Spot the difference #2

One more “spot the difference” puzzle. The top is a copy of Children’s Games by Pieter Bruegel the Elder (1560). The bottom is the same thing with 21 edits of my own (including 8 outright additions, 7 outright removals, and 6 alterations of colour, shape, or number). The solution is here.

Topic Analysis on the New Testament

I have been experimenting recently with Latent Dirichlet allocation for automatic determination of topics in documents. This is a popular technique, although it works better for some kinds of document than for others. Above (click to zoom) is a topic matrix for the Greek New Testament (using the stemmed 1904 Nestle text, removing 47 common words before analysis, and specifying 14 as the number of topics in advance). The size of the coloured dots in the matrix shows the degree to which a given topic can be found in a given book. The topics (and the most important words associated with them) are:

A better set of topics can probably be obtained with a bit more experimentation. Alternatively, here (as a simpler form of analysis) are the relative frequencies of some Greek words or sets of words, scaled to the range 0 to 1 for each word set (with the bar chart showing the total number of words in each New Testament book). Not surprisingly, angels appear more frequently in Revelation than anywhere else, while love is particularly frequent in 1 John:


The triboelectric effect was discovered 2600 years ago by Thales of Miletus. When items in this illustrated (incomplete) list are rubbed together, the low-numbered item gains a positive charge, and the high-numbered item gains a negative charge.

For example, glass rubbed with silk (or, even better, polyester) gains a positive charge, once called “vitreous electricity.” Amber rubbed with wool gains a negative charge, once called “resinous electricity.” Indeed, our word “electron” comes from the Greek ἤλεκτρον, meaning “amber.”

Chemistry can be beautiful: the classic flame test

The flame test occasionally comes up in classic detective fiction: “He snapped off the lights, and we were left with only the sodium flame. In that green, sick glare a face floated close to mine – a corpse-face – livid, waxen, stamped with decay…” (Dorothy L. Sayers & Robert Eustace, The Documents in the Case)

Spectral lines in the image are taken from Kramida, A., Ralchenko, Yu., Reader, J., and NIST ASD Team (2019). NIST Atomic Spectra Database (ver. 5.7.1), [Online]. National Institute of Standards and Technology, Gaithersburg, MD. Photographs in the image are public domain, from Wikimedia Commons.

A planetary fruit salad

Here is a planetary fruit salad – a scale model of objects in the solar system (click to zoom). The Moon and the smaller planets are on the top left saucer. The lower right saucer represents the rings of Saturn.

On this scale (roughly 1 to 2 billion), the Moon is 19 centimetres from the Earth, the Earth is 73 metres from the Sun, Jupiter is 380 metres from the Sun, and Pluto is around 3 kilometres from the Sun.

Object Diameter Scaled Diameter Model
Sun 1,392,700 km 68 cm Beach ball (not shown)
Mercury 4,879 km 0.24 cm Mustard seed (yellow)
Venus 12,104 km 0.59 cm Chickpea
Earth 12,756 km 0.62 cm Chickpea (coloured blue)
Moon 3,475 km 0.17 cm Mustard seed (black)
Mars 6,792 km 0.33 cm Peppercorn (black)
Jupiter 142,984 km 7 cm Orange
Saturn 120,536 km 5.9 cm Lemon
Saturn’s Rings (up to F) 280,360 km 14 cm Saucer
Uranus 51,118 km 2.5 cm Grape
Neptune 49,528 km 2.4 cm Grape
Pluto 2,377 km 0.12 cm Poppy seed

World Population

Some feedback on my last post expressed surprise that Ptolemy’s specification of the Oikoumene now holds holds 80.6% of the world’s population. Above (click to zoom), I have redrawn the classic bar charts of world population which explain this fact. Africa, Asia, and Europe contain about 86% of the world’s population. Ptolemy excluded what we now know to be Southern Africa (which only drops the total to 85%) and didn’t extend his Oikoumene quite far enough to the east.

The chart below shows the same thing, but using NASA’s image of the Earth at night. It can be seen that the spikes on the bar chart correspond to major cities.