Category Archives: Images

Timeline of mathematical notation

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Following up on my earlier timelines about zero and about Hindu-Arabic numerals, here is a timeline for some other mathematical notation, starting with the square root symbol (click to zoom).

0123456789 in Europe: an infographic

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Following up on my earlier post about 0 and 1 in Greek mathematics and my timeline of zero in Europe, here is a timeline for the use of Hindu-Arabic numerals in Europe up to René Descartes (click to zoom).

The history of zero: an infographic

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Following up on an earlier post about Zero in Greek mathematics, here is a timeline for the use of zero in Europe (click to zoom). I have used images of, or quotes from, primary sources where possible (reliably dated Indian primary sources are much harder to find than Greek ones, unfortunately).

Chinese uses of zero are probably also derived from the Greeks, but Mayan uses are clearly independent.

Dante’s Heaven

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In previous posts (Inferno, Purgatorio, Paradiso), I have mentioned the scientific content of Dante’s incredible theological poem, the Divine Comedy. Above, just for fun, is a chart of Heaven (the Solar System) in his Paradiso. Notice the sphere of fire which was believed to surround the Earth.

Rods and cones in the human eye

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I already posted these images (click to zoom) on Instagram. They illustrate the sensitivity to colour of the rods (lower right) and the three types of cones in the human eye. Cone sensitivity data is from CVRL.

Notice that red light is pretty much invisible to the rods. This is why red light does not interfere with night vision, and is used in e.g. this aircraft cockpit:

Houston, we have a problem

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Some years ago, I posted the chart above, inspired by a classic XKCD cartoon. The infographic above shows the year of publication and of setting for several novels, plays, and films.

They fall into four groups. The top (white) section is literature set in our future. The upper grey section contains obsolete predictions – literature (like the book 1984) set in the future when it was written, but now set in our past. The centre grey section contains what XKCD calls “former period pieces” – literature (like Shakespeare’s Richard III) set in the past, but written closer to the setting than to our day. He points out that modern audiences may not realise “which parts were supposed to sound old.” The lower grey section contains literature (like Ivanhoe) set in the more distant past.

The movie Apollo 13 has now joined the “former period piece” category. Released in 1995, it described an event of 1970, 25 years in the past. But the ill-fated Apollo 13 mission of 11–17 April 1970 is now 51 years in the past; the movie is closer to the event than it is to us (although the phrase “Houston, we have a problem” – in real life, “Houston, we’ve had a problem” – has become part of the English language).

The image shows the real-life Apollo 13 Service Module, crippled by an explosion (left), together with a poster for the 1995 movie (right). Maybe it’s time to watch it again?

A Narnian Timeline

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I’ve been on a bit of a Narnia binge recently. Continuing that theme, here is a timeline of the Chronicles of Narnia (click to zoom). The Terran time axis has varying scales (although piecewise linear), since 5 of the 7 Narnia books (53% of Narnian history) are set during 1940–1942. For simplicity, I also assume a piecewise linear mapping of Narnian time to Terran time (see graph below), although the text of the books indicate that the mapping is more complex than that. For Narnian events in the chart, only the vertical position has meaning (the sideways curve is only there to create space).

The Crucifixion of Jesus is included as a significant Terran event, since its Narnian parallel is the key event of The Lion, the Witch and the Wardrobe. Some scholars date this to the year 30, rather than 33.

The chart was produced using R. The curved lines are plotted with colours from colorRampPalette(). Images were added using png::readPNG, as.raster(), and rasterImage(), with circles using plotrix::draw.circle(). For the title, the extrafont package was used.

Four new species from 2020

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In spite of Covid-19, last year saw the description of several hundred new species of plants and animals. The image above (click to zoom) shows four of them.

Top left: The Yoknapatawpha darter, Etheostoma faulkneri (male shown above female) is found only in the Yocona River of Mississippi. It was recently distinguished from the closely related Etheostoma raneyi found in nearby rivers.

Top right: Dendropsophus bilobatus (image credit M. Ferrão, J. Moravec, J. Hanken, A.P. Lima) is a small Bolivian tree frog distinguished by the shape of its vocal sac and its characteristic mating call.

Bottom left: Platylestes kirani (male only shown; image credit Rison Thumboor) is a damselfly from the coastal wetlands of Kerala, South India.

Bottom right: The northern Western Ghats vine snake, Ahaetulla borealis (image credit Geoish) is a tree snake from the Western Ghats of India. It was declared to be a species in its own right after a subdivision of Ahaetulla nasuta.

The “America the Beautiful” quarters

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Just for fun (click to zoom), a map of 49 of the 56 U.S. National Parks, National Forests, and National Wildlife Refuges shown on the “America the Beautiful” quarters. How many have you visited?

Locations auto-extracted from Wikipedia pages using R, and colours indicating elevation, using an elevation dataset from www.worldclim.org (a dataset which treats the Great Lakes as land) and a palette I knocked together.