Perhaps the best measure of the perception of Tycho's influence through the years is that this book is at least the fifth serious biography of him. Less than fifty years after Tycho's death, when the concept of biographical writing had barely begun to be extended from the lives of saints to the lives of kings, the French Catholic philosopher Pierre Gassendi had already conceived the notion of portraying the life and career of the Danish Lutheran astronomer Tycho Brahe. Because he did, and because he wrote to Denmark to get as much information about his subject as he could, we have details of Tycho's life that would probably not otherwise have been preserved. Gassendi used those details – along with Tycho's observations, letters, and published descriptions of his scientific work – to amplify the seven-thousand-word autobiographical sketch written by Tycho in his last years into an eighty-thousand-word biography published in 1654 as Tychonis Brahei, Equitis Dani, Astronomorum coryphaei, Vita. By the following year a second edition had been printed, and reprintings appeared in 1658 and 1717 as the fifth volume of Gassendi's own Opera Omnia.

As was the case for history generally, the nineteenth century was the great period of discovery in Tycho studies. Numerous documents touching on Tycho's life were found in repositories in Copenhagen, Prague, Vienna, and Basel. The most active excavator was the Danish historian F. R. Friis, who, unfortunately, did much of his work after he published the first modern biography of Tycho in 1871.

The ship carrying Tycho's entourage out of Denmark stopped at Köge and Lübeck before discharging them at Rostock sometime before mid-June. It was a city that Tycho had come to know fairly well from the travels and studies of his youth. In particular, it was the place in which, thirty years earlier, he had fought and recuperated from the ill-starred duel with Parsberg. As Tycho stayed there through the summer of 1597, figuratively licking the wounds to purse and pride suffered in the previous year and renewing his acquaintance with the wise old men who had seen him through his earlier crisis, he must have sensed more than one melancholy reverberation from the past. His old friend and agent, Brucaeus, had died in 1593. But the theologian Chytraeus, and the clergyman who may have been Tycho's former landlord, Lucas Bacmeister, were still alive, and there was still a considerable colony of Danes in the city, which Tycho quickly sought out for news and opinion.

The news was that literally on the day Tycho had left Copenhagen, 2 June, the king had ordered a third commission to go out to Hven for some kind of investigation which Tycho could only interpret (but probably wrongly) as further harassment. And on the tenth, an executive order had been issued transferring Tycho's canonry at Roskilde from him to the chancellor, Christian Friis.

As of the end of 1585, Tycho's life and work on Hven had probably proceeded about as he had expected it would when he settled on the island. To be sure, the building of Uraniborg and its ancillary facilities, particularly his instruments, had taken longer than he had thought it would. But the finished product – as epitomized in his underground observatory, Stjerneborg – was better than the minute-of-arc accuracy he had originally sought, and, in addition, Tycho had had the opportunity and hence the obligation to deal with more extraordinary astronomical phenomena than he could possibly have foreseen.

Each comet had contributed grist for Tycho's mill. The one in 1580 had gone around the sun, just as that of 1577 had. The comet of 1582 had shown a tail pointing away from Venus, just as the great tail of the comet of 1577 had. That of 1585 had displayed no tail at all, which, as far as Tycho was concerned, merely meant that its tail was directed behind it away from the sun and was not visible because the comet was in opposition to the sun. The pieces were beginning to fall in place: His observations of the comet of 1585 were in press; his manuscript on the comet of 1577 was going through right after it; and if Tycho had not yet decided to publish a work summarizing the appearances of all the comets he had observed, he soon would.

Until the Danish Reformation of 1536, learned Danish noblemen had inevitably been clergymen. During the Reformation, however, the episcopal offices and episcopal estates that they had just as inevitably monopolized were seized by the crown and turned over to suitably accredited Lutheran “superintendents” of middle-class background who posed no problems in respect to either loyalty or competence. The lower-level cathedral chapters, not offering the wealth or power of the episcopal offices, were still accessible to the nobility. It had been common before the Reformation to reward royal secretaries and various other crown servants with canonical prebends, and it remained so afterward. And because the noblemen who were now excluded from high office in the church began to dominate crown and chancery offices more than ever before, canonry incomes were increasingly diverted to the nobility. After the radical changes of 1536, however, these royal servants were no longer clerics but, instead, Lutheran laymen. From 14 May 1568, Tycho Brahe knew that he would one day be one of them.

Before the Reformation, formal education was associated with clerical celibacy. And because clerical celibacy was a threat to familial continuity, no aristocratic parents could send more than one or two of their sons to university. But after the Reformation they could, and some of them did, not so their sons could become universal men or achieve satisfaction and even glory, in the terms of the Italian Renaissance, but, rather, so they could be better trained to fulfill the traditional role of their class: service to the realm.

30 JULY 1602. MAGDALENE BRAHE TO ESGE BILLE

My most friendly greetings now and always sent with Our Lord.

Dear Esge Bille, trustworthy, especially good friend,

My most friendly and great thanks for all the manifold goodness you have shown my dear mother, brothers and sisters, and me, for which we are obligated to you all of our days and will be found right willing and full ready with our small fortune in all ways to do whatever we can to your honor and service.

This is to inform you most cordially that I could not burden you with this my humble letter but that my dear mother, my brothers and sister, and I long so much to know how you and your dear wife are. God in heaven grant that all things go fortunately and well for you always, to the glory of God, and to your own and our gladness. We wish you this with all our hearts.

My dear mother, brothers and sisters, praise be to God, are all healthy and sound, may God in Heaven continue to help with His spirit and grace. But that our greatest joy and pleasure after God is now gone from this earth, in that God in Heaven has called home our dearest father, now blessed in God, places us in the hands of God, who rules over us all. God grant us to be found again in the realm of God, in the eternal joy which never ends.

anomaly: the angular distance of a body from some reference point, apogee, in traditional astronomy. The mean anomaly is the distance a body would be from apogee after a given time if it were traveling with its average (mean) orbital speed.

apogee: the point in an eccentric or epicycle that is farthest from the earth, or the point in an epicycle that is farthest from the center of the deferent: marked A in Figure A.2.1.

concentric: a circle on which a point moves with uniform speed and therefore with uniform angular velocity, as seen from the center of the circle.

conjunction: the (essentially invisible) position in a planet's orbit at which its longitude coincides with the sun's.

coordinate system: the means by which the locations of celestial objects are specified. They rest on the common (Greek) conception of the heavens as a hollow shell of very large radius, centered on the earth and called the celestial sphere (see Figure A.2.2). Any position (S) on the sphere can be completely described by reference to its angular distance (ø) above or below a plane (LMN) bisecting the sphere, and the angular distance (θ) in that plane between the meridian through S and a given “zero” meridian. Note the resemblance to terrestrial coordinates. The Greeks developed not only the geographical system but also all systems of celestial coordinates. The latter are denominated by their respective fundamental planes, and their components are named as shown in the table A.2.1.

The spectacular discoveries in the lunar theory were the most remarkable results of Tycho's career, but they were also almost the entirety of his scientific work during the last decade of his life. Already by the spring of 1591, when he had finished writing and printing almost all of the ten projected chapters of his 850-page tome on the new star, Tycho was facing the first of a series of distractions that was to plague him to the end of his days. As is so frequently the case in human affairs, most of these distractions were of Tycho's own making. But the most time-consuming – a steady stream of curious tourists whose comings and goings had already turned his summers into periods of negligible productivity – was one that was probably beyond his control.

Tycho's diary for 1590 shows what proportions this activity could assume. Typically for these years, the most frequent visitor was Tycho's sister Sophie, who made a dozen stops, ranging in length from a night to a week. Half a dozen other relatives and friends also made two or three visits each to the island, and several others who seem to be named as friends likewise put in appearances. In addition, numerous groups of unknown and usually unnamed travelers dropped in.

If the five-year delay imposed by the initial requirements of getting established on Hven had gotten Tycho off to a slow start in his work, that situation was only a memory by 1590. By this time, Tycho was well under way in his long-envisioned renovation of the whole science of astronomy. Already in 1588 he mentioned plans for presenting it in the form of a mighty Opus astronomicum, a sort of “New Almagest” that would begin with a discussion of his instruments and proceed from there in much the same way that Ptolemy and Copernicus had done. Even then, Tycho recognized that he was still a long time – five or six years, at least – from this achievement, because he still lacked some of the requisite observations for the slower moving (superior) planets.

Each year, however, there was more competition for his research time, generally from projects he had not originally conceived as part of his “redintegration.” Of longest standing was his cosmological trilogy on the “more recent celestial phenomena,” designed to prove that the prevailing Aristotelian view of the world was simply untenable, that there were no comets below the moon, no solid spheres above the moon, and, by implication, no reason to adhere to any other aspect of traditional, largely a priori, dogma.

At the beginning of 1590, Tycho was still heavily mired in this undertaking. Volume II (De mundi) had been printed and was in the hands of various friends, dignitaries, and acquaintances.

LETTER 1: ESGE JØRGENSEN BILLE TO TYCHO BRAHE, 11 NOVEMBER (NEW STYLE) 1599

Dear Tycho Brahe, my dear brother,

Now and always, I send you my most friendly greetings in the name of Our Lord. I send you my most friendly thanks for all the goodness you have done for me, which you will always find me willing to repay with any service I can render to your honor and welfare.

Dear brother, your letter came into my hands here in Copenhagen through your son, Tyge, and in it you let me know about the good circumstances you have come into at the court of the Holy Roman Emperor, which I (as well as many of your good friends, who asked about you at this Diet of the Nobility) was most pleased to hear. May God continue to give you good fortune.

Concerning the fifty dalers that you asked me to pay to Christian Longomontanus, your son Tyge will undoubtedly tell you about that, because I note that he is coming with that money, otherwise he would certainly have gotten it [from me], regardless of the circumstances.

Concerning your instruments, I have given your son my thoughts and advice on what I consider to be the best way to get them out, which would be by way of Lübeck.

The lines of research outlined in Chapters 3 and 4, while never completely independent, merged into a common subject of study at the end of the 1950s. Since quantum field theory had come to a calculational impasse in strong-interaction physics and since people could not prove on the basis of general field theory axioms all of the analytic properties of scattering amplitudes needed to calculate relations among physically measurable quantities, it became the fashion to postulate or guess (with various degrees of justification) general properties and to make up the rules of the game as one went along. Goldberger was one of the most prolific practioners of this art. He recalls as a particularly appealing aspect of that project:

Let us indicate how this analytic S-matrix program came into existence.

By 1956 Gell-Mann was of the opinion that quantum field theory had no hope of explaining high-energy phenomena and he sketched an alternative program based on general principles and employing unitarity as a central tool in calculations. He acknowledged Heisenberg's original S-matrix program as the ancestor of this project. A crucial step for the dramatic forward progress of this alternative approach to conventional quantum field theory was taken by Mandelstam when he proposed a specific form for a relativistic (double) dispersion relation in the momentum transfer (essentially the scattering angle) variable as well as in the energy variable.

In the previous eight chapters we have presented a fairly detailed case study of the S-matrix program. Along the way, we often pointed out the relevance of certain developments to methodological issues in theory construction and theory choice. In the next chapter the ‘data’ from this and several other episodes in modern physics will be used as a basis for drawing some methodological lessons about theory selection in current science. This chapter is devoted to summary sketches of methodologically relevant aspects of several programs in modern physics.

We begin (Sections 9.1 and 9.2) with an overview of the ‘factual’ content of the S-matrix case study itself and some relevant methodological issues because that may help focus the reader's attention on points important for the argument of the next chapter. Also, those readers most interested in the discussion of methodological issues in Chapter 10 can use the present chapter as an easy and fairly self-contained review of the pertinent historical materials. (Recall, too, that this book has a glossary of technical terms for quick reference.) To demonstrate that those features are not peculiar to S-matrix theory alone in modern physics and, thereby, to broaden the foundation upon which subsequent arguments are made, Section 9.3 provides a summary of some other major episodes in modern physics. This includes a review of certain aspects of the old quantum theory, of early quantum field theory, of quantum electrodynamics after World War II and of gauge field theories.

Here we present some philosophical lessons drawn from, and discussion of, questions raised by this case study. The previous chapters ought to be able to be taken or left independently of this chapter, but not vice versa. That is, some familiarity with the facts of the case study is necessary for an appreciation of the argument of this chapter. We point out specific features of our story that are relevant to constructing and evaluating a methodology of scientific practice. The discussion is not based only upon or restricted exclusively to the S-matrix case study. Several methodologies currently on offer are reviewed in the light of that case study and of the other episodes in modern physics reviewed in the previous chapter. We argue for a multifaceted and evolving description or model of scientific practice.

Since there is a good deal of over and back between the specific case studies and general methodological issues in this chapter, it may be helpful to outline here the structure of the argument to be followed. Some general characteristics of science, as identified by modern philosophers of science, are first outlined (Section 10.1) as a preliminary to comparing them with those features of scientific practice found in the SMT study and in our summary of other major episodes in modern physics in Chapter 9. In Section 10.2 the recent works by Pickering (1984) and by Galison (1987) are used to illustrate the role sociological factors have played in scientific practice in high-energy physics (HEP), both theoretical and experimental.