# An Interview with Ann F. Varela and Manuel F. Varela: Science and Scientists: Who Was Archimedes?

Michael F. Shaughnessy

Figure 1. Bust of Archimedes.

https://pixabay.com/vectors/archimedes-history-antique-1275880/

“*Give me a single place to stand, and I will move the earth*.”

—Archimedes

Michael F. Shaughnessy

1) Archimedes is a name that is often associated with the beginnings of all science. When and where was he born, and what do we know about his early life?

For several millennia Archimedes has been widely considered as one of the greatest mathematicians and scientists who has ever lived. Archimedes’ true birthdate is unknown but is estimated to be on or about 287 BC. His death in 212 BC provides the estimated date of birth, together with a declaration by the Byzantine Greek historian Jon Tzetzes, which reveals that Archimedes was 75 years old upon his death. Archimedes’ birthplace was Syracuse, Sicily, a sovereign society in Magna Grecia. The Romans named the coastal areas of Southern Italy in the modern-day localities of Campania, Apulia, Basilicata, Calabria, and Sicily, as these regions were highly inhabited by Greek colonists.

Archimedes was a gifted adolescent and possessed a natural aptitude for problem-solving. He started his early education in Syracuse and then transferred to Alexandria, Egypt, because of its reputation for excellence in education and research. The Library of Alexandria had conference rooms and oration halls and had become an important, influential location for scholars of that time.

Euclid’s book, *The Elements*, was among Archimedes’ primary resources and most likely motivated his future work. After completing his studies in Alexandria, Archimedes once again returned to Syracuse and devoted his time to contemplation and discovery in numerous subjects, especially if King Hiero II posed a question. Some scholars believe Archimedes was related to King Hiero II.

2) Doing experiments to test theory or theories seems to be what Archimedes is most known for throughout our history. Why is this important in science—even today?

His contemporaries found Archimedes especially infuriating because he offered hints but did not divulge his full techniques. In actuality, Archimedes enjoyed a bit of mischievous behavior with other mathematicians. He would tell them the correct solution to problems, then see if they could work out the problems for themselves.

In modern times, the basis of the scientific method entails making factual observations of phenomena, formulating an explanation called a hypothesis based on the observations, and testing the validity of the proposed hypothesis by experimentation and collection of data. If the experimental data support the hypothesis, then it can become a scientific law. As new laws are accumulated, they can become a theory and used to explain scientific phenomena. If the data do not back the proposed hypothesis, it can be rejected or modified.

In practice, the scientific method involves a continual cycle of observation, hypothesis formulation, experimentation, data collection, and acceptance, rejection, or modification of the tested hypothesis. If accepted, the hypothesis is repeatedly tested. Often, experimental testing involves repeated experimentation to accumulate an extensive amount of statistically valid data. As the supporting data are accumulated by numerous investigators over many years of work, the hypothesis acquires the status of theory if verified, and as new supporting data are amassed, the theory is promoted to the coveted rank of scientific law.

If the hypothesis is rejected or the data do not fully support the proposed explanation, then the hypothesis can be re-tooled, i.e., reformulated, or revised, and it can be tested once again. The new or modified hypothesis is tested vigorously, and the resulting data is interpreted as supporting or rejecting the new idea based on the newly acquired data.

As investigators invoke the scientific method, the concept of the so-called “null hypothesis” comes into play. A hypothesis that does *not* exhibit a statistically significant difference between the experimental (treated) group and the negative control (untreated) group is referred to as a null hypothesis. On the other hand, if the data that tests this sort of null hypothesis does differ statistically between the two variables, i.e., the experimental versus the control groups, then the null hypothesis that presumes no difference between the two groups is said to be rejected. Therefore, rejection of the null hypothesis means that an alternative hypothesis is then formulated to indicate the null hypothesis is contradicted. Failure to reject the so-called null hypothesis is a scientific way of communicating the notion that one cannot truly ever prove that a phenomenon does not exist.

3) Archimedes is also known for the concept of buoyancy in science. Why is this important?

The Archimedes principle maintains that the buoyant force acting on an object is equal to the weight of the displaced fluid. In other words, the upward force is equal to the downward force. See Figure 2.

Figure 2. Buoyancy.

https://commons.wikimedia.org/wiki/File:BALLS.png

The Archimedes principle has various practical uses in the field of medical science, submarine design, water-walking bugs, and geology. First, the Archimedes principle is used to determine bone density by measuring the volume of the inside porous part of the bone, identified as the cancellous bone. The volume ratio of the cancellous bone can be used in various age and health studies, including being an indicator in studies relating to aging, osteoporosis, bone strength, firmness, and flexibility.

Second, teeth volume can also be measured with the Archimedes principle. A technique known as cone beam computed tomography (CBCT) is used to compare teeth density measurements with the Archimedes principle, and CBCT measurements showed that procedure to be a reliable instrument in planning dental procedures.

Third, submarines are designed to travel while wholly submerged underwater and depend on the Archimedes principle to sustain a uniform depth while submerged, along with the maneuvers of diving and resurfacing. The design of submarines uses calculations including the mass, density, and volume of the submarine, together with the displaced water, to determine the required ballast tank size needed. The ballast tank size controls the amount of water that can fill it and, therefore, the depth to which the submarine can drop. See Figure 3.

Figure 3. Ballast tank controlling buoyancy.

https://commons.wikimedia.org/wiki/File:SUBMARINES.gif

Fourth, the Archimedes principle accounts for how some bugs can walk on water. In the last several years, researchers used a method of measuring shadows created by the water-walkers to measure the arcs in the water surface. These depressions can then be used to obtain the water volume that was displaced, leading to the force applied to keep the water-bugs floating. Much interest was shown in understanding the physics behind the water-walking bugs to create biomimetic water-walking robots.

Fifth, there are many instances in studying sedimentation profiles of which the Archimedes principle can be used as an approximation. An adaptation of the Archimedes principle has arisen in a universal principle that provides support for events such as denser particles floating on top of a light fluid.

4) Cones, cylinders, and spheres—what do they have in common, and why is Archimedes associated with them?

As mentioned earlier, Archimedes studied Euclid’s book *Elements,* which consisted of essentially all the findings of Greek geometry up to Archimedes’ point in time. Archimedes continued Euclid’s work more than anyone had before him. Archimedes utilized the “method of exhaustion” to prove his point. This particular method is used to determine the areas and volumes of shapes with arched lines and surfaces, like circles, spheres, pyramids, and cones. Archimedes’ analysis of the method of exhaustion became the forerunner to the current form of mathematics called integral calculus. Although his method is now dated, the advances that finally outdated it did not take place until about two thousand years after Archimedes’ lifetime.

The innovation of which Archimedes proclaimed to be the most delighted was that of the correlation between a spherical object and a circumscribing cylinder of equal height and diameter. He calculated the volume of a sphere to be 4/3 πr^{3} and that of a cylinder of the same height and diameter to be 2πr^{3}. The surface area of the sphere was 4πr^{2} and 6πr^{2} for the cylinder. Therefore, the sphere has the same volume as two-thirds that of the cylinder and a surface area the same as two-thirds that of the cylinder. See Figure 4.

Figure 4. Sphere and cylinder.

https://commons.wikimedia.org/wiki/File:Sphere_inside_a_cylinder_-_Archimedes%27_ratio.svg

5) The lever and Archimedes statement ” Give me a single place to stand and I will move the earth” seem to be somewhat a precursor to all physics—or am I off on this? Leverage seems to be a pivotal element to math, science, geometry, and much more.

Although Archimedes did not invent the lever, he gave the first detailed justification of the principles required. See Figure 5. Those principles include the spread of force through a fulcrum and moving the effort applied through a longer distance than the object to be moved. His Law of the Lever asserts: Magnitudes are in balance at distances inversely proportional to their masses.

Figure 5. Archimedes’ Lever.

https://commons.wikimedia.org/wiki/File:Archimedes%27-Lever.png

He also designed block-and-tackle pulley systems for use in loading and unloading ships. This pully system made it possible to raise and load cargo which would likely be impossible for a human to lift on their own due to its weight or girth.

6) Math and mechanics seem to be a secondary interest of Archimedes, yet these helped support his study of science. Why are both of these relevant to the practice of science?

Archimedes’ interest in mechanics profoundly inspired his mathematical reasoning. Not only did he write compositions on theoretical mechanics and hydrostatics, but he also wrote his dissertation *Method Concerning Mechanical Theorems* that used mechanical analysis as an investigative method for the detection of new mathematical hypotheses.

He was honored in his time and continues to be honored today for his pragmatic applications of mathematics and physics to fashion war machines used in defense of the Greek city-state Syracuse from Roman raiders.

7) Some say that all scientists owe Archimedes an “everlasting debt.” In your mind, how influential was Archimedes in the establishment and foundation of the practice of science?

Scientists in the modern age invariably invoke the practice of experimentally testing ideas proposed in the form of hypotheses. This scientific method of learning forms the foundation of our knowledge. The process is the essential core of scientific investigators all over the world. The practice of science involves formulating ideas, testing these ideas, and forming conclusions. This sort of scientific practice is not limited to scientists. In our everyday lives, whether we are scientists, we often use the scientific method of proposing hypotheses, testing them, gathering data, making conclusions, and revising our ideas. It is a continual process, and it is a universal one that is practiced by non-scientists.

Consider, for example, the case of your phone. We value our phones as indispensable, and if they do not work, it isn’t very pleasant. Let’s say you observe that your phone is nonfunctional. We immediately formulate a possible explanation, a hypothesis, to account for the phone’s non-function.

For instance, one might hypothesize that the phone is merely turned off. We test that hypothesis by manually turning on the phone. Next, we collect data by observing whether the phone turns on. If the phone comes alive, we conclude that the phone was just inadvertently turned off, and we proceed with our lives. However, if the data show that the phone did *not* turn back on after the attempt, then we can revise our hypothesis to propose an explanation that the phone’s battery is dead. We then experiment by charging the phone’s battery for awhile. We record our observations. If the phone turns on, we then conclude that the phone’s battery had been drained, and we proceed with our everyday lives, attached to our phones.

However, if we observe that the phone battery charging failed to permit the device to turn on, then we formulate a revised hypothesis. We now hypothesize, for instance, that the phone is broken. We test that hypothesis by having the phone examined by the carrier, and they begin the process of formulating revised hypotheses. They could speculate that a particular internal phone component is damaged or broken. They test that explanation by replacing the suspect phone component and gather data by observing whether the phone turns on and functions appropriately. In this example, let’s say that it *was *a broken phone part that had been the problem all along. The phone is fixed, and one can proceed with life.

This sort of scientific process cycles continuously in many aspects of our daily lives. We use it daily to explain the various things that we experience each day. The scientific method has not only been used by scientists and non-scientists alike, and the process has become an indispensable means for identifying and solving problems we face. Scientists continue to study the world around us and elsewhere by using the scientific method of reasoning and formulating hypotheses. As we investigate the natural world with its living and non-living phenomena, we become enlightened. We can use this awareness of the natural world to make it a better one for all of us.

8) What have I neglected to ask?

The account of Archimedes’ death is varied. Most reports surmise that he was caught off-guard and was killed by a Roman soldier near the end of the persistent siege of the Romans, but the underlying events differ. One account says that Archimedes was considering the details of a mathematical figure in the sand and said, “Don’t disturb my circles.” At that, the Roman soldier speared him with a blade. Another version places Archimedes outdoors holding mathematical apparatuses (such as dials, angles, and spheres) that the Roman soldier assumed to be valued golden gems, so he executed Archimedes to steal the “gems.”

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