*Figure 1: Evangelista Torricelli*

Most people are familiar with the works of the “Italian Masters”… artists such as Leonardo da Vinci, Michelangelo and Raphael. But Italy has a storied history of masters of other fields, especially mathematics, science and engineering. In this blog series, we’ll take a look at a few of the influential renaissance men from The Boot who helped advance the fields of physics, chemistry, electricity, geometry, and more. These are the multi-talented renaissance men who tackled so many of the problems that now form the backbone of modern science, engineering, and technology.

For this blog, I’ll focus on Evangelista Torricelli (Figure 1), a 17th century mathematician, physicist. Torricelli was a contemporary of Galileo Galilei, and in fact carried on some of the great scientist’s work when he passed away. Although he lived only 39 years, Torricelli proves just how much any individual can effect history if they apply themselves to a field they’re passionate about.

# Evangelista Torricelli (1608-1647)

Evangelista Torricelli was born in Rome in 1608 into a poor family, but managed to rise above his station due to his passion for mathematics. Luckily for Torricelli and for the fields of math and physics, his parents recognized his talents early on and enrolled him in a series of colleges and universities, under the guidance and tutelage of his Benedictine monk uncle. Torricelli was fascinated by Galileo’s ongoing work in astronomy and geometry, and expanded Galileo’s work on the parabolic paths of projectiles. This work caught the older scientist’s eye, and Galileo invited Torricelli to join him in Florence as an assistant and colleague; unfortunately, he passed away only three months after Torricelli joined him. By this point, Torricelli had already achieved enough fame in the field to be appointed to Galileo’s now-empty position as grand-ducal mathematician and chair of mathematics at the University of Pisa. He accepted the position and continued his work there until his untimely death only five years after the appointment. He left behind no family besides an adopted son, but left his mark on the fields of physics and mathematics for centuries to come.

# The Invention of the Barometer

*Figure 2: Torricelli’s mercury barometer*

Torricelli’s most famous and enduring invention was the mercury barometer, which proved revolutionary not just as a way to measure pressure but also as an answer to some scientific quandaries. For isntance, the nature of vacuums was hotly debated, with most physicists still holding to the Aristotelian view that vacuums could not exist in nature (“Nature abhors a vacuum”, as famously attributed to Aristotle). Torricelli countered this view with a simple experiment (illustrated in Figure 2):

- Take a long tube completely full of mercury, sealed at one end and capped at the other.
- Upend the tube and place the capped end in a bowl full of more mercury.
- Upon removing the cap, the mercury will descend, leaving an empty space in the top of the tube.
- The mercury will stop descending at some point, having reached an equilibrium with some other force on the system.

The empty space at the top of the tube couldn’t have been formed by air, so it followed that it was a true vacuum: possible after all, and simple to replicate. Torricelli made a further deductive leap, realizing that the vacuum was not somehow holding up the mercury; rather, it was the pressure of the air on the mercury in the bowl that pressed the mercury back up the tube. When describing the experiment later, he wrote:

*“On the surface of the mercury which is in the bowl rests the weight of a column of fifty miles of air. Is it a surprise that into the vessel…*

*[the mercury] should enter and should rise in a column high enough to make equilibrium with the weight of the external air which forces it up?” [i]*

Later tests with barometers proved that the height of the mercury lowered as elevation increased, confirming Torricelli’s hypothesis concerning the weight of the atmosphere. Torricelli’s explanation of atmospheric pressure as the weight of the air above was revolutionary and defined the idea of atmospheric pressure as we still understand it today. To get a sense of all that weight of air, recall that at sea level standard atmospheric pressure is 14.7 pounds per square inch (psi). Essentially, we all have the weight of a bowling ball pressing down on every inch of our bodies.

The barometer also showed unexpected behavior: the height of the mercury in the barometer fluctuated with changing weather conditions. Since the barometer itself wasn’t changing, Torricelli deduced that the change must be driven externally. The atmospheric pressure itself was changing, leading Torricelli to another revolutionary theory, this time concerning the wind. He posited in a later letter that:

*“winds are produced by differences of air temperature, and hence density, between two regions of the earth.” [ii]*

This was the first such scientific explanation, and has again turned out to be exactly the case. That principle is still one of the guiding factors in meteorology and weather prediction.

Improved versions of his mercury barometer are still in use today for pressure measurement and weather monitoring purposes, though many have switched to using a less-toxic liquid. Even the sensitive pressure transducers Glew Engineering uses in semiconductor equipment, which do not use a liquid, rely on the same principle of comparing varying pressures to a baseline vacuum. Torricelli is indeed honored with his own unit of measurement, the Torr: 1/760 of a standard atmosphere, or 1 mm of mercury (see Figure 2: the mercury in the meter-long tube stood 760 mm high, so the pressure was 760 Torr, or one standard atmosphere).

# Contributions to Mathematics

*Figure 3: Torricelli’s Trumpet AKA Gabriel’s Horn*

Aside from physics, Torricelli also focused his talents and intellect on mathematics and geometry. His work on centroids (the geometric center of a shape) and centers of gravity in objects augmented and propelled forward a burgeoning field that joined mathematics and physics. He also assisted fellow mathematician Bonaventura Cavalieri in developing the first steps towards integral calculus, the theory perfected by Isaac Newton and Gottfried Leibniz in later decades.

Torricelli’s mathematics work threw fire on another hot topic among the scientists of the day: the nature of infinity. His work involved “volumes of revolution”, or the volume of an object formed by rotating a 2-dimensional shape around an axis (imagine taking a circle and rotating it through space about a line off to one side; your result would be a donut-shaped torus). He realized that by rotating the line formed by the equation y = 1/x for x ≥ 1 about the x-axis, he could form a theoretical object with a finite volume but with an infinite surface area (represented in Figure 3, above). That’s precisely as baffling as it sounds, a paradox which provoked many debates among his colleagues. The shape came to be known as Gabriel’s Horn, though some still referred to it as Torricelli’s Trumpet, in recognition of his work.

# Lasting Impact

Although Torricelli is mainly remembered for his invention of the barometer and explanation of atmospheric pressure, his impact in math, science and engineering extends beyond pressure measurement. With his contributions to geometry, his initial steps in the development of calculus, and his ideas about the nature of vacuums and of infinity, Torricelli’s work continues to be felt in science, engineering and math today [iii].

Any other Italian scientists you think don’t get enough attention? Let us know in the comments below!

## References

- [i] Torricelli, V. (1644)
*Collected Works Vol. III*(1919) - [ii] Gliozzi, M.
*Biography in Dictionary of Scientific Biography*(New York 1970-1990) - [iii] O’Connor, John J.; Robertson, Edmund F., “Evangelista Torricelli”,
*MacTutor History of Mathematics archive, University of St Andrews*.

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