The Seasons

It’s solstice time in a few days, so here is an infographic on the seasons (click for hi-res image):

Infographic constructed using R (with DescTools::DrawCircle, rasterImage, layout, and the suncalc package for day length calculation). Images used are a diagram by “Colivine,” paintings by Arthur Streeton and Joseph Farquharson, and two photographs of my own.


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Mosses!

Thinking back to my freshman botany days, here’s an infographic on mosses (click for hi-res image):

Infographic constructed using R (with DescTools::DrawCircle, rasterImage, and layout for dividing the plot area into sections). Images used are all public domain.


Bridges, gender, and Benjamin Lee Whorf

I’ve long been fascinated by the Sapir-Whorf hypothesis – the idea that the structure of language determines (or at least influences) the way that you think. I first read Whorf’s book several decades ago.

A friend recently pointed me at this TED talk by Lera Boroditsky. After years of being sneered at, it seems that Whorf is back in fashion.

And there’s certainly something to Whorf’s ideas. For example, there is solid evidence that the way that you name colours influences the way that you see them (slightly, anyway). There is some exaggeration in the TED talk, though. Australian aboriginal speakers of Kuuk Thaayorre have a unique way of describing directions (in absolute, rather than relative terms, e.g. “there is an ant on your northern leg”). They also navigate well across their tribal lands. But is there a causal relationship? Do aboriginal people with this linguistic feature navigate better than those without it? No, they don’t.

Even stranger is the idea that Spanish speakers, for whom a bridge is masculine (el puente), are less likely to describe a bridge as “beautiful,” and more likely to describe it as “strong,” than German speakers, for whom a bridge is feminine (die Brücke). There really are way too many confounding factors there – people who speak different languages differ in other ways too. So I thought I’d try a quick-and-dirty experiment of my own.

For a set of 17 languages, I counted Google hits for the phrases “beautiful bridge” (e.g. French: beau pont, German: schöne Brücke) and “strong bridge” (e.g. Greek: ισχυρή γέφυρα, Dutch: sterke brug), divided one set of numbers by the other, and took the logarithms of those ratios. The chart below summarises the results. Languages in pink have a feminine bridge, languages in blue have a masculine bridge, and languages in grey have a bridge which is neither (for example, English has no gender, while Dutch and Swedish have merged masculine and feminine into a “common” gender).

The mean values there are 0.95, 1.14, and 1.60, where positive numbers mean more hits with “beautiful bridge” (i.e. the trend runs the opposite way from the prediction), but none of the differences are statistically significant (p > 0.4). Gender does not seem to influence perceptions of bridges.

Interestingly, if we exclude the international languages English and Spanish, there is actually a statistically significant (but weak) correlation with GDP of the relevant nation (p = 0.029, r = 0.58). On the whole, poorer countries are more likely to describe a bridge as “strong,” and wealthier countries as “beautiful.” That makes sense, if you think about it (although Iceland is an exception to this pattern).

How about you? Is the bridge beautiful, or strong?


Belief in God in the US

In another fascinating example of social statistics, Pew have just released a survey of US beliefs about God. The study included multiple questions about the nature and attributes of God, but my mosaic plot below only looks at the first one. The composition of each column is based on the recent survey, while the width of each column is based on religious composition data from a 2014 study by Pew.

In dark blue, 62% of the US believes in God “as described in the Bible.” A further 30% (in light blue) believes in some other god or higher power (or would not describe their belief in God in more detail). In red, 7% believe in no God at all, and in grey, 1% gave no response.

Columns correspond to denominations: Evangelical Protestant, Mainline Protestant, Historically Black Protestant (HBP), Catholic, Other Christian (OC), Jewish (J), Other Religion (Oth), “Nothing in Particular,” Agnostic (Ag), and Atheist (Ath). Numbers in the “OC” and “Oth” categories were not directly provided by Pew, and were estimated using totals provided (these two columns should therefore be taken with a grain of salt).

Among Christians, 92% of Historically Black Protestants and 91% of Evangelical Protestants believe in God “as described in the Bible,” but only 72% of Mainline Protestants and 69% of Catholics do. What’s more, 1% of Mainline Protestants, 2% of Catholics, and 10% of Jews say that they believe in no God at all (i.e. they adhere to their religion only culturally, and are actually atheists).

On the other hand, 90% of those who describe their religion as “nothing in particular” believe in some kind of God or higher power. So do 67% of agnostics and 18% of atheists (clearly, many who claim to be “nothing in particular” are in fact Christians of some form, and many who claim to be atheists are in fact not).

Part of the explanation for this presumably lies in the fact that religion is in flux for many people in the US. Christians switch between the four main groups, some Christians lose their faith, while other people gain faith in Christianity or in another religion. Religious reality is more complex than a handful of numbers might suggest.


Reflections on school performance in the US

The US has just had a release of the 2017 National Assessment of Educational Progress (NAEP) results. They are not good. Of grade 8 pupils in public schools, 65% failed to meet proficiency standards in reading, and 67% failed to meet proficiency standards in mathematics. This is a serious problem, and it is worth getting to the bottom of it.

Doing a multiple regression on average state grade 8 reading scores, the politics of the state governor has no effect (p = 0.67). States vary enormously in the money they spend on education, ranging from $6,575 per pupil in Utah to $21,206 per pupil in New York. This makes no difference either (p = 0.93). What does make a difference is the state poverty rate (R2 = 0.49, p = 0.000000014).

For grade 8 mathematics scores, the story is similar. Politics of the state governor (p = 0.76) and money spent on education (p = 0.51) have no effect, but the state poverty rate does (R2 = 0.55, p = 0.0000000008).

Clearly, poor children do much less well in school, and spending money on schools does not address the problem. Why do poor children do less well in school? Research shows that on day one, poor children have a cognitive and behavioural disadvantage. Poor children eat less well. Poor children are starved of words, because their parents, on average, spend less time talking, singing, and reading to them.

The problems lie at home; the solutions must also lie at home. Rather than spending more money in schools, the US seems to need more assistance to parents at home. For example, the State Library of Queensland has started a wonderful Dads Read programme in Australia. Bookstart in the UK offers a free pack of books to children at 0–12 months and at 3–4 years. Also helpful would be guides to teaching number skills, guides to nature walks, discounts for families at museums, and other assistance in STEM areas (I’m start to feel like it’s time to write another children’s book). Surely this problem with reading and mathematics needs to be addressed with urgency!


Story time at the Dover Air Force Base library, Delaware (USAF photo by Roland Balik)


Pencil charts for visualising colours

As a result of a discussion with a photographer friend of mine, I’ve been thinking (not for the first time) about visualising the colour palette of images. Consider this sunset, for example (a picture I took in Adelaide 8 years ago):

The photograph is rich in yellow and orange. However, the apparent blue in the sky is actually grey, and the apparent grey of the sea is actually brown. If we postulate a standard set of 35 plausible pencil colours, and map each pixel to the closest-matching pencil colour, we get this (I have done the comparison in RGB space):

Then we can visualise the colour palette of the image by showing the wear on the virtual pencils, if each virtual pencil has been used to colour the corresponding pixels. It can be seen that a lot of orange, brown, and grey was used (click to zoom):

Conversely, this beach scene (photographed in Vanuatu in 2016) is rich in blues:

The warm light greys of the beach don’t quite find an exact match among the pencils, but the other colours match fairly well:

And here is the pencil visualisation (click to zoom):

If, rather than using a standard set of colours, we extract the pencil colours from the image itself (image quantisation), fewer pencils will, of course, be required:

The fit to the original image will be much closer as well:

So this is a trick to remember for another day – pencil visualisations!