What is Perspikacia (Part 1)?

                                                                            

There is no logical way to the discovery of elemental laws. There is only the way of intuition, which is helped by a feeling for the order lying behind the appearance.

- Albert Einstein

                                                 

The name Perspikacia is inspired by the Spanish word Perspicacia, which means insight. According to the 16th century French philosopher Rene' Descartes, human intelligence consists of two faculties: sagacity and perspicacity. The former enables reasoning about details to make deductions, and the latter concerns intuition and the ability to discern things directly. In his book "Rules for the Direction of the Mind", Descartes describes insight as follows: "one must focus the vision of the natural intelligence on the smallest and easiest things, and dwell on them for a long time, so long, until we have become accustomed to intuiting the truth distinctly and perspicuously" (Rule 9 - "On The Perspicacity of Intuition"). Sagacity is undoubtedly a very important quality to have in both human and scientific affairs. Science would not be possible without the painstaking work of measurement, tabulation, calculation, and deduction. However, revolutionary discoveries in science happen mainly through the process of direct insight. This series of blog posts try to give a flavor of the kinds of insights that have brought about major paradigm shifts in the physical sciences.

A Geocentric Universe

As far as we know, homo sapiens is the only species that contemplates its immediate surroundings and tries to comprehend the universe of experience and beyond. The ancients gazed at the flickering stars in the heavens and wondered about their true nature. They perceived the cycles of nature such as the periodic movement of heavenly bodies and the changing of the seasons. They saw violent and fearsome forces of nature at work in phenomena such as lightning, storms and fire. They tried to explain natural phenomena using extra-natural agents such as spirits and gods. Even until a few hundred years ago many people believed that there were invisible angels that kept the planets moving around the earth (see Feynman Lectures in Physics Vol. 1, Chapter 7). However, the development of civilization in many parts of the world (such as India, China, Persia, Arabia, and later Rome and Greece) saw a parallel development in science, astronomy, philosophy, and mathematics, where superstition and speculation were replaced by observation and rational thought. 

To the unaided and uncritical eye, the earth seems to be a flat surface that is at absolute rest (barring local features such as hills, mountains, ocean tides, etc). The heavenly bodies such as the sun, moon, and stars seem to move about the earth on a firmament of space that is inert and infinite. Time seems to flow in a definite and absolute manner and history is created by a universal and relentless march of time. The ancient civilizations and later the Greeks contemplated the universe around them and came up with theories to explain various phenomena. There were endless debates among the philosophers about the nature of the universe. Greek philosophers contemplated even abstract concepts such as motion, rest, and the constituents of matter. The philosopher Democritus believed that all matter was composed of indivisible units called atoms. Aristotle (a disciple of Plato) believed that all objects by their very nature tended to stay at rest and needed a force to keep them moving. Zeno of Elea worried about the very possibility of motion since his analysis seemed to show that a person would have to take infinitely many steps to get anywhere (Zeno's paradox). While most ancient cosmologies assumed that the Earth was a flat disc, the Pythagoreans had concluded by the 6th century BC (using observations of eclipses) that the Earth was a sphere. This idea of spherical earth at the center of the universe was further solidified by Plato and Aristotle in the 4 century BC. Plato and Aristotle had a strong belief in perfect circles and spheres as the models for celestial mechanics. But their perfect scheme ran into trouble with precise observations of planetary motion and, in the 2nd century AD, the astronomer Ptolemy introduced the concept of epicycles to resolve the conflict.  In the Ptolemaic universe the earth was still inert and at the center, but the planets moved in perfectly circular orbits called epicycles, that themselves orbited around the earth in perfect circles. This model managed to explain and predict movements of planets to a relatively high degree of accuracy and along with Aristotelian philosophy, became the chief dogma for several centuries. 

Heliocentrism and the Copernican Revolution

For a theory to survive, it should match known observed phenomena, it should have internal logical consistency and it should meet the criteria of "economy" (least number of assumptions). Science progresses when a dogma that does not meet these criteria is questioned and alternative theories are proposed. Social, religious, and political factors may prevent alternative ideas from being accepted and even lead to individual persecution (as in the case of Galileo). But eventually, the truth prevails and better models are embraced. Interestingly, the earliest challenges to the Ptolemaic and Aristotelian dogma came from Muslim astronomers in the 10th century AD.  They accepted the Geocentric view of the universe, but many questioned the static nature of the earth and the circular orbits of the epicycles. Instead, they advocated for the rotation of the earth and proposed elliptical orbits for certain planets. But the first known major challenge to Ptolemaic cosmology came from Copernicus in 1542. While Heliocentric theories had been proposed as early as the 3rd century BC by Aristarchus, it was Copernicus who in his book "On the Revolutions of the Heavenly Spheres", presented a geometric model that unambiguously posited the Earth and the planets moving around the Sun. What is interesting is that the Copernican system did not improve upon known observational data nor did it make any predictions that were better than the Ptolemaic Geocentric system. Copernicus had used circular orbits for the planets just like his predecessors and was in fact forced to introduce epicycles in order to explain certain observed planetary movements. It appears that Copernicus was primarily motivated by aesthetic and mathematical considerations more than anything else. He was applying the principle of Occam's Razor (using the least number of assumptions) to explain the observed motion of planets.  He was also the first person in history to create a complete and general system, combining mathematics, physics, and cosmology. The Heliocentric model collided with the prevailing Aristotelian world view. But apparently, it did not get Copernicus into direct trouble with the authorities. It seems that many people including members of the clergy encouraged him to publish his ideas, but Copernicus was skittish about publicizing his ideas out of fear of angering the establishment. His book was eventually published only around the time of his death at the age of 70. A century later the Italian astronomer Galileo Galilei was not as cautious and got into serious trouble for promoting Copernicus' radical ideas.

Galileo's "Heresy"

The true scientific method began with Galileo, who combined experimentation, careful observation using telescopes, deduction, and insight to uncover laws of nature that were not based on philosophical speculation or established conventions. By dropping objects of different sizes from the tower of Pisa, he showed that all objects regardless of their size fell at the same rate of acceleration (this is known as the "principle of equivalence" and served as a powerful motivation for Einstein's general theory of relativity). Galileo's insights showed that objects have something called inertia that keeps them at rest or in uniform motion in the absence of forces (in direct contrast to Aristotle's idea that everything tended to stay at rest and needed a force to keep it moving). Moreover, he discovered that a frame of reference that is in uniform motion is indistinguishable from a frame of reference at rest (a concept known as "the principle of relativity"). Galileo's main target was the prevailing Aristotelian and Ptolemaic dogma about the Geocentric model of the universe. In his book "Dialogue Concerning the Two Chief World Systems" Galileo advocated in favor of the Copernican Heliocentric model as opposed to Ptolemy's Geocentric model. In his book, Galileo presented a debate between a fictitious philosopher Salviati (representing Galileo himself), and the simple-minded and dogmatic character Simplicius (representing the philosophical establishment). In the debate, Salviati explains to Simplicius that the absence of speed sensations on the earth is not a justification for asserting that the earth is at absolute rest. Instead, he gives an evocative account of a man in a uniformly moving ship who observes water dripping from a bottle, fish swimming in a tank, and butterflies flying in a manner identical to when the ship is at rest. In modern language, Galileo was describing an "inertial frame of reference", a notion that played a central role in Einstein's special theory of relativity more than 200 years later. Galileo's book is a remarkable account of the fallacy of believing in what appears obvious to the senses without critical examination. Galileo was also the first to use a telescope to observe planets and their moons. Using his telescope he observed dark lunar spots (craters) and discovered the moons of Jupiter. The former implied that the moon was not a perfectly spherical body, something that went against the prevailing religious belief in the perfect spherical nature of all celestial objects. Clearly, Galileo's pronouncements did not sit well with his contemporaries. One of Galileo's influential and dogmatic contemporaries (a real-life Simplicius) simply refused to look through the telescope. Eventually, Galileo's views fell afoul of the Papal authorities, and Galileo was tried for heresy and sentenced to house arrest in 1633. Tragically Galileo was kept under house arrest until his death in 1642. His masterpiece was banned by the Catholic Church and remained on its list of banned books until 1835. 

Newton's Universal Laws

The Pythagoreans may have discovered that the earth was not flat, but it took the profound insights of Copernicus, Galileo, Kepler, and Newton to decisively establish a new cosmology in which spherical earth and other planets moved around the Sun in elliptical orbits following definite mathematical laws. Kepler performed a painstaking mathematical analysis of astronomical data observed and recorded by Tycho Brahe and in the process discovered his beautiful laws of planetary motion. Kepler's laws stated that a) planets follow elliptical orbits around the sun, b) a planet sweeps equal areas in equal intervals of time while orbiting the sun, and c) the square of a planet's orbital period is proportional to the cube of the semi-major axis. Newton more than anyone else established mathematics as a powerful tool and a universal language for the physical sciences. In his landmark tome "Philosophiae Naturalis Principia Mathematica", Newton revolutionized man's conception of the universe by writing down his famous Universal Laws of Motion and the Universal Law of Gravitation in a mathematical format. By postulating that the force that kept us wedded to the ground (and made apples fall from trees) was the same force that kept the planets and the moon in their orbits, Newton made arguably the greatest conceptual leap known to man. 

In Newton's Heliocentric scheme planets do not need an agent to keep them moving. They are just moving due to their inertia, having been set in motion at some original time (possibly at the time of the formation of the solar system). What keeps them from flying off is the centripetal force of gravitation. In fact, the moon is simply falling towards the earth in the same way that a baseball falls towards the earth after being thrown in the air. The only difference is that the moon is much farther away and is traveling much faster. As the moon falls towards the earth, the earth curves away thus keeping the moon in orbit around the earth (see Feynman Lectures in Physics Vol. 2). Newton explained that the ocean tides were caused by the gravitation pull of the moon as well as the centrifugal force of the rotation of the earth-moon system. With his newly developed Calculus, he was able to derive Kepler's laws of planetary motion. The mathematics and the science of the Principia were put to spectacular use by Edmund Halley when he accurately predicted the timing of the arrival of Halley's Comet (25 December 1758). Another such application of Newton's laws was the discovery of the planet Neptune. The French astronomer Le Verrier in 1846 tried to explain the irregular motion of Uranus using Newtonian mechanics by postulating the presence of another planet nearby. Using Newton's laws, Le Verrier (and earlier John Adams) made a precise prediction of the mass, orbit, and location of the body that they believed was responsible for Uranus' eccentric motion. The presence of the new planet was confirmed the same year by a German astronomer Johann Gottfried Galle, thus providing a powerful validation of Newton's laws. 

As an interesting aside, Le Verrier tried unsuccessfully to explain the anomalous motion of Mercury in a similar manner. Careful measurements of Mercury's orbit over a period of a few centuries showed that Mercury's perihelion (closest point of approach to the sun) precessed by 43 arc seconds per century. This did not match the calculations made by Le Verrier using Newtonian mechanics. One of the explanations that he offered for the aberration was the presence of a mysterious planet named Vulcan. No such planet was discovered and the precession of Mercury's perihelion remained a mystery until Albert Einstein explained it precisely using his General Theory of Relativity in 1915. 

The Kinetic Theory of Gases and the Atomic Hypothesis

Newton's laws reigned supreme for 300 years and met with spectacular success (barring little exceptions such as the motion of Mercury). While Newtonian mechanics dealt with dynamics of moving bodies, the theory was extended to the study of the motion of bulk matter such as fluids by people like Bernoulli, d'Alembert, and Leonhard Euler. The Industrial Revolution brought steam engines and factories into the scene. People became interested in macroscopic properties of matter such as heat, temperature, pressure, and their relationship to energy and work. Through the work of Maxwell and Boltzmann thermodynamics was shown to be a manifestation of the statistical properties of atoms that they believed were the microscopic constituents of matter. Maxwell and Boltzmann developed the kinetic theory of gases and provided a statistical distribution of velocities of atoms in an idealized gas as a function of the temperature of the gas. Boltzmann's famous equation named after him relates the entropy of a system (a measure of the macroscopic disorder of the system) to the logarithm of the number of possible "micro-states" of the system. The second law of thermodynamics postulates that entropy of a system almost always increases, meaning the disorder of a system tends to increase. A subject of great controversy during Boltzmann's time was the atomic theory of matter. While Maxwell and Boltzmann were firm believers in the atomic hypothesis and used it to explain macroscopic phenomena, some influential physicists and philosophers of the day (such as Ernst Mach and even initially Max Planck) were opposed to such a concept because atoms were not observable at that time. So much so that it drove the depressive Boltzmann to commit suicide in 1906. It was only when Einstein in 1905 and Jean Perrin in 1908 demonstrated theoretically and experimentally that the phenomena of Brownian motion could be used to compute the sizes of atoms that the atomic theory became widely accepted. Boltzmann's entropy equation is carved on his gravestone in Vienna.

The Faraday-Maxwell Theory of Electromagnetism

Statistical mechanics showed that the thermodynamic behavior of matter was fully compatible with Newtonian mechanics since it ultimately involved the statistical behavior of atoms moving according to Newton's laws. However, in the latter half of the 19th century, largely due to the experiments of Michael Faraday, the phenomena of electricity and magnetism were found to not fit Newton's perfect mechanistic scheme. Through a remarkable series of experiments, Faraday provided an almost complete albeit non-mathematical description of electricity, magnetism, and their relationship to each other.  More importantly, the subject saw the establishment of the abstract concept of a "field" in physics. The electromagnetic "field" is an abstract entity that permeates the space around an electrical or magnetic material. One can draw lines of force to visualize them, but they do not represent any material substance or a medium (something that bothered many scientists of the day including Lord Kelvin who accused Maxwell of resorting to mysticism). The application of mathematics (especially vector calculus ) to Faraday's experimental results, resulted in Maxwell's beautiful set of equations that completely described electromagnetic phenomena. Maxwell's equations describe the spatial and dynamic properties of the electric and magnetic fields as functions of each other and as functions of charges and currents. It is the first known instance of unification of two fundamental forces of nature (a theme that continues to occupy physicists to this day). The most spectacular outcome of Maxwell's field theory of electromagnetism was his startling insight that light is an electromagnetic wave. Light was known to be a wave since the early 1800s due to the work of Thomas Young on light interference and diffraction. Maxwell noticed that his mathematics produced a set of wave equations whose velocity factor (computed from the constants of electrical permittivity and magnetic permeability) matched exactly the empirically known speed of light. He then made a dramatic conceptual leap, when he postulated that in fact, light is nothing but an electromagnetic wave. This deep insight was later experimentally verified by Heinrich Hertz and led to the development of much of modern radio and wireless technology. It also set the stage for the twin revolutions of Relativity and Quantum Mechanics in the early part of the 20th century. It is remarkable that what was once simply an object of curiosity at the time of the Greeks, namely the behavior of materials like amber and lodestone eventually turned out to be one of the most fundamental and ubiquitous forces of nature. The solidity of materials is due to the perfect match between the positive and negative charges in the atom and the quantum effects that prevent them from collapsing into each other. All chemical processes can be described in terms of electrostatic phenomena. The neurons in the brain send messages through electrical signals and the human heartbeats due to the electrical impulses sent by the sinus node (a cluster of cells in the upper right chamber of the heart). Most of the modern technology including electronics and electrical systems are the outcome of Maxwell's equations. Most of life and human experience can arguably be described in terms of electromagnetic phenomena. Richard Feynman had this to say in his famous lectures: "From a long view of the history of mankind—seen from, say, ten thousand years from now—there can be little doubt that the most significant event of the 19th century will be judged as Maxwell’s discovery of the laws of electrodynamics. The American Civil War will pale into provincial insignificance in comparison with this important scientific event of the same decade."