Mathematical Cabbage

Math - It's what's for dinner
Math – It’s what’s for dinner

It’s not every day you taste a new vegetable. Especially not one that defies the laws of space and mathematics. But yesterday I found just that at our local organic farm, Green Earth.

They have some exotic stuff there from time to time, even new potatoes that taste like – and I know this is hard to believe – new potatoes, but I was taken aback to see that they had fractal florets, chaotic kale, or to give it a name people actually call it, romanesco broccoli.

Fractals are a phenomenon of nature of course, and you come across them in things from fern fronds to snail shells. But you rarely see them so clearly in three dimensions. Or I should say, more than three. Imagine a wiggly line drawn on paper. It’s an idealised line, so it has only one dimension – length without width. Now we zoom in. Normally when you do that, the section of line you focus on will look straighter than the whole wiggle because you’ll see fewer twists and turns, or even none. But our line is strange. We find that when magnified it still looks every bit as wiggly as it did on the larger scale. It has wiggles within wiggles, smaller-scale twists and turns in between the big ones. This is called self-similarity, and it too is a natural phenomenon. A coastline is still wiggly whether you see it from space or look at where the water meets the sand through a magnifying glass.

If the line is more wiggly than it looked from a distance, that means that it’s also longer than it looked. So if you could somehow keep looking closer and closer forever, you’d find it was always longer. Isn’t that a bit weird? It’s just a line on a finite, two-dimensional sheet of paper, yet somehow it’s infinitely long. That leads to the idea that shapes like this wiggly line, similar on all scales, must somehow be more than one-dimensional – though still less than two. It’s one-and-a-bit-dimensional. Fractionally dimensional. Fractal.

Just as there are wiggly lines that are a bit more than one-dimensional, there are flat patterns that exist in more than two. And there are solid objects – like the romanesco in my hands – that occupy more than three. Of course it doesn’t really extend into some invisible extra space.  The fraction of a dimension is just a clever way of quantifying the self-similarity. Yet looking at it, I feel like I’m wearing 4D classes¹. The symmetrical complexity is fascinating and beautiful. Its spires are made up of spirals made up of spires, spiralling into spire upon spiral spire. Whorls within whorls. Amen.

And gently steamed for about fifteen minutes, mathematics is delicious. Especially organic mathematics.

  1. One red lens, one blue lens, one green lens.

An easy intro to fractals.

And Now For Some Random Facts

Huge ocean sunfish (mola mola) at Outer Bay ex...
In German, the sunfish is sometimes known as Schwimmender Kopf, or "swimming head"

Jell-O is the official state snack of Utah. This is the sort of thing you could make up and people would believe it, but in this case it happens to be true.

Vegetables and fruit served in savoury jelly is sometimes called “congealed salad“, possibly the worst name ever given to something you expect another human being to eat.

Jell-O and other brands of jelly are made of collagen extracted from the boiled bones, connective tissues, organs and some intestines of animals such as cattle and horses. Though contrary to popular belief, there are no hooves in it.

So that’s a relief then.

Ulysses

Was fixing someone’s e-book reader, so for the day that’s in it I put on a copy of Ulysses. I’ll be surprised if he actually reads it on his Spanish holiday of course, but at least I committed larceny against the Joyce estate, something I feel is all our duty. This is the last chance in fact as next year the work will finally be free from copyright, which will take the fun out of it.

On the other hand it may help bring an end to the Great Ulysses Wank, the interminable argument about what is the one true and sole definitive version of a fictional work much revised by the author himself. This quote from Wikipedia should give you the flavour:

According to Joyce scholar Jack Dalton, the first edition of Ulysses contained over two thousand errors but was still the most accurate edition published. As each subsequent edition attempted to correct these mistakes, it incorporated more of its own. Hans Walter Gabler‘s 1984 edition was the most sustained attempt to produce a corrected text, but it received much criticism, most notably from John Kidd. Kidd’s main theoretical criticism is of Gabler’s choice of a patchwork of manuscripts as his copy-text (the base edition with which the editor compares each variant), but this fault stems from an assumption of the Anglo-American tradition of scholarly editing rather than the blend of French and German editorial theories that actually lay behind Gabler’s reasoning.

I can actually hear the skin-on-skin fiction.

 

The Brain – Your Body’s Attic Space

Modified version of an image originally upload...
That's Where I Left My Keys

So I’m working through the wreckage of my past, found dumped in a dozen broken cardboard boxes. This is a fascinating process for me because basically I have no memory. I’m not an amnesia victim, I’ve never had a traumatic brain injury. Well you know, as far as I can say. I just don’t remember things much. This leads to strange revelations, like coming across a comic strip that I have no recollection of seeing before, but which was quite clearly written and drawn by me. The old made new. What’s especially great is if one of these actually makes me laugh.

It’s all right to laugh at your own jokes when you don’t remember being the person who made them.

God my drawing used to be awful though. Stupid I know, but it gets me down. I know I am not by any means a good artist now; my drawing is merely adequate to the task, but I don’t mind that. And it’s not the fact that I wasn’t any good as a child. Why would I be? What’s depressing is that I thought I was.

Seems I really was a fairly bright kid though. I came across a Mensa entrance test that I’d taken but never submitted. Yeah, I considered applying to Mensa once. But then I figured, it’s a club that admits the smartest two percent of the population. Why slum it?

Also there was the small matter of a fee. I looked through it again. Some questions seemed pretty damn difficult even to adult me. In fact I’m not sure if I’d do any better now than I would’ve at fourteen.

Which is also depressing.

I thought I would reproduce one of the questions here. I think I know what the answer is meant to be, but I’m not completely sure there isn’t more than one solution:

In my aquarium I have all together in the same tank (1) garpa fish, which will eat both tennel fish and eels, (2) tennel fish, which eat eels, and (3) eels, which will feed on the dead bodies of garpa fish. The tennel fish can swim much too fast to be caught by the garpa fish, even in a tank. If no other food is given, which will be the last kind (or kinds) of fish left alive in the tank?

  1. Eels.
  2. Garpa fish and tennel fish.
  3. Tennel fish.
  4. Garpa fish.
  5. Tennel fish and eels.

Answer that, and you might be Mensa material. Though do bear in mind that the word means ‘table’.

The Future Called Me On The Phone

The drawing to the right could use a little explanation. No, it doesn’t actually make any sense. Yes, that is a pink rabbit staring at the sun for absolutely no apparent reason. It’s just a random doodle, and it has to be admitted, a pretty crappy one.

What distinguishes it is the fact that I just drew it on my phone. I can’t quite believe it; to get a pen-like line like this on any electronic device would be impressive enough. Yet even a first attempt compares well to drawings on this blog done with a high quality graphics tablet.

But to be able to do that on a device I can carry around in my pocket – a device I can also use to edit and publish the drawing to the web, and make phone calls sometimes, well to me it’s a dream come true.

Have you guessed what it is yet?

More Art, More Science, More Egypt

The Science Gallery
It's This Shape On The Inside Too

I worried I was unfair to Dublin’s Science Gallery so I went back. I’m glad I did, because I was. There is actually a second floor to the place, it was closed because the exhibition was not completely mounted when I wandered in.

I do have my questions about the art on display in the ‘Visceral‘ exhibition, but that’s no bad thing by any means. I urge you to see it for yourself, there’s thought-provoking stuff there. Thought-provoking as in machines guided by rat neurons and bacterial colonies growing into pictures, so it’s well worth arguing over whether it is art, science, or a load of toss. But I’m glad it exists.

But Back To Egypt

Just a couple of hours ago, Egypt swore in the head of the intelligence services as Vice-President. That hardly seems like a move towards a more democratic government, but it may be a way to transition from Mubarak’s rule with the minimum possible fuss.

It could also be seen as the introduction of military dictatorship in all but appearance, with the army’s man rather than a general in uniform taking the helm. It’s inevitable that the military will be power brokers here; just about everything depends on whether they accept the legitimacy of Mubarak’s orders. The next question is whether the military will then support a transition to democracy. There is the possibility that they would simply create a new dictatorship, and tell the people and the rest of the world that we have to support it or the Islamists will take over.

If we accepted that, we’d be betraying the people of Egypt. This is not an uprising in favour of Islamic rule – and certainly, not of military rule. It’s a rejection of oppression, and it’s up to us in democratic countries to demonstrate to the Egyptians that we too are against oppression.

We are, aren’t we?

Science In A Gallery Or Art In A Lab?

Exhibit
Science + Art = Weird Stuff in Jars

So I’m in Dublin’s Science Gallery, a worthy but slightly disappointing project. Passing by, you see it has a cool looking café section jammed into a wedge-shaped window on Pearse Street. That must be part of an interesting place, you think. On going in though, you find that the part is the whole¹.

It has exhibitions, yes. I didn’t warm to the one that’s on right now though. Called Visceral, it uses things out of labs for artistic purposes. Tissue cultures, tubes. It seemed to me less science than cyberpunk. According to blurb, this was “challenging work at the frontier between fine art and biotechnology and forms a series of provocations and puzzles around the nature of the living and non-living”. It sounds like exactly the sort of thing I would find fascinating, but I didn’t even feel particularly intrigued. Possibly I just didn’t find my way into it. I haven’t been in much of a mood to explore the interface between art and biotechnology since I quit drinking.

Maybe the disappointment of the place itself put me into a negative mood. I feel like I should be in favour of the thing, it’s just… The title ‘Science Gallery’ had me expecting more. A science museum of sorts, I suppose. Wonders.

Transparent Horse
Horse Inside

What must be said for it though is that it has probably the best gift shop in Ireland. The perfect place to find an unusual present. What do you give to the person who has everything? A transparent horse, of course. Other lovely things included magnetic tape that actually is tape that’s magnetic, Rubik’s cube salt and pepper mills, and great books including a healthy pile of Ben Goldacre’s Bad Science.

Also it’s one of the rare stockists of Sugru, the multi-purpose polymer beloved of “makers” and other hardware-hacking types. It’s a silicon-based substance that can be moulded to any shape, will adhere to many smooth surfaces, and sets with the texture of tough but yielding rubber. That makes it particularly suitable for human interface things. The name comes from an Irish word for “play”, and I can’t wait to start playing with it myself. My portable hard drive is about to become rugged. And weird-lookin’.

  1. I was quite wrong about this – see here.