### In A Nutshell

In defiance of Church dogma, Galileo Galilei advanced our view of the universe with his heliocentric model of the solar system, making him one of history’s greatest scientists. But Galileo was also a man of his time, steeped in religious superstition. In his most bizarre investigation, Galileo took Dante Alighieri’s description of hell—*Inferno*—quite literally and attempted to measure its exact dimensions. While Galileo’s project may look ridiculous today, it inadvertently formed a foundation for modern science and engineering.

### The Whole Bushel

In the 14th century, Dante Alighieri composed his epic poem *Divine Comedy*, which describes his journey through hell (*Inferno*), purgatory (*Purgatorio*) and heaven (*Paradiso*). Its graphic images of the netherworld have captured imaginations ever since.

For example, the painter Sandro Botticelli’s *Mappa dell’ Inferno* (“Map of Hell”) illustrated Dante’s vision in horrifying detail. Even intellectuals took the poem’s descriptions seriously. In the 16th century, they were actually debating *Inferno*‘s exact geography and geometry.

To resolve the question, the Florentine Academy called in the 24-year-old mathematical genius Galileo Galilei.

An earlier analysis of Dante by Florentine mathematician and architect Antonio Manetti described hell as a gigantic, cone-shaped abyss beneath the Earth with its vertex at the exact center of the planet. It was formed when Lucifer fell to Earth after his rebellion.

From its entrance near Cuma, Italy, nine levels or circles descended to the bottom of the pit where Satan himself dwelled. Jerusalem lay at the center of the base of the cone. The base was enclosed by a vaulted domed roof. This was the version defended by Galileo before the Academy against the rival interpretation by the non-Florentine Alessandro Vellutello. Now what are its exact dimensions?

*Already the Sun was joined to the horizon
Whose meridian circle covers
Jerusalem with its highest point.*

Galileo interpreted Dante’s line to mean that the diameter of the base must be equal to the radius of the Earth. Since the distance from Jerusalem to Cuma was thought to be 2,700 kilometers (1,700 mi), the circle must measure around 5,500 kilometers (3,400 mi) in diameter.

This is Earth’s radius and the depth of hell, 10 times deeper than Vellutello’s estimate.

From this, the angle of the vertex can be calculated as 60 degrees. At this lowest point, Satan dwells and the most wicked are punished by being entombed in ice. Using proportionate scaling and Dante’s text comparing Satan’s size to ordinary objects, Galileo estimated the Devil as being 1,180 meters (3,870 ft) tall. By comparison, the world’s tallest building, Dubai’s Burj Khalifa, is 828 meters (2,716 ft) tall.

These staggering dimensions meant that the span of the domed roof would extend from present-day Marseilles in France to Tashkent, Uzbekistan, enclosing the gigantic Lucifer and all present and future inhabitants of hell. How thick should the roof be to prevent it from collapsing?

For inspiration, Galileo turned to Filippo Brunelleschi’s famed Duomo—the dome of Florence Cathedral. Brunelleschi’s wonder of structural engineering was 45 meters (147 ft( wide but amazingly lightweight at only 4 meters (13 ft) thick.

Using the same method of calculating Lucifer’s size, Galileo scaled these dimensions up proportionally to fit hell’s dome, coming up with a thickness of 460 kilometers (287 mi) for the roof.

But here Galileo made a fatal mistake.

The “simple proportion” method of scaling up would make the roof collapse under its own weight. The proportions were fine for the Duomo, but disastrous for a dome thousands of kilometers in diameter. But the audience was convinced by Galileo’s arguments, and he was rewarded with a lectureship in mathematics at the University of Pisa.

At Pisa, Galileo realized his horrendous mistake. He kept quiet and reworked his equations before someone else discovered his error.

In the process of studying how the strength of materials is altered as their dimensions change, Galileo bequeathed to the engineering world the science of scaling theory.

In his book *Dialogues Concerning Two New Sciences*, Galileo laid down his square-cube law, which says that scaling a structure by the same factor in all directions will increase its weight in proportion to the cube of the scaling factor, but the strength will only increase with the area of the cross-section, which is proportional to the square of the scaling factor.

This rule is still kept in mind by engineers and architects when scaling up beamlike structures.

We may laugh at Galileo’s efforts to measure hell and Satan, but we should be glad that his work resulted in a tangible technological and scientific advancement.

### Show Me The Proof

Featured photo credit: Justus Sustermans

ABC: Galileo, Dante Alighieri, and how to calculate the dimensions of hell

*The Stars of Galileo Galilei and the Universal Knowledge of Athanasius Kircher*, by Roberto Buonanno

*Scientific Discovery from the Brilliant to the Bizarre*, by Len Fisher

Galileo Galilei’s Location, Shape and Size of Dante’s Inferno

*Crashes, Crises, and Calamities*, by Len Fisher