January 17, 2006

Consider a spherical cow, covered in resistors

(Anybody who didn't take an A-level in Physics may as well switch off now. Any readers who sat next to me throughout A-level Physics lessons may wish to consider that it might be their fault I wasn't paying enough attention to be able to work this out. ;-) )

This question's been bugging me for days. I did have an answer, but after a spot of googling showed me I was wrong, I realised I was talking rubbish.

Imagine, if you will, a flat square grid of points, such that every point is connected to the 4 adjacent points by a 1Ω resistor. The grid extends infinitely in all directions. What is the resistance between 2 points on the grid a knight's move apart? (e.g. 2 squares up and 1 across, WLOG) Or, for a simpler starter question, what about between 2 points diagonally adjacent? Or even just 2 adjacent points? (Is that as simple as just 1Ω? My hunch is no.)

Maybe I've missed something while googling for answers to this, but if anyone has a good solution I'd be very interested to hear it! Just to clarify, I have some numerical answers from googling, but I'm far more interested in how they're arrived at than what the actual numbers are.

[Update: Chris has considerably better google-fu than me, and found a solution for the diagonal case. It contains hard maths that I can't really justify spending the time to get my head around in the middle of exam season, alas. There's a paper with even more on this too. Eek!]

Posted by James at 22:59 | Comments (0) | TrackBack
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September 11, 2005

Drink-sodden Armageddon

In a smidgeon under 3 months time, the law in the UK regarding licences to sell alcohol, to put on various forms of entertainment, and to sell hot food/drink after 11pm (late night refreshment) will be changing. The 6 separate current licensing schemes will be brought under a single banner, and in the process the current statutory limits on when a licence to sell alcohol can apply will be relaxed. This isn't to say a licence won't be needed (it certainly will), or that licences will all be 24-hour (they most certainly won't!), but there will be the potential for 24-hour drinking across the UK. Which for some reason has upset people.

Admirable as upsetting the Daily Mail editors might be, it's slightly scary to think that we might be plunging towards a drink-sodden Armageddon. But are we really? Lots of other European countries trust their citizens with the right1 to drink alcohol at just about any time of day they choose, after all, and we're told they don't suffer from our "yob culture" — I suppose the question is, do we need a shift in our culture before we can have late night drinking, or do we need late night drinking before we can have a shift in our culture? And if it's the former, how else do we go about causing this change?

I personally don't think people in general will drink more at a time, more frequently, or more in general, under the new licensing regime. What they will do is get just as insanely drunk as now at a bigger variety of times to normal (making them easier to deal with?), and perhaps start their nights out later. People also won't feel rushed to squeeze as many pints in as possible between the end of Eastenders and last orders, so we should see fewer people getting drunker than they planned, and fewer people throwing up outside pubs/takeaways. Bonus!

The "late night" part of the new licensing rules is just one aspect of the act, anyway. More significant to me is the reduction in bureaucracy for places that currently need multiple licences, and the introduction of distinct "personal" and "premises" licences, which makes sense in a whole bunch of ways, and ought to save licensees a whole bunch of court appearances in the future. For one thing, anyone working for a pub chain as a "relief manager" will simply be able to have a personal licence, and be the Designated Supervisor for any premises in the chain whenever they need to be. At present, I understand every relief manager would need to make a court appearance to be made the temporary licensee at the new premises every time they went to a new pub, although I'm willing to stand corrected on this one.

Some new licensees will face significant problems of course, since currently kebab shops and burger vans don't need a licence to operate at night, and will soon need one to sell anything hot after 11pm. The reasons for introducing these requirements (as explained in that article) are pretty sound, though.

Something else those complaining about the new laws don't seem to realise is that people can already drink until silly hours of the morning if they so decide — pubs I've worked in have had "lock-ins" previously which extend well beyond the hours they've applied to extend their licence to under the new regimes. I can think of at least 2 pubs locally where drinking to 3am or so isn't unheard of, but I can't think of any that have applied for a licence beyond 2am. I suppose some nightclubs in the city centre may have applied for more hours.

So to conclude, the new licensing laws will piss off Daily Mail editors, reduce city centre violence, reduce occurences of vomiting on pavements near pubs, shut down dodgy backstreet kebab shops, regulate the surviving ones better, and allow people to drink legally later avoiding the need for things like lockins, while reducing paperwork for publicans. Sounds good to me.

1 I don't mean to imply that 5am-drinking is some kind of fundamental human right, here, just that some countries allow their citizens to do it.

Posted by James at 23:05 | Comments (4) | TrackBack
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July 01, 2005

Without letting slip

Suppose I were to create an anonymous blog somewhere. How would I go about promoting it, without letting slip that I was associated with it?

Answers on a postcard!

Posted by James at 02:38 | Comments (2) | TrackBack
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June 23, 2005

Wary of editing

Does anybody know what's going on with Zempt? Their roadmap says they want Linux support in version 0.4, but that was released in November last year, and I can only see a Windows version on the download page. The site doesn't seem to offer a lot in the way of contact details, either, except for some crappy web forum. Hope they check their referrers!

I've installed gnome-blog, but it doesn't seem to be particularly clever, lacking any kind of preview facility or understanding of textile markup. I'm wary of editing entries directly in the MT interface at the moment, because firefox is crashing on me a lot at the moment. And of course, Zempt isn't available on my platform.

So, my other question is this: what do other people use to post to their weblogs, if not web interfaces, Zempt, or gnome-blog? Answers which work with MT3 and run under Linux are particularly appreciated :-)

Posted by James at 01:57 | Comments (3) | TrackBack
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March 01, 2005

Budget laptops

My laptop, emerald, is dying. The screen isn't very well connected to the graphics card any more, the case is flaky, the keyboard ropey, and the battery completely useless. It's going to get replaced. Luckily, I have in the region of £700 kicking around ready to spend on a replacement...

An iBook, through the Apple Higher Education Store, will cost me £681 with a 60GB drive, 12" screen, 256MB RAM and bluetooth module, plus I'd want to some extra memory (£27 from Crucial for 256MB extra). But I'm wary about buying into the whole Apple thing, and so I'm wondering if there's anything in the current x86 world that would serve me as well.

So my dear readers, the question is this: where can I get an x86 laptop for no more than £700, which won't fall apart within 2 years, is designed to be portable rather than a mostly-static "desktop replacement", and will happily run an OS other Windows? Built in wireless stuff would be nice, too, although I imagine that's standard these days...

Answers on a comment :)

Posted by James at 17:14 | Comments (9) | TrackBack
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