Looking up to the starsOn the Shoulders of Giants: The Great Works of Physics and Astronomyedited, with commentary and introduction,by Stephen Hawking Running Press: 2002. 1,266 pp. £20, $29.95

Owen Gingerich

I am in two minds about this hefty tome.Should I be embarrassed for Stephen Hawk-ing because an enterprising publisher hasinveigled him into putting his name to a collection of superseded texts? Or should I be outraged that an eminent scientist, butone with no track record in the history of sci-ence, has the arrogance to endorse historicalintroductions for five classics of science?

On the Shoulders of Giants comprisesEnglish versions of texts from five distin-guished cosmologists — Copernicus, Galileo,Kepler, Newton and Einstein — each precededby a 6–8-page commentary on the life andwork of the author. Included in these texts

are Copernicus’ paean to the heliocentricsystem, Galileo’s formulation of projectilemotion, Kepler’s harmonic law, Newton’slaw of gravitation, and Einstein’s equationE4mc 2. However, these key passages are nothighlighted: they are buried in long, tech-nical treatises with no clue as to where tolocate them. Neither will you find Galileo’sarguments for a heliocentric system, norKepler’s law of areas or ellipses, because theappropriate texts are not included.

Each translation has apparently beenchosen for its easy availability, and each now has a more nuanced version currently in print elsewhere. Take Newton’s Principia, for example. For years the standard Englishversion was Florian Cajori’s modernizationof Andrew Motte’s 1729 translation. Withthe appearance of I. B. Cohen’s magisterialtranslation in 1999, the University of Cali-fornia Press withdrew Cajori’s version. OnThe Shoulders of Giants reverts back toMotte’s dated translation.

The choice of Galileo’s text, here titled‘Dialogues Concerning Two Sciences’, is particularly curious. Modern scholars call the book Discourses or Two New Sciences todistinguish it from his Dialogue on the Two

Great World Systems, which was Galileo’s classic defence of heliocentric cosmology that got him into trouble with the Inquisition.The dust-jacket mentions that one of the texts included was considered so “dangerous”that its author was accused of heresy, as if the Dialogue on the Two Great World Systemswere found here. This also seems to be whatHawking expected, because in his introduc-tion he writes: “In Dialogues Concerning TwoSciences, Galileo’s characters, Salviati andSagredo, put forward persuasive argumentsin support of Copernicus.” So they do in theDialogue on the Two Great World Systems, but this work is not included here.

Kepler’s Harmonices mundi libri V is anespecially inept selection. This fifth bookdoes include a splendid nugget — Kepler’smathematical relationship between the cube of the planet’s distance from the Sunand the square of its period — but it is anidiosyncratic work, here presented entirelyout of context. And its title is erroneouslytranslated as ‘Harmonies of the World’. Harmonices looks like a Latin plural, butKepler used a Greek genitive singular end-ing, because, as a great unifier, he believed in a singular ‘Harmony of the World’.

Kepler’s Astronomia nova ranks besideCopernicus’ De revolutionibus and Newton’sPrincipia in the triumvirate of technicallandmarks in the scientific revolution, butit’s not here. And it would have been aredeeming achievement to have includedWilliam Donahue’s scarce translation ofKepler’s New Astronomy in this collectioninstead of part of Harmony of the World.

The commentaries on each author containcongenial anecdotes, some accurate historicaldata, and a dose of modern mythology.Unfortunately, the opening vignette is lit-tered with errors. Hawking stumbles in thevery first line, calling Copernicus a priest,which he most surely was not, although hewas a canon and legal officer at Frauenburgcathedral. Hawking is in good companyhere, because Galileo also described Coper-nicus as a priest, but Galileo had propagan-distic reasons that Hawking lacks.

According to Hawking, Aristotle arguedthat the Earth was round because hulls ofships sailing out to sea disappeared over thehorizon before the sails. The argument wasmade by Ptolemy half a millennium later, butnot by Aristotle. Hawking’s introduction alsosays that Western Christendom placed Hellbeyond the stars; that Copernicus became aprofessor of astronomy at Bologna; that hecompleted De revolutionibus in 1530; thatRheticus relinquished a chair in mathemat-ics at Wittenberg to study under Copernicus;that Copernicus used equants to account for the motion of the Earth; that Osianderplaced the word ‘hypothesis’ on the title pageof Copernicus’ book; and that the world hadscarcely become known to be round whenCopernicus wrote. None of this is true. No

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While out walking in the Florida Everglades,wildlife painter Robert Bateman saw a flash ofpink. Closer inspection revealed it to be a groupof roseate spoonbills, swinging their heads from side to side as they fed on crustaceans.

The resulting painting (above) is one of 200 new works in his book Birds (Pantheon, $40).The paintings are accompanied by shortaccounts of Bateman’s adventures as he soughtout his subjects in their natural environments.

A brush with nature

© 2003 Nature Publishing Group

bibliography is provided, so it is difficult toascertain the source of this disaster. Fortu-nately the other introductions are not as bad:the Kepler introduction benefits from usingthe Dictionary of Scientific Biography as itsunacknowledged source, for example.

The most interesting part of this book isthe general introduction; this is quintessen-tial and thoughtful Hawking, clearly carryinghis own stamp. He writes about the anthropicprinciple: “If the ultimate theory made aunique prediction for the state of the universeand its contents, it would be a remarkablecoincidence that this state was in the smallsubset that allows life.” It is almost worth theprice of the book to get this quotation. ■

Owen Gingerich is at the Harvard-SmithsonianCenter for Astrophysics, 60 Garden Street,Cambridge, Massachusetts 02138, USA.

A trick of themoonlightThe Mystery of the Moon Illusion by Helen Ross & Cornelis Plug Oxford University Press: 2002. 277 pp.£29.95, £45

Maurice Hershenson

When the Moon is near the horizon itappears to be larger and closer than when it is high in the sky. Yet light reflected from theMoon to the eye of an observer on Earth provides the same stimulus, regardless of the elevation of the Moon. This phenomenonis known as the ‘Moon illusion’. A similarillusion is observed for the setting Sun andfor celestial distances between star points atdifferent elevations.

The Moon illusion is arguably the oldestunsolved problem in modern science. It ismentioned in cuneiform script on claytablets from the royal library of Nineveh andBabylon, dating from before the sixth centuryBC, and in a collection of Chinese legendsascribed to the Taoist philosopher Lieh-tzu,dating from the fifth century BC.

Until the past hundred years or so, theillusion was thought to be a consequence ofphysical processes. For example, Aristotle (in the third century BC) and Ptolemy (in thesecond century AD) incorrectly attributed theillusion to the magnifying properties of theatmosphere, and Alhazen (Ibn al-Haytham)related the illusion to the flattened appear-ance of the dome of the sky.

Throughout its long history, the illusionhas been considered by many of the leadingscientists and mathematicians of their day:da Vinci, Kepler, Descartes, Huyghens, Eulerand Reimann, to name but a few. In The Mystery of the Moon Illusion, Helen Ross and Cornelis Plug carefully guide us throughthe history of explanations of the illusion,

treating in turn each aspect of the stimulussituation and its context.

Over the past century it has become clearthat the Moon illusion is psychological, aconsequence of the processes that underlievisual perception. Unfortunately, the authorsdo not provide as clear a picture of the treatment of modern explanations, perhapsbecause there is little agreement among current workers. For example, many mod-ern explanations invoke the size–distanceinvariance hypothesis (SDIH), by which thestimulus (measured as the angular subtenseof the light reaching the eye, or the visualangle) determines how large an object looks(its perceived size) and how far it appears tobe from an observer (its perceived distance).The hypothesis is embodied in a psycho-physical equation relating the physical stimulus (input of the visual angle) to theratio of perceived size to perceived distance.Some theorists treat the SDIH as a funda-mental law of visual perception. Indeed, it is this relationship that makes the Moonillusion such a puzzle, because it requiresthat the Moon looks farther away if it appearslarger, and smaller if it appears closer. This is also why the illusion has sometimes beensaid to be paradoxical.

Modern explanations of the Moon illu-sion propose major changes in the form ofthe SDIH. For example, Walter C. Gogel andDavis L. Mertz retain the traditional formbut allow perceived distance to be referencedsimultaneously by different behaviouralresponses. Thus, the Moon may actuallyappear more distant to people who say: “The Moon looks close.” Lloyd Kaufman andIrvin Rock’s explanation is similar exceptthat they do not include perceived distancein their formulation. Instead, they suggestthat ‘registered distance’ (information about distance) enters the SDIH to determine perceived size. This approach alters the

relationship because distance is now input information, rather than distance percep-tion being output. Verbal statements aboutthe perceived distance of the Moon aredescribed as inferences based on perceivedsize, rather than descriptions of experience:“The Moon looks big so it must be close.”

Don McCready altered the SDIH evenmore by substituting a perceptual outcome(the perceived visual angle) for the stimulusinput (the visual angle). This proposed relationship is not just another form of the traditional psychophysical formulation, buta purely psychological relationship.

Finally, in my own explanation, the SDIHbecomes a special case of a more generalmechanism — a kinetic SDIH — that gov-erns the perception of rigid object motionsin depth. This mechanism automaticallytransforms changing stimulus inputs intoobjects that appear to be rigid but moving inthree-dimensional space. When the stimulusdoes not change, as in the Moon illusion, theperceived distance of the object is deter-mined by contextual stimulus informa-tion, such as the ground and horizon. Theperceived size of the object is determined by distance information processed by themechanism that produces rigid objectmotions. In this case, an object that appearsclose in distance, such as the Moon at thehorizon, is made to appear large in size.

Despite the vast history of research into theMoon illusion, so ably reviewed by Ross andPlug, there is still no single explanation uponwhich even a handful of workers agree. I amleft to conclude, as I did in 1989, that moreresearch is needed, but not on the Moon illu-sion. An explanation of that heavenly para-dox will be obvious once our understandingof visual space perception is clear. ■

Maurice Hershenson is in the Department ofPsychology, Brandeis University, Waltham,Massachusetts 02254, USA.

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Moonrise over the savannah: but just why does the Moon appear larger when it is near the horizon?

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