Eye See
Eye See


Challenged by a colleague to ‘depict the contemplation of self as “I”’, Ernst Mach responds with an image: he draws what he sees of himself when he squints with one eye. Viewing this image through the lens of certain writings and conversations of Wittgenstein from the years 1929–31, I would like to ask: what is this picture saying? And, if anything at all is being said: how is it said? The ensuing discussion of the field of vision and visual space touches – among other things – on a critique of idealism and realism, the difference between complete and incomplete images, depiction in a proposition, and the hand as an element. In this way, the question will lead us to consider possible aspects of the expressive power of Mach’s image.

Table of contents

    Who can decide hastily whether, in the process, the intellect needs images? For example, I can say ‘stone’ or ‘sun’, without these things being present for my senses – yet certainly, when I do, their images are present in my memory. (St Augustine, Confessions, XV.23)

    1. facing time

    Challenged by a colleague to ‘depict the contemplation of self as “I”’, Ernst Mach responds with a picture: he draws what he sees of himself when he squints with one eye. We see parts of his eye socket, nose and beard, and – again only partly – his arms and legs, the seat, the room in which he is drawing, and the distant view out of the window. Outside this, opposite the nose, the white of the background flows out of the picture and around it like a giant question mark. The aim of this presentation is not to reconstruct Mach’s conception of his answer, or probe for the ‘subject as boundary of the world’. Rather, taking this image as such (and viewing it through the lens of certain writings and statements of Wittgenstein from 1929-31), what is attempted here is to ask: what is this saying? And, if anything at all is being said: how is it said?

    As Wittgenstein writes in paragraph 47 of his Philosophical Remarks, the fact that the phenomena of our everyday movements – walking around, being aware of our own body – seem so natural to us is already demonstrated by the fact that nothing about them particularly strikes our attention. ‘We do not perceive that we see space in perspective, or that the image we see is in some way or other blurred towards the periphery of vision.’ Moreover this cannot strike our attention, because it is the form of perception, and it is impossible to contemplate it, because there is no antithesis to the form of our world. ‘By this I mean, that it is remarkable that those who ascribe reality only to things, not to our conceptions, move so unquestioningly in the world of conceptions, and never yearn to transcend it. In other words, how self-evident is the world as given. All hell would have to freeze over before we admitted this was only a tiny image seen from a crooked angle.’ And indeed, this drawing by Mach seems ironically to suggest such a devilish conjuring trick (although, admittedly, long before it was prophesied in the Philosophical Remarks). I still recall how, seeing this picture for the first time, I could not work out what it was supposed to depict. On second viewing it became clear to me. On my third viewing I was struck by the omission of one side, and on the fourth the whole surrounding of the drawing appeared to me to be one single omission. But what is being omitted here? The eye? The head? The edge of the picture, or the background against which the artist’s lines stand out? Finally, my attempt to read the relationships from my own perspective, screwing up my eyes, achieved the most success. I found the attempt successful since it led me to two invisible boundaries. ‘Invisible’, because on the right – looking with the left eye – the boundary disappeared into darkness; while on the left, because I had to turn my head in the effort of searching, the boundary vanished. To be sure, I was unable to find the ‘antithesis’ to my field of vision in this way; and yet it is the most pleasant conceit to place a mirror in front of Mach inside his drawing.

    How then can only one actuality be described in Mach’s picture, as finite as it is boundless? At the end of paragraph 88 Wittgenstein suggests a qualification of this question; for ‘if only the whole field of vision may be described, then why not only the whole flux of visual experiences, since a field of vision can only exist in time?’ Earlier (paragraph 48), Wittgenstein has already stated that, in this flux, our propositions are verified only for the moment, only in the present. And they are not verified in spite of their spatio-temporal nature; rather, the latter must function as the physical actuality of a ruler does to the spatial extension by means of which it measures, when it is applied to reality. One distinction, already made in the conversations with Schlick and Waismann, is a temporal one: the distinction between a time of memory, in which one proposition or image emerges from another through an internal relationship, and a time of physics, in which we might for example enquire (of someone) how things behave. Wittgenstein also makes use of a metaphor, that of the ‘laterna magica’, and says that it is not the soundtrack which accompanies the film, but the music; the soundtrack accompanies the filmstrip in the same way that language accompanies the world. In paragraph 51 of the Philosophical Remarks he writes: ‘If I may compare the facts of immediate experience to the images on the screen, and the facts of physics to the images on the film, then on the film there is a present image as well as past and future images; on the screen, however, there is only the present.’ And it is this present which seems to support that very bold assertion that only the experience of the present moment possesses reality. However, in opposition to what does it possess this reality as present experience? Here, according to Wittgenstein, the word ‘present’ – like the word ‘I’ in other contexts – must already be superfluous; or alternatively, something different is meant by it, something which is not in a space but is a space itself, not delineated from something else. This seems to me to suggest one initial aspect of what Mach’s drawing might be saying, or how it might reveal itself to be a response. The continuation of Wittgenstein’s thought is made clear in paragraph 55: ‘The fact that, if I am awake, I always see out of my eyes is, by contrast, a remarkable and interesting fact.’ Unlike the perspective Mach has drawn, my field of vision is hardly threatened with paralysis. But how, therefore, does it come about that, despite every alteration, it remains my perspective? ‘“I” obviously means my body, since I am in this room; and “I” is essentially something which occupies a position, a position in the same space in which the other bodies are situated.’ (Wittgenstein adds: ‘“Realism”, “Idealism”, etc. [...] indicate that their adherents believe they can express something definite about the essence of the world’ – which means measuring the adequacy of a ruler, as though perceiving the form of perception’.)

    2. hic et nunc: in fact

    An irritating feature of Mach’s drawing, it seems to me, is the fact that it is drawn: in other words, that a certain period of time was necessary to create this (partial) ‘snapshot’ of a field of vision. At the same time, I find myself asking about Mach’s drawing hand, the one holding the pen – is it to be found on the picture’s surface, as the hand which draws, or in the picture itself, as the hand which is drawn? These two observations might appear trivial, and additionally they might already have been made more explicitly by artists elsewhere; nevertheless, here they lead me on to investigate further aspects of the subject.

    In Waismann’s transcripts of their discussions, Wittgenstein states his concept of the image clearly when he writes the following: ‘“The proposition is a logical picture of the fact”, he proposed. “I can insert a picture into a proposition – moreover, a picture which is drawn – and then continue with the proposition. I can, therefore, utilise a picture like a proposition.”’ This, indeed, is because in a sense both things concur with one another, and it is this common property to which Wittgenstein gives the name ‘picture’. However, as he says in the same passage, he could equally well have used a ruler as a symbol. The distinction which emerges in his explanations during these years is that between the complete and the incomplete picture. This arises in consequence of a further development of his concept of elementary propositions. In the final analysis of propositions, it is true, these still emerge always in the form of a direct connection between objects, without logical constants; but they are not independent of one another. If, for example, we replace the symbols in the logical constants ‘p ∙ q’ by the symbols ‘red’ and ‘blue’, this can give rise to the problem – much discussed by Wittgenstein – that this pair determines the same co-ordinates twice over, in other words, that the same point is both red and blue. Syntax forbids this use of words, and in this respect the system of colours reveals itself as like a ruler on which a scale division which agrees with reality, in so doing (to a certain extent) negates the others.

    In order not to lose the theme of the field of vision completely from our own field of vision, I will once again refer to paragraph 88 of the Philosophical Remarks, already mentioned earlier. ‘If I do not describe the field of vision completely, but only a part of it, then it is obvious that there is a kind of lacuna in the facts. Obviously something has been omitted. If I were to paint this field of vision, then I would allow the canvas to peer through in certain places. But canvas also has a colour and occupies space. I could not leave nothing on the spot where something is missing. It is essential, therefore, that my description should contain the entire field of vision, even its coloration; even if it does not say which colour is found in each place. That means, it must say that there is a colour in each place. Does that mean that, insofar as the description does not fill the space with constants, it must fill it with variables?’

    In conversation with Schlick and Waismann, Wittgenstein states that an incomplete picture consists of one in which variables appear in the proposition; the picture must show that it is incomplete. Examples are: ‘I saw two materials of the same colour’ or ‘I saw a square with a circle in it’. Neither of these are enumerations of the kind found in ‘both green, both blue…’ or ‘this circle or that circle or …’ These are just variables, in contrast, for example, to exact numerical data for radius and centre of the circle; and they comply with the form of an incomplete proposition, which is comprehensible as such. Wittgenstein suggests that we think of a portrait from which the mouth has been omitted. This may mean one of two things. First, the mouth is white, like the blank paper. Second, whatever the mouth is like, the depiction is always correct. (But even if I describe completely everything which is in the room, this is still not a complete picture, since I can ask myself what is outside the room.) By contrast, a complete description is given when I say:

    For here we can describe ‘colour boundaries in the field of vision’. In the present case this occurs, for example, through ‘equations of lines and colour indices’. The space is complete, and although one can indeed alter the description, one cannot add anything else to it. The same holds true, however, if I describe a room (completely), for example where the table and chair are positioned; later on I cannot also say ‘and there is also this and that there’. The more incomplete the picture, the more probable it is that it agrees with reality. The fact that the proposition ‘all circles in the square are black’ is not an enumeration of circles, and that it does not have to be concluded with ‘and these are all the circles (in total)’, is connected with the fact that Wittgenstein‘s concept of the picture is derived on the one hand from graphic images, on the other from mathematical ones. (Concerning the use of the word ‘all’ in this case, he speaks of a complete induction, which does not afford proof for all elements, but in the first instance presents its own criterion for ‘all’). I can, therefore, leave one term in a proposition open, and in response to the question ‘How do I know such a proposition?’ I can answer with an endless disjunction of elements. The misleading temptation is to compare the proposition about all the circles in the square with that about all the persons in the room. In this case it seems obvious that one should enumerate the persons, including those who are not in the room. If however I were to allocate names to circles, it would also have to make sense to assert of a particular circle that it is in the square, even if it is not (to give an analogy: ‘this circle is dead, but I still have a photo of it’). Now, certainly many circles are not in this square, and if all are not in it, which ‘all’ are then outside?

    ‘Three rather dark grey circles’

    In paragraph 71 of the Philosophical Remarks Wittgenstein writes: ‘It might, for example, even be a practical idea to give proper names to my hands and those of other people, so that, when speaking of them, one did not always have to speak of their connection to a person, which is inessential to the hands themselves; and also because the conventional mode of expression might give the impression that the hand’s connection with its possessor was something which formed part of the hand’s essence.’

    ‘Visual space essentially has no owner’. What if it transpired, from the discovery of a letter or note by Mach, that the hands in the picture did not belong to him, but that a friend had modelled for him (for example by squatting behind Mach, holding his hands stretched forward), so that Mach had his hands free for drawing? Would we then, in the future, have to describe the picture with the words ‘Mach’s legs, Mach’s upper body, not his arms ... ’, or would we not rather say: ‘We can see two legs, … two arms (elements of the representation). Concerning this last, however, we know today that for the drawing a friend … ’? Would this perhaps weaken Mach’s response to his colleague’s challenge? Wittgenstein continues: ‘Let us now assume that I always see a specific object along with all the others in my field of vision – that is, my nose. Naturally another person does not see this object in the same way. But does that not mean that the visual space of which I am speaking belongs to me? That it is, therefore, subjective? No. Here it is merely grasped subjectively, and an objective space is placed in opposition to it, which, however, is only a construction, with the visual space as its basis.’ It is only in our language of objective space that our visual space is called subjective – or alternatively, that what is directly equivalent to our visual space is called subjective. Mach’s picture is only one possibility of representing this. ‘The essential point is that the representation of visual space represents an object and contains no indication of a subject.’ Even the phrase ‘visual space’ is, according to Wittgenstein, inappropriate, since it contains a reference to a sense organ which is just as inessential to this space as it is inessential to a book that it belongs to a particular person. The fact that I could turn around, and to use such a picture to find out where I am, only means that I am establishing a definite structure of visual space.

    If, however, one’s visual space is now to be isolated as a phenomenon from everything else, what kind of time is appropriate for this visual phenomenon? The time of our conventional mode of expression? ‘It is clear,’ writes Wittgenstein, ‘that the description of memory as a picture is only a metaphor, and does not imply a physical image which we can compare to other things.’ Later, in paragraph 67, he continues: ‘Let us assume that my memory were so good that I could remember all my sense impressions, or that I could produce models of what I see in another – e.g., plastic – form as rapidly as I remember them, i.e. by means of omission or colouring ... [I]f in these models I could indicate what I had seen and what my visual impressions could no longer retain, and if by this means the position of my eyes could also be exactly deduced from the model – would this not be the most direct description imaginable, so that any attempt to capture the phenomenon even more directly would no longer be a description, but rather like an attempt to start before the beginning?’ This could be a further aspect of how we read Mach’s picture as a response. The language with which we attempt to describe language itself proceeds in physical time. ‘With language,’ says Wittgenstein in paragraph 70, ‘we find ourselves, so to speak, not in the realm of the projected image, but rather in the realm of the film. And if I want to make music to the events on the screen, then what it evokes must once again play itself out in the realm of the film.’ On the other hand it is clear for Wittgenstein that we need a form of expression with which we can depict the phenomena in our visual space as such in isolation. ‘“I see a lamp standing on the table”, as it must be understood in our everyday speech, says more than a description of visual space.’ I would add: ‘it appears to me to be so’ does not mean that nothing real is being described, but rather that I am uncertain whether in future I will be able to describe further events like that of seeing the lamp as special cases of the same rule. As Wittgenstein says (paragraph 69), ‘I think that what I call a “sign” must be what is called a “sign” in grammar: something on the film, not the screen’.

    (Translated from the German by Peter Burt)


    1. Augustine, Confessions, Books X and X1, trans. Kurt Flasch (Reclam, 2008)
    2. Ernst Mach, Die Analyse der Empfindungen: und das Verhältnis des Physischen zum Psychischen [‘The Analysis of Sensations, and the Relationship of the Physical to the Psychical’] (Xenomoi, 2008)
    3. Wittgenstein und der Wiener Kreis [‘Wittgenstein and the Vienna Circle’] (Suhrkamp, 1984)
    4. Ludwig Wittgenstein, Philosophische Bemerkungen [‘Philosophical Remarks’] (Suhrkamp, 1984)
    Dejan Makovec. Date: XML TEI markup by WAB (Rune J. Falch, Heinz W. Krüger, Alois Pichler, Deirdre C.P. Smith) 2011-13. Last change 18.12.2013.
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