String Theory

Approx 1900 words
© 2016-2022 James E. McCormack
/ Procyon Works LLC

Modern observers map the sky with a system of stellar longitude and latitude, a technique with roots in Ancient Mesopotamia.

But observers and astrologers had been tracking the planets and defining the stars in the days of Even More Ancient Mesopotamia, before the development of quantitative astronomy and early geometry.

Somehow, these earliest astonomologers managed to craft a map of the visible stars, a detailed account of the sky that all could agree to.

Without longitude or latitude, how might they have done that?

Here, we present an hypothesis which accounts for all of the stars in Ptolemy’s accounting.

The star catalogue of Ptolemy’s Almagest (VII.v – VIII.i) lists more than a thousand stars, with celestial longitude, latitude and magnitude measurements for each.

Ptolemy includes all stars of magnitudes 1, 2 and 3 which are visible from Mediterranean latitudes. But when it comes to stars of lesser magnitudes, Ptolemy’s list is more selective; while some stars of magnitude 4, 5 and 6 are listed, others equally bright go uncited.

How did Ptolemy (and his predcessors and peers) decide which dim stars to include in the catalogue?

We submit that it’s mostly a matter of alignment.

The identification of individual stars was an iterative process, starting with the very brightest of stars, the most striking asterisms. Stars to which one can simply point and say ‘that very bright one there’ – Arcturus, Antares, Altair, Vega and such. Strong asterisms such as the square of the Horse, the hourglass of Orion, the sickle of Leo, or the seven-starred plough/cart/dipper at the back of the Bear. Such obvious figures account for most stars of magnitude 1 or 2, and give shape to the rest of the sky.

Using these primary stars as anchors, a secondary set could be defined. A number of lesser, local asterisms of modest stars were identified; there’s the Triangle [LINK] above the Ram, between Perseus and Andromeda, and flurry of stars near Vega which form the Lyre, and the quadrilateral which forms the. . . uhh, the quadrilateral in Sagittarius [LINK]. In addition to star figures, many stars could be identified by star alignments (more on that in a moment).

Using these secondary stars now as a secondary anchors, further stars can be defined, a tertiary and a quaternary set, and so on, until you decide that you’re done [LINK].

In the course of investigating the starlines of VII.i, we found over and over and over again that the dim stars of Ptolemy’s constellations can be defined by alignments with brighter stars. Unassisted naked eye observation can be used to search for starlines, but after a bit of thought and some experimentation, we conclude that a simple mechanical device was used in charting the stars, long before the invention of longitude and latitude and spherical geometry.

We propose that early viewers mapped much of the nighttime sky using a taut line held at arm’s length to visualize stellar alignments. A string pulled fast in an outstretched bow is a handy tool for such viewing, but a simple bit of thread in hand will do.

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So. This is a proposal so simple, so unextraordinary that our first response is: ‘So?’

Which is the point.

Certain bits of history get overlooked because they’re so mundane.

It’s taken as a given that the ancients had constellations.

But we don’t often stop to ponder how these constellations were defined.

String theory goes a long way toward defining the stars of Ptolemy’s sky.

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By the middle of the second millennium BCE, Mesopotamian observers had developed techniques of celestial geometry, a system of stellar longitude and latitude still in use today; to this end, they invented instruments to measure the positions of stars and planets. But even after the introduction of quantitative astronomy, we suspect that most observers learned the sky by use of starlines and asterisms. In particular, we argue that such figures were helpful for remembering the stars.

Modern readers have the luxury of relying upon external memory devices such as print books and electronic references; to ‘know’ something often means ‘knowing where to look’ for a piece of information. But ancient scholars relied upon the faculty of memory. Before the invention of the printing press, students and scholars actively memorized texts and other information. To this end, scholars of ancient Greece and Rome developed methods and practices to discipline the memory.

Using what today we’d call visualization techniques, a student or scholar could build a ‘Memory Palace’, a virtual space composed of many rooms, each room holding a collection of images and anecdotes relating to a particular topic. It’s a technique which encourages the user to tie any new information to things already known, for facts in isolation are easily forgotten, while facts which fit into a picture or a story are remembered as elements of a larger whole.

Another tool aiding memory was the use of metrical verse. Phaenomena, by Aratus, is an excellent example – a lesson in stellar and atmospheric science, a work of didactic poetry. Meter and rhyme are held in mind more readily than simple text. Viewed through a modern lens, the structure and sound of a poem provides a sort of mental checkbit for one memorizing the material.

So: in the time of Ptolemy, and for a thousand years before, and a thousand years after, dedicated astrologers and astronomers would have memorized the sky. We’ve argued that the use of star alignments; here, we further suggest that the nomenclature of Ptolemy would have helped astronomologers in crafting a memory-palace of the sky.

[This alignment can be viewed at LINK Ptolemy / Lion. ]

The Starlines of VII.i [LINK] cites dozens of starlines and figures;
such an accounting could serve to anchor a memory palace of the sky.

The constellations of the Zodiac predate stellar longitude and latitude. While astrologers eventually adopted and adapted to this new system of quantitative measure, we suspect that most serious observers held on to the old ways of starlines. An astrolabe is a fine tool for quantitative observation, but a taut cord held at arm’s length allows an adept to quickly take measure of the sky.

The modern astronomer’s map of the northern sky derives from Ptolemy’s Star Catalogue .

Ptolemy’s catalog of 1024 stars visible from Alexandria and environs includes all such stars of the first, second and third magnitude, most of the fourth, and some of the fifth and sixth.

Consider how these stars might have been identified.

There are several dozen stars to which one can simply point and say ‘that one there’, and a handful of asterisms easily traced, such as ‘that plough-shaped seven to the north’. And many more of third and fourth magnitude which can be described and defined in relation to these bright ones.

But when you start cataloguing stars of the 4^th , 5^th and 6^th magnitude, you run into a bandwidth problem – there are a lot of dim stars. Ptolemy’s star catalog lists nearly all stars of magnitude 4 or brighter. But when it comes to stars of magnitudes 5, 6, or ‘dim’ (as per Ptolemy), how do you decide which of these stars to list in the catalog, and which to omit?

The dim stars in Ptolemy’s catalog, we argue, can all be defined by alignments involving brighter stars. If the sky of Ptolemy’s day was defined by star alignments, then dim stars which aligned closely with brighter, well-defined anchor stars are the most likely to be noticed.

In the course of exploring the star alignments of Almagest VII.i, we identified many neighboring starlines which define hundreds of the stars in Ptolemy’s Catalogue (VII.v – VIII.i).

While each of the flipbook presentations of the The Starlines of Almagest addresses stellar alignments, in one way or another, several chapters address the puzzle of defining and finding the dim stars of a constellation.

Orion is a large constellation, some 38 stars – the obvious shoulders, knees and belt, along with a blade or two, and a head, and a club, and nine stars forming a skin or shield held up against the onrushing figure of the bull.

The nine stars of the skin are all magnitude 3 (toward the south) or 4 (in the north). This is not a figure you can just point at and say, ‘that one, then that one, then. . .’

In Chapter 11 [LINK], we demonstrate how the stars of the shield or Orion can be defined by alignments with other, more easily defined stars. The face of the Bull and the body of Orion are among the most striking asterisms in the northern sky; here, they serve as celestial anchor-points, defining the modest stars of the shield by way of stellar alignments.

This is a good introduction to how early astronomers mapped the sky with star alignments.

Several other chapters show how brighter stars (‘that one there’ stars) were used to define the magnitude 4, 5 and 6 stars found in Ptolemy’s Catalogue.

Chapters 6 [LINK] and 21 [LINK] explore the stars of the Scorpion’s tail, one of the most easily found asterisms of the sky. We see how a set of bright, well-defined stars can be used to define the less-bright stars of a wide swath of the summer sky.

In contrast, chapters 8 [LINK] and 24 [LINK] pose the inverse question. Given an ill-defined figure such as ‘the water flowing from the jug of Aquarius’, what brighter lights can we use to identify and define this splattering of unspectacular stars?

Another chapter [LINK to chap 2] shows the use of star alignments to set boundaries on a nebular figure between the Lion and the Bear: Coma Berenices, the Hair. We also uncover a couple of hidden stars, which Ptolemy observes but leaves unaccounted. In a separate essay [LINK to 1022], we set forth our own accounting.

Not all star alignments are linear. Chapter 7, for example [LINK], considers a circular geometry in Sagittarius. Not many would notice such a thing; but once noticed. . .

We invite the reader to look at the sky

as it would have been viewed in Ptolemy’s day,

      starline,

           by starline,

               by starline