The original Spirograph

During a recent trip to the Science Museum I happily found myself distracted from the 8 foot by 8 foot calculator in the Mathematics exhibition, by this:

Harmonograph at the Science Museum, London

...and it reminded me of an early blog post of mine about the maths of the spirograph. I had assumed that the spirograph was designed for the sole purpose of entertaining under 5s on rainy days and testing children’s patience with numerous snapped pencil leads. But no, it seems there was a scientific use at the beginning of it’s ancestral line...

Introducing, the harmonograph (ps. before we go any further i am not saying that the Spirograph is defs a direct descendent of the harmonograph, this is purely ill-informed speculation). 

The harmonograph was invented in the 1870s to analyse vibrations and was used in the study of sound. However, predictably, by the 1900s it was already regarded as a scientific toy for creating pretty patterns!

copyright Conor Lawless

The harmonograph works by utilising the swinging motion of two pendulums - one mounted to a pen and one to a drawing table - which swing at right angles to each other with the pen tracing out the resulting combinations of movement onto paper.

Weights can be added or moved up and down the pendulums to vary the speed that they swing at, creating varied patterns.

The Science Museum has a number of curve-drawing machines on show, like Stanley’s and George Adam’s geometric pens which arguably were the first spirographs, but with fancier cogs.

George Adams' Geometric pen at Science Museum, London

Stanley's geometric pen at Science Museum, London

There was also a surprisingly elaborate contraption on display masking as a tool for ornamental turning used on lathes - the geometric chuck.

Geometric chuck at Science Museum, London

This example, at the Science Museum, is the only known example of a 4-stage chuck for use on paper...and boy does it do good things to paper.

The chuck works by drawing the epicycloidal motion of each tier (determined by different sizes of cog) onto the paper at the top of the chuck. The motion of each tier can be superimposed upon another, or other tiers can be fixed so that the motion of only one tier is drawn.

So there we have it, an introductory tour of curve-drawing machines with very little science or maths and a lot of “it makes pretty things”. That’s what I like. But...if you do want some maths - the old Spirograph post has a bit to whet your appetite or you can go all-out with this article - which has some amazing examples and a bit of science behind their construction.

The Science Museum Mathematics exhibition is on the Second floor and is a permanent fixture (for now).

The Theory of Everything

A friend shared this video with me recently, introducing me to Minute Physics and the awesome videos they produce. This one is an introduction to the hypothetical Theory of Everything - a theory I wrestled with in a quantum physics module last year - that links together all physical 'things' and predicts the outcome of any experiment that could be carried out, ever...in theory. Yeah, it's tough to summarise, that's where Minute Physics come in:

Did the Victorians get the sci-art mix perfect?

Eric Schmidt giving the
annual MacTaggart lecture

The Guardian this week brought us all the action from the MediaGuardian Edinburgh International Television Festival, including a hard-hitting lecture from Eric Schmidt, chairman of Google, who delivered a scathing critique of the UK education system at the annual MacTaggart lecture. Eric spoke of it's failure to make the most of the country's record of innovation in computing and engineering (having invented the TV, photography and the computer both in thoery and practice) and highlighted the lack of support for bringing the sciences and arts back together in schools.

While Eric has since recieved criticism for drawing 'naive conclusions', he has also generated support for his back-to-the-abacus way of thinking. Schmidt said:

'Over the past century, the UK has stopped nurturing its polymaths. You need to bring art and science back together. [The Victorian era] was a time when the same people wrote poetry and built bridges - Lewis Carroll didn't just write one of the classic fairytales of all time. He was also a mathematics tutor at Oxford. James Clerk Maxwell was described by Einstein as among the best physicists since Newton – but was also a published poet.'

Lewis Carroll

The Guardian article generated some interesting discussion in the comments section and while they are by no means all positive, it is good to see people talking about what is important in schools and debating whether it is possible or necesary to return to a Victorian-style education system.

The Guardian collated some of the most well-informed comments in a follow-up article if you're interested. It's great to see the Guardian picking up interest in bridging the arts and sciences divide.

If Alby says it, it must be true

'After a certain high level of technical skill is achieved, science and art tend to coalesce in esthetics, plasticity, and form. The greatest scientists are artists as well'
- Albert Einstein


I came across this quote during some lazy google-ing on the Theory of Relativity and thought I'd share it with you.

Indeed, and as any avid readers (hi Mum) will know, I have long held the notion that the creativity and innovation required of scientists to reach new levels of understanding is that very same required of artists to dominate in their field. This snippet articulates what it is I have so inarticulately and unintelligibly tried to portray through a year's worth of posts on Michelangelo, the Vitruvian man, microwaving CDs, Gunther Von Hagens' Bodyworlds, string theory, Facebook, the brain, tattoos, spirographs and numerous other half-formed meanderings. Einstein's observation takes all the fragments of science, art and sci-art I have come across on the web, wraps them in a parcel, puts a tidy ribbon around them and leaves a note that says: 'friends?'

Tim Minchin: a question of science

Here's a little light relief to kick those Monday blues.

Tim Minchin, with his exceptional turn of phrase, observation and impeccable spoken word, spins out a lyrical masterpiece on the subject of science, knowledge and faith. Tim's observations of social interaction are intriguing and it is quite a talent to, in the same nine minutes, make a person laugh to the point of unplanned-urination; and then to honestly think about their readily accepted digestion of common knowledge, the sciences, medicine and religion in whatever ratios they inhabit their life up to this point.

This is a mish-mash of rhyme, anecdote, philosophy, science, knowledge and dinner table etiquette, mixing together social cliche, the immortal words of Puck and touching on every scientists favourite subject - homeopathy!

Tim Minchin's spoken word masterpiece - Storm:

Visualising statistics: internet censorship

Last month's Facebook: mapping earth post provoked some discussion about why the north of Asia was AWOL and why Facebook, which seems to offer something for everyone, hasn't managed to penetrate into the huge hunk of landmass that dominates one half of the world map (read the previous post for a refresh).

The empty spaces occupying rural Africa, the Amazon and central Australia are easily explained away by geographical location, as too are those countries with a lower GDP. However, the Asian countries with captive audiences and technology coming out of their ears have kept Facebook at arm's-length through censorship.  The uber-talented guys at Information Is Beautiful have come up with a very pretty and easy-to-digest analysis of such censorship. Below are the Facebook map from Paul Butler and the censorship map from David McCandless.  Draw your own conclusions.

Anyway, here's the link to the full visualisation. One particularly information-rich diagram is the good old fashioned venn diagram showing the various overlapping reasons for internet censorship in the different regions. It's pretty cool. Have a browse, learn something new, drink a beer (just because).

Facebook: mapping earth

There are six degrees of separation, so they say, and the world is an intricate web of mothers, husbands, colleagues, cousins, friends, enemies, frenemies. But this we're-all-the-earth's-children hippy talk of all being 'connected' is turned on it's tie-dye bandana-adorned head when searching through facebook and finding the right name, a similar face (but the picture's so small, I'm just. not. sure.) and to top it off, no mutual friends.

That is, until now. You may not feel connected to the rest of the world through your photo tags and wall posts and stalking the guy that you're inconveniently in love with, but an intern at Facebook has spent an undisclosed (obscenely large) amount of time poring over data to create this map of the world through Facebook's eyes, forcing you to admit that actually, we are a pretty snug-as-a-bug-in-a-rug close knit family unit.

by Paul Butler (intern), crucial cog in the Facebook machine

Each line connects cities with pairs of friends, with brighter lines sprouting from the cities with the most pairs of friends.

Paul said of his digital creation:

"Not only were continents visible, certain international borders were apparent as well. [...] What really struck me, though, was knowing that the lines didn't represent coasts or rivers or political borders, but real human relationships."

You'll notice that large chunks of the Earth appear to be missing, such as China and most of rural Africa, and this is because Facebook hasn't quite permeated into the pores of their very existence yet...but give it time.

What's the deal with Spirographs?

It’s the heady days of the 1990s.  You’re 8 years old, hair teased into plaits and it’s raining outside.  You’ve grown bored of buckaroo and no one will play scrabble with you so you’re mother (who has a vested interest in expanding your young, neuroplastic brain) whips out the Spirograph. 

You poke your Disney pencil in one of many small plastic holes in the small gear and push it round and round inside the larger gear creating patterns that, at that age, were just darn ‘pretty’; but at the ripe age of 21, we see they are much more than that, they are hypotrochoid mathematical curves.

There is a surprisingly complex mathematical basis for the graphs that are produced and without wanting to give you a stroke, take a quick peek at this handy equation that explains the maths behind these ‘pretty’ shapes.

x = (R+r)*cos(t) - O*cos(((R+r)/r)*t)
y = (R+r)*sin(t) - O*sin(((R+r)/r)*t)
(moving circle outside the fixed circle)
x = (R-r)*cos(t) + O*cos(((R-r)/r)*t)
y = (R-r)*sin(t) - O*sin(((R-r)/r)*t)
(moving circle inside the fixed circle)

Yeah, I know, and I’m sorry, but I don’t expect you to be able to relate to that jumble of letters.  Basically, Imagine a fixed point set inside one circle that travels along the inside of a second circle. The complex harmony of the position of the point and the diameters of the two circles create a complex looping track.  The different hypotrochoids are determined by the differing diameters of the two circles and the position of the point inside the centre circle where the line is drawn from. 

This might help - You can use this applet to change the dimensions of each of the circles to get a better understanding of how the maths affects the resulting shape!

Thanks to Anu Garg for permission to use this applet

An arc generated by a circle traveling along the inside of another circle is not only ruddy beautiful, it is also ridiculously useful!  Guilloché patterns are ‘spirograph-like curves that frame a curve within an inner and outer envelope curve’. So, they are like spirographs but layered over one another.  They are used on banknotes, securities, and passports worldwide for added security against counterfeiting.  If you look closely at any British bank note you will see this pretty pattern in the background.

Phew, I think that’s enough for today.  If you are more Newton than Monet, you can have an epiphanic mathematics-induced high at this page of hypotrochoid equations to wrap your head around.

The Beautiful Math of Coral

The Coral Reef is made up of structures comprising some of the most complicated mathematical models known to man. Mathematicians have long maintained that ‘geometrical hyperbolic space’ (that scalloped, crenulated edge of reefs and kelp) could not be modelled in the real world, however, Margaret Wertheim has found a way; through the art of crochet! Yes, I mean the age-old technique of pulling loops of yarn through other loops with a hook!

I will leave the details of the maths and models to Margaret Wertheim in the TED video below (skip to 5 minutes for the maths-y bit if you just can’t wait!) but she has championed the understanding of maths through this feminine handicraft and in getting away from the obsessive, cerebral, pen and paper mode of mathematical thinking to a more practical approach that, as an aside, creates wonderfully crafted works of art.

The Art in Science

Art is a lie that makes us realize the truth
Pablo Picasso

There are hundreds of types of art; classical greek art, indian art, aborigine art, abstract art, impressionism, expressionism, realism, dadaism and a whole string of other -isms. Traditionally, as a culture, we teach our young to make the choice: Shakespeare or DNA, Rembrandt or fractional distillation, a Ming Dynasty vase or Einstein's Theory of Relativity. So claiming any kind of Art in Science seems like an oxymoron, doesn't it? But this seems to me a false dichotomy. Though one is the quest for truth and explanation and one the expression of individuality, artists have often chosen to take inspiration from scientific principles and have also unknowingly created structures present in science and nature: Be it music's fascination with mathematical patterns and beat; Rudolf Laban's choreography drawn from principles of geometry as the limbs trace lines along fundamental geometric shapes, or the way the pre-frontal cortical areas of the brain are titillated as you appreciate the aesthetics and respond emotionally to a classic Van Gogh; art and science are inexorably intertwined. Deal with it.

Science and writing, particularly, have a lot in common; the need for fresh ideas and attention to detail, a constant questioning and redeveloping of ideas and creating a complete understanding through commitment to a chosen route. I am interested in poetry and creating an understanding or questioning through creative expression, to take a step back from the raw details and mould it into something tangible and expressive. There is so much beauty in nature, I hope that, however naively, I can recreate and represent the fundamental, exquisite details of nature and science by sharing with you other peoples sci-art collaborations.

Welcome to the beautiful world of Science.