To Explain the World: The Discovery of Modern Science

by Steven Weinberg

I chose “Discovery” instead of “Invention” to suggest that science is the way it is not so much because of various adventitious historic acts of invention, but because of the way nature is. With all its imperfections, modern science is a technique that is sufficiently well tuned to nature so that it works—it is a practice that allows us to learn reliable things about the world. In this sense, it is a technique that was waiting for people to discover it.

Science and technology benefit each other, but at its most fundamental level science is not undertaken for any practical reason.

Science is cumulative; each new theory incorporates successful earlier theories as approximations, and even explains why these approximations work, when they do work.

This has become the accepted story but I don't think it's really right. Newton's theory isn't an approximation of Einstein's, it just has approximately similar predictions. They have radically different sets of claims about the world.

The modern idea of chemical elements dates from the chemical revolution instigated by Priestley, Lavoisier, Dalton, and others at the end of the eighteenth century, and now incorporates 92 naturally occurring elements, from hydrogen to uranium (including mercury and sulfur but not salt) plus a growing list of artificially created elements heavier than uranium.

The pedant in me wonders why technetium is treated as natural.

“Of things that exist, some exist by nature, some from other causes.” It was only the natural that was worthy of his attention. Perhaps it was this distinction between the natural and the artificial that kept Aristotle and his followers from being interested in experimentation. What is the good of creating an artificial situation when what are really interesting are natural phenomena?

As late as the nineteenth century, when German universities instituted a doctoral degree for scholars of the arts and sciences to give them equal status with doctors of theology, law, and medicine, they invented the title “doctor of philosophy.” When philosophy had earlier been compared with some other way of thinking about nature, it was contrasted not with science, but with mathematics.

I heard Kuhn make these remarks when we both received honorary degrees from the University of Padua, and later asked him to explain. He replied, “What was altered by my own first reading of [Aristotle’s writings on physics] was my understanding, not my evaluation, of what they achieved.” I didn’t understand this: “a very good physicist indeed” seemed to me like an evaluation.

“The proper measure of a philosophical system or a scientific theory is not the degree to which it anticipated modern thought, but its degree of success in treating the philosophical and scientific problems of its own day.” I don’t buy it. What is important in science (I leave philosophy to others) is not the solution of some popular scientific problems of one’s own day, but understanding the world. In the course of this work, one finds out what sort of explanations are possible, and what sort of problems can lead to those explanations. The progress of science has been largely a matter of discovering what questions should be asked.

Again and again, it has been an essential feature of scientific progress to understand which problems are ripe for study and which are not.

doing scientific research to fill human needs has a wonderful way of forcing the scientist to stop versifying and to confront reality.

it was easy to locate the Sun in the background of stars. Just notice what constellation of the zodiac is highest in the sky at midnight;

how do you find midnight? no clocks

Even though as an undergraduate I knew that I wanted to be a theoretical physicist who would never do experiments, I was required along with all other physics students at Cornell to take a laboratory course. Most of our time in the course was spent estimating the uncertainty in the measurements we made.

Hipparchus made astronomical observations in Alexandria from 161 BC to 146 BC, and then continued until 127 BC, perhaps on the island of Rhodes. Almost all his writings have been lost; we know about his astronomical work chiefly from the testimony of Claudius Ptolemy, three centuries later. One of his calculations was based on the observation of an eclipse of the Sun, now known to have occurred on March 14, 189 BC. In this eclipse the disk of the Sun was totally hidden at Alexandria, but only four-fifths hidden on the Hellespont (the modern Dardanelles, between Asia and Europe). Since the apparent diameters of the Moon and Sun are very nearly equal, and were measured by Hipparchus to be about 33' (minutes of arc) or 0.55°, Hipparchus could conclude that the direction to the Moon as seen from the Hellespont and from Alexandria differed by one-fifth of 0.55°, or 0.11°. From observations of the Sun Hipparchus knew the latitudes of the Hellespont and Alexandria, and he knew the location of the Moon in the sky at the time of the eclipse, so he was able to work out the distance to the Moon as a multiple of the radius of the Earth. Considering the changes during a lunar month of the apparent size of the Moon, Hipparchus concluded that the distance from the Earth to the Moon varies from 71 to 83 Earth radii. The average distance is actually about 60 Earth radii.

It is ironic that Claudius Ptolemy, who had deeply studied the phenomena of refraction and reflection (including the effects of refraction in the atmosphere on the apparent positions of stars) and who as we will see played a crucial role in the history of astronomy, never realized that lenses and curved mirrors could be used to magnify the images of astronomical bodies, as in Galileo Galilei’s refracting telescope and the reflecting telescope invented by Isaac Newton.

My understanding is that quality lensmaking is late medieval. I don't think Ptolemy could have made a telescope.

According to Chalcidius (or Calcidius), a Christian who translated the Timaeus from Greek to Latin in the fourth century, Heraclides also proposed that since Mercury and Venus are never seen far in the sky from the Sun, they revolve about the Sun rather than about the Earth, thus removing another bit of fine-tuning from the schemes of Eudoxus, Callippus, and Aristotle:

For instance, in Ptolemy’s theory the center of the deferent of Venus was displaced from the Earth by 2 percent of the radius of the deferent.*

I'd love a cite for this.

The fact that the Earth and the equant are at an equal distance from the center of the deferent was not assumed on the basis of philosophical preconceptions, but found by leaving these distances as free parameters, and finding the values of the distances for which the predictions of the theory would agree with observation.

The complications, beyond just a single epicycle for each planet (and none for the Sun), had nothing to do with whether the Earth goes around the Sun or the Sun around the Earth. They were made necessary by the fact, not understood until Kepler’s time, that the orbits are not circles, the Sun is not at the center of the orbits, and the velocities are not constant.

Al-Haitam was born in Basra, in southern Mesopotamia, around 965, but worked in Cairo. His extant books include Optics, The Light of the Moon, The Halo and the Rainbow, On Paraboloidal Burning Mirrors, The Formation of Shadows, The Light of the Stars, Discourse on Light, The Burning Sphere, and The Shape of the Eclipse. He correctly attributed the bending of light in refraction to the change in the speed of light when it passes from one medium to another, and found experimentally that the angle of refraction is proportional to the angle of incidence only for small angles.

medicine, such as Ibn Bajjah, Ibn Tufayl, Ibn Rushd, and ben Maimon, who held on so firmly to the teachings of Aristotle? I can think of three possible reasons. First, physicians would naturally be most interested in Aristotle’s writings on biology, and in these Aristotle was at his best. Also, Arab physicians were powerfully influenced by the writings of Galen, who greatly admired Aristotle. Finally, medicine is a field in which the precise confrontation of theory and observation was very difficult (and still is), so that the failings of Aristotelian physics and astronomy to agree in detail with observation may not have seemed so important to physicians.

In this book Oresme reconsidered the idea that the heavens do not rotate about the Earth from east to west but, rather, the Earth rotates on its axis from west to east. Both Buridan and Oresme recognized that we observe only relative motion, so seeing the heavens move leaves open the possibility that it is instead the Earth that is moving. Oresme went through various objections to the idea, and picked them apart. Ptolemy in the Almagest had argued that if the Earth rotated, then clouds and thrown objects would be left behind; and as we have seen, Buridan had argued against the Earth’s rotation by reasoning that if the Earth rotated from west to east, then an arrow shot straight upward would be left behind by the Earth’s rotation, contrary to the observation that the arrow seems to fall straight down to the same spot on the Earth’s surface from which it was shot vertically upward. Oresme replied that the Earth’s rotation carries the arrow with it, along with the archer and the air and everything else on the Earth’s surface, thus applying Buridan’s theory of impetus in a way that its author had not understood.

Whatever the scientific revolution was or was not, it began with Copernicus.

The theory of Copernicus provides a classic example of how a theory can be selected on aesthetic criteria, with no experimental evidence that favors it over other theories.

This work of Copernicus illustrates another recurrent theme in the history of physical science: a simple and beautiful theory that agrees pretty well with observation is often closer to the truth than a complicated ugly theory that agrees better with observation.

Copernicus pointed out one of the prettiest aspects of his heliocentric system: it explained why Mercury and Venus are never seen far in the sky from the Sun.

Already in 1577 Tycho observed a comet, and found that it had no observable diurnal parallax. Not only did this show, again contra Aristotle, that there was change in the heavens beyond the orbit of the Moon. Now Tycho could also conclude that the path of the comet would have taken it right through either Aristotle’s supposed homocentric spheres or the spheres of the Ptolemaic theory.

For the future of astronomy, the most important contribution of Tycho was not his theory, but the unprecedented accuracy of his observations.

I think this undersells it. Not just the accuracy but the broader notion of intense observations to distinguish theories.

In 1597 Galileo received two copies of Kepler’s Mysterium Cosmographicum. He wrote to Kepler, acknowledging that he, like Kepler, was a Copernican, though as yet he had not made his views public.

he showed his spyglass to the doge and notables of Venice and demonstrated that with it ships could be seen at sea two hours before they became visible to the naked eye. The value of such a device to a maritime power like Venice was obvious. After Galileo donated his spyglass to the Venetian republic, his professorial salary was tripled, and his tenure was guaranteed. By November Galileo had improved the magnification of his spyglass to 20 times, and he began to use it for astronomy.

Galileo had a good salary at Padua, but he had been told that it would not again be increased. Also, for this salary he had to teach, taking time away from his research. He was able to strike an agreement with Cosimo, who named him court mathematician and philosopher, with a professorship at Pisa that carried no teaching duties. Galileo insisted on the title “court philosopher” because despite the exciting progress made in astronomy by mathematicians such as Kepler, and despite the arguments of professors like Clavius, mathematicians continued to have a lower status than that enjoyed by philosophers.

Moving to Florence made Galileo much more vulnerable to control by the church. A modern university dean might feel that this danger was a just punishment for Galileo’s evasion of teaching duties. But for a while the punishment was deferred.

!!!

With the exception of those Islamic countries that punish blasphemy or apostasy, the world has generally learned the lesson that governments and religious authorities have no business imposing criminal penalties on religious opinions, whether true or false.

Galileo concluded that the trajectory is a parabola. Galileo does not describe this experiment in Two New Sciences, but instead gives the theoretical argument for a parabola. The crucial point, which turned out to be essential in Newton’s mechanics, is that each component of a projectile’s motion is separately subject to the corresponding component of the force acting on the projectile. Once a projectile rolls off a table edge or is shot out of a cannon, there is nothing but air resistance to change its horizontal motion, so the horizontal distance traveled is very nearly proportional to the time elapsed. On the other hand, during the same time, like any freely falling body, the projectile is accelerated downward, so that the vertical distance fallen is proportional to the square of the time elapsed. It follows that the vertical distance fallen is proportional to the square of the horizontal distance traveled. What sort of curve has this property? Galileo shows that the path of the projectile is a parabola, using Apollonius’ definition of a parabola as the intersection of a cone with a plane parallel to the cone’s surface. (See Technical Note 26.)

In a 1669 article in the Journal des Sçavans, Huygens gave the correct statement of the rules governing collisions of hard bodies (which Descartes had gotten wrong): it is the conservation of what are now called momentum and kinetic energy.10 Huygens claimed that he had confirmed these results experimentally, presumably by studying the impact of colliding pendulum bobs, for which initial and final velocities could be precisely calculated.

Boyle’s work on air pressure was described in 1660 in New Experiments Physico-Mechanical Touching the Spring of the Air. In his experiments, he used an improved air pump, invented by his assistant Robert Hooke, about whom more in Chapter 14. By pumping air out of vessels, Boyle was able to establish that air is needed for the propagation of sound, for fire, and for life. He found that the level of mercury in a barometer drops when air is pumped out of its surroundings, adding a powerful argument in favor of Torricelli’s conclusion that air pressure is responsible for phenomena previously attributed to nature’s abhorrence of a vacuum.

The two figures who became best known for attempts to formulate a new method for science are Francis Bacon and René Descartes. They are, in my opinion, the two individuals whose importance in the scientific revolution is most overrated.

Obviously, light is not a tennis ball, and the surface separating air and water or glass is not a thin fabric, so this is an analogy of dubious relevance, especially for Descartes, who thought that light, unlike tennis balls, always travels at infinite speed.

Descartes and Bacon are only two of the philosophers who over the centuries have tried to prescribe rules for scientific research. It never works. We learn how to do science, not by making rules about how to do science, but from the experience of doing science, driven by desire for the pleasure we get when our methods succeed in explaining something.

In 1712 the Royal Society convened an anonymous committee to look into the controversy. Two centuries later the membership of this committee was made public, and it turned out to have consisted almost entirely of Newton’s supporters. In 1715 the committee reported that Newton deserved credit for the calculus. This report had been drafted for the committee by Newton. Its conclusions were supported by an anonymous review of the report, also written by Newton.

Newton had given to the future a model of what a physical theory can be: a set of simple mathematical principles that precisely govern a vast range of different phenomena.

Newton’s theory can be regarded as an approximation to Einstein’s, one that becomes increasingly valid for objects moving at velocities much less than that of light. Not only does Einstein’s theory not disprove Newton’s; relativity explains why Newton’s theory works, when it does work. General relativity itself is doubtless an approximation to a more satisfactory theory.