Friday, August 13, 2004

More number theory

As the previous post demonstrates, I'm a bit like John Derbyshire. I love mathematics, but I'm not really very good at it. I'm a mathematician manqué. Don't get me wrong: I obtained a good degree in a highly mathematical subject from a very well-regarded university (2:1 Honours Physics, Imperial College, London, 1992), and a higher degree in Electronic Engineering (M.Sc., RF and Microwave Comms Engineering, Bradford, 1994). I have enough grasp of market microstructure theory to be dangerous. But a mathematician I am not. And, oh God, I wish I were. My mathematical knowledge merely enables me to see how badly I suck at maths. If Newton saw further because he was standing on the shoulders of giants, I see further because I am a spider mite clinging to Newton's eyelash.

As the previous post demonstrates, I'm a bit like John Derbyshire. I love mathematics, but I'm not really very good at it. I'm a mathematician manqué. Don't get me wrong: I obtained a good degree in a highly mathematical subject from a very well-regarded university (2:1 Honours Physics, Imperial College, London, 1992), and a higher degree in Electronic Engineering (M.Sc., RF and Microwave Comms Engineering, Bradford, 1994). I have enough grasp of market microstructure theory to be dangerous. But a mathematician I am not. And, oh God, I wish I were. My mathematical knowledge merely enables me to see how badly I suck at maths. If Newton saw further because he was standing on the shoulders of giants, I see further because I am a spider mite clinging to Newton's eyelash.

Thursday, August 12, 2004

Number theory

I had a bit of fun last night coming up with descriptions of numbers, such as 'smallest fourth power [of integers] greater than unity', sixteen in other words. In mathematics these are known as 'exceptional numbers i.e. they have some property that is not shared with any other number. There's a nice little reductio ad absurdum proof that there's no smallest exceptional number: if there were, it would be exceptional.

But here's a real kicker. If we generously allow one to be a prime number, then I have seen it written that the modulus of all primes mod 24 is prime. Is this true? I've verified it in Mathematica* for the first million primes, i.e. from 2 to 15 485 863, but is it true for all primes? If so, twenty-four is a truly exceptional number.

*I dd this, talk about naive:

pt = Table[{Mod[Prime[i], 24], PrimeQ[Mod[Prime[i], 24]]}, {i, 1, 1000000}];

Select[pt, #[[2]] == False && #[[1]] != 1 &]

I had a bit of fun last night coming up with descriptions of numbers, such as 'smallest fourth power [of integers] greater than unity', sixteen in other words. In mathematics these are known as 'exceptional numbers i.e. they have some property that is not shared with any other number. There's a nice little reductio ad absurdum proof that there's no smallest exceptional number: if there were, it would be exceptional.

But here's a real kicker. If we generously allow one to be a prime number, then I have seen it written that the modulus of all primes mod 24 is prime. Is this true? I've verified it in Mathematica* for the first million primes, i.e. from 2 to 15 485 863, but is it true for all primes? If so, twenty-four is a truly exceptional number.

*I dd this, talk about naive:

pt = Table[{Mod[Prime[i], 24], PrimeQ[Mod[Prime[i], 24]]}, {i, 1, 1000000}];

Select[pt, #[[2]] == False && #[[1]] != 1 &]

Under construction

Boy, do I have some work to do to get this thing shipshape. For a start, I need to completely reconstruct my blogroll. Fortunately I hacked together a little PHP/FrontBase SQL thingy a year or so back in which I maintain my favourite blog links. 'Twil be but the work of a moment to adapt it to spit out HTML that I can paste into my template.

Boy, do I have some work to do to get this thing shipshape. For a start, I need to completely reconstruct my blogroll. Fortunately I hacked together a little PHP/FrontBase SQL thingy a year or so back in which I maintain my favourite blog links. 'Twil be but the work of a moment to adapt it to spit out HTML that I can paste into my template.

Rio Torres Valley

I'm testing Blogger's photo capability. This is a test of Blogger's interaction with a service called flickr. Seems to work pretty well.

Anyway, this picture is a pretty good illustration of why I enjoy living in Costa Rica. It's a view across the Rio Torres valley towards the highway leading to Alajuela (one of Costa Rica's major towns). It was taken about twenty meters from my front door. My living room, which has a 4.5m × 2.5m picture window, looks out over this scene as well. As the Prof says, if you don't carry a digital camera with you, you might as well not have one. I always carry my Canon Powershot S110. I don't smoke, so the ultra-compact Elph form factor of the S110 takes up the same room in my pocket that a packet of cigarettes would. It's 2.1 MP, which is ample for web work. I love it.

Anyway, this picture is a pretty good illustration of why I enjoy living in Costa Rica. It's a view across the Rio Torres valley towards the highway leading to Alajuela (one of Costa Rica's major towns). It was taken about twenty meters from my front door. My living room, which has a 4.5m × 2.5m picture window, looks out over this scene as well. As the Prof says, if you don't carry a digital camera with you, you might as well not have one. I always carry my Canon Powershot S110. I don't smoke, so the ultra-compact Elph form factor of the S110 takes up the same room in my pocket that a packet of cigarettes would. It's 2.1 MP, which is ample for web work. I love it.

Where was John Edwards?

I posted this over at the excellent Tim Blair's and am shamelessly recycling it here:

Never mind what Lurch was doing in his dinghy in the Mekong in 1968. The question that the Leftist media have failed to ask is, where was John Edwards? Huh? Huh? Was he in the shit? Was he in the 'Nam, hunting Charlie? Nuh-uh. My sources say he was hiding out in the Piedmont in South Carolina, dodging the draft by enrolling in some organisation known as 'Junior High' (is that a drugs reference?)

I posted this over at the excellent Tim Blair's and am shamelessly recycling it here:

Never mind what Lurch was doing in his dinghy in the Mekong in 1968. The question that the Leftist media have failed to ask is, where was John Edwards? Huh? Huh? Was he in the shit? Was he in the 'Nam, hunting Charlie? Nuh-uh. My sources say he was hiding out in the Piedmont in South Carolina, dodging the draft by enrolling in some organisation known as 'Junior High' (is that a drugs reference?)

Yummy

If Stephen Green can post cocktail recipes then so can I. This is a much cheaper long drink version of God's Own Cocktail, the Kir Royale:

I am swigging one right now, and all is right with the world.

If Stephen Green can post cocktail recipes then so can I. This is a much cheaper long drink version of God's Own Cocktail, the Kir Royale:

3 oz crème de Cassis

3 oz good Vodka (Stoli Blue for me)

large highball, sugared rim, three or four large ice cubes

Fill to top with tonic

Garnish with a couple of fresh Morello cherries if you want to impress a date

I am swigging one right now, and all is right with the world.

The more you know

Something that just drives me nuts: those 'the more you know' segments that NBC incessantly runs. "Hey, parents, don't teach your kids to be racists!" "Make sure you know what Internet sites they're visiting!" Patronising bunch of wankers.

Something that just drives me nuts: those 'the more you know' segments that NBC incessantly runs. "Hey, parents, don't teach your kids to be racists!" "Make sure you know what Internet sites they're visiting!" Patronising bunch of wankers.

Dennis Miller

I just caught the Varsity segment with Michelle Malkin on Dennis Miller's show. The three panellists were all fairly sensible, although Peter Roff made a bit of an ass of himself by criticising Michelle Malkin's book when he clearly hadn't read it. The real eye-opener, however, was that Michelle is even more beautiful than I had imagined. Simply stunning. Why does the right get all the hotties these days?

I just caught the Varsity segment with Michelle Malkin on Dennis Miller's show. The three panellists were all fairly sensible, although Peter Roff made a bit of an ass of himself by criticising Michelle Malkin's book when he clearly hadn't read it. The real eye-opener, however, was that Michelle is even more beautiful than I had imagined. Simply stunning. Why does the right get all the hotties these days?

Hangover, *moi*?

Did I really drink 17 beers last night? Yeppers. Did I feel dreadful this morning? Nope. Leapt out of bed as if rocket-propelled.

Did I really drink 17 beers last night? Yeppers. Did I feel dreadful this morning? Nope. Leapt out of bed as if rocket-propelled.

Wednesday, August 11, 2004

No more tonight? As if!

Anyway, it transpires that turning my recalcitrant fridge to nine was sufficent to make sorbet out of my collection of Nipponese beers. No matter. They remain abundantly tasty even if turned into Slushies.

Anything substantive? Perhaps. Check this:

I'm a scientist, of sorts, so I know that anecdotal evidence is highly suspect. But I live in a country that prides itself on not having an army, on being as unbelligerent as they come. I have heard nothing but anti-Kerry sentiment this evening. The predominant criticism seems to be that he is a waffler. I don't sense any strong pro-Bush sentiment (quite the opposite at times), but Kerry is simply failing to energise his core supporters. OK, so this isn't the States, but we have a very large US population here and as far as I can tell, most people I know are broadly sympathetic to Democratic ideals but will vote GOP anyway, or more likely abstain. Bear in mind that this

Um, yeah, by the way, that

Musings from Costa Rica

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