August 14, 2008 at 3:30 pm · Filed under mathematics, vimeo
I’ve got say it. At first I thought this was pretty cool.
Then I thought that theres almost no real use for it.
In the end I can see some limited use, but not to justify the amount of effort taken to do it. Sorry, hang on, you need to watch this first.
or watch it on vimeo.
Ok, so the gist of it is that you can use a few well placed high quality photographs to increase the resolution and dynamic range of low quality videos. Sounds great right?
Well, yes, but only when you think about the cases it uses. Basically tracking shots of static things, taken in low quality video, like the kind of video an average digital camera takes. So you then take a few still shots of the scene to boost the resolution.
Great, but just why would I do that? Almost the whole reason for taking quick videos like that is not to show a simple scene, but some action that you can’t get with a still shot.
So in review, I would give it about a B-, good effort, but honestly come on guys, not really that useful, though I don’t doubt some of the maths would be very interesting.
More on it here.
April 15, 2008 at 11:36 am · Filed under mathematics
This is in reponse to this xkcd comic.
So what are friendly numbers? Lets do this quick.
We need first to get define a divisor function over the integers, written σ(n) if you’re so inclined. To get it first we get all the integers that divide into n. So for 3, it’s 1 and 3. For 4, it’s 1, 2, and 4, and for 5 it’s only 1 and 5.
Now sum them to get σ(n). So σ(3) = 1 + 3 = 4, or σ(4) = 1 + 2 + 4 = 6, and so on.
For each of these n, there is something called a characteristic ratio. Now that’s just the divors function over the integer itself ( σ(n)/n . So the characteristic ratio where n = 6 is σ(6)/6 = 12/6 =2.
Once you have the characteristic ratio for any integer n, any other integers that share the same chacteristic are called friendly with each other. So to put it simply a friendly number is any integer that shares its characteristic ratio with at least one other integer. The converse of that is called a solitary number, where it doesn’t share it’s characteristic with anyone else.
1,2,3,4 and 5 are solitary. 6 is friendly with 28. ( σ(6)/6 = (1+2+3+6)/6 = 12/6 = 2 = 56/28 = (1+2+4+7+14+28)/28 = σ(28)/28.
You may be now be thinking the following:
- That’s all well and good, but what are they good for?
- Who cares?
So what are they good for?
I dunno. But it’s interesting no? Actually while on the face of it, it all seems quite straight forward it quickly becomes far more complex than you would think.
Some numbers are easily proved to be solitary. Other’s we know to be friendly. But my-o-my there are alot more we don’t know. I mean look. Here is the complete list of friendly numbers we know about. And I mean COMPLETE.
6, 12, 24, 28, 30, 40, 42, 56, 60, 66, 78, 80, 84, 96, 102, 108, 114, 120, 132, 135, 138, 140, 150, 168, 174, 186, 200, 204, 210, 222, 224, 228, 234, 240, 246, 252, 258, 264, 270, 273, 276, 280, 282, 294, 300, 308, 312, 318, 330, 348, 354, 360, 364, 366, 372
That’s it. What about 10, 14, 15, or 20? Don’t know. Infact it’s on the list of unsolved Mathematical problems at wolfram. Doubt there’s a cash prize involved but why not give it a go. It’s harder that it looks.
Wow.
Well done. You read all the way to the end. To give you a treat I present this lovely video. It’s a visualization of Lovely Head by Goldfrapp. Yes it’s got lot’s of maths in. No it doesn’t have anything to do with friendly numbers.
Or even better, watch it in hd.
If you were wondering. No. I didn’t just get this all off the top of my head. You can read more about friendly numbers at wolfram, or wikipedia, and here is where the full list of friendly numbers came from. Personally I find amicable pairs more interesting but then, who really cares about that?
March 31, 2008 at 9:34 pm · Filed under random
Isn’t tea just great?
..
Oh go on then, if you’re making one.
So, what have you been up to?
..
Really? 6ft and blue you say? Wow. That’s just amazing. And unexpected.
I’ve been busy too. New work, new laptop, new kitchen, new favorite mug. This mug’s a slightly darker shade of blue, fits about 24% more brew, and the handle is slightly larger for a firmer and more satisfying grip.
Oh and I’ve been drawing. Just doodles really, but some of them are ok.
There’s more but hey, I’m not a walking internets gallery. Get your own badly scanned drawings and keep you’re cursor off mine.
But where’s that tea you were talking about? Mine’s the dark blue mug.
January 15, 2008 at 4:22 pm · Filed under random
Hey, comics are great right?
Well how about a comic every hour. I know. What a great idea.
Heres today’s hourly comics.
Seriously a comic every hour you’re awake for the whole month of january. How good is that?
Check them all out at suitablyamused.com
November 27, 2007 at 10:29 am · Filed under random
From the look of these shots, the new Watchmen movie is going to be brilliant. And I mean that in the most fully sense of the word. Yes, the movie won’t have the depth of the book, but my word, it looks like its just been pulled off the page.
If you havn’t read Watchmen yet I can’t recommend it enough. If you really ask nice I’ll even lend you my copy.
Its got everything, right down to the posters on the news stand behind the comic book fan.
I love the way each shot seems full of detail, just like the novel, enough so that you can spend ages just noticing tiny details. Anyway, long story short, buy the book now before the movie comes out.
October 25, 2007 at 3:11 pm · Filed under code
Here is an excellent article by Joel Spolsky on 5 ways to make a project fail.
I happen to particularly agree/like this from point 5:
Software development takes immense intellectual effort. Even the best programmers can rarely sustain that level of effort for more than a few hours a day. Beyond that, they need to rest their brains a bit, which is why they always seem to be surfing the Internet or playing games when you barge in on them.
So next time you see me playing a game of surfing the of internets, give me a break, it takes immense intellectual effort. Honest it does.
