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:


Democracy, Religion, and Same-Sex Marriage in Australia

The results of the postal survey are in, and Australia has voted 61.6% “Yes” to same-sex marriage. Or rather, it seems that two Australias voted. The official results have been made available by electorate, which means that they can be correlated with demographic factors (and my readers know that I love doing that). The average age of each electorate had no effect, but religious composition certainly did.

According to the 2016 census, Australia’s stated religious composition looks like this (where the 33.3% “Secular” includes Agnostic, Atheist, Humanist, New Age, and Unitarian Universalist):

The chart below shows a strong correlation (0.82) between the percentage of “Secular” people in an electorate, and the size of the “Yes” vote. If all the “Secular” people voted “Yes” (as seems likely), this means that 58% of the religious people voted “No.” Doing some simple multiple linear regression, there was a statistically significant link between religion and voting “No” for every major religious group. This link was strongest for Muslims, Hindus, Buddhists, Orthodox, the Uniting Church, and other non-Anglican Protestants. It was a little weaker for Anglicans and even more for Catholics, although the Anglican link was quite strong in Victoria, South Australia, New South Wales, and Queensland. The Catholic link was quite strong in the last three of those states.

Electorates in the chart are coloured according to the largest religious group within them. Sydney is 52.7% Secular, for example (as well as 8.6% Buddhist, 1.7% Muslim, 1.7% Hindu, 1% Jewish, 17.9% Catholic, 2.4% Orthodox, 13.5% Protestant, and 0.5% Other Religion). It voted 83.7% “Yes.”

Blaxland is 32.2% Muslim (as well as 9% Buddhist, 3.3% Hindu, 21.2% Catholic, 5.5% Orthodox, 13.2% Protestant, 0.7% Other Religion, and 14.9% Secular). It voted 73.9% “No.”

McMahon is 39% Catholic (as well as 5.9% Buddhist, 12.4% Muslim, 2.9% Hindu, 6.9% Orthodox, 18.5% Protestant, 1.4% Other Religion, and 13.2% Secular). It voted 64.9% “No.”

Barton is multi-religious with 28.1% Secular being the largest group (as well as 5.6% Buddhist, 8.4% Islam, 5.6% Hindu, 0.2% Jewish, 22.6% Catholic, 15.7% Orthodox, 13.3% Protestant, and 0.5% Other Religion). It voted 56.4% “No.”

It does seem that there is a secular Australia, which voted overwhelmingly “Yes,” and a religious Australia of twice the size, which voted mostly “No.” If the disparate religious communities in Australia realise that they have more in common than they have thought, that could have quite a significant influence on Australian politics in the future.


A (distorted) geographical view of the postal survey results


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°

Guns, education, religion, and suicide

My earlier post indicated that gun laws in the US had little impact on the homicide rate, when demographic factors were taken into account. This makes sense – if I want to kill somebody, the lack of a gun will merely prompt me to choose another weapon. But what about suicide? The impulse to suicide is often brief, and easy access to a gun during a suicidal episode may increase the chance of dying.

To test this, I extended my previous dataset with data on educational attainment, data on religiosity, registered gun ownership data from the ATF, age-adjusted suicide rates from the CDC, poverty rates, unemployment rates, and other demographic data. I ran all that through a regression tree analysis, using R.

Suicide rates in the chart (click to zoom) are indicated by colour, ranging from 8 per 100,000 for New Jersey and New York (yellow) to 23.7 for Montana (black). Having a college degree seems to have a protective effect – states on the right of the chart, with more college degrees, had lower suicide rates. This may relate to the higher employability of college graduates. However, states at the top of the chart, with higher high school graduation rates, had higher suicide rates. I am not sure why this is the case.

Among the states with fewer college graduates, religion had a protective effect (this is consistent with other studies). States where 77% or more of the population said that religion was “somewhat important” or “very important” to them are indicated on the chart by triangles. For the states with fewer college graduates, the suicide rate was 13.6 per 100,000 for religious states, and 17.5 for less religious ones.

Finally, the highest-risk states (fewer college graduates and less religious) split according to gun ownership. States with more than 0.008 registered guns per capita are marked on the chart with an inner dot. Among the highest-risk states, the suicide rate increased from 13.9 per 100,000 to 18.6 when more guns were present. This group included Alaska (23.2 per 100,000), Arizona (17.5), Idaho (19.2), Maine (17), Montana (23.7), Nevada (18.6), North Dakota (17.3), Oregon (16.8), and Utah (21.4). Among the more religious states, registered gun ownership did not seem to have an effect (although, of course, registered gun ownership is a poor indicator of true gun ownership).

Thus the data does seem to suggest a link between gun ownership and suicide risk, but only when other risk factors are present (low religiosity and no college degree). This is exactly what we expected, and it means that suicidal (or potentially suicidal) people need to be kept away from guns.


Do gun laws save lives?

Somebody pointed me at this interesting data the other day. The chart above (click to zoom) combines the “Gun Law Score Card” from the Law Center to Prevent Gun Violence in the US with homicide rate data from Wikipedia and voting results from the last US election. Do gun laws reduce the chance of being murdered?

Obviously, “Blue” states tend to have stricter gun laws than “Red” states (an average of B− vs D−). “Blue” states also have lower homicide rates than “Red” states (4.5 vs 5.9), and this is statistically significant (p = 0.012). There is a weak (R2 = 6%) correlation between gun laws and homicide rates, but this relationship is not statistically significant.

Whatever it is that makes you less likely to be murdered in some states than others, it does not primarily seem to be the gun laws. Poverty may be one of the relevant factors, however – median household income explains 22% of the variance in homicide rates, and when this is taken into account, any effects due to gun laws or election results disappear. “Red” states are, on the whole, simply poorer (and, conversely, poor states are more likely to vote Republican and have weak gun laws). Other demographic factors, such as the number of people with college degrees, also seem to have explanatory value as far as the murder rate is concerned. However, the phenomenon of murder does not seem to be understood as well as it could be.


The Three-Body Problem trilogy: a book review


The Three-Body Problem trilogy by Liu Cixin

I recently read (in translation, of course) the popular The Three-Body Problem science fiction trilogy by Liu Cixin. These books explore the idea of first contact, and touch on several topics that I have posted about before (such as the Fermi paradox and the 3-body problem itself). I enjoyed reading them (the first two books more than the third). It was fascinating to read a Chinese view on some of the issues explored.

The novels are somewhat darker than classic Western science fiction, largely due to the shadow cast by the Cultural Revolution. But given the possibility of aliens like the Borg, the Daleks, and the Vang, perhaps interstellar optimism is just naive. And apparently, most contemporary Chinese science fiction is even more pessimistic than that of Liu (one of the characters in the first novel comments on this).

It seemed a little strange that Liu accepts the speed-of-light limit on space travel, but allows faster-than-light communication (which other authors have called an ansible). After all, both relativity and quantum mechanics forbid such a technology. Still, any depiction of truly advanced technology is going to read like fantasy, and the plot did require an ansible (although partway through the trilogy, the speed-of-light limit seemed to vanish even for ordinary communication).

These books (at least the first two) are well worth a read. Wired magazine also posted a review last year, and Nature had an interview with the author.


The Three-Body Problem trilogy by Liu Cixin: 3.5 stars


Logic in a box!

Having recently spent some time teaching a short course on logic and critical thinking, here is the core of the course reduced down to a box of 54 cards. These include:

  • 15 logic cards (summarising basic syllogistic and propositional logic rules),
  • 19 cards illustrating logical fallacies,
  • 5 cards for testing your ability to check validity, and
  • 15 logic-puzzle cards.

If you’re interested, more details can be downloaded from the game page (see the links in the “Downloads” section). The picture below shows some of the cards: