The end of the Renaissance in Europe was characterized by a flourishing of scientific thought. During this time, the basic principles of physics, astronomy, and mechanics were formed — sciences that we are still exploring today. The emergence of the classical scientific tradition naturally led to the emergence of new technological innovations which qualitatively improved society’s standard of living. But in order for new technologies to become a reality, the world needed revolutionaries in science who would create a new scientific basis for their emergence. This article is about the most famous of these scientists.

## The Formation of the Scientific Method: Bacon and Descartes

Despite the rapid development of scientific thought and critical judgment, many scientists of the late Renaissance continued to explain the nature of things with mystical views. The rapid development of astronomy did not displace the interest of a wide range of highly educated people in astrology, a pseudoscience that tried to explain the future and the present by the movement of stars and planets. Scientific minds often tried to find confirmation of their theories in the occult and turned to alchemical recipes in order to expand their knowledge of matter and the universe. As expected, this was to no avail.

This situation fundamentally did not suit Francis Bacon (1561-1626), an English parliamentarian, philosopher, and polymath who was an active supporter of the revolution in science. Bacon condemned the supporters of unconfirmed paradigms and outdated models of the structure of the universe, arguing that only new knowledge and theories, confirmed by experimentation base, can claim to be true.

In order to prove in practice the importance of his scientific method, Bacon designed a scientific laboratory in which he conducted many experiments. The scientific method developed by Bacon was based on the need for scientists to question the veracity of the theories they put forward and to test them through experimentation. Thus, to test the previously existing hypothesis that many diseases are transmitted through contact between sick and healthy people, Francis Bacon proposed exposing healthy people to various experimental variables (one of which was contact with a sick person) in order to determine the specific cause of new cases of the disease. What was important in Bacon’s empiricism was precisely the repeatability and systematic nature of his experiments. He believed that it was not enough to stop experimentation once one had confirmed a hypothesis. Rather, in order to be sure of the truth (or falsity) of the judgment, an experiment had to be repeated again and again until any possible error in the results was reduced to an absolute minimum.

Bacon’s discussion of the importance of critical thinking in science formed the basis of his book, *The Advancement and Proficiency of Learning*, which was published in 1605. Bacon argued the importance of a substantiated and demonstrative scientific approach in science by its universality — any person could repeat the experiments described in his book and personally verify the veracity of his conclusions.

After Bacon’s death, his philosophy of empirical knowledge would form the founding principles of the Royal Society for the Development of Natural Scientific Knowledge, which was born in 1660. The Society would be particularly remembered for the launch of the first ever scientific journal, which was called the *Philosophical Transactions of the Royal Society*.

And although Bacon did not go down in the history of science as an outstanding inventor, it was his recommendations on how to carry out scientific inquiry that would inspire other generations of scientists, namely the French philosopher and mathematician René Descartes (1596-1650). Descartes created what we know as the Cartesian coordinate system, which is the standard x- and y-axis system we still use today. This two-axis graphic system made it possible to plot variables versus time and would become the basis for the emergence of analytical geometry. A clear system of graphs will contribute to the development of a number of scientific disciplines, including astronomy, physics, and engineering. Descartes gave the most complete description of his coordinate system in a supplement to his book *Discourses on Method*, published in 1637.

In his works, René Descartes would also conclude that the Universe itself is not static and is strictly subject to the laws of mechanical motion, but he was not able to accurately describe these laws during his lifetime. Descartes lacked the mathematical tools and the availability of a new number system that would have allowed him to calculate the change in processes over time. There was also a lack of a clear classification of laws that would describe all known types of mechanical movement. However, a person would very soon appear in England who was able to combine all the observations of his predecessors and streamline them in the form of a system of elegant equations that describe these patterns.

## The birth of calculus and gravity: the phenomenon of Newton

Isaac Newton (1643-1727) was born prematurely and weighed so little that his survival was in serious doubt. However, the universe had other plans for him, and at age 18 in 1661, Isaac entered Trinity College in Cambridge, where he fell under the tutelage of Isaac Barrow, at the time one of England’s greatest mathematicians. It was Professor Barrow who formed Newton’s interest in the most important mathematical problems of his time: the need for an algebraic description of time-varying processes.

While the University of Cambridge was closed due to an outbreak of plague, Newton began to work independently and no less fruitfully. He began experimenting with optics, which resulted in him creating one of the first mirror reflecting telescopes. Newton’s telescope had both a much stronger magnification capacity and a tenth the size of its predecessors. The idea for new telescope was enthusiastically received by the Royal Society, of which Newton himself was a member. Subsequently, in 1703, for his colossal contribution to science and natural philosophy, Newton would be elected president of the society.

Isaac Newton was also the first to develop the principles of calculus , a completely new field of mathematics that was able to determine the rate of change of processes over time. Instead of the standard operations of addition, subtraction, division, and multiplication, Newton’s new methodology of calculus used integrals and functions to describe in detail how processes that change over time.

Newton divides his calculus into 2 types:

*Differential*, which works with derivatives to determine the rate of change of a variable over time.

*Integral*, which works with integrals to determine values whose rate of change of which is already known.

Although it was Isaac Newton who first invented calculus and even applied its principles to the description of physical processes, his colleague, the German mathematician Gottfried Leibniz (1646-1716), was the first to develop the notation for this language, which is still used today. Leibniz’s publications were a real blow to Newton, who claimed to have described the method 20 years earlier. A real enmity flared up between the two scientists. Accusing his opponent of plagiarism and wanting to prove it, Newton dug up old notes and calculations which had never before been published. Whether Leibnitz was the first to do what he did or not, his contribution to the refinement of Newtonian calculus cannot be denied, and the creation of calculus is usually attributed to both scientists, since most likely they formulated it independently of each other.

Despite the colossal importance of calculus, it is not the thing for which Newton is most famous. Rather, his greatest claim to fame is the laws he derived that describe the mechanical movement of objects. Newton formulated three laws which described the mechanical movement of objects in space:

*The law of inertia*describes inertial reference systems. Newton argued that if no other forces act on a body, it will either maintain uniform rectilinear motion (if the body was initially in motion), or remain at rest (if the body was initially at rest). Newton called this feature of bodies*inertia*, emphasizing that different bodies have different inertia, which primarily depends on their mass.

*The law of differential motion*describes the relationship between the force applied to a material point of a body and the acceleration received from it. The acceleration vector will always follow the direction of the force applied.

*The law of balancing forces*states that the force applied to an object is equal in absolute value and is directed strictly in the opposite direction from its reaction force. According to Newtonian formulations, force is always the result of interaction of several bodies, without whose participation changes in movement are not possible.

Today, the laws of classical Newtonian mechanics have undergone a number of changes that more accurately describe the processes and forces involved in them, but their basic principles have remained unchanged.

In developing his ideas about forces and the motion they cause, Isaac Newton made the most important discovery of his life, which until then had always been on the surface — he formulated the first theory of gravity as the force of attraction between less massive objects and more massive ones. It was obvious to Newton that the gravitational force he observed had to work on a cosmic scale as well. With the help of a series of calculations, he was able to determine the force that allowed the moon to move while not leaving its near-Earth orbit. So great was his surprise when he realized that this force was the very same as the force of gravity that acted on the famous apple at the moment it fell towards the ground and hit his head.

The result of almost 20 years of Newton’s mental reasoning and calculations would be the book Mathematical Principles of Naturalistic Philosophy (Philosophiae Naturalis Principia Mathematica), published in 1687. The book included descriptions of new methods of integral and differential calculus, Newton’s three laws of motion, and a general description of the principles of gravity.

Along with the development of theoretical knowledge about the principles of the universe, there was also a great leap forward in the field of engineering: new knowledge about materials and their behavior over time would allow outstanding inventors to create innovations that would bring civilization towards the industrial revolution. Read about the most interesting of them in the second part of this series devoted to the technological innovations of the New Age.