Scientific alignment

I was thinking recently about the alignment (in the Dungeons & Dragons sense) of fictional scientists (see diagram above).

I was brought up on the Famous Five children’s stories by Enid Blyton. Perennially popular, even though flawed in certain ways, these novels star a rather grumpy scientist called Quentin (who had more than a little to do with my own desire to become a scientist). Quentin is certainly altruistic:

‘These two men were parachuted down on to the island, to try and find out my secret,’ said her father. ‘I’ll tell you what my experiments are for, George—they are to find a way of replacing all coal, coke and oil—an idea to give the world all the heat and power it wants, and to do away with mines and miners.’
‘Good gracious!’ said George. ‘It would be one of the most wonderful things the world has ever known.’
‘Yes,’ said her father. ‘And I should give it to the whole world—it shall not be in the power of any one country, or collection of men. It shall be a gift to the whole of mankind—but, George, there are men who want my secret for themselves, so that they may make colossal fortunes out of it.’
” (Enid Blyton, Five On Kirrin Island Again, 1947)

However, Quentin works for no organisation (barring some government consulting work) and draws no regular salary. He is clearly Chaotic Good.

Long before Quentin, Victor Frankenstein in Frankenstein (Mary Shelley, 1818) created his famous monster out of selfishness and hubris. However, he also desires to make things right, so Frankenstein seems to me Chaotic Neutral.

On the other hand, the experiments of Doctor Moreau in The Island of Doctor Moreau (H. G. Wells, 1896) mark him as Chaotic Evil. The same is true of the scientist Rotwang in the movie Metropolis (1927), who is the prototype of the evil “mad scientist” of many later films – in contrast to good “mad scientists” like Emmett “Doc” Brown in the Back to the Future movies (1985, 1989, 1990).

In all cases, however, there seems to be a bias towards portraying scientists as Chaotic. This is a little strange, because the organisational structures, processes, and rules governing science in the real world are better described as “ordered” or Lawful (in the Dungeons & Dragons sense). Perhaps chaotic characters are just more fun?

Not that everyone follows all the rules and procedures of course. When I take the What is your Scientific Alignment? test, my personal alignment comes out as Neutral Good.

Looking back: 1987

In 1987, my PhD work at the University of Tasmania was beginning to take shape, and I produced a technical report with some preliminary results. I also started a side-project on functional programming language implementation which was to result in the design of a novel computer (a computer, sadly, that was never actually built, although many people joined in on the hardware aspects).

Also in that year, Supernova 1987A became visible within the Large Magellanic Cloud (picture above taken by the Kuiper Airborne Observatory). The programming language Perl also appeared on the scene, and Per Bak, Chao Tang, and Kurt Wiesenfeld coined the term “self-organized criticality.” Prompted by a discovery in 1986, physicists held a conference session on high-temperature superconductivity, billed as the “Woodstock of physics.” The immediate benefits were somewhat over-hyped, however.

The usual list of new species described in 1987 includes Fleay’s barred frog from northern New South Wales and south-eastern Queensland (picture below taken by “Froggydarb”).

In the world of books, James Gleick popularised chaos theory with his Chaos: Making a New Science, Allan Bloom wrote The Closing of the American Mind (which Camille Paglia called “the first shot in the culture wars”), and Donald Trump co-wrote Trump: The Art of the Deal (nobody imagined that he would be President one day).

Horror writer Stephen King had a good year, with The Tommyknockers and several other novels being published. The term “steampunk” was coined in 1987, and Orson Scott Card’s Speaker for the Dead, the sequel to Ender’s Game, won the Hugo Award for best science fiction or fantasy novel (it also won the Nebula Award in 1986, the year it was published).

In music, The Alan Parsons Project released their album Gaudi (which included the single below), U2 released The Joshua Tree, and Linda Ronstadt, Emmylou Harris, and Dolly Parton released Trio. The Billboard top song for 1987 was the rather silly 1986 single “Walk Like an Egyptian.”

Films of 1987 included 84 Charing Cross Road (based on the wonderful 1970 book by Helene Hanff), Bernardo Bertolucci’s The Last Emperor, Japanese hit A Taxing Woman (マルサの女), sci-fi action film Predator, Australian film The Year My Voice Broke and, of course, the cult classic The Princess Bride (based on the 1973 novel by William Goldman).

In this series: 1978, 1980, 1982, 1984, 1987, 1989, 1991, 1994, 2000, 2004, 2006, 2009.

Revising the Metric System

Relationship between the new SI units (image produced using the igraph package of R)

On May 20, a major redefinition of SI (metric) units comes into force. In particular, the second, metre, ampere, mole, kilogram, kelvin, and candela will be defined as follows:

The second (unit of time)

As it is now, the second will be defined using ultra-precise caesium clocks. Specific microwave radiation from caesium atoms is defined to have a frequency of exactly 9.192 631 770 GHz. That is, counting 9,192,631,770 waves will take exactly one second.

The metre (unit of length)

As it is now, the metre will be defined using the speed of light, which is defined to be exactly 299,792,458 metres per second. That is, the metre is the distance travelled by light in one 299,792,458th of a second (where the second is defined as above).

The ampere (unit of electric current)

The definition of the ampere (amp) has been greatly simplified, taking account of the connection between electricity and electrons. The ampere is a coulomb of electric charge flowing past a given point per second, and the charge on a single electron is now defined to be 1.602 176 634 × 10−19 coulombs. Thus an ampere is about 6,241,509,074 billion electrons flowing past a given point in a second.

As a consequence of this new definition, two important natural constants which used to have defined values (the permeability of free space and the permittivity of free space) now have experimentally determined ones. This will require rewriting pretty much every physics and electrical engineering textbook.

The mole (unit of amount of substance)

The mole represents Avogadro’s number of atoms, molecules, or other particles. Previously, Avogadro’s number was defined to be the number of carbon atoms in 12 grams of pure carbon-12. It is now defined to be exactly 6.022 140 76 × 1023.

The kilogram (unit of mass)

Until 2019, the kilogram was defined by the mass of a specific metal cylinder held in Paris. This has been felt to be unsatisfactory for many years. The current definition uses the fact that the energy of a light photon (in joules) is its frequency times Planck’s constant h, which is defined to be exactly 6.626 070 15 × 10−34.

In practice, a Kibble balance will be used to measure weights by balancing them against an electrically produced force. Units derived from the kilogram include:

  • The newton (unit of force): the force needed to accelerate 1 kilogram at a rate of 1 metre per second squared
  • The pascal (unit of pressure): 1 newton of force per square metre
  • The joule (unit of energy): the energy used in applying a force of 1 newton over a distance of 1 metre
  • The watt (unit of power): 1 joule of energy per second
  • The volt (unit of electric potential): the amount of electric potential across a resistance producing 1 watt of heat per ampere of current
  • The ohm (unit of electrical resistance): the resistance which produces 1 ampere of current when 1 volt of electric potential is applied

See also what NIST has to say about the kilogram.

The kelvin (unit of temperature)

Temperature in degrees Celsius was originally measured on a scale with 0 °C being the freezing point of water and 100 °C the boiling point (at standard pressure). The lowest possible temperature turned out to be absolute zero, −273.15 °C. In 1954, the two fixed points on the scale were changed to −273.15 °C (0 kelvins) and the triple point of water, 0.01 °C (273.16 kelvins).

This definition proved unhelpful for calibrating thermometers intended for very high temperatures, and the current definition uses the fact that the average translational kinetic energy (in joules) of a moving atom of a monoatomic ideal gas is (3/2k T, where T is the temperature of the gas in kelvins, and the Boltzmann constant k is defined to be exactly 1.380 649 × 10−23.

The candela (unit of luminous intensity in a given direction)

The definition of the candela remains what it has been, except that it is influenced by the change in definition of the kilogram (and hence the watt). A light source that emits monochromatic yellowish-green light at a frequency of 540 THz (roughly 555 nm wavelength) is taken to emit 683 lumens per watt, and a light source that uniformly radiates 1 candela in all directions has a total luminous flux of 4π lumens (the constant 683 reflects the human ability to perceive light). The lux is a lumen per square metre.

The dream

When the metric system was first introduced, the metre was defined in terms of the world (1/10,000,000 of the distance between the Equator and the North Pole, measured via Paris). Today, the metric system carries that philosophy to its ultimate conclusion, with all units except the candela defined in terms of the universe. Five of the units are defined in terms of fundamental physical constants: the speed of light (first measured by Rømer in 1676), the charge on the electron (first measured directly by Robert A. Millikan in 1909), the Avogadro constant (measured several ways by Jean Perrin around 1910), and the Planck and Boltzmann constants (first defined by Max Planck around 1900).

The redefined metric system is a little difficult to grasp without understanding modern physics, but fortunately most of us will just keep on using exactly the same measurement instruments as we have done for years.

The modern Trivium and the teaching of science

The “trivium” approach to education derives from “The Lost Tools of Learning,” a 1947 speech by scholar and detective story author Dorothy L. Sayers. This approach takes the seven liberal arts (illustrated above), drops the all-important quadrivium, and applies the remainder in a largely metaphorical way. It is an interesting approach, although it inevitably under-emphasises mathematics. The door to Plato’s Academy was marked “Let no one ignorant of geometry enter (Ἀγεωμέτρητος μηδεὶς εἰσίτω),” and this referred to the most advanced mathematic of his day. I’m not sure that the “trivium” approach to education delivers that level of mathematical knowledge. Then again, does the standard approach?


Science, on the other hand, can be fitted quite well into the “trivium” model. The three stages of this model (largely metaphorical, as noted) are “grammar,” “logic,” and “rhetoric.”

The “grammar” stage (intended for ages 6 to 10 or so) covers basic facts. Science at this level logically includes what used to be called natural history – the close observation of the natural world. Maintaining a nature journal is an important part of this, as are simple experiments, the use of a telescope, collections of objects (rocks, shells, etc.), and simple measurements (such as recording measurements from a home weather station).

Mother and child nature journaling examples from Nature Study Australia Instagram and website

Dorothy L. Sayers has nothing to say about science in the “logic” stage (apart from fitting algebra and geometry here), but the “logic” stage would reasonably include taxonomies, empirical laws, and an exploration of how and why things work the way they do – that is, the internal logic connecting scientific observations and measurements. A degree of integration with history education would provide some context regarding where these taxonomies and laws came from, and why they were seen as important when they were formulated.

Exploring Boyle’s law with a simple apparatus

In the “rhetoric” stage, the “how” and “why” of science would be explored in more detail, along with practical applications and project work (such as entering a science competition, or possibly even collaborating with local academics on a scientific conference paper).

A US Army engineer helps judge high school science projects (photo: Michael J. Nevins / US Army)

I suspect that quite a decent science education programme could be worked out on such a basis. If any reader knows of it having been done, please add a comment.

Eureka! – a book review

Eureka!: The Birth of Science by Andrew Gregory

I recently read Eureka!: The Birth of Science by Andrew Gregory. The book deals with a topic that has long fascinated me – the birth of science. In a previous post I argued that this took place in the 12th century, the age of cathedrals. Gregory takes the view that it happened with the ancient Greeks, and sees Aristotle and Archimedes as among science’s pioneers. He gives a brief defence of this thesis, and provides a quick summary of Greek scientific thought.

Aristotle and Archimedes

I found this book rather short for the subject (177 pages, including bibliography), was disappointed at the lack of endnotes, and found some annoying errors (the Greeks did not consider the universe small, for example – Archimedes took it to be 2 light-years across). But the big unanswered question is: what went wrong? Gregory includes a list of key people at the back of the book, and if you turn that list into a bar chart, you can see that Greek science basically fell off a cliff around 200 BC.

In a brief two-page section towards the end, Gregory suggests that Christianity was somehow responsible for the decline of Greek science, but that simply makes no sense. Was it instead Roman conquest, beginning around 280 BC? Was it the growing separation of aristocratic philosophy from plebeian technology? Was it the replacement of original science by encyclopaedic systematisation (such as that of Pliny)? It would have been nice to have those questions answered.

Goodreads gives this book 3.4 stars; I was rather less enthusiastic.

Eureka!: The Birth of Science by Andrew Gregory: 2 stars

Measuring the Earth this (Southern) Christmas

In around 240 BC, Eratosthenes calculated the circumference of the Earth. The diagram above (from NOAA) shows how he did it. This Christmas, people in the Southern Hemisphere can repeat his work!

Eratosthenes knew that, at the summer solstice, the sun would be directly overhead at Syene (on the Tropic of Cancer) and would shine vertically down a well there. He also knew the distance to Syene.

On 21 December, the sun will be directly overhead on the Tropic of Capricorn at local noon. This table show the time of local noon on 21 December 2017, and the distance to the Tropic of Capricorn, for some Southern Hemisphere cities:

City Local Noon Distance to Tropic (km)
Adelaide 13:14 1270
Auckland 13:19 1490
Brisbane 11:46 450
Buenos Aires 12:52 1240
Darwin 12:45 1220
Hobart 13:09 2160
Johannesburg 12:06 310
Melbourne 13:18 1590
Perth 12:15 940
Santiago 13:41 1110
Sydney 12:53 1160

At exactly local noon, Eratosthenes measured the length (s) of the shadow of a tall column in his home town of Alexandria. He knew the height (h) of the column. He could then calculate the angle between the column and the sun’s rays using (in modern terms) the formula θ = arctan(s / h).

You can repeat Eratosthenes’ calculation by measuring the length of the shadow of a vertical stick (or anything else you know the height of), and using the arctan button on a calculator. Alternatively, the table below show the angles for various shadow lengths of a 1-metre stick. You could also attach a protractor to the top of the stick, run a thread from the to of the stick to the end of the shadow, and measure the angle directly.

The angle (θ) between the stick and the sun’s rays will also be the angle at the centre of the Earth (see the diagram at top). You can then calculate the circumference of the Earth using the distance to the Tropic of Capricorn and the fact that a full circle is 360° (the circumference of the Earth will be d × 360 / θ, where d is the distance to the Tropic of Capricorn).

Height (h) Shadow (s) Angle (θ)
1 0.02
1 0.03
1 0.05
1 0.07
1 0.09
1 0.11
1 0.12
1 0.14
1 0.16
1 0.18 10°
1 0.19 11°
1 0.21 12°
1 0.23 13°
1 0.25 14°
1 0.27 15°
1 0.29 16°
1 0.31 17°
1 0.32 18°
1 0.34 19°
1 0.36 20°
1 0.38 21°
1 0.4 22°
1 0.42 23°
1 0.45 24°
1 0.47 25°
1 0.49 26°
1 0.51 27°
1 0.53 28°
1 0.55 29°
1 0.58 30°
1 0.6 31°
1 0.62 32°
1 0.65 33°
1 0.67 34°
1 0.7 35°
1 0.73 36°
1 0.75 37°
1 0.78 38°
1 0.81 39°
1 0.84 40°
1 0.87 41°
1 0.9 42°
1 0.93 43°
1 0.97 44°
1 1 45°

On having multiple hypotheses which all fit the data

For every fact there is an infinity of hypotheses.” – from Robert Pirsig, Zen and the Art of Motorcycle Maintenance

‘I will read the inventory… First item: A very considerable hoard of precious stones, nearly all diamonds, and all of them loose, without any setting whatever… Second item: Heaps and heaps of loose snuff, not kept in a horn, or even a pouch, but lying in heaps… Third item: Here and there about the house curious little heaps of minute pieces of metal, some like steel springs and some in the form of microscopic wheels… Fourth item: The wax candles, which have to be stuck in bottle necks because there is nothing else to stick them in… By no stretch of fancy can the human mind connect together snuff and diamonds and wax and loose clockwork.’

‘I think I see the connection,’ said the priest. ‘This Glengyle was mad against the French Revolution. He was an enthusiast for the ancien regime, and was trying to re-enact literally the family life of the last Bourbons. He had snuff because it was the eighteenth century luxury; wax candles, because they were the eighteenth century lighting; the mechanical bits of iron represent the locksmith hobby of Louis XVI; the diamonds are for the Diamond Necklace of Marie Antoinette.’

Both the other men were staring at him with round eyes. ‘What a perfectly extraordinary notion!” cried Flambeau. “Do you really think that is the truth?’

‘I am perfectly sure it isn’t,’ answered Father Brown, ‘only you said that nobody could connect snuff and diamonds and clockwork and candles. I give you that connection off-hand. The real truth, I am very sure, lies deeper.’

He paused a moment and listened to the wailing of the wind in the turrets. Then he said, ‘The late Earl of Glengyle was a thief. He lived a second and darker life as a desperate housebreaker. He did not have any candlesticks because he only used these candles cut short in the little lantern he carried. The snuff he employed as the fiercest French criminals have used pepper: to fling it suddenly in dense masses in the face of a captor or pursuer. But the final proof is in the curious coincidence of the diamonds and the small steel wheels. Surely that makes everything plain to you? Diamonds and small steel wheels are the only two instruments with which you can cut out a pane of glass.’

The bough of a broken pine tree lashed heavily in the blast against the windowpane behind them, as if in parody of a burglar, but they did not turn round. Their eyes were fastened on Father Brown. ‘Diamonds and small wheels,’ repeated Craven ruminating. ‘Is that all that makes you think it the true explanation?’

‘I don’t think it the true explanation,’ replied the priest placidly; ‘but you said that nobody could connect the four things. The true tale, of course, is something much more humdrum. Glengyle had found, or thought he had found, precious stones on his estate. Somebody had bamboozled him with those loose brilliants, saying they were found in the castle caverns. The little wheels are some diamond-cutting affair. He had to do the thing very roughly and in a small way, with the help of a few shepherds or rude fellows on these hills. Snuff is the one great luxury of such Scotch shepherds; it’s the one thing with which you can bribe them. They didn’t have candlesticks because they didn’t want them; they held the candles in their hands when they explored the caves.’

‘Is that all?’ asked Flambeau after a long pause. ‘Have we got to the dull truth at last?’ ‘Oh, no,’ said Father Brown.

As the wind died in the most distant pine woods with a long hoot as of mockery Father Brown, with an utterly impassive face, went on: ‘I only suggested that because you said one could not plausibly connect snuff with clockwork or candles with bright stones. Ten false philosophies will fit the universe; ten false theories will fit Glengyle Castle. But we want the real explanation of the castle and the universe.” – from G. K. Chesterton, “The Honour of Israel Gow

A History of Science in 12 Books

Here are twelve influential books covering the history of science and mathematics. All of them have changed the world in some way:

1: Euclid’s Elements (c. 300 BC). Possibly the most influential mathematics book ever written, and used as a textbook for more than 2,000 years.

2: De rerum natura by Lucretius (c. 50 BC). An Epicurean, atomistic view of the universe, expressed as a lengthy poem.

3: The Vienna Dioscurides (c. 510 AD). Based on earlier Greek works, this illustrated guide to botany continued to have an influence for centuries after it was written.

4: De humani corporis fabrica by Andreas Vesalius (1543). The first modern anatomy book.

5: Galileo’s Dialogue Concerning the Two Chief World Systems (1632). The brilliant sales pitch for the idea that the Earth goes around the Sun.

6: Audubon’s The Birds of America (1827–1838). A classic work of ornithology.

7: Darwin’s On the Origin of Species (1859). The book which started the evolutionary ball rolling.

8: Beilstein’s Handbook of Organic Chemistry (1881). Still (revised, in digital form) the definitive reference work in organic chemistry.

9: Relativity: The Special and the General Theory by Albert Einstein (1916). An explanation of relativity by the man himself.

10: Éléments de mathématique by “Nicolas Bourbaki” (1935 onwards). A reworking of mathematics which gave us words like “injective.”

11: Algorithms + Data Structures = Programs by Niklaus Wirth (1976). One of the early influential books on structured programming.

12: Introduction to VLSI Systems by Carver Mead and Lynn Conway (1980). The book which revolutionised silicon chip design.

That’s four books of biology, four of other science, two of mathematics, and two of modern IT. I welcome any suggestions for other books I should have included.