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Dante’s Inferno

Inferno (Italian for “Hell”) is the first part of Dante Alighieri’s 14th-century epic poem Divine Comedy. It is followed by Purgatorio and Paradiso.  It is an allegory telling of the journey of Dante through Hell, guided by the Roman poet Virgil. In the poem, Hell is depicted as nine circles of suffering located within the Earth. Allegorically, the Divine Comedy represents the journey of the soul towards God, with the Inferno describing the recognition and rejection of sin.

(Adapted by RK from Wikipedia, Inferno)

How can a knowledge of physics, earth science and astronomy enrich a reader’s understanding and experience of this classic work of Western Literature? How can reading classic Western Literature enrich a student’s understanding and experience of science? In this lesson I aim to bring science to the reader of poetry – and poetry to the student of science.

Those interested in common core learning standards may find this of use for high school students in particular.

Common Core reading standards: grades 9-10

Common Core reading standards: grades 10-12

In this story, Dante finds himself travelling through the nine circles of Hell, which are based on Christian theology as described in the New Testament and the writings of the Church Fathers. However, readers should take note that many of the details are unique to Dante, and do not officially represent the teachings of any faith.  With that in mind, here is the geography of hell:

Dantes Inferno 1

Another representation of the circles of hell:
dante_s_inferno_by_somnium_maris-d68js14

There are meaningful connections between ELA and science. Although it is primarily a religious poem, Dante discusses several elements of the science of his day.

The Purgatorio repeatedly refers to the implications of a spherical Earth, such as:

* the different stars visible in the southern hemisphere
* the altered position of the sun
* and the various time-zones of the Earth.

For example, at sunset in Purgatory it is midnight at the Ebro (a river in Spain), dawn in Jerusalem ( יְרוּשָׁלַיִם ), and noon on the River Ganges:

Just as, there where its Maker shed His blood,
the sun shed its first rays, and Ebro lay
beneath high Libra, and the ninth hour’s rays

were scorching Ganges’ waves; so here, the sun
stood at the point of day’s departure when
God’s angel—happy—showed himself to us. [34]

Dante travels through the centre of the Earth in the Inferno, and comments on the resulting change in the direction of gravity in Canto XXXIV (lines 76–120).

{ adapted from http://en.wikipedia.org/wiki/Divine_Comedy#Scientific_themes }
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Scientists today know that our Earth is not hollow; however, engineers often drill extensive tunnels through the outer portion of the Earth’s crust. In physics it is common to consider gedankenexperiments (German for “thought experiments”) They are not performed in order to actually build something, but to encourage one to use basic principles of physics to analyze an interesting phenomenon, and as a result, that which is learned from the gedankenexperiment may prove enlightening or lead to new physical insights.

Gedankenexperiments (Wikipedia)

{ image from http://www.alrightso.com/tunnel-thru-earth.php }

tunnel-thru-earth

As taught at the amazing physics resource HyperPhysics, by Carl R. Nave, we have this analysis:

Suppose you could drill a hole through the Earth and then drop into it. How long would it take you to pop up on the other side of the Earth?

Your initial acceleration would be the surface acceleration of gravity (given here for Earth; this value varies on other worlds)

but the acceleration would be progressively smaller as you approached the center. Your weight would be zero as you flew through the center of the Earth. For our hypothetical journey we will assume the Earth to be of uniform density and neglect air friction and the high temperature of this trip….

For the full analysis see How long would it take to fall through the Earth? HyperPhysics

http://hyperphysics.phy-astr.gsu.edu/hbase/mechanics/earthole.html
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A little earlier (XXXIII, 102–105), Dante queries the existence of wind in the frozen inner circle of hell, since it has no temperature differentials.

Inevitably, given its setting, the Paradiso discusses astronomy extensively, but in the Ptolemaic sense. What did Ptolemy’s model of the universe look like? The Earth was believed to be in the center, and the moon, Sun, stars and other worlds were on invisible crystal spheres, rotating around our own world. In two dimensions it could be drawn like this:

Ptolemy solar system
In three dimensions an artist could represent the crystal spheres thusly:

The Paradiso also discusses the importance of the experimental method in science [light and optics], with a detailed example in lines 94–105 of Canto II:

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.

This topic is related to https://kaiserscience.wordpress.com/physics/light/light-geometric-optics/

paradisomirror

A briefer example occurs in Canto XV of the Purgatorio (lines 16–21), where Dante points out that both theory and experiment confirm that the angle of incidence is equal to the angle of reflection.

Other references to science in the Paradiso include descriptions of clockwork in Canto XXIV (lines 13–18), and Thales’ theorem about triangles in Canto XIII (lines 101–102).

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Anthony Dekker (Canberra Area, Australia) writes about the science in Inferno

http://scientificgems.wordpress.com/2013/03/21/science-in-dantes-inferno/

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.

Antipodes_LAEA_inverted Antipodes_LAEA

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.

{ http://scientificgems.wordpress.com/2013/03/23/science-in-dantes-purgatorio/ }

Dante’s Purgatory, described in the sequel to the Inferno, is a mountain in the South Pacific (the antipodes of Jerusalem).
{image from  http://www.thefinalclub.org/work-overview.php?work_id=12 }

Purgatory-Diagram(1)

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

{ image from http://galleryhip.com/dante-purgatorio-map.html }

Inferno_purgatorio_e_paradiso

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

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Robert Lamb, in “Science Goes to Hell: Dante’s Gravity and Lucifer’s Math” writes:

Gravity in Hell

“Inferno” sees Dante descend deeper and deeper into Earth’s interior (here’s the map), toward the very center of the planet. He encounters constant historical figures and contemporary celebrities along the way, but gravity doesn’t appear to change.

Gravity, of course, has everything to do with mass. Geophysicist Fred Duennebier points out here that a journey into the depths of the Earth wouldn’t change things for you. There’d be less mass underneath you pulling you down, but there’d still be all that mass overhead to balance things out.

It gets really interesting when Dante and his guide Virgil make it to the very center of the planet, where Satan is trapped in a frozen lake. In fact, Dante’s Inferno puts the exact core at Satan’s groin region. Dante and Virgil escape Hell by climbing down the devil’s furry flanks — and then down suddenly becomes up. You can read the whole passage here.

Naturally, such a feat would be impossible for any number of reasons — the least of which being that the center of the Earth is a solid mass. But the manner in which Dante depicts the exact center as a kind of zero point actually carries some scientific weight.

An introduction to gravity

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In the 20th century an amazing sequel to Dante’s Divine Comedy was written, Inferno.

Inferno is a fantasy novel written by Larry Niven and Jerry Pournelle, published in 1976. It was nominated for the 1976 Hugo and Nebula Awards for Best Novel.

http://en.wikipedia.org/wiki/Inferno_%28Niven_and_Pournelle_novel%29

A book review can be found here:

Dante Meets Vatican II in Sci-Fi Hell, by Robert R. Chase, First Things, 3/23/10

http://www.firstthings.com/web-exclusives/2010/03/dante-meets-vatican-ii-in-sci-fi-hell


2 Comments

  1. […] la tierra media, el purgatorio de Dante, pues por debajo de ella, encontramos la Semantica y la semiotica y por encima la linguistica y la […]

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