## Pendulum experiment

With my Science Club class of 7-10 year olds, I did an experiment to test what factors influence the period of swing of a pendulum, and to measure the strength of Earth’s gravity. I borrowed some brass weights and a retort stand from my old university Physics Department and took them to the school. Then with the children we did the experiment!

We set up pendulums with different lengths of string, measuring the length of each one. With each pendulum length, we tested different numbers of brass weights, and pulling the weight back by a different distance so that the pendulum swung through shorter or longer arcs. For each combination of string length, mass, and swing length, I got the kids to time a total of 10 back and forth swings with a stopwatch. I recorded the times and divided by 10 to get an average swing time for each pendulum.

Here’s a graph showing the pendulum period (or “swing time” as I’m calling it with the kids), plotted against the mass of the weight at the end.

Pendulum period versus mass. The different colours indicate different pendulum lengths.

Here’s a graph showing the pendulum period (or “swing time” as I’m calling it with the kids), plotted against the swing distance (i.e. the amplitude).

Pendulum period versus swing distance. The different colours indicate different pendulum lengths.

These first two graphs show pretty clearly that the period of the pendulum is not dictated by either the mass of the pendulum or the amplitude of the swing. If you look at the different colours showing the pendulum length, however, you may discern a pattern.

And here’s a graph showing the pendulum period plotted against the length of the pendulum.

Pendulum period versus length. The line is a power law fit to all the points.

In this case, all the points from different pendulum masses and swing amplitudes but the same length are clustered together (with some scatter caused by experimental errors in using the stopwatch). This indicates that only the length is important in determining the period. This matches the first order approximation theoretical formula for the period of a pendulum, T:

T = 2π√(l/g),

where l is the length and g is the acceleration due to gravity. To calculate g from the experimental data, I squared the period numbers and calculated the slope of the best fit line passing through zero to (iT2). Then g = 4π2 divided by the slope… which gives g = 10.0 m/s2.

The true value is 9.81 m/s2, so we got it right to a little better than 2%. Which I consider pretty good given the fact that I had kids as young as 7 making the measurements!

Although this is an “other science” entry on this blog and not a proof of the Earth’s roundness, I’m planning to combine the results of this experiment with our ongoing measurement of the sun’s shadow length of a vertical stick at the end of the year, to calculate not only the size of the Earth, but also its mass. It’ll be interesting to see how close we can get to that!

## Colour naming experiment, part 2

A couple of months ago I wrote about a colour naming experiment that I was planning to perform with the students in the Science Club that I volunteer to teach at a local primary school. You may want to go back and review that post, as today I’m going to talk about the results of the experiment.

I go back to teach the Science Club again next Monday, so it was time to sit down and analyse the results. I went through the answer sheets that the children filled (there were 12 of them, one of the students was sick that day) in and typed the names of each colour from each child into a spreadsheet. I thought it could accumulate the totals and make pie charts for me, but I discovered that I needed to manipulate the data first using a COUNT() function or something. While pondering whether to do this or to export all the data to CSV and write a Python program to do the gruntwork, one of my friends pointed me at this pertinent xkcd comic.

That inspired me to do all the processing in Python, and I discovered to my pleasant surprise that my machine already had the matplotlib library installed, so I could produce pie charts directly from Python. (Without sucking the munged data back into a spreadsheet again to to the graphs as I feared I might have to do.) Anyway, long story short, here are the results (click the image for a huge readable version):

[I should point out that of course the colours in this image as displayed on your computer screen are not exactly the same as the colours printed on the paint sample charts that I assembled and gave to the children, because of the vagaries of colour calibration of monitors and the limited colour gamut of the graphic file format. Consider them only an approximation of what the children actually saw.]

That’s a lot to digest. Here are some highlights:

Firstly, here are the colours for which the largest number of people agreed on the name:

Out of 12 people, three colours had 7 of them agree on what the colour should be called, and one colour had 6 people agree. There was no colour in the entire sample for which a 2/3 majority agreed on the name, let alone anything approaching unanimity. 31 of the 35 colours sampled had less than half the people agree on the name of the colour.

At the other end of the spectrum (ha ha!), here are the colours that had the most different names assigned:

Four colours had, in a sample of just 12 people, nine different colour names assigned to them. Three of these colours also had one or two students unable to decide on a name in the time allowed, and they left it blank on the answer sheet.

I should point out that names that were on the answer sheet are written in lower case with an initial capital, while names that the students chose to write-in are written in all-capitals, and “NONE” indicates a student who didn’t give that colour any name. I gave them what I thought was a generous amount of time, but some of the students complained that it was too difficult and obviously struggled to complete the task. I did ask them beforehand if any of them knew they were colourblind, and none of them did. While there are two or three somewhat bizarre names assigned (“brown” for the colour that most kids identified as “lavender” for example), I don’t see any real evidence that any of them are indeed colourblind (confusing reds and greens, for example).

Another thing you’ll notice if you examine the large image of all the pie charts is that the same colour word is used for several different colours, many times over. For example, “olive” is used to describe three different shades of green, as is “tree green”, while “carrot” is used to describe three different shades of orange, “turquoise” is used for three different shades of blue, and so on.

The conclusion from all of this? This basically confirms the research findings that I quoted in the first post on this experiment – that people are incredibly inconsistent when it comes to naming colours. If you say “olive”, or “carrot”, or “turquoise”, people have a reasonable general idea what sort of colour you mean, but many will not be thinking of the same shade of colour that you will, and will fail to pick it out of a line-up.

The second part of the experiment – showing that people are inconsistent with themselves would require me to ask the children to do this entire task a second time. I was planning on doing this, but given how much some of them complained about it the first time, I think I’ll spare them doing it again, and do something a bit more fun with them instead. Hopefully however, when I show them the results on Monday they’ll think it’s pretty amazing and cool, like I do.

## Colour naming experiment

Firstly, sorry for the delay in getting a new proof written. I’ve been travelling, and then got sick on the flight home and was mostly incapacitated for two weeks. And I have deadlines for other stuff that then got in the way.

But one of those deadlines also involves science, and it’s pretty cool so I thought I’d share it with you. I do volunteer work with CSIRO’s STEM Professional in Schools program. As a professional scientist, I am partnered with a primary school and visit the school several times a year to talk to and engage the students with science topics. In past years I’ve mostly done presentations and Q&A sessions, but this year the school science coordinator suggested running a science club with some of the keenest science students from each year.

My Science Club is made of 13 students from years 2 to 6 (so ages 7 to 11). I’m running several experiments with them throughout the year. One of them is actually Eratosthenes’ method of measuring the size of the Earth, modified slightly. I’m getting the kids to measure the length of a vertical stick’s shadow every day at noon. At the end of the year I’ll help them plot the length versus day of the year, and we’ll fit a sine curve and extract the parameters to let us calculate the size of the Earth.

This Monday, I have another Science Club meeting, and I’ve been preparing a different experiment, on colour perception and naming. This is a cool topic that I’ve been interested in ever since I attended an imaging conference and saw some talks about the psychophysics and cultural psychology of colour perception. What I’ve done is to visit a local hardware store and raid their set of house paint sample brochures. Then I cut them up:

I had way too many colours, many of which were very similar to others, so I selected a representative subset to try and span as much of the colour space as I could. Then I arranged them and used double sided tape to stick them into manila folders:

A couple of hours later, and I had 13 folders with identically laid out colour swatches inside:

I used a marker to label all the swatches in each folder with a number. There are 35 swatches:

Now, here’s the experiment: On Monday in Science Club I’ll give each of the students one of the folders. I’ll also give them a potential list of colour names, with over 100 possible colour names on it:

Their task is to look at each colour, decide which name is the best name for it, and write the colour number on the sheet next to that name. Repeat for all 35 colours. So a lot of the names are going to be left unused. And I’ve included a few write-in slots for any cases where a student is positive that a certain colour really must be called “nasty bruise” or whatever. I’ve been careful to pick names that young children can relate to, and avoid weird things like “heliotrope” and “malachite” that they’ve probably never heard.

The science behind this experiment is that we’re all pretty good and consistent at naming very basic colours like red, and yellow, and blue, but when it comes to naming more subtle shades we are actually highly inconsistent. Is that particular shade of red: rose red, or raspberry, or cherry, or something else? Ask a lot of people and you’ll get a lot of different answers. There are classic studies showing this. (And yes, Randall Munroe of xkcd did a similar thing online a while back and published the results.)

There’s also a study showing that people are inconsistent with themselves, if given exactly the same task a few weeks later. Nearly everyone changes their mind on what certain shades should be called. So this is my experiment with my Science Club! I’m not going to tell the kids that we’ll be repeating this task later in the year. It’ll be interesting to see how closely they can reproduce their own results then, and also how closely their answers align with one another.

Basically, I’m doing something that happens with all good science. I’m replicating an experiment to see if I can reproduce the results. And now that I have this experiment ready to go, I’ll get on to writing up another proof that the Earth is a globe… hopefully within the next few days.