[Public domain], via Wikimedia Commons
I’d like to return to our previous series on the Italian Masters, focused not on the usual masters or painting and sculpture but on the masters or science, mathematics, and engineering. So far in the series I’ve written about the accomplishments of Volta, Cassini, Venturi and Torricelli. Today, I’d like to look at one of the greats: Galileo Galilei. Galileo is most famous today for standing up for heliocentrism against the Catholic Church and spending the last years of his life under house arrest as punishment. However, Galileo didn’t let controversies or confinement stop him, and accomplished a great amount of research in not only astronomy, but physics, engineering and mathematics as well.
Galileo Galilei (1564-1642)
Galileo was born in 1564 in Pisa. His father was an accomplished lute player and music teacher, and passed on his lute skills and appreciation for music theory to Galileo and his siblings. In fact, his youngest brother was a quintessentially clichéd starving musician, relying on his older brothers for support. Despite Galileo’s initial studies in music and medicine, he found his true interest to be mathematics after taking a course in 1582 on Euclid’s Elements, a 300 BCE treatise on mathematics and geometry. He spend the next 10 years studying, researching, teaching, publishing, and making connections with the other natural philosophers of the era. His academic work culminated with his appointment as Chief Mathematician at the University of Pisa and “Mathematician and Philosopher” to the Duke of Tuscany in 1610, positions which he held through his house arrest and until his death in 1642.
A New Era of Astronomy
Figure 1: Jupiter and the four Galilean moons: Io, Europa, Ganymede and Callisto (not to scale)
By NASA/JPL [Public domain], via Wikimedia Commons
Galileo’s most recognized contributions to science come from his time behind the eyepiece of custom made telescopes in the period from 1609-1619. As the first person to turn the newly-invented telescope towards the night sky, Galileo was the first to observe many stellar phenomena. His documents from the time include the discovery of the moons of Jupiter (Fig 1), a study of the phases of Venus, descriptions of Saturn and Neptune, an interpretation of the existence of sunspots, and the deduction that spots on the moon were shadows caused by mountains and craters. One of his most mind-blowing discoveries (at the time) was that the Milky Way was in fact composed of innumerable stars, rather than nebulous light as everyone had previously imagined. Galileo’s observations of the heavens and his research into the motion of bodies led him to fully support the Copernican view of a heliocentric solar system, a viewpoint which so famously got him in trouble with the Catholic Church and earned him an imprisonment sentence from the Roman Inquisition. He was ultimately vindicated, though it took the Church 350 years to admit it.
Physics of Bodies in Motion
Before he picked up a telescope later in life, Galileo’s focus was on physics. He was especially interested in determining the behaviors of moving and falling objects. In particular, Galileo focused on challenging two prevailing Aristotelian views: that heavier objects would fall faster than lighter objects, and that objects would not remain in motion if the force that moved them stopped acting on them.
Galileo held that objects with different weights falling in a vacuum would experience the same rate of acceleration. While there’s some debate as to whether his famous experiment of dropping objects out of the Leaning Tower of Pisa actually happened, we know he experimented with inclined planes (ramps) and proved his hypothesis. He also correctly determined for the first time that under uniform acceleration, the distance travelled by an object is proportional to the elapsed time squared (recall that acceleration is given in units of m/s2 or ft/s2). As for bodies in motion, Galileo believed that objects in motion would retain their velocity in the absence of opposing forces. If this sounds familiar, it’s because it is essentially Newton’s First Law of Motion: that objects in motion will remain in motion if no force acts on them. Galileo’s spent much of his house arrest composing his magnum opus Discourses and Mathematical Demonstrations Relating to Two New Sciences, summing up his life’s work and discoveries on materials science and the motion of objects (the “Two New Sciences” in question).
Galileo was also an engineer, though the term didn’t really exist yet. His earliest invention was a “thermoscope”, the predecessor to the thermometer, using his discovery that liquid density varies with temperature changes. With a thin tube of water, the height of the water inside would change based on its temperature. The same principle of density-dependent temperature measurement controls the colorful Galilean thermometers some people use as decoration, though Galileo himself did not build such a device.
Figure 2: Geometric and Military Compass
Compass image: By Sage Ross (Own work) [GFDL or CC BY-SA 3.0], via Wikimedia Commons
Galileo also devised a Geometric and Military Compass (Fig 2) in the 1590s, based on his research into geometry, physics, and the motion of falling bodies. The compass had a multifunctional utility not dissimilar to the pocket slide rules that were used until the 1970s. It gave mathematicians a shortcut for constructing ideal polygons and calculating the areas and perimeters of different kinds of shapes. It also served cannoneers as a way to quickly determine appropriate cannon elevation and amount of gunpowder necessary for cannonballs of different weights and sizes.
Lastly, although Galileo himself didn’t invent the telescope (that honor belongs to three spectacle and lens makers in the Netherlands), he did custom make his own. After he received a sample from the Dutchmen in 1609, he immediately set out to perfect the lens grinding and polishing himself. Through his own careful assembly, he managed to increase the possible magnification from 3x to 9x, allowing him to be the first person to set eyes on the moons of Jupiter.
I don’t know if it would be to his chagrin or his amusement, Galileo’s most visible impact at this point might be exasperating teachers with countless school essays about “the scientist who fought for what he believed in, even though the world didn’t agree”. However, as engineers and scientists, we do have to admire his tenacity in exploring the unknown and challenging common knowledge. Galileo was one of the first to imagine that everything in nature could have a systematic, mathematical explanation, even if he couldn’t calculate it at the time. He was also one of the first scientists to consider how to ensure that scientific experiments were rigorous and repeatable. Science and engineering owe him a debt for pushing the limits of knowledge in the face of money problems, illness, grief, controversy, and imprisonment. There was truly no stopping him.
O’Connor, John J.; Robertson, Edmund F., “Galileo Galilei”, MacTutor History of Mathematics archive, University of St Andrews. Retrieved on March 10, 2016.