Gennady Gorelik


A few good reasons to celebrate Galileo’s jubilee


1. The first modern physicist in the Universe

2. What is truth? Galileo and two Popes

3. Cognitive optimism and personal humility, or how much post-modern physics is like the pre-modern one



     Galileo Galilei. Portrait by Ottavio Leoni. 1624


According to a theoretical physicist Lee Smolin, some of his colleagues believe that the period of modern physics initiated by Galileo is over, and that we live in “the age of postmodern science, in which mathematical consistency suffices to demonstrate the correctness of our theories, and experiment is neither possible nor necessary”. If it is so, the 450th anniversary of Galileo’s birth last year would be somewhat saddened. But while we are still waiting for the first real secret of superstring multiverse to be discovered by postmodern theorists, there are good reasons to look around the only Universe we have for sure and to ponder the multitude of Nature’s secrets discovered by followers of Galileo.


1. The first modern physicist in the Universe

The new physics was born in the 17th century, when its development accelerated a hundredfold. Einstein saw in Galileo the father of modern physics and explained the key novelty -- the freedom to invent fundamental notions, which might seem “illogical”, but the new theory based on these notions is verified empirically.

To convincingly verify a theory, it should be expressed in an exact language, and empirical data should be measurable. That is why indispensible are the two tools of physics – experiment and mathematics. These tools were actually used, two millennia before Galileo, by the first real physicist Archimedes who was also a great mathematician and engineer-inventor. Four centuries before Galileo, Roger Bacon clearly stated that “without experiment it is impossible to know anything thoroughly” and “no science can be known without mathematics.”

However to create a new fundamental theory paramount is another tool, described by Einstein as “the boldest speculation [to] bridge the gaps between the empirical data.” This tool made physics modern, and Galileo was the first one to use it when he invented a new fundamental concept of “motion in vacuum”.

In Archimedean physics all the notions would describe something visible or tangible like weight, density, geometrical form, whereas vacuum, or void, was invisible and intangible. Moreover, it was proclaimed illogical by Aristotle, the founder of logics and greatest philosophical authority for many centuries, who allegedly logically proved the nonexistence of nothingness, or vacuum. Galileo never experienced vacuum with his senses, but pondering his empirical data, he invented “vacuum” as a physical  rather than philosophical – notion. Whereas in philosophy the criterion of truth is pure reason, in physics the highest judge is experience. The notion of “invisible” vacuum was justified by experiments and proved to be extraordinarily fruitful by leading to discoveries of the law of inertia, the principle of relativity, and the law of free fall. It was the beginning of modern physics.

Thus Galileo discovered that fundamental notions do not have to be evident, and their validation is a result of a whole scientific enterprise joining theory and experiment. As Einstein emphasized, “Concepts can never be derived logically from experience and be above criticism. … Unless one sins against logic, one generally gets nowhere”. The logic of the previous theory or common sense is assumed here, but when a notion is being invented there is no other logic.

Galileo’s “vacuum” has been followed by other “invisible” fundamental notions invented in the same way: Newton’s “gravity”, Faraday-Maxwell’s “field”, Planck’s “quanta”, Einstein’s “photons”and “space-time”, and so on. It was this type of inventiveness that became the main propeller of modern science.

Galileo's inventiveness was encouraged by Copernicus’ boldest speculation to take a careful look at the planetary motions from the Solar point of view, as if by observer located at the Sun. Copernicus recalculated the astronomical sky of a terrestrial observer to the sky of a solar one and came to results both startling and convincing for an astronomer. Yet, for a physicist it was a great challenge to explain why such huge velocity of the Earth as 30 km/s is not felt by the terrestrials. Galileo believed that physical explanation of celestial phenomena had to be based on earthly empirical evidence, and he came to such an explanation by means of the concept of “motion in vacuum”.

Galileo’s astro-physical feat was rewarded by the opportunity to see in the sky things nobody had seen before. Most amazing astronomical discoveries were made by the first astrophysicist in the Universe.

In 1609, Galileo, having heard about the Dutch invention of telescope, improved the new device and directed it at the starry sky that fascinated him the physicist. His diligent and insightful observations were rewarded with a series of remarkable revelations.

First, he revealed - through his telescope - that the Moon looked “like another Earth” with mountains and valleys, rather than an ideally smooth sphere postulated by Aristotle for any celestial object. This discovery supported Galileo’s belief in the unity of the Universe, its both sublunary and superlunary parts. This belief was the basis for his quest of terrestrial explanation of celestial phenomena by relying on earthly experiments with pendulums, inclined planes and free fall.

The most striking, however, was the discovery of the four new “wandering stars”, or planets (from the Greek word “wandering”), in addition to the six planets known since time immemorial. Whereas the six old planets wandered (for a terrestrial observer) in tricky ways against background of the “fixed” stars, the new four small planets moved quite regularly, with certain periods, always in close proximity to one big planet, Jupiter (those small planets are known now as Galilean satellites of Jupiter). It was a visible manifestation of Copernican view of smaller celestial bodies revolving around a big one.

Galileo’s astronomical discoveries were quickly confirmed by astronomers starting with Kepler, an overt Copernican, and including Jesuit astronomers. This was sufficient for Galileo’s European fame, and for an ode composed in his honor by cardinal Barberini, future Pope Urban VIII. However, the discoveries turned out to be insufficient to validate Copernican astronomy for earthly common sense. Although the first clear demonstration - Foucault pendulum – was two centuries away, Galileo thought that he had already an important and convincing one – the explanation of earthly tides as the result of the two motions of the Earth - around its axis and around the Sun. It is not so, but а great physicist can be right even when being wrong

Galileo’s specific idea of explanation was wrong, but quite right was his ambition to explain tides on the basis of his physics. He oversimplified the problem by failing to engage his own physical discovery – the law of free fall, the first fundamental result in investigating gravity. The notion of universal gravity was within his reach, but apparently it had been too much for one man. It took Newton to develop the theory of universal gravity and, based on it, the true theory of tides. Yet,  great Newton, sensitive to priority, in his famous “Principia” acknowledged the contribution of his forerunner:
“Galileo discovered that the descent of bodies observed the duplicate ratio of the time, and that the motion of projectiles was in the curve of a Parabola; experience agreeing with both, unless so far as these motions are a little retarded by the resistance of the Air.”

Though Galileo had attained his main physical results before he made his first telescope, his striking astronomical discoveries were of great importance both for him personally and for the rise of modern science. He started to record his telescopic discoveries in his native Italian, but soon switched to Latin, the international language of high European culture, apparently as soon as he realized the scale of the breakthrough. Indeed, his book “The Starry Messenger” published in March of 1610, became a sensation.


2. What is truth? Galileo and two Popes

Impressive astronomical achievements helped Galileo to become the Mathematician and Philosopher for the Grand Duke of Tuscany. The new position allowed him to dedicate his time to science without need to teach to make a living.

Crowned with great scientific fame Galileo decided to openly advocate Copernican astronomy, although 13 years earlier he wrote to Kepler:

“I have for many years been a partisan of the Copernican view because it reveals to me the causes of many natural phenomena that are entirely incomprehensible in the light of the generally accepted hypothesis. ... I do not publish my findings because I am deterred by the fate of our teacher Copernicus who, although he had won immortal fame with a few, was ridiculed and condemned by countless people (for very great is the number of the stupid).”

Galileo had also had a supernatural reason to change his mind and to go public with his advocacy of Copernican worldview. He was grateful to God's grace” for letting him to make his discoveries, and the high mission to reveal the long-sealed truth about the Universe  could encourage him to justify the honor. His struggle to enlighten humanity is well too known to retell it again. In his writings, he described his experience of scientific research and its results in vernacular Italian rather than in professorial Latin. And he chose a vivid form – dialogues between three characters of different levels of education and freedom of thought.

His two major books published in the last decade of his life became the European textbook on the new way of making science and on intellectual freedom in general. The new science was not only about gaining new knowledge about the  Universe, but also about freeing of some old “knowledge” which did not stand the trial of the new scientific thinking and experimental verification. First of all the new astro-physics had undermined old astrology

Nowadays it seems strange that Galileo taught astrology to medical students and made horoscopes for himself and his daughters. It was quite usual in those days, however, that physicians were supposed to draw horoscopes for their patients, and that renown astronomers Brahe and Kepler would also figure as prominent astrologers. Kepler believed that astronomy and astrology were as close relatives as mother and daughter, and although he wrote about the 'foolish daughter' and the 'wise mother,' he meant “bad” astrology engaging “in mad ravings with the uneducated masses,” but he believed that “genuine astrology” was “a testimony of God's works” and “by no means a frivolous thing”. One should keep in mind that for many centuries the main authority both in astronomy and astrology was Ptolemy with his two books – “Almagest” and “Tetrabiblos”.

Galileo’s discovery of the four new planets, the “moons” of Jupiter, did undermine astrology. If for millennia astrology did not take into account the influence of these planets in all the horoscopes, then all the horoscopes were wrong. On the other hand, the newly-discovered fundamental laws of nature provided such an example of exact knowledge, that recipes of astrology looked too doubtful. Anyway, the first modern physicist happened to become the last scientist involved in the art of astrology. In the 1630s he wrote about a celebrated astrologer:

“I am astounded that Morino has such an extremely high regard for astrology and that he claims with his conjectures (which to me appear uncertain, if not very uncertain) to establish the certainty of astrology; and it would really be a wonderful thing if - as he promises - he can, shrewd as he is, place astrology in the highest position of the human sciences; and I shall wait with great curiosity to see this marvelous innovation”.

To scientific objections against astrology Galileo could add a personal one, if in horoscopes for himself he saw nothing about his forthcoming ordeal - the trial of the Inquisition and the imprisonment for the remainder of his life.

Nevertheless, he went through his ordeal for the benefit of science - wrote his main book, and, in addition, proved that a physicist can be holier than a Pope and have a better opinion about God.

The Copernicanism and its defense by Galileo, assessed at the Holy Office, 24 February 1616, according to the “understanding of the Holy Fathers and the doctors of theology”, was proclaimed “foolish and absurd in philosophy” and “in regard to theological truth … at least errouneous in faith”. So, the new theory was rejected, firstly, because it was scientifically wrong, and, only secondly, because it contradicted the clerical authority. The clerics evidently exceeded their competence. But in those days not only unscientific people were sure that the Earth on which they so firmly stood, was immobile. The conviction was shared by most scholars, including the great astronomer Tycho Brahe who managed to imbed Copernican astronomy into geocentric worldview.

So, no wonder, that Pope Urban VIII, was skeptical about Galileo’s astrophysics. He permitted Galileo to discuss the Copernican system as a hypothesis and to compare it with the system of Ptolemy as another hypothesis. The Pope, however, rejected the claim to discover the true working of the Universe created by the Almighty. Such a claim, to the Pope’s mind, blasphemously underestimated God’s omnipotence and overestimated the human ability to comprehend God’s purpose. So, it was a theological reason to initiate the notorious trial (in addition to mundane ones).

Three and a half centuries later, Pope John Paul II formed a commission to “study the Galileo case more deeply”. Summing up the results of this study, John Paul II stated that it was Galileo who was right in his approach to the Bible, rather than the theologians who opposed him. Thus, since John Paul II was canonized, one could say that Galileo was holier than Pope Urban VIII.

Learning from history, John Paul II pointed out that it is a duty for theologians to keep themselves regularly informed of scientific advances” to take them into account in their teaching. Setting an example, he remarked that “after Einstein and within the perspective of contemporary cosmology” neither terrestrial nor solar points of view - as the view from the center of the Universe - holds the importance they once held. Apparently, John Paul II was familiar with a Einstein’s popular book “Evolution of physics,” where one could read that “the struggle, so violent in the early days of science, between the views of Ptolemy and Copernicus” became “quite meaningless.

From this phrase, a reader who does not master Einstein’s theory of gravity, might think that Copernicus and Galileo strived in vain to prove the Earth’s movement, and that, if not theologically, then scientifically, right was Pope Urban VIII, and that Galileo should speak not about the real truth but about hypotheses more or less plausible. The same Einstein’s book states that “The greatness of Copernicus' discovery can be appreciated only from the physical point of view”, but it failed to explain how these words could be compatible with the “meaningless” difference between the views of Ptolemy and Copernicus. Such an explanation would have to deal with quite complicated question about inertial frame of references in a curved space-time.

History of physics, however, even without such complications helps to understand that Galileo was right in his seeking of truth. Yes, Newton made it clear that the key issue was not the center of the Universe but the universal laws of motion, but the path to Newton's laws was opened by the laws of inertia and free fall discovered by Galileo. Further, without Newton's mechanics Einstein’s theory of gravity could not have emerged. So, the working of the Universe was being discovered step by step. Each step led to a deeper truth and was necessary to make the next step. Einstein, having built a new theory, realized more than once that his theory was not complete and final truth, and his greatest theory of gravity is still waiting to be modified by quantum theory. But in post-Galilean physics it does not devalue the old theories in the areas of their applicability.

Pope John Paul II quoted Einstein: “What is eternally incomprehensible in the world is that it is comprehensible”. It the words of the Pope, this intelligibility was assured by “transcendent and primordial [God’s] Thought imprinted on all things”. Galileo's belief in human ability to comprehend the working of the Universe was based, rather, on his belief in the wise love of the Creator to humanity created as His likeness by endowing humans with creative abilities to understand the world to rule over all the earth.

Next centuries gave many more reasons for this belief. The miraculous order of the Universe revealed by Galileo, Newton, Maxwell, Plank, Einstein, Bohr and their followers, required reconstructing and deepening of the scientific picture of the world. The success of such reconstructions means that the Universe is quite friendly to humans. It is a simpler hardware than the simplest radio. If great Newton were to get hold of a radio receiver in his hands, he would be unable to understand it, and would have to wait a few centuries until electrodynamics was discovered and developed. Nonetheless, some important laws of the Universe were understood back in the 17th century by means of very simple experiments and mathematics, compare to the ones of today. “Subtle is the Lord, but malicious He is not” - this is how laconically Einstein expressed his belief in the knowability of the world. Like Galileo, he wwas of better opinion about the Creator than many of the Roman popes.

One should not be too harsh in judging the clerics who failed to keep themselves informed of the scientific advances in the 20th century. It was not easy. Most successful was a Catholic priest Georges Lemaitre who became an astrophysicist, discovered the fact of expansion of the Universe, and, basing on Einstein’s theory of gravity, made a stunning conclusion that the expansion began with the explosive birth of the Universe from a super-dense state. Thirty years later, not long before becoming the President of the Pontifical Academy of Sciences, the astrophysicist in soutane, at a conference on astrophysics, stated that the theory of cosmological Big Bang

“remains entirely outside any metaphysical or religious question. It leaves the materialist free to deny any transcendental Being. … For the believer, it removes any attempt at familiarity with God… It is consonant with the wording of Isaiah speaking of the “Hidden God”, hidden even in the beginning of creation. … There is no natural limitation to the power of mind. The Universe does not make an exception, it is not outside of its grip.”

This is how a free thinking theologian saw science and religion in the 20th century. It was not so in the 16-17th centuries, when all the free thinking founders of modern science not only were believers but also were supported by their biblical faith.


3. Cognitive optimism and personal humility, or how much post-modern physics is like the pre-modern one

The differences between the founders of modern science were no less interesting than their similarities. The most interesting difference was the one between Kepler and Galileo.

Kepler was seven years younger, but lived actually in the era of pre-Galilean physics, since the principal works of Galileo in physics were published only after Kepler’s death. Kepler sent his books to Galileo, enthusiastically supported his astronomical discoveries and seemingly was not offended by the fact that Galileo did not respond to his results.

This disregard is sometimes explained by Galileo’s failure to appreciate or understand, or even by his jealousy, but the most important difference was in styles and worldviews of Kepler and Galileo.

Kepler could be called an astro-mathematician since he dealt only with astronomical objects, and his main tool was mathematics. In astronomical observations, he was looking for hidden mathematical harmony of the universe and relied on leap of mathematical imagination. The first such leap the 25-year-old Kepler made when he explained the “cosmographic mystery” of the number and orbital radii of ALL THE SIX planets: he imagined that their six orbs were circumscribed and inscribed by ALL THE FIVE regular polyhedrons. This solution, however, became a mathematical mirage 13 years later when Galileo discovered new planets.

By that time, basing on huge store of astronomical observations, Kepler at last discovered real laws –two laws of planetary motion. Again he relied on a mathtvatical leap - the idea that the planetary orbit was an ellipse. In physicist’s eyes, it was just empirical data elegantly expressed though unrelated to any earthly experiment. Elegant formulas could impress scientists and support their belief in the existence of some fundamental laws. Kepler himself apparently underestimated his new planetary laws and still hoped to develop his old solution of the “cosmographic mystery” into a “Harmonices Mundi” (The Harmony of the World)”.

The only connection with the earthly experience which he added was... music. In pre-Galilean science it looked not as strange, as it does nowadays: back then, music was one of the four higher sciences (quadrivium) along with arithmetic, geometry, and astronomy. Kepler tried to implement the ancient idea of the harmony of celestial spheres by making connections between astronomical quantities and harmony of sounds made by the “souls of heavenly bodies” (in astrology it would be the interaction between celestial and human souls). There was a lot of astronomical quantities and many more relationships between them... All these relations, alas, vanished into thin air of history, except one which became the third law of Kepler, who, however, never explained how music helped him to discover it.


Music also played an important role in Galileo’s life, both in developing his soul and in preparing his mind for experimental investigations. Young Galileo took part in the research of his father, a musician and musicologist. Trusting his empirical ear and experimenting with strings, Galileo’s father tested, refuted, and revised the views presented in the books of ancient theorists. In turn, physicist Galileo, to probe the essence of physical phenomena, in his research relied on smart experiments he devised rather than on ancient philosophers.

Striving to understand the Universe, astrophysicist Galileo relied not on mathematics as such, but rather on pondering his real physical observations and then invented new physical concepts like “motion in vacuum “, which let him to discover physical laws of inertia, of relativity and of free fall.


Having leaped four centuries forward, we found ourselves, as some theorists say, in the era of “post-modern physics” which relies so much on leaps of mathematical imagination and so little on experiments, as pre-modern Kepler used to do. Does this mean that post-modern theorists might discover something like Kepler’s planetary laws? A historian of science can not guarantee such a luck, since the lawless history rarely repeats itself. Moreover, such a luck would not suffice most ambitious post-modern theorists who are dreaming about the complete and final solution of the cosmographic mystery including the whole expanding Universe of ours and much more.

Galileo had no such dreams, nor were they shared by  Richard Feynman who said four centuries later:

“Suppose Galileo were here and we were to show him the world today and try to make him happy, or see what he finds out. And we would tell him about the questions of evidence, those methods of judging things which he developed. And we would point out that we are still in exactly the same tradition, we follow it exactly - even to the details of making numerical measurements and using those as one of the better tools, in the physics at least. And that the sciences have developed in a very good way directly and continuously from his original ideas, in the same spirit he developed.”

Among Galileo’s ideas deserving admiration and contemplation, was his belief that “the action of light results from motion and that of the swiftest type”. He thought so contrary to his distinguished contemporaries Kepler and Descartes who believed, like Aristotle, that light was the presence of something, rather the movement of something, in other words, that light propagates instantaneously, or its speed is infinite. Galileo suggested a way to measure the speed of light by two observers with lamps and clock. Several decades later, the astronomer Römer did measure the speed of light by improving Galileo’s scheme and using his astronomical inheritance. Römer realized that movement of each of Jupiter’s satellites discovered by Galileo provides a combination of a lamp and a clock, and that, therefore, to measure the speed of light, one observer would be enough. It took a few more centuries for Einstein to realize that the motion of light, indeed, is “of the swiftest type,” and to make this fact the basis of his theory of relativity.

Another idea of Galileo was much more mathematical and no less instructive. Thinking about how to mathematically describe accelerated motion, Galileo came to the problem of the infinity of points on the trajectory. The concept of such an “actual” infinity was invalidated by Aristotle in the same logical way as he invalidated the notion of vacuum, but Galileo found constructive approaches to both notions. In physics, pondering the comparison between the motions in water and in air, he came to the idea of motion in a waterless and airless vacuum. In mathematics he asked how to compare two different actual infinities such as the moments of time and positions in space in the motion of a freely falling body, or, purely mathematically, the infinity of integers and infinity of their squares.

It was Descartes who tamed actual infinity by arithmetizing geometry, and that was enough for all the needs of modern physics. Two centuries later Georg Cantor defined infinite cardinal numbers and presented a mathematical way to compare different infinities. Physicists, however, still have no need of this mathematical notion.

This shows that the relationship between physics and mathematics is not as simple as one could read in the title of the famous article “The Unreasonable Effectiveness of Mathematics in the Natural Sciences “ by E. Wigner. Actually, the text of the article discusses the miraculous effectiveness of physics, using mathematics as its language and tool.

This effectiveness was first discovered by Galileo by inventing the method of modern science. His efforts resulted froь an amazing union of bold cognitive optimism and personal humility. While investigating “Nature’s abstruse reasons and modes of operation”, Galileo found himself in “a sea with vacua and infinities and indivisibles and instantaneous motions” and questioned his ability to reach dry land. He believed, however, that it was “possible to arrive at the true and primary causes” of natural phenomena and perceived his work as “merely the beginning, ways and means by which other minds more acute than [his] will explore remote corners” of the “vast and most excellent science” he had just opened up.

This cognitive optimism related to the whole curious humanity and coupled with personal humility, was just a belief, yet -- an extremely fruitful one. It was inherited by Newton who seemed to himself like a boy playing on the sea-shore, finding smooth pebbles and pretty shells, with the sea of undiscovered truths before him. This belief supported successors of Galileo and Newton - Maxwell, Planck, Einstein, Bohr, etc. - in inventing brand new words of science and in developing science into the main source of new technology and the most powerful tool of human history.

Galilean belief is the golden mean between the belief in the Full and Final theory of Everything and the disbelief in the lawfulness of the world. Even in the 20th century the effectiveness of physics was a great miracle for Einstein. How incredible was then cognitive optimism in the 16th century, when no fundamental law of physics had yet been discovered?!

The same combination of optimism and humility is expressed by Freeman Dyson: “If it should turn out that the whole of physical reality can be described by a finite set of equations, I would be disappointed. I would feel that the Creator had been uncharacteristically lacking in imagination. I would have to say, as Einstein once said in a similar context, “Da konnt' mir halt der liebe Gott leid tun” (“Then I would have been sorry for the dear Lord”).”


Not by science alone lived the optimistic inventor of modern physics. His were also music, poetry, family problems and joys. He also loved wine in which he saw “light held together by moisture” and which, alas, in his last months was forbidden to him. So why not we, with a glass of wine in hand, celebrate Galileo’s 450th anniversary, thanking him for the light he shed on the working of the Universe, and congratulating all of us, the heirs of Galileo Galilei?


“There it was that I found and visited the famous Galileo, grown old, a prisoner to the Inquisition, for thinking in astronomy otherwise than the Franciscan and Dominican licensers thought,” -  John Milton in his speech to the English Parliament in 1644, pleading for the freedom of the press