I was given the book Information is Beautiful by David McCandless. It is a book which attempts to address the fact that we are given lots of information which we can’t form a mental picture of. (The author says, “Every day, every hour, maybe even every minute, we’re looking and absorbing information via the web.” Speak for yourself; I like a good night’s sleep.) The book is described as a “visual miscellaneum”, a kind of Schott’s Miscellany in pictures.
One self-referential page describes “Types of Information Visualization”, most of which are used in the book. He lists bubble chart, bubble comparison, bubble race, bubble race with strings, bubble clusters, bubble network, bubble treemap, bubble star ring, infographic, charticle, matrix, family tree, mind map (tidy or organic), concept map, bubbles (nested), polar grid (simple, segmented or semantic), sun burst, coxcomb, icicle pie, mandala (simple or complex), radar, spiral, concept fan, fan, synergy map, bubble mind map, Venn bubbles, decision tree, “dunno what to call it” [looks like a network to me], conetree, icicle tree, treemap, flowchart, sankey, or periodic table. If (unlike me) you know what more than a few of these things are, you can get some idea of what the book is like.
Some displays work better than others. The Great Firewall of China is a map of China, the border done in banned search terms, and the countries outside made up of names of websites inaccessible from China, whose interior is a blank. The Moral Matrix, however, which gives the attitudes of various religions or sects to moral issues, is less good since it is too black-and-white (conceptually): does atheism bless gay marriage, for example?
One method of presenting information is the printed word. The book includes a two-page essay on Postmodernism by Mary Klages of the University of Colorado. Now I don’t know any mathematician who thinks postmodernism is a good thing: the relativity of “truth” leaves us undefended against regiments of circle-squarers, angle-trisectors, etc. Indeed, the article itself exposes the contradictions in postmodernism. We are told how postmodernism rejects, or deconstructs, the “grand narratives” that societies depend on, such as “peace on earth”, and replaces them with local “mini-narratives”. Having been told this, we are presented with what look suspiciously like the grand narratives of postmodernism: “think global, act local”, “equal rights for all”, “multi-culturalism”, “consensus”, etc.
Another item took us through a little detour of thought. “Articles of War” gives us the most-edited Wikipedia pages. These include the one on the Pink Floyd song “Money”. What is the time-signature? Is it 7/4, 7/8, or 21/8? We put on the record to have a listen.
An aside for the non-musical. The numerator in such a fraction is the number of beats in a bar of music. The denominator has no real meaning, but simply tells us what kind of note is used in the written music to represent a single beat. So 7/4 means “seven crotchets in a bar”. If you listen to the song, you will hear that the riff on which it is based does have seven beats; a single occurrence of the riff makes quite a long bar, so 7/4 would seem appropriate. Where does the 21 come from? In a lot of music, especially popular genres, the division of a beat is not uniform. Instead of “da-da-da-da-da-da-da”, musicians will typically play “da–di-da–di-da–di-da–“. If you chop a beat into three equal parts, you will find that the “di” typically occurs approximately two-thirds of the way between the two strong beats on either side, so you could write “da” as two quavers and “di” as one, giving 21 quavers in Floyd’s seven-beat riff. (Indeed, precisely once in the riff, there is such an off-beat.)
Personally I don’t like this practice. No musician would ever feel bound to play this off-beat precisely two-thirds of the way through the bar. John Adams write a piece called “40% swing” (if I recall correctly) to illustrate that, with modern technology, you can vary the position of the off-beat arbitrarily, and communicate your intention to electronic instruments via a MIDI interface. (Indeed, another page of the book, entitled “X is the new black”, tells us, among many other such facts, that “MIDI is the new sheet music”.) I have heard Indian percussionists doing the same thing.
While we were having these thoughts, the Floyd moved into the instrumental break of their song. Since noodling in 7 beats to the bar is quite challenging, they switched to 8, and dropped back to 7 when the verses began again. This reminded me of something, so I got out Sgt. Pepper, and played “Within you, without you”. The song is in 4/4, but the instrumental break switches to 5/8, and must have been quite demanding on the musicians.
Talk of time signatures gives me the opportunity to plug one of my favourite music groups, Makám, from Hungary, who delight in them and make the most obscure time signatures sound completely natural. I saw them live twice; two interesting stories there to tell one day.
Anyway, while listening to The Beatles’ music, the words impressed themselves on me. I would regard The Beatles as the epitome of modernism in the 60’s: after all, what better expression of a Grand Narrative than “All you need is love”? But in his song, George Harrison sang, “Try to realise it’s all within yourself, no-one else can make you change”, which seems to fall on the postmodern side, according to Klages’ essay. So what is going on?
If you would like to see more, the author of the book has a website at informationisbeautiful.net.