Her pale fire she snatches from the sun

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:


Advertisements

MODSIM Conference, Day 1

I am attending the MODSIM International Congress on Modelling and Simulation in Hobart, Tasmania. It promises to be another great event.

I spoke today on “Sampling bias and implicit knowledge in ecological niche modelling.” Out of the many interesting talks I listened to, one that stands out is “The Waroona fire: extreme fire behaviour and simulations with a coupled fire-atmosphere model” by Mika Peace. It introduced me to “pyrocumulonimbus clouds,” and some of the complex weather–fire interactions in severe bushfires. This is certainly a phenomenon that needs to be better understood.


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.