Above is an analemmatic sundial. The idea is to orient the sundial facing south, and then place a vertical pointer on the central figure-8 track, in a position corresponding to the date. The sundial above shows a simulated shadow for 2:15 PM yesterday. It can be seen that the sundial tells the time reasonably well, thanks to the inbuilt adjustment for variation in solar position.

For large-scale analemmatic sundials, like the one below, people can stand on the central figure-8 track and act as a human pointer. A sundial like this is fun to have in the garden.

Here are blank sundials for some Southern Hemisphere cities:

The ShadowsPro software will also generate sundials like these, if anyone is particularly enthusiastic.


Voting patterns in the United States

Because of my interest in social statistics, I’ve been exploring county-level results from the US 2016 presidential election. The map below (click to zoom) summarises the results (blue for Democrat and red for Republican, coloured according to how strongly counties voted one way or the other). Nine of the more extreme counties are highlighted.

Most of the variance in this data can be explained by demographic factors such as race, age, education levels, local unemployment, rural-urban continuum code, and median household income. The latter is particularly interesting, and the chart below provides a summary.

On a scale from −0.5 being 100% Republican to +0.5 being 100% Democrat, the curve shows the average vote of counties by 2016 median household income (where the averages are weighted by county population sizes, and LOESS smoothing is used to draw the curve). Overlaid on the diagram is a bar chart for the total population of different median household income groups (the scale for this bar chart is on the right).

It can be seen that, at the very poorest end, votes are balanced between Democrat and Republican. For example, here are the 7 poorest counties in the United States, by median household income. They are all rural:

Above that bottom end, votes trend Republican, with the peak Republican vote occurring at median household incomes around $40,000. Above about $56,000, counties swing Democrat, and the Democrat vote increases with increasing wealth. For example, here are the 4 richest counties in the United States, by median household income. They are all part of the Baltimore–Washington metropolitan area:

Essentially, the Republican Party seems to have become the party of the poor, particularly the rural poor. Indeed, the (population-weighted) median of 2016 median household incomes for Democrat-majority counties was $61,042; while for Republican-majority counties it was $52,490 ($8,552 less). For a visual perspective, the map below limits the previous one to counties with a 2016 median household income below $56,000. It is precisely because the Republican Party has become the party of the rural poor that these maps are mostly red. I had not fully appreciated this before analysing the data (although others have), but it certainly explains much of recent politics in the US. However, predicting the results of the next presidential election would require some solid demographically linked polling data as well as a good voter turnout model.

Powers of 10: the Australian version

In the footsteps of the classic short film, we explore the powers of 10 (click to zoom).

We begin with a classic NASA photograph of the Earth seen from Saturn, with a field of view (in the distance) about 100,000,000 km across. We zoom in by a factor of 10 to see the Earth and the Moon beside it. After three more such jumps (to 10,000 km), the Earth fills the frame. Three further jumps (to 10 km) zooms in on Melbourne, Australia. Two more jumps show us the city centre (1 km) and St Paul’s Cathedral (100 m). Another two jumps (to 1 m) give us a small boy on the grass beside the Cathedral. Two more give us the iris and pupil of his eye (1 cm) and a small patch of his retina (1 mm). Finally (at 100 µm or 0.1 mm), we see red blood cells inside a blood vessel in his retina. Fifteen jumps in all, zooming in by 1015.

Sea levels in the Pacific

I recently visited Port Vila, capital of the Pacific island nation of Vanuatu (the photo above is from the Port Vila waterfront). Port Vila is the site of a sea-level measuring station. It is interesting that, although local newspapers are deeply concerned about sea level rise, the average sea level rise between 1993 and 2017 at Port Vila was essentially zero (see chart below, which uses LOESS smoothing of monthly measurements).

How can this be? Aren’t global sea levels rising at 2–3 mm per year? Well, “global sea level” is a rather theoretical concept. Ocean temperatures are not uniform. Some islands are rising out of the ocean. Others are sinking. Air pressure, and the El Niño Southern Oscillation cycle, have a huge effect on sea levels too. As they say, it’s complicated.

The NASA map below shows that some areas of the Pacific have actually seen a long-term reduction in sea level (independent of any upward or downward movement of land). Other areas, of course, have seen quite rapid increases (the increases and decreases average out to a rise of about 3 mm per year). The map covers data only up to 2008, however. Since 2008 was roughly the peak for the Port Vila data, it doesn’t quite explain the last decade of the graph above. If I had to guess, I’d assume that some of those sea-level-decrease areas on the map had shifted a bit.

Support for Kavanaugh vs support for Trump

Brett Kavanaugh has been in the news rather a lot lately. The chart above shows support for his appointment to the US Supreme Court, for various demographic groups, as per a 1 October Quinnipiac University Poll. This is compared to the 2016 Trump vote for those same groups, as per CNN exit polls (in both cases, some missing information had to be inferred using the data provided plus census data). The area of the circles shows the size of the various groups.

Responses to Kavanaugh seemed largely to follow partisan lines. Democrats mostly went one way, Republicans the other. However, white women seemed to support Kavanaugh less than expected, perhaps because they were more likely to believe the accusations made against him. Minority groups, on the other hand, were more supportive of Kavanaugh than of Trump, perhaps because of concerns about evidence, corroboration, and due process. Overall, it seems to almost balance out, though – I must say that I can’t see any support here for a “blue wave” at the November elections.

Would y’all like to see a map?

The word y’all is used as a second person plural pronoun in the United States (although in my travels I have also heard it used as a polite singular). The map above (click to zoom) shows the average frequency of use by state, according to the 2003 Harvard Dialect Survey. The usage is primarily Southern.

English needs a second person plural pronoun, it seems to me. What do all-y’all think?

Image produced using the maps package of R. Other visualisations of the survey exist.


I’m off soon to Vanuatu for a holiday. Above (click to zoom) is a map of this island nation (produced using the raster package of R, with my own colour palette). The map outlines are from (which is missing an island, unfortunately). Elevation data is from the Shuttle Radar Topography Mission (with additional void fill using a lower-resolution dataset).

The overlay in red shows light visible at night (from NASA’s Earth at Night). Apart from the two main towns of Luganville and Port Vila, the active volcanoes on Ambrym and Tanna are clearly visible (take a closer look at Ambrym’s lava lake here).

Not highlighted is the active volcano on Ambae, an island which held 4% of the nation’s population until it was recently evacuated – consider helping the evacuees via Anglican Aid.