Sliding Blocks of Time

Here’s a small foretaste from Astronomical Calendar 2016. Since I’m having to work with rising anxiety to get it ready for the printer,  I might as well spin off blog posts from it.  For one thing, you may be able to point out features I could improve.

I came to the bit about “The Sun’s Progress through the Constellations” (on page 32 in Astronomical Calendar 2015).

Precession isn’t something we’re born with understanding of. We often have to think twice (at least, I do) about which way the astrological signs of the zodiac slide in relation to the astronomical constellations. Does the Sun cross the boundary into the real starry Aries before or after it enters the astrological sign of the same name?  When astrology says the Sun should be in Aries, is it “still in Pisces” or “already in Taurus”? It’s one of those many two-way hesitations that plague the mathematically non-instinctive.

It was to make the matter clearer to myself that I devised the little diagram:


Even while making it I had felt it could communicate its message more immediately with if I added some color.  So this time around I set about doing that.

The program that draws it is named acsuent.for – gobbledegook, to anyone but me. I have to have a sort of shorthand to locate what I want among the 321 Fortran programs I seem to have written. It’s short for “Astronomical-Calculating SUn ENTering-constellations program.” Its initial purpose was to find for any year the 25 dates when the Sun enters the 12 zodiacal signs and the 13 (because of Ophiuchus) actual constellations along the ecliptic. But at some point I made it also produce this diagram.

I now thought it would be easy to apply blue to the two boxes for Aries, for example. But it took me several more hours than I had expected. This is typical of efforts to correct or extend a program.

To draw and fill the box for Aries, instead of just drawing a line at the date when the Sun enters Aries, the program has to know at that same moment the date when the Sun will enter the next constellation, Taurus; but the only other date it could be told to remember at that moment was the one it had previously calculated, for entering Pisces. So it was drawing the boxes, but at the moment of calculating for Aries it was drawing the box for Pisces; which was confusing. As I was going to bed I realized (this also is typical of arrivals-at-solutions) the simple answer: deal with the events in backward order. Just change the line

DO J=1,25


DO J=25,1,-1

I’m sure you see what I mean. In Basic, a language that many people used to know, it would be

FOR J = 25 TO 1 BY -1

There remained a problem with the constellations that cross the line for January 1 and therefore have to appear in two parts. To help me gaze at the problem, I used colors for the problem boxes and slid them out from where they were hiding:


It was about then that I thought this example of wrestling with a process might be interesting enough to tell you about.

I saw how to solve the problem by use of the number 0, and at last:


Yes! Clearer, I think, is the sliding downward (later in time) of the constellations in relation the signs, like geological formations on either side of a fault; and that the Sun now makes its way from Taurus into Gemini almost exactly at the date (the June solstice) when it’s supposed to be advancing from Gemini into Cancer; that the imaginary signs are equal spans whereas the irregularly shaped constellations’ widths along the ecliptic vary; that the Sun spends the longest time in Virgo, and the shortest in Scorpius (because Ophiuchus usurps a stretch of the ecliptic).

Using three shades of color proved clearer than two; and, by trial, using them in the order from darker to lighter proved clearer, emphasizing that the four quarters of the year start at the equinoxes and solstices.

I’m limited to black and blue (actually, cyan) in printing all but a few pages of the Astronomical Calendar, because four-color printing is far more expensive. But on the monitor, we can do what we like.


You may have an opinion on choices of colors. I think they should keep to the rhythm of three. (So it’s hardly possible to make the “watery” constellations bluish, or for me to indulge my feeling that the letrer A is green.)

And finally: how about running the program for distant epochs, and seeing the changes made by precession?

Here side by side are the states of the constellations as now and a thousand years ago.


The change looked even more vivid when I had the two diagrams in windows on top of each other on the monitor, before pasting one into the other, and could flick from one to the other with a keystroke (control-F6) and watch the constellations jump.

A thousand years ago, the constellations were half a constellation-width back. The Sun was only in the middle of Gemini, not its end, when the sign was changing from Gemini to Cancer. But wait – is my thick line for the solstice in the right place? Yes, according to Jean Meeus’s Astronomical Tables, page 326, the solstice in 1016 fell on June 16 (Julian calendar).

I feared that “Capricornus” off the bottom betrayed yet another glitch that I had to find and eradicate. But no, it was right: I had told the program to write each constellation’s name two millimeters down from the date where the Sun enters it, and when I greatly magnify the diagram I can see that there are two lines at the bottom: a very narrow strip for Capricornus. In 1016 the Sun entered Capricornus (as my program also told me) in the early hours of December 31.

Let’s try for two thousand years ago, around the time when the astrological signs were fixed:


Yes, the constellations are back alongside the signs. Back then the Sun really did enter Aries when the casters of horoscopes said that it did. It’s a bit false to talk about the boundaries of the “real” constellations back then. If there were boundaries, they were loose; those we now draw on starry maps were finally agreed only in 1930.

All this about one four-inch-high marginal embellishment for the Astronomical Calendar. Not, so far, a strategy for saving time in making these blog posts.

–I see one more glitch. The names of Capricornus and Scorpius in the astrological column should be “Capricorn” and “Scorpio”. I thought I had fixed that in the program, but realize it was only in the calculating and not in the plotting part of the program. I’m not going to re-make all those illustrations now.



13 thoughts on “Sliding Blocks of Time”

  1. If you think this is confusing now, just wait another 2000 years when the astronomical are not one, but TWO constellations apart from the astrological ones.

  2. Fascinating, Guy!

    I’ve had a long-standing interest in the mechanics of precession generally, and it’s always good to tackle the subject from different angles, I think.

    What struck me in reading through this is how little human behaviour has changed across the millennia. We begin with people looking at star patterns in the night sky. Everything’s fairly fluid, and constellations can be thought of as linked, or interacting together if desired (e.g. in some conceptions, Libra was previously the claws of Scorpius). Then along comes someone keen to stamp their own version of “order” and “authority” on this easy-going system, but who has no strong interest in reality where that gets in the way of their “ideal model”. So the astrological constellations become codified into 30° long stretches of the ecliptic each, irrespective of where the actual star patterns lie, and that becomes the only accepted “official” standard.

    A couple of millennia later, astrology having fallen from grace rather under the new paradigm of science as to who can claim “authority” over the stars, and astronomers decide to rigidly codify ALL the star patterns, not just the near-ecliptic ones, but still using similarly neatly-ruled boundaries, all mathematically precise and orderly. So now we have large open spaces of sky with scarcely a visible star in them called “constellations”, and constellations broken up to fit the line of the ruler (e.g. Argo Navis or the Great Square of Pegasus), taking with the Oxford English Dictionary that “constellation” actually means “A number of fixed stars grouped together within the outline of an imaginary figure traced on the face of the sky”!

    1. “Constellation” has certainly run through several senses, as most words do. If “A number of fixed stars grouped together…” is the last sense that the OED gives, it has failed to includ the further meaning of an area defined by boundaries. I could check this but haven’t done so yet; do you know that (as I learned from my wife Tilly) you can now access the OED online through your library card number? At least you can in ny county. It’s a wonderful resource; it gets updated, and it rambles almost indefinitely into fuller information (thus back into other languages).

      The official lines are already somewhat askew in relation to the map of the sky (they were defined in relation to the map of 1875)

  3. Very interesting, thank you! I really liked the diagram when I first saw it on this year’s Calendar. But when seeing several diagrams for different dates side by side it is even more clear and dramatic. If those other diagrams didn’t made it into the next year’s Calendar, I would strongly suggest including them in the third edition of the Companion (in the ‘Precession’ chapter) ;-)

    1. You’re very right; I would like to get all such non-year-specific features into my Astronomical Companion, where there would be room to expand them.

  4. Guy, it’s interesting for us readers of the Astronomical Calendar to get some insight into your tribulations in making the diagrams ~ I could hardly even understand your description of getting the programming right for making the stellated diagrams for AC15 (particularly the shading)!

    Is it fair to say that a significant fraction of the time in preparing an Astronomical Calendar is getting the programming right for your specialized diagrams? If that is the case, have you ever considered crowd-sourcing them? For the above diagram, for example, how many times would you use that diagram? Even though you now have the code to create an accurate diagram of the Sun’s astrological and astronomical position for any year, how often will that be used? Would it have been more efficient to farm out the job of creating that diagram to someone who could draft it by hand (I don’t mean hand-drawn, but drawn on the computer without programming) for one or two cases?

    Your spatial diagrams are too hard to “draw” without being plotted by a program, but diagrams such as the above would not be too difficult and would be almost exactly accurate.

    1. Thanks, but crowd-sourcing would never work for me. Instead of working back and forth with myself, sometimes for a few minutes and sometimes for three days, I would find myself working back and forth for weeks with someone with whom I was trying to bargain at long distance about what kind of product I am thinking of. The struggle to create it myself IS the development of the conception of it.
      My program for the sun-entering, a relatively small one, has become 411 lines (including 79 that are “comments”), but like all my programs it draws on my library of about 560 subprograms (modules that do things like drawing shapes or finding Julian dates or solving Kepler’s equation). It’s an interdependent system, and I can’t expect any other cook to stir this stew with me.

      1. I meant to add that you can never be sure something won’t be used again. This particular diagram could have been used once and left as it was, but the idea of improving it could lead to other extensions – it could become a series of pages, a flick-diagram like on the pages of my eclipse book! I could play with it if I want to because it’s just a program in my computer; I couldn’t do that if it was a piece of paper or an image created by someone else.

        1. Guy, I completely understand your desire to work through that creative process yourself and gradually build up your own personal library of tools. As an analyst, I tend to work pretty much the same way. I like to do things myself and over time have maintained and expanded my own knowledge base of data, analysis, reports, and notes that allow for easy extension to new projects. Probably explains why I never migrated into management LOL!

      2. I have very mixed feelings: on the one hand I greatly appreciate the unique individuality of the Astronomical Calendars and Companions; on the other I worry that once you’re no longer able to produce them, no one else will, either. The only solution is for you to live a very long time!

        1. There’s a long story of organizations that have considered taking over the Astronomical Calendar from me and after much fuss have decided not to.

  5. Fascinating. Thanks.

    I just remember that the “first point of Aries”, i.e. the northern Spring equinox, appears against the stars of Pisces. Everything else falls into place from there.

    And regarding Scorpius and Ophiuchus, I get irritated with modern astronomers who denigrate astrology by accusing the ancient astrologers of missing an entire constellation. As you say, the modern constellation boundaries are a modern invention. The stars that represent Ophiuchus’ legs are faint and do not present an arresting pattern. To an actual observer, the Moon and planets passing through that part of the sky most obviously appear north of Antares and the other stars of Scorpius.

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