**Recovering Archimedes’ Lost ‘Method’**

Over the previous decade I have had the great privilege and good fortune to work with the Artisans of Florence — International and the world renowned Gabriele Niccolai, whose family’s life work, past on from generation to generation, has involved researching, re-discovering and reconstructing the machines of Leonardo da Vinci. Thanks to his efforts, he now holds the world’s only patent on da Vinci technology for the recovery of the designs for Leonardo’s *Drumming Robot*, from which spawned a truly unique blockbuster travelling exhibition called *Da Vinci Machines and Robotics** *which also includes da Vinci’s long lost *Robot Lion, Gymnasium and Clockwork Drone.*

Some five years ago, when Mr. Niccolai revealed to me his plans to create the world’s first and completely unique travelling, interactive exhibition on the *Science of Archimedes* I was very excited. One question, however, stuck in the back of my mind. Despite the fact the Archimedes of Syracuse is widely regarded as the father of modern science, there is very little existing information about the great man or his life from reputable sources, and we are largely left with myths and legends. Undeterred, Mr. Niccolai and his colleague Luigi Rizzo, Lead Historical Researcher and CEO of the Artisans of Florence, embarked upon a truly Herculean effort to create a large scale travelling exhibition of functional Archimedian technology. Remarkably, in the process of doing so, they wound up recovering Archimedes’ long lost method, an intuitive scientific framework that not only provides an (ironically) ‘new’ way to view modern science, but holds the potential to create a paradigm shift in the way in which science is taught.

The problem was that of all of Archimedes’ works (ten treatises in total) only fragments of nine have survived. These fragments are copies of copies, and translations, mainly from Arabic, most of which were made by medieval monks with little scientific training or interest. The tenth treatise, *On the properties of light and mirrors*, is completely lost. The team began by studying and reconstructing ancient machines of the era based on ancient Egyptian pictographs and historical anecdotes from the Greek historian Herodotus. Despite my many years working with the team, it still amazes me how engineers and craftsmen uncover long lost secrets though the practical application of their craft that historians and scholars tend to miss by purely studying texts. Although it would take years to formulate the ‘big picture’ I recall that the artisans had remarked very early on that all of the ancient machines exploit the properties of balance or equilibrium to do work, and in fact that in their essence, all machines (including modern machines) really consist of just two simple machines, the inclined plane and the lever.

It is well known that most ancient texts which have survived to modern day were passed down to us through copies by scribes and in commentaries by other historical authors. Our second avenue of research was to undertake a comprehensive historical survey by consulting ancient texts, including the ancient Roman text by Vitruvius *Di Architectura*, Taccola’s Codex, da Vinci’s Codices, Piero’s Archimedes Manuscript, Pacioli’s *Geometry* and annotations of scientific experiments by Galileo Galilei. From these it became clear that many of the giants of science that followed Archimedes had access to his teachings and in the cases of da Vinci and Galileo, used them to improve the science of their own times.

The third avenue of our study was only made possible by the outstanding work of rare book curator William Noel and the *Friends of Archimedes** *whose dedicated restoration of the only original text by Archimedes’ gave us a real insight into the motivations of the ancient thinker, however it would take us another five years of collaborative research and experimentation until we reached the conclusion that Archimedes’ theoretical approach was collectively more akin to Analytical Mechanics than Newtonian Mechanics.

Analytical Mechanics, formulated in the 18th Century, examines the energy of complete systems. By contrast, Newtonian Mechanics examines how objects are acted upon by forces. Analytical Mechanics led to the development of the theory of Thermodynamics and provided the theoretical framework for the machines of the Industrial Revolution. Archimedes’ Method, misunderstood and forgotten, was in fact classical Analytical Mechanics; in its simplest form, systems in or near equilibrium (balance) which required just a small amount of introduced effort in order to achieve a large amount of work.

We can now use Archimedes’ Method to study and describe the physics of motion in an alternative, more intuitive way by looking at complete systems. Archimedes used his method across a multitude of fields. For example, in Mechanics he used his method with a set of scales to discover new knowledge about the properties of shapes and objects such as volume, weight and density. In Hydrostatics he used the properties of compressible fluids (like water) to analyse how connecting parts of the fluid (systems) affect each other in order to balance objects. In Mathematics he used a method to arrive at previously unreachable limits: The Exhaustion-sum (or the sum to infinity which we now call Calculus).

In modern terminology we can say that Archimedes applied his Method equally to both Physics and Mathematics. Each time he made a discovery in one of these two fields he would then use it to prove a hypothesis in the other. In this way he often expanded the knowledge of both fields. The underlying principle of all of this was the concept of **equilibrium** in relation to mechanical **systems** (machines).

Underpinning his ‘method’, his personal philosophy foreshadowed the spirit of modern empirical scientists. This could be simply and eloquently described as:

**Experiment, theorise, test the theory, re-fine the theory.**

In the modern museum environment where the merits of hands on experiential learning are valued, it is a rare thing to be able to look back 2000 years into the past and experience for oneself the technology and ideas that shaped our modern world, and to be able to do so in a simple and intuitive way, that audiences of all ages can appreciate and understand. I am very proud to be part of a team who have been able to rediscover the lost method of Archimedes, the father of modern science, so that it can be used to inspire a modern generation of future scientists.

I would like to thank Dr. Barnhart and the team at the *US Space and Rocket Centre* (NASA) in Huntsville, Alabama (USA) for hosting the world premiere of the *Science of Archimedes Exhibition**, *which is on display until February 2017.