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Posts Tagged ‘History of Science’

Shut Up and Calculate

Friday, January 13th, 2012

Andreas Osiander (1498 – 1552) was a Lutheran theologian who is best remembered today for his preface to Nicolaus Copernicus’s (1473 – 1543) book on heliocentric astronomy: De revolutionibus orbium coelestium. The preface, originally anonymous, suggested that the model described in the book was not necessarily true, or even probable, but was useful for computational purposes. Whatever motivated the Lutheran Osiander, it was certainly not keeping the Pope and the Catholic Church happy. It might have been theological, or it could have been the more general idea that one should not mix mathematics with reality.  Johannes Kepler (1571 – 1630), whose work provided a foundation for Isaac Newton’s theory of gravity, took Copernicus’s idea as physical and was criticized by no less than his mentor, Michael Maestlin (1550 – 1631) for mixing astronomy and physics. This was all part of a more general debate about whether or not the mathematical descriptions of the heavens should be considered merely mathematical tricks or if physics should be attached to them.

Osiander’s approach has been adopted by many others down through the history of science. Sir Isaac Newton—the great Sir Isaac Newton himself—did not like action at a distance and when asked about gravity said, “Hypotheses non fingo.” This can be roughly paraphrased into English as: shut up and calculate. He was following Osiander’s example. It was not until Einstein’s general theory of relativity that one could do better. Even then, one could take a shut up and calculate approach to the curved space-time of general relativity.

Although atoms were widely used in chemistry, they were not accepted by many in the physics community until after Einstein’s work on Brownian motion in 1905.  Ernst Mach (1838 – 1916) opposed them because they could not be seen. Even in the early years of the twentieth century Mach and his followers insisted that papers discussing atoms, published in some leading European physics journals, have an Osiander-like introduction. And so it continues: in his first paper on quarks, Murray Gell-Mann (1929) introduced quarks as a mathematical trick.  If Alfred Wegener (1880–1930) had used that approach to continental drift it might not have taken fifty years for it to be accepted.

We see a trend: ideas that are considered heretical or at least unorthodox—heliocentrism, action at a distance, atoms, and quarks—are introduced first as mathematical tricks. Later, once people become used to the idea, they take on a physical reality, at least in people’s minds.

In one case, the trend went the other way. Maxwell’s equations describe electromagnetic phenomena very well. They are also wave equations. Now, physicists had encountered wave equations before and every time, there was a medium for the waves. Not being content to shut up and calculate, they invented the ether as the medium for the waves. Lord Kelvin (1824 –1907) even proposed that particles of matter were vortices in the ether. High school text books defined physics in terms of vibrations in the either.  And then it all went poof when Einstein published the special theory of relativity.  Sometimes, it is best to just shut up and calculate.

Of course, the expression Shut up and calculate is applied most notably to quantum mechanics. In much the same vein as with the ether, physicists invented the Omphalos … oops, I mean the many-worlds interpretation, of quantum mechanics to try to give the mathematics a physical interpretation. At least Philip Gosse (1810 –1888), with the Omphalos hypothesis, only had one universe pop into existence without any direct evidence of the pop. The proponents of the many-worlds interpretation have many universes popping into existence every time a measurement is made.  Unless someone comes up with a subtle knife[1] so one can travel from one of these universes to another, they should be not taken any more seriously than the ether.

The shut up and calculate approach to science is known as instrumentalism—the idea that the models of science are only instruments that allow one to describe and predict observations. The other extreme is realism—the idea that the entities in the scientific models refer to something that is present in reality. Considering the history of science, the role of simplicity, and the implications of quantum mechanics[2] (a topic for another post), realism—at least in its naïve form—is not tenable. Every time there is a paradigm change or major advance in science, what changes is the nature of reality given in the models. For example, with the advent of special relativity, the fixed space-time that was a part of reality in classical mechanics vanished.  But with an instrumentalists view, all that changes with a paradigm change is the range of validity of the previous models. Classical mechanics is still valid as an instrument to predict, for example, planetary motion. Indeed, even the caloric model of heat is still a good instrument to describe many properties of thermodynamics and the efficiency of heat engines. Instrumentalism thus circumvents one of the frequent charges again science: namely that we claim to know how the universe works and then discover that we were wrong. This is only true if you take realism seriously and apply it the internals of models.

The model building approach to science advocated in these posts is perhaps an intermediate between the extremes of instrumentalism and realism. The models are judged by their usefulness as instruments to describe past observations and make predictions for new ones; hence the tie-in to instrumentalism. The models are not reality any more than a model boat is, but they capture some not completely determined aspect of reality. Thus, the models are more than mere instruments, but less than complete reality.  In any event, one never goes wrong by shutting up and calculating.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod


[1] The Subtle Knife, the second novel in the His Dark Materials trilogy, was written by the English novelist Philip Pullman

[2] In particular Bell’s inequalities.

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The Origins of Science

Friday, January 6th, 2012

The true origins of science are lost in the mists of time. Possibly it started when some Australopithecus observed that a stick with a knot at the end was more effective in warding off a rival for its[1] mate than one without a knot. Since then the use of the scientific method has occasionally intruded into mainstream life but until the seventeenth century was always beaten back into the ground by philosophers, theocrats, and the proponents of common sense: Of course the earth is flat[2] and no, stones do not fall from the sky.  But in the seventeenth century science “took” and began its path to mainstream acceptance. To be definite, I would take the date for the emergence of science to be that night in 1609 when Galileo first pointed his telescope to the heavens.  Two questions then present themselves: 1) Why was it so late in the advance of civilization that science arose and 2) Why did it arise when and where it did? The first question was addressed in a previous post and the second will be addressed here.

The date chosen for the beginning of science is rather arbitrary since science did not spring full blown out of nothing. There were precursors and aftershocks but the early seventeenth century is as good a starting point as any. And it was not just in astronomy. In 1600, William Gilbert, (1544 – 1603) published his work on magnetism, De Magnete, Magneticisque Corporibus, et de Magno Magnete Tellure, and in 1628 William Harvey (1578 – 1657) released his work on blood circulation, De Motu Cordis.  Back in astronomy, Johannes Kepler (1571 – 1630) published his first book on elliptic planetary orbits in 1609 (1609 was indeed a propitious year) and a multi volume astronomy text book about ten years later.  So back to the basic question: why so much activity then and there?

There are a number of different reasons. The first is a slow accumulation of ideas that suddenly reached a critical point and took off. Even Galileo Galilei’s father, Vincenzo Galilei, played a role. He helped put music theory on an empirical and mathematical basis, and influenced his son towards applied mathematics. Inventions also played a role; for Galileo to point his telescope at the heavens, the telescope had first to be invented. Besides the telescope, the invention of the printing press around 1440 by Johannes Gutenberg[3] played a key role. It greatly increased the ease with which new ideas could propagate. It played a key role in the Protestant Reformation and allowed Nicolaus Copernicus’s (1473 – 1543) ideas of a heliocentric planetary system to spread throughout Europe. It also played a key role in disseminating Galileo’s ideas.

But there is more than that. In the thirteenth century, Western Europe began to rediscover the ancient learning of the Greeks, especially Aristotle. This came by way of the Arab world which added original contributions (e.g. Arabic numerals) to the store of knowledge and also collected information from other sources, for example, India (e.g. zero). Building on that foundation, Western Europe built an academic tradition at universities and monasteries.  This mostly consisted of scholasticism and the worship of Aristotle but it did set the stage for intellectual debate and the pursuit of knowledge as an end in itself. In the end, science destroyed the scholasticism and the worship of Aristotle that had laid the foundation for its success.

The rediscovery of Greek learning in the thirteenth century had a surprising side effect. The Greeks were long on rational thought, but regarded the things of the world as changing and unpredictable, probably due to their belief in capricious Gods and fickle Fates. Christian Europe believed in a supreme, omnipotent God. This lead at least one part of the church to regard science, the study of how the world worked, as sacrilegious since it seemed to imply a limit on what God could do.  But combine the Greek ideal of rationalism with the idea of an omnipotent being and suddenly things change.  The very concept of perfect was taken to imply rationality. Hence, the perfect God must be rational and create a rational and ordered universe; namely one in which it made sense to look for orderly laws. Indeed, in nineteenth century England, it was a common belief that God ruled through orderly natural laws.  And of course, it was a scientist’s role to discover these laws.

Religion played another role. The Protestant Reformation was a shift from the authority of a man, namely the Pope, to the written word of the bible. Science was also a shift from the authority of a person, Aristotle, to the unwritten word, namely the universe. The people of the time talked of God’s word and God’s work and considered both worthy of study; study without the need for a human intermediary.

The Protestant Reformation also destroyed a source of central authority—the Catholic Church. This, coupled with political fragmentation (especially in Germany) led to more change. There was no longer any central authority to suppress new ideas, yet enough rule of law to allow fairly rapid communication (again thanks in part due to the printing press). For example, Galileo’s works were published by the Jewish publishing house of Elsevier in protestant Holland while he was under house arrest in Italy by the Catholic Church.

It is also no accident that astronomy was one of the first sciences. It had “practical” applications: astrology (Kepler was a noted astrologer) and the calculation of religious holidays, most notably Easter. It was also sufficiently complicated so the motions of the planets could not be predicted trivially, but sufficiently simple to be amenable to treatment by the mathematics of the day. Hence, it became the Gold Standard of science.

As noted in the first paragraph, science has had from the beginning three main opponents (using anachronistic terms): the academic left, the religious right, and common sense. For Galileo, the academic left was represented by the natural philosophers, the religious right by the Catholic Church that the philosophers sicced on him, and common sense by those who “knew” heavier objects fell faster than light ones.  At various times, different ones of these have been predominated: editorials attacked the idea of rocks falling from the sky (meteorites) or rockets working in space were there was no air to react against. In the 1960s, the main opponents were the academic left with the idea that scientific laws were mostly, if not entirely, cultural and postmodernism remains an opponent of science. But today, the main opposition to science comes from the religious right with evolution being the main fall guy. But same three protagonists—the academic left, the religious right and common sense—have remained and will probably remain into the indefinite future as the main opponents of science. As it was in the beginning, is now, and ever shall be. World without end. Amen.

Additional posts in this series will appear most Friday afternoons at 3:30 pm Vancouver time. To receive a reminder follow me on Twitter: @musquod


[1] Note, gender neutral pronoun

[2] In British Columbia and Switzerland it is crinkly rather than flat.

[3] Although the Koreans may have invented it earlier.

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