Science in Dante’s “Paradiso”

In his Paradiso, which completes the trilogy begun with the Inferno, Dante travels through the (Ptolemaic) heavens, which look like this:

While most of Dante’s astronomy has been rendered obsolete by discoveries that began with Copernicus, Dante did understand the nature of the Milky Way. The Paradiso, it is true, expresses a degree of doubt regarding this:

As, graced with lesser and with larger lights
between the poles of the world, the Galaxy
gleams so that even sages are perplexed;
” — Paradiso, XIV, 97–99, tr. Mandelbaum

However, Dante’s Convivio provides the correct explanation:

In the Old Translation [Aristotle] says that the Galaxy is nothing but a multitude of fixed stars in that region, so small that we are unable to distinguish them from here below, though from them originates the appearance of that brightness which we call the Galaxy … Avicenna and Ptolemy seem to share this opinion with Aristotle.” — Convivio, II, 14, tr. Lansing

Milky Way; photo by “”

In the Paradiso, Dante discusses more than just theology and astronomy. He somehow manages to work in Thales’ theorem, for example (Paradiso, XIII, 101–102). What’s more, having told us in the Purgatorio (XV, 16–21) that “the angle of incidence is equal to the angle of reflection,” Dante now proposes an actual experiment in optics (no, it wasn’t Galileo who invented the experimental method!):

Yet an experiment, were you to try it,
could free you from your cavil – and the source
of your arts’ course springs from experiment
Taking three mirrors, place a pair of them
at equal distance from you; set the third
midway between those two, but farther back.
Then, turning toward them, at your back have placed
a light that kindles those three mirrors and
returns to you, reflected by them all.
Although the image in the farthest glass
will be of lesser size, there you will see
that it must match the brightness of the rest.
” — Paradiso, II, 94–105, tr. Mandelbaum

The image above (click to zoom) is the result of replicating Dante’s proposed experiment with the Persistence of Vision Raytracer. The unnecessary third mirror tells us that Dante is here also speaking allegorically about the reflection of Divine light, and that – hinting at 1 Corinthians 13:12 – he is looking forward to his final vision of the Trinity, in what is after all a theological poem:

That light supreme, within its fathomless
Clear substance, showed to me three spheres, which bare
Three hues distinct, and occupied one space;
The first mirrored the next, as though it were
Rainbow from rainbow, and the third seemed flame
Breathed equally from each of the first pair.
” — Paradiso, XXXIII, 115–120, tr. Sayers

See also science in the Inferno and in the Purgatorio.

Science in Dante’s “Purgatorio”

Dante’s Purgatory, described in the sequel to the Inferno, is a mountain in the South Pacific (the antipodes of Jerusalem). This painting by Agnolo Bronzino shows Dante gazing at the mountain:

Being in the Antipodes, the stars are naturally different, as all inhabitants of the Southern Hemisphere know:

Then I turned to the right, setting my mind
upon the other pole, and saw four stars
not seen before except by the first people.
Heaven appeared to revel in their flames:
O northern hemisphere, because you were
denied that sight, you are a widower!
” — Purgatorio, I, 22–27, tr. Mandelbaum

Dante has a nice description of time zones too (though with an average error of about two hours):

As when his earliest shaft of light assails
The city where his Maker shed His blood,
When Ebro lies beneath the lifted Scales
[i.e., midnight]
And noontide scorches down on Ganges’ flood,
So rode the sun; thus day was nightward winging
When there before us God’s glad angel stood.
” — Purgatorio, XXVII, 1–6, tr. Sayers

See also science in the Inferno and in the Paradiso.

Science in Dante’s “Inferno”

It is a common myth that the medievals thought that the world was flat. One of many proofs to the contrary is in Dante’s Inferno, written in the early 1300s. This poem depicts the standard medieval view of a spherical Earth – and, since the poem is set at Easter time, it’s appropriate to revisit it this month. In the poem, Dante actually travels down a Hell described as conical, through the centre of the Earth (long before Jules Verne!), and up into the Southern Hemisphere:

Dante correctly describes the shift in direction of gravity when passing through the centre of the Earth, and the effect of travelling to the Antipodes:

And he to me: You still believe you are
north of the center, where I grasped the hair
of the damned worm who pierces through the world.
And you were there as long as I descended;
but when I turned, that’s when you passed the point
to which, from every part, all weights are drawn.
And now you stand beneath the hemisphere
opposing that which cloaks the great dry lands
and underneath whose zenith died the Man
whose birth and life were sinless in this world.
” — Inferno, XXXIV, 106–115, tr. Mandelbaum

That is, by travelling through the centre of the Earth, Dante and Virgil arrive in the South Pacific, directly opposite Jerusalem, at about 32°S 145°W, around 460 km south of Rapa Iti.

Dante suggests here that the Southern Hemisphere is largely covered by water. There was an ancient belief in a Terra Australis, but Dante has rearranged geography so that the Southern Continent becomes a single, though extremely high, mountain. It was several centuries later that explorers like Abel Tasman and James Cook resolved the Terra Australis question.

See also science in the Purgatorio and in the Paradiso.

Nor any drop to drink

Water, water, every where; and all the boards did shrink. Water, water, every where; nor any drop to drink.” – The Rime of the Ancient Mariner

The maps below, from the Gravity Recovery and Climate Experiment satellites, show US underground water in surface soil, in the “root zone,” and in deeper groundwater aquifers (amazing that they can detect underground water from space, isn’t it?).

As of September 2012, it was still very dry down there, especially in Texas, and the drought continues in the central USA. Let’s hope for some good rains there. Click here for more information and an animated time series of the data.

Progress on the 3-body problem

The three-body problem involves finding the possible orbits for a set of three celestial bodies all affecting each other gravitationally. For example, a triple star system like HD 188753, seen here in a NASA artist’s impression (as viewed from a hypothetical moon of a possible planet):

The three-body problem has posed a challenge since Isaac Newton. A recent paper by Milovan Šuvakov and Veljko Dmitrašinovic, entitled “Three Classes of Newtonian Three-Body Planar Periodic Orbits” and accepted for publication in Physical Review Letters, presents several new families of solutions to the gravitational equations. Here are two of the solutions – the “Figure 8” (previously discovered by Cristopher Moore in 1993), and the “Ying-Yang 1a” (one of those discovered by Šuvakov and Dmitrašinovic):

Some of those orbits border on the chaotic! See also the draft paper by Šuvakov and Dmitrašinovic here and their gallery of images here.

Cassini looks back at Rhea

This NASA photograph, taken by the hard-working Cassini spacecraft, shows Saturn’s moon Rhea. It was taken on March 10, 2013 from a distance of 280,317 kilometers, following a low-altitude fly-past on March 9. See here for larger versions of the image and see here for more details and for images taken during the fly-past.

Habemus Papam

The Pope (left) and the Vatican Advanced Technology Telescope or “Pope Scope” (right)

The world has a new Pope, Francis. What does that mean for science? Well, some past papal scientific milestones are these:

The Jesuit order, from which Francis comes, has a tradition of being involved with science, although Teilhard de Chardin was a step too far for them. And Pope Francis does in fact have a scientific background: he studied chemistry before becoming a priest.

Looking forward to MODSIM 2013

Every 2 years, the Modelling and Simulation Society of Australia and New Zealand holds an international congress. The 20th International Congress on Modelling and Simulation (MODSIM2013) will be combined with the 22nd National Conference of the Australian Operations Research Society (ASOR 2013) and will be held at the Adelaide Convention Centre in Adelaide, South Australia, from Sunday 1 to Friday 6 December 2013. See for more details. Initial abstracts are due on April 8.

It promises to be a great event. I plan to be there and to chair a session on Homeland Security & Emergency Management Applications of Modelling & Simulation.

Conference venue (click for photo credit)