Becoming aware of the nearest stars is an event that makes the blood tingle; it is like emerging from a hole in the ground. As newborn babies we see a jumble, and gradually it becomes a world of’objects, some within reach; we forget that experience, but later relive it as we learn that there are fields over the horizon and cities a train-ride away and countries beyond the sea; and we can live it a third time if we learn of the stars beyond the weather. Perhaps that experience is less surprising now that it can be reached through an app on a smartphone; it was still blood-tingling when I had it.
Not long after I started the Astronomical Calendar, I found someone’s booklet on how to make a three-dimensional model of the stellar neighborhood. The stars may have been the fifty or so nearest known at that time, and I don’t remember whether their positions were given in light-years or parsecs (a parsec is about 3.26 light-years). The instructions were to use a cardboard box, cut its front open, paint its interior black, make pin-holes in its top and bottom at the given X-Y positions, and stretch black cotton threads vertically between the pin-holes, with knots tied at the given Z heights on the threads to position beads representing the stars. I thought of making this model and painting a picture of it, for the cover of the Astronomical Companion which I was then compiling.
My student friend and helper Doug Roosa volunteered to make the model in this more robust way:
The uprights are bicycle spokes (Doug worked in a bike shop), screwed into the wooden base, and cut off at the heights for the stars. The small red beads are red-dwarf stars, of spectral type M; the few larger yellow and white beads are dwarf stars of types G, F, and A, including the Sun (in the middle), Alpha Centauri, Sirius, Procyon, and Altair.
The scale seems to be about a centimeter to a light-year. The beads are vastly larger than they should be, otherwise they would be far too small to see. The Sun’s true width is about 1/7,000,000 of a light-year, and the nearest star, Alpha Centauri, is 4.4 light-years away.
The viewpoint is about the same as in the eventual Astronomical Companion version, which however is reduced to a smaller radius, so that Altair does not appear. There are no giant stars near enough to be in the model. It’s our good sample of starry space: the smaller, the commoner; the huger, the rarer.
This model – the local cloud of fifty or so stars, with the yellow Sun in the middle – is a sculpture with the beauty of meaningfulness, though it deserves a good dusting and re-straightening of its spokes after years of perching on furniture and transporting from place to place.
But when, back then, I tried to make my drawing of it, I realized the difficulty of finding an eye-position from which no bead was hidden, and the greater difficulties of exactly maintaining any eye-position, and of knowing definitely which side of a stalk another should appear. You just can’t draw such a thing exactly as you see it. What was needed was more calculation. So another student, Jack Schwacke, helped us by writing a small program, turning the X-Y-Z positions of the stars into X-Y positions on paper, as seen from a viewpoint. I must have chosen the viewpoint, but it was probably as from infinite distance, this early program being a simple one that did not calculate true projection. I chose to replace the spokes, standing up from the base ten parsecs below the Sun, with stalks, standing or hanging from the equatorial plane through the Sun. And later I learned trigonometry.
This became the origin of my whole style of three-dimensional plotting.