Learning Outcomes

Discussion
During the medieval period, people had to face significant pressure due to a series of questions raised about the existing system of knowledge and human existence. When they tried to solve these problems with the help of methods and knowledge of that time, it was realised that they couldn’t reach a scientific solution unless they revise the existing methods of inquiry. Some of the inventions and discoveries made in the Middle Ages (e. g. the invention of gunpowder) led to problems which asked for immediate reaction in a variety of fields. In order to find solutions, more and more intellectuals dared to study nature objectively and to apply the results of contemporary scientific thinking. This led to an enormous increase in the quantity and quality of innovation and eventually resulted in the “Scientific Revolution” of the16th and 17th centuries. The key sciences were mathematics, chemistry and astronomy, and the key men were Francis Bacon and Isaac Newton.
The following inventions of the medieval period have had lasting importance.
Mechanical Clock: The invention of mechanical clocks enabled people to accurately keep track of time. The knowledge of not only what hour it was, but even what minute and second it was, changed the way people scheduled their days and work patterns.
Printing Press: While printing technology had been developed in 11th century China, it was the 15th century German Johannes Gutenberg and his printing press that started a new era of the mass production of books. Until the rise of computers in the 20th century, books and the printed word remained the dominant form of media for the world’s knowledge.
Gunpowder: Gunpowder was invented in China sometime between the 9th and 11th centuries. The knowledge of the invention spread throughout Eurasia in the 13th century, and it revolutionised warfare and made previous military technology and many medieval castles obsolete.
Water and Wind Mills: While mills were in use from antiquity, it was in the Early Middle Ages that they became very popular. Throughout the medieval period, new and ingenious forms of mills were invented, which allowed people to harness the energy from natural forces like rivers and wind, a process that continued to the present day.
Paper money: It has a very important advantage over coins made from precious metals because they were easier to transport anywhere, and proved to be a great benefit to merchants. However, the concept of placing value on a marked piece of paper was started in the 13th century only. In the 17th century, regular banknotes started circulating in Europe as the common currency.
Along with other inventions, a change in the way of thinking replaced the old Theo- centric notions. This movement based the generation of new knowledge on observation, experimentation, and the use of reason. This period was characterised by the use of reason to achieve new knowledge and questioned the old notions about human existence. Advanced knowledge paved the way for many more innovative ideas and inventions during the early modern times.
Let’s have a brief look into some of the outstanding inventions:

• Compound microscope (1590) – Teenager Zacharias Janssen in- vented the first compound micro- scope, likely with assistance from his father Hans Janssen, who made eyeglasses for a living.
• Thermometer (1593) – Galileo Galilei created the first thermometer, which was actually a thermal scope. It allowed water temperature changes to be measured for the first time.
•  Adding machine (1645) – Blaise Pascal invented the adding machine.
•  Telescope (1608) – Hans Lippershey invented the refracting telescope.
•  Slide rule (1632) – William Oughtred invented the slide rule, which further sped up the process of completing complex calculations.
•  Cartesian coordinate system (1637) – Rene Descartes invented this system, which is better known as the x-y axis for graphs.
•  Barometer (1643) – Physicist Evangelista Torricelli invented the first barometer. His invention was a mercury barometer.
•  Probability/statistics (1654) – Blaise Pascal and Pierre de Fer- mat together invented the mathematical foundation for statistics and probability.
•  Calculus (1665) – Sir Isaac New- ton invented calculus, though he didn’t publish it until 1687. Calculus is the mathematics of continual change.
•  Reflecting telescope (1667) – Sir Isaac Newton further advanced
•  science by making the first reflecting telescope.
  The following are some of the leaders of Scientific Revolution:
  5.4.1 Rene Descartes (1596-1650)
  

Fig. 5.4.1 Rene Descartes
Rene Descartes was a French lay Catholic philosopher, scientist, and mathematician, widely considered a seminal figure in the emergence of modern philosophy and science. So, he was regarded as the father of Modern Mathematics as well as the father of Modern Western Philosophy. His philosophical methodology consisted of scepticism (rejection of authority) and rationalism (an assertion of self- confidence). Descartes’ method is deductive and he rejected Aristotelian logic as sterile. Mathematics was central to his method of inquiry, and he connected the previously separate fields of geometry and algebra into analytic geometry.

He was responsible for the increased attention given to epistemology in the 17th century through his ‘Theory of Doubt’ and ‘Deductive Method’. The Theory of Doubt or Cartesian doubt was a methodical doubt in a way of seeking certainty by systematically doubting everything. He argued that any knowledge could just as well be false as the sensory experience, the primary mode of knowledge, is often erroneous and therefore must be doubted. Cogito Ergo or ‘I think, therefore I exist’ is the principle of this doubt. The only certain rule in this world is the reality of our own existence because of the presence of our cognition. It found that even his doubting showed that he existed, since he could not doubt if he did not exist. Descartes thought we shouldn’t assume anything unless it could be proven through a chain of reasoning and the scientific method.
Coordinate geometry was introduced by Fermat and Descartes, ignoring rather than solving the foundational problems which had prevented the Greeks from taking this step (viz: the lack of any well understood number system which could account for incommensurable ratios). This development is important to science because it makes geometry quantitative and permits the use of algebraic methods. Geometry must be quantitative for it to be useful in science and engineering, and algebraic methods permit more rapid development of mathematics than the less systematic (if more rigorous) methods required by the Greek axiomatic approach to geometry.
5.4.2 Francis Bacon (1561-1626)
Francis Bacon was born into a prominent
wealthy family in London, England, on January 2, 1561. He was one of the leading figures in natural philosophy and in the field of scientific methodology in the period of transition from the Renaissance to the early modern era. He was a critic of Aristotle. His laws of science by gathering and analysing data from experiments and observations marked the beginning of the end for centuries old natural philosophy of Aristotle. This scientific method unleashed a wave of new scientific discoveries, particularly in the hands of devotees such as Robert Boyle.

Fig. 5.4.2 Francis Bacon
Throwing Out Aristotle
“The corruption of philosophy by the mixing of it up with superstition and theology, is of a much wider extent, and is most injurious to it both as a whole and in parts.” (Francis Bacon, Novum Organum, 1620).

Most scholars in the early 1600s blindly accepted the doctrines of Aristotle. Aristotle used the deductive method of reasoning. He would move from a general rule to specific facts. He started with rules he had developed from logical arguments. Bacon’s objective was to replace this methodology with a new body of scientific knowledge secured by experiments and observations. Bacon’s most significant work, Novum Organum (The New Tool), described what came to be called the ‘Baconian Method of science’. He championed the inductive method in science. This means moving from specific facts to a general rule. The method starts with observation of particular instances (data collection). After that, proceeds to an inductive leap which means arriving at a conclusion or general principle from the collected particular data. Thus, the inductive method provides general principles through observation and experimentation.
In other words, Bacon gives us an outline of his conception of the scientific method in Novum Organum. This method involved collection of particulars through observation and systematic experimentation, putting down this data in writing in a proper and well- arranged fashion, deriving axioms (general principle) by certain method and rules from the above particulars, and finally deriving new particulars from these axioms so that the axioms could confirm their own extent.
For example, the inductive investigation could have involved measuring the electric conductivities of a number of solid materials such as silver, gold, iron, platinum, lead, copper, zinc, tin, brass, sulphur, phosphorus, wood, table salt, granite, sand and sugar. The specific results would allow you to state the general rule that metals conduct electricity better than non-metals. Thus, through the inductive method, Aristotle’s rule turned out to be wrong. Bacon argued that Aristotle’s method ended up with a defective understanding of Nature because it didn’t follow scientific methods.
Bacon conceived that Nature never tells you her secrets easily. To find it, one should employ hard work and vigorous interrogation. So scientific methods need to devise experiments that ask Nature the right questions. Only then one might succeed to find the truth. Nature would not reveal the truth to philosophers such as Aristotle, who thought they could sit in and coax her into revealing her secrets simply by thinking. Instead of logical speculations, one needed to gather solid data first to guide scientific thought.
He also objected to the tendency of Aristotle, Plato, and others including Pythagoras to mix scientific ideas with religious ideas. Bacon believed that the two should be kept separate. He was highly suspicious of people who said the laws of nature were there as part of a greater purpose. He thought they were there to be discovered and, if possible, exploited.

5.4.3 Natural Philosophy: Theory of the Idols
Bacon’s doctrine of the idols represents a stage in the history of theories of error and functions as an important theoretical element within the rise of modern empiricism. According to him, the human mind is not a ‘tabula rasa’ or blank slate. Instead of an ideal plane for receiving an image of the world, it is a crooked mirror that has implicit distortion. He does not sketch a basic epistemology but underlines that the images in our mind right from the beginning do not render an objective picture of the true objects. Consequently, we have to improve our mind, i.e., free it from the idols, before we start any knowledge acquisition.

• Bacon warns the student of empirical science not to tackle the complexities of his subject without purging the mind of its idols. On waxen tablets you cannot write anything new until you rub out the old. With the mind it is not so; there you cannot rub out the old till you have written in the new.
  He interprets Aristotle’s syllogism in relation with sophisticated fallacies. There is no finding without proof and no proof without finding. But this is not true for the syllogism, in which proof and invention (middle term in syllogism) are distinct.
  To him, Judgement by syllogism presupposes—in a mode agreeable to the human mind—mediated proof, which, unlike in induction, does not start from sense in primary objects. In order to control the workings of the mind, syllogistic judgement refers to a fixed frame of reference or principle of knowledge as the basis for “all the variety of disputations”. The reduction of propositions to principles leads to the middle term. Bacon deals here with the art of judgement in order to assign a systematic position to the idols. Within this art he distinguishes the ‘Analytic’ from the detection of fallacies. Analytic works with “true forms of consequences in argument”, which become faulty by variation and deflection.
  He called the wide variety of errors in mental processing the Idols of the Mind. There were four idols: Idols of the Tribe, Idols of the Cave, Idols of the Marketplace, and Idols of the Theatre.
  Idols of the Tribe: The Idols of the Tribe made the false assumption that our most natural and basic sense of thing was the correct one. He called our natural impressions a “false mirror” which distorted the true nature of things.
  Idols of the Cave: The Idols of the Cave were the problems of individuals, their passions and enthusiasms, their devotions and ideologies, all of which led to misunderstandings of the true nature of things.
  Idols of the Marketplace: There are also Idols formed by the intercourse and association of men with each other on account of the commerce and consort of men there. For it is by discourse that men associate, and words are imposed according to the apprehension of the vulgar. And therefore, the ill and unfit choice of words wonderfully obstructs the understanding.
  Idols of the Theatre: The final Idol of the Theatre, is how Bacon referred to long-received wisdom, the ancient systems of philosophy, the arbitrary divisions of knowledge and classification systems held onto like dogma. Without emptying one’s mind of the old ways, no new progress could be made. This would be an important lasting value of the Baconian view of science. Truth must be reasoned from first principles.
  Bacon’s Public Career
  Bacon at the age of 15, aimed to become a lawyer and he left for London. But soon he was placed as the English Ambassador to France for two years. Thus, he performed diplomatic duties on behalf of Queen Elizabeth’s government in France and hence learned politics and diplomacy. But after his father’s death, he returned to England and began to engage in his work as a lawyer. His legal and political careers eventually carried him to the highest position in England’s legal profession.

•  At the age of 20, he became a Member of Parliament.
•  At the age of 42, he was knighted for his service to King James, becoming Sir Francis Bacon.
•  At the age of 52, he was appointed as England’s Attorney General
• At the age of 56, he reached the top, becoming Lord High-Chancellor of England in 1617.
•  In 1621, his public career ended in disgrace as he was accused of corruption, sent to prison and fined a huge fine. But the prison term lasted only a few days and the fine was remitted. He retired to study and writing.
  5.4.4 Sir Isaac Newton (1642-1727) 

5.3.3 Sir Isaac Newton

Sir Isaac Newton was an Englishman, physicist, astronomer, mathematician, theologian, alchemist, and government official who made an epoch in modern science through his outstanding inventions. He was the revolutionary scientist in world history for his Theory of Universal Gravitation, his Laws of Motion, and his theories in optics, as well as the invention of differential calculus. In addition, Newton invented the reflecting telescope, and made numerous other contributions to his fields of study. His Classical mechanics comprises the four main fields of modern physics (alongside the later fields of electricity and magnetism, thermodynamics, and quantum mechanics). He was one of the first men to assume that the natural world is governed by universal laws that can be expressed mathematically.
Newton emphasised that conclusions are drawn from experiments: “But hitherto I have not been able to discover the cause of those properties of gravity from phenomena, and I frame no hypotheses; for whatever is not deduced from the phenomena, is to be called an hypothesis; and hypotheses, whether metaphysical or physical, whether of occult qualities or mechanical, have no place in experimental philosophy.”

Isaac Newton was born on Christmas day December 25, 1642 in Woolsthorpe, Lincolnshire. The young Newton seems to have been a quiet, not particularly bookish, lad, but very ready with his hands; he made sundials, model windmills, a water clock, a mechanical carriage, and flew kites with lanterns attached to their tails. Throughout his life he built mechanical devices and fashioned his own tools for high precision work.

5.3.4 Newton’s sculpture by Eduardo Paolozzi displayed outside the British
Library in London
Newton joined Cambridge in 1661. At this time the movement of the Scientific Revolution was well advanced, and many of the works basic to modern science had appeared. Astronomers from Nicolaus Copernicus to Johannes Kepler had elaborated the heliocentric system of the universe. Galileo had proposed the foundations of a new mechanics built on the principle of inertia. Led by René Descartes, philosophers had begun to formulate a new conception of nature as an intricate, impersonal, and inert machine. Newton discovered the works of Descartes and the other mechanical philosophers, who, in contrast to Aristotle, viewed physical reality as composed entirely of particles of matter in motion and who held that all the phenomena of nature result from their mechanical interaction. However, their theories still had holes, which Isaac Newton then filled. Newton’s contribution to scientific thought included his four basic laws: three laws of motion and the law of universal gravitation.
Year of Great Discovery
The year 1666 is known as Newton’s annus mirabilis (miraculous year–more precisely the two years 1665-1666), when he was about twenty-four years of age. He later recalled, “For in those days I was in the prime of my age for invention & minded Mathematics & Philosophy more than at any time since.” (By “philosophy” he meant physics.) These were intense periods of intellectual endeavour at Woolsthorpe. Freed from the restrictions of the limited curriculum and rigours of university life, Newton had the time and space to develop his theories on calculus, optics and the laws of motion and gravity.
Calculus: Calculus has uses in physics, chemistry, biology, economics, pure mathematics, all branches of engineering, and more. It’s not an overstatement to say Newton’s insight in the development of calculus has truly revolutionised our ability to pursue new branches of science and engineering. It is used in problems when a quantity changes as a function of time, which is how most problems behave in reality. Isaac Newton changed the world when he invented Calculus in 1665.
Newton started by trying to describe the speed of a falling object. When he did this, he found that the speed of a falling object increases every second, but that there was no existing mathematical explanation for this. The issue of movement and the rate of change had not yet been explored to any significant degree in the field of mathematics, so Newton saw a void that needed to be filled. He began work on this right way, incorporating planetary ellipses into his theory too to try to explain the orbit of the planets. He found that by using calculus, he could explain how planets moved and why the orbits of planets are in an ellipse.
At its most basic, calculus is all about studying the rate of change of a quantity over time. In particular, it can be narrowed down to the study of the rate of change and summation of quantities. The two categories of calculus are called differential calculus and integral calculus. Differential calculus deals with the rate of change of a quantity such as how the position of an object changes compared to time. Integral calculus is all about accumulation, or summing up infinitely small quantities. The fundamental theorem of calculus is what connects these two categories. This theorem guarantees the existence of anti-derivatives for continuous functions.
Calculus is used in all branches of mathematics, science, engineering, biology, and more. There is a lot that goes into the use of calculus, and there are entire industries that rely on it very heavily. Engineering is one sector that uses calculus extensively. Mathematical models often have to be created to help with various forms of engineering planning. And the same applies to the medical industry. Anything that deals with motion, such as vehicle development, acoustics, light and electricity will also use calculus a great deal because it is incredibly useful when analysing any quantity that changes over time. So, it’s quite clear that there are many industries and activities that need calculus to function in the right way.
Newton’s Optics: While waiting out The Plague he began to investigate the nature of light. White light, according to the prevailing theories, was homogeneous. His first experiments with a prism provided the true explanation of colour. Passing a beam of sunlight through a prism, he observed that the beam spread out into a coloured band of light (spectrum) like a rainbow. While others had undoubtedly performed similar experiments, it was Newton who showed that the differences in colour were caused by differing degrees of refrangibility. A ray of violet light, for example, when passed through a refracting medium, was refracted through a greater angle than a ray of red light. His conclusions, checked by ingenious experiments, were that sunlight was a combination of all the colours and that the colours themselves were monochromatic (his term was “homogeneal”), and separated merely because they were of differing refrangibility.
5.4.5 Isaac Newton’s Four Basic Laws
Newton’s Four Basic Laws: Isaac Newton developed a simple theory, four basic laws: three laws of motion and the law of universal gravitation, perhaps best- known work is gravity.
Newton’s theory of universal gravitation says that every particle in the universe attracts every other particle through the force of gravity. The theory helps us predict how objects as large as planets and as small as individual colliding molecules will interact; it shows us the way earthquakes ripple through the Earth’s crust and how to build buildings that can withstand them. His simple equation for universal gravitation, written in 1666 when he was 23, helped overthrow more than a thousand years of Aristotelian thinking (reinforced by Greek astronomer Claudius Ptolemy) which said that objects only moved if an external force drove that motion.

5.3.5 Representative image of Newton’s Gravitational Theory

The law of universal gravitation states that “two bodies in space pull on each other with a force proportional to their masses and the distance between them.” For example, the large objects orbiting one another, like the moon and earth, actually exert noticeable force on one another. It may seem like the moon is orbiting a relatively static earth, but actually the moon and the earth are rotating around a third point between them. That point is called the barycentre.
As per this law, every object in the universe attracts every other object with a measurable force (however slight). The force is:

• Directly proportional to the prod- uct of two objects’ masses
•  Inversely proportional to the square of the distance between the objects
• This principle can be expressed in the equation: F = G mM / r^2

Here in this equation: ‘F’ is the magnitude of force, ‘m’ is the mass of the smaller object, ‘M’ is the mass of the larger object, ‘ r’ is the distance between the objects’ centres of mass and ‘G’ is the gravitational constant.

Newton’s 3 Laws of Motion
1. An object in motion tends to stay in motion and an object at rest tends to stay at rest unless acted upon by an unbalanced force.
2. Force equals mass times acceleration (F=ma)
3. For every action there is an equal and opposite reaction.

Newton’s first law of motion concerns any object that has no force applied to it. An object not subject to an external force will continue in its state of motion at a constant speed in a straight line. Now, suppose someone is on ice skates, just standing in the middle of an ice rink. What’s going to happen? The person just stays in the middle of the rink. But if they are on ice skates and moving forward at two miles an hour, they will continue to move straight ahead at two miles an hour until something pushes them or stops them. Hence, the first law describes the behaviour of an object subjected to no external force.
The second law then describes the behaviour of an object that is subjected to an external force. Let’s take the same example, if a person is on ice skates moving forward at two miles an hour and they are pushed from behind, they now go faster in the same direction. If they are pulled from behind, they slow down. If pushed from the side, they change direction. If the force of push is bigger and high, it results in more change. Similarly, if the object is heavier, the resulting change may be less. An object is either subject to a force or it isn’t, so the first two laws are sufficient to describe the behaviour of the object.
But what may be the behaviour of the object or thing that applied the force? What happens to it? The force felt from a push is felt in the opposite direction, but in the same amount. Let’s again consider the same example, if a person is on ice skates and someone pushes them, they accelerate forward because of the force and the other person goes backwards because of it. ‘To every action there is always an equal, but opposite reaction’. This forms the third law of motion.
These three simple laws explain a lot, but they become incredibly powerful when combined with the prime law, that is, the law of universal gravitation, which says that gravitation is an attractive force, a very significantly attractive force.
Take any two objects with mass and there will be an attraction between them, along the lines connecting their centres of mass. This pull will be proportional to the product of their masses, making one twice as heavy, twice the attraction. And it will be inversely proportional to the square of the distance between them, move them twice as far away, feel only one-fourth the pull.
When these three laws of mechanics and the law of universal gravitation are used together, we suddenly have an explanation for Kepler’s elliptical orbits. Not only that, we can explain the tides, the motion of cannonballs, virtually everything we see in the world around us.
Principia Mathematica: Newton’s Principia attracted the attention not only of scientists but also from philosophers. In Principia -its full title is the Mathematical Principles of Natural Philosophy- Newton lays out his laws of motion, law of universal gravitation and an extension of Kepler’s laws of planetary motion. It is a book that helped define the Age of Reason and it is Newton’s most celebrated achievement. He proposed that the universe is mainly an empty space crisscrossed by powerful but invisible gravitational forces. Whether tiny atomic particles or giant planets, the attractive pull between two objects is proportional to the product of their masses and decreases with the square of the distance between them.
The publication history of the work is quite interesting. It was in 1684 when Newton lived in self-imposed isolation at Cambridge, that the work progressed. The young astronomer Edmond Halley approached Newton for the answers of some questions. Thus, Dr Halley’s was the catalyst for the creation of Newton’s principia. Halley continued to manoeuvre with great diplomacy, coaxing Newton through the process of getting the three parts of the Principia finished. Halley went to great lengths to bring Newton’s work to paper, paying for the publication himself as the Royal Society had run out of funds.
Newton was a sincere religious believer, who said his discoveries were inspired by God. He devoted more time to the study of Scripture than to science. Newton wrote, “This most beautiful system of the sun, planets, and comets, could only proceed from the counsel and dominion of an intelligent being… All varieties of created objects which represent order and life in the universe could happen only by the willful reasoning of its original Creator, Whom I call the Lord God. “Newton believed that God’s creation of the universe was self-evident given its grandeur. He also warned against using his laws to replace the creator. He said, “Gravity explains the motions of the planets, but it cannot explain who set the planets in motion. God governs all things and knows all that is or can be done.”
During his late life, Newton wrote lavishly on theology. He received a knighthood from the queen of England in 1705 (the second scientist to have been knighted in England). He died in 1727 from mercury poisoning, likely caused by Newton’s work in alchemy. Newton never married. He is widely regarded as one of the most important people who ever lived. Many of his ideas still hold true and his equations are still used to this day and have secured his place in history.

Recap