Photo: Mark Jones
I see that many Americans are excited by the upcoming royal wedding between Prince Harry and Meghan Markle. I have even heard suggestions that Meghan will be the “first mixed-race princess” in England.
This is, of course, nonsense. Technically, Queen Elizabeth II is herself “mixed-race.” Among other things, she is descended from Zaida of Seville (1070–1100), an Arab princess (daughter to Al-Mu’tamid ibn Abbad). Zaida fled Seville after the savage Almoravid takeover, taking refuge with King Alfonso VI of Castile. Zaida converted to Christianity, took the name Isabella, and became the mistress (and later wife) of King Alfonso. Queen Elizabeth II is her descendant:
In his short work The Sand Reckoner, Archimedes (c. 287 BC – c. 212 BC) identifies a number larger than what he believed was the number of grains of sand which would fit into the Universe. He was hampered by the fact that the largest number-word he knew was myriad (10,000), so that he had to invent his own notation for large numbers (I will use modern scientific notation instead).
Archimedes’ began with poppyseeds, which he estimated were at least 0.5 mm in diameter (using modern terminology), and which would contain at most 10,000 grains of sand. This makes the volume of a sand-grain at least 6.5×10−15 cubic metres (in fact, even fine sand-grains have a volume at least 10 times that).
Archimedes estimated the diameter of the sphere containing the fixed stars (yellow in the diagram below) as about 2 light-years or 2×1016 metres (we now know that even the closest star is about 4 light-years away). This makes the volume of the sphere 4×1048 cubic metres which means, as Archimedes shows, that less than 1063 grains of sand will fit.
A more modern figure for the diameter of the observable universe is 93 billion light-years, which means that less than 1095 grains of sand would fit. For atoms packed closely together (as in ordinary matter), less than 10110 atoms would fit. For neutrons packed closely together (as in a neutron star), less than 10126 neutrons would fit. But these are still puny numbers compared to, say, 277,232,917 − 1, the largest known prime!
The chart above shows approximate radiation releases (in becquerels) for some major nuclear disasters. It should be interpreted with caution, since some radioisotopes are more dangerous than others. For example, the releases from Three Mile Island were largely noble gases (mostly xenon), and that incident appears to have had few detectable environmental or health effects. Ticks on the vertical axis of the chart go up logarithmically, in steps of ×1000. For comparison, radium and bananas are also listed.
Chernobyl reactor #4 in 2007, encased in concrete
Following up on my “origins of the alphabet” chart, here is one for numerals. The chart was produced using R, and the pictures are purely illustrative – unlike the pictures in the alphabet chart, they do not relate to the origins of the symbols.
Shakespeare writes “the moon’s an arrant thief, and her pale fire she snatches from the sun” (Timon of Athens, Act 4, Scene 3). He is, of course correct. The moon merely reflects sunlight, and produces no light of its own. One way of telling this is that moonlight actually displays the same telltale absorption spectrum as sunlight:
Our eyes tend to perceive moonlight as “blueish” or “silvery,” but that is because of the way our eyes work at low light levels. Long-exposure photographs under moonlight, like this one, look much like daytime shots:
Anaxagoras (499–428 BC) seems to have been the first to discover that the moon shines only by reflected light:
Anaxagoras also explained that solar eclipses occur when the moon moves between the earth and the sun. Total solar eclipses are dark precisely because the moon produces no light of its own:
This chart shows the origins of the Phoenician, Hebrew, Greek, and Latin alphabets. The Phoenician alphabet is adapted from Egyptian hieroglyphs, but the exact pictorial origins are rather uncertain. The specific Phoenician alphabet used is from here. The chart was produced using R.
An instructive saga in the history of engineering is the story of the British airships R100 and R101. As part of a grand social experiment, the R100 was built by private industry (it was designed by Barnes Wallis), while the R101 was built by the British government (specifically, by the Air Ministry, under Lord Thomson). The R100 worked fine, and made a test flight to Canada in August 1930 (the trip took 78 hours). Here is the R100 over a Toronto building:
The R100 was huge. Here is a size comparison of the R100 (219 m long) and an Airbus A380 (73 m long):
While the government-built R101 used servo motors to control its gigantic rudder, the R100 team had worked out that the rudder could actually be operated quite easily by hand, using a steering wheel and cables. The government-built R101 was beset by poor choices, in fact. It contained overly heavy engines, a steel frame, and too much dead weight overall. After construction, the R101 had to be lengthened by inserting a new 14-metre section in the centre, in order to increase lift. This alteration caused a number of problems. Its design also allowed the internal hydrogen-filled gasbags to chafe against the frame, there were serious problems with the outer covering, and several “innovative” design ideas were never properly tested.
There was enormous political pressure for the R101 to fly before it was ready to do so. On the evening of 4 October 1930, it departed for India with a crowd of VIPs on board. It never arrived, crashing in bad weather over France, and bursting into flames. The disaster led to the R100 also being grounded, and the British government abandoned any thoughts of flying airships (as the rest of the world was to do after the Hindenburg disaster).
There are all kinds of lessons to be drawn from the saga of the R100 and the R101. One of them is that optimism is not a viable strategy for safety-critical engineering. Another is that engineers test things. As Kipling says, “They do not preach that their God will rouse them a little before the nuts work loose.” A third is that risky designs and fixed deadlines simply do not mix.