Chapter 1: Mechanics before Galileo
Introduction: What is Mechanics?
Mechanics (in the meaning that we care): area of knowledge that treats of motions and tendencies to motions in material bodies.
It is important to many other sciences as well as philosophy.
Some Key Questions Dealt with in Mechanics
Motion
- Is motion a relative term?
Distance
- How do we measure distance? Is it relative and/or comparative?
Time
- What is time? Is time change? Can we have change without time and vice versa?
- In the past, humans had two measures: their pulse and the length of the day.
Speed
- How early and how the notion of speed emerges in our life?
- Distance divided by time
Acceleration
- Measure of the change of a speed.
“…it is important to realize that few if any of these notions come to us as givens; rather they had to be created, improved, and perfected, which processes may take years if not centuries and possibly mind of surpassing brilliance.”
Part I: Mechanics in Antiquity
Aristotle (384 – 322 BCE)
Two main works: Physics and On the Heavens
He was aware of the two main systems of thought of earlier Greek thinkers: the Atomists and Plato.
Atomists
- Leucippus (fl. ca. 480 BCE), Democritus (d. ca. 361 BCE), Lucretius (96? – 55 BCE)
- They refused to draw any distinction between the terrestrial and the celestial regions.
- They stressed an empirical methodology, rather than a reliance on religious or metaphysical considerations.
- They rejected a teleological approach to nature (don’t ask questions about purpose).
Plato (ca. 427 – 347 BCE)
- Great stress on mathematics (like the Pythagoreans)
- The ultimate elements of physical bodies are geometrical (Timaeus).
- He divided the celestial realm, where the gods dwell, from the terrestrial.
Aristotle
- Rejected the Platonic view that mathematical forms are the constituents of physical bodies.
- Mathematics and physics are distinct disciplines.
- It is very important to ask “why” questions about nature.
- Physics and astronomy are distinct disciplines (in subject matter and methodology)
- The heavens contain perfect bodies while terrestrial bodies are imperfect and do not move eternally.
- Method of limited empiricism. “The task of the physicist is to determine the nature, the essence, of the physical body.”
- “Aristotle’s conception of physics, substantially more than Plato’s, assigned a role to experience, to observing carefully how nature behaves.
Aristotle on Place, Motion, and Void
On Place
- Bodies move toward their natural place.
- Earthy bodies fall toward Earth, and fire and air have their natural place above us.
On Motion
- 2 categories: Natural (e.g. earthy bodies or fire) and Violent (e.g. projectiles thrown)
- “Every thing in motion is necessarily moved by some thing.”
- Aristotle’s goal was to provide a causal analysis of motion rather than simply a description of the motion.
On Void
- Rejected the existence of void space.
- It makes no logical sense to speak of the existence of nothing.
- Concluded that a vacuum or void is impossible because the speed of the body in a void would be infinite.
Difference of Aristotle with Modern Conception
- Aristotle’s central goal of his physical writing was to explain change.
“Aristotle’s physical system was widely recognized for nearly two millennia as the most impressive physical system ever created.”
Mechanics in Later Antiquity
Archimedes of Syracuse
- “Made very impressive analyses of how to determine specific gravity, of various problems in hydrostatics, and of the laws governing the mechanical device known as the lever.
John Philoponus (ca. 500 CE)
- Questioned Aristotle’s claim that the rate at which bodies fall is proportional to their weight.
Part II: Mechanics in the Medieval Period
The Mertonians, Oresme, and the Mean Speed Theorem
It is widely believed that science sand to a very low level during the middle ages until the scientific revolution. This can be exemplified by a quote in Henry Smith Williams’s The Great Astronomer, “The reader will note that this page, as well as the next two, are blank. This is the most graphic method the author can devise to show that, astronomically speaking, nothing happened during the Middle Ages.”
This is not true, as Pierre Duhem has shown in his ten-volume Le système du monde: Historie des doctrines cosmologiques de Platon à Copernic.
Group of medieval scholastics at Merton College of Oxford University and of the University of Paris (1350)
- Problems of motion
- Relationship between acceleration, average speed, and the distance traversed by a moving body.
Nicole Oresme (ca. 1325 – 1382)
- Sought a precise, quantitative method for discussing how forms or qualities increase or decrease (“intension and remission of forms”)
- Such a form or quality could: 1. Remain constant; 2. Change at a constant rate; or 3. Change at a nonconstant rate.
- Merton Mean Speed Theorem: For a uniformly accelerating body, how are average speed and distance traversed related to each other?
Oresme and these scholastics wished to understand not primarily the motion of bodies, but rather to understand change itself, whether it be the motion of bodies or the growth in grace in a person’s soul.
All the equations derived from Oresme’s and the scholastics’ work are useful to describe motion but not to explain it. It was also important their applicability to nature.
Part III: Two Major Problems in Early Modern Mechanics
1. Does the Earth itself move?
2. Is motion purely relative?
The Problem of the Possibility of the Earth’s Motion
Aristarchus of Salmos (third century BCE) suggested that the Earth not only rotates but also that it revolves around the Sun. It was not before Copernicus published his De revolutionibus orbium coelestium in 1543 that the heliocentric system gained substantial supporters.
One of the reasons why there was so much opposition to Copernicus’s hypothesis was that it contradicts many of the known laws and principles of mechanics of the ancient tradition. By adopting this system, much of this traditional physics must’ve been dropped. It also was difficult to imagine that we could be moving at great speed without us noticing it (e.g. 67,000 mph). This system also deprived the Earth from its central position and by doing this, the Aristotelian idea of bodies moving toward the center of the world fell to pieces.
The Problem of the Relativity of Motion
Protagoras of Abdera: “Of all things the measure is man…”
Is motion purely relative, or is there a way of defining the motion of a body that is independent of the objects around it?
Aristotle argued that motion is not relative.
Great discussion of the middle ages of the problem of the relativity in motion
- Jean Buridan (ca. 1300 – ca. 1358): he concluded that the evidence ponts toward the traditional position of the Earth’s immobility.
- Nicole Oresme: like Buridan, Oresme ultimately sided with the traditional view that the Earth does not move. He also said (regarding the idea of the Earth’s rotation): “It is impossible to demonstrate from any experience that the contrary is true.” We won’t notice if the sphere of the stars or the Earth moves.
Two important comments of the discussion: 1. Although they understood the problem, none opted the view that motion is purely relative; 2. It is important to explore the thesis concerning whether and how considerations of the relativity of motion affected the development of mechanics. Some say this provided ground for great advances in mechanics such as the law of inertia.