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.
A poem to wish everybody a Blessed Easter in these difficult times.
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:
- 1. theos, pas, Christos, mē, kurios – a general topic about God and Christ
- 2. megas, gē, theos, aggelos, horaō – an apocalyptic topic, found especially in Revelation
- 3. gunē, anēr, sōma, laleō, kosmos – advice about men and women, found especially in the Pauline Epistles
- 4. ginomai, theos, laos, hēmera, horaō – a general topic
- 5. paschō, psuchē, chronos, makarios, peirasmos – a topic associated especially with James and 1 Peter
- 6. hamartia, haima, pistis, diathēkē, prospherō – sin and sacrifice, associated especially with Hebrews
- 7. pantote, paraklēsis, kauchaomai, prosōpon, chairō – a topic associated with the Pauline Epistles
- 8. nomos, hamartia, pistis, dikaiosunē, ethnos – sin and the Law, a topic associated especially with John, James, and the Pauline Epistles
- 9. agapētos, ouranos, tēreō, epignōsis, krisis – heaven and judgement, a topic associated especially with 2 Peter, Colossians, and Jude
- 10. Iēsous, pisteuō, patēr, kosmos, theos – a general topic about faith in Jesus
- 11. Paulos, pas, anēr, Ioudaios, theos – a topic about Paul, found especially in Acts and Philemon
- 12. ergon, pistis, kalos, idios, pas – work and faith, a topic associated especially with the Pastoral Epistles
- 13. basileia, huios, aphiēmi, proserchomai, archomai – Jesus talking about the Kingdom in the Synoptic Gospels
- 14. legō, mē, erchomai, horaō, Iēsous – a general topic
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.”
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.
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.
|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|
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.
The letter K is a little out of date, and there is probably a better choice out there for Y, but here is a science-based alphabet poster.