Claudius Ptolemy refined the Earth-centered cosmic model in the 2nd century CE.

     It is quite apparent that the Sun and Moon move regularly overhead from East to West, along with the planets and stars, giving the appearance that they go around the Earth, and ancient peoples accepted this appearance as reality. Plato held this belief, but left it up to later philosophers to work out the details because his goal was merely to interpret the heavens as an aid to spiritual belief. Aristotle followed in his footsteps, and he too left it to later philosophers to explain the evidence. With the notable exception of the Pythagoreans, early philosophers believed that a dome of stars rotates overhead daily from East to West along with the seven objects Moon, Mercury, Venus, Sun, Mars, Jupiter and Saturn, which however rotate overhead at progressively slower rates, seeming to move relative to the stars from West to East as the entire ensemble moves from East to West. The figure is a 15th-century view of this structure. 

     However, a great difficulty was that regularly five of the celestial lights--Mercury, Venus, Mars, Jupiter and Saturn--periodically retraced their their motion relative to the stars before resuming it once again. This phenomenon, known as retrograde motion, conflicted directly with the common belief that spheres, circles, and uniform circular motion were geometric and kinematic ideals, and was all the more egregious since the heavens were supposed to be perfect. Yet philosophers generally preferred to accept this appearance as reality rather than challenge their faith in the principle of circular perfection. They held steadfastly to an idea that was of human manufacture and downplayed the evidence of Nature, with the result that they regarded retrograde motion as aberrant. We know now that retrograde motion is an artifact of perception that arises from the motion of the observer, and is resolved by allowing the Earth itself to move; i.e. ancient thinkers failed to consider that they were at the center of their own perceptions and that their observing platform the Earth was itself in motion. 

     This is why in Hamlet the false king Claudius, who is named for the geocentricist Claudius Ptolemy, insists that Prince Hamlet's "retrograde" motion is "a fault to nature." Just like most ancient philosophers, Claudius thinks that Nature should take the blame for the seeming aberration, and not his own thinking. 

Nicholas Copernicus (1473-1543) placed the Sun ("Sol") at the center of the Universe.

 To Copernicus, the Earth becomes just another planet. Only our Moon retains its old geocentric rank. This arrangement distressed theologians who interpreted the displacement as an affront to holy scripture, which emphasized the central role of humanity in Creation. In fact, Copernicus withheld publication of his theory and the evidence supporting it for over 35 years "on account of the fear that [he] felt." Shakespeare characterizes king Claudius as a fanatical geocentricist willing to commit murder in order to establish a base for the old paradigm. Copernicus's book De Revolutionibus (Orbium Coelestium) (On the Revolutions (of the Planetary Orbs)) published in the year of his death, set the planets in orbit in the same direction around the Sun (which is counterclockwise when looking from the North). From the Sun outward, the planets known at the time were: Mercury, Venus, Earth, Mars, Jupiter, and Saturn. Their periods of revolution with respect to the stellar background increase in the same order, so inner planets with smaller orbits overtake slower planets with larger orbits. As they do so, observers on Earth see outer planets fall behind, seeming moving backward when seen against the backdrop of the stars. This apparent motion was -- and still is -- known as retrograde motion. In Hamlet, the false king Claudius refers to Prince Hamlet's desire to return to Wittenberg as "retrograde" to the royal couple's desires, because Wittenberg University in Germany was the first to teach Copernican heliocentricism. 

Tycho Brahe (1546-1601) combined the best of both Worlds.

The King of Denmark was so impressed with Tycho's work on the New Star of 1572, that he ceded to him a small island from which he could pursue his study of the sky. This island, Ven, is located in the Sound between Denmark and what is now Sweden. North-north-west a short distanhce away from Ven lies the town of Helsingor, from which Elsinore Castle in Hamlet takes its name. Tycho built an observatory on the island from which he made visual observations. He argued that that if the Earth revolved about the Sun as Copernicus proclaimed, then stars should appear to change their positions (i.e. to show parallax). His measurements showed they did not, so he concluded that they must be very distant. Without attempting to quantify effects of glare, visual acuity, the atmosphere, etc., he thought that the apparent angular size of stars in the sky was their real angular size, which meant that they would have to be enormous, far greater than the Sun. Moreover, he thought the Earth too ponderous to move, so he set it at rest at the center of motion of planets and a thin shell of stars. But he took seriously the fact that Mercury and Venus are always within about 45 angular degrees from the Sun and therefore were likely to orbit it, so he placed these planets along with Mars, Jupiter, and Saturn, in orbit about the Sun while it and the Moon orbited the Earth. He placed the sphere of stars not far from the most extreme position of Saturn as the cartoon on the left shows. He considered his model to be a great achievement because it was the smallest of all contemporary models and therefore conformed to another common belief that empty space served no purpose. He published his model in a book in 1588.

The bold leap to infinity of Thomas Digges (c.1546-1595)

In 1576 in a popular almanac Prognostications Everlasting published by his father Leonard, Thomas Digges made a bold leap by embedding Copernicus's Sun-centered planetary system in an infinite plenum of stars. His memorable essay, entitled (in short) A Perfit Description of the Planetary Orbes was written in vernacular English rather than Latin, which was the scholarly language of the time. Consequently, it gained wide distribution among the general public. The essay included a summary of the first chapter of Copernicus's De Revolutionibus (Orbium Coelestium) ("On the Revolutions of the Planetary Orbs"), and staunchly advocated acceptance of the Copernican hypothesis combined with boundless space filled with stars as a model of reality. The Diggesian model was a stark contrast to the old model of Earth-centered planetary orbits encased in a shell of stars. The new model required thinking beyond appearances, and upset people stuck in the old ways. In particular, poets, philosophers, and theologians who had been concerned that Copernicus had removed the Earth from the center of the Universe and so sidelined humans who were supposed to be the prime concern of the Almighty, continued to question and oppose the new paradigm. In 1996, I posited that William Shakespeare was a notable exception, as evidenced from analysis of his Hamlet.     

The Ghost and the New Star

Hamlet opens on an observing platform at Elsinor Castle, named for the Danish town of Helsingor on the Sound that separates Denmark from modern Sweden. It is about midnight on a frosty night and the guard is changing. The soldiers recall that on the previous two night a ghost that resembled Old Hamlet, the recently deceased King, appeared from the direction of "yond same star that's westward of the pole."  There are many stars lying west of the North Pole Star, but this one seems special, and in 1998, Donald Olson and colleagues identified it as the New Star of 1572. A professor at Wittenberg Universityin Germany first saw it on November 6, 1572. We know today that this object was a supernova outburst. It is known technically as SN1572 and popularly as Tycho's Star because Tycho observed it and in 1573 published a book on it. Thomas Digges observed it too. He published in 1572, and Tycho greatly admired the quality of his data. The figure on the left is from Thomas's book, and the bright star shows its location in the constellation Cassiopeia. 

The SN1572 identification leads to a chronology of act 1 based on historical records that fit the timing of events in the play. I have suggested that Shakespeare elected to have SN 1572 erupt on All Souls' Day, November 3, 1572, at 1 a.m., three days before its first sighting. Geographical longitudes were well enough known for the bard to know that Helsingor's time is not quite 1 hour ahead of time in England, where the ghost appears shortly after midnight, i.e. at the start of All Souls' Day. This is the first hint that the ghost has something to do with England, even though the play is set in Denmark. All Souls' Day commemorates the souls of faithfully departed Christians, and Old Hamlet has just been murdered. Since Hamlet represents Thomas Digges, his father Leonard represents Hamlet's father, and indeed, according to Thomas, his father died in 1571! Also, when the play opens on November 6, the soldiers have a hard time recognizing one another because it is dark. We now know the reason--the Moon was New and below the horizon. The Ghost of Old Hamlet tells his son that Claudius murdered him, and since Claudius represents the old geocentric paradigm and murders the father of the new paradigm, we wonder whether Leonard plays an important sub-textual role. After the ghost leaves, Hamlet and Marcellus exchange greetings as if they were falconers, which is odd and associates the Ghost with the falcon of philosophy, Leonard Digges.

Rosencrantz and Guildenstern

The usurper King prevented Hamlet from returning to the University of Wittenberg, and to please Hamlet's mother who is now his wife, he endeavors to cure Hamlet of what he perceives as "madness." This diagnosis appears to involve melancholia, so to cheer him up, the King summons two of the Prince's childhood friends, Rosencrantz and Guildenstern, who he says are "neighboured to his youth," i.e. they are about his age. Rosencrantz and Guildenstern are two courtiers who between them represent the two components that comprise Tycho's hybrid model, and Hamlet represents Thomas Digges, who was born within a year of Tycho in about 1546.

Tycho was a vain individual and is possibly the most artistically depicted astronomer of all time. In 1586, on the occasion of his fortieth birthday, an engraver portrayed him framed by pillars and an arch, as shown on the right. The structure bore the family shields of his 16 great-great-grandparents, with those of the males on the arch, supported by pillars bearing those of the females. The shields of Eric Rosencrantz and Sophie Guildenstern are in leading positions on Tycho's right.  The engraving has errors, which were corrected in a second portrait, shown below, yet in so doing, the engraver committed other errors. In the first portrait, the lighting comes from the left, but in the second portrait, it comes from both left and right.   

Yet the most egregious error is one found in both engravings. When a hand rests on a flat surface, the thumb can bend roughly in the plane of the surface, but Tycho's hands in both cases show his fifth (little) finger bending as if it were a thumb. In the first depiction Tycho's right hand is deformed, in the second depiction the left hand is deformed, and in both cases the other hand clutching gloves appears deformed too. Each hand is attached to wrong arm, so the hands appear to be swapped. No other depiction shows the same feature and when Tycho's remains were exhumed in 1901, no digital deformity was reported. The engraver based his depictions on a sketch by an artist Tobias Gemperle employed at Tycho's astronomical observatory, who once had illustrated a book on human physiology and is unlikely to have erred unintentionally. Tycho had an abrasive personality and probably the  artist was pulling his leg, but Tycho evidently was not aware of it. In 1590, Tycho sent to a leading English scholar, copies of his 1588 book along with four copies of the second engraving. He requested that one of the books be sent to Thomas Digges, and that an English poet pen an encomium in his honor. Tycho's engraving must have accompanied the gifted book because Thomas's son Dudley had a copy. No-one knows what became of the other copies, but heretofore it has appeared that no English poet obliged Tycho with paeans of praise. However, the present cosmic allegorical interpretation of Hamlet shows that Shakespeare refers to Tycho's portrait on multiple occasions, but the most informative is what Hamlet says on meeting Rosencrantz and Guildenstern. What he says before the arrival of the acting troupe, whom Claudius had hired to cheer him up and cure him of his Diggesian proclivities, is further evidence.

Hamlet's transformation

Claudius welcomes his two allies Rosencrantz and Guildenstern by informing them of "Hamlet's transformation." He explains, "nor th'exterior nor the inward man / Resembles that it was," which means that the Diggesian model (a.k.a. Hamlet) has a new planetary system and infinite space, replacing the bounded geocentric model of Claudius Ptolemy. The courtiers' job is to restore Hamlet to his senses. After Hamlet meets the courtiers, they are soon at odds. Hamlet knows why they are at Elsinore and who summoned them, and says, "I could be bounded by a nutshell and count myself the king of infinite space, were it not that I have bad dreams. The "nutshell" represents the shell of stars bounding Tycho's tiny Universe, where a nut is something of trifling value. Thus, even if Hamlet were to live in such a place, he could still proclaim belief in infinite space except that he would be afraid to do so. After all, in 1600, Giordano Bruno was burned at the stake for a similar belief that he espoused 8 years after Digges published his. 

Ven's location

Hamlet ends his direct interaction with the courtiers by saying, "I am but mad north-north-west. When the wind is southerly, I know a hawk from a handsaw." At the time, "wind" was synonymous with "direction," so the Prince speaks of a location for which NNW and S are relevant. Tycho's island observatory fits. Elsinore (a.k.a. Kronberg) Castle in Helsingor is NNW of Ven, and Wittenberg University is S of Ven. The former is the bastion of bounded geocentricism, the latter the site of the first lectures on heliocentricism. Hamlet is "mad" (disgruntled, upset) when he thinks of the former, but he know's what's what (knows a hawk from a handsaw) when he contemplates the latter. The two winds blowing onto Ven are the influences on Tycho's hybrid model of a stationary Earth and the bounding shell of stars as in the Copernican model. Yet, not much wit is needed to distinguish a bird from a carpenter's tool, and the young Hamlet, who has attended Wittenberg University, is surely more able than that. 

Hawk and handaw

"Handsaw is a corruption of "hernshaw," a type of heron, but still, these two birds are readily distinguished. Perhaps Shakespeare is writing metaphorically. Hamlet has just finished referring to Tycho's appearance in the engraving with its medallion and extravagant dress ("appurtenance," "fashion," "garb," "show"). Hamlet has ended his dialogue by referring to Tycho's upbringing; "uncle-father" and "aunt-mother" refer to Tycho's childhood adoption by his uncle and aunt, so perhaps "hand-saw" refers to the engraver's artistic tool by which he severed and swapped Tycho's hands. Shakespeare compares the superior vision of a hawk (about 10-times better than a human's) to Tycho's visual observing. Shakespeare compares the observing capabilities of Tycho to one whose acuity is 10 times better, which is possible only with optical aid. Possibly, Shakespeare compares Tycho to Leonard Digges who developed a telescope. Doubt is suspended when we recall that a leonard is a type of hawk.

Phases of Venus

If Shakespeare intends a subtext about the superior discriminatory power of a telescope, surely he would provide evidence for it. Ophelia is at the docks bidding farewell to her brother Laertes, when he regales her with a flood of advice on her relationship to Hamlet. He starts with, "nature crescent does not grow alone / ... but as this temple waxes / The inward service of the mind and soul / Grows wide withal." I know of only one editor who believes that Laertes is speaking metaphorically of the Moon, which indeed does behave in the manner described. Rather, since the context is love, the conceits refer to Venus, who is the mythical goddess of Love. The inference is that planet Venus passes through phases like the Moon, which does occur as it orbits the Sun, as shown. While a few people can see the larger crescent phases, telescopic magnification is needed to see the smaller images with phases growing "wide."

Craters on the Moon

The Moon is the mythical goddess of Chastity, which Laertes introduces by warning Ophelia not to open her "chaste treasure" to Hamlet's "unmastered importunity." Laertes urges her not to "unmask her beauty to the moon," and to keep out "of the shot and danger of desire." He refers to lunar craters by warning that virtue (i.e. the virtue of chastity) "scapes not calumnious strokes." In another conceit, he refers again to lunar craters and possibly also to the lesions of syphilis. "The canker galls the infants of the spring / Too oft before their buttons be disclosed / And in the morn and liquid dew of youth / Contagious blastments are most immanent." Cankers on plants are lesions of circular shape and with raised edges resembling craters formed by projectile impact. Lunar craters are widespread, just like the syphilis contagion against which chastity was then the only defense. Lunar craters are not far away, and visible only telescopically. 

Mars and Jupiter

After the death of Old Hamlet, his wife married his brother Claudius, whom young Hamlet knows to have murdered his father. Hamlet has occasion to berate his mother for what is culturally regarded as an incestuous marriage. He asks her to look upon Old Hamlet's picture and "See what a grace was seated on [his] brow; / Hyperion's curls, the front of Jove himself, / An eye like Mars, to threaten and command." It is reasonable to think that Hamlet identifies his father, for he uses the past tense ("was seated") and likens him to the deity Jupiter who threatens and commands, like a King. Jupiter has an "eye like Mars," not "an eye like Mars' [eye]." Hamlet refers to two planets: Mars is resolved into a disk, and Jupiter has an "eye" that resembles it. A likely explanation is that the eye is Jupiter's Great Red Spot, and since Jupiter rotates once every 10 hours, the "eye" seems to blink. Mars, Jupiter and the Great Red Spot can be resolved only telescopically.     

Mars and Jupiter resolved, and how Shakespeare acquired his data.

          The ability to discern the surfaces of Mars and Jupiter leads to an important conclusion: the observer would see that these planets are always gibbous in appearance, never crescent, which disproves all geocentric models. (In those cases, the Sun and the two planets would orbit the Earth at different rates and thus would show all phases). Rather, the planets orbit the Sun and since their orbits lie outside the Earth's, we humans see their disks fully or nearly fully illuminated. These empirical data prove heliocentricism! (Having Mercury and Venus revolve about the Sun as in Tycho's model only supports heliocentricism for those two planets.)

          Copernicus entitled his magnum opus "On the Revolutions (of the Celestial Orbs)", and in act 5, scene 1, Hamlet explains the connection. He says:

                                "Here's fine revolution and we had the trick to see it."

He refers to the Sun-centered revolution of the planets, and even more importantly, he tells how the data were acquired. The primary meaning of "trick" dates to the fifteenth century and means "a crafty or fraudulent device," a "contrivance or invention." Prior to the more widespread use of telescopes, optical devices were often used to deceive people and were regarded as fraudulent, so Shakespeare's use of "trick" is apt, but he tells us that he used such a contrivance or invention to prove the Copernican "revolution." 

          Furthermore, he follows this with elaborate arithmetic that shows that Hamlet is 30 years old. As we have posited, Hamlet stands for the Diggesian model, and Thomas Digges was born in about 1546. Adding 30 gives the year 1576, which is the very year that Thomas's essay on the infinite Universe appeared! The conclusion seems inescapable, that Thomas and his father Leonard, developer of the Perspective Glass telescope, knew these results before 1576. An earlier date of 1572 follows from Thomas's first book entitled (in translation), Mathematical Wings and Ladders. "Wings" refers to the capacity of a leonard to attain heights, and "Ladders" refers to the means to access the prime focus of his telescope, whose design was probably a reflector and a precursor to the Herschelian design. This is evidence too that in 1572, Leonard was not deceased as his son had announced the year before, and further evidence of the well-known thorough mixing of the work of both Diggeses. For further evidence for early sixteenth-century telescopy, see Shakespeare and Saturn: Accounting for Appearances.

The sky is falling

Shakespeare conflates a millennia-old tale with Elizabethan social hierarchy to satirize the threat to the old cosmic order. In that worldview, the Earth is the center of everything just as a monarch is the center of society and head of the state religion. In the conceit, all subjects, civil, ecclesiastical, or cosmic, revolve about this center, and if it is at risk, entire structures that depend on it, are too. The geocentric King Claudius fears the threat posed by upstart heliocentricism and its Diggesian extension to a sky of infinite extent. His geocentric ally Guildenstern says: "Most holy and religious fear it is / To keep those many many bodies safe / That live and feed upon your majesty," and his twin Rosencrantz worries that: "The cess of majesty / Dies not alone...It is a massy wheel...To whose huge spokes ten thousand lesser things / Are mortised and joined." Rosencrantz likens Claudius to the center of the Ptolemaic machinery with its massive invisible cogs and wheels. If the King loses his position, 10,000 "lesser things" come crashing down as well. These 10,000 lesser things represent the number of visible stars in the sky, a number that surprisingly is correct to half an order of magnitude (6,000 is a closer estimate). [Image: S. Molau and P. Jenniskens, NASA Ames Research Center.]

Milky Way

 The travelling thespians arrive and Hamlet tests them. A player recites a poem about the savagery of Pyrrhus that made "milch the burning eyes of heaven." The player refers to brutality that brings tears to the eyes and blurs eyesight. Thus the sharp images of stars take on a milky appearance, and conversely, when sharp vision replaces blurry vision, poorly resolved images no longer overlap and the milky appearance disappears. At the turn of the 13th century, Roger Bacon reported that with the help of optical magnification, the Milky Way could be resolved into discreet stars, and at about the same time Bartholomeus Anglicus knew this too. Shakespeare echoes the result.  


 A digger unearths three skulls. The third is that of Yorick, a name that is a variation of George. It is named for  Georg Rheticus, the first Copernican who in 1550 predicted times of planetary positions (ephemerides). The script has many clues to Yorick's abstract identity. The first skull is Erasmus Rheinhold's who calculated ephemerides in 1551 but was not a heliocentricist. The second skull is a lawyer's, and Leonard Digges was trained as one. He was a man of "infinite jest" and a good daddy, where "Infinite jest" conflates his sense of humor and recalls his son's report on infinite space. Leonard needed and must have calculated ephemerides, and Yorick represents these three early computers.  

Harriot, Fortinbras

Hamlet systematically associates attributes of the courtier Osric that also pertain to the life and accomplishments of Thomas Harriot. Harriot wrote about the New World in 1588, drew pictures of the Moon in 1609,  and his mathematical research was published posthumously. Hamlet ridicules the paucity of Harriot's publications and in the process resumes his parody of Tycho's portraits. 

Fortinbras invades Poland "to gain a little patch of ground" which "the Polock never will defend" and which is unsuited for agriculture. It is Copernicus's grave, which the Polish mathematician cannot defend because he is in it. Fortinbras "gains" heliocentricism and returns to Denmark, but instead of saluting the Danes, he salutes the English ambassadors. This unifies the (Polish) Copernican and (English) Diggesian components of the New Worldview. Hamlet arranged for the English to kill Rosencrantz and Guildenstern, and he himself kills Claudius. Bounded geocentricism perishes, and although Hamlet dies, the New Philosophy prospers.