Modeling the Heavens: Sphairopoiia and Ptolemy's Planetary Hypotheses

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Modeling the Heavens: Sphairopoiia and Ptolemy’s Planetary Hypotheses

Elizabeth Hamm Saint Mary’s College of California

This article investigates sphairopoiia, the art of making instruments that display the heavens, in Claudius Ptolemy’s Planetary Hypotheses. It takes up two questions: what kind of instrument does Ptolemy describe? And, could such an instrument have been constructed? I argue that Ptolemy did not propose one speciﬁc type of instrument, but instead he offered a range of possible designs, with the details to be worked out by the craftsman. Moreover, in addition to exhibiting his astronomical models and having the ability to estimate predictions, the instrument he proposed would have also shown the physical workings of the heavens. What emerges is both a clearer idea of what Ptolemy wanted the technician to build, and the purpose of such instruments.

1. Introduction Ptolemy wrote the Planetary Hypotheses for both astronomers and instrument- makers. Most studies of this text concentrate on its meaning for the former, but there remain many questions surrounding its meaning for the latter.1 This article investigates the purpose of Ptolemy’s Planetary Hypotheses in light of what he says about instrument-making. It takes up the following questions: what kind of instrument does Ptolemy describe? And, could such an instrument have been constructed? I argue that he did not have one speciﬁc design in mind, but instead he offered craftsmen options for the content, design,

Research for this article was supported by the Saint Mary’s College Faculty Development Fund. I would like to thank the anonymous reviewers from this journal for their generous comments and constructive feedback. 1. For the astronomical models in the Planetary Hypotheses see Willy Hartner 1964; Bernard R. Goldstein 1967; Otto Neugebauer 1975, pp. 900–26; N. M. Swerdlow 2005; Dennis Duke 2009; and Elizabeth Hamm 2011. Andrea Murschel discusses both the astronomical models and the implications for instrument-maker and she offers a detailed account of Book II (Murschel 1995).

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and operational methods. In addition to exhibiting his astronomical models and estimating planetary positions, the instrument Ptolemy described would have also shown the physical workings of the heavens.

2. BookIofthePlanetary Hypotheses The Planetary Hypotheses was written sometime after Ptolemy’s comprehensive and influential astronomical work, the Almagest. It offers an account of celestial motion and dimensions based on models presented in the Almagest. It includes a number of changes to the parameters and models, and it examines the structure of the heavens. The entirety of the text, except for the tables that conclude it, exists in Arabic, translated from the original Greek, and in Hebrew translated from the Arabic.2 Only the first part of Book I has survived in Greek.3 The text commences with a brief statement of what was accomplished in the Almagest, and then promptly turns to the aim of the work: Here we have taken on the task to set out the thing itself briefly, so that it can be more readily comprehended by both ourselves and by those choosing to arrange the models4 in an instrument ( ), either doing this in a more naked ( ) way by restoring each of the motions to its respective epoch by hand, or through a mechanical ( ) approach, combining the models with one another and with the motion of the whole.5 Indeed, this is not the accustomed manner of sphairopoiia ( );6 Ptolemy states that this text was written for two audiences: “both ourselves and those choosing to arrange the models in an instrument.” By “ourselves,” Ptolemy refers to astronomers like himself. The second audience includes craftsmen who wish to arrange the models from the Almagest into an instrument ( ) in one of two ways: hand operated or mechanical ( ). This instrument is not the type used to take observations, but instead one that would show his astronomical models. Ptolemy offered

2. The tables at the end of the text are lost. Murschel discusses the tables and recon- structs them (1995, pp. 52–3). For information about the Arabic and Hebrew manuscripts see J. L. Heiberg 1907, pp. ix–x, Goldstein 1967, p. 5; Regis Morelon 1993, pp. 9–10, and Elizabeth Hamm 2011, pp. 10–11. 3. For information about the Greek manuscripts see Heiberg 1907, pp. vi–x and Hamm 2011, pp. 10–11. 4. Taking to refer back to . Following Toomer, I have translated as model. For a discussion of Ptolemy’s use of this word see G. J. Toomer 1998, pp. 23–4. For a list of variations in the manuscript see Heiberg 1907, pp. 70–106. 5. Taking to refer to . Heiberg 1907, pp. 70–72. 6. Heiberg 1907, p. 70. Unless otherwise stated, all translations are my own.

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the technician choices in how to display the models, indicating that he did not have one definitive design in mind. With the first option, the manual choice, each celestial body would be moved to its appropriate position for a given date by hand. The second option, the mechanical choice, has the models connected to one another, possibly through a series of gears, so that moving certain parts of the model would drive the movement of other parts. While this initial description is brief, Ptolemy elaborated by contending that he did not want the device built in the accustomed manner of sphairopoiia. This is the only instance in Ptolemy’s extant works where the word sphairopoiia is used. Indeed, this word is used only a handful of times in the existing Greek corpus. It has several different meanings, including: making something into a ball or sphere, a branch of mechanics, or a particular astronomical device. The latter two senses are found in the works of several scientific writers and include the construction of celestial globes, armillary spheres, and other devices that displayed celestial models.7 Ptolemy is forthright about why the device he describes should not be constructed in the accustomed style of sphairopoiia: he thinks that style makes the craftsmanship, rather than the astronomical models, the object of display. After explaining that the instrument should be constructed so that each motion is returned to its starting point either manually or by combining the models to the motion of the whole mechanically, he states: Indeed, this is not the accustomed manner of sphairopoiia ( ); for this [sort of manner], apart from failing to represent the models, presents the phenomenon only, and not the underlying [reality], so that the craftsmanship ( ), and not the models, becomes the exhibit. But rather [the manner] where the different motions under our view are arranged together with the anomalies that are apparent to observers and subject to uniform and circular courses, even if it is not possible to intertwine them all in a way that is worthy of the aforementioned, but [instead] having to exhibit each [model] separately in this way. (Heiberg 1907, pp. 72–4) Ptolemy wanted the device to be built in a style where the planets’ appearances and the structures of the models were exhibited. He claimed that the traditional style of sphairopoiia accomplished the former, but not the latter. The earlier instruments, which only showed the phenomena, managed to combine the models of all of the celestial bodies into one instrument. Ptolemy wanted his instrument to show the underlying motions and the planetary positions. He had a complete mechanical instrument

7. James Evans and J. Lennart Berggren discuss this in more detail (2006, pp. 52–3). Also see Sylvia Berryman 2009, pp. 81–87.

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in mind, but he did not know if such an instrument could be built. Recognizing the challenge of building a comprehensive instrument, he offered the craftsman the option of displaying each model in a separate instrument. Although he did not give speciﬁc directions, Ptolemy intended for the text to be a resource for technicians and astronomers as indicated by the opening sentences. He did not provide a detailed design; however, he made some recommendations. He suggested that the astronomical models should be displayed as circles instead of spheres. Concerning the positions and arrangement of the circles causing the anomalies, we will apply the simpler version in respect to the method of instrument-making ( ), even if some small variations will follow ( ), and moreover we ﬁt the motions to the circles themselves, as if they are freed from the spheres that contain them ( ),8 so that we can gaze upon the visual impact of the models bare and unconcealed. (Heiberg 1907, pp. 72–5). The inner workings of each planetary model would be easily viewable, he stated, if the components of the models were displayed as circles instead of spheres. A secondary benefit to using circles instead of spheres is that such a decision would require less material, possibly making the device easier to build, and less expensive. Additionally, his willingness to sacrifice some accuracy, small variations or differences, for the sake of instrument-making shows that he accepted that making such instruments required compromises with complete accuracy.

3. Book I.B. and Book II of the Planetary Hypotheses The second half of Book I (Book I.B) and Book II cover material original to the Planetary Hypotheses, such as descriptions of the sizes and distances of the planets, the theory of nested spheres, and the physical attributes of Ptolemy’s astronomical models.9 While the topics of Book I (parts A and B) and Book II differ, the theme of instrument-making is woven through- out the entirety of the work. In Book II Ptolemy offered two different options for the structure of the heavens. Both build on his discussion of the distances of the planets in Book I.B where he explained that the furthest one planet is able to reach from the Earth is the closest the planet above it can reach (Goldstein 1967,

8. Τaking to refer back to . Greek-A: . 9. For a discussion of the textual difﬁculties in Book II see Murschel 1995, p. 37.

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pp. 5–12). The first option Ptolemy presented consisted of a series of nested spheres. The second option consisted of equatorial sections. He claimed that an entire sphere was not necessary and that all of the heavenly spheres, except for the sphere of the fixed stars, could be replaced with manshūrāt, which means “sawn-off pieces.” Ptolemy described the shapes as similar to a tambourine (duff ), belt (nit.âq), armband (siwâr), and whorl ( fulkah)(Heiberg1907,pp.113–14; Langermann 1990, 19). Ptolemy claimed that either set of structures would produce the same results (Heiberg 1907, pp. 114–15; Goldstein 1967, p. 37).10 But while he thought that both models would account for the phenomena, he claimed that nothing useless would be made in nature (Heiberg 1907, p. 118; Goldstein 1967, p. 39). Consequently, a complete sphere was not necessary when a partial sphere would suffice. This choice aligns with hisstatementsfromBookIandBookIIconcerninghiswishforthe models to be shown as circles instead of spheres, since the equatorial sections, unlike complete spheres, would give the viewer the ability to peer into the instrument and examine its inner workings (Heiberg 1907, p. 121; Goldstein 1967, p. 41).11 Moreover, although he does not say this himself, the equatorial sections would also allow the planetary latitude theories to be viewed.12 Ptolemy stated that an instrument could provide an analogy for the functions of the heavens (Heiberg 1907, p. 121; Goldstein 1967, p. 41). Likening the heavens to a celestial animal (al-h. ayawân al-falakiy), he said that each star has an animate (nafsâniy) power (Langermann 1990, p. 20). Each planet moves itself and it passes its motion to the bodies adjacent to it and, as a result, the unwinding spheres described by Aristotle in the Metaphysics would be unneccessary (1074a1–6). A working device could illustrate Ptolemy’s idea that one body’s motion can be the cause of, and coordinated with, the motion of another body and that there is no need to counteract any motions. Ptolemy briefly discussed an example of dancers in a circle holding hands or a circle of people perform- ing a weapons show. In this example the individuals are able to move in uni- son, without hindering one another. Ptolemy did not subscribe to a strictly

10. Murschel translates this as “mathematical investigation shows that there is no dif- ference between these two types that we describe” (1995, p. 51). 11. Murschel translates this as “If [an instrument maker] constructed for [the celestial motions] a model from simple circles or from things whose shapes are like tambourines in the plane of the ecliptic…then he would make [the structure and motion of the heavens] a clear and lucid matter for everybody” (1995, p. 36). 12. Ptolemy introduces a new latitude theory in the Planetary Hypotheses. For a discussion of the changes he makes from the Almagest see Swerdlow 2005.

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mechanistic explanation of heavenly motion, since he believed each planet had a soul, which moved the spheres or equatorial sections. While he did not contend that the instrument he discussed would demonstrate all the con- cepts of heavenly motion, he thought it was possible for the instrument to show one speciﬁc concept, namely that parts of his astronomical model could move in conjunction with other parts (Heiberg 1907, pp. 116–17, 120–21; Goldstein 1967, pp. 38–9, 41).

4. What Type of Instrument? What might the instrument Ptolemy wanted the craftsman to build look like, and could such an instrument have been built? There is not one direct answer to this question, since Ptolemy is not speaking about a speciﬁcinstru- ment. Instead, he has offered the craftsman options: the instrument could represent one celestial body or all of them, and it could be hand operated or mechanical. The simpler version, a hand operated device representing a single celestial body, might have resembled an early equatorium. The tables at the end of the text, which are lost, could have, in theory, been used to set the device. Such an instrument would have been used for calculation and offered a visual representation of the motion of a single body, either the sun, moon or a planet. The more complex version, where the device is driven mechanically and all of the celestial bodies are represented, requires more conjec- ture. There are examples of devices predating Ptolemy that could estimate planetary positions and offer visual displays of the heavens. Cicero described a device, attributed to Archimedes, which displayed the movements of the celestial bodies in a single device.13 The Antikythera mechanism, a device from the second century B.C., also used a series of gears to display positions of the Sun, Moon, and planets, but not models of their motions. Although we cannot directly connect Ptolemy’s instrument to these earlier examples, they attest to a tradition of constructing devices that could be used both for display and computation. When considering whether an instrument like the ones Ptolemy describes could have been built, it is important to note that Ptolemy’s other writings indicate that his interest in instruments was not a ﬂeeting one. He was well versed in the use and construction of different types of observational and musical instruments. In the Almagest he discussed instruments such as a meridian

13. In the story that Cicero recounts, Gallus describes a sphaera solida, and then brings out a newer kind of sphaera. The term sphaera solida is translation of the Greek technical term for celestial sphere, ( ). The second device is not a celestial sphere, but something quite different. Clinton Walker Keyes [1928] 1966, pp. 41–3. In De Natura Deorum Cicero mentions a sphaera constructed by Posidonius. H. Rackham 1967, pp. 206–09.

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ring, a meridian quadrant, a parallactic instrument, and an armillary sphere (Toomer 1998, pp. 61–3, 217–19, 244–47). In the Planisphaerium he described a plane astrolabe (Neugebauer 1949, p. 241). In most instances Ptol- emy provided a brief description of the instrument, an explanation of how it worked, and some details about its construction, such as necessary mate- rials and dimensions.14 Some of these instruments, like the meridan ring in Alexandria, were public objects, some he designed, such as the meta-helikôn (a musical instrument), and others he may have commissioned.15 In the Suda, a Byzantine encyclopedia, Ptolemy is reported to have written a book on mechanics.16 All this bears out that Ptolemy had experience with many different instruments, which he used, described, and designed. The different period relations that Ptolemy presented in the Planetary Hypotheses might have an explicit connection to instrument-making. Ptolemy includes two different types of period relations: simple period relations and complex period relations. The former related planetary restitutions in anomaly to Egyptian years. The latter combined several motions together into a period relation: the solar motion with respect to the equinox, the motion of the apogee, and the anomalistic motion (Duke 2009; Hamm 2011, pp. 168–177). This type of period relation was unique and Ptolemy did not explain why he decided to include it. Of course, the relations are given for long periods, to such precision, that can have no practical use in the working of the mechanical models. Evans and Carman show how the complex period relations might have been used with the pin-and-slot mechanism to exhibit planetary motion (2014, pp. 164–66). The pin-and-slot mechanism, used in the Antikythera mechanism, allowed the moon’s chang- ing speed to be displayed. By offering an explanation for the inclusion of complex period relations in the Planetary Hypotheses, they say that this “sug- gests a continuous tradition of working with pin-and-slot mechanisms at least from the time of the Antikythera mechanism (second century BC?) to Ptolemy’s own day (second century AD)” (Evans and Carman 2014, p. 165). While the use of the pin-and-slot mechanism might explain Ptolemy’sinclusion of the complex period relations in the Planetary Hypotheses, its use would contradict Ptolemy’s appeal to the craftsman to construct an instrument

14. For example, Ptolemy offered a detailed description of the armillary sphere in Book V of the Almagest. He explained the overall appearance of the instrument and how to construct it and he discussed the details, such as how he joined two rings together at diamet- rically opposite points so that the rings form right angles (Toomer 1998, pp. 217–19). 15. In the Harmonics Ptolemy discussed some musical instruments at length, such as a monochord, in the Harmonics. Andrew Barker offers a discussion of Ptolemy’s instructions for building a meta-helikôn, an unique musical instrument that Ptolemy describes (2009). 16. Suda On Line: Byzantine Lexicography at http://www.stoa.org/sol/; Evans and Carman 2014, p. 171.

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showing the underlying reality of the models. The pin-and-slot mechanism would not accomplish this goal, as Evans and Carman observe. Also, Ptolemy does not allude to the use of such a device.

5. Conclusion Ptolemy was clearly familiar with a tradition of sphairopoiia since he refers directly to such a tradition, but his comments about the instrument he describes lack detail. Although he may have included the complex period relations because he anticipated that this device would include something like the pin-and-slot mechanism, we must remember that Ptolemy suggested an instrument in principle only. He included the speciﬁc parameters for the astronomical models, and he made some recommendations for craftsmen, such as using circles or equatorial sections, but he left the design of the instrument up to the individual choosing to build it. That Ptolemy was willing to sacriﬁce some accuracy for the sake of instrument-making demonstrates the importance he placed on the physical construction of a device exhibiting his models (Heiberg 1907, pp. 72–5). While Ptolemy said that he made accommodations for the technician, his models are complicated and displaying these models would require an extremely skilled hand. The less ambitious options Ptolemy offered for the design of this instrument, where only one astronomical model was displayed and the components of the instrument could be moved by hand, would certainly have been feasible to construct, although the small incli- nations of the circles for latitude would not be easy to make or use. The more ambitious options, however, where all of the models for the celestial bodies are displayed in one comprehensive mechanical device, would have been much more challenging, if not unworkable. Aside from the questions surrounding the feasibility of constructing the different types of the instrument described, the Planetary Hypotheses attests to Ptolemy’s interest in models, both models used for computations and tangible models that represented the motions of the heavens. Additionally, the Planetary Hypotheses is an example of an astronomer speaking directly to those who build instruments that display the heavens, and it gives us insight into one astronomer’s approach to this art.

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