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 esti- mate predictions, the instrument he proposed would have also shown the phys- ical 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 instru- ment 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 astro- nomical models and the implications for instrument-maker and she offers a detailed account of Book II (Murschel 1995). Perspectives on Science 2016, vol. 24, no. 4 ©2016 by The Massachusetts Institute of Technology doi:10.1162/POSC_a_00214 416 Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/POSC_a_00214 by guest on 30 September 2021 Perspectives on Science 417 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 comprehen- sive 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 instru- ment ( ) 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. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/POSC_a_00214 by guest on 30 September 2021 418 Modeling the Heavens 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 some- thing 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 mo- tions 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. Downloaded from http://www.mitpressjournals.org/doi/pdf/10.1162/POSC_a_00214 by guest on 30 September 2021 Perspectives on Science 419 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.