Archive: mathematics

Today’s XKCD led me to look at the Wikipedia article ‘List of numbers‘ out of curiosity.

I was surprised to see listed among the ‘notable integers’ were a few telephone numbers, such as 999 and 911. I guess these were included on the basis of their “cultural meanings”, although they are not integers. (They have since been removed from the article.)

But I was surprised that the most culturally significant telephone number of the past decade — that’s right, 118 — was left out. So I decided to fix that.

Notable integers, including 118

(Don’t worry, I only did this in Firebug, not on Wikipedia itself.)

This is the final selection of my overview of twenty interesting Warp albums from the record label’s twenty years. To read the other parts of this series, please check the table of contents on the right.

Jamie Lidell — Multiply

Multiply coverJamie Lidell is clearly a very talented person. His voice is incredible, but perhaps more incredible is the fact that in his earlier career he contrived to hide it. His work as part of Super_Collider (along with Cristian Vogel) and his début album Muddlin Gear were dark, murky, electronic affairs. Although Jamie Lidell sang from time to time, he didn’t show it off.

With Multiply his sunnier persona was unleashed. Instead of the dark and glitchy music of his earlier material, Multiply is very clearly influenced by soul and funk.

But this album is anything but conventional and boring. Jamie Lidell’s considerable skills as an experimental and electronic musician are fully utilised too. This gives Multiply a great crossover appeal. This is on the brighter side of the border that separates pop from experimental music. But clearly there was no way to stop him from pushing the boat out a little bit. This makes Multiply equally enjoyable for those who like to tap their feed and those who like to stroke their chin.

Here is the odd video for the song that effectively introduced me to Jamie Lidell, ‘The City’:

Boards of Canada — Geogaddi

Geogaddi coverWhile most favour Boards of Canada’s earlier album Music Has the Right to Children, for me it’s all about Geogaddi. To me, this album is endlessly fascinating, and always an intense listen.

Geogaddi is the darkest of Boards of Canada’s albums. Their other material is known most for its innocent, childlike and nostalgic qualities. Geogaddi retains an element of that, but with a dark undercurrent running throughout.

The music is more complex and multi-layered. Hidden messages are peppered throughout, and some tracks reveal more about themselves when played in reverse. There are hidden references to religion, the occult, mathematics and numerology. Some even say it is a satanic album. (As a joke, the album lasts 66 minutes and 6 seconds — a silent track, ‘Magic Window’, was inserted at the end.)

Whether Boards of Canada were trying to send some sort of message by planting these references is doubtful. Such references are few and far between on Music Has the Right to Children, and absolutely non-existent on the follow-up album The Campfire Headphase. I think the references were planted in Geogaddi to create a talking point and nothing more.

It certainly got fans talking. This webpage lists a full selection of mysterious messages and trivia about the album, even with a track-by-track breakdown.

Needless to say, leaving aside the hidden messages, the music itself is fantastic. Geogaddi is an unsettling album to listen to, but nonetheless hugely enjoyable and an intense experience.

One of my highlights is ‘Gyroscope’, which manages to fuse great music with one of my other interests as it incorporates samples of a numbers station. This is a fan-made video for the track.

Prefuse 73 — One Word Extinguisher

One Word Extinguisher coverWith One Word Extinguisher, Prefuse 73 effortlessly fused experimental electronic music with energetic hip-hop to create a unique-sounding album. The album is jam-packed with ideas — perhaps too many of them. An idea is allowed to develop just as far as it will go and no more, making this an album of many, mainly short tracks.

The music is also quite diverse, fusing many of Prefuse 73′s musical interests, spanning hip-hop, IDM / glitch, rock music and perhaps even a little bit of jazz. As such, the album is a fantastically colourful and diverse journey. There is not much chance to catch your breath.

There are also plenty of collaborations on this album. While he went a bit overboard with the concept in the following album, Surrounded by Silence, on this album the right balance is struck. I particularly like ‘Dave’s Bonus Beats’, containing drumming by David Lebleu from post-rock group The Mercury Program. The track comes complete with the answerphone message sent to Scott Herren to confirm that the drum track had been sent, adding a personal layer to the music.

During this period, Scott Herren was clearly at his creative peak. Very soon after the release of One Word Extinguisher came the accompanying Extinguished, a distinct album made of the “out-takes” from One Word Extinguisher! For a collection of out-takes, Extinguished is surprisingly good — indeed, almost as good as the original album.

At the same time as the material released as Prefuse 73, Scott Herren was also churning out quality albums as Savath & Savalas, a project more focussed on folk and Spanish-influenced music. Sadly, his subsequent material has not been nearly as good. In contrast to the exciting explorations of his earlier music, Scott Herren began to use the same recognisable formulas over and over. I have since lost interest in Prefuse 73.

Nonetheless, One Word Extinguisher remains an excellent album. Here is a track towards the end of the album, ‘Styles That Fade Away With a Collonade Reprise’.

Grizzly Bear — Veckatimest

Veckatimest coverWarp played a blinder by signing Grizzly Bear. Their pre-Warp album, Horn of Plenty, was charming but not particularly special. After signing to Warp, they came up with the wonderful Yellow House which was full of hidden beauty.

This year, with Veckatimest, Grizzly Bear have released an indie-rock / chamber-pop masterpiece which has propelled them onto the cusp of stardom. Every track is a winner. Gently enticing and maturely constructed, I can’t get enough of this album. This album ought to become a rock classic.

Grizzly Bear is easily the greatest triumph of Warp’s recent policy to diversify further from electronic music. I look forward to hearing what they come up with in the future.

Here is the lead single, ‘Two Weeks’:

BBC Radiophonic Workshop after 50 years

A series of posts

  1. Fifty years of Radiophonic influence
  2. Radiophonic re-releases

Regular readers may know that I have an interest in electronic music. 2008 has been a bit of a treat for fans of the BBC Radiophonic Workshop. This year marked 50 years since the establishment of the hugely influential sound effects and music department of the BBC. That, combined with a coincidental discovery of new tapes, has brought a feast of Radiophonic Workshop-related CD releases during the year.

I love the work of the composers of the BBC Radiophonic Workshop. For anyone with even a passing interest in electronic music, some of these CDs are an absolute must. Over the years, the Radiophonic Workshop produced some of the world’s most famous electronic music.

It is probably most famous for providing music to Doctor Who. The Radiophonic Workshop was, however, originally set up to meet the growing demand for music and effects to be used in experimental plays and “radiophonic poems” on the Third Programme for which suitable library music could not always be found.

But eventually, the Radiophonic Workshop’s music and effects were in fact used by programmes in every single department of the BBC, meaning that few people in Britain can have been untouched by this magical music. Low-budget education programmes made particularly frequent use of the Workshop’s output. An early exposure to experimental electronic music inspired many to become electronic musicians themselves.

Of course, almost all music produced today is electronic in some form. What we take for granted was largely pioneered by a rather unexotic bunch working away painstakingly in a Maida Vale studio. Initially, the equipment they worked on was old and unreliable even by contemporary standards, having been recovered from the BBC’s “redundancy plant”.

At first no-one could work at the Radiophonic Workshop for longer than six months, as the BBC had a fear that prolonged exposure to electronic music could cause mental illness! Meanwhile, the time-consuming musique concrète techniques largely employed in the 1960s would have many of today’s musicians, who practically have electronic music on tap, running for the hills. Brian Hodgson says he once stayed up for three successive days and nights in order to meet his deadline.

“Radiophonic” music was made possible by the increasing availability of tape recorders which allowed inquiring minds to manipulate sounds in interesting ways. The majority of early electronic music was made by cutting and splicing tapes, changing their speed in order to create the right notes and sounds. Delia Derbyshire always carried with her a book of logarithms so that she could make the calculations required to do her work.

BBC Radiophonic Workshop -- A Retrospective artwork One CD released this year, BBC Radiophonic Workshop — A Retrospective, provides an excellent overview of the output of the Workshop over its forty year life. It showcases the extraordinary diversity of the Radiophonic Workshop. It ranges from a comedy belch produced in 1959 for The Goon Show, to the 1997 theme tune for Michael Palin’s Full Circle, via local radio station jingles and news stings.

The double disc compilation is arranged in chronological order, allowing the listener to track the development of electronic music-making techniques over time. The earlier tracks are, oddly enough, the ones that have stood the test of time much better.

The introduction of the synthesiser may have enabled composers to create electronic music much more easily and quickly. But it also brought with it a set of identikit sounds that were mostly devoid of the charm of the earlier compositions. In my personal view, even though the mastery of the composers remains fairly high throughout, the quality of the sound diminishes as the CD goes on, particularly from the mid-1980s onwards.

By that time, Radiophonic Workshop was struggling to set itself apart. While in the 1960s and 1970s the Workshop had unrivalled access to excellent electronic music making equipment, the 1980s brought about the more widespread availability of such equipment, along with a quality that today sounds rather naff. Soon enough the Radiophonic Workshop found itself being undercut by freelance musicians.

With the BBC’s cost-cutting era under John Birt well under way, the Radiophonic Workshop struggled to justify its existence. It was finally wound up in 1997, just short of its fortieth birthday, by which time just one composer, Elizabeth Parker, was working for it.

Although it is easy to let romance get the better of you, listening to the CD makes me think that the Radiophonic Workshop had ceased to be relevant by then. Fifty years ago, electronic music was a largely unexplored area, ripe for experimentation. By the 1990s, any musician could make music from his home that sounded just as good as what the Radiophonic Workshop could produce.

Nonetheless, there are some real gems to be found on this album. Maddalena Fagandini’s ‘Interval Signal’ is hypnotic and magical. Along with Delia Derbyshire’s ‘Dance from “Noah”‘, it sounds decades ahead of its time. Meanwhile, Peter Howell’s ‘Greenwich Chorus’ sounds so fantastic that it reportedly jammed the BBC’s switchboards when it was broadcast.

This excellent retrospective CD was just one of many Radiophonic wonders that we were brought this year. My next post will look at some of the other Radiophonic Workshop-related gems that have been unearthed.

Apologies. My first post back after a wee break does not involve much input on my part. I usually reserve these kinds of items for the linklog. But there is a quote that I just have highlight here because it makes me want to run along the ceiling in sheer frustration at the human race.

(Emphasis mine.)

A LOTTERY scratchcard has been withdrawn from sale by Camelot – because players couldn’t understand it…

To qualify for a prize, users had to scratch away a window to reveal a temperature lower than the figure displayed on each card. As the game had a winter theme, the temperature was usually below freezing.

Tina Farrell, from Levenshulme, called Camelot after failing to win with several cards.

The 23-year-old, who said she had left school without a maths GCSE, said: “On one of my cards it said I had to find temperatures lower than -8. The numbers I uncovered were -6 and -7 so I thought I had won, and so did the woman in the shop. But when she scanned the card the machine said I hadn’t.

I phoned Camelot and they fobbed me off with some story that -6 is higher – not lower – than -8 but I’m not having it.

“I think Camelot are giving people the wrong impression – the card doesn’t say to look for a colder or warmer temperature, it says to look for a higher or lower number. Six is a lower number than 8. Imagine how many people have been misled.”

HOLY SHIT! This is how bad standards of numeracy have become. Unbelievable.

Incidentally, my time off this blog was due to the fact that I was being educated. A certain Tina Farrell might have benefited from it more.

Via Chicken Yoghurt.

Update: Chris Applegate reminded me of a point that I was going to make here, but I forgot to write it before publishing.

It is the fact that this person just couldn’t resist blaming someone else for the problem. There is not the slightest hint of her taking any personal responsibility. Even worse is the fact that Camelot have actually caved in, which will vindicate this stance in her mind.

There is this spinning woman who is doing the rounds on the internet at the moment. Thinks she’s really clever by looking like she’s turning clockwise when she’s actually turning anti-clockwise, while in actual fact she was turning clockwise all along! And anti-clockwise. At the same time.

Apparently, whether you perceive the woman to be turning clockwise or anti-clockwise tells you which side of your brain you use the most. Immediately it was obvious to me that the woman was turning clockwise. I felt a bit smug. After all, clockwise must be the side of the brain that makes me intelligent, witty, good looking and a mathematical genius.

Err.

If clockwise, then you use more of the right side of the brain…

RIGHT BRAIN FUNCTIONS
uses feeling
“big picture” oriented
imagination rules
symbols and images
present and future
philosophy & religion
can “get it” (i.e. meaning)
believes
appreciates
spatial perception
knows object function
fantasy based
presents possibilities
impetuous
risk taking

Are they calling me a girl or something?

Seriously. Looking at the lists, I would have always guessed that I would have been the left side of the brain. Not that I wish to blow my own trumpet, but I always consider myself to use logic, have attention to detail, reasonably good numerical skills and reality based. I am far to strategic for my own good, in the sense that I always spend so long thinking about things that I miss the boat.

Not that the skills for the right side of the brain are that bad. But I just don’t see it. I have less spatial awareness than Stevie Wonder, a dire imagination and I’m apathetic about symbolism. I am only religious in the sense that I am a Pastafarian. As for risk-taking, I can’t climb a ladder without completely crapping myself beforehand.

As if to compound the matter, the the article states that most people see the woman turning anti-clockwise. Brilliant! Other people are mathematical genii. I do little more than believe.

I believe, and I also live in a fantasy land. So what if I believe that I am a left-brainer? Or is that just a fantasy? This was all getting a bit too much for me.

I struggled to comprehend the situation. When I first loaded the page it was patently obvious to me that the woman was turning clockwise — there were no two ways about it. But I knew that she could turn anti-clockwise as well. In order to regain a modicum of self esteem, I strained my hardest to get the woman to turn anti-clockwise. It’s Magic Eye for the noughties.

And blow me down. It worked! It happened when I began to lose my focus while staring at her neck. I started to feel a little bit sick. It’s quite earth-shattering to see someone who has only ever turned clockwise suddenly decide to turn anti-clockwise. What’s more, I was now just as adamant that the woman could only possibly ever turn anti-clockwise, and surely never clockwise.

But soon enough I was able to switch between clockwise woman and anti-clockwise woman at will, as though I was flicking between The God Channel and BBC Four. My tip: look at the shadow that the sticky-out foot makes on the floor.

Now I feel much better. I can switch between clockwise and anti-clockwise at will. This must mean that I am brilliant at everything.

Also: Hehehehe. Boobs.

Seriously though. Does the illusion fail to work if it is a boobless man? What about that funny pose she is pulling? She doesn’t know if she’s slipping on a banana or if she is a little teapot, short and stout.

Flashboy was similarly freaked out by the strange levitating woman.

Aaaannyway. How did they decide that clockwise equals the right side and vice-versa? I have not seen any solid science on this — just a crappy Digg-magnetic article on an Australian newspaper. Part of me suspects that this article either

  1. Is a pile of horseshit
  2. Got the lists for the left and right sides of the brain the wrong way round

I’ll have my eye on Ben Goldacre’s blog for this!