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“I’m deuterawhat?” – colour vision at Orkney Science Festival

No need to look so sad, Garry. You're special. — No need to look so sad, Garry. You’re *special*.

You’re deuteranomalous, Garry.

The distressed man on the right is Garry McDougall. Garry’s just found out that his colour vision is not the standard-issue colour vision that most of us have. He made this discovery while watching my talk on the science of colour vision, in Kirkwall as part of the Orkney International Science Festival 2018.

Garry and I were part of a team funded by the Institute of Physics to perform at the festival. Also on the team were Siân Hickson (IOP Public Engagement Manager for Scotland) and Beth Godfrey.

Garry needn’t look quite so woebegone: he’s not colour blind, and he’s in plentiful company – about 1 in 20 men have colour vision like his.

Normal metameric lights — To Garry, these two lights looked different.

How did Garry’s unusual colour vision come to light? In one of the demos in my talk, I compare two coloured lights. One (at the bottom in the picture on the right) is made only of light from the yellow part of the spectrum. The other (at the top) is made of a mixture of light from the red and green parts of the spectrum. If I adjust the proportions of red and green correctly, the red/green mixture at the top appears identical to the “pure” yellow light at the bottom.

Except that to Garry it didn’t. The mixture (the top light) looked far too red. By turning the red light down, I could get a mixture that matched the “pure” yellow light as far as Garry was concerned. But it no longer matched for the rest of us! To us, the mixture looked much greener than the “pure” yellow

Garry metameric lights — To Garry, these two lights looked the same.

light; the lower picture on the right shows roughly how big the difference was. This gives us an insight into how different the original pair of lights (that we saw as identical) may have appeared to Garry. It’s not a subtle difference.

We can learn a lot from this experiment.

Firstly, we’re all colour blind. The red/green mixture and the “pure” yellow light are physically very different, but we can’t tell them apart. “Colour normal” people are just one step less colour blind than the people we call colour blind.

Secondly, it shows that there’s no objective reality to colour. People can disagree about how to adjust two lights to look the same colour, and there’s no reason to say who’s right.

Thirdly, it shows that Garry has unusual colour vision. Our colour vision is based on three kinds of light-sensitive cell in our eyes. They’re called cones. The three kinds of cone are sensitive to light from three (overlapping) bands of the spectrum. Comparison of the strengths of the signals from the three cone types is the basis of our ability to tell colours apart. Garry is unusual in that the sensitivity band of one of his three cones is slightly shifted along the spectrum compared to the “normal” version of the cone. This makes him less sensitive to green than the rest of us, which is why the red/green mixture that matches the “pure” yellow to Garry looks distinctly green to nearly everyone else.

Garry isn’t colour blind. He’s colour anomalous. A truly red-green colour blind person has only two types of cone in their eyes. Garry’s kind of colour anomaly is quite common, affecting about 6% of men and 0.4% of women. It’s called deuteranomaly, the deuter- indicating that it’s the second of the three cone types that’s affected, ie the middle one if you think of their sensitivity bands arranged along the spectrum.

My thanks to Siân Hickson for the photographs.

Ben on rocks — Exploring the coast at Rerwick Point.

Showery weather meant that we were treated to many magnificent rainbows, like this one seen at Tankerness.

A note to deuteranomalous readers

Please don’t expect the illustrations of the colour matches/mismatches above to work for you as they would have done if you’d seen them live. A computer monitor provides only one way to produce any particular colour, so the lights that appear identical to colour “normal” people (image duplicated on the right) will also appear identical to you, because, in this illustration, they are physically identical.

A machine full of noises

Sarah Kenchington and I made this machine for the Full of Noises festival in Barrow-in-Furness in August 2018.

Sarah designed and made the bicycly bits that raise the table-tennis balls from the pit into the hoppers at the top, and I made the two devices that the balls descend through on their way to the cow bells and glockenspiel.

The complete machine also included other noise-making devices and an exercise-bike powered drive system, both made by Sam Underwood. It was housed in a greenhouse. Here’s a video of the whole thing in action at Full of Noises.

We shot the video in this post in a hurry on a dark damp Tuesday morning before packing the machine up to take it to Barrow, so it comes with apologies for the poor lighting in places.

The peg board (Galton board) that appears from 1:13 to 1:31 is an established classic (see below if you want to make one). The swinging-ramp ball-feeding device (2:09 to 2:18) is a revival of something I designed for the Chain Reactor.

What’s new from me is the arrangement for feeding the balls from the wire chute into the swinging-ramp assembly (1:56 to 2:18). Its operation should be clear from the video, except perhaps for one detail. Because this device may jam if it tries to collect a ball that has not quite arrived at the bottom of the wire chute, and because the timing of the arrival of the balls is erratic, it’s necessary to maintain a queue of balls in the chute to guarantee that there’s always a ball in place at the bottom to be collected. To achieve this, we arranged that the average rate of ball delivery into the chute (determined by the number of spoons on the bicycle chain) was greater than the rate of collection of balls out of the chute, and had an overflow route for the excess balls. Once three balls have accumulated in the chute, any further balls are diverted back into the ball pit (2:30-2:40).

Sarah and I are very grateful to Edinburgh Tool Library for the use of their Portobello workshop, and to Bike for Good and Magic Cycles for donating bicycle parts.

Making the Galton board

Chris Wallace and I discovered while making the Chain Reactor that the horizontal spacing of the pegs on a Galton Board is important. If the spacing is too great, a ball that sets off rightwards will tend to keep going rightwards, and vice versa. To get good randomisation, the ball should rattle between each pair of pegs, and to get this to happen, the gap between the pegs should be only slightly greater than the diameter of the balls. This in turn means that the pegs need to be precisely placed to avoid there being pairs of pegs that don’t let the balls through at all.

In that project we achieved the necessary precision by making the position of each peg (a bolt) adjustable, but with something like 100 bolts, this difficult job was very tedious and sorely tried Chris’s patience.

This time round, I developed a system that let me get every hole in the right place first time. Firstly, I cut the board into four strips so that all parts of it were accessible to a pillar drill. This guaranteed that every hole was accurately perpendicular. Secondly, I made a drilling jig (top right) to get the hole spacing correct. After drilling each hole, I put the peg (the bolt on the right-hand part of the jig) into the just-drilled hole, and the drill for the next hole into the drill hole on the left-hand part of the jig. The spacing between the peg and drill hole is adjustable using the long bolt. Thirdly, I made a large custom table for the pillar drill (bottom right), with a fence arrangement so that each row of holes was straight.

When I was doing the drilling, the only measurements I had to make were to get the first hole in each row in the right place with respect to the previous row. It took me a few hours to perfect the drilling arrangements, but then only an hour or so to drill 90 holes, all exactly where I wanted them.

Puff pastry

NOTE: the video that previously headed this post is no longer available. It shows the mixing of two thick sheets of coloured silicone material that had the apparent consistency of clay. One sheet was laid on the other sheet, and the pair were rolled up. The roll was squashed flat by passing it through a pair of rollers. It was then rolled up again, squashed flat again, rolled up again, squashed flat and so on. Remarkably, after only 4 such cycles the mixing was done to the satisfaction of the operators.

I was rather taken by the video above, which I first saw on Core77. I started wondering how many times you have to put the roll of silicone material through the machine to get satisfactory mixing of the two colours of material. The people in the video consider the job done after four passes. What does that mean in terms of the thickness of the red and white layers within the material?

The roll is a rather complicated object, so I worked with an idealised version of the real process, where the sheet emerging from the rollers isn’t rolled up, but cut into several pieces which are stacked up before being passed through the rollers again. I came up with the following:

After only 2 passes, the layers in the slab are too thin to see with the naked eye. And by some margin, too: there are over 600 of them and they’re only a fortieth of a millimetre thick. If you made a perpendicular cut through the slab, it wouldn’t appear to have red and white layers in it.

After only 4 passes, a standard compound microscope operating in visible light wouldn’t be able to resolve the layers in the slab.

After only 6 passes, the layers would be thinner than the width of the molecules of the silicone material. At this stage the concept of red and white layers no longer makes sense.

These results will only apply to material near the centre of the roll. It’s easy to see from the video that material near the edges is not mixed so well.

The calculation

From the video, it looks like there are about 9 turns in the roll. Each time the roll is flattened by the rollers, those 9 turns are converted into 18 layers. The resulting sheet is rolled up and passed through the rollers again, multiplying the number of layers by 18, and so on.

This doesn’t work at the sides of the roll. We’ll ignore that complication, and work with a flat analogue of the actual situation. We’ll assume that we start with two long rectangular flat sheets of material, a white one and a red one, laid on top of each other. We’ll cut this assembly into 18 identical pieces, and make a stack of them; this stack will have 36 layers. We now flatten this stack in the rollers, cut it into 18 pieces, stack them up (giving us 648 layers), and repeat.

On emerging from the roller, the sheet appears, by eye, about 1.5 cm thick. We’ll assume that we start with two layers of half this thickness. The table below shows the number of layers and the thickness of each layer after 0, 1, 2, 3… passes through the rollers.

Number of passes	Number of layers	Layer thickness (m)
0	2	7.50 × 10^-3
1	36	4.17 × 10^-4
2	648	2.31 × 10^-5
3	11 664	1.29 × 10^-6
4	209 952	7.14 × 10^-8
5	3 779 136	3.97 × 10^-9
6	68 024 448	2.21 × 10^-10

We can identify various milestones, as follows:

Limit of visual acuity. A person with clinically normal vision can resolve detail that subtends roughly 1 minute of arc at the eye. At a viewing distance of 30 cm, this corresponds to about 0.1 mm (10^-4 m). The layers of material are much thinner than this after only 2 passes. If you made a perpendicular cut through the slab of material, after two passes you wouldn’t be able to see the layered structure. (This might not be true if the cut was oblique.)

Limit of standard light microscopy. A compound microscope working in visible light can resolve detail down to about 200 nm (2 × 10^-7 m). The layers become thinner than this after only 4 passes.

Single-molecule layers. The question here is the number of passes needed before the layers are less than a molecule thick (at which point the idea of layers fails). The difficulty is that molecules of silicones are long chains, and these chains are almost certainly bent, so their size is ill-defined. This part of the calculation will be hugely approximate. We’ll be as pessimistic as possible, assuming that the molecules are roughly straight and that they lie parallel to the layers in the slab of material.

A common silicone material is polydimethylsiloxane or PDMS. This consists of a silicon-oxygen backbone with methyl groups attached. The lengths of carbon-silicon and carbon-hydrogen bonds are 1.86 × 10^-10 m and 1.09 × 10^-10 m respectively. So the width of the molecule is going to be, very, very approximately, of the order of 4 × 10^-10m. The layers are thinner than this after only 6 passes.

Faces in the snow

A hollow impression of my face in the snow.

The hollow face illusion is a wonderful visual effect in which a hollow mask of a face appears to be convex, like the face itself. Making a hollow mould of your face (for example using plaster) is difficult and potentially dangerous. However, last weekend my attention was drawn to an easier and safer way.

I was walking down from Coire an Lochain in the Scottish Highlands with a group from the Red Rope club, when I saw my friend Maia standing on the path ahead, chuckling. She’d been making face imprints in a steep snowdrift, and they showed the hollow face illusion beautifully.

The procedure needs no explanation (see right). The snow needs to be fresh and soft; you’d be surprised how hard it is to push your face into what feels to your hand like very soft snow. The tip of my nose is noticeably flattened in the picture above.

Ben and Matthew on skyline — Near Coire an Lochain on the day in question. (Readers familiar with Highland place names will realise that I’m not giving much away here.)

The kinetic energy of a drifting tectonic plate…

…is broadly similar to the kinetic energy of me and my bike as I pedal along.

According the the theory of plate tectonics, the outer layer of the Earth is divided into a number of separate plates, which very slowly drift around, opening and closing oceans, causing earthquakes, and thrusting up mountain ranges.

A moving body has energy by virtue of its motion: kinetic energy. Kinetic energy is proportional to a body’s mass and to the square of its speed.

Now tectonic plates move extremely slowly: the usual comparison is with a growing fingernail. But they are also extremely heavy: tens of millions of square kilometres in area, over 100 km thick, and made of rock. I wondered how the minute speed and colossal mass play out against each other: what’s the kinetic energy of a drifting tectonic plate?

There are so many variables, that vary such a lot, that this calculation is going to be extremely approximate. But the answer is delightfully small: the kinetic energy of the tectonic plate on which I live, as observed from one of the plates next door, is about the same as the kinetic energy of me and my bike when I’m going at a reasonable pace: about 1500 joules.

Me struggling up one of the many steep roads in NW Scotland. Here, the kinetic energy of me and my bike is much less than the kinetic energy of a drifting tectonic plate. In fact the speed of me and my bike is probably less than that of a drifting tectonic plate. — Me struggling up one of the many steep roads in north-west Scotland. Here, the kinetic energy of me and my bike is much less than the kinetic energy of a drifting tectonic plate. In fact the *speed* of me and my bike is probably much less than that of a drifting tectonic plate ;-).

This is a fun calculation to do, but we shouldn’t get carried away thinking about the kinetic energy of tectonic plates. Plates are driven by huge forces, and their motion is resisted by equally large forces. The mechanical work done by and against these forces will dominate a plate’s energy budget in comparison to its kinetic energy.

But the calculation does provoke an interesting thought about forces and motion. I can get my bike up to full speed in, say, 10 seconds. If the Eurasian plate were as free to move as my bike, and I were to put my shoulder against it and shove as hard as I could, it would take me about 500 years to get it up to its (very tiny) full speed.

In both cases, I’m giving the moving object roughly 1500 joules of kinetic energy. How come I can give that energy to my bike in a few seconds, but to give it to the plate would take me centuries?

I’ll return to that thought in a later post.

The calculation

Depending on how you count them, there are 6-7 major tectonic plates, 10 minor plates, and many more microplates. The plates vary hugely in size, from the giant Pacific Plate with an area of 100 million km², to the dinky New Hebridean plate, which is a hundred times smaller. The microplates are smaller still. Plates also vary a lot in speed: 10-40 mm is typical.

I’m going to be parochial, and choose the Eurasian plate for this calculation.

Let’s call the area of the plate a and its mean thickness t. Its volume is then given by at, and if its mean density is ρ, then its mass m is ρat.

A body of mass m moving at a speed v has kinetic energy ½mv². So our plate will have kinetic energy ½ρatv².

The area of the Eurasian plate is 67,800,000 km² or 6.78 × 10¹³ m², and its speed relative to the African plate is (the only speed I have) is given as 7-14 mm per year. We’ll use 10 mm per year, which is 3.2 × 10^-10 ms^-1. The thickness of tectonic plates in general varies roughly in the range 100-200 km depending upon whether we are talking about oceanic or continental lithosphere; let’s call it 150 km or 1.5× 10⁵ m. The density of lithospheric material varies in the range 2700-2900 kg m^-3; we’ll use 2800 kg m^-3.

Putting all of these numbers into our formula for kinetic energy, we get a value of 1500 joules (to 2 significant figures, which the precision of the input data certainly doesn’t warrant).

Now for me and my bike. I weigh about 57 kg, my bike is probably about 10 kg. Suppose I’m riding at 15 mph, which is 6.7 ms^-1. My kinetic energy is almost exactly…

…1500 joules!

The closeness of these two values is unmitigated luck*, and we shouldn’t be seduced by the coincidence. Just varying the speed of the plate in the range 7-14 mm would cause a 4-fold change in kinetic energy, and there’s the variability in plate thickness and rock density to take into account as well. The choice of bike speed was arbitrary, I guessed the mass of the bike, and I’ve since realised that I didn’t account for the fact that the wheels of my bike rotate as well as translate.

However, what we can say is that the kinetic energy of a drifting continent is definitely on a human scale, which leads to a new question:

Suppose the Eurasian plate were as free to move as my bicycle, and that I put my shoulder against it and shoved, how long would it take me to get it up to speed?

From the figures above, the mass of the plate is 2.85 × 10²² kg. If I can push with a force equal to my own weight (about 560 newtons) then by Newton’s 2nd Law I can give it an acceleration of about 1.96 × 10^-20 ms^-2. Rearranging the equation of motion v = at, where v is the final speed, a is the acceleration, and t is the time, then t = v/a. Inserting the values for v and a, we get t = 1.6 × 10¹⁰ seconds, or about 500 years.

* I didn’t tweak my assumptions: what you see above really is the very first version of the calculation!

Edinburgh Mini Maker Faire 2017

On 16th April Sarah McLeary and I had a busy day at the 2017 Mini Maker Faire in Edinburgh (part of the science festival). We showed the paraboloidal castings that we’ve been working on together, and I showed developments in my irregular polyhedra since I showed them at the 2015 Mini Maker Faire.

As well as plaster casts, we’ve tried slipcasting porcelain using our paraboloidal moulds, squirting the slip on as the mould spins to try and get a lacy structure. You can see one of these near the front left of the table. I’ve also been having a go at making irregular puckered plane-based tilings (standing up at the back of the table). I will write more about both of these projects before too long.

punters.