Since, as I believe, the mind from the first contains within it the basic amp; essential forms of reality, it is not surprising that, before I have any clear knowledge of what the contents will be, I have already conceived the form of my projected book. It is ever thus with me: in the beginning is the shape! Hence I foresee a work divided into five parts, to correspond to the five planetary intervals, while the number of chapters in each part will be based upon the signifying quantities of each of the five regular or Platonic solids which, according to my Mysterium, may be fitted into these intervals. Also, as a form of decoration, and to pay my due respects, I intend that the initials of the chapters shall spell out acrostically the names of certain famous men. Of course, it is possible that, in the heat of composition, all of this grand design might be abandoned. But it will be no matter.
I have taken as my motto that phrase from Copernicus, in which he speaks of the marvellous symmetry of the world, and the harmony in the relationships of the motion amp; size of the planetary orbits. I ask, in what does this symmetry consist? How is it that man can perceive these relationships? The latter question is, I think, quickly solved-I have given the answer just a moment ago. The soul contains in its own inner nature the pure harmonies as prototypes or paradigms of the harmonies perceptible to the senses. And since these pure harmonies are a matter of proportion, there must be present figures which can be compared with each other: these I take to be the circle and those parts of circles which result when arcs are cut off from them. The circle, then, is something which occurs only in the mind: the circle which we draw with a compass is only an inexact representation of an idea which the mind carried as really existing in itself. In this I take issue strenuously with Aristotle, who holds that the mind is a tabula rasa upon which sense perceptions write. This is wrong, wrong. The mind learns all mathematical ideas amp; figures out of itself; by empirical signs it only remembers what it knows already. Mathematical ideas are the essence of the soul. Of itself, the mind conceives equidistance from a point, and out of that makes a picture for itself of a circle, without any sense perceptions whatever. Let me put it thusly: If the mind had never shared an eye, then it would, for the conceiving of the things situated outside itself, demand an eye and prescribe its own laws for forming it. For the recognition of quantities which is innate in the mind determines how the eye must be, and therefore the eye is so, because the mind is so, and not vice versa. Geometry was not received through the eyes: it was already there inside.
These, then, are some of my present concerns. I shall have much to say of them in the future. For now, my lady wife desires that the great astronomer issue forth into the town to purchase a fat goose.
Fröhliche Weihnachten! Johannes Kepler
Loretoplatz Hradcany Hill Prague Easter Day 1605
David Fabricius: in Friesland
As I have delayed long in my promise of a further letter, so it is right all the same that I should sit down now, on this festival of redemption, to tell you of my triumph. As, my dear Fabricius, what a foolish bird I had been! All along the solution to the mystery of the Mars orbit was in my hands, had I but looked at things correctly. Four long years had elapsed, from the time I acknowledged defeat because of that error of 8 minutes of arc, to my coming back on the problem again. In the meantime, to be sure, I had gained much skill in geometry, and had invented many new mathematical methods which were to prove invaluable in the renewed Martian campaign. The final assault took two, nearly three more years. Had my circumstances been better, perhaps I would have done it more quickly, but I was ill with an infection of the gall, and busy with the Nova of 1604, and the birth of a son. Still, the real cause of the delay was my own foolishness amp; shortness of sight. It pains me to admit, that even when I had solved the problem, I did not recognise the solution for what it was. Thus we do progress, my dear Doctor, blunderingly, in a dream, like wise but undeveloped children!
I began again by trying once more to attribute a circular orbit to Mars. I failed. The conclusion was, simply, that the planet's path curves inwards on both sides, and outwards again at opposite ends. This oval figure, I readily admit, terrified me. It went against that dogma of circular motion, to which astronomers have held since the first beginnings of our science. Yet the evidence which I had marshalled was not to be denied. And what held for Mars, would, I knew, hold also for the rest of the planets, including our own. The prospect was appalling. Who was I, that I should contemplate recasting the world? And the labour! True, I had cleared the stables of epicycles amp; retrograde motions and all the rest of it, and now was left with only a single cartful of dung, i.e. this oval-but what a stink it gave off! And now I must put myself between the shafts, and draw out by myself that noisome load!
After some preliminary work, I arrived at the notion that the oval was an egg shape. Certainly, this conclusion involved some geometrical sleight of hand, but I could not think of any other means of imposing an oval orbit on the planets. It all seemed to me wonderfully plausible. To find the area of this doubtful egg, I computed 180 sun-Mars distances, and added them together. This operation I repeated 40 times. And still I failed. Next, I decided that the true orbit must be somewhere between the egg shape amp; the circular, just as if it were a perfect ellipse. By this time, of course, I was growing frantic, and grasping at any straw.
And then a strange amp; wonderful thing occurred. The two sickle shapes, or moonlets, lying between the flattened sides of the oval and the ideal circular orbit, had a width at their thickest points amounting to 0.00429 of the radius of the circle. This value was oddly familiar (I cannot say why: was it a premonition glimpsed in some forgotten dream?). Now I became interested in the angle formed between the position of Mars, the sun, and the centre of the orbit, the secant of which, to my astonishment, I discovered to be 1.00429. The reappearance of this value-. 00429-showed me at once that there is a fixed relation between that angle, and the distance to the sun, which will hold good for all points on the planet's path. At last, then, I had a means of computing the Martian orbit, by using this fixed ratio.
You think that was the end of it? There is a final act to this comedy. Having tried to construct the orbit by using the equation I had just discovered, I made an error in geometry, and failed again. In despair, I threw out the formula, in order to try a new hypothesis, namely, that the orbit might be an ellipse. When I had constructed such a figure, by means of geometry, I saw of course that the two methods produced the same result, and that my equations was, in fact, the mathematical expression of an ellipse. Imagine, Doctor, my amazement, joy amp; embarrassment. I had been staring at the solution, without recognising it! Now I was able to express the thing as a law, simple, elegant, and true: The planets move in ellipses with the sun at one focus. God is great, and I am his servant; as I am also,