have such a machine!...)... I'm thinking of constructs such as the "amb" operator in Scheme.

Oh... while typing this I was watching the first episode of the new Apprentice series... it's become so miserable and negative now. All of the contestants are miserable, Sir Alan looks miserable... they are all desperately unhappy. It seems to me, in the first series, he got some really impressive candidates... a few "leaders" (such as James Max) who were able to bring out the best in the team despite all of the negative energy.  But then again, it's no wonder that, after that first episode, they can't find any good contestants. What sane person would want to work for Sir Alan? He's all about "business is all about being aggressive, you're either a winner or a loser"... you'd have to be a masochist to want to work for him. All of the smart people realise that there's so much more to life, and relationships... and anyway, business (and life) is about co-operation so much more than it's about competition...

The program has completely jumped the shark... but I'll probably still watch it anyway. At least until the really fit blonde contestant drops out.



Wednesday, March 18, 2009

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I've been watching the epic documentary series "Earth Story" on a new TV channel that's opened up here in the UK.

Sometimes, the simple facts about the evolution and origin of life on Earth just "glance off you" - you can't absorb the enormity of it. But this is not one of those times. Right now, I'm feeling... numinous.


Monday, March 16, 2009

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OO vs Scheme

A few months ago I posted this:

"So, my plan is, I'm going to write a moderately complex algorithm (a symbolic differentiator) in C++, C#, Scheme, and then OCaml (or maybe F#), and write up my experiences. I'm teaching myself Scheme at the moment..."

Well, I have some progress to report. Here's a fairly lengthy write up of the experience so far.



Wednesday, January 28, 2009

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Bubbles, psychology and the Blue Eyed Islander puzzle

I've just finished watching  Evan Davis' TV series "The City Uncovered"... This came on TV not long after Niall Ferguson's "Ascent of Money". Both are very good series trying to explain the current financial system and where it came from.

But they have both really annoyed me with their ridiculous attempts to explain the phenomena of "bubbles", or "boom and bust".

Niall's series pretty much said "Bubbles are caused by a herd instinct. Human beings are irrational, and we tend to all get ahead of ourselves, and that's how bubbles happen". (I'm paraphrasing here)

Evan's documentary went even further. He even interviewed one guy, John Coates, who reckoned that not only is it human "psychology" that causes bubbles, but that in particular it is male psychology, and the way that people react. Coates argued on tonight's TV program that testosterone makes people overly bullish, and cortisone makes them overly bearish, and that if only we had more women and older men doing the trading, then bubbles would not happen.

So, both seem to be saying "Bubbles are caused by human nature, and by the fact that people are ruled by their emotions".

I find this "explanation" so simplistic as to be offensive.

They should just admit that nobody really has a proper understanding of boom and bust.

I think the key to understanding the cause of boom and bust will be through the mathematics of puzzles like the Blue Eyed Islander puzzle. If you haven't heard of this puzzle before now, I advise you to visit that link first, and have a good think about it, then come back to read the rest of this!

It's a fantastic riddle. What's incredible about it, once you finally understand the answer, is that the public announcment of a seemingly inconsequential piece of information (I say "seemingly inconsequential" because everybody already knew that at least one person has blue eyes), ends up changing the situation entirely.

When the visitor says to all of the islanders in a public announcement that "at least one of you has blue eyes", each of the islanders now knows that a second islander now knows that a third islander now nows ... that a 100th islander now knows that at least one person has blue eyes. This is the abstract change in information that allows all 100 blue eyed monks to deduce the colour of their eyes after 100 days.

In the real world, the total amount of information that you acquire directly is actually pretty small. Most of the information that we acquire comes from other people who've acquired it from yet other people. Collectively, a population of a hundred million people might all know enough to deduce something, if we could all share that information with each other - but it's not even practical for us to be able to share our knowledge.

Think about this too: Nobody can point to any single event that caused the great stock market crash of October 24th 1929. Only 2 months earlier markets were booming and seemingly placid. What information was gained by everybody to cause them to realise that, indeed they were in a bubble?

I think it's very similar to the Blue Eyed Islander puzzle. You're an islander, you're looking at 99 other blue eyed islanders. You think you yourself might have blue eyes, but without the information about what the other islanders know, you can't be sure.

You're an investor. You think you might be in a bubble - prices keep going up - but you're not sure what the people who are buying know. If you knew everything that they knew, and could process all that information, then you'd be able to tell if it's a bubble or not. And it's not just a "greed/fear" thing. If you're a professional investor, whose job it is to trade in that market, you have to decide, each day, whether the market you are in is a bubble or not.

I remember listening to an analyst on CNBC back in 1995, after the Dow had recently risen something like 60%, to 5000. She thought it was a bubble, and had set an end of year target of 3000. Staying out of the market, playing it "safe" would have been just as costly as buying into it a few years ago.

I don't know what causes booms and busts either, but I do know it's a hell of a lot more complicated than testosterone.


Thursday, January 15, 2009

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Xmas in Australia 2008

My friend Pad and I went to Australia this last Xmas.

Also, for all you American and English readers, you might want to take a look at my friend Chris' web page - the The Septic's Companion: A British Slang Dictionary. It's quite a good read actually!



Thursday, November 20, 2008

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Explosion in my head

Sometimes, I'll go for months without having any really inspiring thoughts.

Then, like buses, three will come at once.

"Blade Runner: The Final Cut"

I watched this the other weekend in Hi Definition, and I have to say that it stayed with me. I immediately watched it again. It's not often I'll watch a movie twice in the same day. It was that good. If only I could see it on "the big screen" again.

I have a lot I could say about this XKCD comic.

Are the laws of physics computable? Consider the mandelbrot set. You can approximate the Mandelbrot set with a computer program... but you can never draw it completely accurately in a finite amount of time. Nobody knows of an algorithm which can tell you, in a finite time, whether any given point belongs to the mandelbrot set... and it's this non-computability of the mandelbrot set that makes it infinitely detailed no matter how far you zoom into it....  Personally, I agree with Roger Penrose. I think there must be some sort of "halting problem" aspect to the laws of physics.

Functional programming vs OO (Object Oriented programming)

"Is a set of sheep also a set of animals, given that all sheep are animals?".

Most people would quite naturally and reasonably answer "yes" to this question.

But in OO, this is quite a common mistake to make when designing a class hierarchy if you also allow your "set of animals" to be a mutable set (i.e. you can change the contents of the set over time). This is because it then becomes possible to add, say, a "cow" to your "set of sheep", breaking the invariant that a homogeneous list of "sheep" contains only sheep....

I see this as a failure of OO. When such an obviously "correct" answer is the wrong answer in the "OO" methodology, it's the methodology that's broken.

People naturally think in terms of "immutable" concepts. We're not actually very good at "simulating" little machines in our head.

But also, I've realised that all I ever do now when writing "my style" of OO code is to write anonymous, immutable implementations of interfaces anyway... I write "factory methods" which "compose" immutable objects out of other immutable objects into chains of delegating implementations of interfaces, splitting apart the different bits of functionality to the scope in which they were created. Up to now, it seemed verbose, but necessary in order to model things correctly and keep the right information in the right parts of the program.

Now I've realised that what I'm really doing is a horribly syntactically verbose form of functional programming.

I think we've reached the end of the road for "Object Oriented" programming... All of the stuff about Decorator, Factory Method... they're all just ways of doing what comes naturally, with better language support, in a purely functional language like OCaml or F#.

So, my plan is, I'm going to write a moderately complex algorithm (a symbolic differentiator) in C++, C#, Scheme, and then OCaml (or maybe F#), and write up my experiences. I'm teaching myself Scheme at the moment...

Oh, and if you're interested, I've finally fixed the RSS feed for this site...



Saturday, October 18, 2008

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Just a small update.

1. I really need to stop using the word "actually"

2. I wish I had started doing the part time Mathematics degree 3 years ago. It is fantastic!!

3. It seems to me that we may just have reached "the bottom" of this crisis... it is looking like the banking bailout has worked, and people are lending to each other once more... We will not enter "financial armageddon"... at least not yet

The last point is quite important for me with respect to political motivations.

I was all set to vote Tory, but I must say, like Mr Krugman, I was very impressed by the speed and decisiveness of the UK Labour government in dealing with the current crisis, and the leadership role they played in getting other governments to adopt similar plans. To understand what a profound accomplishment this was, you only had to observe the incompetence of the US government and its inability to do the same in the crisis.

The UK government correctly analyzed the problem (or listened to the right people who correctly diagnosed the problem), and reacted swiftly and decisively, with a well constructed plan that precisely targeted the cause (insufficient bank capitalization).

Whatever Gordon Brown and Alistair Downing may fail at otherwise, they can rightly claim that "they did good" here (in contrast to, for example, Paulson and Bush)... This really was a case of good government saving thousands of jobs and billions of dollars of "lost growth"...



Tuesday, September 23, 2008

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Well, it's been a long time since I last updated this blog. Sorry about that.

Barclays Capital

I've taken up a position a Barclays Capital - working on their fixed income exotics risk system.

The Credit Crunch

Well, to say that this is an "interesting" time to be working in the city is an understatement!

I refer to the following blogs to keep me "up to speed" about what's going on and, more importantly, why: - a really top notch analysis. - much more frequently updated, and with a strong left-wing bias - but very readable and not so "dumbed down".

Alan Greenspan

I also recommend reading Alan Greenspan's "The Age of Turbulence". The first "half" is mostly a biography - very interesting and readable. For one thing, despite being a "Libertarian Republican", he is very critical of Bush, and praises Bill Clinton... (of course, in hindsight this is an easy choice)... He also praised Gordon Brown.

The second half is perhaps even more interesting because he outlines his own views on how the global economy etc. should work... and states as his main thesis that "free market economies are incredibly resilient"... oh, and yeah, all except the epilogue was published July 2007, just before the shit hit the fan.

A particularly interesting chapter ("The Condundrum") claims that the Fed didn't actually have anywhere near as much control over "real"interest rates (the rate people/banks *actually* had to borrow money at), as people normally thought...  He mentions several times when the Fed raised rates, but long term rates actually went down after an initial "jump up"... He credited this to "disinflationary forces" due to globalization... I find this argument actually easy to agree with (that the Fed doesn't have anywhere near as much control over real interest rates as people think) precisely because we're having the exact opposite problem now (The Fed is lowering rates but LIBOR etc. remain unchanged).

Gordon Brown

Personally, I'm in favour of high taxes and government spending, if it's done efficiently, and not too centralized. However, I don't think that Labour has done a very good job at all with tax payer's money - not compared to, say, Denmark.

I was pretty sure that Gordon Brown was doomed to lose the next election (I hope he does!) - but after hearing his sound bite: "No time for a novice" - I can see it for the political genius that it is. Both David Cameron and David Milliband come across as completely inexperienced naive "show pony's" given the scary problems we are facing right now. I think Brown could pull off a campaign with this premise...


I'm working on an article to describe how to write "parallelizable" scripting languages implemented on top of a "grid" of computers (such as Data Synapse)... but...


I'm also starting an undergraduate Maths degree at Birkbeck University... so I might not have much time for blogging for at least a couple of months (then again, this isn't much of a change from the last few months in any case ;-0)




Wednesday, July 23, 2008

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Relational Grid

Over the years working in risk systems for banks, the structure of what we have to do has always been the same.

  1. Load the input data for your calculations: "Give me all of the details of all of the trades that belong to book 'ABC'"
  2. Based on that input data, generate what you want to do: "For each of the following scenarios ('FTSE20%UP', 'FTSE20%DOWN', ...), perturb the market data appropriately and value the book"
  3. Split the stuff that you want to do into lots of separate "tasks": (e.g. Value trade '101452' for scenario 'FTSE20%UP')
  4. Farm out those tasks onto a "grid" of computers (thousands of them) so that they can be executed in parallel
  5. Store the results in a reporting database
  6. Generate reports based on what you got from the reporting database

There's third party software readily available to do step 4 for the most part.

But what I presented for steps 1, 2 and 3 are just examples. Usually, they are much more complicated - and people are always coming up with new stuff - due to changing market conditions, new trades, new types of market data (and hence new ways of "perturbing" them). All this means that you usually require some programmer to write code (and they usually have to write a new report at the end too). Because all of this takes too long, the trader usually just doesn't bother - and has to make do with some ad-hoc measure instead. There are only so many hours a day to perform "ad hoc" reports, and "what if" analysis.

If only you could drive the whole thing backwards from step 6, and have it automatically figure out steps 1 through 5...

That would dramatically decrease the turnaround time (merely a few days to generate some new risk measure or new scenario report).

That's what I'm working on at the moment... and I honestly think it's the coolest idea I've come up with in a long time (who wants to hear false modesty anyway!).

So you just type in something like:

select tradeId, tradevalue.value,
from trades, tradevalue, scenario, marketdata
where trades.bookId in ('ABC')
and tradevalue.trade_xml = trades.trade_xml
and =
and marketdata.trade_xml = trades.trade_xml
and marketdata.valuation_date = 'today'
and = scenarios.perturbed_market
and in ('FTSE20%UP', 'FTSE20%DOWN')

and it would automatically execute your query on the grid of computers for you.

The trick is, many of the above "tables" aren't really tables - they're grid tasks. The "tradevalue" and "scenarios" tables above are not real tables in a database - it just looks that way. In reality, for each new "trade_xml, market" input combination, a new grid task is created. One way of looking at the "grid tasks" is that they are infinitely big tables - they have an infinite number of rows. Each "row" in that table is an execution of a grid task. But we always use them by "joining" to other tasks, in effect specifying the inputs to those tasks.

Also, just like how relational databases allow you to define "views" for commonly used sub-queries, and as an abstraction layer, you can compose grid tasks out of subtasks in a similar way. For example, if you were using montecarlo techniques to value your trades, your "tradevalue" task might really be another "join" and "group" operation over hundreds of different "sample paths":

define view tradevalue as
select average(pv)
from tradevalue_path
where tradevalue_path.seedpath > 1 and tradevalue_path.seedpath < 1000

(the above "view" is still infinite because we have not specified trade_xml yet).

By providing a library of "primitive" grid tasks, users can then write their own custom components or "views" and compose them together to quickly generate the sorts of answers they need to see - without needing to go through a 2 or 3 month release cycle while the new reports and "grid code" are written.

Of course, you wouldn't actually have to use SQL to define all this - any system for specifying joins, projections, grouping etc. will do. SQL is a bit too high level actually. I've used an XML format instead. But writing some sort of "SQL parser" on top wouldn't be hard. The hard part is the algorithm to get from your "relational algebra" representation to individual tasks to be performed on your grid.

What do you think? Comments and suggestions welcome.


Monday, May 26, 2008

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Whitby Golf Course

This is the bit where I gloat to everyone who spent a long rainy weekend in London about what I did on the bank holiday weekend...


Monday, February 18, 2008

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The Human Supercomputer

I'm trying to work through a physics book that a friend from work lent me. It's hard going - I have to read each new concept over and over again, until finally "inspiration" hits and I find a way of understanding the concept that they are trying to express.

I think that what makes a lot of it so much "hard work" is that I am having to translate from the author's "view"of things into my own. I suspect that it's like this for most people. Mind you, I'm not claiming that my way of seeing and understanding things is better than the author's - I reckon most times it's far inferior. Most times, my different "viewpoint" simply makes it harder for me to learn and understand things that other people already know.

It would all be a lot simpler and more efficient if I just saw things the same way as the person who is trying to teach me... Then, there would be no ambiguities, or opportunities for mis-understandings. I wouldn't have to "backtrack" and learn whatever things they implicitly "knew".

But then, also, I would be them. And maybe, say one time in a couple billion, my perspective ends up being unique and better, and I get to see something that, perhaps, no-one else in the world would have been able to recognize. That time, I would be able to contribute to the sum of human knowledge, in absolute.

In fact, I had this "revelation" today that this is one way of seeing the human race - it's like all 5 billion of us are individual "nodes" in a massively parallel human "supercomputer", set to the task of discovering the answer to life, the universe and everything.

So maybe Douglas Adams wasn't so far from the truth after all!



Tuesday, November 27, 2007

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In two words: It blows (during the offseason anyway). There's no night life and everything's closed. This all would have still been fine: I planned to play golf and scuba dive, except that on the first day, I stumbled, and grabbed a nearby fence that didn't look anywhere near as sharp as it actually was. 5 stitches although two of them have come out already. I've left out the thumbnail for those of you who don't want to look.

Hopefully the remaining ones can come out in the next couple of days.


Friday, November 16, 2007

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The flat above mine caught fire last night!!!


Friday, November 16, 2007

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Terence Tao

What a legend! As well as being a brilliant mathematicion who won the Fields medal last year, he is also Australian, appears to be a living counter-example to the supposition that all brilliant mathematicians suffer from aspergers syndrome, and most importantly for me, has placed all of the lecture notes from the undergraduate mathematics classes he has taught on the web.

It's the latter that I've really enjoyed reading over in the past week. He has a nice informal style, without losing clarity, and unlike so many others, he somehow manages to present the material at the right level for someone such as me to understand.

Being a genuine prodigy, he also has encouraging words to say to those of us who aren't prodigies (or even very good ;-) ), yet have an interest in mathematics.

If you want an example of what I am talking about, check out this article he wrote about Fourier transforms, in which he starts by explaining how you can decompose any function into "odd" and "even" components, and then generalizes that to arrive at Fourier transforms.



Friday, November 2, 2007

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Pascal's wager (revisited)

There's a new video circulating the web via YouTube, arguing that we should really start preparing for the possibility of Global Warming.

The jist of it is: "Well, the worst that can happen if we cut CO2 emissions and man-induced global warming is not real is that we cause a global recession, whereas the worst that can happen if we don't cut CO2 emissions and global warming is real is that we have a huge catastrophe".

In my opinion, it's nothing more than a re-hash of "Pascal's wager".

Pascal argued along the lines of "If you're a determined Atheist, and there is a God, then you're doomed to eternal damnation, whereas if you're a determined Theist and there is no God, then you're not really that worse off than the atheist"...

So! A question to all of the people who were convinced by that YouTube clip: "Are all of you convinced to become Born-Again Christians too?"

I didn't think so.

What's wrong with the argument?

It comes down to the fact that stating "possibilities" is never enough.

It's "possible" that there's some Christian God who exists who will damn to hell anyone who does not believe in him.

It's also possible that there's some "Devil God" who will particularly go out of his way to torment those irritating "Christians" who believed in "God" instead of the "Devil".

It's also possible that there's actually a God, and his name is "JungoJunga", and he will damn to eternal damnation anyone who does not ritually give obeisance to a strand of knotted rope every day.

How is a "Theist"-fearing person to behave?

I can almost understand the poor Romans who even had a place in their ritual ceremonies for any Gods that they might not know about!


Possibilities, without probabilities, are meaningless.

It's possible that our actions are causing global warming, and that unchecked, this will cause untold damages to human kind.

But it's also possible that what we are doing has virtually no impact on global warming, and that doing otherwise will cause even more significant starvation, poverty and hardship to billions of people in the world who might otherwise have been better off.

The guy begins his argument with "What's the worst that can happen?" The fallacy is in believing that somehow we can actually imagine this. What's the worst that can happen? By imposing his own version of "Pascal's wager" he presumes to know.

But maybe, the worst that can happen is that in 10,000 years an asteroid will hit the earth and wipe out all life as we know it, regardless of what we've done. Maybe, our only chance of survival, as a society, is to colonize Mars, or the Moon, but only if we don't spend time and resources on reducing our CO2 emissions?

That's a simplistic argument of course: But I'm just trying to make the point that there's no such thing as a "safe course of action", and justifying a course of action based on no other reason than: "we're ruling out a possibility that someone thought was possible"... well, that's really stupid thinking. If that sort of argument works for you, then Pascals' wager ought to work for you too.

I'm not saying that global warming isn't happening, and I'm not saying that mankind is not the cause of global warming, and I'm not even saying that it's not something that needs to be thought about.

I'm just saying that arguments of this nature - arguments without evidence, only based on possibilites - are fundamentally meaningless.



Tuesday, August 14, 2007

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Nurburging 2007

One of my more, shall we say, interesting travel experiences...



Monday, July 23, 2007

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Good software: Copilot Bad software: Adobe Acrobat

When my Dad innocently uninstalled Adobe Acrobat Reader 6 (because he thought he didn't need it), he ran into this problem. Unfortunately, he found also found that he couldn't re-install it either. Or even use the Microsoft "system restore" facility to go back to what he had before. Or install any other Adobe application!

Just try following the advice on the Adobe website!:

"This is a topic that is easily resolved. The solutions have been posted by me, Graffiti, MarkATS and others.
Now-you need to do the uninstall by using Add/Remove Programs first. Then you will want to do the rest manually-IF-you cannot find the Microsoft Uninstall Utility. Even then-you MUST find ALL references to Adobe Reader (all versions) and remove them from the Registry as well as remove ALL Reader folders.
WARNING_Editing the Registry is Dangerous! You do so at your own risk.
Yes, there are programs to help you-again please SEARCH for solutions. "

How do you fancy talking someone through the above over a phone line? I certainly didn't fancy it. As it turns out, the above advice wasn't really correct anyway.

Unfortunately, my Dad was desperate though - he uses the program as an integral part of the work that he does (to generate pdf files that he distributes to clients). So aborting Adobe altogether wasn't an option, much as I would have liked to do this... because they really deserve to go out of business for writing such crappy software

I can not believe how a software company like Adobe could make such a pig's ear of their flagship product. Unforgiveable.

They deserve to go out of business.

On the other hand, Fog Creek software, authors of Copilot, deserve to have money rain down on them. Using this program, I was able to remotely fix my Dad's computer... it simply wouldn't have been fixable from over here otherwise.



Wednesday, July 18, 2007

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Exit Fest


Tuesday, June 12, 2007

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Some nostalgia

Well, it's 3am and I couldn't sleep.I've been thinking about the summer of 1995, which was a pretty big year for me. I went on exchange to University of Illinois that year, and in the summer, went backpacking around Europe. I wrote a whole blog on it at the time, (back then, writing html and posting a website was sooo cutting edge!!! ;-) )

Sadly, I've lost the blog, which was posted on the University website... Out of reach of the wayback machine...

But perhaps I can recreate some of it here - I still have the photos, and I've scanned some in from Gimmelwald, which was one of the more memorable episodes.


Wednesday, June 6, 2007

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Long time no update

Work has been really busy... Moving in has been really busy... I realise that I've yet to even post the pictures from my most recent trip to Australia (over Xmas!).

There, that's a picture of my sister Kate, and Dad.

I didn't even get a chance to mention the flat warming!

Anyway, work is getting less busy, I've moved in, and I've found the cable to connect my camera to the computer. So I should be posting more frequently from here on...



Tuesday, March 27, 2007

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New Address

I am now the proud owner of

Flat 16, Chequer Court
Chequer Street

As of Saturday this week (March 31st) that will be my permanent new address.


Tuesday, March 20, 2007

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Where I am moving

"However, supposing even that you have a passing acquaintance with Golden - lane, have you penetrated farther still in your explorations, and been in and out, here and there, among the Chequers? In a word, do you know Chequer-alley?
    Don't pretend that you have an acquaintance with it because you have seen the name painted up over a narrow, squalid, forbidding entry to a dark court, and have concluded that it was a mere foul cul de sac, or a neglected byway to some adjacent street. If that has been your conclusion, you were never more mistaken in your life. Chequer-alley means a whole zigzag neighbourhood, an agglomeration of alleys and courts, intersecting as wretched and poverty-stricken a district as can be found in all London-a puzzle-map of poverty, a maze of misery, in which the unaccustomed visitor might grow heart-sick and dizzy in the effort to find his way amidst the tangle of hovels and close yards; of which a key is not to be found in any map that I know of; the names of which are probably unsettled by any board of works, local or metropolitan; a vast sty in the midst of this Great City where 20,000 human beings herd together in a condition so wretched, that had a traveller to some distant land sent back a description [-250-] of a native colony disclosing such destitution, vice, and ignorance, we should at once have asked why no missionaries had been despatched to remedy a state of things more repulsive than many narratives of heathen life which have claimed and found immediate response from Christian effort."

Well, it has improved somewhat since 1870.



Monday, March 19, 2007

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I just got back from a week's skiing in Vail.



Friday, February 23, 2007

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Flat buying

Sorry for such a long time since my last posting. Work has been very busy (in a satisfying way), and also, I am buying a flat!! That's right, I am getting on the much touted "property ladder" (I really hate that phrase, implying that property is some sort of risk free investment that will always go up faster than inflation).

I'm viewing the investment as a hedge. I'll always need somewhere to live - by locking in a 7 year fixed rate mortgage, I'm locking in how much I'll have to pay for that ability. I would be nice if the value went up, but that's not really why I am buying the place.

Anyway, all of this has sucked up all of my time. I'll try to put some more details and pictures from Australia up on the weekend.



Thursday, December 7, 2006

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Too much maths?

I've been reading over my last few posts and concluded that I have been, probably, too geeky.

So, in a feeble attempt to rectify this: What a fantastic victory for the Australians over England in the cricket! I mean, the Ashes contest is not technically over yet (but really, it is). I went to bed Monday night thinking it would just be a draw, and woke up to the radio announcing that Australia were 10 runs away from victory!

I don't think England should be so hard on themselves, to be honest. Collapses happen in cricket all the time, and the English team, while capable of beating Australia, just doesn't have the same depth.

My own personal view is that the next Ashes will be a much closer affair - England has a really talented team that is much younger. In a couple of years, they'll be stronger, wiser and tougher. In contrast, the Australian team will be without Warne and McGrath.



Saturday, December 2, 2006

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What on earth does Cricket have to do with credit derivatives?

My disappointment of watching England do so well in the cricket this morning was tempered by one exciting insight I had: Batting scores must approximately follow a Poisson distribution. That is, you could model a batsman's score by saying that for each ball, there's a certain chance that he'll get out. If he doesn't get out, he'll make some runs. Keep repeating this over a large number of deliveries and the batsman's score must closely resemble a Poisson distribution.

Of course, this is hardly and exact model - for one thing, the probability of defaulting varies with time - for the first few deliveries when they are not "settled", and much later when they start to get tired and their concetration lapses, the probability of getting out will be higher.

Anyway, a Poisson distribution is also often used as a simple model of the "time to default" of a company (if the company defaults before the maturity of the bond then you lose whatever cash flows were still going to be paid out).

Whereas, on the other hand, golf scores are much more likely to follow a Gaussian distribution...

Better than Karl's Calculus?

A friend at work lent me their copy of "Calculus" by Michael Spivak. This book is even better than Karl's Calculus (although Karl's website is free and available online).

I had always thought that a mathematics book that pretty much proceeded with a statement of theorems followed by their proofs would be a dull read, and somewhat incomprehensible. On the contrary - because he proves and/or defines everything in precise detail, paying careful attention to using exactly the correct notation, he takes nothing for granted about what you, as the reader, might already know. To give you an idea of how fundamental it gets, he starts by simply defining the properties of numbers. The first, is that a + (b + c) = (a + b) + c.

So all this actually makes the book incredibly comprehensible. I'm still toiling through it. Definitely recommended.



Saturday, November 4, 2006

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The Gulf Stream

"The notion that the Gulf Stream is responsible for keeping Europe anomalously warm turns out to be a myth"

I read American Scientist whenever I can get my hands on it - it's much better than, say, "Scientific American" or "New Scientist" because it tends not to "dumb down" its articles. Particularly, the Computer Science columns by Brian Hayes are nearly always exceptionally good reading.



Wednesday, October 25, 2006

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Big numbers

So I had dinner with some friends last night and was asked the riddle "How many zeroes are there at the end of 1 million factorial?". That is, 1,000,000 * 999,999 * 999,998...1 is some very big number- How many zeroes are at the end of it? Well, after some hints from my questioner and a day to think about it, I have today figured out that the answer is 249,998 - which might seem clever and make me proud except that the guy I was talking to was asked this as part of a maths competition and figured it out in his head!

So, 1,000,000 factorial might seem like a very large number, but it's peanuts really. I already knew about a Googol (a 1 with 100 zeroes after it) and a Googolplex (a 1 with a Googol of zeroes after it)... But how about Graham's number?

I laughed out loud when I read this:

"Although the solution to this problem is not yet known, Graham's number is the smallest known upper bound. This bound was found by Graham and B. L. Rotschild (see (GR), corollary 12). They also provided the lower bound 6, adding the qualified understatement: Clearly, there is some room for improvement here."

It is funny, when you start to try to get your head around just how incomprehensibly big this number is. I would argue that the "room for improvement " statement is the biggest understatement ever made!

If you found this interesting, you might also want to read this.



Tuesday, October 24, 2006

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Regression fitting

I was talking to someone at a party last Sunday and mentioned that you can derive the least squares fit regression formula using only very simple calculus. "What sort of horrible party was this?" I hear you exclaim... a fair enough point... I was talking to a Maths teacher though... so I don't think he minded talking about this. Anyway, maybe if I write this up on my web log I won't feel compelled to bring it up in social conversation in the future.

I also referred to this earlier, but here's the exact derivation for a simple linear regression. Suppose I am trying to fit a line to 3 points. Also, just to keep matters simple for now, I'm going to say that the line passes through (0,0) (this is the most useful form anyway if you start looking at things like stock returns over small time scales).

So my three points are:

(x1, y1)

(x2, y2)

(x3, y3)

And I'm trying to fit a line with the formula y = Bx to these points. I'm trying to find the best value of B, the slope, for this line.

My line won't be able to pass through all three points exactly. I've drawn the deviation of each point from the straight line with a vertical red line.

The least squares fit regression minimizes the expected value of the square of this deviation. That is, we're trying to minimize the term:

Error(B) = (Bx1-y1)^2 + (Bx2-y2)^2 + (Bx3-y3) ^ 2

So we're trying to minimize the error as a function of B. If we expand this out we get ( x1^2 + x2^2 + x3^2 ) . B^2 + some stuff . B + some more stuff. Our error term, as a function of B, is a parabola that points "upwards". So when the slope of this parabola is zero, we know that we've found its lowest point.

Therefore, we just have to find the point at which the slope is zero to find the value of B that will minimize Error(B). That is, we solve for d[Error(B)]/dB = 0.

d[Error(B)]/dB = 2 . (Bx1-y1) . x1 + 2 . (Bx2 - y2) . x2+ 2 . (Bx3 - y3) . x3 which has to equal 0

Dividing both sides by 2:

(Bx1 - y1) . x1 + (Bx2 - y2) . x2 + (Bx3 - y3) . x3 = 0

Expanding out:

B.x1.x1 - x1.y1 + B.x2.x2 - x2.y2 + B.x3.x3 - x3.y3 = 0

And solving for B we get:

B = [x1.y1 + x2.y2 + x3.y3] / [x1.x1 + x2.x2 + x3.x3]

Which can also be expressed as E(xy) / E(xx). That is, the covariance of X w.r.t Y divided by the variance, if X and Y have 0 mean.

You can extend this technique to fitting a linear function to more than just one variable, in which case you are solving for multiple different "slopes" of a regression "plane", which will involve solving a system of linear equations (one for each independent variable). It's all very doable though. Handling a non-zero Y intercept is not too bad to incorporate into this too - one way is just to add one more "independent" variable whose value is always 1. Whatever co-efficient has to be added to that for your "best fit" is just your 0 intercept.

I personally think they should give this as an example of a "minimization/maximization" problem when they teach calculus, instead of the usual stories of farmers trying to maximize the area of their fields for planting crops etc. At least, that is what I was telling the Maths teacher.



Monday, October 23, 2006

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Ethics and guilt

Until just a few days ago, I believed that our "conscience", or potential to feel "guilt", was an innate ability we had that allowed us to distinguish right from wrong. A moral compass if you will.

Now, I am not so sure. I think, speaking for myself, I feel guilty whenever I know that something I have done has caused someone else to suffer or to be unhappy.

But think of all of those situations where no matter what course of action you take, you cannot avoid making someone unhappy.

People who have fought in wars sometimes talk about guilt they felt over having killed an enemy soldier. Were they wrong to do so? I say no. They weren't.

Almost every time that I have resigned from a job to go work for someone else, I've felt guilty about the fact that I know that it's leaving them "in the lurch". Does that mean it was morally wrong to do so? Of course not!

I think it must be a big problem for people in positions of authority (fortunately, I'm not one of those yet!). Once you are in charge of a group of people, inevitably you will end up being in a position where to keep one person happy is to frustrate someone else - yet to do your job effectively you must choose between them.

There are loads of examples - I am sure you can think of better ones than these.

After a while, we learn to harden our hearts to this feeling. We tell ourselves things like: "I can't be all things to all people".

As bad of a moral compass that "guilt" appears to be, I don't think we have a better one. At least, not one that I would trust. Any sort of rigid, ideological principle or set of commandments: "1. Don't Lie 2. Pay your taxes 3. Don't Murder" etc. is much too coarse for most situations.

Furthermore, the people who scare me the most are those puritanical moralists who stick rigidly to a code at all costs, in spite of what they may actually feel about the matter. I bet at least some of the 9/11 hijackers felt pangs of guilt when they were brought face to face with their terrified hostages on the plane, despite the belief that what they were doing was right. Or go see Arthur Miller's The Crucible for another good example of terrible things done in the name of righteousness.

So don't harden your heart too much.



Sunday, October 22, 2006

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Scuba diving

Well, after a short trip to Sardinia I am now an officially certified PADI Open Water Scuba diver.

The great thing about Scuba diving that I had not realised is that the fish don't swim away - you can float just 3 inches away from a fish and look at it. Very cool! It's also very relaxing - you try to take deep breaths so that you consume your air supply efficiently and can stay down for longer.

This picture is me and me "dive buddy" Patrick. We both were taking the course at the same time. An important rule in diving is to stay with your dive buddy, so that in case you run out of air (a drill that we practised quite a bit) you can use their secondary regulator rather than immediately swimming to the surface and risking decompression illness.

Here we are demonstrating the sign language to indicate that "everything is OK". You don't give a "thumbs up" when under water unless you are signalling that you want to go to the surface.

Here also (from left to right), is a picture of Claire, Agnieshka (Patrick's wife), Patrick, and James (Claire's husband). Claire and James were experienced scuba divers who also went diving with us. Great people!




Friday, October 6, 2006

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Space is Big

I had a drunken discussion with someone at a party last night in which I tried to explain that there are more stars in the visible universe than there are grains of sand on all of the beaches on earth (there's about 10,000 grains in a fistful of sand, more than the number of stars you can see with the naked eye). They didn't believe me - but there's quite a large amount of evidence to support this extraordinary, awesome statement.

I also recommend checking out 


Wednesday, October 4, 2006

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I've accepted an offer to work for the Royal Bank of Canada on a new Credit and Fixed Income derivatives risk management system that they are writing. I'm quite looking forward to it.

Meanwhile, I've got some pictures from a recent trip that my Dad and I made to Lulworth Cove - it's a spectacularly beautiful part of the English coastline.


Thursday, September 28, 2006

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Tiger Woods will win!

Here is my prediction: Tiger Woods will win all four majors next year (2007). After watching some shots played today in the WGC American Express tournament... he is back to the level he was at in 2000. I think 2007 will be the next coming of the Tiger! ;-) I was just looking on BetFair - but cannot find a place to bet on this.



Friday, September 15, 2006

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Email broken

Apologies for the fact that the "" domain has been broken over the last few days. I think I have gotten all of the problems sorted out now. If you sent an email to over the last few days it's quite possible I did not receive it.

I've fixed all of this properly - nothing to do with Yahoo anymore - so I suspect I will not have any further problems.



Thursday, September 14, 2006

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No longer with Citadel

As of Tuesday this week I am no longer employed with Citadel. I will be taking some time off, but here's my Resume in the meantime.

Evidently, I have some more time now to post more of my thoughts on this page. So let's start with an interesting discussion I had with a guy a few weeks ago...

Some Information Theory 101

Compression is a magical thing when you think about it (or at least, when I think about it). Through some magical algorithm, I can take a sequence of bits and yet somehow communicate exactly the same information using less bits. It seems like it must somehow be breaking the "TANSTAAFL" principle ("there ain't no such thing as a free lunch").

How does it work? How do you know if you've found the best compression algorithm? Well, the trivial answer is to pick a compression algorithm that compresses an entire sequence down to 1 bit. A bit like if you've already had a big discussion with someone beforehand:

"If I call you up and say "yes", then this means that you should go down to the post office, write a letter to Joe Bloggs in Philadelphia and ask for more money, whereas if I say "no", you should go to New York and tell Syd Forrester that the deal is off".

Here, we have written a compression algorithm that compresses two possibly complicated messages into a single bit:

1="write a letter to Joe Bloggs in Philadelphia and ask for more money"

0="go to New York and tell Syd Forrester that the deal is off"

"But that compression algorithm can only send one of those two sentences. It's not a real compression algorithm", you say. But I would argue, if you know in advance that those are the only two possible messages that you will ever send, then you can say that this was an optimal compression algorithm.

That's a really good point (in my not so humble opinion ;-) ): To understand whether a compression algorithm is correct and determine how efficient it is, you have to be able to enumerate all of the possible things that you might wish to compress.

And in fact, it doesn't take too much more thought to define what the optimal compression algorithm would be: You simply enumerate all of the possible things that you might wish to compress, and list them in decreasing order of their probability of being sent. You then assign binary numbers to each possible message, assigning the shortest binary number to the most common "uncompressed" message.

How efficient is your "compression" protocol? You calculate the expected number of bits per "compressed message" and compare it to the expected number of bits per "uncompressed message".

So, for example, if I was going to send the following binary sequences with the following associated probabilities:

"101" - 40%

"100" - 25%

"11" - 20%

"10" - 10%

"1" - 5%

That is, if I send messages, I will be sending the sequence "101" 40% of the time, but sending the sequence "1" only 5% of the time.

If I did not compress this, my expected number of bits sent per message would be 3 * 40% + 3 * 25% + 2 * 20% + 2 * 10% + 1 * 5% = 3.45 bits per message.

An optimal compression algorithm would have to encode these using the shortest "encrypted" sequences for the most common encodings:





"100" = "1"

That is, the "compressed" version of "101" is simply the sequence "0". The "compressed" version of "10" is the sequence "11", and so on.

The "expected" number of bits per message then becomes 3 * .05 + 2 * 0.10 + 2 * 0.20 + 2 * 0.25 + 1 * 0.4 = 2.25 bits.

Note that there's more than one "equally powerful" compression algorithm in this case - I could have swapped some of the mappings above.

What about if all messages that I could send are equally likely? In that case, this is the perfect definition of a purely random message, which as we would expect, cannot be compressed.

That is, we define something as incompressible by saying that there exists no such mapping that will lower the expected number of bits per message.

Notice - it doesn't make sense to talk about any "particular" message in isolation - it only makes sense to define compression over a "distribution" of possible messages.

Of course, the optimal compression algorithm might be huge expressed as above - a gigantic "switch" statement containing all possible input combinations and what the resultant output combination should be. Can you compress the compression algorithm? Only by defining the machine that it runs on - otherwise it all gets very tautological.

I suspect that real complication comes down to two things if you're actually trying to write a compression algorithm in practise:

  1. How do you enumerate/approximate all of the possible messages that might be sent, and their associated probabilities?
  2. How can you write a compact and efficient compression algorithm that emulates the "optimal" compression algorithm as closely as possible?

I welcome any feedback on this.


Wednesday, August 2, 2006

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A few weeks ago I went with some friends to Kinsale, Ireland, for a golfing holiday. I forgot my camera, but fortunately, Tom "Guns" Oswald managed to take a bunch of photos in which some of us manage to always look fantastic, whereas others of us always look like we're drunken idiots... (I'll let you figure out who looks like who...)

I should warn though... it seems like his website is hosted on a crap server - you'll need to be patient to wait for the pictures to actually show up...



Monday, July 24, 2006

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Skip the middle men when you book vacations.

First, there was Thomas Cook, and that whole debacle. I recently booked golf for a group of us travelling to Barcelona through a company called the "UK School of Golf", that runs the web site We were playing at a course called "Club de Bonmont Terres Noves". For one thing, those pictures aren't accurate - nearly all of the holes had ugly condominiums built next to them, rather than the beautiful natural scenery shown in the pictures. Of course, the active construction work (bulldozers, jack hammers etc.) didn't really add to the atmosphere either.

Here's a letter that I've sent to them after we got back:

To: The management of Barcelona Golf Holidays (UKSG)
Dear Sir/Madam,
Our "Barcelona golfing experience" was ruined by the following:
  • Rather than the 60 minutes we were advised that it would take us to get to Bonmont golf course from the airport, it was more like 2 hours. We had to pass through 4 separate toll booths on the way to the course from the airport.
  • There were no golf carts available to us at the course. So we walked the course, in Spain, in summer, at the hottest time of the day.
  • There was loud, continuous construction work (jack hammers, bull dozers etc.) next to the first 4 holes. It defies belief that anyone could charge so much money for a round of golf in such conditions.
  • We were not able to complete our round because the course was "closed" at 7pm due to a concert (we could not tee off at 2 due to it taking us so much longer than expected to arrive at the course)
  • We realised that it would have cost us less to pay for our green fees in person, at the golf course, than booking through your company. My copy of the "Green Fee Prices 2006" picked up from within the pro shop lists 72 euros per person - this worked out at over 10% cheaper than the rate charged by your company.
  • Ironically, one of us couldn't make it - so we paid for 5 rounds of golf, needing only 4. I distinctly remember discussing my uncertainty about the numbers with "Jackie" over the phone, and whether it would be better for me to book less and sort out any additional necessary reservations when we arrived. I distinctly remember her telling me that I would be better off booking through your company, as I would "certainly pay more if I sorted out the additional green fee at the course". Obviously, this advice was incorrect, to our considerable expense. I also believe that it was deliberately misleading and self-serving - cynically calculated to maximise the profit of your own company regardless of our own situation.
It states on your website "Very few companies have the expertise or knowledge in booking golf holiday packages to Barcelona".
I think I could have done a better job. I certainly could have done it more cheaply.
I should have been more suspicious when I read this phrase in your terms and conditions: "We provide no level of service for green fee only bookings, in the event of any cause of complaint you must take it up with the golf course concerned and any refunds due are entirely at the discretion of the course and must be paid directly to you at the time of play. " 
Evidently, we're not the first unsatisfied customer. Nevertheless, perhaps I can ensure fewer people make the same mistake I did: I am posting this letter on my website and will endeavour to ensure that it comes up readily when other people search for "Barcelona Golf" in their web browser.
yours sincerely,
Paul Hollingsworth
These "package holiday" companies are a dying breed. The fact is, you're always going to get a better value deal for your money by booking it yourself. They know this, and know that their only chance of actually making money is to swindle you.


Saturday, May 13, 2006

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Still not getting mail

I still seem to be getting only about 20% of emails sent to I can tell this because my "spam" folder is virtually empty.

I decided that I've had enough of this, and tried to transfer my domain name to someone else... After 30 minutes of dedicated searching I finally found an actual phone number to contact Yahoo on their website. At this point, I just want to get the domain pointing to my streamline account. The customer service guy was quite unhelpful. The "email" contact for the domain name registered with networksolutions is a Yahoo email address - but he claims that they couldn't actually help me - I have to contact networksolutions myself.

So I'm going to have to fax network solutions and get control of the account that way. Shortly after that, I'm cancelling my Yahoo account.



Thursday, May 11, 2006

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Missing email?

If you've sent mail to recently, it's quite possible I did not receive it. I conducted a test myself today - not only does mail sent to not make it to me, it doesn't get bounced back either. So people don't even know that I didn't get it. I am sure that they have "reconfigured" something on their side that has broken my account, in the worst possible way.

If you want to send me a mail and be sure I get it, send it to

I am going to ditch Yahoo domains just as soon as I can get my domain name transferred to someone else who can host a domain name without with fking it up. This is not the first time this sort of crap has happened. Excuse the language - but I am a bit pissed off about this.


Sunday, May 7, 2006

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The Moebius

I just read about this.

"Seven undercover agents meticulously repeated a five-minute slice of time for twelve consecutive repetitions. Starbucks employees and patrons were frightened, confused, and ultimately entertained as they found themselves stuck, without escape, in the middle of a time loop. "

In my opinion: Genius!



Thursday, April 20, 2006

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Long time no update

What can I say? I've been busy.

First, I've been to the Masters:

I've also bought a car. It's a 1996 Subaru 2.0 litre Turbo... estate... also known as "The Colgate Crusader" due to its toothpaste complexion.Ugly it may be - but it really goes... faaast, and I actually fit int it, which is more than I could ever say of my old Nissan Micra. Here's a picture of it:



Sunday, March 12, 2006

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I just finished reading Fooled by Randomness by Nassim Taleb. This guy is really arrogant:

"I have to confss that my optimal strategy (to soothe my boredom and allergy
to confident platitudes) was to speak as much as I could, while totally
avoiding listening to other people's replies by trying to solve equations in
my head"

I can't believe he has many friends... But it's a good read.


Saturday, March 4, 2006

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Site dead.

It looks like took over Interaccess, where this site used to be hosted, and screwed it up. They were over-expensive anyway.

So I've switched to to host my web page. Mainly because they offered me a 3 month free trial and instant activation (the account was working within 2 minutes of me registering it). I've also grabbed



Monday, February 13, 2006

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Last week, I went skiing in Courchevel.


Sunday, January 8, 2006

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I spent this previous Christmas and New Year's Eve in Australia. For me, there's no better place to go to in December.



Thursday, December 8, 2005

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A rebuttal

My very good friend Greg in Australia, a staunch Catholic, has replied with a very good rebuttal to my atheistic comments.

He hasn't convinced me - but I figure in the interests of trying to make my website more interesting, I will post his reply here:


I refer of course to your woolly thinking regards to what a belief in God entails, your arguments could read the same way in reverse.

Why should a lone individual care for the fate of mankind or the planet 200 or 5000 years hence?

If all this is about is me and those that I care for, why should I take any action that limits my lifestyle or enjoyment after all this is all there is; there is an urgency to life that propels me to take all I can for me and mine and who cares for those I cant see or those who cant effect my life.

Yet a theist, in this case a Catholic, is called to a life of service of the other.

Self sacrifice to provide for the other is held to be the highest form of love.

The world around us is a gift from God and not a resource to exploited, it is this gift and the sense of stewardship that this engenders - towards life and the planet that leads us to an understanding that 200 or 5000 years is not too large a timescale to consider, it can only be this application of a duty to the infinite nature of God, that leads us to a position that goes beyond or lifetime or the lifetime of our children.

A belief in the Godhead is not a get out of jail free card like you seem to suggest, it is however a calling to a higher duty and with the taking of that duty there comes a great weight of responsibility.

If you as an atheist fail, then you damn the future of mankind, If I as a theist fail then I damn myself as well as that future... "

He argues, quite rightly, that a Christian has no more barriers to acting morally and in the best interests of the human race than an atheist does.

My rebuttal would surely have to go along the lines that a Christian can have no incentive to imagine a future 5000 years hence... let alone plan for it... but who am I to tell Greg what he can and cannot do? ;-) As I said, my rebuttal needs some work...




Sunday, December 4, 2005

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I was talking to someone tonight and was finally able to articulate why, exactly, I am an atheist.

I'm not just an agnostic. I choose to believe that there is no God.

Both a belief in God, or a belief that there is no God, are acts of "faith" - neither position can be proven - but having a belief either way affects what actions you take in your life.

I choose to believe that there is no God because I think that both myself, and mankind in general, are better off if we did not believe in God.

Consider the point of view of a religious person who believes that there's some God watching over us and everything we do, and judging us on account of that. So long as you've lived your own life "justly", or have seeked out "forgiveness" appropriately, you don't need to worry. God has everything else in hand!

Why would you ever think it was your responsibility to worry about where mankind will be in the next 200 years, or the next 5000 years, if you believe that in actual fact, our entire existence is just part of a "grand design" that has been conceived by some "uber being"?. Surely, their grand design wouldn't entail our own extinction, therefore, we don't need to worry about that!

Belief in God fosters a potentially fatal lack of responsibility for our own actions and future. It encourages a "head in the sand" attitude to mankind's real situation and problems.

We're it. We're all there is, and we're on our own. Nobody is going to bail us out of any problems that come our way. We have to solve all of them ourselves.



Thursday, December 1, 2005

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Another way to look at the "mean", and deriving the "least-squares" regression formula

An interesting thought occurred to me recently. I've been trying to understand the "regression" fitting formula.

Say that we had a prediction or estimate for a value, and then we collected four data points: x1, x2, x3 and x4. We then want to determine how good our estimate is. We might calculate it by adding up the squares of the deviations from the "estimate":

The "variance" of the deviation of "x" from our estimate "u", would be defined as:

variance(u) = [(x1 - u)^2 + (x2 - u)^2 + (x3 - u)^2 + (x4 - u)^2]

(we square the differences because we only care about the magnitude of the differences rather than the sign... and yes, I could divide by 4 so that I get some sort of an "average" variance... but it doesn't really matter for my purposes).

Consider how the above formula behaves as the estimate gets closer, and then further way, from the four points:

Where's the lowest point?

At which point would our estimate minimize this variance?

Because variance(u) is always positive and, as a function of u, is a parabola, we just need to find the point where the slope of the variance(u) is 0. The slope is the derivative of variance(u) with respect to u. If you work this out, you'll get

d[variance(u)]/d[u] = -2(x1-u) -2(x2-u) -2(x3-u) -2(x4-u) = -8u - 2*(x1+x2+x3+x4)

So to find the point where this is zero:

-8u - 2*(x1+x2+x3+x4) = 0

4u = x1+x2+x3+x4

u = 1/4 * (x1+x2+x3+x4)

Which is... surprise surprise, the conventional definition of the mean of the four points!!!

So that's one way of understanding just what the mean or average really is. It's saying "if we were to pick a single point to estimate x1, x2, x3 and x4 that minimized our error, well, this is what we mean by the mean". (Sorry about the pun).

It's a back-to-front way of understanding it - people usually learn about means before they learn about variance - but the great thing about this is that you can use the exact same method to derive the formula for a least-squares fit regression line... or in fact, as a way to fit almost any function to a set of data points.

e.g. say you had some arbitrary estimation function:

u = estimate(alpha, beta, gamma)

And you want to fit it to a set of data points so that it minimizes the error of your estimate... you just use the same technique - except that you need to differentiate your "variance" function with respect to alpha, beta and gamma:

d[variance(u)]/d[alpha] = 0

d[variance(u)]/d[beta] = 0

d[variance(u)]/d[gamma] = 0

and so on.

This is how (I think) multi-variate regression works... where your estimation function might be:

u = alpha + beta*x + gamma*y

Of course, it can get complicated - especially if there are "local minima" in your fit. In that case, as you change some parameter for your estimate, it becomes a better fit, and then a worse fit, and then finally an even better fit than before... you would get multiple solutions to the equations above, and would have to choose the best one out of all of the combinations. Or worse still, some parameters might not have a "solution" for the best fit - for example, you might find that no matter how high you made your beta, a higher beta still would make it a better fit (but never a very good fit).

You might think that this is the sort of thing I do at my new job, but you'd be wrong. I don't know where this came from - but it's pretty neat eh?


Saturday, November 26, 2005

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Those "fine" fellows at Camden Council

I am going to a "fake hair" party tonight - so I thought I would drive to a fancy dress shop in Camden town to get a wig. I'm driving around looking for a parking space, and see "Residence Parking only" - finishing at 5:30pm on Saturday.

I check the clock in the car - 5:29. Fantastic - no problem - "good thing I left it so late to pick up a wig" I tell myself.

So I park my car and check out the shop, which turned out to be filthy. The guy wanted 35 pounds for a greasy filthy disgusting wig he pulled out of a plastic bag full of old wigs (and which he had dropped on the floor).

So I go back, perhaps 45 minutes later, to find my car is not there!

At first I thought it had been stolen. My car is not a nice car - it's a Nissan Micra 1.0 LX - who would want to steal that? So anyway, I'm dialing 118118 to find out the number to call to report your car stolen when a parking attendant tells me that it's probably been towed. He calls up the "depot" - sure enough, they have it.

Oh yeah, it turns out, my car clock was wrong.

He starts being defensive "Youshouldn't have parked your car in the residence only parking area".

It's a good 20 minutes walk to the depot - so I walk there to pick it up. It's not an easy place to find - well tucked out of the way near Kentish Town tube station.

I only find out when I am there, that I'm not allowed to pick it up without proof of ownership (the keys aren't sufficient apparently).

So I have to go back home and collect something "with my name on it, that shows that I own the car". The guy was helpful - if I was able to find anything inside the car with my name on it, this would also do.

Supposedly, this is to prevent people stealing cars by pretending that they own them.

I catch the bus back to my flat and dig out my car insurance certificate, and head back.

45 minutes later, I get back there, and the woman says that because the car insurance certificate I happened to pull out of my papers was not the current one, it was not sufficient. She suggested I call the car insurance company and have them fax it their office. The car insurance company (Churchill) say that their customer support line closed at 5pm - the best they can do is tell the woman over the phone that yes, my car is still insured with them.

This is not good enough for those "fine" fellows who have chosen a career working for the parking department of Camden Council. They need something they can photocopy - the boss wouldn't have it any other way.

So I go back to my flat again, and dig out the current car insurance.

I go back, pay 200 pounds, (50 pounds for the parking fine (100 if I waited 14 days to pay it), and 150 pounds to take my car back out of the depot).

What gives them the right to do this?

Seriously, I wonder what these people tell their friends they do for a living at dinner parties."Yeah, well I work in the parking enforcement industry... in laymen's terms, I clamp people's cars. Have you had your car clamped around Camden? Yep, that was probably me."

Well, it turns out, that they have found that the solution to this problem is to hold their own dinner parties: the British Car Park awards, no less!

I found the above link because I googled the manager of the Camden Carpark Compound - a Mr Graham Essl - who was a runner up for the "Parking Enforcement Award" this year:

"After a career which has seen him serve as a Royal Navy diver, police officer and undertaker, Graham Essl has been responsible for reforming the running of Camden's car pound since 2001. He has computerised retrieval systems and improved staff morale at the car pound — which is very much a frontline operation."

Well done Graham! Great job! Keep up the great work! I can understand why staff morale might be big problem - glad to hear you've made so much progress in solving it.

I am not making this up, although it is ... unbelievable.



Sunday, November 20, 2005

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Track Day

Well, my new job is very exciting stuff. Hence, I haven't had much time to update this site. But anyway, I went on a track day recently, and here are some pictures from that (not many - battery in my camera was dead).


I also went on a trip with some friends to Vilnius, the capital of Lithuania. I didn't really get very many good pictures, and haven't had a chance to write anything up. I was just going to put a zip file of all the pictures on the web server - but it has run out of space too! Well, here are some pictures taken by Ethan, who went with us,

It was a great weekend, but also quite exhausting.

I had thought that I would enjoy not doing anything this weekend - but strangely enough after going to the gym yesterday, and for a long run today, I still have loads of energy. So I'm now going to head out to watch "The Libertine", by myself, on a Sunday night (there's nothing good on TV right now anyway).



Monday, October 31, 2005

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Well, I got in from South America this morning. I start my new job tomorrow, and figuring that it's all going to fade from my mind pretty quickly, I've written up everything I could remember.



Saturday, October 8, 2005

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South America!

Well, I said I would hang around in London waiting for inspiration to hit, and it did, the very next day, by way of an email from someone in Rio de Janeiro who was reading my website. They said (among other things) "Come to Rio de Janeiro. It´s a nice place." ... so I figured... why not!?

See how easy I am?

So I have booked a return ticket to Rio de Janeiro leaving Sunday night (that's tomorrow!).

Here's the rest of my intended itinerary:

  • Monday 10th - Thursday 13th Rio de Janeiro, staying at the "Mellow Yellow" backpackers hostel.
  • Thursday 13th - Monday 17th Buenos Aires, staying at "El Firulete Hostel". I plan to eat a lot of steak during this period.
  • Monday 17th - Thursday 20th El Calafate, staying at the "Albergue Buenos Aires" hostel. Here I hope to go on some day hikes around Patagonia and see the famous Perito Moreno glacier.
  • Thursday 20th - Sunday 23rd Bariloche, will hopefully be able to do some more hiking around here.
  • Sunday 23rd - Thursday 27th Iguazu Falls
  • Thursday 27th - Saturday 29th, Rio de Janeiro again.
  • Saturday 29th I fly back to London, just in time to start work at my new job.

The one downside to this is that because of the huge distances involved, you either get overnight buses which take a very long time, or you get flights. I got flights - but because these are hard to book, my travel itinerary is unfortunately a bit inflexible. I much preferred the situation when I travelled around Europe by Eurail train, in which you could pretty much get on a train at any time and didn't really have to plan an itinerary..

Anyway, it's done now. I can always ad lib - if I trully end up deciding that a particular flight is a mistake, I won't make the mistake of lettig sunk costs affect my judgement. I'll just take a bus and forget the money I paid for the flight. It is only money after all, and it's time that I don't have right now.

In other news - I screwed up the sofware that updates my website - so I had to redo the template that generates it... The plus side is, the Archive link now allows you to see all previous updates to my site. The negative is that something else is probably broken.



Saturday, October 1, 2005

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Time to spare

Well, yesterday was my last day working of UBS. It's been a long stint - four and a half years - and I didn't resign from the position lightly. It's a good place to work and I really liked my co-workers there.

I'll be joining a hedge fund in their London office, helping them with their High Frequency Trading operation in London, and am in the enviable position of having negotiated for a whole month off before I start.

My only problem now is, I haven't figured out what to do. Spain seems like a nice choice - but I suspect I'll get bored going there on my own. Lots of people have recommended South America (Brazil and Argentina) - but oddly enough this also has not really caught my imagination. It's a bit like wanting to sleep in after a big night out when it's a beautiful day outside - I feel I really ought to take advantage of this time in some special way, but right now I guess I'm just too drained to want to do anything really ambitious.

I'm just going to chill in London for a week and wait for inspiration to hit... There's something really appealing about just getting in a car and going somewhere, which is probably what I'll do, when I figure out where.



Monday, August 22, 2005

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We played some cricket in Regent's Park last Saturday.

I have been carried off with the rest of the country wth Ashes fever. The last two test matches have been absolute nail-biters, because both England and Australia appear to be very closely matched. Australia won the first game easily, to no-one's surprise as England have not had the Ashes since 1988.

However, England have since struck back and seriously look to have Australia on the ropes. We did well to almost win the second game after some poor batting, but fell just 2 runs short... But what a game it was! It was by far the most exciting game of cricket I've ever seen, and Richie Benaut, who's been commentating on the cricket for the last 20 years thought the same thing!

The third test was a draw, thanks to a heroic 7-hour, 156-run batting stint by captain Ricky Ponting, on a tricky pitch, before a hostile English crowd. Once again, the result was uncertain up to the very last ball.

Thanks to that draw, Australia now need only win one of the next two tests to retain the Ashes. However, if England win both, they will win the Ashes...for the first time in 20 years. Such a result was unthinkable before the series started.

The 4th test starts this Thursday.

Hedging Demo

I've written a spreadsheet that demonstrates how a dynamically maintained portfolio follows the price of an option - but only if you get the volatility right at each point until the option expiration.



Sunday, July 24, 2005

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I went to the driving range last night and noticed a copy of "The Sun". Here's what was on the front page yesterday:

Since that went to print, it's become apparent that the guy was completely innocent.




Saturday, July 9, 2005

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Google Earth is Amazing!

I have been playing around with Google Earth today. It is absolutely incredible the detail that is available for many places. This is my flat in London. Here is where I went to High School in Sydney. And here is where I grew up for the first 18 years of my life.

Irritatingly, a large portion of Sydney is not in high resolution - so you can't actually zoom in on the Sydney Opera House or Harbor Bridge yet. I'm sure they'll fix this eventually.


Thursday, July 7, 2005

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Overslept this morning

I overslept badly this morning and woke up at 9am. I'm supposed to be in at work by 8am. Anyway, I caught the number 43 bus into work - lots of people on the bus. There were already reports of explosions on the tube when I was on the bus. Then there was a report that a bus had exploded. At Highbury corner the bus stopped: we all had to get out - no buses, taxis or tube into the center. I figured I may as well go home - so I caught the bus back, and here I am back at home, watching the news.

So anyway, for anyone who cannot get in contact with me due to cell phones etc. not working, I am fine.




Wednesday, June 29, 2005

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I just spent a weekend in Berlin.


A practical demonstration of Ito's Lemma

One of the first things that you come across when reading any derivation of the Black-Scholes equation is the use of "Ito's Lemma". To me, it's even now quite an unintuitive thing to grasp... So I wrote up a spreadsheet that demonstrates that Ito's Lemma is true. It shows an example function of first a "normal" variable and of a stochastic "brownian motion" variable. It does not have any embedded macros and is safe to download. Try hitting F9 (recalc) on it a few times and you'll easily see that it works... so at least now I know what it means, even if I'm not sure how I would actually prove it yet...



Tuesday, May 31, 2005

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I spent this past bank holiday weekend in Latvia:


Wednesday, April 13, 2005

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The Apprentice

I don't normally go in for reality TV shows, but the BBC's "The Apprentice" has really got me in.

Today, in the "firing session", Sir Alan Sugar said something very close to:

"Saira, you're a rude, abrupt, abrasive and pushy person..."

I think the irony of the situation escaped him: he could have been describing himself at that moment.

It was all true, what he said about Saira - but she was in tears afterwards.



Tuesday, April 12, 2005

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My deep thought for today

I read something by Sir Martin Rees, the Astronomer Royal, in the Guardian today:

"I'd like to widen people's awareness of the tremendous timespan lying ahead — for our planet, and for life itself. Most educated people are aware that we're the outcome of nearly 4bn years of Darwinian selection, but many tend to think that humans are somehow the culmination. Our sun, however, is less than halfway through its lifespan. It will not be humans who watch the sun's demise, 6bn years from now. Any creatures that exist then will be as different from us as we are from bacteria or amoebae.

Our concern with Earth's future is, understandably, focused upon the next 100 years at most — the lifetimes of our children and grandchildren. But awareness of this longer time horizon, and the immense potential that human actions this century could foreclose, offers an extra motive for proper stewardship of this planet."

I don't necessarily share his view that humanity as a species will still be evolving genetically anymore - but I really like the idea that we ought to be thinking of ourselves as being at the start of our history in the universe, rather than at the end.

We've only been able to read and write for a few thousand years. Where will we be and what will be doing a thousand years from now? A million years from now? A billion? Those timescales sound nonsensical, but that future for us really does exist for us (provided we don't mess it up!).

All too often we forget that we have only just begun.



Monday, April 4, 2005

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I just got back from a weekend skiing in Chamonix.


Tuesday, March 29, 2005

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New York

I just got back from a trip to New York.



Sunday, March 6, 2005

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Taylor series

At work, I've been learning about Taylor series expansion. Essentially, if a function is analytic (and most ordinary functions you learnt about in school are), then this means that it can be equivalently replaced with a polynomial whose co-efficients are determined by the curvature of the function at a particular point. By curvature I mean, for a given point on the function, you just tell me the rate of change of the function at that point, and the rate of the rate of change of the function at that point, and so on and so on and so on. I can also determine this curvature just by looking at the way a function changes over some small range of values (which can be as small as you like but not 0).

So really, saying that a function is analytic is saying: just looking at that function across some small range of values is enough to tell me about its behaviour everywhere else.

It only just occurred to me how strange that really is when you think about it.

I was thinking that the name for this might be "holism" after watching those David Suzuki documentaries where he showed each piece of a hologram still contained enough information to reconstruct the original... but after looking up the definition it does not seem to apply as well as I thought.

There certainly ought to be a word for this. It reminds me of the Mandelbrot set and other fractal structures, where again, in a sense, you find copies of the entire "structure" even when you zoom in on some small subset...

Anyway, it's all very mysterious and fascinating, because I still don't really understand it.

A philosophical thought

Another thought that's been mulling around in my head: We are all hopeless at predicting the consequences of our actions, and no-one can predict the future. This is probably the strongest argument then for why "the ends do not justify the means".

Go Tiger

Finally, I am really looking forward to watching the final round of the PGA Ford Championship at Doral tonight. It is looking like Tiger Woods is finally back on form - ably demonstrated by him crushing a drive that carried 330+ yards over the trees to land on the green of a par 4. The only golfer to actually land the ball on that green all week. He was also the only golfer to reach the 600 yard par 5 in two all week. Now that Woods is driving the ball long and straight again, who can stop him?

Well, despite all of this, he is still 2 shots behind Phil Mickelson, who is also displaying fantastic form. The two make up the final pairing in the final round tonight and they are both playing their best golf. It hasn't been this good since the final round of the 2001 Masters.

All this inspired me to try play some golf today but the weather is still so cold... so I opted out... but I can't wait until spring.


Tuesday, February 15, 2005

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St Anton

I just got back from a week skiing in St Anton.



Sunday, January 30, 2005

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I just discovered Wikipedia. For stuff like Mathematics, it's a great idea and works well . But it will never be a serious competitor to Encyclopedia Brittanica. To see why, just check out the George W. Bush page. First, I found the disambiguation page, which at the time of writing stated:

"George Bush can refer to several people, one of whom have been Presidents of the United States:

  • George W. Bush - George Walker Bush, a notorious serial cat rapist.
  • George H. W. Bush - George Herbert Walker Bush, 41st President of the United States (1989–1993)
  • George P. Bush - George Prescott Bush, son of Jeb Bush
  • George Bush (1796–1859), biblical scholar and distant uncle of the two presidents. "

Then you start reading the "George W. Bush" page and find that it has been overrun by people with a political agenda. Consider this:

"Katherine van Wormer, a professor of social work and writer on addiction treatment, claimed in an Irish Times article on 6 May, 2003 that Bush seems to have the mindset of a "dry drunk," an alcoholic who still exhibits thought patterns that accompany alcoholism. She bases this view on her perception that his public speeches express rigidness, obsessiveness, impatience, and grandiosity. "

What I think is most pathetic, is that the person who added this, keeps reverting it, and trying to justify it, claiming that they really are being objective and neutral and "just reporting facts".




Saturday, January 29, 2005

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At work, each week we revise a section of the book "Financial Calculus". It's quite a good book, but it occurred to me, while trying to get my head around Stochastic Calculus, that I never really understood normal calculus.

For example, why is the sum of a limit equal to the limit of the sum? What is a limit really anyway? Why can you raise a number to a fractional power - what does it mean to do that? What about raising a number like "e" to the power of another number. How would you write a computer program to calculate that number to arbitrary precision? Why is the slope of "e^x" always equal to itself? How do you prove that?

I found that I couldn't really answer these questions properly - and it's because the way I was taught calculus sucked. I was taught how to "do" calculus in terms of "infinitesimals" - dy/dx is the ratio of two "really really tiny quantities". But what the hell does that mean? Why is it ok to multiply, add, divide these numbers? The worst, though, is I frequently ran into arguments along the lines of "well, dx + dx squared - the dx squared term becomes neglible compared to dx so we can just cancel that out". I remember listening to those arguments all the time and it really pissed me off because it doesn't make any sense. You can't reason about infinity, or infinitesimals - or at least, I can't, except in the most abstract and useless sense.

OK, some people might even argue that talking about "slopes" and "areas" and "infinitesimal quantities" actually does have some intuitive benefit, and with your intuition you can get a long way (I managed to even do well at university physics classes, where we used calculus all the time, simply by using my intuition about what I was doing when I integrated or differentiated something).

But as soon as you try to apply this intuition to Brownian Motion - you're lost at sea.

Anyway, all is well again because I have found the most amazing site: He builds up everything, and I mean everything from the foundations. He starts out with integers, then defines fractions, then defines what a "limit" is, and only then defines what a "real number" is, in terms of the limit of a sum of fractional numbers. You can understand all of calculus without ever needing to define what infinity means, or make these dodgy arguments about "terms becoming neglible".

It turns out, the rest of the mathematical community agreed that reasoning with "infinitesimals" didn't really make sense either.  So why on earth do people still try to teach it that way?

Richard Feynman

I just started reading Richard Feynman's Nobel prize speech... this cracked me up:

"That was the beginning, and the idea seemed so obvious to me and so elegant that I fell deeply in love with it. And, like falling in love with a woman, it is only possible if you do not know much about her, so you cannot see her faults. The faults will become apparent later, but after the love is strong enough to hold you to her. So, I was held to this theory, in spite of all difficulties, by my youthful enthusiasm."


Monday, January 10, 2005

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I just got back from skiing in Zermatt over the New Year. It was fantastic.


Tuesday, December 21, 2004

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The saga of my mail access continues. I sent a complaint to Yahoo asking them what the problem is, and this was their reply. The key part of their response:

"please reply with the following information:

* Yahoo! ID
* Domain Name
* Zip Code, Alternate Email Address, or Date of Birth (provide only one)
* Last 8 digits of the credit card used to pay your account
* Credit card type
* Email address in question
* Password for email address in question"

Is this for real!? The fact that they only ask for the last 8 digits of my credit card number might seem more benign, but the first four digits just indicate whether it's VISA, Mastercard or whatever (so they would know the first four digits if I answered their email in the way they were expecting), and the next four are usually just the issue date of the card - both pretty easy to guess. What's more concerning is that obviously whoever these fraudsters are, they were able to read my original complaint to Yahoo without any problems (and I submitted that complaint over their web interface... or thought that's what I was doing...)

To be honest, I am even more amazed at my own naivety. I first read the email this morning and my first thought was "well, I don't have time to supply all this information this morning... I'll have to reply tonight. Man, I hope they don't read any of the sensitive emails I receive"... Yes, I actually thought that, before sanity set in... I'm still amazed that they read my original complaint somehow.




Sunday, December 19, 2004

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Yahoo mail problems

I've been getting reports from some people that mail that is sent to me gets bounced... confirmed by the fact that I haven't received any spam email in the last 24 hours. I'm having difficulty sending mail too. If you've sent me a mail and I haven't replied, try sending it again... Sorry for the inconvenience - I'll try to get it sorted out as soon as I can.



Sunday, December 5, 2004

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I just got back from a trip with some mates to Krakow, Poland. It's a fantastic place - beautiful, friendly people, great nightlife.



Sunday, November 21, 2004

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Ascent of Man

I just finished watching episode 4 of "The Ascent of Man".

It was mesmerizing.

In this episode, Prof. Bronowski started by discussing Pythagoras' theorem, but weaved it all into an overall discussion of Christianity, Islam, and a general discussion of how mankind has perceived space and time throughout the ages. I am also amazed, not only by the material, but by the delivery. Several segments involve him speaking/lecturing, to the camera, for 10-15 minutes, uninterrupted, all the while delivering profound insights and amazing ideas - with never an "um" or "err". I am so impressed by this guy - it's such a shame that he is dead now, and that nobody is making TV like this any more.


Sunday, November 14, 2004

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The meaning of life

My friend Dave in Chicago kindly grabbed the entire series of The Ascent of Man via bit-torrent for me, and I have started watching some of it. Well, with a typical Sunday night before work melancholic mood striking me, I thought I might write down some philosophical thoughts.

I grew up as a typical WASP (White Anglo Saxon Protestant), and went to a somewhat religious school that taught us all the usual christian ideas. What I still respect and admire most about Christianity above other religions (and maybe this is just displaying my own ignorance here), is its concept of a loving and forgiving god. Other religions seem to emphasize other things (e.g. peace, nirvana, transcendence, reincarnation, eternal life) - but none of these other ideals are as attractive a thing to me, as the concepts of love and forgiveness.

All that being said, I am not religious; in fact, I am an avowed atheist. This does not mean that I do not believe that there is something very mysterious about consciousness, or that I believe that our own experience of existence can be explained by a "materialistic" outlook. I just don't think that any of the religions that I have heard of have come any closer to capturing the essence of what life is about than pure science and reason alone. In fact, I think science and reason have gone a good deal further to helping us understand our place and purpose in the universe than any religion.

For a while, I was an agnostic - the turning point was after I watched a series called "Cosmos" by Carl Sagan, which really inspired me with the idea that I could find my own meaning in life without resorting to some supernatural entity. I really recommend it as a fantastic series. Choosing to be an atheist really was a "choice" for me, or to put it another way, a matter of faith. By "faith", I mean making a decision in favour of one unprovable set of beliefs, and discarding another. By "unprovable", I mean I can no more prove that God does not exist than a theist can prove to me that he does - but from a faith point of view, I believe that there is no god, because I choose to, and I think I am better off for doing so. Obviously, if God suddenly wrote his name in fiery letters in the sky, well, then I would have to re-assess my atheist pursuasion ;-)

So what do I think is the meaning of life? We all die - but I think my purpose in life is to find something, some cause, or some person, that I would happily trade my life for. That's not to say that I would have to sacrifice my life in order for it to be meaningful - I want to live of course! - but I think the "litmus" test for me having found meaning in my life would be that I could identify something in it - some person, or some cause, that I would die for if it were necessary. For many people, this can be as simple (yet so profound!) a thing as their kids (most parents would die for their kids), or even just someone that they love - I haven't found it yet - so I'm leaving my options open. The universe is so huge, I have faith that I'll find meaning in it eventually, and for now, that is enough.

Right, that was pretty deep. I've just turned on the TV and Kylie Minogue's "locomotion" is playing, which has killed the mood like a bug hitting a car wind-screen.


Saturday, November 6, 2004

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Right - I am going to change how I update this thing. Quantity doesn't beat quality, and some of these entries are just pure dribble. So from now on, I'm only going to update it with worthwhile stuff - although that means it might not be updates as frequently.


So without further ado, here are the pictures from Chicago (I finally got hold of a camera to connect my camera to my computer).


I also updated my Norway page with some better pictures, and changed it to use thumbnails.



Thursday, November 4, 2004

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Oh well, another 4 years. I nearly choked when I read this article:

'President Bush praised voters for a record turnout and thanked them for "a historic victory." Vice President Dick Cheney went a step further, calling it a "mandate."'

 I cannot believe that after only just barely winning the election by a few percentage points, Dick Cheney is calling the election victory "a mandate". He really is Darth Vader! This is all quite scary - if you go to The National Review you'll see how these guys are thinking (there is an article on that site called "Who needs unity?").

gym rat

Played the first round of an informal "squash tournament" last night with 3 mates. It was great fun. Then again today I went to the gym for a "personal training" session and the guy nearly killed me. We did the usual squats, bench press, shoulder press, crunches, etc. - but what killed me was a new thing called "Box Jumps" where you crouch down, then jump up and stand up on a platform, repeatedly, for a minute. I was exhausted after that. Then he had me do it again. Walking down the stairs afterwards, my legs almost collapsed underneath me.



Sunday, October 31, 2004

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Right - sorted out all the bills...  Once I find the cable to connect my camera up to this computer I'll also post some pictures up from Chicago.

Just watched "The English Patient". I've seen it before - I had forgotten just how depressing it really is. It is full of lines like "I cut my heart out each night, and each morning it was full" and "The poison leaks out of you each morning, after the long dark night". Just how much sorrow and misery they could milk out of one movie!? Ironically, the movie was quite uplifting - - you can't help thinking as you're watching it "I am so glad that I am not this guy" ;-)


Saturday, October 23, 2004

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Finally back!

After 6 weeks away from London I am finally back! Just spent a very enjoyable week at "Quantfest" in the Stamford office of UBS. It is an event where all of the Quant and IT guys meet together and talk about what they're doing. It was great fun - I met a lot of really good people and learnt a lot (or really, learnt a lot about what I don't know - which is actually a good thing to learn...)

I came back to find two summons in my mail to appear before a magistrates court for not paying my council tax: One for my old flat in Greenwich, one for the new flat in Highgate. I thought I had already paid the one for Highgate... and amazingly Greenwich council hasn't figured out that I do not live there anymore... oh well, hope this all does not matter too much...



Saturday, October 23, 2004

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Well I've been stuck here in Chicago for 3 weeks... tomorrow morning I am flying to Stamford for a week, then finally, after six weeks, I'll be back home in London. I am looking forward to it... You can only put the rest of your life on hold for so long.

Music-wise, and I know this will probably sound quite sad - but I discovered the song "Rosanna" by Toto. I know - totally uncool - but I really like it nonetheless: after listening to this song, I was inspired. I discovered it was named after Rosanna Arquette, and that Peter Gabriel also named a song after her. She must be an incredible woman.


Saturday, October 23, 2004

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What an incredible country. I will post a better write-up when I get back to London... for now... check out the cool pictures...


Wednesday, September 8, 2004

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I've been absolutely flat out the last couple of weeks:

Last Monday, I went to a BBC Proms concert - Prokofiev Symphony No. 5 and Debussy L'apres Midi d'une Faune were great! Andre Previn's violin concerto was way too existensialist and sparse for my taste though.

Also last week, I've had some friends visiting from the US. We were out every night last week, and saw the Australia vs Pakistan 1-day cricket match on Saturday. That was my first ever cricket match... it was great fun and terrific weather for it. My American friends also got a real taste of Australian "yobbo" culture from the guys sitting behind us. The most memorable cry: "Bet there's a couple of turtle heads poking out of your "!$hole now fellah!" after a head-high bowl.... absolutely classic.

Then on Sunday, we drove down to Sandwich and played 36 holes of links golf at the Princes course. Was sublime.

It's been a fantastic week - absolutely loving this Indian summer we are having.

This week, I've been really busy with work. One of the cool things - a discussion group where we go through the "Rennie and Baxter" book I referred to below.

Finally, my mate and I have been finalizing plans to drive around Scandinavia for the next two weeks... We're starting out in Copenhagen, then figured we'll drive counter-clockwise via Stockholm, Oslo, Bergen... ending up back in Copenhagen on the 22nd. After that, I fly to Munich for Oktoberfest.

But that's just a rough plan. Basically, we're just going to ad-lib it. We thought about going up to Tromso north of the arctic circle until we realised just how far that is (26 hours of driving, 1000 miles). For myself, I am just really looking forward to the scenery around all those nordic Fjords.

After vacation, I'm heading straight over to the Chicago office for a couple of weeks for more work stuff - so this is probably going to be the last update for a good long while (about a month)...



Monday, August 30, 2004

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Democrats vs Republicans = The Future vs the Past

I just saw the headline "Republicans to Open Convention with 9/11 tribute" on one of the new sites. To me, this epitomizes why I don't want the Republicans to win. I'm sick of this "doom & gloom" message. As cynical as this sounds, I still think they are trying to scare the population into voting for them.

I also do not think it is going to work Back when Bob Dole was competing against Bill Clinton for the Presidency, I remember seeing one of the TV debates, in which Bob Dole was going on and on saying how bad things were. He was trying to scare the population into voting for him. In contrast Bill Clinton was saying "No, you're wrong. The future is bright - we're about to enter some really good years".

I think the same sort of thing is happening this election.



Monday, August 23, 2004

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iRobot review

So last update, I was going to review iRobot but yet again ended up maudlin on about my own life (such moods are more common on a Sunday evening are they not?).

Anyway, what did I think of the actual movie? It was OK - but it's downfall was that the stunts and computer animation were just too unrealistic. The robots looked extremely cartoony. They needed some proper physics based modelling, IMO. The stunts, especially the one where his car is being attacked by all of the robots, was on the James Bond side of unreality.

Finally, I found the characterisation to be a little flat. Actually, this is a general problem with Isaac Asimov's writing. He came up with fantastic ideas (psycho history, the laws of robotics) and plotlines (although this movie plot did not really share anything with his actual plots) - but his characters, especially his women, were always pretty two-dimensional. This came across in the movie.

I would rate this movie with 7/10, whereas Blade Runner would get 10/10.

It was still worth seeing though.



Sunday, August 22, 2004

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iRobot and dreams

I went to see iRobot the other night with a friend.

As I've said before, I was a huge Isaac Asimov fan when I was growing up. When I was a young, up and coming computer geek ( ;-) ), what inspired me to spend hours getting something to work on a computer was wanting to write my own game. That got me into being a real "bit-head" - very interested in getting the ultimate low-level performance out of a computer. For instance, I can even tell you now, without having to look it up, that location 53280 in the Commodore 64's memory address space controlled the border colour it displayed on your television set... oh man I cannot believe I just admitted that I still know shit like that - it is sad I know!!

Anyway, Isaac Asimov's robot stories inspired me to dream that I could write my own conscious "computer program". I mean, just think, nobody has done this, but if you could do it, it would be among human kind's greatest accomplishments... What a thought for a young kid to have!!!

So for a long time, I thought very long and hard about how I might try to do this. I thought a lot about how I think, with the purpose of seeing if there was some way to model this in a computer program. I thought about self-awareness... I didn't even get close to writing an "intelligent" program, but I learnt an awful lot. At one point, when I was studying computer science, I even intended to go on and do a Ph.D in artificial intelligence...

Well, time went on and it became apparent that the heady days of AI were already over by the time I was looking to enter the field - they had already made their promises to industry, sucked up all the funding they were going to get, and failed to deliver anything close to what they promised. Netscape had just IPO'ed and the Internet was taking off, so I figured I had a better chance to do something really cool by going into industry.

I still do not regret this decision... if you look back to all of the big accomplishments in computers over the last 50 years, UNIX, C, GUIs - a lot of the cool stuff was done by companies such as Xerox PARC, AT&T Bell, SGI, HP, Sun, and dare I admit it, Microsoft.... academia does not seem to have accomplished anywhere near as much (a few algorithms and data structures...) OK I am thinking this is actually quite debatable (a lot of the "fundamentals" that all of these other accomplishments are based on did come from academia), but the real point is that you didn't have to go into academia to do ground-breaking new things in computers.

Another point I guess I should make, is that dreams are important, even if you never end up following them all the way through to their conclusions... and in a way, the more ambitious the dream, the better. I never really did write a complete computer game (it was going to be a flight simulator). I never wrote an "intelligent" conscious computer program (my dreams were oh so ambitious weren't they?)... but those dreams inspired my career and my interests. If it wasn't for those dreams and the impact they had on me, I wouldn't be half the person I am now. They still motivate me today.

If you ever have kids, make sure to nourish and nurture their dreams too, no matter how unrealistic they may be.


Friday, August 20, 2004

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Rocky moment

I've started going running in the mornings - I'd forgotten how much fun it is. I know, you're thinking "running in the morning is fun?" - but really, the key is, drink some coffee before you go, and start slowly... By the end of it you'll be wide awake and feeling very good.

Well anyway, there's a gigantic, long, very steep hill on the way back to my flat. Up until now, I've always had to stop half way up, panting in great heaves and gasps. Well, today, I paced myself a bit more slowly, and went all the way up the top without stopping. I seriously considered acting like Rocky at the top.... but it was all downhill from there so I just kept going, and anyway, if I'd stopped, I probably would have collapsed ;-)


Thursday, August 19, 2004

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Table Tennis

Came home from the gym and switched on the TV to see the women's Olympic table tennis. I am actually a little curious why this sport would need to be split between women and men. I cannot see what advantage men would have over women or vice versa, which presumably was always the original reason for splitting sports up like this....

Anyway, they are incredible - the reflexes they must have are insane. I wonder how much coffee they are allowed to drink beforehand?

A regular

Also at the gym today, the woman at the Deli shop gave me a free orange juice, just because I am a regular and did not otherwise have enough cash on me. These sorts of things make my day! (she's quite a looker too, although of course she is not single :-( ). Anyway, I am so proud to be considered a regular! ;-)


Sunday, August 15, 2004

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Where are you Tiger?

Well, I've been watching the PGA Championship, and have to say I am simply not enjoying it as much. I think I know why: it's because Tiger Woods isn't winning. I miss the times when he used to be that much better than everyone else.

Think back to the year 2000, when he won the US Open by 15 shots, won the Open Championship by 8 shots and then won the PGA Championship and Masters the following year... If you don't yet have a feeling for how astounding this accomplishment is, imagine a football team that won the World Cup Championship final game by 15 goals to 0, and then just to show it wasn't a fluke, went on to win, I dunno, the Euro Cup by 6 goals to 0. And remember too that with golf, it's not just one guy battling against another: the winner has scored better than a field of 150 other players all playing the same course. That's why it's so difficult to win a golf tournament - let alone win it by such unbelievable margins.

Here was a guy who was making history and doing unbelievable things. I felt priviledged to be able to witness it. His bogey free final round of 67 on that sparkling Sunday at Pebble Beach was golf perfection.

But there's also a sense of nostalgia: 2000 was a great year regardless. 9/11 had not happened, the economy was fantastic (it was the height of the dot-com bubble). The mystical and completely irrational side of me believes that somehow, we need Tiger to start winning again ;-) Other people clearly agree with me - god is not in his heaven and all is not right with the world ;-)

I don't think he's past his prime though - he'll be back and I don't even think we've seen the best of him yet. It ought to be easier for him to find that form again because he's had it once before - he has such an athlete's swing. If nothing else, remember this: all the guys who are beating him at the moment (Darren Clarke, Ernie Els, Vijay Singh) are all older than he is...


Sunday, August 15, 2004

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Today, I accomplished very little. Woke up with a delayed onset hangover due to being out almost every night this week, then tried to organize plans for a trip to Scandanavia next month with a mate. We intend to rent a car and drive around, but discovered they were going to charge us 200 pounds to drop it off in a different location to where we pick up! It's cheaper to fly! Anyway, got as far as booking the tickets to Copenhagen where I will visit Sofus - hopefully, the plan is to end up in Munich for Oktoberfest.... Anyway, by this point it was all getting to be far too much like work, so I went out for a run around Hampstead Heath... I wasn't really into that either though: I ended up walking a fair bit.

When I got back I just watched the PGA Championship on TV (which was also a bit dull... I think I might finally be cured of golf... but then again I have thought this before - all it takes is one good round and I will be hooked again).

Oh, I also channel-hopped over to what is possibly the most tasteless, soulless program I have ever seen... Watching it, I felt sick, yet also oddly fascinated before I finally wrenched myself back to watching the golf. I guess it was similar in many ways to being at the scene of an accident.

So basically, I was a complete slacker today.



Friday, August 13, 2004

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Have just been watching "The Bicentennial Man" on TV. I was a huge Isaac Asimov fan: his robot novels inspired me to enter into computer science, with the hope that one day I would write a "conscious computer program". The way he described the 3 laws of robotics, it really seemed plausible that we could do this (write a conscious algorithm).

Anyway, I thought very long and hard about this way back when I was 16 and amazingly even then I came to the conclusion that it was impossible. However, my conclusion was not really a "destructive" conclusion - what I realised is that there is something incredibly special about consciousness, and that no "algorithm" could capture it... At the time, I thought that I held a priviledged position in seeing something that nobody else could see. From that point on I took a very smug, intellectual disposition, because I figured I had to be smarter than everyone else if they didn't understand this brilliant insight that I had.

But then I read the book "Godel Escher Bach" by Douglas Hofstadtfer. This is a trully amazing book, because even though Douglas seems to understand things exactly the same way that I understand them - I could not deny that he "got it" and understood what was special about consciousness - he draws a completely contradictory conclusion to the one that I drew. How is it possible that someone else who clearly understands the issues as I see them can draw such a completely different conclusion? Well, this was my first exposure to what I think is called a "paradigm". The idea being that two people who have a different paradigm don't actually disagree in any objectively measurable way, but still they disagree...

I'll tell you what... I need to actually write an essay that explains succinctly why I believe that there is something fundamentally special about consciousness... but there's no place for it in a daily blog entry.... when I write it, I'll post it here. Watch this space...



Wednesday, August 11, 2004

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Well, today I grew sick of listening to "Zero 7" and resumed my alphabetical song search... and discovered Eple and hence the group Royksopp and their Melody AM album. Another fantastic album. I feel spoilt to have discovered two great albums in such a short space.... I tell you, music is my life - when I am listening to good music, I come alive, and become ten times the person I was before. My brain goes in to overdrive and a million ideas flood into my head faster than I can write them down... but I'll try now:

Communism vs Capitalism

Centrally Planned vs Free Market economy

Trying to make a difference vs Going with the flow

It is ironic that the best possible intentions often lead to the worst possible results, and vice versa

The worst wrongs are committed in the name of righteousness

There's a pattern here... and my intuition tells me that there is a really deep insight along this train of thought but I cannot think of it yet.

Going in another direction: Which is bigger? The physical universe, or the totality of ideas? The physical universe is big... We hide it from ourselves every day but it's easy enough to remind yourself with the knowledge that there are more stars in the universe than there are grains of sand on all the beaches of the world. On a clear night, if you look into the heaven you can only see almost infinitesimal fraction of stars that actually exist in the universe. Somewhere out there I am sure there is intelligent, conscious, life that is completely unlike us. Yet I feel that the universe of ideas is bigger... The universe of ideas seems like the Mandelbrot set, or anything that is "fractal" in nature... an undefinable thing, rich and without any limit...


Tuesday, August 10, 2004

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New job

Today, I confirmed my move over to the Equities Quantitative research group at UBS. Basically, I'm going to be filling a role that I have designated to myself as "IT-bitch", at least in the short term - but in the long term I am hoping this will add another dimension to my career.

There are a number of positives to this move for me. One big plus for me is that I will once again be doing C++ coding, which is in itself so much more interesting than Java simply because there are so many more tools you can bring to bear against a problem: writing your own user-defined types, template meta-programming, and most importantly, the necessary control over low-level efficiency such that you do not need to sacrifice high-level designs to achieve your performance goals. I'll also get a lot of exposure to numerical methods, an aspect of computer programming that I haven't had much experience in before now (except a rudimentary course at university). The biggest plus for me is that by sitting up on the trading floor and having a lot more interaction with the traders and users, I will hopefully have the opportunity to learn more of what we call inside the bank "the business" (i.e. how the bank actually makes money).

The downside is that a lot of the work I'll be doing probably won't be as "glamorous" as I'd like - a lot of boring crap like organizing the release of software libraries.

IT Party

Also today, UBS held an "IT" party this evening. It was quite entertaining - free beer, and in savvy recognition of the (estimated) 5:1 ratio of men to women, the organizers decided to get "Girls Aloud" in to perform some of their songs... I would not be too surprised if they disband soon... this gig (performing for the IT department of an investment bank) is probably a new low for them... Ah anyway, we all enjoyed it... "great scenery" ;-)

London taxis

After the party I took a cab home - so allow me finally to remark on what great conversations I nearly always have with London taxi drivers. This guy was from the East End. I started talking about how I grew up in Australia, then lived in Chicago, then moved to London, and we started talking about family, the purpose of life, relationships, all of it. It's a psychotherapy session, getting a London taxi (well, some might argue that they are as expensive as seeing a psychologist too I suppose ;-) ). I once read an article about some guy in Los Angeles who was insistent on getting a London Taxi built for him... but he missed the point entirely: it's not the actual black taxi vehicles that make London taxis special, it's the drivers. Everyone of them that I have met has been a "salt-of-the-earth" character, and of course, to even be able to drive a taxi they must know the most direct route to anywhere in London. You can just hail a London taxi outside Waterloo and say, for example, "I want to go to Smiths on Smithfield in Farringdon" and they will know it. Whatever you do, don't insult them by offering direction advice. Some people wonder "is there anything that the UK is best at?". Well, London has the best taxis in the world.


Monday, August 9, 2004

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Just started reading "Financial Calculus" by Martin Baxter and Andrew Rennie and have to say that, so far, I am finding it to be very good. The way I was taught the binomial model was in terms of "risk neutral probabilities" and derivative prices at each node in the tree - whereas the way I finally got to understand derivative pricing was to think in terms of a risk-neutral portfolio at each node in the tree, and to forget about these "probabilities" and just think of solving two simultaneous equations at each node to determine what the risk-neutral portfolio should be. See binomial.cpp for an example. I remember finally exclaiming "give me a spot process, and any payoff function at expiration, and I can tell you the price, and how to hedge it" - I thought I had gained such a deep insight! Well, the first 10 pages of this book have described things exactly this way - I could have saved so much time if I had just read this book first!

Other than that, it's been an exhausting day. Did not sleep very well last night, but still made it to the gym this evening - going to crash now...


Sunday, August 8, 2004

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New site design

Well, finally, as promised, I've rebuilt my entire website using Citydesk. and turned it into a proper blog. Parts of it are still busted and it doesn't look very polished yet: the transition over wasn't a very automatic thing. I'll fix stuff as I find it. Now that I can update this thing easily, I'll probably update it a lot more regularly. Even though I don't really expect many people to read my drivel, the idea is, when you write for an "audience", it forces you to express your thoughts more clearly... I'm certainly going to try and update things clearly. Hopefully, over time, this "blog" will become a sort of public diary, which I can read over years later on, just like a photo album...


I bought an IPod a few months ago, and a friend of mine very kindly put 9,223 songs onto it beforehand... so my current pastime is to just listen to all songs in alphabetical order, and when I hear an artist I like, I flip over to listen to all songs by that artist. The latest such artist is Zero 7... they are fantastic! I particularly like "Distractions"... The other thing I tend to do is, when I really like an album, I just listen to it over and over again... until I am sick of it... in fact, already, I am beginning to appreciate that some of their songs are maybe a bit too mellow...


Saturday, August 7, 2004

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Microsoft's service pack 2 cannot come soon enough. I have a firewall installed, and thought I was reasonably safe, but at 5:35pm my computer rebooted itself, and then would not let me log on again - every time I tried to log in, winlogon.exe would crash! To fix, I had to log in to the recovery console, and from an inspired guess, went into my system32 directory and deleted all .dll files that had a timestamp of today... This is scary though - it should not have been possible - I am a "sophisticated" user - I know not to execute attachments etc. etc.

After this experience, it is plain to me that Windows XP security is a joke.

I just completed "Capital Markets 2" - a very intensive introductory course at UBS which was all about derivative pricing and risk management. The key thing I learnt? "If you can hedge something, you can price it". Well, being a programmer, often the best way for me to understand something is to write a program - so that is what I have done. I decided to write a program that would be as generic as possible. It is extremely inefficient (O(2^n)), but my goal was to write something very "clean" and general-purpose rather than taking short cuts that would limit its applicability. To be done: american style, time-varying volatility, dividends, multiple products... My goal is to make it as general purpose as possible...


Tuesday, June 15, 2004

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OK... so after the last post - you can see I am still really lazy. I'm going to have to upgrade my ksh scripts and make this an actual weblog - then it would be a lot simpler for me to jot down thoughts (done now!).

I had some thoughts recently about where languages could be heading.

Increasingly, it distresses me that so many people I meet who are my age and younger are actively pessimistic about the future. People actually believe that 100 years from now, their children's children will be worse off than we are now. The chief reason for the gloom? Environmental catastrophe. However, it's this pessimistic outlook that so many people have scares me more than any impending environmental doom. When people have no hope, they stop trying to make things better... it becomes a self-fulfilling prophecy. All the worst things seem to be done when people have no hope. The moon landing gave people a good 30 years of inspiration - we need something like that again to inspire us...


Saturday, February 14, 2004

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Wow how time flies. It's been a year since I last updated this page - it hasn't changed at all - but I feel like I have changed a lot! I'm probably going to update this page a fair bit more from now on. I just went skiing in Les Arcs - hence the new picture to the right. More pictures probably to follow... but for now, Me, Tim and Adam (noone really knows why Tim is staring like that - he does this alot) and Adam and Anthony.


Sunday, February 2, 2003

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Compare George Bush's address to Ronald Reagan's address in 1986. Personally, I much prefer the Reagan address. Bush's is so austere - I found the biblical Isaiah reference to be of little "comfort" or "hope". Reagan inspires with "The future doesn't belong to the fainthearted; it belongs to the brave. The Challenger crew was pulling us into the future, and we'll continue to follow them." On the other hand, Reagan also said "We don't hide our space program. We don't keep secrets and cover things up." which ironically looks like a much better description of the NASA of today than the NASA of 1986.


Friday, January 31, 2003

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Someone pointed out that CoWriteOnlyDispatch did not build properly because it was missing some header files. I have fixed this now.


Thursday, January 30, 2003

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I've been re-watching Cosmos by Carl Sagan. 20 years later, it is still simply superb. A grand tour of the state of science, the universe, and our place in it. He doesn't just "inform" - he hypothesizes and wonders about the deepest questions. Inspirational stuff.


Sunday, December 29, 2002

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Well I just got back from spending Christmas in Sydney. Knocks the socks off anywhere else this time of year! Quite depressed to be back in London now with rain and going to work tomorrow. Here is a picture of my Dad and myself just before I flew back. How long do you think the tan will last? ;-)


Saturday, November 9, 2002

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 I have moved to London, UK! Actually, that happened a few months ago - but it is only now that I have finally got around to getting Internet access at home and so had a chance to update this page.


Monday, February 18, 2002

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I just discovered Quines. Pretty cool huh? Here is a quine I've written. It's ANSI C++, doesn't depend on ASCII characters and no line is longer than 80 characters.


Monday, June 18, 2001

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Some of you may have noticed that the ScriptAdapter didn't work when instantiated on top of an out-of-process or COM+/MTS component. Well, it does now.



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