Archives for April 2012

April 2012 (8)
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Visualizing four million digits of pi

I came across this remarkable image a couple of days ago. It shows four million digits of π encoded as colored pixels, with one pixel per digit. Each digit has a slightly different color. The page also allows you to search for digit strings up to six characters long and the page will find them in the image, if, of course, the string is there. This raises a couple of questions. The first one is this: given that π expressed as a decimal is infinitely long, can you find any digit string in it...

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“The Islanders” by Christopher Priest

While we were away last week in Paris for the Marathon, I finished The Islanders , a novel by one of my favorite authors, Christopher Priest. Well, actually, I find it hard to call it a novel. It is novel certainly, but a novel? To call it so might imply that it has some kind of plot and a protagonist who changes and learns throughout the story. Instead The Islanders is something way more. First of all, it is structured as a gazetteer, a guidebook to the Dream Archipelago, a belt of islands that...

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More TVM–calculating the IRR

My insurance company allows me to pay for our car insurance by monthly premiums instead of the usual premium once every 6 months. For this option, they just divide the total six-monthly premium by six to give the monthly premium, and then charge a $5 “processing fee” per month on top. I decided to take a look at how much this actually cost me. (For background on the Time Value of Money – TVM – see parts 1 and 2 .) Let’s say, for sake of argument, that our total car insurance...

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Fake magazine renewal notice

As a household, we subscribe to a few magazines. Hence we get renewal notices for those magazines regularly, and, the magazine subscription industry being what it is, we usually get two or three renewal notices per magazine subscription. On average maybe a couple per month. All well and good, no problem. In today’s mail I got this renewal notice for The Economist : The only issue is I do not actually subscribe to The Economist . I did, a few years ago, and liked it, but I never really found time...

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A birthday shock

Today is my birthday. For the first time ever, my sister Nicola sent me a text to say Happy Birthday. Yay for modern technology, especially international texting of birthday wishes from England. Her sending me a text wasn’t the shock though. The shock was the previous texts displayed on the timeline: the last time she texted me was when Mum was dying in hospital two years ago. So yeah, yay for modern technology. Especially the fact that I still have texts from two years ago saved on my phone. Sigh...

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Tightening the feedback loop when writing LaTeX expressions for MathJax

A couple of my recent blog posts have been about the Time Value of Money ( one , two ). They’re full of mathematical expressions, but I was tired of writing these expressions out in Microsoft Word’s equation editor, taking a snapshot of the result, and inserting the result as an image in the post. Instead I decided to try out MathJax , a quite remarkable JavaScript library that renders math expressions at run-time in the client. The big problem that I had was writing expressions in LaTeX...

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PCPlus 305: How your operating system works

OK, I’ll admit it. This one is dead weird. Even when writing it, I wasn’t quite sure where I was going with it so it turned into this essay on what happens when you boot a PC and why the BIOS is antiquated beyond belief. I then threw in a bit about memory management and file systems. I guess you’ve just got to read it to, er, gain the full perspective. I think it’s something I’d have enjoyed reading back in the 90s, but nowadays it’s appears dated. But then, the BIOS is very dated and we’re still...

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Time Value of Money (part 2)

Last time we discussed that money has a time component to it, that it changes value with time. We derived the basic formula for TVM ( Time Value of Money ): \[ P_N = P_0(1 + i)^N \] That is, the future value (FV) after N periods is equal to the present value (PV) multiplied by a geometric factor depending on the interest rate. Let’s explore. Suppose you went to a bank and said you wanted a $1000 loan repayable in one payment after a year. The bank offers you 6% per annum. How much would your...

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