Physics: a Short History From Quintessence to...

PHYSICS: A SHORT HISTORY FROM

QUINTESSENCE TO QUARKS

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CONTENTS

List of Figures vii

Introduction: The Greek Way

. Invention in Antiquity Physica Applications Dumbing down

. Selection in Islam Falsafa Mixed mathematics Departures

. Domestication in Europe At the interface Alma mater Fresh imports

. A Second Creation Revolution or integration? The invention of physics Institutional frameworks Physics and enlightenment

. Classical Physics and its Cure Standard models Physicists as librarians Woes and wonders in The profession


v

. From Old World to New Legacies of World War I The legacy enriched Other interwar business Americanization

. The Quintessential

References Further Reading Index


CONTENTS

vi

LIST OF FIGURES

. Schools of Athens. Public Domain.

. Geometrical foundations of the world. Adapted from Cornford, Plato’s cosmology(Indianapolis: Bobbs-Merrill, n.d.), pp. –.

. Ptolemaic bric-a-brac.

. Sabbath machinery. Photo Researchers/Mary Evans Picture Library.

. Lecture in a House of Wisdom. White Images/Scala, Florence.

. Astral history.

. Computer in brass. Public Domain.

. Size of the Earth.

. The magnificent elephant clock. Public Domain.

. Stoned students. The Art Archive/Pinacoteca Nazionale Bologna/Gianni Dagli Orti.

. Motion pictured.

. Heliocentric advantages.

. Applied physics around . Bodleian Library.


vii

. Royal Academicians. Photo Scala, Florence.

. The Earth–Moon eddy in the solar vortex. © Digitaal Labo KU Leuven (Central Library, ms. , f. r).

. Diversion from politics. Bodleian Library.

. Planetary motion geometrized.

. Newtonian tides.

. Fashionable lecturing around . Bodleian Library.

. A physics institute around . AIP Emilio Segre Visual Archives, Brittle Books Collection.

. Desktop physics. Mary Evans Picture Library.

. The palace of electricity. Mary Evans Picture Library.

. A small piece of big physics. U.S. Department of Energy, Fermilab Research Alliance LLC.

. Patent on the cyclotron. Public Domain.

. Birth and death in the microworld. Plate ., “Successive decay of the �-meson, � –> µ –> �.”C.F. Powell, P.H. Fowler, and D.H. Perkins, The study ofelementary particles by the photographic method. Oxford:Pergamon Press, .

. Very big science. CERN.


LIST OF FIGURES

viii

The Scale’s but small, Expect not truth in all.

Wenceslaus Hollar, A new map of the Cittiessof London and Westminster,

Precision is not to be sought for alike in all discussions.

Aristotle, Nichomachean ethics, b


ix

INTRODUCTION:THE GREEK WAY

The Superconducting Super Collider (SSC), the dream ofAmerican high-energy physicists, would have had a circum-ference of kilometers and a price tag of billions of dollars. Itsproponents justified the expenditure on several grounds. Onthe high ground, it would probe the universe to philosophicaldepths and thus “keep faith with the Greeks.” Below ground, itwould advance tunneling technique and give society perfectsewers. Congress cancelled it in .The undertaking represented by the SSC might be the way to

an ultimate physics. But it is not the Greek way. In antiquity,physics was philosophy, a liberal art, the pursuit of a free manwealthy enough to do what he wished. He did not aim toimprove sewers and, since he had no need of public money,did not have to claim that he would. Nor did he want apparatus,since he seldom experimented, or mathematics, since he seldomcalculated. The few ancient applications of mathematics to


physics constituted a mixed science devoted to the descriptionof phenomena rather than to the search for principles.

In the tripartite division of Greek philosophy, physics stoodbetween logic and ethics. It inquired into the principles regulat-ing the physical world from the high heavens to the Earth’scenter, and from the human soul to the life of the least of livingcreatures. It thus functioned as a natural theology—definingman’s place in nature—and as a necessary approach to ethics,or the principles of a good life. For two millennia the mainpractical value of physics lay in the ethical consequences of itsversions of the way the world began and persists.

Greek physics, with its eye to ethics, its indifference to math-ematics and experiment, and its independence of states andcourts, is sufficiently distinct from an enterprise conducted bysalaried teams requiring elaborate technologies and mathemat-ical analyses to deserve a different name. Let it be physica andthose who cultivated it physici. This short book describes some ofthe ways by which ancient physica became modern physics. Itdoes not ransack history to find items in ancient and medievalscience that look like physics, but sketches the place and purposeof physica in the societies that supported it. Hence the primarysite(s) of cultivation receive special emphasis: the independentprivate school (antiquity), court and library (Islam), university(later Middle Ages), court again (Renaissance), academy (lateseventeenth and eighteenth centuries), university again (modern-ity), and university-government-industry (postmodernity). Ofcourse, successive forms did not annihilate their predecessors.Academies of science survive, primarily as honorific societiesand depositories of history, although a few flourish as national


PHYSICS: A SHORT HISTORY

channels for funding, consultation, and outreach. The scientificadvisory apparatus of government may be considered the des-cendant of courtly science; and the Greek schools, with theircharacteristic discursive style, continue in the myriad seminarsinwhich theworld’s nascent science is presented and anatomized.

The story of the SSC may do service as a double symbol:through its cost, size, and design, of the transformation of physicainto physics; through its cancellation, of the ongoing dilution ofthe dominance of the United States within an increasingly com-petitive international system.


INTRODUCTION: THE GREEK WAY

Fig. . Schools of Athens. Raphael’s evocation of the intellectual vigor, diversity, and discursiveness of Greekscience.


1

INVENTION INANTIQUITY

Tradition follows Aristotle in identifying the earliest physicias some gentlemen of Miletus, a flourishing Greek city onthe coast of Anatolia, and in specifying half a dozen other Greekspeakers as their successors. In this philo-Hellenic creationmyth, no Greek physicus learned anything of any importancefrom a barbarian during the years between the times ofthe eldest Milesian, Thales, and Aristotle. The story that Pythag-oras, if he existed, did so partly in Egypt, suggests outside input;and studies of cuneiform texts reveal a natural knowledgeamong the Babylonians in some ways more advanced thanthat of the ancient Greeks. Still, the essential criterion thatAristotle used to identify his predecessors was not that theywere Greek, but that they had conquered a paralyzing prejudice.Despite robust contrary evidence, they believed that the naturalworld runs on law-like principles discoverable by the human


mind and immune from interruption or cancellation by med-dling gods and demons.

Whether or not the Milesians deserve the blame or credit forthis bold departure, it underlies and circumscribes all forms ofphysica, natural philosophy, and physics. Its implications gofarther even than replacing caprice by law-like behavior. Sincethe gods displayed all too faithfully the traits and behavior ofhuman beings, de-deifying implied (to speak Greek) deanthro-pomorphizing. The progress of physics has continued toremove human quirks and qualities projected on to nature.Thus nature, or the objective world, came to lose not onlybenevolence, malevolence, and color, but also such apparentlyindispensable attributes as space, time, and causality.

Of the four main schools of ancient philosophy, Aristotle’spaid greatest attention to physica (see Figure ). Having a particu-lar interest in zoology, he derived his fundamental principleswith an eye to the classification of animals. Because of hisemphasis on physica and because his philosophy dominatedduring the Middle Ages and beyond, convenience advises takingit as normative. In antiquity, however, it had to compete withPlatonic, Epicurean, and Stoic philosophies. The fluctuatingmarket share of a school reflected the reputation of its leaderas well as fad and fortune. Typically, its premises, library, andother assets passed from the founder to his senior disciples, and,perhaps consequently, the schools bore names suggestive moreof real estate than of scholarship: the Academy (Grove) for thePlatonists, Lyceum (a shrine) and Parapatos (a place for walking)for the Aristotelians, the Stoa (Porch) for the Stoics, and theGarden of Epicurus.



During the years from the founding of the Academy inAthens and its refounding in Alexandria, the four schoolsunderwent many reversals of fortune, including dissolutionsand amalgamations. When operating, they were forums forfree discussion of the sort practiced in political circles, butcentered on studies pursued for personal improvement ratherthan for civic or financial advancement. Although they hadmembers who studied with them for decades, they also admit-ted students who sampled each in turn. When Romans likeCicero frequented the schools of Athens they took advantageof this Lernfreiheit. The Pythagoreans did not form such aschool, as they did not tolerate deviations from their doctrinesand way of life, and acted ruthlessly against members whorevealed their secrets.

Physica

Although physica ran from astronomy through zoology topsychology, limitation of coverage to cosmology and cosmog-ony, as in this book, is not unacceptably anachronistic providedwe recognize that the same principles of structure and changeapplied to all natural processes. This truncated physica corres-ponds to the books of Aristotle dealing with general principles(Physica), the heavens (De caelo), the region between the Moonand the Earth (Meteorologica), and the creation and destruction ofthings on or in the Earth (De generatione et corruptione). Thesebooks (and the rest of the corpus from logic to ethics) becameavailable in a standard format edited around BCE from thelecture notes Aristotle bequeathed to his successors. They


INVENTION IN ANTIQUITY

constitute the main parts of a theory of everything, or, as themoderns say, a TOE.

Cosmologies

The first TOEs Aristotle stepped on belonged to the Milesianmonists. He then took onmore generous materialists: Leucippusand Democritus, who allowed two principles, atoms and thevoid; Empedocles, who accepted the three Milesian elements(water, air, fire) and added earth to complete the tetrad; andAnaxagoras, who admitted an infinite number of different sortsof stuff. There were also those whose matter had no stuff at all,Pythagoras notably, for whom number had an independentexistence—a concept that made no sense to Aristotle. ThePythagoreans’ deduction that there must be a counter earthcirculating opposite ours around a central fire (to raise thenumber of heavenly bodies to the holy tetractys) proved toAristotle both the falsity of their physica and the nonsense towhich numbers can lead.

Aristotle’s teacher, Plato, had some sympathy for Pythagoreannumerology and a belief in the importance of mathematicalpatterns for cosmological architecture. He took as his materialnot only mathematical abstractions but also supersensible ideal-izations of classes of objects: for example, the Idea “Horse,” inwhich individual horses “participate” more or less, but alwaysimperfectly. Consequently, although Plato was optimistic aboutthe possibility of knowing the ideal world and even the supremeGood that made the Ideas and their relations intelligible, he didnot allow the possibility of true knowledge of the things of this



world. Since no material individual could express an Idea per-fectly, our physica can never be other than fuzzy.

Physica comes from “physis”meaning “nature,” which, accord-ing to Aristotle, “is the source or cause of being moved or beingat rest.” What makes things move? The early physici adumbratedfour causes of change that Aristotle later codified. The monistsand the atomists considered only the material cause. Empedo-cles and Anaxagoras provided action by taking some principlesto be active and others passive—vague glimpses of efficientcauses. Others saw the need to explain order in a universe ofchange and hinted at a teleological or final cause, such as set by acosmic Mind. And Plato supplied a fourth cause, the formal, theIdea in which a thing participates.

Aristotle’s inventory of the cosmological ideas of his predeces-sors, including anticipations of the four causes of change, wasnot an idle retrospective. It confirmed, and even proved, that hehad not overlooked anything fundamental. “Of all who havediscussed principles and causes none has spoken of any kindexcept those which have been distinguished in [my] discourseson Physics. They are all unmistakably, though obscurely, trying toformulate these.” Aristotle’s TOE, thus established as complete,makes use of some special concepts. A substance is any individualthing. The collection of its properties constitutes its form, which,contrary to a Platonic Idea, occurs only in unionwithmatter. Formcan be divided, although only mentally, into essence, which makesa substance the sort of thing it is, and accidents, which can changewithout causing the substance to alter its essence or kind. Theessences of the four elements are easily stated: fire is dry, hot, andabsolutely light; air is hot, moist, and relatively light; water is cold,



moist, and relatively heavy; earth is cold, dry, and absolutelyheavy. The elements can transform into one another, as fireevaporates water into air. An essence is usually compatible witha wide range of accidents: Socrates may be warm or cold, butheated or cooled too much he will cease to be Socrates.

It may now be intelligible to state that a substance’s matter andessence are its material and formal causes, and that the activequalities hotness and moistness are the principal efficient causesof change. The final cause is the purpose for the existence of aform. Heavy bodies have gravity so as to fall toward the center ofthe world, and light bodies have levity so as to be able to risetoward the heavens, to restore order disrupted by the activity ofanimate creatures or the revolutions of the celestial spheres. Thesespheres and the stars and planets they carry cannot bemade of thefour elements, whose forms require that they move when unim-peded in a straight line toward or away from the world’s center.There must therefore be a fifth element, a quintessence, which,obeying its formal and final causes, circulates around the uni-versal center. With these few principles and some ad hoc adjust-ments, Aristotle worked his way from the Mind of the UnmovedMover, which, as it can think only of the most sublime thing, canthink only of itself, down to the mind of man, which, though noless selfish than the Mind of the Universe, is subject to frequentchange like everything else below the quintessential heavens.And where there is change, there cannot be certainty; the besta physicus can do is to find a “rule [that] applies to what is alwaystrue or true for the most part.”A few deductions from Aristotle’s approximate physica that

came under sustained scrutiny will give some impression of its



general character. Every motion, whether change of place orcolor or species, requires an external mover. Since none isavailable in a vacuum, where there literally is no place (noreference material) by which a body could orient itself, therecan be no vacuum. Hence the flight of an arrow implies a vortexin the air, which cedes a place to the tip while slipping in behindto provide a push at the tail. The ambiguous role of the air,offering both resistance and propulsion, made an obvious diffi-culty. Another awkwardness arose from the absolute dichotomybetween terrestrial and celestial physics. Because the heavenscannot change, transient phenomena that appear to take placethere, like comets and meteors, must have their seat with light-ning and the weather in sublunar regions.

Nothing, however, is more obvious than that the Sun influ-ences the weather. How? Sometimes Aristotle wrote as if hethought that the Sun was hot, which would violate his pro-scription against terrestrial qualities in heaven. More often, heascribed the seasonal powers of the Sun to its annual revolu-tion, which, together with the rolling of the quintessentialspheres, continually stirs up the sublunary regions. These dis-turbances cause moist and dry vapors to rise from the earth.Precipitation results from the moist exhalation, winds from thedry. “The same stuff is wind on the earth, and earthquakesunder it, and in the clouds thunder.” Lightning and thunder aredry exhalations breaking free from the clouds like pipssqueezed from a fruit. The rainbow is a reflection from theclouds. Aristotle described it, in a manner unusual for him,geometrically: the Sun, the eye of the observer, and the centerof the bow lie on a straight line that cannot exceed a certain



angle with the horizon. This factoid would have a long andinfluential history.

Despite the continuing operation of final causes, the world isnot in perfect order. The frictional drag of the turning lunarsphere on the stationary region of fire below it produces suchanomalies as fiery meteors in the air, mountains above sea level,and water below earth. In the big picture, however, the universeresembles an onion. Peeled from the outside in, it discloses thefixed stars, the planets and luminaries in the conventional orderSaturn, Jupiter, Mars, Sun, and Moon, and, in slight disorder, theelements Fire, Air, Water, and Earth. What is outside the skin?Here the onion analogy fails. There is literally nothing there. Andjust as there is no space not included in the visible universe, therewas no time at which it did not exist.

Cosmogonies

Aristotle’s world picture thus lacked a creator. So did the atomictheory of Democritus, who, nevertheless, offered a creation storyfor the visible universe. It began to be when a clutch of the infinityof atoms bouncing about in the infinite void happened to cometogether in a great vortex fromwhich the largest fell to the center,forming the Earth. Fromwhat remained, centrifugation producedthe air, the luminaries, the planets, and the stars. Although allthings are made of the same dull stuff, they appear different to usbecause our sensory systems can build rich images from the fewproperties (size, shape, motion) of their constituent atoms. Epi-curus added a spontaneous “swerve” to explain howatoms, fallingin parallel through the void, occasionally collide and concatenatea world. According to him, the soul can exploit the swerve to



choose to live the good life in an otherwise pointless universe.Since the Epicurean did not have to fear gods in this life oranything in the next, he could take moderate enjoyment of theflesh and free employment of the mind as the greatest goods. Theinevitable erosion of all sound doctrine has transformed Epicurus’sober happiness into selfish hedonism, and his name into aneponym for refined pleasure.

Whereas the atomists allowed for the creation of manyworlds in space and time by random accretion of their parts,the Stoics supposed that the single cosmos they admitted, geo-centric like Aristotle’s, is alternately destroyed and recreated. Inplace of disparate atoms, the Stoics put a continuous primematter; and in place of bumps and grinds, “pneuma,” a self-moving elastic compound of fire and air that gives matter itscohesive and other properties. Strict causality applies every-where, guaranteed and effected by the spatial continuity of thepneuma, whose changing tension drives the world throughrepeated identical thermodynamic cycles. The system wouldseem to rule out free will decisively. But since ethics required afree acceptance of fate and the mental preparation necessary tomeet it, Stoics had to find a way around the strict causality of theirphysics. Their solution was nomore plausible than the Epicureanswerve. As an alterative to strict atomism, however, the Stoicconcept of a space-filling active elastic spirit had a future.

In contrast to the Peripatetics with their unchanging uncre-ated cosmos, and the atomists and Stoics with their random andcyclical worlds, the Academics had a full cosmogony, with acreator as well as a creation story. As told by Plato’s mouthpiece,the mathematician Timaeus of Locris, the Demiurge who made



the realm of Ideas and theWorld Soul used what he had left afterrolling out the celestial equator and the paths of the planets tomanufacture a swarm of human souls. These he sent to stars inthe realm of Ideas to await planting in bodies created by thelesser gods to whom he assigned the task of making the sensibleworld. At the end of life, the rational soul returns to its domicilestar if its human possessor had lived a good life; if not, the soulreincarnates in a lesser being. Our animal parts, the gift of thegods, serve merely to keep our head, the seat of our reason, fromrolling around on the ground.

Used properly, our rational soul can bring us through obser-vation of the motions of the heavenly bodies to the discoveryof number, time, and harmony, and to the contemplation ofthe Ideas. We might then perceive that the Ideas of the fourelements and the quintessence are linked to the mathematics ofthe five regular solids. The plane faces of three of them (thetetra, octa, and icosahedron) are equilateral triangles, and con-sequently the elements corresponding to them (fire, air, andwater) are interconvertible (see Figure ). The remaining two,the cube and the dodecahedron, are the “Ideas” of the earth andthe universe as a whole. We should not press the obviousdifficulties. The lesser gods who created the material worldwere not entirely competent. “[I]t is fitting that we should, inthese matters, accept the likely story and look for nothingfurther.”

Roman worlds

Although foreign students from Rome added little of note toGreek physica, they turned much of it into useful summaries and



compendia. During the last years of the Republic, Lucretiusversified Epicurus’ atomism. During the reign of Caesar Augustus,the poet Ovid made a conspicuous place for Pythagoreanism inhis Metamorphoses. Under the Emperor Nero, Seneca composed ameteorology on Stoic principles—cut short, unfortunately, byNero’s invitation (which Seneca could scarcely refuse) to commitsuicide. And in the years before his fatal inspection of Vesuvius

(fire)

(air)

(water)

First levelSecond level

In the case of equiangular triangular faces:

Second Level First Level

Solid

1 pyramid

1 octahedron

1 icosahedron

SolidEquilateral facescomposed of

6 elements

Equilateral facescomposed of

2 elements

Elements

Octahedron

Icosahedron

=

=

= = = =

=

=

=

=

=

=

4

A A I GC

B H

D E F

G

H

I

B

C

8

20 120 60

3 pyramids or1 octahedron+ 1 pyramid.

15 pyramids, or6 octahedra +3 pyramids, or3 icosahedra.

6 pyramids, or3 octahedra, or1 Icosahedron+ 1 pyramid.

24

48

12

24

Fig. . Geometrical foundations of the world. The faces of the cube come inaggregates of elementary isosceles right triangles ACB; those of the pyramid,octahedron, and icosahedron come in aggregates of various sizes of elemen-tary -- degree triangles IGH. The diagram shows how the second levelaggregates from the first and, in the case of the three solids with equilateraltriangles as faces, how the solids can transform into one another. Adaptedfrom Cornford, Plato’s cosmology (Indianapolis: Bobbs-Merrill, nd), pp.–.



during its eruption of CE, Pliny the Elder crammed into one ofthe books of hisNatural history a qualitative survey of the worldfeaturing a God unpolluted by commerce with human beings, anaturalistic account ofmeteors, comets, and eclipses calculated tofree humankind from fear of lesser gods, some hints at atomismand stoicism (physica of chance and necessity), and a few bars fromPythagorean music of the spheres.

Lucretius begins his poem with the customary invocation of amuse, in this case Venus, after which he disobligingly announcesthat his great purpose is to remove her and all the other gods fromhuman concerns. The atoms cavorting in the infinite void followthe laws of necessity apart from the occasional unintelligibleswerve that gives spontaneity to the world and freedom to thewill. No external agency can interfere with this process. Therefore,although you are nothing but chance congeries of buzzing par-ticles, be joyful, submit to fate, and fear not the impotent gods.

The lengthy exposition of Pythagorean doctrine that Ovidjams into the last book of his catalogue of beings that transforminto beasts treats only briefly the founder’s physica, his teachingsabout “The great world’s origin, the cause of things | what natureis, what god, and whence the snow | what makes the lightning,whether thunder comes | from Jove or from the winds whenclouds burst wide | why the earth quakes, what ordnance con-trols | the courses of the stars | and the whole sum | of nature’ssecrets.” Most of Ovid’s account of Pythagorean thought con-cerns metempsychosis and vegetarianism, a belief and a practiceindissolubly connected. If souls transmigrate, how can you tellwhether your ox, your faithful brother at the plow, was not infact your late brother?



This sound teaching fell on deaf ears. Ovid admitted as much;Seneca, writing half a century later, reported that in his timewould-be Pythagoreans could not even find a teacher. But that,according to Seneca, merely mirrored the sad state to whichphilosophy in general had fallen in his time: “Many philosoph-ical lineages are dying out without a successor.” His Naturalquestions, an attempt to reinvigorate Stoic physica, reconstructedthe meteorology of the Stoa and the Lyceum to answer thequestions whose solution Ovid credited to Pythagoras—thecauses of the wind and weather, thunder and lightning, andearthquakes. All of these problems had been standard in physicasince the time of Thales. They were, as they still are, of greaterimportance to humankind than the doings of Demiurges. InSeneca’s meteorology, high winds, thunder, and earthquakesaccompany the expansion of previously constrained pneuma.Breaking from Stoic authority, he enrolled comets, famous forbad reputations, among the planets and toyed with the possibil-ity that their daily motions, and those of the stars in general,arise from a revolution of the Earth rather than from the turningof the great celestial vault. As his placement of comets suggests,the interconnectedness of the Stoics’ space-filling active pneumadestroyed the barrier between the heavens and the Earth char-acteristic of Aristotelian cosmology.

Seneca puffed up his meteorology with moral reflections thatappear to be its reason and result. If you do not inquire into thematerial foundation of the world and the nature of its creator orguardian, or speculate whether he still creates (if he ever did) orhas retired, whether he thinks only of himself and whether hecan amend fate, you enslave yourself to merely human affairs.



Life would not be worth its pain and suffering were it not for theopportunity to learn that nature, fate, the world, providence, andGod are different names for the same thing; that God did notmake the world exclusively for human beings; that life is asentence of death; and that philosophy, by dispelling fear ofdeath, is the only healthy way to resign oneself to fate. Seneca’seloquent combination of moralizing and meteorology made theNatural questions the authority on the physical problems it treatedfor most of the Latin Middle Ages.

Had Plutarch’s dialogue on the markings on the Moon notsuffered an eclipse of centuries, Seneca’s stoicism would havefaced a sprightly challenge in medieval times. Plutarch freelycriticized most ancient systems. As a probe and goad he askedthe obvious question: why do we not see the Sun’s image on theMoon as we see it on the sea? Since the answer depends onknowledge of the Moon’s makeup, it was beyond the compe-tence of mathematicians. What then did the physici have to say?Plutarch’s spokesman replied that the Peripatetic model of theMoon as pure quintessence is nonsense; the mottled, imperfectlunar surface betrays some admixture in its makeup. The Stoicview—that it is made of a sort of pneuma—is worse, since air andfire cannot reflect visual rays. We are left with the Platonicaccount that the Moon is more “earthy” than heavenly. Itsrugged surface acts as if composed of a great many randomlyoriented mirrors, which can unite visual and solar rays withoutproducing an image.

What keeps the rocky Moon from falling on the Earth? “[T]herapidity of its revolution, just as missiles placed in slings are keptfrom falling by being whirled around in a circle.” What keeps it



close to Earth? A literal law of nature: “the position of earth laysan action against the Moon and she is legally assignable by rightof propinquity and kinship to the earth’s real and personalproperty.” Is the Moon inhabited? Very likely, but by creaturesas different from us as we are from fish, and also by disembodiedsouls improving themselves for their next incarnation. Plutarch’sideas about the Moon, minus its role as host to rehabilitatingsouls, recur in Galileo, Kepler, and many lesser heroes of theScientific Revolution.

During the philosophical downturn mentioned by Seneca, thePlatonic Academy did not exist. It had come to a temporary endin the destruction that accompanied the Roman conquest ofAthens in BCE after a period of intense skepticism about thepossibility of achieving any secure knowledge about anything. Itrevived in CE with a curriculum based on “Neoplatonism,”invented in Rome by Plotinus, who died in CE, and system-atized by his disciple Porphyry. Plotinus was not a skeptic. Hisconfident speculations rose above even the Demiurge, whoseemployment as creator, even if only of the rational realm andthe lesser gods, seemed to him incompatible with occupying theacme of the divine pyramid. How did the Demiurge relate to theimpassable God or Good that Plato had put in charge of every-thing? Plotinus’ answer was that God stands immovable at thehead of a chain of created and creating “emanations.” The first ofthese emanations, Intellect, contains the Ideas; the second, Soul,contains Nature; the next is the Demiurge. Plato had not sup-plied much information about the natural world created by theDemiurge’s collaborators, and his thesis that we cannot knowsuch things in principle did not encourage elaboration of



Timaeus’ hints about polyhedra. So Neoplatonism grafted onAristotle’s physica as its account of the visible universe created bythe demigods employed by the Demiurge.

Another easy conflation assimilated the top of the Neopla-tonic power chain—the One, the Intellect, and theWorld Soul—with the Christian Trinity. In the orthodox view, God did notemploy a vicar in his creative works. But several Christian sectsstill competitive in the fourth century taught that God the Fathercreated only spiritual beings, one of whom, Jehovah by name,broke the chain of spiritual emanations and materialized hissuccessors. Neoplatonism was the leading philosophy, and itsco-inventor Porphyry the most effective critic of Christianity, ofthe late empire. His opponents, the architects of Christianityconcerned to achieve standardization of belief, faced the chal-lenges of harmonizing discrepancies among the four canonicalgospels, explaining evil in the creation of a beneficent deity, anddefining the relationships among the Persons of the Trinity. Themost abstruse of their conundrums probably could not have beenconcocted without the language and concepts of Aristotelianphysica and Neoplatonic philosophy.

Applications

Physici and their speculations had less to offer to princes thanapplied mathematicians who could give practical advice. Thegreatest of them all, Archimedes, worked for a tyrant ofSyracuse. Although best known now for his detection of acounterfeit crown and his legendary feats in defense of Syracuse,Archimedes preferred to be remembered in the manner of a



physicus, as a liberal artist. According to Plutarch, he regarded hispractical accomplishments as “mere accessories of geometrypracticed for amusement” and “every act that ministers to theneeds of life as ignoble and vulgar.” Plutarch added that Plato hadchastised two clever mathematicians, Eudoxus and Archytas, forturning their hands to practical things, and becoming “corruptorsand destroyers of the pure excellence of geometry.”

In contrast to the many useful applications of geometry,applied physica could only veneer a practical man. Vitruviusrecommends in his Ten books of architecture, which dates fromthe early Roman Empire, that the student learn physica to be ableto judge excellence, to achieve authority, and to grow “courte-ous, just, and honest.” More obviously, knowledge of “the prin-ciples of physics [as taught] in philosophy” was needed forconstructing waterworks; of the principles of musical intervals,for tuning catapults; of astronomy, for choosing sites for build-ings; of meteorology, for avoiding places exposed to winds,lightning, and earthquakes. None of this related to the mainbusiness of construction, and for good reason. Physica knewnothing about the strength of materials. When it came to foun-dations, Vitruvius could only advise to “dig down . . . as deep asthe magnitude of the proposed work seems to require.”

Amore lasting application of physical principles occurs in thewritings of Ptolemy, who seems to have been associated with theLibrary and Museum of Alexandria, in effect a state institution.He distinguished his astronomy, enshrined in the books of hisSyntaxis mathematica or Almagest (as it is usually named after itsArabic translation), from his four books of astrological inter-pretation, the Tetrabiblos. The Almagest considers planets only as



moving points; the Tetrabiblos ascribes to them the active elem-ental qualities that bring their influence down to Earth. The Sunis primarily hot and secondarily dry, the Moon primarily moistand moderately warm, and the planets warm, moist, cold, anddry in different degrees depending upon their distances from theluminaries and the Earth. Judged by temperature and humidity,Jupiter, Venus, and Moon are beneficent, Mars and Saturn evil-doers, and Sun and Mercury ambiguous. From this astrophysicsPtolemy derived a physical anthropology that explained whyEthiopians are black, Scythians white, inhabitants of the tem-perate region medium in color, civilized, and sagacious, andhimself mathematical.

Although the astrophysics of the Tetrabiblos admitted earthlyqualities into the celestial regions, Ptolemy’s astronomy revolvedin the quintessence of the Aristotelian universe. According toAristotelian celestial mechanics, each planet and luminarytravels on a sphere concentric with the Earth. But none of thePeripatetics, including that Eudoxus whom Plato criticized fordoing carpentry instead of geometry, could “save the phenom-ena” consistently with the concentric principle. The obviousexplanation of the notable alterations in brightness of theMoon and the planets is their changing distance from Earth. Somathematicians dismissed Aristotle’s spheres in favor of non-concentric circles on which to mount celestial objects.

Ptolemy’s Almagest saves the phenomena by displacing theEarth from the center of the Sun’s circular orbit, thus represent-ing the “first anomaly” (which arises from the ellipticity of theEarth’s orbit) as an effect of perspective (see Figure a). Sincethe Moon and planets also have a first anomaly, the circles



representing their orbits (the “eccentrics”) also have centersdisplaced, though in different directions and magnitudes, fromthe Earth’s. To save the “second anomaly,” retrogradation, duringwhich a “superior” planet (Mars, Jupiter, or Saturn) appears to

A

BP

A

(a)

(c)

(b)

B

P

C E

CQ E′

C

C′

C′

E

Fig. . Ptolemaic bric-a-brac. (a) Saving the first anomaly: P, the planet orbitingat constant velocity on a circle centered at C (“the eccentric”); EA, CB, directionsof P as seen from E and C, respectively. (b) Saving the second anomaly: C0, thecenter of P’s epicycle, moves cc (counterclockwise) on eccentric C as P moves ccaround it, both motions at constant velocity. (c) The equant: C0 moves cc withconstant velocity around Q (“the equant point”) where QC = CE0 = CE/.



reverse directions periodically in its orbit around the Earth, theAlmagest plants the planet on an “epicycle” turning at constantspeed around its center, which rides on the planet’s eccentric (seeFigure b). The combination also explained the change in bright-ness, provided that themotionswere so tuned that retrogradationoccurred in mysterious synchronization with the motion of theSun. A splendid refinement, mimicking the first anomaly almostperfectly, made the center of the epicycle rotate with constantvelocity around an “equant” point placed as far on one side ofthe center of the eccentric as the Earth was on the other (seeFigure c).

This brilliant, complex bric-a-brac violated good physics bypostulating revolutions around unoccupied points without giv-ing any physical reason for their position or motion. They werefictions introduced for description, not explanation. Ptolemywas not content with the division of labor by which physiciaimed at the truth about substance and mathematicians atdescription of its accidents. Reversing the usual precedence, hedeclared the priority of mathematics over physics in the Almagestand exemplified it in the astrophysics of his Hypotheses of theplanets. Here he made the Sun run in a groove between twoconcentric spheres whose common center is offset from thecenter of the Earth. Each superior planet rides on a marble(a reified epicycle) running in a similar groove between anotherpair of eccentric spheres. Accepting the Aristotelian (and Stoic)prohibition of a vacuum, Ptolemy close-packed his system sothat the apogee of one celestial body coincides with the perigeeof the next, and the greatest distance of Saturn lies in the vault ofthe stars. Knowing from eclipse observations the average lunar



distance in terms of the Earth’s radius r and, from his astronom-ical calculations, the ratios of the radii of the epicyles andeccentrics of each planet, Ptolemy could work up through hisclose-packed system to find the distance to the stars, which hemade out to be just shy of , terrestrial radii (r).This number, though vastly less than the true radius of

Saturn’s orbit, was large enough to suggest the insignificanceof human kind, especially when expressed in miles. Eratosthenesof Cyrene, one-time head of the Library of Alexandria, convertedr to human measure by determining the angle Æ between thevertical and the direction of the Sun’s rays at Alexandria atnoon at the same instant that it stood overhead at Aswan,, stadia due south. Since Æ equals the difference in latitudebetween the two places, Eratosthenes could calculate, from�r:,= �:Æ, that r� ,miles (see Figure ). The radiusof the visible world would then be million miles. Thesenumbers were scarcely bettered before the seventeenth century.

Among other enduring pieces of mixedmathematics from theHellenistic period are Archimedes’ demonstration of the law ofthe balance (in equilibrium, a weight’s distance from the fulcrumis inversely proportional to its magnitude), his hydrostatics withits associated concept of specific gravity, an anonymous treatiseon mechanics incorrectly attributed to Aristotle, and parts oftexts on optics by Euclid and Ptolemy. The optical works,which are mainly geometry, presuppose at least three physicalprinciples of interest: the rays responsible for vision originatefrom the eye, change direction abruptly at the surface betweenmedia of different density, and take the shortest path between eyeand object. Thus the angles of incidence and reflection are equal.



In a treatise perhaps written by Ptolemy, the author offeredexperiments to confirm the law of reflection and the breakingof visual rays when they strike an air–water surface. The methodgave results that differ insignificantly from Snell’s law for anglesof incidence up to �. The Ptolemaic author observed thatrefraction must also occur at the boundary between air andether (or fire or quintessence) and, although he could not calculatethe amount, rightly stated that the effect makes celestial objectsnear the horizon look higher in the sky than they are.

The pseudo-AristotelianMechanica exceeds the scope of physicain being addressed to mechanical problems. But it begins withsome physics talk about the marvels of circular motion, inwhich contraries exist simultaneously. In a spinning wheel, thehighest point moves forward and downward as the lowest pointmoves backward and upward; and the rim, though larger thanthe hub, moves faster. Pseudo-Aristotle explains that the shorterthe spoke, the closer its extremity to the stationary center. By anassumed principle of continuity, the proximity inhibits themotion. On the principle that longer radii are moved moreeasily through a given angle than shorter ones, the authordelivers the law of the lever and deftly applies it to oars, rudders,sails, wheels, pulleys, capstans, wedges, tooth extractors, andnutcrackers. From the nutcracker he proceeds to the head-cracker later known as “Aristotle’s wheel.” Two circles fixedtogether concentrically roll horizontally. Although the largerlays down a longer path than the smaller, they stay together.Why? “It is strange . . . and wonderful.” The wonder rolled all theway to Galileo, who took many hints and problems from theMechanica believing that they came from Aristotle.



Ancient applications of what today would be deemed engin-eering physics included the hydraulics of the magnificent systemof aqueducts, tunnels, and fountains that supplied Rome’s water.“There was never any desseine in the whole world enterprisedand effected, more admirable than this,” so said Pliny, the experton marvels. The ancients also knew of the suction pump andwaterwheel but made little use of either. Perhaps the best knownof their waterworks apart from aqueducts push water aroundfor theatrical effects. The greatest impresario in this line, themilitary engineer Hero of Alexandria, opened his treatise oningenious devices with proofs that air is corporeal and that, inunion with the other elements and principles, it can produceuseful and amazing effects. To produce amazement, place twofigures before a hollow altar on a pedestal filled with wine.Conceal hollow tubes inside the figures and the wine-filledpedestal, and run them from the interior of the pedestal tobowls the figures hold. Then kindle a fire on the altar. The airwithin it expands, pushing the wine in the pedestal into thebowls and thence, as a libation, into the fire. Alternatively, usethe pressure to open a door mysteriously (see Figure ). Suchgames did not lead to steam engines.

Dumbing down

Owing to disinterest, disturbances, or the rise of Christianity,Latin speakers gradually ceased frequenting Greek schools, andeducated Greek slaves, who taught their language to many anaristocratic family, became scarce. Knowledge of Greek, and thecopying of Greek texts, dwindled, to arrive functionally at zero



by the time the Ostrogoth Theodoric became King of Italy in. Curiously, Theodoric knew more Greek than his learnedLatin subjects, having been deposited as a boy in Byzantium asa hostage for the good behavior of the Goths who lived onits borders.

Christian education beyond the Latin schools that taughtskills useful to orators and bureaucrats was haphazard and, inthe higher reaches of biblical interpretation, largely self-taught.That might help account for the breadth of opinion, and

Fig. . Sabbath machinery. Air heated by the fire on the altar pushes water andsteam from the vessel H into the pot M, which, in descending, pulls ropes thatcause the axles they encircle to rotate and open the temple door.



frequency of heresy, among the early self-made theologians.Many of them knew the Latin classics and the writings of theFathers East and West. They conveyed snippets of the physicathey knew in their Bible commentaries, particularly on the sixdays of creation (Hexaemeron), and in general the Bible offeredthe energetic exegete a wider range of physical subjects than theschool texts did the grammarian. However, Augustine’s call inhis De doctrina christiana for a dictionary of ancient science toassist understanding of Scripture met with only partial success.

Lacking such a text in the fifth century, Latin admirers ofphysica resorted to the many compendia copied or composedduring the time of troubles. Of first importance was Pliny’sNatural history. Drawing on him and others, Macrobius Theodos-ius, perhaps a Greek-speaking bureaucrat in the service of Theo-doric, sugarcoated the liberal arts in a Commentary on the dream ofScipio that would suit the taste of the Middle Ages. In the dreamon which Macrobius hangs his learning, Cicero describes a visitof the deceased Scipio Africanus, the scourge of Carthage, toScipio’s grandson. Africanus reports that the souls of true states-men dwell in the Milky Way between their incarnations onEarth, and he transports young Scipio there to compare thevastness of the heavens and their harmonious revolutions withthe pettiness and discord of the greatest terrestrial empires.

Proceeding downwards from the soul emporium of the MilkyWay, Macrobius defines the equator, horizon, meridian, andcolures, the ecliptic and eclipses, the zodiac and the solstices;describes the apparent motions of Sun, Moon, and planets up tothe first anomaly; and surveys the Earth’s five climes, impene-trable torrid zone, and surrounding ocean. Though impressive



to its inhabitants, Earth, being but a speck compared with theheavens, is easily sustained in the world’s center by the pressureof air exerted equally on all sides. Thus suspended, its inhabit-ants can appreciate the reason that the Demiurge gave planetsand luminaries their particular distances and periods. They makeheavenly music keyed to the intervals Pythagoras discoveredby plucking lute strings on Earth. If Macrobius knew that theseintervals differed altogether from the planetary parameterscalculated by Ptolemy, the discrepancy did not bother him.He referred quantitative details to people “disengaged fromserious matters.”

While descending from the MilkyWay to its temporary abodeon Earth, the pure soul acquires the properties it will need fromthe planetary spheres: reason from Saturn’s, power to act fromJupiter’s, boldness from Mars’, sense perception and imaginationfrom the Sun’s, passion from Venus’, speech and analyticalcapacity from Mercury’s, and, from the Moon’s, the final prep-aration, the ability to perform the physical functions incident tolife among the dregs of creation. Macrobius conveys muchinteresting misinformation in describing this journey: forexample, that the planets shine by their own light, the Earthdoes not reflect sunlight, and Venus and Mercury circulatebetween the Sun and Mars. Giving Plotinus as his authority,Macrobius makes the planets and luminaries merely the signs,not the movers, of future events. The soul has free will andAfricanus urges Scipio to make good use of his, live the morallife, and insure that his soul returns to the Milky Way.

Macrobius’ blend of physica, Neoplatonism, numerology,metempsychosis, moralizing, and misinformation was not the



only vehicle of transmission of ancient texts produced by high-level civil servants (if such he was) in and around the court ofTheodoric. For some time Theodoric’s chief advisor was theCatholic Boethius, scion of a high patrician family, whose old-fashioned education gave him fluent Greek, and whose concernthat philosophy might be lost prompted him to undertake aLatin translation of all of Aristotle. He began with the Organon(Aristotle’s logical treatises), which was immediately useful inhead-to-head religious controversy and so could serve as aTrojan horse for the rest of Peripatetic philosophy. Boethiusdid not complete much of his project, however, before Theo-doric, believing him to be a traitor, had him killed. Whileawaiting execution, Boethius wrote his famous Consolations ofphilosophy, in which a Christian Neoplatonic world view gavehim the resolve to face his misfortune stoically. Together withAristotle’s logic and the application of high philosophy to con-solation, Boethius bequeathed to medieval letters a short tracton music, which covered the terrestrial and celestial types, andthe harmony of the soul. He was succeeded as Theodoric’sminister by a lawyer, Cassiodorus, equally committed to pre-serving ancient learning but in a form more useful to Christiansthan translations of Aristotle. He set up a monastery for whoseinmates he rendered the seven liberal arts in a manner suitable toChristians struggling to preserve some remnants of Romanculture in an increasingly barbarous world.

The most popular rendition of the seven liberal artsbequeathed to the Latin Middle Ages was a work of the fifthcentury, the Wedding of Mercury and philology, of whose authorC.S. Lewis remarked that “this universe, which has produced the



bee-orchid and the giraffe, has produced nothing stranger thanMartianus Capella.” Martianus set forth what he knew about theliberal arts in lectures by philology’s bridesmaids. They delivertheir wisdom in excerpts from ancient primers or enunciationsof propositions without proofs. Much of what they say is unin-telligible. Thus Astronomy, having stepped from her ball ofheavenly light, declared that during the , years she spentin Egypt studying her subject she learned that celestial natures,“circling by their own surging, are diffused the entire wayaround in globular belts and circles.” After this venture intophysica she described the apparent motions of the planets andluminaries, defined the equator and zodiac, tried to explain howto measure the Earth, climbed back into her ball, and, like theantiquity she represents, flew away.



Fig. . Lecture in a House of Wisdom. The site is the library in Basra, the timethe thirteenth century.


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Among the Christians who equipped themselves withAristotle’s Organon to dispute about the nature of theTrinity and other enigmas were followers of the patriarch ofConstantinople, Nestorius, who was excommunicated in CE.When expelled from the Roman Empire they settled in Persia, atJundishapur, a town built years earlier to house captiveRoman soldiers. There the Nestorians built an important schooland hospital in which they enlarged their study of Aristotle andGalen. Vigorous missionaries, the Nestorians became experts intranslating difficult texts between unrelated languages. The earlyArabian conquests to the east increased the scope of Nestorianmissionary activity. The caliphs usually considered them as alliesbecause they had enemies and beliefs in common, and theQur’a ̄n recognized them as fellow “People of the Book,” pro-vided they paid their taxes.

The first era of Arabian expansion ended in the mid-eighthcentury. The dynasty that had presided over most of it, the


Umayyads, headquartered in Damascus, succumbed to a clanwith Persian backing, the Abbasids, who built a new city, Bagh-dad, as its power base. Nestorian learning found a growingaudience in the eclectic urban elite drawn to the new capitalfrom around the conquered lands. In the director of thehospital at Jundishapur became the Abbasids’ court physician.Syriac-speaking Christian doctors soon swarmed in the newcapital. They supplied the translators who made Aristotle “ThePhilosopher” in the Arabic language.

The project to render Greek science into Arabic lasted threecenturies. The translators had to invent many new technicalterms, even a word for philosophy, for which they adopted thetransliteration falsafa. In the early ninth century, the AbbasidCaliph al-Mamūn (–) established an academy or researchcenter and library at Baghdad, the House of Wisdom, whichgathered works by Greek medical writers and mathematicians aswell as Aristotle. By every Aristotelian treatise except thePolitics existed in Arabic, together with many books like theMechanica incorrectly ascribed to him (see Figure ).

The wealthy of Baghdad supported this activity, which, duringthe heyday of the House of Wisdom, centered on a wide com-petitive search for ancient manuscripts. This unusual treasurehunt had to do with the rapid rise of the Islamic state. Lackingadministrative experience, the Arabian conquerors employedthe dı̄wa ̄n, or bureaucratic offices and procedures of the PersianEmpire, to tax, survey, and keep records. The new empire keptits books in Persian until late Umayyad times when it shifted toArabic. That required translation of the dı̄wān manuals, which



probably included introductions to arithmetic, geometry, andbranches of applied mathematics.

The shift to Arabic opened the bureaucracy to place huntersand, insofar as careers were open to talent, intense competition.Mastery of applied mathematics may have helped people withambitions of upper-level appointments; hence the hunt formathematical treatises in depositories in Byzantium and else-where. Once domesticated by this process, mixed mathematicsbecame a pursuit in its own right, though still supported for itsapplications to administration, engineering, and religious obser-vance. Thus, unlike the Greeks, most Muslim physici and math-ematicians were courtiers, officials, or functionaries.

The arts of reasoning and persuasion, useful for makingheadway in Baghdad’s sophisticated philosophical salons and aname in religious controversy, again served as a stalking horsefor the rest of Aristotle’s system. The early Abbasids favored aliberal form of kala ̄m (scholastic exegesis of religious writings),Mu’tazila, which allowed wide scope to reason in the interpret-ation of obscure or implausible passages in Scripture and in theattainment of moral as well as philosophical truth. The Aristo-telian corpus showed what reason unaided by revelation couldachieve. It also bore directly on such practical matters as astrol-ogy and meteorology, and hylomorphism (the doctrine of formand matter) provided the vocabulary for discussion, if not theingredients for solution, of most questions about everydayexperience.

These practical considerations may be taken as the efficientcause of the translations and the commentaries and compendia


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descended from them. The principles of knowledge, and theways to wisdom, might be adduced as formal and final causes.There remains the material cause. It was paper. The Arabsbecame acquainted with this Chinese invention during theirconquests in Central Asia. A paper mill operated in Baghdadbefore to help meet the needs of record keepers. Morepaper became available just when al-Mamūn’s translatorsneeded it. A large market in books developed, supplied by anassembly line, or rather circle, of scribes who simultaneouslytook dictation from an author or scholar. The scribes readback what they had taken down and the dictator, if satisfied,“authorized” the copies. The system produced more, and morefaithful, versions of the originals than monastic scribes couldmake one at a time on vellum or parchment. Colossal librariescame into being, the largest, at , or , volumes,being over a hundred times the size of their nearest competitorsin the West.

Central administration of the new empire proved impossible.As soon as the great expansion peaked in the eighth century itsparts began to separate. In the tenth century, caliphates split offin Egypt under a dynasty claiming direct descent from theProphet’s daughter Fatima, and in Andalusia under a branch ofthe Ummayads. At the same time, the Abbasids lost all power inthe East to Turkish and Persian shahs and emirs. These arrange-ments proved fleeting: in the Umayyads lost Andalusia tofundamentalist Muslims from North Africa; in the Fatimidsgave way to the Kurd Saladin; in the Mongols destroyedBaghdad. Nonetheless, a common language for literature andadministration, and conversions to Islam, kept the disparate



political elements together as a cultural, religious, and commer-cial “empire.”

Because of the wide distribution in place and time of nichesfor its cultivation, falsafa could develop only in fits and starts inIslamic lands. Hence the enormous energy devoted to producingdigests, encyclopedias, and commentaries on standard materialby the most gifted of the Islamic philosophers, and a reason thatthey did not develop a physica much different from what theyinherited. Another reason is that, in contrast to mathematics,physica had consequences for faith. Aristotle’s Indifferent God,whether pure or, as was largely the case, Neoplatonized, couldbe Islamized, as he was Christianized, only at the expense of thelogical consistency of the system. To insist on pure Aristotle,with his eternal world and perishable soul, invited theologicalopposition.

Falsafa

The House of Wisdom established in Baghdad by al-Mamūnincorporated the library of his father, Harun al-Rashid, theCaliph of the Thousand and one nights, and an observatory forother nocturnal activities. It also sponsored expeditions to meas-ure the size of the Earth. Like the House’s translation project, itsastronomical and geographical observations arose from Greekprompts. Al-Mamūn wanted to check Ptolemy and Eratosthenesfor the surer estimate of the size of his empire and the relativepositions of the principal places in it. Geography flourishedwherever encouraged and, with history, made the largest bodyof literature in the Islamic languages during the Middle Ages,


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apart from religion. The great figure of the House of Wisdomwas not a geographer, however, but an exemplary polymath,the founder of Arabic Aristotelianism, al-Kindī. He is a goodexample of the generalization made earlier about the socialstatus of Muslim savants. His father, from Yemen, was governorof Kufa in Iraq, whence al-Kindīmade his way to Baghdad. In hisversion of Aristotle, the visible world consists of the four restlesselements, the lazy circulating quintessence, form, matter, sub-stance, and accident, and runs on the four causes. The UnmovedMover transmits motion, and brings about substantial change,through the rotation of the heavens. This stationary Being isNeoplatonic in holding in its mind the Ideas and Forms ofcreated things and Qur’ānic in knowing the particulars of thephysical world it created and the characters and deeds of every-one alive and dead. With this adjustment, al-Kindī’s world pic-ture became the standard model of Aristotelian physica until thetwelfth century, when defenders of falsafa in Spain advocated astricter reading of the Philosopher.

At first the amalgam fared well, especially in the hands of al-Fa ̄ra ̄bī, the son of a Muslim general. Born in remote Turkestanand schooled by a Nestorian Christian, he arrived in Baghdad toearn the sobriquet of “Second Teacher,” Aristotle being the first,for his presentation of Peripatetic philosophy improved by theinsights of Islam. His ideal syllabus, The attainment of happiness,advises the truth seeker to begin with things easiest tounderstand—numbers and geometrical figures—and proceedgradually toward the material world. The journey leads throughoptics, astronomy, music, and mechanical principles taken asArchimedean abstractions to physica, the science of the things



that make up the world. Proceeding again from the least materialto the most, the pursuit of happiness sets out from the heavenlybodies and descends through the four elements to stones and theEarth’s interior.

Having understood the four causes of all the species andactions of the physical world, the inquisitive mind inquiresabout beings more perfect than nature and natural things, andsublimes to metaphysics. Beginning with the soul and intellectof the rational animal, it discovers the way of human perfectionand climbs back up the chain of principles, peeling away thematerial aspects, ascending through ever more perfect rationalcreatures to the First Principle, the Being too perfect for descrip-tion. The fulfilled mind now understands the nature and place ofeverything in the universe, including the Islamic state: for thecaliph relates to his hierarchy of subordinates down to thelowest citizen as the First Principle relates to created beingsfrom the highest intellect to the densest stone.

This clear teaching and the support of the Abbasids did notsuffice to establish a new Lyceum in Baghdad. Neither al-Kindīnor al-Fa ̄ra ̄bī led continuous academic lives in the capital.Al-Mamūn’s effort to impose Mu‘tazila failed and his successorsoppressed its representatives. The House of Wisdom almostperished and al-Kindī had to leave. Al-Fāra ̄bī retained the sup-port of his caliph, with the unhelpful consequence that theywere driven out of Baghdad together. After the Second Teacherdied eight years later in Damascus, falsafa moved far into Persia,where in it produced one of its finest flowers, Ibn Sīna ̄(Avicenna), in Bukhara, in what is now Uzbekistan. Extrava-gantly precocious, he drifted around Persia in search of


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knowledge, often serving as a physician to the reigning power.His capacious memory held the entire Qur’a ̄n, and much ofGreek medicine, mathematics, and physica, which he pouredinto an antidote to ignorance and insomnia entitled The cure.

The cure proposes the same project as al-Fa ̄ra ̄bī’s Attainment ofhappiness, but arranges the steps in the order of the Aristoteliancanon. Thus after the Organon come the basic principles ofphysica, their applications to the celestial and sublunar realms,the mysteries of motion and the human mind, and then math-ematics. The last topic is First Philosophy, culminating in know-ledge of the One who operates in the Neoplatonic manner ofemanation and delegation. Seeking the unification of all know-ledge and practice under one set of principles sanctioned by theQur’a ̄n’s insistence on the oneness of God, Avicenna took onhuman activities (prayer, prophecy, politics, law) as well as thenatural and supernatural worlds, and the techniques, the logicand mathematics, necessary to study them.

Avicenna’s widely read works ended, or suspended, the pro-ductive cultivation of falsafa in the eastern reaches of Islam. Thatwas owing primarily to al-Ghaza ̄lī (Algazel), a conscientioustheologian well versed in kala ̄m and falsafa. After isolating him-self for some years to ponder the relations between reason andrevelation, he announced that kala ̄m could resolve nothingimportant for faith, and that falsafa was inimical to it. He empha-sized the particulars in which the Unmoved Mover differed fromthe God of Islam, and pointed out revealed details missing fromfalsafa, such as the Last Judgment, the resurrection of souls, andthe dissolution of the world. He allowed the practice of kalāmwhere helpful in persuading wavering believers of a rationalistic



tendency; but, in general, he thought theology and the Sufism towhich he inclined would do better without it. His position hadthe strength of logic and of a new Seljuk ruler in Baghdad, whofavored a stronger orthodoxy than the more relaxed religion ofthe Abbasid caliphs.

The last stage in Aristotle’s journey through Islam jumpedtwo continents, from Persia to Spain, and over a century, fromAvicenna to Ibn Bājja (Avempace), the long-serving vizier of thegovernor of Granada, and Ibn Rushd (Averroes), one-time cadi,or religious judge, in Seville and Cordoba. Both insisted on apurer Aristotle than al-Kindī’s, although with reservations. Thebetter known of the two, Averroes, made his career as a phys-ician and protégé of the Almohad Caliph Abd al-Mu’min beforebecoming cadi. His literalist renderings of Aristotle and hisopposition to al-Ghaza ̄lī’s teachings made him the target oftraditionalists worried by the successes of the Christian recon-quest of Spain. Eventually a high court in Cordoba condemnedhis approach.

The problems raised by the schism between astronomy andphysics appear to have worried Averroes for most of his philo-sophical life. As a preliminary to their resolution, he tried toseparate Aristotelian cosmology from the Neoplatonic andIslamic accretions it had acquired since the time of al-Kindī.That this mélange had become the default falsafa appears fromthe fable of “Hai Eb’n Yockdan,” as its hero was named in itsEnglish translation. Abandoned on a desert island as an infant,Yockdan had plenty of time to think about nature and his placein it. Step by logical step, he invented a Neoplatonic universe onwhich, after instruction by a passing holy man, he successfully


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grafted Islam. Averroes declared war on Yockdans. In perceptiveanalyses of the Aristotelian corpus that would earn him the titleof “The Commentator” in the Latin West, he removed the chainof creating and created beings between the One and the lunarIntelligence, restored the eternal cosmos and the IndifferentMover, severely criticized both Avicenna and al-Ghaza ̄lī, andallowed that Aristotle had possessed as much of the truth as aman can obtain without revelation. One of these truths was thatPtolemaic astronomy perpetrated a sham: it might be goodmathematics, but it had nothing to do with the real world. TheCommentator thus left the Aristotelian corpus as the Arabs hadfound it years earlier, so that it might almost be said of thegigantic effort of falsafa what Omar Khayyam said of himselfafter hearing the saints and doctors dispute: “[I] evermore cameout by the same door as in I went.”

The blunting of kala ̄m and discouragement of falsafa coincidedwith an important change in the Islamic educational system.The Abbasid House of Wisdom, with its library and observatory,and its even grander reproduction in Cairo by the Caliphal-Hakīm around , were the high end of a type reproducedin several places in Iraq and Fatamid Egypt. Most in factwere little more than libraries, though some offered inkand the ubiquitous paper to their readers. Originally givenover to the “foreign sciences,” the libraries either died out orconverted to cultivating the “Islamic sciences” of law, religiousstudies, and Arabic philology. They did not constitute an edu-cational system.

In early Islamic times, regular elementary education tookplace in the mosques. But from the eleventh century, schools



founded by traditionalists under a provision (wafq) that allowedthe endower of a public institution to retain family control overit after his death took over. Mainly Sunni institutions, thesemadrasas excluded the foreign sciences that had flourished inthe largely Shia, Persian-inspired, libraries. The great conquerorsin the East, Hūlagū Khan, Timur, the Seljuks, were great foundersof madrasas, which helped to inculcate a standard faith andreduce religious controversy. Teaching relied on staggeringfeats of memorization, first of the Qur’ān, then of the sayingsof the Prophet (hadith) and the foundations of the law (fikh). It issaid of one overachiever that he died having dictated only, folio pages of the texts he knew by heart.

Mixed mathematics

Astronomy

Astronomers arrived at Averroes’ view of Ptolemy’s construc-tions by a steeper path. They began, as did the philosophers, bymastering the translations prepared by denizens of the BaghdadHouse of Wisdom. That included checking the parameters trans-mitted in the Almagest. After eight centuries, shortfalls betweenPtolemy’s predictions and observation had become conspicu-ous. For years or so, until around the year , astronomersworking in the Islamic East labored to improve the parametersand the methods by which Ptolemy had deduced them. Thushumankind came to have good values for the inclination of theecliptic, the position of the Sun’s apogee, the precession of theequinoxes, and other desiderata.


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Two social factors underpinned this steady progress. Theeccentric astronomer Ibn Yūnus, who served the Fatamids anddied faithfully in on the day he had calculated would be hislast, specified one of these factors: “observation of the starsagrees with religious law, for it allows us to know the time ofprayers and of the sunrise and sunset that mark the beginningand end of fasting.” Hence Islamic astronomers investigatedassiduously topics of only passing interest to Ptolemy, like theduration of dawn and dusk, and conditions for glimpsing thefirst appearance of the new Moon. Also, astronomy taughtthe direction to Mecca, the qibla, from any place assigned, whento plant, and how to get from one place to another for commerce,pillage, or pilgrimage. Thus, in contrast to physica, the study ofthe stars, gently recommended in the Qur’ān (., ., ., ,.–), had the support of religious leaders. It also had thesupport of secular rulers, not only because of its help in imposingreligious conformity and in guiding caravans, but also because ofits foundational role in astrology. Ibn Yūnus was an expert on thesubject and his primary patron, the Fatamid Caliph al-Hakīm, thebuilder of Cairo’s House of Wisdom, was devoted to it. IbnYūnus’s huge zij, or handbook of astronomical information, con-tains tens of thousands of bits of astronomical-astrological data.

The second social factor in the progress of Arabic astronomywas continuity. Whereas physica convulsed periodically, astro-nomical observation went on almost continuously, in two differ-ent senses. For one, observatories, even if they did not outlast theirfounders, supported frequent determinations of the positions ofthe luminaries and planets, whereas Ptolemy had calculated hisparameters from very few strategically timed observations.



Astronomers designed observational programs to last for anentire circuit of Jupiter ( years) or, even more optimistically, ofSaturn ( years). The Islamic lands were fruitful in astronomers,zijēs, and monumental instruments. For example, at Rayy, kilometers south of Teheran, al-Khujandī, who died in ,built a sunken sextant with a radius of meters made of woodsheathed in copper and graduated to tenminutes of arc.With thisgiant, paid for by the local Persian strongman, he made exactdeterminations of the obliquity of the ecliptic and the latitude ofthe instrument.

By Ptolemaic astronomy had reached its apogee. Astron-omers had corrected its parameters via observations with sub-stantial instruments, invented newways to deduce the parametersfrom observations, simplified its mathematics with plane andspherical trigonometry, and replaced the cumbersome ancientnotation with “Arabic” (that is, Hindu) numerals. What morewas there to do? The approaches of three Persianmathematiciansof the mid-eleventh century—al-Bīrūnī, al-Khayyāmī (OmarKhayyam), and Ibn al-Haytham (Alhazen)—will indicate theoptions available.

Al-Bīrūnī, whose erudition was extraordinary even for aMuslim scholar, suffered in good measure the peripeteias ofIslamic savants dependent on courts. During his lifetime thenorth-east fringe of the territory claimed by the powerlessAbbasid caliphs changed hands several times. Born and educatedin Khwa ̄razm, he fled civil war to seek patronage in the frag-menting kingdoms around him. He met al-Khujandī, observed atthe great Rayy sextant, and found temporary employment withfleeting strongmen, one of whom built him an observatory.


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After the murder of this Maecenas, al-Bīrūnī continued hisastronomical and geographical observations in and aroundGhazna (Afghanistan). The powerful Ghaznavid Sultan Mah-mud knew so little about astronomy that he rejected as heresythe assertion that in the far north the Sun sometimes doesnot shine for days. Al-Bīrūnī enlightened him and Mahmudreciprocated by giving al-Bīrūnī the opportunity to become thesage of the age. Following the Ghaznavid armies to the east, hemastered Sanskrit, determined geographical positions, andbrought back much miscellaneous Indian lore.

Most of al-Bīrūnī’s writing concerns astronomy, geography,and geodesy. Although Ptolemaic in conception, his astronomyanalyzes other views, for example, the possibility that the appar-ent motion of the stars arises from a rotation of the Earth. Hegave an Indian as well as a Greek source for this idea andreported Ptolemy’s objections to it (bodies dropped from atower would land west of its foot) and the response (all bodieson a rotating Earth would participate in its motion even whenfalling). As many others would do, al-Bīrūnī accepted Ptolemy’sobjection, although an incident he recorded suggests that forcesbeyond his predilections and the demands of his patrons mayhave recommended his acceptance of the traditional view. Hehad shown an instrument for finding the time of prayers to anorthodox legalist. The man decried its use because it boreByzantine names of the months and so opened an entry forthe infidel.

Khayyam also suffered the vicissitudes of the Islamic savantfor whom good fortune, “like snow upon the desert’s dusty face,”never lasted long. Born in Khurāsa ̄n shortly after the Seljuks



conquered the province, he spent his most productive yearsserving Sultan Malik-Shāh in Isfahan. The sultan and his viziersupported an observatory, where, under Khayyam’s direction, agroup of astronomers issued their own zij. He or they alsodeveloped a new calendar with a tropical year closer by threeparts in ten million to the truth than the Gregorian rule. Theidyll ended with the death of Malik-Shāh and the assassination ofhis vizier. The new regime halted the calendar reform, beggaredthe observatory, and welcomed the orthodox, who opposedKhayyam’s Avicennan world view and poetical free thinking.The line of astronomy he represented, which sought progress inthe next place of decimals and required ongoing dependablefinancing, thus came to an end in Isfahan.

The third example, Alhazen, took the bold position, laterpushed by Averroes, that Ptolemaic astronomy had to bereworked to conform to physical principles. He seems to havebeen a man of unusual confidence, since he proposed to theFatamid Caliph al-Hakīm—the patron of Ibn Yūnus—a plan toregulate the flow of the Nile. When the plan failed, Alhazenthought it advisable to feign the insanity that his wild projectsuggested. He recovered his wits when al-Hakīm died anddirected them to optics as well as to the shortcomings ofPtolemy. Insisting that the rules of astrophysics required thatevery rotation ascribed to celestial objects had to be performedby a material shell or sphere turning with constant velocityaround its own center, and that no void could exist in theheavens, Alhazen reified all the deferents and epicycles ofmathematical astronomy as so many nested globes and mar-bles, as portrayed in Ptolemy’s Hypotheses. This produced only a


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qualitative version of a physical astronomy, as it lacked areplacement for equant motion.

The three directions of astronomy represented by al-Bīrūnī,Khayyam, and Alhazen came together briefly and dramaticallyin the work of Nasīr al-Dīn al-Tūsī. From a family of Shia jurists,al-Tūsī received a full Islamic education from several masters,including a follower of Avicenna. Political turmoil in his home-land (like Khayyam he came from Khurāsa ̄n) discouraged the lifeof the mind, so al-Tūsī accepted an invitation to work in thefastness of a tough Shia sect that specialized in murder. In thecompany of these Assassins and their grand master, “the OldMan of the Mountains,” he wrote many important tracts, someon ethics, which they certainly needed, others on logic, philoso-phy, and mathematics. After a quarter century in his unusualacademic setting, al-Tūsī upgraded to the service of a grandsonof Genghis Khan, Hūla ̄gū, who destroyed the Assassins in ,conquered Baghdad and terminated the Abbasids in , andestablished his power from the borders of the Byzantine Empireto the fringes of China.

Though a little rough, Hūla ̄gū had an interest in astronomyand astrology, and encouraged al-Tūsī to gather up manuscriptsbefore his less learned followers ate them. (Perhaps Hūlāgū owedhis civility to the Nestorian Christians, from whom his fatherhad chosen his mother and he his favorite wife.) Hūla ̄gū erectedan observatory for al-Tūsī in the new Ilkhan capital of Marāghain Azerbaijan. This institution, which Hūlāgū not only paid for(which was to be expected) but also, exceptionally, endowed,attracted several excellent astronomers, boasted a library and alibrarian, and housed several large instruments including a



mural quadrant and an armillary sphere. One of its first prod-ucts, the result of years of observation and calculation was, ofcourse, a zij. Al-Tūsī and his collaborators disliked the Ptolemaicmodels on which they had to base their calculations, and, takingtheir manifesto from the Aristotelian physica eclipsed since al-Ghazālī’s victory over Avicenna, developed new planetarymodels. This departure, imitated in the fourteenth century byIbn al-Shātir of Damascus, a liturgical technician (he kept trackof religious time), turned out to be a useful step, when, using thesame models, Copernicus took a greater stride.

Physics

With some imagination, a savant can find verses in the Qur’a ̄n(., ., .) that encourage the study of astrology andoptical phenomena. The greatest investigator of light during theIslamic Middle Ages was Alhazen. As in his astronomy, so in hisoptics but to better effect, he attempted to combine Aristotle’sphysica with geometrical models. Thus, in contrast to mostmathematicians, he ascribed vision to rays from a luminousbody entering the eye (intromission) rather that to rays fromthe eye falling on the body (extramission). He distinguishedbetween primary light (from self-luminous bodies like the Sun,planets, and fire), secondary light (from all points on an opaqueor transparent body illuminated by primary light), reflected light,and refracted light. This allowed him to state that the Moonshines by secondary, not reflected, light, which rebounds from apolished body only at the angle of incidence—a mathematicalversion of Plutarch’s description of the lunar surface.


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According to Alhazen, rays proceed rectilinearly in all direc-tions from every point on a body shining by primary or sec-ondary light. How then can all the forms and colors they bringto the eye be received without confusion? He answered that raysstriking the surface of the crystalline humor perpendicularlydominate the image. As for reflected and refracted light, hewas content to define the directions of their actions by experi-ment. He confirmed in detail the equality of the angles ofincidence (i) and reflection, and gave qualitative rules relating ito the deviation d = i� r suffered in refraction, r being the angleof refraction.

Many mathematicians who wrote on astronomy also wroteon mechanics, notably, in the Baghdad school, al-Khwārizmī,whose name inspired an English common noun (“algorithm”),and Tha ̄bit ibn Qurra, a money changer from Harrān whobecame a master of all the mathematical sciences; and, amongthe Eastern astronomers, al-Bīrūnī, Khayyam, and Avicenna.They built on Archimedes’ theories of the lever and floatingbodies, Aristotle’s concepts of weight and motion, and pseudo-Aristotle’s analysis of simple machines (Mechanica). The essentialinterest of their work lies in its comparative realism: theyendeavored, more successfully than in their astronomy, tounite the physical and the mathematical. Thus they did notneglect the weight of the beam when analyzing the equilibriumof a balance or the operation of a lever; and they invented orperfected a “balance of wisdom” with which to measure thespecific gravity of anything submersible in a liquid withoutprovoking a chemical reaction. In the case of two-componentalloys, algebraic manipulation of the measurements evinced the



percentage of the ingredients and gave a more convenient wayof detecting counterfeits than Archimedes’ method of droppingthem into his bathtub.

The most detailed account of Islamic statics and hydrodynam-ics comes in al-Kha ̄zinī’s Book of the balance of wisdom, whichincludes an extensive table of the specific gravities of metalsand minerals made by al-Bīrūnī. Al-Khāzinī, who wrote between and , was the well-educated Byzantine slave of thetreasurer of the Seljuk court at Merv in Khurāsa ̄n. He debutedin the normal fashion of court astronomers, with a zij dedica

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