Replicating Mathematical
Inventions: Galileo’s
Compass, Its Instructions,
Its Students
Mario Biagioli
School of Law and Department of
沟通, UCLA
Questions about how closure is achieved in disputes involving new observa-
tional or experimental claims have highlighted the role of bodily knowledge
possibly irreducible to written experimental protocols and instructions how to
build and operate instruments. This essay asks similar questions about a sce-
nario that is both related and significantly different: the replication of an
发明, not of an observation or the instrument through which it produced.
此外, the machine considered here—Galileo’s compass or sector—was
not a typical industrial invention (like a spinning jenny), but a mathemat-
ical invention (a calculator), 那是, a machine that produces numbers, 不是
yarn. This case study describes some of the similarities and differences between
replicating experiments, traditional machines producing material outputs, 和
mathematical inventions yielding calculations or information. This compari-
son indicates that, as in other kinds of replication, the replication of mathe-
matical inventions involves texts (the calculator’s instructions) but that in this
case bodily knowledge cannot be properly described as either tacit or explicit. 它
rather takes the shape of memory—muscle memory—that may be recalled from
reading the instructions.
Questions about the process through which closure is achieved in disputes
involving new observational or experimental claims have highlighted the
key role of bodily and possibly tacit knowledge deemed to be irreducible
to written experimental protocols or instructions about how to build and
operate instruments. (柯林斯 2010). This essay asks some of the same
questions about a scenario that is related but significantly different: 这
replication of an invention, not of an observation and/or the instrument
through which it produced. 此外, the machine considered here,
Galileo’s compass or sector, was not a typical industrial invention (喜欢,
科学观点 2022, 卷. 30, 不. 3
© 2022 由麻省理工学院
https://doi.org/10.1162/posc_a_00422
437
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438
Galileo’s Compass
说, a spinning jenny), but a mathematical invention (a calculator), 那是,
a machine that produces numbers, not yarn. To put it in Jim Bennett’s
条款, I analyze the specific problems posed by the replication of mathe-
matical instruments (which yield calculations), not philosophical ones
(which yield physical effects) (Bennet 1986, PP. 1–28).
Replication means something rather specific in cases like Galileo’s com-
pass where knowledge and property are intertwined, where discussions of a
third party’s ability to use and reproduce an instrument were inextricably
tied to determining not only what the invention was, but who owned it.
(Although no patent was actually involved, this controversy was framed by
the logic of patent law and the customs of inventors as reflected in that
法律). Experimental replications are epistemological affairs, the focus being
on the reproduction of instruments and the claims they produced. 那
kind of replication did apply to Galileo’s compass, whose copies were made
to reliably reproduce the same calculations. In addition to that, 然而,
the fact that the inventor could disseminate functioning copies of an inven-
tion was seen as conclusive evidence that the inventor “possessed” the
invention precisely because s/he could transfer it—alienability being a cru-
cial element of the definition of property. Being able to have somebody else
use the invention meant that the invention was not just a stable material
entity reliably producing the same effects but was also, 同时
and for the same reasons, a stable object of property. The construction of an
object as stable is a condition of possibility to both experimental replica-
tions and to the transfer of inventions but, as I hope to show, the param-
eters of that construction overlap only partially.
Another significant difference between the dissemination of Galileo’s
calculator and the replication of observational or experimental claims is
that the actors whose replication mattered the most were not what Harry
Collins has called the “core set” of authoritative scientists in a given field,
or the members of the Royal Society who witnessed and certified Boyle’s
实验, but rather the students, many of them unnamed, who bought
the compass from Galileo and paid him to teach them how to use the
instrument. Their ability to learn from Galileo and remember how to
set up and operate the compass to make it perform its operations played
a fundamental role in settling a bitter controversy about the identity and
inventorship of the instrument. Bodily knowledge alone, 然而, was not
enough to secure the replication of the compass. Texts were as important in
this controversy as they are in scientific controversies, except that they
belonged to the humble and much understudied genre of the instruction
manual that taught, or rather reminded, users how to operate the device.
最后, textuality played another distinctive role in this case that—quite
surprisingly—was eventually litigated as a dispute regarding book
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科学观点
439
plagiarism rather than the appropriation of an invention. The boundary
between text and machine was a porous one, necessarily so, largely because
of the ways in which the compass performed its calculations.
These and other features that will be discussed in a moment indicate
that there was something rather specific, perhaps unique, to the replication
of mathematical inventions, especially calculating instruments, 像他们
straddle the lines between objects of knowledge, knowledge-making
物体, and saleable goods. The tense relationship between computer algo-
rithms and modern intellectual property law suggests that those difficul-
ties may have mutated in time but have surely not disappeared (Samuelson
等人. 1994, p. 2320; Sherman 2019; Diaz 2019).
Between Descriptions and Instructions
在 1606, while teaching at the University of Padua, Galileo printed the
Le operazioni del compasso geometrico et militare (1606).1 It was a short book
describing the use of a multi-purpose sector or “compass” that enabled
mathematically unskilled users to perform a wide range of commercial
任务 (currency exchange, compound interest, ETC。) as well as ballistic cal-
culations like the so-called problem of caliber: starting with the charge of
powder known to be right for a certain shot with a cannon of a given bore
and a ball of a given material (说, stone), calculate the charge of powder
to be used for the same shot with the same cannon, but with a cannonball
of a different material (说, iron) (Heilbron 2010, PP. 100–2). Different sets
of lines laid out on the two hinged flat legs of the instrument enabled
different types of calculations, with the help of an additional divider
(如图. 1). Fitted with a brass appendix, the sector could also function as a
squadra, a popular instrument among artillerymen (如图. 2). Useful to mer-
颂歌, 银行家, land-surveyors, military engineers, and gunners, Galileo’s
compass was probably the most versatile and sophisticated calculator
available at that time.2
1. Galilei, 伽利略. 1606. Reprinted in Galilei, 伽利略. 1890–1909, 卷. 二, PP. 365–424.
This summary of the events of the dispute is based on Stillman Drake (1976); Antonio
Favaro (1907–8); Stillman Drake (1978); Silvio Bedini (1967). A more complex perspective
is in Roberto Vergara Caffarelli (1992). Noteworthy among the recent literature are Matteo
瓦莱里亚尼 2010, PP. 27–38; Nick Wilding 2014, PP. 38–49; John Heilbron 2010,
PP. 100–104. An overview of the history of the sector and its varieties, see Michael Williams
and Erwin Tomash (2003).
For the background to Galileo’s development of his compass, and the similarities
and differences between Galileo’s instrument and other sectors available at the time see
Paul Lawrence Rose (1968); Filippo Camerota (2000); Stillman Drake (1977); Alex Marr
(2011).
2.
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440
Galileo’s Compass
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数字 1. The compass as illustrated by Capra, showing the use of the divider.
The compass, Galileo argued, showed that it was not inappropriate for
the tyrant of Syracuse to have asked Archimedes if there was an easy way to
learn mathematics (Galilei 1890–1909, 卷. 二, p.369). Many centuries
之后, Galileo had proven that there was indeed a royal road to mathematics,
a mechanical one that, like modern computers, allowed people to perform
科学观点
441
数字 2. Galileo’s compass set up as a gunner’s squadra. Image used with
permission of the Collection of Historical Scientific Instruments, 哈佛大学.
operations without understanding them3 (Favaro 1891, p. 369). The delivery
of streamlined mathematical enlightenment to the young aristocrats he
tutored was not the book’s sole goal, 然而 (Galilei 1890–1909, 卷. 二,
p. 370). Galileo claimed that he had decided to publish the Operazioni after
hearing that someone was “preparing himself to appropriate” the instrument:
[这] put me in need to secure, with the testimony of print, both my
works and the disrepute of he who might appropriate them. It is the
case that, as far as my protection is concerned,4 I am not short of
testimonies of Princes and other great Gentlemen who, 自从 8 年
前, have seen this instrument, and from me have been taught how to
use it. It will suffice to mention only four of them. One was [……] 这
Prince of Alsace, [……] the Archduke of Austria, [……] the Landgraf of
Hesse, [……] and the Duke of Mantua.5 (Galilei 1890–1909, 卷. 二,
p. 370)
3.
“[D]esiderando che non restino per la difficolta’ e lunghezza delle communi strade
privi di cognizioni tanto a’ nobili Signori necessarie, mi rivolsi tentare di aprire questa via
veramente regia, la quale con l’aiuto di questo mio Compasso in pochissimi giorni insegna
tutto quello che la geometria e l’aritmetica, per l’uso civile e militare, non senza lunghis-
simi studii per le vie ordinarie si riceve …” Galilei 1890–1909, 卷. 二, p. 369.
4. Galileo used the now-archaic expression “far cauto,” which, taken literally, 会
mean “to make cautious,” but in fact meant “to assure” or “to give assurance” (Percolla
1889, p. 150).
5. The instruments for the Archduke and Landgraf were made of silver and are no
longer extant, while the Duke of Mantua’s brass compass is now in the Collection of
Historical Instruments at Harvard. Mazzoleni’s April 1607 affidavit mentions the two silver
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442
Galileo’s Compass
Luckily for Galileo, he already had a text he could quickly take to the
printer and publish as the Operazioni: the manuscript instructions manual
he had been selling to the students who took classes with him on how to use
the compass. 这些年来, a scribe produced copies of the text as needed.6
Notice that while stating to have mobilized the “testimony of print” to
secure his claim to the compass and make sure that those who planned to
plagiarize him would be exposed for what they were if they pursued their
devious plans, Galileo also added that the recognition of his inventorship
was already safely established by the numerous testimonies of his stu-
dents.7 Setting aside for a moment the apparent tension between mobili-
zing the “testimony of print” while also stating that his students provided
conclusive evidence of his inventorship, the book did not prove to be the
effective deterrent he expected it to be. About a year later, Galileo was
bringing an action against Baldassarre Capra in the Riformatori court in
威尼斯, accusing him of having plagiarized the Operazioni in his own book
on the compass: Capra’s 1607 Usus et fabrica circini.8
During the proceedings, he repeated that his inventorship of the com-
pass was established by the fact that, over an arc of ten years, he had “con-
ferred and communicated” it to “very many Gentlemen and great Princes
from various countries,” well before he decided to print the Operazioni
(Galilei 1890–1909, 卷. 二, p. 539). The same point was made in the
opening section of his Difesa (Galilei 1890–1909, 卷. 二, p. 518), the book
compasses and their recipients (Galilei 1890–1909, 卷. 二, p. 535). Galileo promised more
silver compasses to the Medici (Galilei 1890–1909, 卷. X, p. 149) but it seems that by
that time the compasses were produced in Florence by Medici artisans (probably by a
Maestro Raffaello, Galilei 1890–1909, 卷. X, p. 157) and then sent to Galileo for delin-
eation (Galilei 1890–1909, 卷. X, PP. 155–7). On the negotiations between Galileo and
the Gonzaga see Galilei 1890–1909, 卷. X, PP. 106–7.
6. The bills of Galileo’s scribe, Messer Silvestro, are reproduced in Galilei 1890–1909,
卷. XIX, PP. 166–7.
official complaint to the Riformatori.
7. He would repeat those two points in Galilei 1890–1909, 卷. X, PP. 171–2, 在他的
8. Consisting of three officials, the Riformatori dello Studio di Padua was a committee of
the Venetian Senate that oversaw both the University of Padua and all aspects of the book
publishing business in Venice. 除其他事项外, the Riformatori were in charge of the
university staff (both the number and fields of teaching positions, and the scholars to fill
他们), the curriculum, and the course catalogue. Concerning the publishing business, 他们
oversaw book licensing, book importation, as well as the Library of St Mark (Andrea Da
Mosto, L’Archivio di Stato di Venezia, 卷. 1 (Roma: Biblioteca d’Arte Editrice, 1937),
PP. 216–18. Their control of the press was rather granular, down to the appointment of
official proof-readers (Horatio Brown, The Venetian Printing Press (纽约: Putnam’s Sons,
1891), p. 175).
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科学观点
443
chronicling the dispute that Galileo published shortly after the trial, 和
elsewhere in that text:
Ten years ago I started to have these Instruments made, and every
year I have communicated and shared them with Gentlemen of
various nations [… where] few or many of these Compasses of mine
can now be found, brought there by the Gentlemen who received
them from me together with their instructions, both oral and
written. (Galilei 1890–1909, 卷. 二, p. 533)
The same language appears, virtually verbatim, in the previous paragraph9
(Galilei 1890–1909, 卷. 二, p. 533). It is important to notice that Galileo
did not simply invoke prestigious witnesses as credible people who could
testify to the fact that he had his instrument by a certain date, but as peo-
ple to whom he had taught how the compass worked. 合在一起,
these statements indicate that Galileo took the crucial evidence of his
inventorship of the compass to be embodied rather than textual, instilled
in the mind and hands of his students over almost ten years, and confirmed
by the students’ testimonies (introduced as evidence at the trial) that they
materially received the compass and training directly from him. 仍然, 和我们一样
will see, the embodied evidence of inventorship could only be conclusive if
intersected with the textual evidence provided by the Operazioni.
In connecting inventorship to the ability to teach and transfer the
发明, Galileo was adopting the legal definition of inventorship com-
mon at the time; a definition he was familiar with having applied for and
received a Venetian patent for a water pump a few years earlier (比亚焦利
2006A, PP. 1129–72). To receive a patent, an invention had to be new,
though the definition of “new” has significantly changed since then
(Biagioli 2006a, p. 1132). But perhaps the most significant difference
between Galileo’s context and ours is that patenting in late sixteenth-
century Venice did not necessitate describing the principle or idea of one’s
invention in sufficient detail to enable a third party to build and use it.
That requirement was introduced in different countries around 1800
(Biagioli 2006a, p. 1132). Instead of what we now call an enabling spec-
ification of the invention, in sixteenth-century Venice and in virtually
every other European country at that time the inventor had to show that
s/he had reduced the invention to actual practice—what Galileo called
“reduction to perfection”—and that the invention performed the useful
9.
“I say that it has already been ten years since, having reduced to perfection an
instrument of mine which I called the Geometrical and Military Compass, I started to show
it to various Gentlemen, showing them their use and giving them the Instrument and its
instructions laid out in writing.”
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444
Galileo’s Compass
function the inventor had claimed for it. Perhaps one could say that while
inventions are now legally disclosed through text and diagrams in the pat-
耳鼻喉科应用, in the early modern period they were conveyed through
apprenticeship, by transmitting the embodied knowledge necessary to
build and operate it. This distinctly “materialistic” or “pre-representational”
perspective construed the invention as the specific device or working model
submitted to the patent-granting authorities, not as the “idea” or “principle”
of that machine or of others equivalent to it. Existing only in re, an invention
was not yet what we call an object of intellectual or intangible property.
Galileo himself conveyed his patented water pump, “viva voce, with a mate-
rial model”10 (Galilei 1890–1909, 卷. X, p. 87), while the engineer Giu-
seppe Ceredi commented in 1567 that “anyone who believes to have found
some ingenious beautiful things takes his models [to Venice] to obtain priv-
ileges” (Ceredi 1567).
Somewhat surprisingly, Galileo did not patent the compass but, had he
tried to do so, he would have qualified as its inventor by virtue of having
produced and sold it. Even better, the fact that he could teach the compass’
operations to his students (and that the students kept signing up for his
tutorials) proved that what he had was not a prototype but a fully func-
tioning calculator on which he had built a successful business. His capacity
to teach the invention proved that he possessed it to begin with. 在
同时, this apparently straightforward definition of inventorship did
not provide an easy way to identify precisely what the object was that
Galileo was the inventor of. “I can transfer, therefore I have.” Yes, but what
did you transfer? And did you always transfer the same thing?
One way to address this question was to require inventors to produce
and deposit a working model. But because Galileo never patented his com-
pass, there was no official model of it and, without that, no clear record of
what could count as his invention, or whether it had enough of a stable
identity to be treated as an object. Until 1601 he produced, 教过的, 和
sold a series of different compasses, which he referred to as one single
invention—“my compass.” Under normal circumstances, it would not
have mattered that he was the clear inventor of an unclear invention. 作为
he told the Riformatori at the trial, had he not been warned of a lurking
plagiarist, he would have liked to continue to improve the compass for a
while longer, before printing a book to make that final version “very
10.
“Io non mi trovo disegno buono per spiegar la fabbrica et l’applicazione della mia
macchina per cavar acqua: pero’ [……] con la viva voce e con un modello materiale, li potro’
dare migliore satisfazione …” Galileo to Baccio Valori (四月 26, 1602), Galilei 1890–
1909, 卷. X, p. 87.
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科学观点
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well-known and very widely disseminated”11 (Galilei 1890–1909, 卷. X,
p. 172). The identity of his invention could have remained a moving target for
a few more years, but fear of appropriation changed that. It had to be frozen.
Because Galileo primarily used it as a component of his instrument
making and teaching business, “Galileo’s compass” referred to whatever
the instrument was that he taught and sold to the students at a given time,
in the same way “Ford cars” refer to whatever cars a Ford dealership hap-
pens to be selling, irrespective of the fact that models change every year.
然而, concerned about a possible dispute, Galileo felt he needed to
give the instrument a more distinct and stable identity so as to stake
and better defend his claim to its inventorship. The objects involved in
disputes over observational or experimental claims become clearly identi-
fied at the closure of those disputes, but here we see that the compass was
stabilized in preparation for a dispute over its inventorship, as the result of
becoming a potential object of appropriation. 在此背景下, the Opera-
zioni functioned as a “NO TRESPASS” sign that marks the property it
is supposed to protect, identifying it in the process.
One of the ways in which modern patent law determines whether an
inventor has the invention s/he claims to have depends on his/her ability
to represent it in sufficient detail to enable a third party to replicate it.
Neither Galileo nor early modern Venetian patent law, 然而, 想法
that publishing a verbal or pictorial description of an invention proved
that one actually had such invention. You could use a publication to claim
or advertise that you invented something, but that could not prove that
the invention actually existed and that you possessed it. The description
could be inaccurate or even fictional, disclosing an invention that did not
工作, could not work, did not exist, or could not possibly exist.12 For
实例, Galileo argued that Capra was not the inventor of the compass
described in the book he had published on it because his description of
its operations, riddled with errors, did not make sense.13 They looked geo-
metrical but they were, as he put it, “worse than hieroglyphs”—mysterious
11.
12.
13.
In the introduction to the Operazioni he also mentions that, due to time con-
菌株, he decided not to include a detailed fabrica section in the book (Galilei 1890–
1909, 卷. 二, p. 370).
Several of these issues are discussed in Paolo Galluzzi 2020, PP. 163–211.
“[S]occorso mi fu dalla fortuna apparecchiato; e questo fu un grandissimo numero
di nefandissimi errori sparsi per tutta quell’opera [……] la quale crasissima ignoranza stimai
[……] potermi essere per saldissimo argomento, quando tutte le altre giustificazioni mi fus-
sero mancate, a far costare la verità, col dimostrare lui impudente, e non meno stolto,
usurpatore delle invenzioni mie.” The same argument was repeated in the Difesa (在
PP. 547–8, twice) and at p. 546, concerning another alleged appropriator. Also at
p. 555: “quanto da questo apertamente si comprendeva come egli mai non aveva consid-
erate, non che pratticato, questo Strumento, del quale si faceva inventore.”
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Galileo’s Compass
marks nobody could decipher at that time14 (Galilei 1890–1909, 卷. X,
p. 559). Along those same lines, you could claim to have invented a per-
petual motion machine, but there could be no functioning referent behind
that verbal or textual claim. 最后, the mere existence of a publication
could not certify that its author even understood what s/he wrote in it.
One could claim inventorship of a properly functioning instrument
described in a publication but could be later shown to have lifted that
description verbatim from some other source without comprehending
what s/he was copying.
A publication could, 最好, describe an invention but could not certify
that the author of that publication was the inventor of the invention it
described because “having an invention” typically meant being able to
show it at work and teach it to a third person.15 A publication, 然而,
was perfectly appropriate to secure authorship of any type of claim or work
reducible to textual form: a scientific claim or observation, a poem, a music
分数, or the description of an instrument. One could easily be the author
of a book about the compass without being the inventor of that compass.
Galileo’s opponent, Baldassarre Capra, largely fell in that category. 尽管
Galileo wanted to produce, teach, and sell his instrument (and thus be rec-
ognized as its inventor primarily in relation to his teaching business),
Capra seemed primarily interested in receiving authorship credit for the
book he wrote about the compass, with the goal of gaining visibility
and securing a job as a physician, possibly a court physician. 目前还不清楚,
实际上, that Capra ever built the instrument. Their goals and strategies
could have remained complimentary. Galileo could have had his compass
and Capra his book.
然而, for reasons whose analysis would exceed the confines of this
文章, each of them took extra steps that created overlaps, and thus con-
flict. Galileo was mostly concerned with the compass as an invention to
teach and sell, writing its instruction manual for pedagogical purposes,
not as a publication. 最终, 然而, he turned those instructions into
a book to warn off a possible copier he had heard about (WHO, at that point,
may or may not have been Capra). 反过来, Capra may have initially
14.
“Non sono molto esercitato nell’indivinare i sensi di figure non geometriche, 嘛
peggio che ieroglifiche, poste senza costruzione, senza demostrazione, e forse senza propo-
sizione e senza proposito, e poste più, per mio avviso, per spaventare le menti de i semplici.”
(Galilei 1890–1909, 卷. 二, p. 559).
15.
Symmetrically, being able to teach an invention to others showed that that person
possessed that invention (and thus was an inventor according to the early modern meaning
of the term). 然而, unless a working model of that invention was deposited somewhere,
there would have been no way to determine the identity of the invention taught by the
inventor. Such was Galileo’s predicament.
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科学观点
447
planned to publish a compendium book about the compass, helping him-
self to material published by other mathematicians, including Galileo’s
manuscript instructions, which was not an unlawful action according to
the laws of the day. 最终, 然而, Capra’s book ended up including
an implicit but easily recognizable accusation that Galileo, contrary to his
high-decibel claims in the Operazioni, was not the compass’ inventor. 这
complicated and energized Galileo’s further response. He had started by
fearing that somebody was going to appropriate his compass as an inven-
的, but ended up taking Capra to court claiming, 除其他事项外,
that Capra’s book was injurious to his honor. Galileo was not able to pro-
duce any evidence that Capra had actually copied and sold his compass,
but reframed his attack based on the publication of Capra’s book, claiming
that he had libeled him by implying he had lied about being the true
inventor of the instrument. The ensuing dispute was as virulent as it
was confusing, involving claims that continuously straddled the line
between plagiarism of books and appropriation of inventions or between
scholarly norms and Venetian laws.
讽刺地, the Operazioni was the first book Galileo ever published,
though he only became an author to buttress his status as an inventor.
And while he relentlessly accused Capra of having plagiarized his instru-
蒙特, in the end he pursued him for something resembling libel and for
other book-specific injuries, like having copied the Operazioni into his Usus
et fabrica circini. 最后, because Galileo had not patented the instrument,
the dispute did not and could not take the legal form of patent infringe-
蒙特. It was litigated, 反而, as a book plagiarism case in front of a spe-
cialized politico-bureaucratic body overseeing both the University of
Padua and the Venetian publishing industry. Capra was condemned for
having copied substantial parts of Galileo’s book and translating them into
Latin, and for having stained Galileo’s honor and that of the university
where he taught (Galilei 1890–1909, 卷. X, p. 560). The compass itself
was not mentioned in the sentence given that this had become a book pla-
giarism and libel case, and yet the instrument was clearly part and parcel of
the court proceedings. In preparation for Capra’s interrogation, a small
desk was brought in with Capra’s book and Galileo’s compass on it (Galilei
1890–1909, 卷. X, p. 550).
仍然, at the core of this remarkably complex set of claims, moves, 和
slippages between books and machines the question remained: what was
Galileo’s compass? How could that question be settled? And how would
the relationship between the compass and its instruction manual factor
into that determination? Although Galileo ended up pursuing Capra
not for the appropriation of his instrument but for having stained his
honor (by accusing him not to be the inventor of the compass and
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448
Galileo’s Compass
implying he had appropriated it from somebody else), he still had to show
that he was the true and legitimate inventor of his calculator, so as to prove
that Capra had libeled him. The identity of the instrument was absolutely
central to that determination despite the fact that property per se was not
the issue. 换句话说, Galileo had to show that he was the inventor of
the compass so as to prove that Capra had libeled him, not to argue that
his property rights had been violated.
Why Not Patent?
It is worth asking why Galileo did not try to avoid all this trouble by tak-
ing out a patent on the compass instead of publishing the Operazioni. 很多
of that, 我认为, had to do with the fact that the compass, being a math-
ematical invention, straddled the line between text and machine, 之间
the domain of copyright law and that of patent law. We have seen the
replaying of similar tensions in modern debates over the intellectual prop-
erty status of software, specifically on whether it is an authorial work or
“a machine made of text” (Samuelson et al. 1994, p. 2320).
Venice had granted patents for centuries, and Galileo himself sought
and obtained a patent for a water pump there in 1594.16 The novelty of
his instrument should not have been an issue. It was not as unique as
Galileo claimed it was—there were several instruments by Italian and
European mathematicians that displayed family resemblances to
Galileo’s—but it easily exceeded the strictly local standards of novelty,
那是, “new in Venice” rather than “new in the world” required for pat-
ents in the early seventeenth century17 (Biagioli 2006b, PP. 147–52).
While he did not explain his decision not to seek a patent for the compass,
we know that he previously patented a water pump, going so far as to
borrow money to have a good model produced (Renn and Valleriani
2001, PP. 481–503). What made the compass different from the water
pump? 还, does it mean that there was some commonality between
the compass and the telescope, given that he did not patent it either?18
16. On the water pump patent see Galilei 1890–1909, 卷. XIX, PP. 126–9. 上
protection of invention in Venice see Giulio Mandich (1948, PP. 166–224, 1960, PP. 378–
82); Frank Prager (1946, PP. 109–35); Roberto Berveglieri (1995); Luca Mola (2004,
2007). On the protection of printed books see Leonardas Vytautas Gerulaitis (1976);
Horatio Brown (1891).
17. Prior art would not have been a problem unless there was already an established
local manufacture of that instrument in the area, which was not the case.
18.
Independently from whether he did or did not actually patent a specific invention,
pump, compass, telescope, Galileo always acted as an early modern inventor. This is espe-
cially exemplified by his secretive attitude and reluctance to disclose the “secret” of his
inventions or instruments; a non-disclosure that early modern patent law, unlike the cur-
rent one, had no problem with. He never published a book about the pump, and the books
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科学观点
449
It is possible that, given how easy it was to copy the compass, 这
authorities might not have bothered to grant a patent.19 Its simple
mechanical design (two flat metal legs hinged at one end) and its very vis-
ible calculating lines (much closer to a text than to the gears of a machine)
made copying a compass probably easier than either producing a pirated
edition of a book. 例如, when Galileo decided to present Prince
Cosimo de’ Medici with two silver compasses in 1606, a Medici official
had a Florentine artisan prepare the blank instruments according to his
specifications. The same official then had a certain Master Raphael, 问题-
ably an engraver, inscribe the calculating lines on the legs using as a
he published about the compass and the telescope did not describe how to produce those
仪器. In early modern terms, they were usus, not usus et fabrica books (on Galileo’s
non-disclosure of the telescope see Biagioli 2006c, PP. 119–29). What seemed to matter
the most to Galileo when he decided whether to patent or not his inventions was the nature
of the device and the business model through which he planned to extract value from it.
The pump was a machine he obviously hoped to sell for others to use. The compass, 反而,
was an instrument her extracted value from not just by selling it but mostly by teaching it.
It does not look like he ever thought about the telescope as something he would enrich
himself from selling it en masse, focusing instead on the value he could extract from the
discoveries he was able to make with that instrument. His view of the telescope’s value,
然而, changed quite radically very early in 1609, after he realized the philosophical
importance of the discoveries he was making. Prior to that, he had pitched his telescope
to the Venetian authorities as a military instrument, seeking a reward for it. While that did
not take the shape of a patent, it was not conceptually removed from the logic and protocols
for the protection of inventions, especially military inventions. I have tried to show that, 在
事实, Galileo presentation of his telescope to the Senate in the summer of 1609 may have
occurred at the same time, and in competition with, a similar presentation by a northern
European inventor who was seeking a reward (probably folded together with a patent) for a
competing telescope from the Venetian Senate. 总共, Galileo’s showcasing of the tele-
scope was formally congruent with a patent application for a military technology, 哪里的
invention cannot be sold on the market (which would defeat its military value for the Sen-
吃) but is instead “donated” to the Republic in exchange for a reward. Military inventors
would typically receive pensions or positions at the Arsenal, or a mix of both, while Galileo
received tenure and a much higher salary from the university. The two types rewards are
materially different and involve different institutions, but they share the same logic: a gift
of a technology to the Senate with the guarantee of not divulging the invention to anybody
别的, in exchange for a secure position and/or monetary compensation. 所以, while it is
formally correct to say that Galileo never received a patent for the telescope, the modalities
he followed in his presentation were formally comparable to the protocols that a inventor
would follow while pursuing a patent for a military technology in Venice (比亚焦利 2010,
PP. 203–30, 特别是. 224–9). If Galileo initially perceived the telescope as a kind of invention
to be patented, that would indicate that the compass was different from both of his other
inventions. Both the pump and the telescope were just machines. The compass was some-
别的事.
19. On the failed attempts to patent the earliest telescopes in the Netherlands see Van
Helden (1977).
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Galileo’s Compass
template another compass Galileo had left in Florence with that same
Medici official the previous summer, “so that, with that example, he will
be unable to make any mistake” (Galilei 1890–1909, 卷. X, p. 157).
That one could make virtually identical copies of compasses is both
important and anomalous because, in the early modern period, copying
machines was much more likely to yield imitations than identical replica-
系统蒸发散. Galileo’s telescopes, despite being rather simple devices, were never
even close to identical, due to the hand-grinding of the lenses.20 Exact
copies of complex machines had to wait till about 1800 with the introduc-
tion of interchangeable parts manufacturing.21 But if you had access to one
of Galileo’s compasses and knew a skilled artisan, you could have a virtu-
ally identical replica made of it. Its “textual” form made it easily reproduc-
ible. Copying a compass was a lot closer to making a measuring rod than
to reproducing a windmill.
此外, while copying a complex machine would have required an
understanding of that machine, the Medici official could rely on an artisan
WHO, while skilled at engraving or fine metalwork, could copy the compass
without needing to understand what it did, or how to use it.22 He just
measured and transferred the lines and their divisions from one leg onto
其他. The compass, in sum, could be copied almost the way music or
film is pirated today, by people who can press a button but do not need to
know anything about music or film. None of the tacit knowledge that may
have been required to copy a TEA laser or Boyle’s air pump was involved
in copying Galileo’s calculating instrument (柯林斯 2010; Shapin and
Schaffer [1985] 2017). This had much to do with the fact that unlike
Pascal’s, Leibniz’s, or Babbage’s calculators, Galileo’s compass calculated
through lines, not complex gears; lines could be replicated as easily as
words in a book (琼斯 2016).
Between Brass and Paper
The compass was not a unitary instrument like a telescope or an air pump,
but a material platform for several different sets of lines, each defined by its
20. Arguments about the impossibility to produce identical copies of machines (作为
opposed to the possibility of producing identical editions of books) were commonly
deployed to differentiate between patent law and copyright law, and to argue that inven-
tions could only receive weaker protection than printed books because of that. On this
wide-ranging debate, see Burrow (1773, p. 56).
21. The exception were devices like cannons that could be produced by casting, 和
then bored to the appropriate caliber. While we could say that they were “mass produced,”
these were very simple machines with no moveable parts.
22. This was obviously not the case with early calculating machines through complex
gears rather than lines, see Jones (2016).
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科学观点
451
specific division, which could be inscribed on either the recto or verso face
of the compass’ flat legs. The specific choice of lines varied from
instrument-maker to instrument-maker though some, like those to perform
simple arithmetical calculations, tended to be present in most exemplars. 在
one case, the instrument-maker, Michiel Coignet, included so many lines
that he literally ran out of space. His answer was to distribute the lines over
two instruments; a choice that raises the question of whether Coignet’s
instrument was one or two or whether, 反而, we should identify the com-
pass not with its hinged flat legs but with its formal features—the
lines—treating each set as a distinct instrument, or as a distinct “software
app” running on a “general” brass computer23 (Hulpeau 1626).
As these calculators circulated, mathematicians added new lines of their
own invention and dropped old ones. 在他的 1612 Latin translation of
Galileo’s Operazioni, Bernegger added two sets of lines, while commenting
on how many more the instrument could accommodate. 在 1610, Johann
Faulhaber published a book on an instrument nearly identical to Galileo’s,
which was in fact based on Faulhaber’s study of an instrument that he later
learned to be one of Galileo’s. Even in this case, Faulhaber picked and
chose some lines of Galileo’s while adding more of his own (德雷克
1978). The same kind of bricolage of new and old sets of lines is found
in the compass brought to Padua around 1602–3 by Jan Zugmesser, A
German mathematician who joined the household of the Archbishop of
Cologne and a few years later, 在 1610, became a critic of Galileo’s tele-
scopic discoveries. Zugmesser’s compass contained some of the lines of
Galileo’s instruments, as well as different ones24 (Galilei 1890–1909,
卷. X, PP. 366, 370, 417, 492). Around the same time, Clavius, the chief
mathematician of the Society of Jesus, published his Geometria practica
where he illustrated a flat-legged brass calculating compass. Together with
a copy of the book, Clavius sent Galileo a letter in December 1604 询问
for one of his compasses because “although in my Geometria practica I have
included a similar instrument shown to me by a certain German, I like
yours much better because of the variety of its uses” (Galilei 1890–
1909, 卷. X, p. 121). While appreciating its specific qualities and
23.
If we define an instrument in terms of its material parts, then we could say that
Coignet’s was either two instruments or one instrument in two parts (like a book with two
chapters). But if we define the instrument in terms of its function, then there would be as
many instruments as lines, no matter the number of material platforms those lines are
spread over.
24.
See also the discrepancies in the different reports of this event: Cornaro in Difesa;
Hasdale in Galilei 1890–1909, 卷. X, p. 370; Heilbron 2010.
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Galileo’s Compass
versatility, Clavius perceived Galileo’s compass as a member of a known
class of instruments.25
In the case of the telescope, copiers needed to reverse engineer its optical
scheme and learn how to grind lenses that were significantly different from
those produced by spectacle-makers (Helden 1977, PP. 1–67). 相比之下,
copying the compass was more like copying a text from an easily accessible
original. The lines were right there, engraved on the brass legs for every-
body to see (Figs. 1 和 2). While laying down the lines and their division
was a precision job, artisans were able to simply copy the divisions off
another compass, as the Medici engraver did in 1606. 此外, 这
lines could have been copied even by taking a tracing of the instrument,
那是, by using the instrument as a plate to print itself. That printout
alone would not have produced a workable paper compass; 图像
would have been reversed, but it would have contained all the information
needed to produce a functionally identical brass instrument (Jardine 2016,
PP. 36–42). A tracing could have been an interesting option if one had
access to a compass only briefly, without enough time to measure the spac-
ing of the marks on the lines.
Text-like features of the compass can be also found in its mobility and
evolution, which may be compared to the circulation, commentary, edit-
英, abridging, of books and manuscripts. Each compass might be seen as
an anthology of new and old lines of calculation—an edited instrument, 所以
to speak.26 The ease with which the compass could be edited, abridged
and expanded into a different instrument had the symmetrical effect of
making it difficult to trace what the original edition was, and the identity
of its author. Tracing the compass’ prior art would have been a philolog-
伊卡尔, rather than engineering challenge. Stillman Drake has proposed to
identify Galileo’s compasses by checking if they “have exactly the scales …,
in the same order of arrangement and with the same abbreviations and
25. As confirmed by the fact that Clavius did not even mention the name of the Ger-
man artisan in his book, thus treating the compass and its maker as effectively generic
(Clavius 1604, PP. 4–5).
26. This does not mean that the notion of priority could not apply to these instru-
ments and that Galileo’s authorship claims were groundless. 相当, we are dealing with a
complicated scenario of composite authorship, one where each contribution, each set of
线, is individual and distinct and, 像这样, can be potentially traced to its author; A
bit like the infringement of a free software license can be easily assessed by comparing
the disputed sequence of instructions with that of the original archived code. 理论上
the “intellectual property” aspects of a calculating compass like Galileo’s are much easier
to assess than whether or not the script of a Hollywood movie has plagiarized Jane Doe’s
小说 (或者是否, 说, Divini plagiarized Torricelli’s telescope lenses). 同时,
while the forensics would be simpler, at least in principle, what is hardly manageable is the
actual research work necessary to reconstruct the genealogy of a specific compass.
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科学观点
453
markings”—an approach that seems closer to that of philologists than
historians of technology (德雷克 1978, p. 31). 总共, the compass was a
strange kind of machine that resembled a text or a print in ways that
would have made patenting both difficult and toothless. 和, unfortu-
nately for Galileo, the compass could not be protected as a text either
because printing privileges did not cover machines; unless they were
printed paper instruments, which the compass could have easily been.27
Joined at the Hip
There is another less obvious textual dimension to the compass that greatly
impacted the way it could be claimed and replicated as an invention: 它是
symbiosis with its instructions. The Operazioni had such a tight relationship
with the compass that Galileo warned that the instructions book would
be “completely useless to those who receive it without the instrument”28
(Galilei 1890–1909, 卷. X, p. 370). And even those who already possessed
the instrument would have difficulties understanding the text unless they
had previously listened to Galileo’s instructions and observed his hands-on
demonstrations. (Galilei 1890–1909, 卷. X, p. 370). He reiterated the same
point at the trial:
Have I not written [in the Operazioni], and have I not said viva voce a
thousand times that the book without the Instrument is worth
nothing? And that even with the Instrument but without direct
instruction and without seeing its uses demonstrated in practice, 这是
tedious and difficult and unable to deliver [the compass’] 最多
attractive features? (Galilei 1890–1909, 卷. X, p. 370).
The symbiotic relation between instructions and instrument was even
stronger when the instructions existed only in manuscript form, 这是
for about nine of the ten years during which Galileo produced and sold the
compass prior to the dispute with Capra. In that period, he often referred
to the compass and the instructions in the same sentence, 这是
consistent with what we find in his accounting records, indicating that
they were sold together (Galilei 1890–1909, 卷. X, p. 586). 相似地, 这
affidavits from Galileo’s students that were produced at trial consistently
reported having received from him both the instrument and the instruc-
系统蒸发散. We find the same in Galileo’s correspondence, where friends who
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27. 车工 1989, PP. 23–42; 金格里奇 1971, 1993; Bryden 1997; Bennett 2003,
PP. 140–1; Eagleton and Jardine 2005; Karr-Schmidt and Nichols 2011; Jardine 2016;
Karr-Schmidt 2017.
“[右]endera’ questo trattato del tutto inutile a chi senza lo Strumento ei pervenisse
28.
nelle mani.”
454
Galileo’s Compass
asked him for a compass also asked, in the same line, for the instructions.
Galileo himself followed that practice when sending his instruments as
gifts (Galilei 1890–1909, 卷. XIX, PP. 150, 151, 154). 最后, 那里
are two instances in which the compass and the instructions are referred
to as the same thing, or perhaps two embodiments of the same object.
Writing to Galileo from Florence in 1604, a court official reported that
the Medici welcomed Galileo’s decision to dedicate “said instrument
and its instructions” to Prince Cosimo, conveying the sense that this
was one gift in two complementary parts—machine and text29 (Galilei
1890–1909, 卷. X, p. 144). 然后, as we have seen, Galileo referred to
his compass as something that he both made and printed: “I have given
[the compass] to many gentlemen of various countries, always presenting
myself as its author and inventor. As a thing of mine, I had more than one
hundred built in Padua and other cities. As a thing of mine, I have
recently printed it”30 (Galilei 1890–1909, 卷. 二, p. 543).
No matter whether we take Galileo’s claim literally or metaphorically, 它
is clear that the Operazioni was not, by his own admission, a free-standing
book about the compass that a reader could understand without help.
Printing only sixty copies (which he distributed himself, 从家里) 印迪-
cates that he did not intend to deliver the slim book to a general audience,
but simply meant “to give it out with the instrument” as a memory aid for
its users (Galilei 1890–1909, 卷. X, p. 370). Given that the book
described only the use of the compass, not its construction, it could be
relevant only to readers who had the compass already. 反过来, 它会
have been useless to those who only wanted to learn more generally about
the instrument. The instructions could only function with that instru-
蒙特, and the instrument with those instructions31 (Galilei 1890–1909,
卷. 二, p. 370). As a hyperbole-prone but perceptive admirer put it: “with
这 [Operazioni] you have given a soul to the compass”32 (Galilei 1890–
1909, 卷. X, p. 256). Without the instructions, the compass was lifeless,
unable to perform its functions. Like a computer without software.
29. Vincenzo Giugni to Galileo, 六月 4, 1604: “[……] la volontà di V. S. esser
d’indirizzare detto strumento et ragion d’esso all’Altezza del Principe nostro.”
30.
“[我]o l’ho conferito da dieci anni in qua a moltissimi Signori di diverse nazioni,
chiamandomene sempre con tutti autore et inventore; io, come cosa mia, ne ho fatti fab-
bricare più di cento in Padova ed in altre città; io finalmente come cosa mia l’ho stampato.”
“Aggiugnesi che il tacere io la fabrica dello Strumento [……] renderà questo trat-
tato del tutto inutile a chi senza lo Strumento ei pervenisse nelle mani. E per tal causa ne ho
io fatte stampare appresso di me 60 copie sole, per presentarne insieme con lo Strumento.”
32. Andrea Morosini to Galileo, 九月 4, 1609, “Con quello dell’uso ha dato
31.
l’anima al compasso”.
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科学观点
455
Virtually identical to the 1601 manuscript version of the instructions,
the Operazioni were old wine in a new bottle that Galileo produced in
response to two contingencies.33 The first was the need to secure a public
notice of his priority to try to block possible appropriators (Galilei 1890–
1909, 卷. X, p. 172). The second had to do with the fact that, for most of
its life, Galileo’s compass had not been a stable object.34 Because the Oper-
azioni did not describe the instrument itself but only its uses, the book
could not function as a proper “no trespassing” sign as it was not clear
where exactly the claimed property started or ended. 还, it could not
function as a priority registration either, given that it did not properly dis-
close the instrument—a public disclosure that, according to Galileo, 他
had already delivered through teaching it to students.
Galileo’s invocation of the “testimony of print” therefore referred to
something more specific and technical. It was a function the Operazioni
performed not primarily through its content but through the traces of its
出版物. 那是, it did not just function as a text but as an object—a
bureaucratic object constituted by administrative practices such as its
licensing and its registration with the Venetian printers’ guild. 伽利略
33. Because of space constraints, I can only mention two more: Securing a longer-term
university contract, and producing a suitable gift for Prince Cosimo de’ Medici. Concerning
第一个, Galileo’s last four-year contract expired in September 1604 and he had been teach-
ing on a year-to-year basis since (Galilei 1890–1909, 卷. XIX, p. 114). He had been
pushing for both the renewal of his university contract and a substantial raise (Galilei
1890–1909, 卷. X, PP. 105, 147, 149–50, 157–9). The Operazioni seemed to help his case.
When the new contract came on August 1606 it mentioned the forthcoming book as one of
the reasons for his reconfirmation and a hefty 50% salary increase (Galilei 1890–1909,
卷. XIX, p. 114). Galileo had received the license for his book only six weeks before, 在
六月 26. Concerning the second, by dedicating the Operazioni to young Prince Cosimo,
Galileo was trying to lay the groundwork for his move to the Medici court which he even-
tually obtained in 1610. 自从 1601, Florentine courtiers had been pressing him to ded-
icate the compass to prince Cosimo to strengthen his relationship with the future grand
duke (Galilei 1890–1909, 卷. X, p. 84). It took Galileo about five years to follow up on
the suggestion, making it a somewhat stale gift (the compass being ten years old by then),
but it all seemed to work out in the end ( Wilding, Galileo’s Idol, p. 44). Right after Galileo
expressed his desire to dedicate the book to Cosimo in June 1605, the grand duchess
Christina invited Galileo to come to court that summer to teach mathematics, 包括
the sector, to the prince (Galilei 1890–1909, 卷. X, PP. 144, 149).
“This is one of those subjects that do not allow themselves to be described or
understood with clarity and ease unless they are first heard viva voce or observed while
practiced. And this would have been a powerful reason to prevent me from print this work
had I not heard that somebody [……] was getting ready to appropriate it. This put me in
need to secure, with the testimony of print, both my works and the reputation of he who
might appropriate them,” Galilei 1890–1909, 卷. 二, p. 370. He repeated this claim—“to
block the road to those who wanted to steal my labors”—in his April 9, 1607 denunciation
of Capra to the Riformatori (Galilei 1890–1909, 卷. X, p. 172).
34.
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456
Galileo’s Compass
was not claiming his invention by making it public in the Operazioni, 但
rather producing a timestamp through the book for his claim that he had an
invention which, following the customary practice of inventors, 他不是
fully disclosing. (在这个意义上, the Operazioni functioned a bit like a cipher
or like the plis cachetés that scientists used to deposit by the thousands with
the Secretary of the Paris Academy of Science to secure a timestamp for
the claim that they had a claim they were not disclosing) (Berthon 1986,
PP. 71–8). Filling in what the claim was was done by the students.
From Memory, With Text
The way the Operazioni did ultimately provide effective evidence of
Galileo’s inventorship of the instrument it did not disclose becomes clearer
when we read the affidavits that his students submitted at the trial.
Giovanfrancesco Sagredo, the Venetian patrician later immortalized in
Galileo’s Dialogue, 写了:
I faithfully state [……] that already about nine or ten years ago I
received from [……] Galileo Galilei [……] one of his instruments which
he calls the Geometrical and Military Compass, and a similar one,
shortly after, with some lines slightly modified, and others extended
to handle larger numbers. And this instrument is exactly the same as that
whose use he printed a year ago under this title: The Operations of the
Military and Geometrical Compass, and whose instructions I received in
writing and voice together with the instrument at the
aforementioned time [……]35 (Galilei 1890–1909, 卷. 二, p. 534).
Jacques Badover (who would later play a role in Galileo’s development of
the telescope) confirmed that:
我 [……] declare and testify as the truth that [……] not only did I see
various of his Geometrical and Military Compasses, but I received
其中之一, and also its instructions. I was also shown [by Galileo]
the rules he followed to build it and mark its divisions, which at that
time he was busy with. And he modified and improved them
compared to those he had placed in the other Compasses he had
previously caused to be produced. 和, furthermore, I saw [……] 如何
35.
“Faccio fede [……] aver gia’ [……] dieci anni in circa havuto dall’Eccellentissimo Sig.
Galileo Galilei Lettor di Matematiche in Padova, uno de’ suoi strumenti chiamato da lui,
Compasso Geometrico, & Militare, & un’altro simile, poco dopo con alcune divisioni un
poco mutate, & con altre estese a maggiori numeri, il quale strumento e’ quello stesso a’
punto, del quale l’anno passato ne stampo’ l’uso sotto questo titolo: Le Operazioni del Com-
passo [……], la qual dichiarazione hebbi in scrittura, & in voce insieme allo strumento al
sopraddetto tempo [……]”
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科学观点
457
many of these same instruments were by their aforesaid Author
communicated to various Gentlemen of different nationalities.
And that instrument is the same as the one whose operations have
been printed last year by the Author here in Padua with the title
Operations of the Geometric and Military Compass of Galileo Galilei…36
(Galilei 1890–1909, 卷. 二, PP. 534–5).
Both Sagredo and Badover explicitly acknowledged the mutations the
compass underwent over the years, but then crucially invoked Galileo’s
1606 book as providing a snapshot of the instrument’s latest and
permanent incarnation, which they were familiar with. That seemed to
create a stable version of reference for the object Galileo claimed to have
been appropriated by Capra.
But the evidence of the compass’ stability and identity provided by
Sagredo and Badover is essentially different from what one could have
derived from a patent model. It did not result from matching a device
one has seen with the one instantiated by the archived replica. Notice that
neither student stated that they simply and directly identified the instru-
ment they were taught by Galileo with the one described in the Operazioni.
Both carefully stated, 反而, that the book contained the uses of such
instrument: “this instrument is exactly the same as that whose use he printed”
和, “that instrument is the same as the one whose operations have been printed
last year,” thus confirming that the instrument itself was not described in
the book. So how could the Operazioni be said to establish the identity of
an instrument it did not describe? And how could the testimony of his
students provide evidence that Galileo was the inventor of the instrument
he claimed to have been appropriated by Capra (and that Capra instead
implied that Galileo had copied from somebody else)?
The answer is right there in the affidavits. The Operazioni did not
describe the instrument, but Sagredo and Badover could testify that the
book still indexed the instrument it did not describe because they were
able to recognize the instructions listed in the Operazioni as those they
themselves had learned to perform on the compass Galileo had given
36.
“Io Giacomo Badovere Francese espongo et attesto come è la verità, che [……] 非
pure viddi diversi de’ suoi Compassi Geometrici et Militari, ma ne fui gratificato di uno, et
di più della sua dichiarazione, mostrandomi in oltre le regole che teneva intorno al modo
del comporlo et segnare le sue divisioni, intorno alle quali in quel tempo era occupato, et ne
mutò et migliorò alcune da quello che ne gli altri suoi Compassi, prima fatti fabricare sino
a quel tempo, haveva posto. E più, viddi [……] come molti de i medesimi strumenti furono
dal sopradetto suo Autore communicati a diversi Gentil’huomini di diverse nazioni: il quale
strumento è il medesimo che questo, le cui operazioni sono state l’anno passato dall’Autore stampate
qui in Padova sotto il titolo di Le operazioni del compasso geometrico et militare di Galileo
Galilei …”
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458
Galileo’s Compass
and taught them in person.37 His former students did not identify the
instrument by virtue of having seen it and subsequently being able to
match its look with a static image or model of record. More than on
their eyes, the identification relied on the mental and muscle memory
of how they had moved the instrument to perform various calculations,
after Galileo had taught them how, and how that memory matched the
instructions printed in the book. 换句话说, Sagredo and Badover
did not identify the instrument (the way an ornithologist may match a
photo of a bird with an image of reference), but they rather re-cognized it not
as an object they had seen already but one they had used before. Notice that,
unlike matching, recognition requires a movement back in time, not to
recall an object but a movement. In this sense it is not a “replication” of
an event in the present (喜欢, 说, an experiment) but the precise recollection
of a knowledge-producing action in the past—an action that could only
involve a user.
The Operazioni played a crucial role in this process of identification, 但
not as textual descriptions of the instruments, which they were not. 它
functioned as a memory device or “time machine” that returned Sagredo
and Badover to Galileo’s house, a few years back. The book did not mirror
the compass but the students’ memory of what they had done, there and
然后. (At the trial, Galileo claimed that Capra could have not possibly
understood the compass given that he did not even know how to hold
it in his hands)38 (Galilei 1890–1909, 卷. 二, p. 584). Thanks to the
memory of their experience learning and using the compass, Sagredo
and Badover were able to align all the various evidential elements that,
held together, constitute a distinctive object: (1) Galileo had that inven-
tion because he had taught and transferred several versions of it to them;
(2) that invention had eventually developed a stable identity; 和 (3) 这样的
identity was indexed (but not described) by the Operazioni.
At a time when invention was defined not by what it was but by what it
做过, it should not be surprising that the identity of an invention would not
depend on the static match between two representations—a machine on
one hand and its description of record on the other—but on a match
between the embodied memory of the users and the text of its instructions.
The identifying match was not between two objects but between two
37. That they were able to identify the instrument through its instructions, 没有
its description, confirms how symbiotic the relationship between instrument and instruc-
tions was. It also makes Galileo’s friend’s aforementioned statement that the Operazioni were
the “soul of the compass” sound less hyperbolic.
38. Also related: “Costui non è un sonator di liuto, che erri nell’aria, nella battuta, nel
contrappunto; erra nel tener lo strumento in mano, appoggiandosi le corde al petto, 编辑
applicando la man destra alla tastiera” (Galilei 1890–1909, 卷. 二, p. 587).
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科学观点
459
doings, one embodied and one described textually in the instruction
手动的.
Instructions as Models?
Having repeatedly differentiated the role of the Operazioni from that of a
模型, it may seem strange to conclude by trying to analogize them. 但
there is a specific sense in which the instructions could be seen as function-
ally equivalent to a working model, 那是, not a model resting on a shelf,
but one that displays how the invention works in time, as it performs its
function (Pottage 2011, PP. 621–43). Instructions are textual and working
models are material, suggesting an essential qualitative difference between
the two. But in fact both instructions and working models, when inserted
back into the pedagogical practices of which they were integral part, 分享
a crucial feature: they show and/or simulate time, enabling an understand-
ing of the invention in motion, either continuous motion (as in a wind-
mill) or step-by-step motion (as in Galileo’s compass). It is that pattern of
motion that identified it—a movement that lawyers construe as the prin-
ciple or idea of the invention, and mathematicians regard as the steps con-
stituting a calculation (Pottage 2011, p. 625).
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