S.G. Sterrett Original Scientific Paper
Department of Philosophy UDK 167/168 Витгенштајн Л.
Wichita State University 14 Витгенштајн Л.
PICTURES, MODELS, AND MEASURES1
Abstract. In this paper, I enrich the context of Wittgenstein’s Tractatus given over a
decade ago in my book Witttgenstein Flies A Kite (and related earlier works dating
from 2000). I’ve since located a sketch reprinted from a 1914 Paris magazine showing
a lawyer using a model bus and dolls to depict a traic accident; I present it here
along with a discussion of the modelmaker movement of that time. he modelmaker
movement was a movement at the intersection of popular culture and technical
expertise that really needs to be understood and recognized in discussing Wittgenstein’s
use of Modell and Bild. I discuss its role in relation to experimental models used in
scientiic research. Other new aspects presented here include: the very special role of
model-lying clubs (known in Germany as Modell-Flugverein); the use of scientiic
forensics in courts of law, really just beginning then (c. 1914), and a part of popular
culture as well; the signiicance of more recent work by others on Boltzmann’s personal
interest in light, and on the widespread but now-forgotten discussion of dimensional
analysis in the history of physics. I conclude that all these lend support to the views on
the Tractatus I laid out in my book, and summarize and elaborate on some of them here,
inasmuch as space permits. More generally, I argue that the philosophical community
interested in interpreting Wittgenstein’s early works stands to gain from becoming better
acquainted with the scientiic and technological developments of the milieu in which
they were conceived.
Introduction
The Tractatus was completed almost one hundred years ago. That is recent
enough that readers tend to feel comfortable taking the terminology of
pictures, models, and yardsticks to have the connotations familiar to us today.
Many commentators rely on their own familiarity with the terminology
of pictures, models and yardsticks when discussing the text. This is likely
attributable to lack of better options: Wittgenstein directed that all his books
and papers were to be disposed of when he left Cambridge, so there is little
to go on from that early period, in terms of his personal effects. Another
shortcoming in historical sources commonly consulted by academics writing
on early 20th century analytic philosophy is that history of science and
technology has not been as integrated into philosophy as, say, history of logic
1 This paper is based on the paper of the same title presented at the 2015 Pacific APA
Meeting, Vancouver, BC April 1–4, 2015 in the Invited Symposium: ‘Wittgenstein’s ’Picture
Theory’’ 1 pm Friday, April 3rd.
Belgrade Philosophical Annual 30 2017 DOI 110.5937/BPA1730099S
100 S.G. Sterrett
and literature has. Though lack of his personal effects may be the reason for
looking to Wittgenstein’s milieu for the contextual cues in reading his works,
in general I think there is something of value to be gained in looking at
the context specific to an author at the time they wrote a text, anyway. The
availability of materials following the massive digital archiving of magazines,
newspapers, and journals that has occurred in the last two decades now
makes it possible to bring things into discussion that were not as convenient
to locate a decade or two ago.
My hope in this paper is to enrich discussion about pictures, models and
measures in the Tractatus by providing context about technology and science
in the life of the author of the Tractatus (e.g., circa 1889–1919). Situating his
remarks and works in that landscape should yield a more complete account
of what was being said, and thus aid in sorting out some puzzling passages
and themes.
Situating This Paper
There have of course already been some works that consider the contribution
that research in intellectual history might add to understanding the Tractatus,
and some of these tend towards the scientific and technical. McGuinness
researched Wittgenstein’s years studying engineering: at the Technische
Hochschule (THS) in Charlottenberg near Berlin, at the Kite-Flying
Station in Glossop near Manchester, and at what is now the University of
Manchester, where he was enrolled as a research student in aeronautical
engineering. McGuinness identified the courses in Descriptive Geometry
and Graphical Statics taught at the THS as important to Wittgenstein’s idea of
the proposition as picture. (McGuinness 1988/1995, p. 61) Janik & Toulmin
(1996) explore overarching intellectual movements in Vienna, including
art and music2 What my contribution here provides in terms of historical
context is somewhat more specific to the interests and situation of the author
at the time in his life when he wrote the Tractatus, but it is in the same spirit
of providing context for that work. I believe the work presented here pulls the
curtain on something that was ubiquitous in science and technology at the
time, but has since disappeared from view—certainly from the view of most
philosophers and philosophers of science today: the language of dimensions,
2 Hamilton’s ‘Wittgenstein and the Mind’s Eye’ in Klagge, James C. (2001) Wittgenstein:
Biography and Philosophy, Cambridge University Press discusses Wittgenstein’s time
at the Technische Hochschule in Charlottenberg and so is another such contribution.
Hamilton (2001) emphasizes the use of visualization in engineering, and does not
mention wind tunnels or experimental scale models. Hamilton (2001) puts a great deal
of emphasis on the significance of the coursework at the THS in Descriptive Geometry,
though fails to mention that Brian McGuinness had a decade earlier made the claim that
the notion of ‘proposition as picture’ owed much to reflection on Professor Jolles’ classes
in Descriptive Geometry and Graphical Statics. (McGuinness 1988, p. 61)
Pictures, Models and Measures 101
sometimes referred to as dimensional analysis or the theory of dimensions.
There has been some recent work in philosophy on the history of the concept
of dimensions in science, however, hopefully portending a resurgence of
interest. (Mitchell 2017; de Clark 2016, 2017; Walter 1990) This element of
Wittgenstein’s milieu—dimensions (in the sense of dimensional analysis and
dimensional equations) was often referred to as the language of science at
that time (as opposed to the current tendency to confer that status on logic,
set theory, model theory, or differential calculus). I first presented my own
speculations on an interpretation of the Tractatus in which the puzzling
account of objects in the Tractatus becomes clear when seen on analogy
to dimensions, in a submission to HOPOS 2000 in Vienna in late 1999; it
appeared the following July in the book of abstracts for the HOPOS 2000
program3 I gave a short version of the paper at HOPOS 2000 and a longer
3 As the online archive of HOPOS conferences and workshops does not at present include
the year 2000, the abstract of my talk at HOPOS 2000 is not available on the HOPOS
website. Hence I provide it here:
‘’Physical Pictures: Models in Engineering Practice circa 1914 and in the Tractatus.’
In 1914, Wittgenstein recorded an incident in his Notebooks that he later mentioned
to several friends as occasioning a major insight for his views in the Tractatus that
propositions represent by being pictures. The entry reads: ‘In the proposition a world is
as it were put together experimentally. (As when in the law-court in Paris a motor-car
accident is represented by means of dolls, etc.)’ This incident, he said, was pivotal in
coming to the view in the Tractatus that propositions represent by being pictures. In his
later writings as well, investigations of what it is to understand a proposition remain tied
to investigations of what it is to understand a picture.
Numerous scholars have looked to Hertz’ Principles of Mechanics as the element of
Wittgenstein’s milieu from which he drew the notions of model and picture used in the
Tractatus; that they have done so may be due to a brief parenthetical remark in a much
later section of the Tractatus. However, I think that a far more relevant source of a notion
of model in Wittgenstein’s milieu was the engineering scale model. The methodology of
scale modeling is strikingly different from analytical methods, in just those ways that are
important to the notion of picturing found in the Tractatus: the primary notion is that of
translatability between two physical situations, rather than between a physical situation
and a mathematical or linguistic representation, or, even, between two physically similar
situations whose similarity is established by showing that they are both instantiations
of the same more general equation or general description. The notion fits well with the
remark: ‘The essential nature of the propositional sign becomes very clear when we
think of it made up of spatial objects (such as tables, chairs, books) instead of written
signs (3.1.4.3.1)’ It’s also significant that the methodology of scale modelling can be used
when one has no theory by which the behavior of the model can be predicted, or, even, a
theory of the phenomenon being investigated.
Since wind tunnels were already in use in Germany when Wittgenstein did his
engineering studies there, the concept of scale model would actually have been in the
milieu much earlier than the pivotal 1914 notebook entry. However, the methodology
of scale modeling was then more a matter of engineering practice than it was a formal
methodology. At the time Wittgenstein recorded the insight about a world being ‘put
together experimentally’, the field was at a threshold as far as the formalization of its
methodology; logical and mathematical foundations of the practice were just then
beginning to be developed. It was in 1914 that Buckingham’s proof about the minimum
number of dimensionless groups needed to identify physically similar situations was
102 S.G. Sterrett
version later that year titled: ‘Physical Pictures: Engineering Models circa
1914 and in Wittgenstein’s Tractatus.’ (Sterrett 2000) At the time I offered it
as an original and unprecedented suggestion, somewhat speculative, resulting
from many years of thinking about the methodology of scale models and the
Tractatus. It was speculative in the sense that the interpretation of the text
had come first; searching for historical evidence afterwards.
Subsequently, i.e., over the last twenty years, I have delved further into
both the history and the philosophy of the concept of ‘physically similar
systems’ and the theory of dimensions. (Sterrett 2006; Sterrett 2009; Sterrett
2017a; Sterrett (forthcoming a)]. I can say without reservation that all this
further work made the suggestion seem far less speculative than when I
initially presented it. The few unconnected historical bits that I had to go on
when I first presented at HOPOS 2000 on the role of dimensional analysis
and scale models in the scientific and technical milieu in which Wittgenstein
conceived and wrote the Tractatus, were merely to establish the existence of
the methodology of experimental scale models (physically similar systems) at
the time, and show it was part of his world. This has since been supplemented
to give a somewhat fuller account of the cultural ubiquity of other kinds of
scale models, clarifying the role of experimental scale models among other
kinds of scale models of that time, their especially tight connection to the
history of flight in the year 1914, and indications that Wittgenstein not only
would have been well placed to appreciate their role, but that he most likely
did in fact have such an interest. In addition, some recent work on the history
of dimensional analysis by others now makes it clear that Wittgenstein’s
interest in physics (as opposed to engineering) during his youth was another
possible source of knowledge of the theory of dimensions. (Mitchell 2017; de
Clark 2016; 2017; Buchwald 1994, p. 200ff; Walter 1990, Ch. 4) Though my
initial analogy between dimensions in science and objects in the Tractatus
did not crucially depend on any particular historical claims, it turns out that
all the above support the suggestion that the theory of dimensions and the
notion of physically similar systems were relevant to Wittgenstein’s interests.
Pictures and Models
While many have attributed a ‘picture theory’ and/or ‘Bildtheorie’ to
Wittgenstein, I am not aware of Wittgenstein ever having used the term
‘picture theory’. What I have noticed is that there is a point in time before
presented in London. I’ll also explain why I think the use of a scale model in the context
of a courtroom, rather than a laboratory, lent significance to the incident.’ (From: HOPOS
2000, Third International History of Philosophy of Science Conference, Vienna, July 6–9,
2000. Abstracts. Booklet with letterhead graphics for Institute Vienna Circle: Society for
the Advancement of Scientific World View. Imprint: kognito Berlin Conference website:
http://ivc.philo.at/hopos/2000.htm)
Pictures, Models and Measures 103
which Wittgenstein does not use the word often translated as ‘picture’ (Bild)
in connection with a proposition; but that, after that point, the word and its
cognates appear frequently in his writings. They occur not only in his writings
in the weeks immediately afterwards; many works written even decades later
feature ‘picture’, both as a verb [abbilden, tr. as depict] and as a noun [bild, tr.
as picture].
That point in time—i.e., the point in time before which Wittgenstein does
not use the word ‘picture’ in connection with a proposition, and after which
he frequently does so—is recorded in the notebooks he kept while serving
in the military, so we know the date (September 29, 1914), and we know
what, according to him, occasioned the insight he regarded as so crucial. We
know this not only from the notebook entry itself, but from the fact that he
recounted the vivid memory he retained of the occasion on which he had this
pivotal insight to several friends, multiple times. (von Wright n.d., p. 20 fn. 9;
p. 20–21) What occasioned it, he said, was reading about the use of physical
miniatures (‘puppen’)—a miniature model—to portray a traffic accident in a
courtroom. The description itself found in the notebooks, made on the day he
recorded the occasion, actually appears very unassuming on its face, in itself
giving no sign of the importance he seemed to later place on it, as it is placed
inside parentheses. After ‘In the proposition a world is as it were put together
experimentally’ [Im Satz wird eine Welt probeweise zusammengestellt.] he
puts in parentheses the following phrase: ‘As when in the law-court in Paris
a motor-car accident [automobilungluck] is represented by means of dolls
[puppen], etc.’ Though, that he had some sense of the importance he expected
it to hold for his project is indicated in a note that follows directly after: ‘This
must yield the nature of truth straightaway (if I were not blind.)’ (p. 7)
If Wittgenstein is talking about physical objects like dolls, as it seems he
is, you would expect him to talk about models rather than pictures. David
Stern’s commentary is helpful here: regarding the use of ‘picture’ rather than
‘model’ in the term ‘Picture Theory’ that is used by so many commentators,
Stern explains: ‘Wittgenstein used the word ‘Bild’ to talk about the model, a
term usually translated as ‘picture’; [...] While both words cover such things as
images, film frames, drawings, and paintings, the idea of a three-dimensional
model is more readily conveyed by the German ‘Bild’ than the English ‘picture’.
(Stern 1995, p. 35–36) However, I would amend Stern’s comments, in a way
that does no damage to his point, with the recognition that we actually do
in fact see Wittgenstein use the word model, too—notably, to relate Bild and
Model. This is in T 2.12: ‘A picture [Bild] is a model [Modell] of reality.’ [Das
Bild ist ein Modell der Wirklichkeit.] Stern is not the only major commentator
on Wittgenstein who seems not to notice this line of the Tractatus, though,
so I would like here to highlight the fact that in the Tractatus there is this
explicit use of the word ‘Modell’ in the German text; thus the occurrence
of the word model in various English translations of Tractatus T 2.12 is not
104 S.G. Sterrett
solely a matter of the translator’s choice of how to interpret the term ‘Bild.’
In T 2.12, then, Wittgenstein is relating Bild to Modell [of reality]. This is in
line with Stern’s view, i.e., that the picture theory ‘involves generalizing from
what models, pictures, and the like are supposed to have in common, and
treats two-dimensional pictures as just one kind of Bild.’ [Stern, Mind and
Language, p. 36]
Instead of relying solely on notions of model readily available to us, we
can also look at the context in which Wittgenstein wrote this. I don’t mean
where Wittgenstein was located physically, but the cultural context in which
the German word Modell ought to be interpreted: How was the word used
then? What connotations were associated with the word then? A look at the
usage of the term ‘Modell’ at the time Wittgenstein wrote this line in the
Tractatus shows that in the late nineteenth and early twentieth century it was
often used in conjunction with models of machinery, including steam boilers,
engines, and automobiles, and that by 1914 it had become used frequently
in association with model airplanes. And, in fact, as I’ll show below, when
used in conjunction with airplane, Modell took on additional connotation:
airplane models were used not just as models to inform, illustrate, and delight,
but as experimental models meant to advance research. It is anachronistic to
look at the role experimental models have in scientific and technical practice
today, however. Interest in miniature models of machinery was a cultural
phenomenon: there were clubs that eagerly sought the membership of young
people still in school as well as of distinguished scientists; there were wellattended
public competitions and exhibitions reported on in newspapers, and
magazines devoted to the topic flourished. The magazines featured vendors
providing specialized products for the activity of building and furnishing
models. Some even thought of it in more epic terms, as a movement. It cut
across social classes, countries, disciplines, and professions.4
For context here, I look, not just at a particular point or period of space and
time, but at how Wittgenstein navigated through the various opportunities the
world presented to him. His interest in design and construction of airplanes
is consistent over many years. This is known largely from comments reported
by others. McGuinness, who spent many hours interviewing family, friends,
and acquaintances of Wittgenstein, writes that his sister said of Wittgenstein’s
interest when he made the choice to go to England to do research at the KiteFlying
Station in Glossop and study engineering in Manchester to long after:
‘As long as he worked in aeronautics at all, his aim seems to have been to
4 The closest analogue I can think of in current society is the cultural phenomenon of
computer games: there is a whole subculture built up around online computer games,
and many different communities, clubs, events, and publications have formed around
the activity of computer gaming. For children, the currently popular computer game
Minecraft might be an analogue in some ways to the cultural phenomenon of modelbuilding
in the late 19th and early 20th century.
Pictures, Models and Measures 105
design, build and fly a machine himself’. (McGuinness 1988/2005, p. 69) He
mentioned his strong interest in aeronautics to Russell even after he had left
engineering study at Manchester. It appears that he still had some interest
in engineering while at Cambridge studying logic. We know this due to a
letter of Russell’s. In managing the collection of Wittgenstein’s books and
papers he’s received, which he had agreed to buy when Wittgenstein had
decided to dispose of them, he writes to Wittgenstein asking him what he
ought to do with his parcels from engineering firms, at least some of which
I take to be printed materials. [Wittgenstein in Cambridge, Letter No. 90,
p. 127] Even though Wittgenstein had his books disposed of in 1914, they
were not destroyed nor lost to posterity; rather, Russell kept at least some of
them. From Russell’s collection, we know that among the books Wittgenstein
had while he was in Cambridge were many about the history of flight, as
explained below.
Other indications of the context that is relevant to Wittgenstein’s early
thought and writings are the desires he had about where and what to study.
In 1906, Wittgenstein had wanted to study with Boltzmann, and biographers
have assumed it was his interest in physics that explains this desire. However,
when Boltzmann died that year, Wittgenstein went to the Technische
Hochschule (THS) in Charlottenberg near Berlin to study engineering,
not physics. Oystein Hide, who identified, catalogued and reviewed the set
of books in the Russell archive thought to have belonged to Wittgenstein
(2004) believes that many of the books on the history of flight that we know
of in that collection were purchased from an antique bookseller during the
time Wittgenstein was a student at THS. This independently indicates that
Wittgenstein had an ardent interest in flight at the time, an interest we know
continued in the years to follow as he left Vienna to move to and study in
England. And, the visits to antique booksellers to purchase books on the
history of flight indicates that he fed that interest in activities outside of
the formal schoolday. Wittgenstein seems to have regarded his experience
at the THS as a waste of time. Knowing how he spent his time outside of
formal school classes, we can attribute to him both a lack of interest in his
engineering classes at THS and an ardent interest in designing, building and
flying an airplane.
Wittgenstein’s interest in flying as a boy does not need any special
explanation, as it was a very common interest for a boy at that time. But the
form that interest took—the kinds of books he bought, his huge decision to
move to England to pursue flight research in spite of his poor grasp of the
English language, and his interest in spending months in a relatively isolated
location doing research at the Kite-flying station—is somewhat singular.
Here, it seems to me, Boltzmann’s interest in and advocacy of flight research
may well have played an important role—as McGuinness also implies
(McGuinness 1988/2005). Boltzmann’s ‘On Aeronautics’ was a major lecture
106 S.G. Sterrett
delivered to one of the most important societies for scientific research. It was
a well-attended public lecture given near Wittgenstein’s family’s home in the
Allegasse in 1895, when Wittgenstein was six years old, was reported on in the
newspaper afterwards, and reprinted in early editions of the German editions
of his Populäre Schriften. I provided an English translation (‘On Aeronautics’)
as an appendix to my book, as no English translation of it was available.
Boltzmann stressed the value of studying kites in flight, presenting kiteflying
as crucial scientific research that could be carried out using a child’s
toy. What is interesting is Boltzmann’s remarks on the relative superiority of
England over Germany with regard to their expertise in experimental models.
As I noted (Sterrett 2006), when Boltzmann was asked to write an encyclopedia
article on Modell, he tried to refuse the request and suggested that instead
the editor ought to get someone from England, where there are experts on
models. (Blackmore 1995, p. 57) It is also worth noting that Boltzmann talks
specifically about models of flying machines, and what he says about them
is significant: ‘A distinction must be observed between the models that have
been described and those experimental models that present on a small scale a
machine that is subsequently to be completed on a larger, so as to afford a trial
of its capabilities. Here it must be noted that a mere alteration in dimensions is
often sufficient to cause a material alteration in the action...’
What Boltzmann describes here is the kind of model that, unlike many
other scale models, is an experimental scale model. Then he goes on to say that,
unlike the previous models he has been describing and making observations
on, these are different—in how they serve as models, and in the considerations
for constructing them—and he explains that the theory behind understanding
how experimental (scale) models are to be constructed is the theory of
dimensions: ‘... the various capabilities depend in various ways on the linear
dimensions. Thus the weight varies as the cube of the linear dimensions, the
surface of any single part and the phenomena that depend on such surfaces are
proportionate to the square, while other effects—such as friction, expansion
and conduction of heat, &c., vary according to other laws. Hence a flyingmachine,
which when made on a small scale is able to support its own weight,
loses its power when its dimensions are increased. The theory, initiated by Sir
Isaac Newton, of the dependence of various effects on the linear dimensions,
is treated in the article Units, Dimensions of.’ (Boltzmann 1974, 220)
Boltzmann’s mention of Isaac Newton in connection with experimental
models of flying machines explains an anomaly in Oystein Hide’s catalogue
of Wittgenstein’s books at the Bertrand Russell Archives. I noted that
Wittgenstein obtained a copy of Newton’s Principia.; this is very plausibly
due to Boltzmann making the point he did about Newton in this lecture, of
which Wittgenstein was almost certainly aware. Wittgenstein also obtained
a copy of Galileo’s Two New Sciences, a precursor to Newton’s writings on
Pictures, Models and Measures 107
the problem, which discusses the problem of experimental scale models in
almost the same terms that Boltzmann put it: in Galileo, a support structure
for a ship when built on a small scale, loses its strength when built in the
same proportions but of a larger size. These two purchases are anomalous;
there aren’t other books of that sort among his collection. Wittgenstein
owned no other books by Galileo, and the book he bought, an English
translation of Two New Sciences was very rare, difficult to find, and costly.
[see Sterrett 2006, p. 130–131] I speculated that Wittgenstein’s interest in
these rare books was due at least in part to Boltzmann’s remarks in his
encyclopedia entry ‘Modell’, since Boltzmann mentioned Newton’s theory
of dimensions as the basis for understanding scaling, and it is well known
that Galileo also takes up the topic in Two New Sciences. If Boltzmann’s
advocacy of flight research—he was concerned that Germany was behind
other nations—was salient in Wittgenstein’s life, it would explain the path
Wittgenstein navigated: first trying to study with Boltzmann, then studying
engineering in Germany, but leaving for a country considered better suited
to make advances in flight research at that time: England. I also noted that
Boltzmann’s formulation of the problem reiterated and reinforced the way
the problem of heavier-than-air flight was presented in Jules Verne’s Robur
the Conquerer in German (Clipper of the Clouds in England) which was
very popular among boys of Wittgenstein’s generation.5 I also discussed
the role of Viennese engineer Otto Lilienthal in the history of flight and in
Wittgenstein’s boyhood milieu. (Sterrett 2006, Ch. 2) Lilienthal’s fame has
stood the test of time and he is widely recognized as a pivotal figure for his
human gliding experiments.
It turns out that Boltzmann’ interest in flight was even more intense
and practically-oriented than I had realized: Boltzmann and Lilienthal knew
each other. Dahmen (2007) has devoted an entire article to the topic of
Boltzmann’s advocacy of research into heavier than air flight. He presents and
reviews the correspondence between Ludwig Boltzmann and Otto Lilienthal.
Boltzmann evidently was interested in purchasing a glider from Lilienthal and
it sounds like he was planning to carry out research using it himself. Thus
Boltzmann’s remarks about the theory of dimensions explaining the behavior
of experimental models of a flying machine in his article ‘Model’ are more
than a disinterested observation about the methodology of models; he may
have been thinking of staking his safety on it. The last line of that essay, about
the solution to the problem of flight requiring someone who is not only a
genius, but also a hero, could allude to the need for such personal risk-taking.
The remarks Boltzmann made in his article on models for Encyclopedia
Brittanica then take on much more significance. In summary, he made these
5 The presentation of the problem of heavier than air flight in Verne’s novel as a scaling
problem much the same way Boltzmann presented it in his encyclopedia article, ‘Model’,
is discussed in Sterrett 2006, p. 25 - 27.
108 S.G. Sterrett
important points: (i) It is not correct to think of experimental scale models
of flying machines in the same manner as the other kinds of models he
discusses. For the other kinds of models he discusses, he said, ‘it is perfectly
clear that these models of wood, metal and cardboard are really a continuation
and integration of our process of thought.’ But experimental models cannot
be regarded this way, he says. Thus the view of models as ‘a continuation
and integration of our process of thought’ is not the proper account of the
methodology of experimental models. Rather, (ii) the methodology of
experimental scale models of flying-machines is the theory of dimensions.
Importantly, he goes on to say that (iii) experimental scale models include
not only models in which mechanical forces are involved, but ‘models of
thermal, electro-magnetic and other engines—e.g. dynamos and telegraphic
machines’. This naturally invites the question as to whether the method used
for experimental models of flying-machines, i.e., the method of dimensions
we find the beginnings of in Newton, might be extrapolated from mechanics
to thermodynamics and electrodynamics, and, even, generalized so as not to
be specific to any particular physical phenomena.
The Model Engineer
None of the biographical work on Wittgenstein indicates that models of
airplanes had a role within the THS school curriculum, and Wittgenstein
later spoke of his education there as being of little value. Yet, there was more
to intellectual life than school. Did his hours outside school include model
building? It is hard to answer this for his specific years at THS, but it is
known that he built a model of a sewing machine (McGuinness 1988; p. 45;
178) while quite young, and that he was known at school for having a model
airplane. The significance of model airplanes to the epic problem of heavierthan-air
flight was that some, but not all, of them were successful examples
of heavier-than-air flight, and the ones that were successful could actually be
set in competition with each other, experimentally. Model airplanes powered
by large, strong rubber bands could fly for extended periods (on the order of
a minute or longer).6 The model of a sewing machine was a working model
as well. As Boltzmann indicates, the experts on making models were to be
found in England. But what kind of expertise is he talking about here; is he
talking about expertise in making the kind of models that Wittgenstein would
have had as a boy, e.g., airplane models and models of sewing machines to be
constructed by hobbyists?
6 As Wittgenstein was just about to leave research in aeronautics, an international cup
(now known as the Wakefield Cup) for “aeromodels” was established, and was first
awarded in April 1911 at a competition held in the Crystal Palace in London. One
account is available at old.fai.org/f1-free-flight/wakefield-international-cup/427-ciam/
ciam-f1/ciam-wakefield/33215-lord-wakefield-of-hythe-1880-to-1941
Pictures, Models and Measures 109
You might wonder why a distinguished physicist writing an encyclopedia
article would even take note of the skill of hobbyists or the expertise involved
in a toy-maker’s craft. But it is anachronistic to use the kind of categories
we’d use to characterize models now, such as toy versus scientific model, to
describe the models of the late nineteenth and early twentieth century. In that
encyclopedia article on models, Boltzmann mentions the model collection
in the US Patent Office; these would in most cases be working models of the
machines for which a patent was sought, though they would not necessarily
be models used for scientific and technical research.7 The goal would be to
illustrate how the machine worked; thus some scientific knowledge would be
drawn upon in designing the model to ensure that it would work in a way
that illustrated how the larger machine being modeled worked.
One manifestation of the cultural status of models is the magazine
Model Engineer begun in 1898 in the UK, and still being published today.
What was modeled? Boats, of course. But also steam boilers. Engines of every
kind. Windmills. Tractors (‘Traction Engines’) Railway cars for all sorts of
specialized purposes. Screw Propellers. Automobiles, too. These kinds of
models often aimed to please the eye as well as to illustrate how the machine
operated; thus, they usually reflected the proportions of the thing modeled,
at least for the visually prominent outlines. A few examples to illustrate how
the art of crafting small objects was intermixed with the employment of
mechanical principles
may be helpful here in
evoking the context in
which the word model
was used circa 1914.
First, here is an entry
about a model boiler
from the magazine The
Model Engineer and
Electrician in 1908, that
illustrates that ‘working
model’ was taken in an
extremely literal and
precise sense: here, the
author is proud of the
fact that the efficiency
of the model boiler is so
close to the efficiency of
the boiler it models.
7 A discussion of this collection, with excellent photographs, is online at ‘Invention and
the Patent Model’, The National Museum of American History at http://americanhistory.
si.edu/invention-and-patent-model
110 S.G. Sterrett
Many models were propelled by engines that really operated; often
various types of substances found in the household could be used as fuel,
such as paraffin or alcohol. The engines burned the fuels and the processes
inside them were very like full-sized engines, operating at high pressures,
as shown by the following article about providing safety valves for your toy
model engines:
These magazines featured original (i.e., only one was made) handmade
models with descriptions of the materials, processes and tools used. Model
hobbyists shared their experiences and advice, but some items, such as
model boilers and model engines, required so much work and practice to
get right that they were manufactured for sale to hobbyists for use in their
constructions, too. A model toy-engine might propel a boat, or a tractor, or
even an automobile. The 1908 Model Engineer and Electrician prominently
featured a model automobile; the wheels are 3 inches in diameter, and the
automobile is 13 inches long and over 7 inches high.
Pictures, Models and Measures 111
As Boltzmann noted, experts in constructing small models of machines
could easily be found in England; the implication is that one would have
trouble doing so in Germany or Austria at that time. The movement in
England spread to the US, too, with model clubs, exhibitions, and magazines
thriving there, too. Once one knows what to look for, examples of this
cultural phenomenon can probably be found in any number of places. For
example, in a recent biography of Ann Dunham, mother of President Barack
Obama, we read that her great-great grand-uncle Frank W. McCurry, born in
1893 (four years after Wittgenstein), who ‘climbed derricks as a child in Peru
[Kansas] and went on to become a pharmacist, a chemical engineer, and an
oil company vice president, acquired a certain degree of fame, as an adult, for
an unusual hobby. Over forty-five years, he built, fine-tuned, and continually
updated a fully functioning scale model of an oil refinery, made largely out of
glass. The model refinery, which had two catalytic cracking units and actually
produced gas from oil, traveled to high schools and colleges all across the
country’. (Scott 2011) Such accomplishments encountered in isolation from
the model engineer community appear as quirky personal interests, but
making exquisite working models of complex machinery was not in fact such
an unusual hobby in the US and the UK during the early twentieth century.
112 S.G. Sterrett
In some fashion, the movement spread to Europe, too: In the June 1914
issue of Popular Mechanics, it is reported that ‘there is a famous German
model shop in which exquisite miniatures of bridges, boats, steamers and
models for demonstration and experimental purposes are made’. Besides
the report on steamboats made for exhibition, there is this amazing news:
‘A model of a universal rolling mill for I-beams, with a capacity for beams
up to 40 in. high, was recently made in this shop, and the little model was
so perfect that machine-steel billets could be rolled into I-beams only 3/4-in.
high. Bridges, lifts and intricate machinery which cannot well be installed for
exhibition purposes are shown in miniature, and this firm is kept busy, orders
coming to it from all parts of the world.’ [‘Miniature Models Made in Big
Shop’ Popular Mechanics, June 1914.]
By 1914 the idea of a child making miniature models, rather than merely
playing with them, appeared in an advertisement in Popular Mechanics: ‘Say
Fellows! Build the Brooklyn Bridge ... in your own home—build it like real
engineers with real solid steel girders, beams, plates, bolts and nuts... . Build
traveling cranes, elevators, towers, aeroplanes, power derricks, Ferris wheels,
printing presses and automobiles that really run and work—build all your
own toys ...’
Recalling Boltzmann’s point about why experimental scale models are
different than other kinds of models that we use as ‘a continuation of our
thought’, i.e., that an experimental model that works when built at one size
may not work when using the same proportions but built of a different size,
we can see that often a model builder would have to take into consideration
factors other than just those needed to scale the linear dimension of the model,
Pictures, Models and Measures 113
if the goal was a working model. Yet
these were still not experimental (scale)
models in the sense needed for scientific
research. In the mind of someone who
pondered the relationship between
miniature machines and the machines
they modeled, the model engineer
movement might occasion the same
question that was so fundamental to
solving the problem of heavier-than-air
flight: how to scale up from the model
to a full size machine—but the model
engineer hobbyist would not really
need to solve that general question in a
rigorous manner. Ad hoc measures for
a specific model, used in conjunction
with scientific and technical
knowledge, trial and error, and sharing
of information via clubs and magazines,
was in many cases enough to produce
models that performed as intended.
Not all, however: a recurring theme in
the magazine was controversies over
how to design the screw propeller for
a model marine vessel. And flyingmachines
were enough of an exception
that those interested in model flyingmachines
often formed their own clubs.
Although the model engineer
movement was strongest in the UK and
the US, we have seen that there was a
shop selling these highly engineered
working models of machines and
machinery that had achieved fame
and was flourishing in Germany by
1914. Another movement in Germany
around that time was the interest in building and flying model aeroplanes.
An article entitled ‘Modell-Flugvereine’ [Model Flying Clubs’] in the Deutsche
Luftfahrere Zeitschrift of December 20, 1916, gives an account of this cultural
phenomenon in Germany8, from which I quote:9
8 ‘Modell-Flugvereine’, Deutsche Luftfahrer Zeitschrift, 20 Dec. 1916, p. 368. Smithsonian
Collections Online, http://tinyurl.galegroup.com/tinyurl/5jzP75. Accessed 7 Jan. 2018.
9 Original in German. The translation is my own, with a few changes suggested by Jasmin
Özel.
114 S.G. Sterrett
It is well known that our earliest and first designers and aviation
pioneers, such as Lilienthal, Etrich, Langley, Chanute, Wright and
others, experimented with their ideas on models and gained their first
experiences through various and iterated model constructions.
In many cities of the German Reich, a movement that began in
1912 led to the founding of clubs whose members were concerned
exclusively with the construction of model airplanes. Not for entertainment
or play, but for teaching younger members: to teach them about
the concept of ‘heavier than air’ aircraft, in order to help them develop
a proper understanding of the construction of such aircraft. And for
them, upon understanding, to give older members fresh suggestions
for continuing their experiments, when daunting failures occurred, as
they often do, when trying out a new model.
How this building of aircraft models and the association of modelmaking
supporters in clubs with each other increased the personal
knowledge of each individual and enabled them to accomplish what
would undoubtedly not have been so quickly and effectively achieved
without these studies on models, is becoming revealed in this war, in a
fortunate way. It is a commendable fact that, with very few exceptions,
almost all members of model clubs that have been drafted or joined
as war volunteers serve in the Air Force, where their service excels,
both among the aviation troops and the aircraft pilots . Others found
recognition of their abilities in technical service. Their prior knowledge
shortened their training and facilitated their understanding and their
ability to absorb new technical difficulties. The value of model making
is evident here. However, a lack of education and orientation of the
public eye—and, an unfortunately often intentional lack of regard
for this field of expertise on the part of many experts—can lead to a
misjudgment of the value of modeling.’
Wittgenstein left Manchester in 1911 for Cambridge, which is before the
movement took shape, according to this article; however, between 1911 and
the summer of 1914, he made trips back to Vienna numerous times. In fact,
he spent time in Vienna in July 1914. (This is based on the return address
of his letter to G.E. Moore from that visit.10) When he requested to join the
military, he had hoped to be assigned to the part of the military that had to do
with aeronautics, which, at that time, was located in the Balloon division.11
It is more than plausible that he would be interested in the existence of this
Modell-FlugVereine movement and, given his family connections, and his
experience living in Germany while studying at the THS, that he would be
able to learn of its existence and a little about its activities.
10 Wittgenstein in Cambridge shows that ‘Letter to G E Moore’ [from Wittgenstein] has
a return address from the house at Neuwaldeggerstrasse 38, on outskirts of Vienna.
(McGuinness 2008, p. 75)
11 http://www.wittgensteinchronology.com/7.html
Pictures, Models and Measures 115
The Model in Law-Court
As explained above and in previous work, my own evaluation of the role of
the event Wittgenstein placed so much emphasis on—of the miniatures being
used in a courtroom to portray a traffic accident—is that intellectually the
moment was more a matter of Wittgenstein’s recognition that he had come
across what he had been looking for, than it was a brand new realization
or a moment of transformation. That is, I believe that the moment was
significant, but that the significance it held was more like the significance
of an artist or writer coming across just the needed item or inspiration to
proceed with their efforts, as opposed to the significance of a moment of
conversion dislodging an opposing view. That is—as I think is often the case
with sudden insights—I think that Wittgenstein’s ideas about propositions
had already been developing, and seeing the use of miniatures to depict an
accident used by a lawyer in a law court suddenly gave him a metaphor or a
way of organizing those thoughts in an especially perspicuous way. The way
I described it in my book was that, when he had an insight occasioned by
the magazine article’s description of a miniature setup used in a law-court
that served up to him what he needed to formulate his thoughts about the
proposition-as-a-picture and picture-as-a-model, it was like the recognition a
sculptor has in lighting on an appropriate item to use as a found object in an
sculpture already partially envisioned. (Sterrett 2006, p. 251–252)
A great many people have written about Wittgenstein’s reading of the
use of miniatures in the courtroom. According to von Wright’s memoirs,
Wittgenstein mentioned it to many friends on many different occasions
(von Wright, n.d. 20 fn 9); noone, so far as I am aware, has ever located the
newspaper account or the court case about the traffic accident that occasioned
his insight. My concern, however, has been, not that the newspaper account
has so far not been located, but that these discussions have not put the use
of miniatures in the courtroom in their historical context. The context of the
history of science and technology is especially relevant here, for it reveals
that there was a time when miniatures were not just toys, but scientific
objects. As for the depiction of the use of models of a traffic accident in a
magazine, I have, in spite of the expenditure of an inordinate amount of time
on fruitless efforts to locate it, finally happened upon something close to it:
a magazine account of the use of a miniature car and bus to depict a traffic
accident, which was published in 1914. This is consistent with a report that
Wittgenstein, much later, spoke of seeing ‘a newspaper notice which said
that in Paris at a legal proceeding about a traffic accident, the accident was
presented with dolls and a little bus.’ (Klagge 2016) The sketch of the lawyer
using the miniatures is credited to a French publication published in Paris
(L’Illustration). It is striking that the mention of dolls and a little bus match
this illustration, too. I cannot be certain, in the sense historians demand,
that it is the same depiction of what happened in the lawcourt or even
116 S.G. Sterrett
that it depicts the same accident, but I think it is at least fair to say that the
illustration and accompanying text depict the sort of use of miniatures in a
courtroom that was a newsworthy practice in 1914.
The caption on the illustration reads: ‘Reproducing a Traffic Accident in
a Lawyer’s Office’ and the accompanying text, a brief news item, is: ‘LAWYER
STUDIES ACCIDENT WITH PLAT AND TOYS. A London lawyer, who
specializes in personal-injury litigation, in studying a case to place the
responsibility for the accident, and obtain a clear idea of the different phases
of the affair, reconstructs the whole occurrence on a plat or plan of the
locality, placing miniature vehicles representing the parties in such position
that the questions of right of way, traffic regulations, rules of the road, and
such matters, are clearly shown. Thus equipped, he is able to place his case
lucidly before the court.’
Pictures, Models and Measures 117
The illustration depicts a bus that has collided with a smaller wheeled
vehicle in the intersection of a road. Three other vehicles are shown
approaching the same intersection. Several things are notable about the news
item. First, it mentions that the lawyer is interested in ‘the different phases’ of
the accident. In the case of a collision, this would mean the lawyer is interested
in the relative positions of the vehicles and their trajectories before, during,
and after the point in time that the vehicles collided. Second, it mentions
that the lawyer reconstructs ‘the whole’ occurrence and does so in a specific
context, ‘a plat or plan of the locality’. Some of the large sheets of paper on
the table the lawyer is working on are raised in relief, simulating hilly terrain
that blocks the view of the two vehicles approaching the intersection from
each other. Thus the lawyer would be interested not only in the trajectories
of motion of the center of motion of the vehicles as they approached the
intersection before colliding, but in the trajectory of all the visible points on
the vehicles, and their relation to the line of sight of the occupants (dolls) in
the vehicles.
The way of using the model setup pictured I have just described is not
quite the same as using the models as experimental models scientifically, or
as experimental engineering scale models; that would require one more step:
designing the setup so that the model setup and the actual setup it models
are physically similar systems (i.e., similar in the sense of a certain kind
of behavior such as kinematic behavior (same motions and velocities), or
dynamic behavior (same forces)). The kind of behavior relevant here would
be behavior relevant to some claim important in the trial. As explained in
(Sterrett 2006, 2009, 2017a, and 2017b), to say that two setups are physically
similar systems is always with respect to some specific behavior, and the
behavior of interest here would depend on the claims in the lawsuit. If the
claims in the lawsuit turned on a measurement such as how fast a car was
going, or how much impact force the victim sustained, the kinds of similarity
would be kinematic similarity and dynamic similarity, respectively.
Before and After 1914
My views on the nature and significance of the event occasioned by
reading about the use of miniature models in the courtroom are informed by
looking at various elements of Wittgenstein’s milieu that provide the context
in which Wittgenstein viewed the magazine article about ‘representing by
means of dolls’. Besides the various modelmaking movements mentioned
above, another part of the context is the scientific research community, which
was distinct, as an institution, from self-appointed researchers such as the
Wright Brothers and Otto Lilienthal. Yet, in terms of individuals participating
in the activities, there was extensive interlacing between such institutions
and communities; here Boltzmann’s interest in Lilienthal’s gliders is a good
118 S.G. Sterrett
example. One formal such crossover was Edgar Buckingham, a physicist at the
National Bureau of Standards in Washington, DC, who was loaned to the US
Advisory Committee on Aeronautics. In particular, the year 1914 was a year
especially marked by advances in research using scale models, theoretically as
well as practically; in my paper ‘Physically Similar Systems: a history of the
concept’ (Sterrett 2017a) I called 1914 ‘the year of physically similar systems’
due to there being so many publications germane to the topic appearing that
year in the UK and in the US. One of these was the relatively understated,
straightforward presentation of the foundations of the methodology of
experimental (scale) models that Buckingham wrote in a publication that
had been created to disseminate short communications about research of
especial and/or urgent importance, sent out from US to other countries; the
Journal of the Washington Academy of the Sciences; after that year, it became
the Proceedings of the National Academies of Sciences, which is eminent to
this day. Buckingham’s short communication published in July 1914 was
under the PHYSICS rubric, and was entitled ‘Physically Similar Systems’.
Reading the literature of that era, it is clear that news about technology and,
especially, about aeroplane technology in 1914, was eagerly and urgently
exchanged across borders and oceans—remember, there had already been a
‘Victorian Internet’ for quite some time by then—a transatlantic cable and an
extensive network of electronic telegraph communications, and publication
channels to disseminate the news were in place. (Standage 1998) So research
in Washington DC easily made its way to Vienna where Wittgenstein was
in mid-1914, practically instantaneously when necessary, and on a regular
basis via such formal channels, as well as by more informal means. And, there
were many other important publication events related to the topic that year;
practically one per month [Sterrett 2006; Sterrett 2017].
How did the events of 1914 figure into the writing of the Tractatus? That
is, what difference is due to whatever important insight was gained in 1914?
I provided a sort of answer to this in my book. Illustrating with figures, I
showed how two important discussions of how a proposition depicts given
in the Tractatus—(i) of the proposition as a picture, and (ii) of gramophone
records and a symphony score having the same logical form—underwent
development during the war, based on the Notebooks Wittgenstein kept
during the war. I also provided some historical scientific and technological
context crucial to understanding his use of gramophone records in the latter
discussion.
Here I’ll refer to the figures presented in my book, Wittgenstein Flies A
Kite: A Story of Models of Wings and Models of the World [Sterrett 2006] to
illustrate how the events of 1914 discussed above figured into the writing of
the Tractatus.
The juxtaposition of sketches portrays the development of two-part
accounts into three-part accounts, which occurred during the war. Juxtaposing
Pictures, Models and Measures 119
Figures 1A and 1B shows that the pre-1914 view of a symphony (the two
two-part sketches in Figure 1A) is developed into the post-war view in the
Tractatus (the three-part relation in Figure 1B). Juxtaposing Figures 2A and
2B with Figure 4 shows that the pre-1914 view of propositions (the two twopart
sketches in Figures 2A and 2B) is developed into the post-war view in
the Tractatus (the three-part sketch in Figure 4).
Thus, the sketches that portray the two (post-war) views of themes (i)
and (ii) I find in the Tractatus (of the proposition as a picture and of the
gramophone record and symphony score having the same logical form,
respectively) are Figure 1B and Figure 4, respectively.
120 S.G. Sterrett
Pictures, Models and Measures 121
122 S.G. Sterrett
As I see it, there is a development of the two themes (i) and (ii), as
follows:
— Prior to mid-1914, Wittgenstein would have had experiences with the
fairly new technology of producing music from the grooves of a gramophone
record, and, due to the family he grew up in, was party to many critical
conversations about the nuances of producing music from musical scores
via musicians’ performances (whether by playing an instrument, or by voice/
whistling). This is shown on Figure 1A from my book: basically, what the
sketches in Figure 1A depict is that a properly trained musician can produce
a symphony from the score (written in musical notation); and that at least
some musicians can also produce a musical score from hearing a symphony.
In addition, Figure 1 depicts that a gramophone machine enables one to
produce a symphony from the lines on a gramophone record. (There is no
mention of the symphony performance producing a gramophone record,
though.) It is interesting that the technology of recording sound in lines was
developed years before this—the phonautograph, which produced records
that were valued as two-dimensional visual records of sound, without any
interest in their value as means of producing/reproducing sound. (Sterrett
2006; Sterne 2003; Sterne & Akiyama 2012) The phonautograph was very
well-known as a scientific device; it is reported that every schoolchild read
in their science textbook how a phonautograph could produce these visual
records of sound, and that the nature of sound could be studied from these
visual records. As for the possibility of producing sound from these graphical
or visual records, the inventor of the phonautograph showed only scorn
at what he regarded as the trivialization or vulgarization of his invention.
Thus I take Wittgenstein to be knowledgeable of both phonautographs and
gramophones, and that in choosing to mention the gramophone, rather than
the phonautograph, he means to refer to the process of producing sound from
the lines on the gramophone record.
— Also, prior to mid-1914, in the pre-war Notes on Logic, Wittgenstein
had worked out a view about the relationships between propositions, signs,
and symbols. The pre-war view is shown on Figures 2A and 2B (reproduced
from Sterrett 2006). So, he already had that much, well before the insight
in Autumn 1914: i.e., he had already said that the correspondence between
a propositional symbol and reality depends on the simples that the symbol
contains, and ‘that a certain thing is the case in the symbol says that a certain
thing is the case in the world’. He had written, regarding propositional signs,
that ‘if an x stands in the relation R to a y the sign “xRy” is to be called true
to the facts and otherwise false’. He had written, regarding the human skill of
understanding propositional signs, that ‘I understand the form “xRy” when I
know that it discriminates the behavior of x and y according as these stand in
the relation of R or not’. And, regarding propositional truth functions: ‘In two
molecular functions that have the same T-F schema, what symbolizes must
be the same’.)
Pictures, Models and Measures 123
So he already had that much; what happens after the crucial insight in
Autumn of 1914 gets developed?
One thing to take note of and reflect upon is that Wittgenstein focuses
on pairs of seemingly dissimilar representations: ‘At first sight a proposition—
one set out on the printed page, for example—does not seem to be a picture
of the reality with which it is concerned. But neither do written notes seem
at first sight to be a picture of a piece of music, nor our phonetic notation
(the alphabet) to be a picture of our speech.’’ (4.011) Now, notice: He does
not appeal to examples in which similarity is based on visual or geometrical
similarity. That’s very important. It is often missed.
— In the Tractatus, as depicted in Figure 1B, the lines on the gramophone
record, and the musical notation of the symphony score, which Wittgenstein
describes as two things which ‘appear to be very different at first’, are shown
to ‘stand in the same internal relation’ of depiction, which is what having the
same logical form amounts to. (Sterrett 2006; 216) His account of having the
same logical form involves processes that result in a musical performance:
the musician’s abilities in being able to ‘obtain the symphony from the score’
and the ability to employ a process that likewise yields the symphony from
the lines on a gramophone record. This is what having the same logical form
amounts to: translatability, though by no means a direct correspondence
between points on the gramophone lines and notes in the symphony score.12
It’s worth emphasizing here again that Wittgenstein did not appeal to
the geometric characteristics of the lines on the gramophone record, even
though, in his day, the patterns that the lines that a musical performance
recorded on a gramophone disc or roll made were often appreciated as twodimensional
drawings (such as magnified traces of wavy lines made by a
phonautograph needle used to record voices and other sounds. Likewise, in
physics, Mach’s famous schlieren photographs capturing shock waves visually
were widely reproduced and had become part of popular and artistic culture.)
The gramophone example is used to make a point about propositions: ‘A
gramophone record, the musical idea, the written notes, and the sound-waves,
all stand to one another in the same internal relation of depicting that holds
between language and the world’. [T 4.014] What they all have in common,
though, he says is ‘logical structure’ [Ogden translation]
If geometric or visual similarity is not what Wittgenstein appeals to in
explaining that the musical score and the lines on a gramophone record
have the same logical form, what does he appeal to? Intertranslatability
via serial processes. The processes he appeals to include ones that involve
skill, training, and conventions about notation, as well as some mechanical
processes. This is, I think, a very important thing to notice. It does not mean
12 There are a number of other relevant points associated with Figure 1B discussed in ‘Pictures
of Sounds: Wittgenstein on Gramophone Records and the Logic of Depiction’ (Sterrett 2005)
124 S.G. Sterrett
that those spatial relations or visual similarity do not play some role in the
processes of translation, but the account of logical form is not in terms of,
and certainly not reducible to, them. Here I suspect Wittgenstein is following
Frege in thinking that it is the notion of translation, rather than the notion of
interpretation, that is relevant in understanding logical form. In his criticisms
of formalism in mathematics, Frege argued against the use of uninterpreted
formulae in mathematics and logic. (Sterrett 1994) (We are not always careful
in distinguishing the terms; for Frege, translation is from one meaningful
entity to another; interpretation, as the formalists meant it, was from one
uninterpreted statement to an interpreted one.)
How is the account of logical form that appears in the discussion of the
gramophone in the Tractatus related to the experience of reading about a
miniature setup used in a courtroom to portray something about a traffic
accident?
Models in a Nexus of Fault and Responsibility
It would be nice to know a little more about how the miniature setup of the
traffic accident was discussed in the magazine or newspaper that Wittgenstein
read; what kind of evidence was the miniature setup supposed to provide?
The setting was a law-court, not a scientific laboratory or even a forensic one.
The miniature automobiles involved in the setup are often referred to as ‘toys’
by commentators on Wittgenstein, though I am not aware that Wittgenstein
ever did so in his Notebooks.
The miniature cars involved may well have been regarded as toys by some,
but we have seen how exquisitely detailed technically many of them were.
We have seen that in the late nineteenth and early twentieth century, scale
models that were serious affairs and scaled to be used as experimental models
for particular scientific research or forensic investigative purposes were often
called toys, too. We have seen that modelmaking combined art and science,
and that by 1914 there were modelmaker hobby clubs and ‘modelmaker’ was
a skilled profession in the UK and the US—and that these kinds of miniature
models with exquisite technical detail were known in Europe as well. Even
rigorously scaled models were sometimes made to be aesthetically pleasing as
well as being precision pieces of machinery. Modelmakers of such charming
models were known to protest that calling their productions toys failed to
do justice to the craftsmanship, knowledge, and precision required in order
to produce properly scaled behaviors. Different materials had to be used to
provide appropriately scaled densities and flexibilities; surfaces had to be
modified to give appropriately scaled mechanical behaviors. So I think one
point to keep in mind is that someone with Wittgenstein’s knowledge and
interests in aeronautical engineering, in which precision scale models were
absolutely essential, could hardly suppress knowledge of the logical and
Pictures, Models and Measures 125
mathematical basis for using scale models in physics, when viewing such a
miniature setup.
There are some cultural and ethical aspects to the significance of such a
court case around 1914, too.
First, the issues of the burden of proof for proving fault in automobile
accidents, and whether injury and death caused by automobile accidents
should be covered under criminal law or not, were still undergoing change
and clarification. There were even questions of ethics involved as to
what kinds of considerations were relevant in applying the existing legal
doctrines to the situation of automobile accidents (e.g., consideration of riskspreading;
role of ownership, role of vehicle being under one’s control, role
of negligence). (Deak 1931) This might be something to keep in mind with
respect to Wittgenstein’s later remark that the most important point of the
Tractatus was an ethical one—what it did not say.
Secondly, it is also significant that, in 1914, an important revolution
in the use of physical evidence in court cases that would set the agenda for
methods used in forensic investigation to this day, was just beginning. The
Frenchman Edmond Locard, a protege of Bertillion who claimed to have
used the fictional Sherlock Holmes as his inspiration and guide, had just
been given a laboratory in Lyon (France) in 1912 in rooms attached to the
courthouse, for such scientific investigations. The question of what kind of
physical evidence could be admitted, and what it could be used to prove, was
of interest to the public, as it hadn’t really been settled yet. Other laboratories
were established based on Locard’s methods: first in 1914, there was one in
Quebec (Cimon 2014); many others followed. Locard is known best for the
methods he developed and disseminated using the microscope for making
minute distinctions, such as between many different kinds of dust particles
and, following his teacher Bertillion, for the use of various biometrics for all
sorts of imprints a person might leave behind. (Berg, 1970) However, Locard
was also very much interested in collisions; in his laboratory in Lyon he
worked on detecting cause and fault in automobile collisions: what did the
evidence left behind from an automobile collision, such as skid marks left
by tires, tell people about the collision that had taken place? This is a matter
of reading the collision from the skid marks, but in a courtroom, one would
also want to show how the skid marks could have been created by a certain
sequence of events that was the fault of one of the drivers. Could one and the
same model have served both to illustrate something such as who had the
right of way and also to prove that skid marks (lines) left on the road could
be translated into a certain sequence of events?13
13 Here there is a very close analogy between the lines on the gramophone record that can
be used to reproduce a symphony performance with some, but not perfect, fidelity, and
the lines on the road that can be used to reproduce the scene of a traffic accident with
some, but not perfect, fidelity.
126 S.G. Sterrett
Referring again to the illustration in the magazine article I found
showing a personal-injury lawyer seated at a table on which a large piece of
paper covering the entire tabletop has been lain: note that the outlines of the
roads leading into an intersection are sketched on the paper. Five ‘miniature’
vehicles are on the table; although referred to as ‘miniatures’ in the article,
they are large miniatures: most of the automobiles must be at least the size of
a breadbox, it appears to me, and they look quite detailed. There are several
doll occupants in the vehicles, and they seem arranged with care, in different
postures; some are unprotected, their vehicles being open like a convertible.
One three wheeled vehicle is toppled. The account says that the lawyer
is ‘studying a case to place the responsibility for the accident’ and to get ‘a
clear idea of the different phases’ of it. We are told that he acts out ‘the whole
occurrence’ so that ‘the questions of right of way, traffic regulations, rules of
the road, and such matters’ are made clear. The lawyer also uses the model to
communicate: ‘Thus equipped, he is able to place his case lucidly before the
court’. (Popular Science 1914) This account seems to fit with Wittgenstein’s
mention of dolls (puppen); it is the injury to the humans that is of most
importance to the personal injury lawyer. This account also fits well with von
Wright’s description that ‘At the trial a miniature model of the accident was
presented before the court. The model here served as a proposition; that is, as
a possible state of affairs’. (von Wright n.d, p. 21)
One striking (to me14) thing is the context of this ‘found object’ (the
model of a traffic accident): a court of law. Much of what the lawyer wants
to present using the model involves conventions and, especially, violations
of ‘traffic regulations’ and ‘rules of the road’. The physical aspects of the
model are surely part of judging whether there have been violations, as well
as in determining the sequence of events that led to an injury, and to how
the injury was caused. But whether there have been traffic violations, and
who had the right of way, involves rules and conventions as well. In the
Notebooks, in following up on his thoughts about a proposition as a picture,
Wittgenstein remarks that a picture might be used to portray how not to
fence. (Wittgenstein 1979, NB 5 November 1914 entry) The model might be
used to portray a violation of a traffic rule, or it might be used to portray a
state of affairs that did not occur, say, in showing negligence, to show what
would have happened (a possible state of affairs) had a driver acted otherwise
than he or she did.
Another striking thing in the account of the model of a traffic accident
in this magazine article is the mention of the dynamics of the model: ‘the
different phases’; ‘the whole occurrence’, which draws attention to the
miniature model of the traffic accident as a dynamic model. There is, after
14 I mentioned it at the end of Sterrett (2000) ‘Physical Pictures: Engineering models circa
1914 and in Wittgenstein’s Tractatus; long version at http://philsci-archive.pitt.edu/661/1/
Sterrett-UNC-CH-PPTalk2.pdf As for the more substantial content of the talk, the
content in Sterrett 2006 supersedes that talk.).
Pictures, Models and Measures 127
all, a vehicle that has been overturned, and one that is in the process of
turning a corner. Certainly the way the lawyer is using the model is, at first,
investigatively, or experimentally, to examine the situation and the possible
ways it might have developed to yield the outcomes known to have occurred,
and the possible ways it could, counterfactually, have developed.
As I explained in my book, what I see in the Tractatus is an account
of how propositional sign, truth function, and world are related that looks
very much, even in details, like an analogue of the account of using model
experiments—e.g., ships, aeroplanes, propellers—to represent actual or
imagined ships, aeroplanes, and propellers circa mid-1914. Actually, the
methodology used—physically similar systems—is very general. The quote
from Hertz’ preface that the form we give our images in thought is such that
‘the necessary consequents of the images in thought are always the images of
the necessary consequents in nature of the things pictured’15 is often cited
in connection with Wittgenstein’s Tractatus, but I do not think Hertz meant
to be saying anything novel with that statement in the preface; statements to
that effect are quite common in nineteenth century physics. The idea that
one can formulate a picture or model—a concrete physical setup as well as
an imagined or mathematical one—and set up a correspondence between
them such that the consequents of manipulating quantities in the model that
correspond to the thing modeled are the corresponding consequents in the
thing modeled was also quite common. When it was an equation rather than
a physical model, and the consequent a matter of mathematical deduction,
Hertz’ statement would fit, too. The use of dimensionless parameters as
a criterion for this kind of similarity between two physical systems—i.e.,
similarity of systems S and S’ (which is the terminology used to describe
the relationship between a model being tested experimentally and the thing
it modeled) exists when the relevant dimensionless ratios formed from the
corresponding quantities in the two systems are equal—was also developed
in physics in the second half of the nineteenth century. What I often found,
though, was that mathematicians, physicists or engineers writing about
similar systems and similarity would often comment that the methods were
not well enough known, that they were powerful and elegant and that there
was much to be gained by adopting them. (Sterrett 2017a)
Experimental Models and Measurement
What happened in July 1914, with the ‘Physically Similar Systems’ short
communication (Buckingham 1914) was significant, though, in that the
method was generalized so that it no longer involved deriving the required
15 Quoted in David G. Stern’s Wittgenstein on Mind and Language, p 37, from Heinrich
Hertz: The Principles of Mechanics, Tr. by D.E. Jones and J.T. Walley. (Dover, New York
1956)
128 S.G. Sterrett
criteria from an equation that described the phenomenon. Rather, similarity
criteria (the dimensionless ratios that must have the same value in each of
the two systems (model and thing modeled)) could be derived from the
‘most general form’ of a physical equation, which contained no arithmetical
constants. The most general form of a physical equation was written using
the notation of functions. This often sounds not really possible; where
does the information come from, if not from an equation of physics such
as a partial differential equation? The reason it is possible is due to what is
built into the system of measurement (as explained in Sterrett 2009; 2017a;
Sterrett forthcoming b). It is the July 1914 formulation of similarity between
physically similar systems as a methodology of using model experiments, that
I use to draw the analogy shown by comparing Figure 3, below, with Figure 4
(above); the analogy is between experimental models and propositions in the
Tractatus, respectively.
Pictures, Models and Measures 129
Beyond exhibiting the sketches in Figures 3 and 4 from my book here, I
am not going to lay that analogy out again in this talk, as it is given in my book.
I’d like to point out, though, some of the historical and biographical details
supporting this suggestion. Here are just a few such details: Most saliently,
the topic of similarity in science and engineering was prominent in the
years immediately preceding 1914, and the short communication ‘Physically
Similar Systems’ (Buckingham 1914) came out when Wittgenstein was already
back from Norway, and staying in Vienna, where access to scientific news
and literature was excellent. A timeline in my ‘Physically Similar Systems: a
history of the concept’ (Sterrett 2017a) shows the intensity of publications
related to similarity throughout 1914. I cite lots of other supporting details
in the book. Another one quite close in time to the 1914 insight was that
the use of mechanical similarity was cited in a Nobel Prize Lecture given in
December 1913 that received wide coverage in the Press, including cartoon
caricatures of the Nobel Laureate, Heike Kamerlingh Onnes, as ‘Dr Zero’
in newspapers and magazines (the Prize was for achieving the liquefication
of helium). Wittgenstein was in Vienna during that time period, too; even
though he had been in Norway in 1913, he came back to his family home
in Vienna for Christmas of 1913. Onnes had helped derive a more general
‘theory of corresponding states’ in physical chemistry than van der Waals’
initial version, and cited Newton’s theory of mechanical similarity with awe.
Wittgenstein could hardly have missed the association of Onnes’ work with
model experiments, as Newton and, to some extent, Galileo, were often cited
in the scientific and engineering literature on using experimental models
as the first to use and write about similitude. With regard to the homage to
Newton, as I have explained above and note in my book (Sterrett 2006), the
recently discovered fact that Wittgenstein purchased exactly the two works
by Newton and Galileo that were cited in the literature on dynamic similarity
and physically similar systems seems to indicate an awareness of the kinds
of allusions Onnes and others made regarding the theoretical foundation for
similarity in physics.
Models, Physically Similar Systems, and the Tractatus
These historical and biographical facts are merely supportive, though, as
opposed to propelling me towards the conclusion initially: my main reason
for thinking that the methodology of physically similar systems, which by the
time of Wittgenstein’s reading of the magazine article in September 1914 had
just been presented in the short communication ‘Physically Similar Systems’
(July 1914), is in fact the analogy itself that holds between the account of how
models portray in it, and the account of a proposition given in the Tractatus.
In particular, the ‘no logical constants’ principle that Wittgenstein referred to
as the Grundgedanke of the Tractatus has a clear analogue in the account (i.e.,
130 S.G. Sterrett
equations in science that contain arithmetical symbols are replaced by ones
that do not contain any such connectives, by employing functional notation).
Most significantly, the analogy yields an account of objects that I find
aligns perfectly with the statements in the Tractatus about objects and facts
composed of objects, sans logical constants. Whereas the methodology of
experimental models speaks of the ‘most general form of a physical equation’
as containing no algebraic constants, Wittgenstein writes of the ‘general form
of a proposition’ containing no logical constants.
— Whereas, in the dimensional equations used in Buckingham’s July
1914 ‘Physically Similar Systems’ paper, dimensions or quantities combine in
only certain ways to form dimensionless parameters, in the Tractatus we are
told that objects combine in only certain ways to form states of affairs’.
I see the way objects function as completely analogous to the way that
dimensions do.
One thing that is not shown on the figures in my book is how the elements
in the model correspond to the elements in reality. This is very straightforward,
although implicit: since the similarity of the two systems is a matter of certain
key dimensionless parameters (ratios) having the same value in the model as
in the thing modeled, one can simply show the correlation between model
and thing modelled from those ratios alone. To take an easy case, consider
Mach number, a degenerate case16 of a dimensionless parameter: (velocity of
a moving body v)/ (velocity of sound in the fluid at the fluid conditions that
obtain vs). Suppose we have a case in which similarity is established by the
Mach number being the same in the model as in the thing modelled (again,
a degenerate case). Then, letting v depict the velocity in S and V depict the
velocity in S’, we can say that v/vs
= V/Vs
We can then say that the velocity
v corresponds to the velocity V vs
/Vs
; this gives the model its ‘feelers’, which
shows exactly how the velocity in the model corresponds to the velocity in the
thing modeled. Measuring one of these two velocities can be used to tell us
what the other, corresponding, velocity is. With this in mind, we can make
good sense of the following statements in the Tractatus (Wittgenstein 1974):
2.1511 That is how a picture is attached to reality; it reaches right out
to it.
2.1512 It is laid against reality like a measure.
16 I use here the simple case of Mach number, which I called a degenerate case of a
dimensionless number, to illustrate how the corresponding quantities can be identified
from the dimensionless ratios, to keep the calculation simple. A clear nontechnical
description of ‘degenerate’ is ‘In mathematics, a degenerate case is a limiting case in
which an element of a class of objects is qualitatively different from the rest of the class
and hence belongs to another, usually simpler, class.’ (Wikipedia 26 January 2018) Mach
number is a degenerate case of a dimensionless ratio in the sense that the only kind of
quantity it contains is velocity, and hence is a limiting case of dimensionless ratios, which
can contain many different kinds of quantities.
Pictures, Models and Measures 131
2.15121 Only the end-points of the graduating lines actually touch the
object that is to be measured.
2.1513 So a picture, conceived in this way, also includes the pictorial
relationship, which makes it into a picture.
2.1514 The pictorial relationship consists of the correlations of the
picture’s elements with things.
2.1515 These correlations are, as it were, the feelers of the picture’s
elements, with which the picture touches reality. (Wittgenstein 1974)
And, as for the statements following just after the above lines in the
Tractatus, the ones about the picture having something in common with
what it depicts: clearly, though we do not need to be using the same units
in the model and what it models, the systems of measurement need to
have some things in common (e.g., we need to be using the same system of
measurement between the model and the thing modelled (not necessarily the
same system of units, but of the same system of measurement) in order to
use this method to construct a model that is able to picture what it models.
(Sterrett forthcoming b) So, that makes sense too. (Exactly what they must
have in common is, I think, part of the investigation in the Tractatus.)
Who Can Understand the Tractatus?
While I don’t want to repeat the arguments in the book here, I would like to
point out that the analogy I laid out in the book (depicted by the juxtaposition
of Figures 3 and 4) addresses what I think is a common worry about what’s
known as Wittgenstein’s ‘Picture Theory’. The worry, I think, is that just
knowing that the elements of a picture correspond to elements in reality
doesn’t yield enough to guarantee that the picture will track reality. ‘Having
the same logical form’ just seems too scanty a basis to most people, I suspect.
Then, there is the problem with the point that, as Wittgenstein says, ‘The
possibility of propositions is based on the principle that objects have signs as
their representatives’. I think readers are bound to ask how this is supposed to
be guaranteed, too.
I consider some of these worries to be genuine worries about endorsing
what commentators call the Picture Theory—at least the Picture Theory
as it is often understood. I don’t think it is very easy for a reader of the
Tractatus to understand how the proposition as a picture is supposed to
account for what it purports to account for in any rigorous way. In fact,
I think Wittgenstein knew others weren’t going to understand his point,
yet, that he felt that what he wrote was correct. He did, after all, write in
the preface that, although he wasn’t sure he had accomplished the task of
expressing the thoughts expressed in the book very well, that ‘the truth of
the thoughts that are here communicated seems to me unassailable and
132 S.G. Sterrett
definitive’. (Wittgenstein 1974, pgs. 3–4) I’m going to go with that line:
Wittgenstein didn’t count on anyone being able to understand the thoughts
he tried to express in the Tractatus, yet he thought the truth of those
thoughts was ‘unassailable and definitive’.
I find that the key to making sense of the thoughts he attempts to
express in the statements in the Tractatus about objects, states of affairs,
and propositions is to recognize that his account draws on the existence of
quantitative science, i.e., the existence of measuring systems and equations
that express relationships between measured quantities. It is in the design
and standardization of systems of measurement—which, in a coherent
system of measurement, include a connection to reality, as a coherent system
of measurements17 requires that the units that have different dimensions
associated with them be ‘coherently’ related to each other, which involves
establishing physical relationships; as a result, the relationships between
dimensions (kinds of quantities) are formalized. Since I see dimensions as
analogous to objects, this explains many of the otherwise inscrutable claims
about objects we find in the Tractatus.
Again, the historical and biographical details are supportive of my
suggestion. First, there is the context that, in 1914, many physicists and
engineers would know what a dimension was, and would be quite competent
in using dimensional equations. They would consider it quite natural to
think of combining dimensions, which can be done without any arithmetical
connectives, and which come into play when expressing a dimension in terms
of combinations of others. I say this because significant debates on the topic
of which units should be used in physics were still in very recent memory in
1914; and these debates required the language of dimensions. In fact, Hertz
had entered the debate with a very philosophical argument; Jed Buchwald
discusses it in his book The Creation of Scientific Effects (Buchwald 1994,
Chapter 12) In his argument, Hertz uses the notation of dimensions, i.e., he
writes ML2
T2
to indicate the dimensions of the units of work; M, L and T
denote respectively the dimensions Mass, Length and Time.
I think of a dimension as a kind of quantity. But—and this might have
been difficult for even scientifically trained commentators and readers of
the Tractatus coming upon it after 1930 or so to imagine—not only the
system of units, but the issue of how many basic units were needed in
order to be able to do physics, was in flux in the late nineteenth century.
There were the basic units of mass, length, and time, as in Newton’s day,
but there was the new question of how to handle units for measurements
made of quantities regarding electricity and magnetism. It was easy enough
to define units of each, in terms of a laboratory procedure involving an
17 There are two characterizations of coherence of a system of measurement; this is one of
them. I discuss the topic at length in Sterrett forthcoming b (‘Relations Between Units
and Relations Between Quantities.’)
Pictures, Models and Measures 133
electrical or magnetic pole. But, it was impossible to answer: ‘Which is
more basic: an electrical pole or a magnetic pole?’ Contradictions arose no
matter which system of units was preferred; in addition, many additional
units were added and adopted, without increasing the number of basic
units, because they were more practical to use. Some argued that three
basic units (mass, length and time) were sufficient. It wasn’t until 1901
that the Italian Giovanni Giorgi showed that by adding a fourth basic unit,
and hence admitting a fourth dimension (a fourth basic kind of quantity)
to the system of units, that the global physics community could solve the
problem in an especially desirable way, in that the resulting system of
units would not conflict with the use of the practical units already used in
everyday technological and laboratory work. In 1914, though, these had
not yet been adopted formally. The topic was still live, and so was the
language that was then considered the language of science: dimensional
analysis. And, we do see Wittgenstein bring up measurement, as in his
statement quoted above, that a proposition is laid against reality like a
measure.
Secondly, I don’t think Wittgenstein says nearly enough to explain
what’s needed to the reader who does not know very much about model
experiments, dynamical similarity, and similar systems. In his defense,
someone writing in 1914, which I have called ‘The Year of Physically Similar
Systems’ (Sterrett 2017a), coming on the heels of Onnes’ fame, might assume
that the whole family of similarity concepts had finally won the day in physics
and were going to be as common as the notion of gravity from now on. That
is what Boltzmann foresaw (Sterrett 2006, p. 113; Boltzmann 1974). Sadly, the
opposite happened and the war seems to have disrupted collective memory
about them.
Also, the arguments about the basis for measurement in the new physics,
and the role of measurement standards in physics, had basically been made.
It is true that, in 1914, it would still be awhile before the solution Giorgi
proposed around 1900/1901 was eventually adopted by the international
agencies charged with deciding such things—but the debates that delved into
the fundamental questions of measurement in electromagnetism, were over.
So, even though there would still be active discussion of them in 1914, and
the language of dimensional analysis would then still be quite well known,
the occasions for using it in debates in which the question of how many
different dimensions were needed was a live question were fewer and fewer.
The result is that we philosophers are put in a deficient position with respect
to understanding comments about measurement and modeling unless
we are willing to go back and learn what physics was like in 1914—and I
don’t mean current reconstructions of what was known in 1914 phrased in
anachronistic terms.
134 S.G. Sterrett
So, I’d like to make a suggestion about understanding Wittgenstein’s
Tractatus, at least the parts of it associated with the so-called ‘Picture Theory’:
I suggest that it might help if we as a philosophical community get to know
the scientific milieu in which the Tractatus was conceived a little better,
including the language and methods of physics of the day. Especially, the
language and methods, including systems of measurement, of the (physics)
logic underlying the use of model experiments.
References
Anonymous (1914). ‘Lawyer Studies Accident with Plat and Toys’, Popular
Science, June 1914: 819.
Berg, Stanton O. (1971). ‘Sherlock Holmes: Father of Scientific Crime and
Detection’, Journal of Criminal Law, Criminology & Police Science, 61: 446–452.
Blackmore, J.T. (1995). Ludwig Boltzmann, His Later Life and Philosophy,
1900–1906. Book One: A Documentary History. Boston Studies in the
Philosophy of Science, Vol. 168. Kluwer Academic Publishers.
Boltzmann, Ludwig, (1974). McGuinness, B.F. (Ed.) Theoretical Physics and
Philosophical Problems: Selected Writings (Vienna Circle Collection).
Boston, MA: D. Reidel.
Buchwald, Jed Z. (1994). The Creation of Scientific Effects. Chicago: University
of Chicago Press.
Buckingham, Edgar (1914). ‘Physically Similar Systems’, Journal of the
Washington Academy of the Sciences, 4: 345-376.
Cimon, Denis, Desharnais, Brigette & Dicaire, Catherine (2014). ‘One
hundred years of forensic sciences in Quebec: the evolution of scientific
techniques since 1914’, Canadian Society of Forensic Science Journal, 47
(3): 148–169.
Dahmen, Silvio R. (2009). ‘Boltzmann and the Art of flying’, Physics in
Perspective, 11: 244–260.
Deak, Francis (1931). ‘Automobile Accidents: A comparative study of the law
of liability in Europe 1931’, University of Pennsylvania Law Review and
American Law Register, 79: 271–305.
de Clark, Sybil G. (2016). ‘The dimensions of the magnetic pole: a controversy
at the heart of early dimensional analysis’, Archive for the history of the
exact sciences, 70: 293–324.
de Clark, Sybil G. (2017). ‘Qualitative vs quantitative conceptions of
homogeneity in nineteenth century dimensional analysis’, Annals of
Science, 74: 299–325.
Pictures, Models and Measures 135
Hansluck, Paul N. (1902) The Model Engineer’s Handybook, A Practical
Manual on Model Steam Engines Embracing Information on the Tools,
Pictures, Models and Measures. Materials and Processes Employed in their
Construction. London: Crosby, Lockwood, and Son.
Hertz, Heinrich (1956). The Principles of Mechanics. New York, Dover: D.E.
Jones & J.T. Walley. Hide, Oystein (2004).’Wittgenstein’s Books at the
Bertrand Russell Archives and the Influence of Scientific Literature on
Wittgenstein’s Early Philosophy’, Philosophical Investigations, 27: 68–91.
Janik, Allan and Toulmin, Stephen (1973). Wittgenstein’s Vienna. New York:
Simon & Schuster.
Klagge, James C. (2001). Wittgenstein: Biography and Philosophy. Cambridge:
Cambridge University Press.
Klagge, James C. (2016). Simply Wittgenstein. Online edition Simply Charly.
McGuinnes, B.F., Ed. (2008). Wittgenstein in Cambridge: Letters and
Documents, 1911–1951. Blackwell.
McGuinness, B.F. (1988). Wittgenstein: A Life: Young Ludwig 1889–1921.
Berkeley: University of California Press.
Mitchell, Daniel Jon (2017). ‘Making Sense of Absolute Measurement: James
Clerk Maxwell, William Thomson, Fleeming Jenkin, and the invention
of the dimensional Formula’, Studies in History and Philosophy of Modern
Physics, 58: 63–79.
Scott, Janny (2011). A Singular Woman: The Untold Story of Barack Obama’s
Mother. New York: Riverhead Books/Penguin.
Standage, Tom (1998). The Victorian Internet: The Remarkable Story of the
Telegraph and the Nineteenth Century’s On-line Pioneers. New York:
Bloomsbury.
Stern, David G. (1995). Wittgenstein on Mind and Language. New York:
Oxford University Press.
Sterne, Jonathan (2003). The Audible Past: Cultural Origins of Sound
Reproduction. Durham, N.C.: Duke University Press.
Sterne, Jonathan & Akiyama, Mitchell (2012). ‘The Recording That Never
Wanted to Be Heard and Other Stories of Sonification’, In Pinch, Trevor &
Bijsterveld, Karin, Eds. The Oxford Handbook of Sound Studies, 544–560,
Oxford & New York: Oxford University Press.
Sterrett, Susan G. (1994). ‘Frege and Hilbert on the Foundations of Geometry’,
available at philsci-archive.pitt.edu/723.
136 S.G. Sterrett
Sterrett, Susan G. (2000). ‘Physical Pictures: Engineering models circa
1914 and in Wittgenstein’s Tractatus’, long version at philsci-archive.pitt.
edu/661/1/ Sterrett-UNC-CH-PPTalk2.pdf.
Sterrett, Susan G. (2002). ‘Physical Pictures; Engineering models circa 1914
and in Wittgensteins’s Tractatus’, In Heidelberger, M. & Stadler, F., Eds.,
History of Philosophy of Science: New Trends and Perspectives, Vienna
Institute Yearbook 2001: 121–135.
Sterrett, Susan G. (2005). ‘Pictures of Sound: Wittgenstein on Gramophone
Records and the Logic of Depiction’, Studies in History and Philosophy
of Science, 36: 351-362.
Sterrett, Susan G. (2006). Wittgenstein Flies A Kite: A Story of Models of
Wings and Models of the World. New York: Pi Press/Penguin.
Sterrett, Susan G. (2009). ‘Similarity and Dimensional Analysis’, In Meijers,
A., Ed., Handbook of the Philosophy of Science, Volume 9: Philosophy of
Technology and Engineering Sciences, 799–824, Amsterdam: Elsevier/
North Holland.
Sterrett, Susan G. (2017a). ‘Physically Similar Systems: A History of the
Concept’, In Magnani, L. and Bertolotti, T., Eds., Springer Handbook
of Model-Based Science, 377–411, Berlin/Heidelberg: Springer-Verlag.
Sterrett, Susan G. (2017b). ‘Experimentation on Analogue Models’, In
Magnani, L. and Bertolotti, T., Eds. Springer Handbook of Model-Based
Science, 857–878, Berlin and Heidelberg: Springer-Verlag.
Sterrett, Susan G. (forthcoming a). ‘Theory of Dimensions’ In Knox,
Eleanor and Wilson, Alastair, Eds., Routledge Companion to the
Philosophy of Physics.
Sterrett, Susan G. (forthcoming b). ‘Relations Between Units and Relations
Between Quantities’, In Schlaudt, Oliver, DeCourtenay, Nadine, and
Darrigol, Olivier, The Reform of the International System of Units (SI):
Philosophical, Historical, and Sociological Issues.
Von Wright, G.H. (n.d.). Wittgenstein. Minneapolis: University of Minnesota
Press.
Walter, Maila L. (1990). Science and Cultural Crisis: An Intellectual
Biography of Percy Williams Bridgman (1882–1961). Stanford: Stanford
University Press.
Wittgenstein, Ludwig (1922). Tractatus Logico-Philosophicus. C.K. Ogden,
Trans. International Library of Psychology, Philosophy and Scientific
Method. London: Routledge.
Pictures, Models and Measures 137
Wittgenstein, Ludwig. (1974). Tractatus Logico-Philosophicus. Revised
edition. D.F. Pears and B.F. McGuinness, Trans. London: Routledge.
Wittgenstein, Ludwig (1979). Notebooks 1914–1916, 2nd edition. G.H. von
Wright & G.E.M. Anscombe, Eds. G.E.M. Anscombe, Trans. Chicago:
University of Chicago Press.