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.

Steve Jobs – An Astonishing Career

Steve Jobs
The best technology CEO since Thomas Edison?

There would always have been more to do. This is a good time for Steve Jobs to depart. Apple is at its peak; both triumphantly successful and wealthy, yet simultaneously admired and even loved. Since the company returned Steve Jobs to his – there is a strong temptation to say ‘rightful’ – leadership role, it has been on an almost unparalleled tour de force.

It began so apparently simply, with products that looked more like quick fixes for the mess he found Apple in than parts of any masterplan. The iMac was in all respects except one an obvious stopgap, an almost desperate attempt to stem the flood of computer users away from the Mac to PC. Make them cheap and paint them bright colours. But stopgap products don’t normally become best-sellers. And more subtly, attractive design revitalised the idea that a computer could be a consumer product.

The diversification into media players too seemed like a quick way to bolster revenues, and yet it evolved into a product that utterly conquered the top end of the phone market. And kept evolving, into one that some say will replace the laptop and the desktop. How the hell does that happen? Whether it was a secret plan of astonishing foresight, or ‘merely’ an extended run of inspired improvisation, virtually everything Jobs touched turned to gold.

In one of those coincidences, I was joking on the phone with my girlfriend yesterday about the news that Apple’s stock was now worth more than that of all the banks in the eurozone combined. (This, on top of having more ready cash than the US government.) I said that gold and Apple shares were the only things people dared invest in now. But what if Steve Jobs resigns? It’ll be like if gold suddenly evaporated.

Will Apple stock plunge? I doubt it, but it will fall some. It has fallen a little already, even though the news only went public after Wall Street shut for the night. Markets are nervous animals. But share price means little to a company that has no need to raise money. What does matter is whether they will continue to be great.

One strongly suspects that the attention to detail in Apple products, the integration of the technical and the aesthetic, is a direct expression of Steve Jobs’ personality. Without that obsession actually in the driving seat, will Apple continue to make great, pioneering products?

For the foreseeable future, I think they will. But somehow it won’t be the same.

Tablets In Court – Continued

As for your “Apple is killing the [tablet] marketplace”, as companies like Palm/HP and RIM are showing: there’s plenty of competition that’s doing fine without toe-ing the copying line.

~ Comment by reader Azijn

Not so much, it seems.

HP have thrown in the towel, after their tablet being on the market for an astonishingly brief three weeks. The world’s largest computer manufacturer doesn’t think it can make its money back on tablets. What chance does a relative minnow like RIM have?

Both HP’s WebOS and RIM’s QNX are – or were – really interesting and attractive operating systems, and it’s true that they’re arguably a lot less similar to Apple’s iOS than Android is. (Though it has been argued by some that they’re a little bit too similar to each other.) But it’s immaterial; only Android has the ecosystem of apps to compete with iOS. For the foreseeable future, there is no other realistic alternative to the iPad.

Samsung have clearly being sailing close to the legal wind – in part perhaps to establish just what can and can’t be copyrighted. It’s interesting legally because many of the laws being invoked by Apple were designed to prevent counterfeiting or passing-off of fake goods. Now clearly Samsung are not passing-off. Their products say ‘Samsung’ on the front in large letters. But they know that Apple have managed to create an aura of sexiness around their products. Is the iPhone the ideal size and shape? Is it the most beautiful design possible? It doesn’t matter; people now want something that looks like that. So to compete, it may be necessary to look as similar as you legally can. Perhaps Samsung will argue in court that consumer electronics is more like the fashion industry now.

But I would be happier to see companies attempting to innovate with Android instead. HTC have tried of course, but for sheer inventive madness I think you have to hand it to their neighbours Asus.

Libya – Beginning Of The Start

Muammar Abu Minyar al-Gaddafi (in Dimashq, Syr...
On the positive side, at least we won't be seeing much more of the world's most failed moustache

Sorry for the absence yesterday. I was helping an 11-year-old jailbreak an iPhone. It seems they still have children here in the future.

And I was also waiting for the full-time result from Libya. It isn’t over of course, in the sense that innocent people haven’t finished dying yet, but the end of the Gaddafi regime does seem inevitable now.

How will we know it’s truly gone? Simple. That’ll be when the rebels start fighting each other. What unites them all, apart from the conviction that Gaddafi could be defeated? Not a lot. Democracy? No one really fights for the opportunity to lose an election.

They’ve already managed to assassinate their own military leader in what was, even in the most charitable view, a factional revenge attack. So that doesn’t exactly bode well.

And even if the Gaddafis are out out of the picture, some of the forces nominally fighting for them will probably be happy to continue the war of their own behalf, and will seek common cause with factions within the rebellion. So in all likelihood we’re now moving from a two-sided war to a multi-polar conflict.

Celebration seems a little premature.

China, The Vatican, And Ireland

Pope Benedictus XVI at a private audience (Jan...
I'll Get You For This, Kenny

This is priceless. Our Taoiseach‘s recent outburst against the Vatican has been taken up by the official Chinese media – which is not really a different thing from the Chinese government – in support of its campaign against the Catholic Church.

What campaign? Well basically, the government think they should appoint Catholic priests, rather than the Catholic hierarchy. Much as they have an ‘official’ Dalai Lama, etc. Ain’t that an interesting idea?

Wow, I really don’t know which way to jump on this one. Much as I think the Vatican should basically not do anything anywhere at all, a state-appointed priesthood is an extraordinarily totalitarian idea.

Well OK, the English invented it. But that was back when England was really very totalitarian. It’s as opposite to the separation of church and state as is possible. On the other hand, I think it would be great if Catholics in Ireland cut ties with Rome.

It’s a power struggle between two quite different yet equally objectionable powers – when I think about, probably the two most powerful absolutist regimes on Earth. And now Enda Kenny is caught in the middle.

Maybe I’ll just get some popcorn and enjoy this one.

The TV Is Watching Back

So a company in San Francisco has come out with a TV that watches you. Via a built-in Internet connection it reports on what you’re viewing and returns Web content that relates to the programme you’re trying to watch, and – for all I know – vice versa.

I should sue.

Western Civilization

That’s from a webcomic I did – in 2003.

My idea was actually a more advanced version of what San Francisco company Flingo is offering. They don’t have a camera built in so that you can participate in the televisual experience. Their offering just monitors your viewing to provide you with information about the programmes you’re looking at, and to provide you with better-targeted advertising. Imagine – targeted advertising! Where’s my wallet?

At least my dystopia rewarded you for being observed:

Western Civilization 2

The strip was called Doubt.It, basically because I’d just bought this web domain and I wanted to use it, but it saw print under its “real” name, Western Civilization. I liked that comic, even if trying to do it every day made for some really crappy drawing.

It’s ages now since I’ve done any comic, when I think about it. Maybe one day.

Democracy Is Over

OECD member states (as of 2006)
Organisation of Economically Crippled Democracies

So those young anarchist protesters ten years ago were right, globalisation did bring devastation and exploitation. Not to the Third World though. It actually turned out to be quite a treat for a lot of people there. In Europe and the US however, it has led pretty much directly to the collapse of democracy.

Globalisation has de-privileged the ordinary people of the West. And by the ordinary people, I mean anyone whose income derives from work rather than from ownership. Increasingly they find that they are in competition for employment not with the people of their own countries, or even with those of other Western countries, but all possible people.

In particular of course, people who aren’t the descendants of generations who fought for better working conditions, better wages, and democracy. Bluntly put, the work conditions and democratic freedoms enjoyed in the West were created when wealthy people needed a great deal of skilled and unskilled labour.

Conditions for the poorest improved suddenly and drastically at only two times during Western history. The first was after the Black Death. That decimated the peasant labourers, but it meant that afterwards there was a shortage of them. They could reject the previous conditions of their employment, which were more or less slavery, and start bargaining.

The second time was in the late 19th and early 20th centuries, when the Industrial Revolution created renewed demand for labour. Conditions in factories were of course horrific at the start when the supply of poor people exceeded the demand, but that turned around and labour was able to organise and gain much safer conditions and better wages. Ultimately, it gained political representation and universal suffrage.

Easing up conditions of trade with the rest of the world has completely undermined the position of the workforce – right up to the most skilled. Yet at the same time it has created new opportunities for business. With plunging labour costs, profitability has generally soared. But the tax base of most Western countries is not the wealth of business owners. To say the least, these are the people who can afford not to be taxed. They can afford the accountants. They can afford the lawmakers. So the tax base is collapsing. The countries of the West are simply running out of money, one after another.

But what can we do? It seems too late to introduce protectionism. The only option is to extract more money from the people who profited by exporting jobs – the corporations, and in particular the super-rich personally. But all the major political parties clearly do not dare to, they are helpless in the face of wealth.

Welcome back to serfdom.