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Figure 3.1:

Modeling the Cosmos – Developing a Digital Research Environment for the Computational History of Ancient Astronomy

(© Ido Yavetz & Luca Beisel)

Modeling the Cosmos – Developing a Digital Research Environment for the Computational History of Ancient Astronomy

Ido Yavetz & Luca Beisel (Tel Aviv, Israel)

Abstract

We are developing a digital tool for the simulation of pre-modern astronomical models. The software will enable the visualization and reconstruction of homocentric and epicyclic astronomical models and the study of their dynamics in an interactive virtual environment.

Zusammenfassung:

Modellierung des Kosmos – Entwicklung einer digitalen Forschungsumgebung für die computergestützte historische Astronomie der Antike

Wir entwickeln ein digitales Werkzeug für die Simulation von vor-modernen astronomischen Modellen. Die Software wird die Visualisierung und Rekonstruktion von homozentrischen und epizyklischen astronomischen Modellen und die Untersuchung ihrer Dynamik in einer interaktiven virtuellen Umgebung ermöglichen.

3.1 Background: Ancient Astronomy and the Question of Visualization

In his commentary on Aristotle’s De Caelo from the sixth century CE, the philosopher Simplicius declares the explanation of planetary motion the central task for ancient Greek astronomy:

“Plato lays down the principle that the heavenly bodies ’ motion is circular, uniform, and constantly regular. Thereupon he sets the mathematicians the following problem: what circular motions, uniform and perfectly regular, are to be admitted as hypotheses so that it might be possible to save the appearances presented by the planets?” ¹

Eudoxos in the 4^th century BC first developed a theoretical model to account for the motion of the heavenly bodies, as the superposition of mutually inclined, nested spheres, that rotate uniformly around a common center. As simple as the underlying mathematics of the Eudoxan model seem to be, the nested rotations of the spheres and the traces the modeled planets produce prove extremely difficult to grasp from verbal descriptions of the model and static illustrations alone. The moving geometry requires visualization to become evident, a fact that the ancients were very well aware of. Plato himself pointed to the need of visual representations to demonstrate the intricate dynamics of the models of geometric astronomy:

“Vain would be the attempt to tell all the figures of [the planets] circling as in dance, and their juxtapositions, and the return of them in their revolutions upon themselves, […] - to attempt to tell of all this without a visible representation of the heavenly system would be labour in vain.” ²

A geometrical reconstruction and visualization of the theoretical models of premodern astronomy is inseparably linked to the understanding of their epistemic context and significance. Newly available simulation software makes possible a new route for analysis and representation of theoretical astronomy from the days of Aristotle to Tycho Brahe. Key concepts that underscore the new approach are interactivity and real-time 3D rendering, coming together in encompassing virtual environments. In our project, we are developing such a platform for the computational history of astronomy.

3.2 Project Description

3.2.1 Overview

Figure 3.2:

Screenshot of our prototype showing Ptolemy’s model for the planet Mars (blue trace), presented next to real observational data for the retrogression of Mars (red trace).

We are developing an encompassing digital research environment for the history of pre-modern astronomy. Our software aims to fulfill two purposes.

• Firstly, it will serve as a platform for original research in the history of astronomy by providing researchers with a set of building blocks to put together pre-modern astronomical systems from their verbal and diagrammatic descriptions and thus interactively explore the options and constraints of the historic sources (Fig. 3.2).

• Secondly, it is a novel endeavor in educational technology, enabling the academic teaching and studying of the history of astronomy by means of interactive visualizations.

3.2.2 Technology

We are developing the virtual planetarium in the C# programming language on the Unity real-time development platform. Unity is an innovative and ambitious runtime environment, originally designed for the creation of computer games, but recently broadening the scope to become an all-encompassing framework for real-time interactive 3D content. With its competence in interactive simulations and cross-platform deployment, Unity in recent years has proven to be an excellent technological framework for the field of archaeoastronomy.³

Another great benefit, which will be of great use at a more advanced stage of our project is Unity’s competence in Virtual and Augmented Reality technology. Under the hood, our planetarium can already be displayed in VR, eventually leading to encompassing room-scale experiences of the models, for example in public-facing exhibitions.

3.2.3 Stage of Development

Development of the virtual planetarium has begun in January 2018 at the Cohn Institute for the History and Philosophy of Science at Tel Aviv University. In the final stage, the software will feature the following models:

• the Homocentric Spheres of Eudoxos (in their reconstructions by Schiaparelli⁴ and Yavetz⁵)

• the Homocentric Spheres of Kallippos (also reconstr. Schiparalli and Yavetz)

• the eccentric model of the Sun by Hipparcos⁶

• the lunar, solar, and planetary models from Ptolemy’s Almagest⁷ and Planetary Hypotheses.⁸

3.2.4 Functionality

Unlike many previous endeavors to visualize ancient planetary models, our models are fully modular and interactive (Fig. 3.2). This means that all of the dynamic parameters of the geometrical elements (rotation, inclination, etc.) are exposed and changeable.

Our software presents the theoretical planet model next to its real-world counterpart, which moves according to observational data. For this we parse planet ephemeris tables from NASA and Caltech’s HORIZONS web-interface.⁹

Such functionality of visualizing historic planetary models and comparing them to observational data in order to study discrepancy, has to our knowledge, never before been brought together in a unified environment.

3.2.5 User Interface

Our modern user interface (Fig. 3.3) aims to provide a well-arranged and intuitive control of the program on all levels of involvement.

Figure 3.3:

User Interface of the Virtual Planetarium

1. Model selection dropdown

2. Slideshow controls, allowing the navigation through a series of models or presentation slides

3. Undo all changes to the current model and revert it to the original parameters

4. Toggle chart/night Mode

5. Camera Angle Toggle (third person view, earthly observer view, top view)

6. Parameter menu

7. Numerical input field for parameter value

8. Numerical slider for parameter value

9. ±step buttons for parameter value

10. Deactivate parameter

11. Legend

12. Hyperlinked legend entry

13. Calibrations menu (allows adjustments of e. g. the playback speed)

14. Calendar

15. Calendar controls (Reset, Step Back, Play Backwards, Play Forwards, Step Forward)

16. Planet coordinate display

17. Divergence Interface, showing the deviation between two planets

18. Appearances menu (allows adjustments of e. g. the opacity of different elements)

3.2.6 The virtual planetarium as a tool for study and teaching

In addition to its research use, the planetarium is also conceived to be a productive tool for self-study, course-accompanying study and in-class demonstrations in the history of astronomy. An important feature in this regard is our interactive slideshow interface (Fig. 3.4), in which the textual mention of a celestial feature is hyperlinked to its visual representation, allowing for very evident interactive explanations and demonstrations. We imagine this functionality to serve as the base for prospective full-fledged classes on different subject matters in the history of astronomy which could be taken or hosted from inside the software.

Figure 3.4:

The interactive slideshow interface of the planetarium

3.2.7 The virtual planetarium as a tool for original research

As a first example for the potential of the planetarium for original research, we chose to continue Ido Yavetz’ line of study into alternative configurations of the homocentric theory.¹⁰

In this work, Yavetz argued generally that the homocentric models of Eudoxos and Kallippos prioritize the geometrical form of planetary paths relative to the fixed stars, at the expense of the planets’ temporal behavior. Revisiting Yavetz’ reconstruction from 1998¹¹ with the prototype presented here, we were able easily to specify and demonstrate the extent of the model’s temporal inadequacy beyond his 1998 analysis (Fig. 3.5).

A new tool brings about new discoveries. Once completed, we expect the virtual planetarium to facilitate relevant contributions to current debates in the history of astronomy, such as a refinement of the error margins of the Ptolemaic models, the resurgence of homocentric astronomy in Bologna and Al-Andalus¹² and the performance of Tycho Brahe’s models.

Figure 3.5:

Reconstructing Yavetz’ 1998 interpretation of the Kallippos model with the planetarium prototype

Left: The planet model (blue) against real Mars (red) from a terrestrial observer’s viewpoint.

Right: The simulation at a later date. Note the close agreement between the path traces of the modeled planet and real Mars and the large discrepancy between the location in time.

3.2.8 Additional Screenshots

Figure 3.6:

The Zodiac and the planets moving according to NASA ephemerides

3.3 Bibliography

DI BONO, MARIO: Copernicus, Amico, Fracastoro and Ṭūsī’s Device: Observations on the Use and Transmission of a Model. In: Journal for the History of Astronomy 26 (1995), 2, pp. 133–154.

DUHEM, PIERRE: To Save the Phenomena. An Essay on the Idea of Physical Theory from Plato to Galileo. Chicago 1969.

FELDHAY, RIVKA & F. JAMIL RAGEP (eds.): Before Copernicus. The Cultures and Contexts of Scientific Learning in the Fifteenth Century. Montreal 2017.

Figure 3.7:

The Homocentric Spheres of Eudoxos

(Reconstruction Schiaparelli)

FRISCHER, BERNARD & JOHN FILLWALK: A computer simulation to test the Buchner thesis: The relationship of the Ara Pacis and the meridian in the Campus Martius, Rome. In: Digital Heritage International Congress (DigitalHeritage) (2013), pp. 341–345.

FRISCHER, BERNARD; ZOTTI, GEORG; MARI, ZACCARIA & GIUSEPPINA CAPRIOTTI VITTOZZI: Archaeoastronomical experiments supported by virtual simulation environments: Celestial alignments in the Antinoeion at Hadrian’s Villa (Tivoli, Italy). In: Digital Applications in Archaeology and Cultural Heritage (DAACH) (2016), pp. 55–79.

FRISCHER, BERNARD ET AL.: New Light on the Relationship between the Montecitorio Obelisk and Ara Pacis of Augustus. In: Studies in Digital Heritage 1 (2017), No. 1.

GOLDSTEIN, BERNARD R.: The Arabic Version of Ptolemy’s Planetary Hypotheses. In: Transactions of the American Philosophical Society 57 (1967), No. 4, pp. 3–55.

NAHMIAS, JOSEPH IBN: The Light of the World. Astronomy in al-Andalus. Translated by Robert G. Morrison. Berkeley 2016.

PLATO: Timaeus, 40. Translated by Jowett.

PTOLEMAEUS, CLAUDIUS: Ptolemy’s Almagest. Ed. by CLAUDIUS; G. J. TOOMER. London 1984.

SCHIAPARELLI, GIOVANNI VIRGINIO: Die Vorläufer des Copernicus im Alterthum. Historische Untersuchungen. Leipzig 1876.

Figure 3.8:

Ptolemy’s Moon Model from the Almagest, including Umbra and Penumbra to visualize lunar eclipses.

YAVETZ, IDO: On the Homocentric Spheres of Eudoxus. In: Archive for the History of Exact Sciences 52 (1998), pp. 221–278.

YAVETZ, IDO: A New Role for the Hippopede of Eudoxus. In: Archive for the History of Exact Sciences 56 (2001), pp. 69–93.

YAVETZ, IDO: On Simplicius’ Testimony Regarding Eudoxan Lunar Theory. In: Science in Context 16 (2003), pp. 319–329.

ZOTTI, GEORG; FRISCHER, BERNARD & JOHN FILLWALK: Serious Gaming for Virtual Archaeoastronomy. In: Studies in Digital Heritage 4 (2020), 1, pp. 51–74.

1 Duhem: To Save the Phenomena, 1969, p. 5.

2 Plato, Timaeus, 40 (transl. Jowett).

3 Frischer & Fillwalk, 2013, pp. 341–345; Frischer et al., 2016, pp. 55–79; Frischer et al., 2020, pp. 51–74.

4 Schiaparelli, 1876.

5 Yavetz, 1998, pp. 221–278; Yavetz, 2001, pp. 69–93; Yavetz, 2003, pp. 319–329.

6 Ptolemaeus, ed. by Toomer: Ptolemy’s Almagest, 1984.

7 Ptolemaeus, ed. by Toomer: Ptolemy’s Almagest, 1984.

8 Goldstein, 1967, pp. 3–55. Zotti et al., 2020, pp. 51–74.

9 Online access via https://ssd.jpl.nasa.gov/horizons.cgi, last checked at April 29^th, 2021. Star positions are taken from the 1997 HIPPARCOS star catalogue, using Ptolemy’s Almagest model for precession.

10 In his computer-aided research from the late 1990s, Yavetz discovered alternative configurations of the homocentric models, challenging the exclusivity traditionally awarded to Schiaparelli’s reconstruction and showed that the evidence of the models that came down to us does not reduce into a single exclusive reconstruction, and that other reconstructions are possible on the same factual basis.

11 See footnote 5.

12 Feldhay & Ragep (eds.), 2017. Di Bono, 1995, pp. 133–154. Nahmias, 2016.