Alexandrov said [pdf] of their relationship:
“in 1979 this friendship celebrated its fiftieth anniversary and over the whole of this half century there was not only never any breach in it, there was also never any quarrel, in all this time there was never any misunderstanding between us on any question, no matter how important for our lives and our philosophy; even when our opinions on one of these questions differed, we showed complete understanding and sympathy for the views of each other.”
No quarrels, no misunderstandings, complete understanding and symapthy for 50 years…. that really sets the bar for the rest of us.
One issue which is often discussed is sensationalism. By having racier, more exciting stories than their rivals, a newspaper or TV channel hopes to attract a bigger audience. And of course it is audience size, rather than accuracy or quality of output, which measures success. So dramatic stories are privileged over dull-but-worthy ones, and everything must be dressed up to seem as spicy as possible.
I exaggerate, perhaps, but the process is well known and much analysed. But there is another, deeper phenomenon, at play: Harrabin’s law. It doesn’t depend on the cynicism of the press, but begins with the observation that news, definitionally, has to be new. So commonplace or ongoing situations are unlikely to be included. Conversely, the more uncommon an event is, the more newsworthy it is. So rather than providing a summary of the state of the world, the news represents a daily freakshow of uncommon occurrences. It is, by its very definition, utterly unrepresentative of people’s wider experience.
I was impressed by this idea, because it gives a simple causal mechanism whereby many important facts about the world go unreported, for the very reason that they are happening all the time. So newsdesks prioritise rarities such as train and plane crashes over the daily carnage on our roads. Serial killers and terrorists get top billing, while domestic violence chunters along below the radar. The Congalese war, which has been raging for over a decade, claiming millions of victims, makes the news so rarely that many people remain unaware even that it is happening. Meanwhile skirmishes in previously peaceful regions are guaranteed headline status. Deaths due to ecstasy are reported; those due to alcohol are not. How could they be? After all, they are happening constantly. But it is in knowing the things which are happening day in day out which gives us a truer picture of the world we live in.
As you might expect, Harrabin’s law has political consequences. Firstly, it distorts people’s perception of risk. The classic example is the person who is terrified of flying, but thinks nothing of driving to work daily. But it isn’t just at the individual level that problems occur. Terrorism is a rarity in the UK, and therefore by Harrabin’s law, it gets reported and discussed a great deal. Hence, governments are under immense pressure to act using any resources necessary. How domestic violence could benefit from the same media exposure! (Of course, if it hardly ever happened, then it would get it.)
The implication seems clear: we don’t need news. What we need is importants. (Of course the two may sometimes coincide.) As for how to bring this revolution about, and how to decide what qualifies as important and what does not… well, I’ll leave that to another day.
Dick Lipton has an interesting post about the history of mathematical notation, and how it affects the thinking of those who use it. During the discussion he references a mathematician I had never heard of, one “Johann Gauss”. Well, it turns out that was indeed the great man’s name!
UPDATE: it occurs to me that this post might be incomprehensible to the non-geek community. The point is that Gauss – one of the greatest of all mathematicians – is near universally known as Carl Friedrich Gauss. I am quite surprised that I have managed to get this far through my life without knowing his full name.
I just ran into Tom Henderson’s Punk Math Manifesto:
The video’s an appeal for funds taken from Kickstarter, but it looks like the target’s already been reached. (Not that a few more pennies would go unappreciated, I’m sure.)
I definitely dig the philosophy, fleshed out in more detail in this interview. So it’ll be good to see the project develop.
Having said all that, punk’s not really my genre. Maybe I should try experimenting with some Jazz Geometry, or Death Metal Model Theory.
Circle packing is a classical topic in discrete geometry. As Axel Thue and László Fejes Tóth showed, if you want to fit as many identical circular coins on a table as possible (all sitting side by side, no piling up or overlapping), the best you can achieve is for around 90.7% of the table to be covered. This is done by arranging the coins along a hexagonal lattice.
That’s fine, but we can pose the same problem, using coins which are not circular. Now here is an interesting question: which shape is the worst packer?
Then the answer is conjectured to be the smoothed octagon, with a maximum packing density of around 90.2%.
The smoothing is done by rounding off each corner with a hyperpola which is tangent to the two meeting sides, and which asymptotically approaches the two sides beyond those.
[Image from Wikipedia]
I’ve been doing some updates around this place. If things look rickety it’s because I am now phping and htmling myself. I’m having fun with it, but if I’m honest I don’t really know what I am doing. In fact, I don’t even know the difference between php and html. Luckily I have a tame professional webdesigner who should be able to repair any havoc I wreak.
The most important change is that this blog is finally equipped with an RSS feed. I encourage you to subscribe, because posting is likely to remain erratic, so the old fashioned method of clicking over here every once in a while might prove frustrating. Having said that, I do have a few posts lined up for the days ahead.
In celebration of this great step forward, I have decided to officially baptise this blog. Hereafter it will no longer be known only as “Richard Elwes’ blog”, but as “Simple City”.
In other news, my book Mathematics 1001 is now out… sort of. If you live in the USA, then it is definitely and unambiguously out. I think the same is true in Canada. For residents of the UK, the book is currently in a quantum out/not out state. The wave function seems to depend what sort of outlet you try to buy it from. It is not yet in the shops, but it is, I believe, available online. The official final release date here is 6th November. For citizens of Australia, and other countries, well, I don’t know. But it should be out soon, at least.
Anway, I am collecting book reviews (hooray!) and errata (boo!) here. So far there are barely any of either, but that will certainly change within the next couple of weeks. I’ll confine the updates to those pages rather than blogging them, so if you’re interested then check back there occasionally. (If you have any information for me about such things, then I’d be very grateful if you could drop me a line, or leave a comment here.)