Bridges, gender, and Benjamin Lee Whorf

I’ve long been fascinated by the Sapir-Whorf hypothesis – the idea that the structure of language determines (or at least influences) the way that you think. I first read Whorf’s book several decades ago.

A friend recently pointed me at this TED talk by Lera Boroditsky. After years of being sneered at, it seems that Whorf is back in fashion.

And there’s certainly something to Whorf’s ideas. For example, there is solid evidence that the way that you name colours influences the way that you see them (slightly, anyway). There is some exaggeration in the TED talk, though. Australian aboriginal speakers of Kuuk Thaayorre have a unique way of describing directions (in absolute, rather than relative terms, e.g. “there is an ant on your northern leg”). They also navigate well across their tribal lands. But is there a causal relationship? Do aboriginal people with this linguistic feature navigate better than those without it? No, they don’t.

Even stranger is the idea that Spanish speakers, for whom a bridge is masculine (el puente), are less likely to describe a bridge as “beautiful,” and more likely to describe it as “strong,” than German speakers, for whom a bridge is feminine (die Brücke). There really are way too many confounding factors there – people who speak different languages differ in other ways too. So I thought I’d try a quick-and-dirty experiment of my own.

For a set of 17 languages, I counted Google hits for the phrases “beautiful bridge” (e.g. French: beau pont, German: schöne Brücke) and “strong bridge” (e.g. Greek: ισχυρή γέφυρα, Dutch: sterke brug), divided one set of numbers by the other, and took the logarithms of those ratios. The chart below summarises the results. Languages in pink have a feminine bridge, languages in blue have a masculine bridge, and languages in grey have a bridge which is neither (for example, English has no gender, while Dutch and Swedish have merged masculine and feminine into a “common” gender).

The mean values there are 0.95, 1.14, and 1.60, where positive numbers mean more hits with “beautiful bridge” (i.e. the trend runs the opposite way from the prediction), but none of the differences are statistically significant (p > 0.4). Gender does not seem to influence perceptions of bridges.

Interestingly, if we exclude the international languages English and Spanish, there is actually a statistically significant (but weak) correlation with GDP of the relevant nation (p = 0.029, r = 0.58). On the whole, poorer countries are more likely to describe a bridge as “strong,” and wealthier countries as “beautiful.” That makes sense, if you think about it (although Iceland is an exception to this pattern).

How about you? Is the bridge beautiful, or strong?


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The Sand Reckoner

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!


Sunset on a flat earth

Earlier, I wrote a post on why people know that the earth is round. Evidence such as star movement, the obscuring of distant objects by the earth’s curvature, and aircraft flight times shows that the earth is not flat:

In this post, I want to temporarily put on the “hat” of a flat-earther. They claim that the sun is a “spotlight” which travels across a circular flat earth like this:

That is at least a well-defined model, crazy though it might be, and therefore can be tested. Here is a computer render of the spring sun at sunset on that assumption (as seen from, say, San Francisco, at the moment that the sun disappears from view):

Three obvious problems with the flat-earth model are visible in this picture:

  • The sun is much too small: only 40% of its noontime diameter (because it is 2.5 times as far away as at noon)
  • The sun appears oval, rather than circular, because the “spotlight” is being seen obliquely (click to zoom if you can’t see the shape)
  • The sun is much too high in the sky (24° above the horizon)

In reality, of course, the sun at sunset is a circular disk that gradually slips under the horizon. Oops. No, the earth is not flat.


Religion in the Australian Census

Following up on my earlier post, here is a chart of religion in Australia, by age (as per the 2016 Census, with percentages on the vertical axis relating to the population of Australia as a whole, and excluding people with no religion specified). Coloured areas in this chart indicate the total number of people for each religious group:

The changing religious landscape is revealed by the variation with age. For people aged 65, the population is 25% Catholic, 24% secular, 22% Anglican, 16% other Christian, 7% Uniting Church, 2% Buddhist, 1% other religion, 1% Muslim, and 1% Hindu.

For people aged 25, it’s 47% secular, 21% Catholic, 11% other Christian, 8% Anglican, 4% Muslim, 3% Hindu, 3% Buddhist, 2% Uniting Church, and 2% other religion. The chart below shows these relative percentages, for each age cohort.

Immigration and children are keeping the Catholic Church stable in size, but the Uniting Church is in collapse, and the Anglican Church is not doing much better (other data suggests that it’s in collapse outside of Sydney). The “big three” non-Christian religions (Islam, Hinduism, and Buddhism) are more than 10% of the age-25 demographic. The chart also shows the impact of student-driven Indian immigration to Australia over the past decade or so – there is a visible peak for Hinduism around age 33.

There seems to be something odd about the religion given for young children up to age 13 or so – some parents (especially Catholics) seem to be listing young children as “no religion.” This might reflect delayed baptism. However, it also seems that many children lose their childhood religion in late teens and early adulthood.

Mean ages for adults within the different groups are Hindu: 37.1, Muslim: 37.7, secular: 42, other religion: 42.6, Buddhist: 43.5, Catholic: 48.6, other Christian: 50.4, Anglican: 54.8, and Uniting Church: 55.8. The last two groups in particular are skewed towards older people.


Looking back: 1982

In 1982 (35 years ago!) I finished my basic undergraduate degree, majoring in Mathematics and Computer Science (after sniffing around the job market, I continued my studies for an honours year). This was the year that the compact disc and the Commodore 64 computer came out:

Also that year, Stephen Cook won the Turing award for his work on computational complexity theory. The then Soviet Union landed two spacecraft in the hellish inferno that is Venus, and took photographs:

It was also a year of conflict – Argentina started a war with the UK over the Falklands Islands, and Israel invaded Lebanon. On a more positive note, there were several movies which became cult classics, such as Tron, E.T., and Conan the Barbarian. The superb science fiction movie Blade Runner stood out from the crowd (even with the flaws in the original cinema release):

In literature, Isabel Allende published her debut novel, as did Kazuo Ishiguro. In music, The Alan Parsons Project released their album Eye in the Sky and Australian band Icehouse (originally Flowers) released their classic single “Great Southern Land”:

Overall, it was a great year (apart from the wars).


Australians know that the world is round

Following up on my earth-measuring post, people have known for more than 2,000 years that the earth is round. In 350 BC, Aristotle wrote “The evidence of the senses further corroborates this [that the earth is spherical]. How else would eclipses of the moon show segments shaped as we see them? As it is, the shapes which the moon itself each month shows are of every kind straight, gibbous, and concave-but in eclipses the outline is always curved: and, since it is the interposition of the earth that makes the eclipse, the form of this line will be caused by the form of the earth’s surface, which is therefore spherical. Again, our observations of the stars make it evident, not only that the earth is circular, but also that it is a circle of no great size. For quite a small change of position to south or north causes a manifest alteration of the horizon. There is much change, I mean, in the stars which are overhead, and the stars seen are different, as one moves northward or southward. Indeed there are some stars seen in Egypt and in the neighbourhood of Cyprus which are not seen in the northerly regions; and stars, which in the north are never beyond the range of observation, in those regions rise and set. All of which goes to show not only that the earth is circular in shape, but also that it is a sphere of no great size: for otherwise the effect of so slight a change of place would not be quickly apparent.” (On the Heavens, II, 14).

Around the year 700, Bede wrote “We call the earth a globe, not as if the shape of a sphere were expressed in the diversity of plains and mountains, but because, if all things (terrestrial) are included in the outline, the earth’s circumference will represent the figure of a perfect globe. Hence it is that the stars of the northern hemisphere appear to us, but never those of the southern; while on the other hand, the people who live on the southern part of the earth cannot see our stars, because the globe obstructs their view.” (De Natura Rerum). Australians verify his statement about stars every night.

I have commented previously on how the medieval poet Dante described time zones on a round earth:

In more recent times, we have pictures from space:

Aristotle and Bede mention the stars. Not only do the visible stars vary with latitude, but in the Northern Hemisphere they rotate around Polaris, while in the Southern Hemisphere they rotate around the South Celestial Pole, as in this photograph taken in Chile:

Sailors at sea have long known that the earth is round. From a vantage point 20 metres above sea level, one can see a complete ship 17 km away. Beyond that, the distant ship goes “hull down,” and only the upper parts of it are visible (from 34 km away, the lower 20 metres of a distant ship will be hidden). Closer to sea level, the distance is much less. This photo, taken in Spain by “Santifc,” shows the phenomenon (and similar observations can be made at some Australian beaches):

And, of course, the aircraft flight times to and from Australia can only be explained by the fact that the earth is round:


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