The more you know

Isaac Newton

He was born, in the year Galileo died, in Lincolshire, England. Some say he was born in 1642, because Lutherans in England did not accept the Catholic Gregorian calendar. So for the British he was born on Christmas day 1942, for Catholics on January 4, 1943. His father had died in the English Revolution, fighting for the monarchy (on the side of Charles I). He still manages to study (even alchemy and physics) thanks to the help of wealthy people.
His mother abandons him and is practically raised by his grandmother. His life was spent almost entirely in Cambridge, becoming a friend of the wighs (1688-89 glorious revolution with the deposition of the Stuart dynasty). He was appointed supervisor of the Mint and was president of the Royal Society.
His main work, from 1687, is “Principia mathematical philosophia naturalis”.
In this work there are the principles of mechanics and the law of universal gravitation. He devoted a lot of time to writings on chemistry and theology, which were however destroyed in a fire caused by one of his experiments.
He was strange: he hardly ever washed. He tended to be lonely. He died in 1727.
The concept of gravity was not exactly invented by Newton: there was a certain Hooke (An Attempt to Prove the Motion of the Earth from Observation) who in 1676 had used the concept of gravity in this book. However, Newton was able to quantify it.
The characteristics of a force are intensity, direction, direction and point of application.
A big news is that Newton understands that the physical laws that apply to earth can also be applied to celestial bodies.

How do you get to the formula of the gravitational law?

Let’s imagine a stone tied to a rope. If we spin the rope and at a certain point we cut it, the stone starts at a tangent. By the principle of inertia the body tends to go straight. If the speed that makes the earth revolve around the sun were too low the earth would fall on the sun, if it were too high it would go off on a tangent. The force of gravity for the earth performs the same function as the rope for the stone.
By combining Kepler’s third law and the centrifugal force formula, Newton’s law is not exactly obtained (at most an approximation of it, as Popper claims), but it is shown that the force of gravity is proportional to the mass and inversely proportional to the square of the distance.
Newton is able to quantify force, because he understands that the concept of force can be both the cause of every movement that occurs on earth, and of every movement that occurs between the planets.
Newton is the first to understand that the same concept of force can be applied to both the earth and space (Descartes also took a step forward, removing the distinction between celestial and terrestrial physics).
In the field of mathematics, he outlined the rules of analysis and provided the definition of LIMIT, DERIVATIVE and INTEGRAL.
Each of the three had already been discovered separately, but Newton gives a logical arrangement to the infinitesimal calculus. Leibniz had also discovered infinitesimal calculus, in fact the annotation (the symbols) of the integrals that are studied in mathematics is that of Leibniz.
The Rules of the method are almost axioms (he exposes the physical theory on the geometric model, on the model of Euclid).
1) Rule of simplicity: “More numerous causes of natural things must not be admitted than those that are true and sufficient to explain the phenomena”. The nature is simple and therefore we need to refer to a small number of causes. Idea which is called “Occam’s razor”.
2) Rule of the uniformity of nature: “Therefore, as long as it can be done, the same causes must be attributed to natural affects of the same kind”: as long as there are no contrary reasons we attribute the same causes to the same effects. If we see stones falling in Europe or America, we do not think that the causes are different. Nature is regular, uniform.
3) Rule of generalization (inductive): “The qualities of bodies that cannot be increased and decreased, and those that belong to all the bodies on which it is possible to implant experiments, must be considered qualities of all bodies”. Primary qualities cannot disappear; when we do not perceive them we still believe that they are inseparable qualities of the substance. If I think of the length of the atom that I do not perceive, I still understand that it must necessarily exist, because matter has among its qualities that of spatiality. We will see that Locke, 3 years after the Principia publishes “The essay on the human intellect” and exemplifies this rule: he says that all our knowledge comes from experience, so we attribute qualities to bodies based on what we perceive. For example, if I take a grain of wheat, I perceive it in all its sensitive qualities. Let’s imagine cutting it, at a certain point it becomes so small that I do not see it, but I can understand with the reason that if a grain was extended, even half, and still half up to the atom is extended. All these qualities (mass, extension, force of inertia) he calls them primary qualities. However, not all qualities enjoy these properties. The color, the smell, the taste are not maintained. If I take a grain of wheat that is so small that I can’t see it, it doesn’t even have a color. These qualities are called secondary qualities.
In Newton and Locke the initial intention for which the distinction was made changes; Galileo had posited these two types of qualities for a methodological purpose, (science deals directly with measurable qualities) from which he had also drawn an ontological consequence (there are two levels of reality, one objective and one subjective). Newton and Locke, on the other hand, were convinced that in reality this was the case.
I see that this pen is impenetrable, like the desk, the chair…. So I understand that all solids are impenetrable, this is an induction. Also with regard to solids and liquids with reason I can understand that, where one atom is, there cannot be another one and that therefore there are conditions in which it is impenetrable. The extension, the hardness, the impenetrability of the whole comes from the extension, the hardness, the impenetrability of the part. In principle, infinite division exists (with reason I can think that a thing can be divided infinitely), in practice it is not possible.

The quantity of matter is defined as follows by Newton: it is the measure of the same obtained from the product of its density by the volume (mass). However, he does not claim that gravity is essential to bodies. Only the force of inertia is immutable. In addition, gravity decreases as you move away from the earth. In practice he says that it is not necessary to explain the force of gravity, he was aware of the fact that his explanation had limits (it was not clear for example how this force could be transmitted in a vacuum). With experience one can only understand that there is an inertial mass. This mass that resists force (if I kick a stone ball, it gives me more resistance than a normal ball) is a primary quality, but one cannot immediately identify inertial mass (or inherent force) with gravitational mass. We cannot treat gravitational mass as an essential quality. Unlike Newton, Descartes had been able to convincingly explain his interpretation, even if it was later wrong.
4) Rule of induction: “In experimental philosophy, the propositions obtained by induction from phenomena must, despite the contrary hypotheses, be considered true or rigorously or as much as possible, until other phenomena intervene, by means of which or they are made more exact or are subject to exceptions “. The conclusions drawn by induction (generalizing or using Bacon’s method) must be considered true until something intervenes that alters the initial conditions. If I say that all crows are black, this has always been confirmed by observation, but in principle we are not really sure that it is always true.
Since the inductive method is used in physics, Newton points out that the laws of physics hold true until proven otherwise. One might therefore think that science is not as certain as it appears, since the inductive method is not absolutely safe. For Newton, the scientist must not make uncontrollable hypotheses, that is ad hoc hypotheses (such as saying that the moon is spherical because it has a transparent matter surrounding it, because at the time it was not a verifiable hypothesis). This means the famous phrase “I make no assumptions”. By scientific hypothesis, on the other hand, we mean an interpretation that the scientist proposes to analyze and control it (will it be true that the speed of falling into a vacuum is not conditioned by mass?).
Fifth rule: “I consider phenomena not only what is known to us through the five senses, but also the things that, thinking [in scientific theory], we intuit in our mind.” We consider everything that appears to us to be something and we can explain it. Among these things there may be some that we do not perceive, but which nevertheless fall within the scientific claims and as such we consider them to be endowed with reality. For example atoms (when the microscope was not yet known), time, force….
Why didn’t Newton publish the 5th rule?
He truly believes in what is said in the rule, in the sense that even if we don’t see time, it’s not that we don’t include it in the physical laws. Newton believed his rule could be misleading. He feared that he might give credit to the scholastics, who used the Aristotelian theory (in which there are entities, as act and substance, which are not empirically demonstrable). Therefore, their method could also fall within, be assimilated to the scientific field. If a type of weed caused sleep, the scholastics as an explanation said that it possessed vis dormitiva. They then used fictitious entities to explain everything, even if in the end nothing was explained.
Newton’s fear was to give credit to these entities. So this 5th rule only used it, and he didn’t publish it, it was only contained in the manuscripts.
Newton believed that “curiosity is the mother of science”, it is not a vice, morally reprehensible, as St. Augustine believed. If man is not curious he will never arrive at scientific theories.


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