Splitting Images Understanding Irreversible

: Multistable figures or Kippbilder combine reversibility and ir-reversibility in an interesting way. While the so called first aspect change introduces an irreversible split, all subsequent aspect changes can be understood as an endless chain of reversible changes. And it is exactly because of this complex combination of an eventful moment and an undirected repetition of the same, Luca Di Blasi argues in his paper ‘Split-ting Images. Understanding Irreversible Fractures Through the Aspect Change’, that Kippbilder can provide an interesting model for understanding better dramatic, existential, even religious events and their consequences.AfterdiscussingthespecificityoftheRubinvaseanditsaspect changesandfocussingthenonthedistinctionbetweenfirstandfurtheras-pectchanges,DiBlasisuggeststheproductivepotentialofthemultistable figureasmodelforeventfuleventsindiscussingtheconversionofPaulandhis hōs mē (‘as if not’).


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The Rubin vase and duck-rabbit have two things in common: not only are they famous multistable figures, or Kippbilder, but before being discovered by scientists and philosophers, they both started their career as simple jokes.The duck-rabbit Kippbild appeared for the first time in 1892 in a satirical review (Fig. 1), 2 and a visual jest, which contains four profiles of the French royal family (Fig. 2), inspired the Rubin vase (Fig. 3). 3 There is obviously a difference between a gag and the Damascene Conversion of Paul, which I will try to explain with the model of aspect changes at the end of this paper.A connection between all three examples lies, however, in an eventful moment, something that happens immediately and changes everything: the punchline, the eureka moment in the aspect change, the existential split in the conversion.In contrast to usual understandings of Kippbilder, which focus on the relationship between perception, cognition, and language, this paper will try to demonstrate that Kippbilder can be a helpful model for understanding better dramatic, existential, and even religious events and their consequences.
The starting point of the first section of this paper is the assumption that the aspect change of the Rubin vase is not completely analogical to the one between duck and rabbit.The Rubin vase consists in the close entanglement of two different aspect changes, one between faces and vase and one between figure and ground.The latter inverts an initial distinction and can therefore be called 'inversional aspect change'.At the end of the section I will reapply -as a kind of hostile re-entrythese insights to the theoretical means that helped develop the notion of the inversional aspect change, namely George Spencer Brown's notion of distinction, and indicate its limits.The moment we try to apply the inversional aspect change to political questions, however, we are confronted with further limitations.
In the second section, I want to discuss the aspect change of the duck-rabbit Kippbild, which might be specified as a 'splitting aspect change' in order to distinguish it from the inversional aspect change.My aim is to show that there is here a basic difference between the first aspect change, which introduces a split, and all subsequent aspect changes, and that we have to keep this difference in order to better understand the complexity of the Kippbild.The exclusion of further aspect changes necessarily leads to a deceptive overcoming of the split through a 'totalitarian' retransformation of an aspect into a 'whole' image, although reducing the aspect change to an endless change between two possibilities also undervalues the split.
Only if we understand and adhere to this complexity, I would claim, can we use the Kippbild as a model for dramatic, splitting events.In the last section, I will try to briefly suggest its potential in discussing the figure of Paul and his hōs mē ('as if not').

. M O R E T H A N A D I S T I N C T I O N : T H E I N V E R S I O N A L A S P E C T C H A N G E O F T H E R U B I N V A S E
Fig. 3. 'Rubin vase' (Rubin, Synsoplevede Figurer, image 3).
In this section, I am interested in the specificity of the aspect change of the Rubin vase and in its difference to that of the duck-rabbit.In order to explain it, I want to use an example, even if it is more of a metaphor than a precise fit, and might thus be as misleading as it is helpful.Before Galileo Galilei, we thought that the sun was moving around the earth; after him we know that it is exactly the opposite: the earth is moving around the sun.This sounds familiar, but what is wrong with it?In the case of the heliocentric notion, we have two movements that can easily be confused: the movement of the earth spinning (the cause of our geocentric understanding of the sun moving around the earth) and the additional movement of the earth around the sun, which has nothing to do with our impression of the sun moving around the earth.While it is true that the earth is moving around the sun, this is not the inversion of the impression that the sun is moving around the earth.Its inversion is that the earth is spinning.
Something similar is going on when we compare the relation between the faces and the vase in the Rubin vase with the relation between duck and rabbit.Why?To begin with, we see (as in the case of the duck-rabbit) only a single figure: a vase or faces.In contrast to the duck-rabbit, however, after the aspect change we not only see another figure, but we cannot avoid becoming aware of the question of the ground, because what was ground before the aspect change becomes figure after it and vice versa.Thus we can say that the aspect change of the Rubin vase consists of at least three relevant distinctions: not only the distinction between faces and vase, but also the distinction between vase and ground, and its inversion, between faces and ground.
The duck-rabbit Kippbild is different.Here the figures change as well, but their relations to the ground do not.Therefore, in the case of the duck-rabbit Kippbild, the ground does not matter, so it normally remains unmarked.It is only when comparing it with the Rubin vase that we are (now) mentioning and noting it.But even after noting it, the ground of the duck does not differ from that of the rabbit.The figureground relation does not change with the changing of the figures.In consequence, after noting the ground of the duck-rabbit we are able to make the same three distinctions as in the case of the Rubin vase (rabbit-ground, duck-ground, and the distinction between these two distinctions).However, these three distinctions remain an empty abstract possibility that is not grounded in a perceptional experience.The only relevant change here therefore remains the change from one figure to the other, without the parallel change of the figure-ground relation.Even though we can indicate and name the ground, we do not see it as a figure . 5 But what exactly is the difference between naming the ground as ground, (changing from figure to ground) and inverting the figureground relation?In order to approach this question, it might be helpful to leave for a moment the field of multistable figures.Let's instead take another picture as an example, which looks similar to different pictures Rubin used and which was painted in the same year, in 1915: Kasimir Malevich's famous Black Square (Fig. 4).Fig. 4. Kasimir Malevich, Black Square (1915).
Like in the case of Rubin's pictures, the tension between figure and ground seems to play an important role here, as its complete title Black Square on a White Field already indicates.By mentioning or naming both sides of the distinction, Malevich demonstrated awareness of the fact that he was dealing with a distinction.This means, in the terms of the logician Spencer Brown, that he crossed the boundary between the initial indication, the black figure, towards another side, and by naming it as ground or 'white field', he also named and indicated this other side.But what distinguishes this awareness of both sides of a distinction -figure and ground -from their inversion?
In contrast to Rubin's pictures, Malevich obviously didn't intend the black square as a ground.In his text 'From Cubism and Futurism to Suprematism: The New Realism in Painting', written in 1915/16, 6 he does not mention the possibility of the inversion of figure and ground, and the title Black Square on a White Field even stresses the stability of the figure-ground relation, connecting and fixing the ground with the white colour and the figure with the black one.To see and to name the white part of the painting ('white field') is not enough; an inversion occurs only in the moment we are able to see the ground as figure (in this case, for example, a white window-frame, from which we can look into a black night).
We can now see more clearly that crossing the indicated side of a distinction and naming the other side is neither equal to, nor a condition for, an inversion.Instead of inverting the original distinction, cross-ing the boundary rather seems to favour a second-order perspective from which one can name or indicate both sides of a distinction without necessarily having experienced an inversion.This difference becomes evident if we compare the stable figure-ground relation of the Black Square, as understood by Malevich, with another picture in Rubin's book.In contrast to the Black Square, this picture is intended to let us perceive an inversion of figure and ground.We are expected to perform the inversion of an initial distinction (Fig. 5).This picture allows the distinguishing of inversion and multistability at the same time.In contrast to the Rubin vase, the inversion occurs here without the involuntary eureka moment that is typical of multistable figures.The eureka moment seems to be connected to the first recognition of a figure or gestalt as such, something that does not hold for the black and white side of Fig. 5, since these sides arguably do not belong to anything we would recognize.Fig. 5 thus provides the possibility of distinguishing not only the indication of an unmarked side and inversion, but also the inversion of figure and ground from an inversional aspect change.What Rubin's vase and his other figures share is, however, the potentiality to visualize that -as Niklas Luhmann has repeatedly said, and as follows from Spencer Brown's Laws of Form -in operating with distinctions, we are dealing with asymmetrical differences. 7The two sides of the distinction are not symmetrical, because only one side is initially indicated.Each distinction implies first the focus of one side and the neglect of the other.Starting from this indication, we can then, in a second step, cross the boundary and mark the as yet unmarked side.
relation is asymmetrical as well, since here the figure is privileged in the sense that it attracts our attention.
While crossing a distinction and naming its unmarked side favours the misunderstanding that this might be sufficient for the symmetrization of asymmetrical distinctions, the inversion provides a possibility for dealing with asymmetries that goes beyond such mere crossing.Because of its potential capacity not only to illustrate hierarchical differences, but also to invert them, the inversional aspect change apparently favours the possibility of seeing asymmetrical distinctions, for example asymmetrical power relations, the other way round.
This does not, however, mean that applying the inversional aspect change (and inversions in general) to politically asymmetrical (for example, power) relations would be unproblematic.First, the equalization of hierarchies by complementing one hierarchy with the opposite one might be interpreted as the anticipation of an equality to come, but it might also appear ambivalent because such a (symbolic) anticipation to a certain degree obscures existing hierarchies.Second (and more relevant), while, for example, deconstruction can be read as a strategy of fighting existing hierarchies without falling into the trap of reproducing the basic asymmetry, this seems to be exactly what the inversional aspect change leads to.The basic asymmetrical distinction is not scrutinized by it.Instead of deconstructing or questioning this asymmetry, the inversional aspect change perpetuates it by inverting it.Finally, what the inversional aspect change is not providing is the experience of the other aspect as figure (subject) and as devalued at the same time.It permits perception of the 'ground' as figure, but only by reducing at the same time the former figures in the ground.

. O U T O F T H E B L U E -D U C K -R A B B I T : T H E S P L I T T I N G A S P E C T C H A N G E
Starting from the analysis of the difference between the Rubin vase and the duck-rabbit Kippbild, I tried in the first section to figure out the difference between distinction and inversion.The analysis finally led me to what might be designated as a basic characteristic of Kippbilder, namely the so-called eureka moment, the involuntary aspect change.
In this second section, I would now like to focus on this eureka moment, not psychologically (as the time interval between one aspect and the other), 9 but rather structurally as an eventful split that changes everything.In order to do so, I will look at the aspect change genealogically and, so to speak, in super slow motion.Also, I will turn towards the duck-rabbit Kippbild, but not because of its philosophical reputation (acquired through Ludwig Wittgenstein's extensive discussion of the figure in his Philosophische Untersuchungen).
10 Rather, since the duck-rabbit Kippbild is somehow simpler than the Rubin vase, it permits us to focus on the change from one aspect to another without a parallel (and easily confusing) inversion of figure and ground.
Since I am more interested in the Kippbild as a structural model for the description of events and their consequences than as a model for the connection between language, perception, and cognition, I will use the term 'aspect' in the sense of a relativization and ignore other possible meanings.(In line with this formalization, I will symbolize the aspects with abstract figures like the semicircle and the rectangle in Fig. 6.)At the same time, I will juxtapose this formalization with a certain dramatization in order to constantly foreshadow the model's potential possibilities applications to existential, and even religious, events and their consequences.
Prima facie, the relation of the aspects is both symmetrical and circular.No linearity, no progress occurs: only the endless change from one aspect to the other, from one side of the distinction to the other.While this is true, it is certainly far from being an exhaustive description.Seen in a genealogical way, we do not start with two aspects -a duck and a rabbit -since we do not start seeing two aspects immediately (Fig. 6).Nor do we have first one aspect, and then a second one.The notion of the aspect in which I am interested here already implies a relativity that at the very beginning is not yet given.We have, first, what appears as one (a whole picture), and then, after we see the 'second aspect', we have two aspects.
11 But this does not mean that we have first a whole, which is then simply divided into two aspects (Fig. 7).
Rather, we have something like this (Fig. 8): First we have a whole (the larger circle), and then the sudden introduction of something new (the black square), which is completely different from what now appears as the 'first aspect'.(In the following I will do without quotation marks, even though one should bear in mind the problematic use of the terms 'first aspect' and 'second aspect'.)This new aspect is not connected to the first aspect, save through its power to split and transform it retrospectively into an aspect.And vice versa: calling something an aspect when it comes out of the blue and is not dialectically connected to the former whole, already implies a connection or relation to the relativized whole.We have here a reciprocal relativization of the former whole, which appears as a first aspect through the emergence of something new, which in turn can itself only be read as a second aspect through the relativization of the first aspect.In this sense, the very notion of the aspect (again, in a purely formal understanding) implies a reciprocal aspectualization and relativization, and thus a relation.At the same time, both aspects keep an independence one from the other, and do not appear as halves of a comprehensive whole that require supplementation.Such a whole does not exist anymore, and therefore both aspects cannot really be called parts.In Fig. 8, this transformation of the former whole into a mere aspect is indicated by a reduction of the circle's size; the -slightly differentinterdependence between the second aspect and the former whole is indicated by the double arrow between them.The first aspect change is thus the moment of a break and reciprocal 'aspectualization', which changes everything.However, Fig. 8 is not yet precise enough, since it does not take into account that after this retroactive aspectualization of the former whole, this whole disappears.The moment we see the second aspect, the whole becomes inaccessible; it is gone, eliminated, or more precisely, it is there only as a reminder of something lost.(This transformation is suggested in Fig. 9 through the pale colour of the big circle.)And this means that this wholeness can become relevant and an object of desire or nostalgia only after the split, which, again, is not a split of itself into two, but rather a split by the appearance of something different.But what is remarkable is that this wholeness appears neither as purely constructed (there was integrity, a whole, before) nor as something that was simply already there, since what appeared as integrity and wholeness actually turned out to be only limited.Even if one were to go one step further and claim that before the aspects there was no whole (since the notion of the whole always implies parts, or in our case, aspects 12), then one would have to say that the multistable figure is initially a 'whole' that is not a whole, and then after the aspect change consists of 'parts' that are not parts.
By means of the aspect change, we are able to demonstrate a misunderstanding full of consequences that can arise at the very moment of the split/loss of the whole.The wholeness has not only become inaccessible and thereby possibly an object of desire in the very moment of its disappearance; there is also almost necessarily the danger of imagining it in the shape of what once appeared as an intactness, but turned out to be only an incomplete aspect.Imagining the intactness in the shape of the first aspect means privileging, mystifying, and totalizing one (contingent) particularity: the contingency of the first.While denying the integrity altogether does not take into account the experience and persistence (in the form of a memory of this experience) of the lost integrity, its vi sualization tends to be bound to the lost whole (the first aspect) and necessarily falls into the totalitarian trap.The whole is imagined through what turned out to be particular.
The converse is also true: even after the reduction/relativization of the former whole, one might be tempted to perceive its relativized remainder -the first aspect -as a particular, but nevertheless exceptional, representative or reminder of the lost integrity.Here the first aspect becomes a symbol of the isolated, limited, undivided, and sacred exception inside a world broken into parts.(This double temptation is suggested in Fig. 9 in the way that the symbol of the lost integrity and of the first aspect share the form of a circle, and thus continue to be connected even after the appearance of the new aspect, when it has become evident that the circle, in excluding, so to speak, the square, cannot be the right symbol of a totality or integrity.)But there is a parallel risk: There is not only a special relation between the first aspect and the lost integrity, but also one between the second aspect and the split.The second aspect is ambivalent.It can be understood as something distinct and new, but at the same time it has to be equally understood as something that splits the situation and relativizes the former whole -and in consequence necessarily itself -into a mere aspect.Therefore, even though the first aspect is no less connected to the division than the second aspect, the latter appears more related to the split condition.
In this sense, it is not enough to say that the appearance of another aspect provokes a richer understanding of the world, since after it we were able to see the world from an additional perspective.Even though this is true, it is also true that it is exactly this new aspect that reduces retroactively what appeared as a whole to an aspect.It is (not exclusively, but also) because of this prior reduction that the introduction of a new aspect appears as enriching.We did not have first one, and then two; we had first one (a whole), and then a split of the whole by the appearance of something else, and thus one that is more and less at the same time.We have neither an addition, nor a division; we have neither one added to another nor one divided into two, but one divided by another.Thus we have more (another) and less (the split and the reciprocal aspectualization) at the same time.The split and the impossibility of coming back to a simple whole, or a state of integrity, is the price for the addition of aspects and views.
Even though both aspects of a Kippbild are closely connected, the relation between both is -as already suggested -not completely symmetrical.The first aspect is not necessarily connected with the second one.Someone might simply not see the second aspect, and then there is for him no aspectualization and relativization (and Kippbild) at all.In this case, there is not only no second aspect, but neither is there a first one.We have the intactness, that's all.(This very possibility might limit any attempt to overcome particularism.Since there is always at least the theoretical possibility that someone does not experience the aspect change -what Wittgenstein called 'aspect blindness' -there are no means to force him or her to accept it.In consequence, there is always the possibility of just simulating -towards others and/or towards oneself -aspect blindness and thereby defending a position that turned out to be limited or particular.) In the case of the second aspect, things are more complicated.Its status is from the very beginning paradoxical because it is not only between being a whole and an aspect; this very ambivalence lets it appear as representative of the new condition of the (split) whole.The new aspect can somehow be separated from the old one because it comes 'out of the blue' (it was neither predictable nor deductible from the first aspect), but not completely because it is also true that it comes 'out of the duck' or 'out of the rabbit'.Because of this specificity, the second aspect is less than the first aspect (it was never a whole image) and more at the same time: in its own dividing dividedness (between independence from and splitting relation to the former whole), it performs and represents the split and the splitting, and thus the new condition (the new whole), which consists exactly in the split.
This complicated relation between first and second aspect requires further aspect changes in order to persist.Stopping the aspect change on the side of the first aspect would retrospectively make the emergence of the new appear as the emergence of a mere phantom.Instead of an aspect change, we would rather have the short appearance of something else that immediately disappeared again.If the Kippbild stabilizes on the side of the second aspect, we would have either the gradual (although perhaps never-ending) replacement of the old integrity through a new one, or (as frequently occurs in religious conversions) its radical retrospective revaluation (e.g. the negativization of the life before the conversion as sinful).In both cases, stopping the aspect change would be equivalent either to a decision in favour of a limited but stable, less exhaustive but also less exhausting aspect, or to an attempt to 'retotalize' an aspect to a (deceptive) whole.This is the reason that the aspect changes that follow the first one are relevant: they accomplish the reciprocal aspectualization and guarantee the persistence of the split by making the stabilization of one aspect impossible.
In order to get an adequately complex description of the aspect change, we have thus to understand the importance of the further aspect changes and to preserve the difference from the first one: only the latter introduces a new element or aspect and a split, and at the same time reduces the former image by transforming it into an aspect.Moreover, only in the first aspect change does something like an event really occur.The first aspect change is not a matter of decision or intention.It could arguably occur even without knowing that there is another aspect.While the further aspect changes may become somehow intentional, the first one is the occurrence of something we can experience (or not), but cannot choose or even anticipate voluntarily.This is why only this first aspect change bears the quality of a eureka moment, a proto-epiphany, and no one can really expect someone else to experience it.The disregard of the further aspect changes restabilizes one of both aspects and leads to the totalitarization of one aspect.Ignoring the difference between first and further aspect changes, in contrast, reinscribes the first aspect change retrospectively in a chain of normalized and banal repetition of more and more voluntarily executable, endless, and senseless aspect changes from one aspect to the other and back, transforming it thus into something like a drawing of distinctions.In other words, the complexity of the aspect change vanishes if we stabilize it by stopping it at a certain moment, but it also vanishes if we reduce it to an endless and senseless repetition.
Between the dramatic first aspect change and the normalized one, there is another relevant aspect change that mediates between both.The Kippbild as Kippbild does not start immediately with the experience of something new -the first aspect change -but rather with the 'return' to the first aspect (which indeed is not a return, but a change into something new, in so far as it is, again, not the return to a whole, but to a relativized aspect).Only at this moment can we really start speaking of a Kippbild, because as long as there is no 'return', the whole dynamics of the aspect change has not yet been developed; instead, we have a change from one state to another.The second aspect change initiates the normalization of the dramatic eureka moment into the endless repetition of aspect changes.
One consequence of this understanding is that inside the Kippbild model there is one possibility for making a decision.This is not self-evident, because the Kippbild model does not seem to provide any choice at all: the first aspect change is eventful and not a matter of decision.The event (the first aspect change) is so dramatic exactly because it changes any former condition, so that after it, we cannot switch between a former situation (whole, integrity) and a new one (aspect, split).After the split, the former situation (the whole) simply does not exist anymore as a whole, but only as an aspect.And an endless repetition of aspect changes cannot provide any possibility for deciding between either aspect.
Nevertheless, there is still a possibility for deciding, but it lies neither in choosing between one aspect and the other, nor in choosing between split and not split.The only choice we have is to accept (or not) the complexity of the aspect change, or, translated into an existential sphere, to accept (or reject) the split and at the same time the desire for getting rid of it.Only the adherence of both the notion of a lost integrity and the persistence of the split can cover the complexity of the situation.Even if for practical reasons we are forced to opt for one or the other, this decision cannot fundamentally change the situation.For example, even if we go on living in the apparently same conditions as before the event (an option that might be privileged by fidelity and/or by a certain conservative tendency against a complete change of circumstances), after the split it would result in self-deception if we tried to imagine this condition (the first aspect) as still integrated.
The same is true, however, for the decision in favour of the splitting second aspect.This option is encouraged by the fact that the new aspect reveals the narrowness of what now appears retrospectively as an integrated whole, and bears the power of a completely unfolded potentiality, the magic of a new and renewing beginning.Since the second aspect provides the illusion of better representing the new (split) whole (as the first aspect provides the illusion of representing a still integrated one) it is particularly fascinating -but only as long as there is no decision in favour of it.Opting for the new aspect is equivalent to the attempt to replace a lost whole through a new (totalitarian) whole.In this case, it is the neglect of this split and splitting character of the new aspectsplit between whole and aspect, between independence and relation to the other aspect -that would necessarily lead to limiting it to exactly what it revealed the first one to be.
But what is more, even opting for the split (by which, again, the second aspect appears more closely connected than the first one) as split, its affirmation is paradoxically equivalent to the attempt to get rid of it (and, in existential terms, its pain) through the cancellation of the very idea of something like integrity and the transformation of the split into repetition.This can be related to the endless aspect change, even though the Kippbild is here in that sense limited and misleading, as it suggests an endless aspect change between two aspects rather than between always different ones.
In short, the only decision that respects the complexity of the aspect change lies in the refusal of two different kinds of reduction.One consists of negating the split, in trying to stop the aspect change -making a decision in favour of one aspect and thereby hoping to finally get rid of the split altogether.The striving for the 'final dissolution' of any split and thus tension might remind us of the Nirvana principle as proposed by Sigmund Freud.The other, more complicated, option consists in the affirmation or revaluation of the split and the denial of any integrity at all -the striving to get rid of the very notion of any reminder of a lost integrity.This option is not directly reductive, in so far as the intactness indeed no longer exists, but it easily leads to the reduction of the aspect change by mastering it.We walk here a fine line between accepting the split and transforming it in an active attitude, becoming more and more able to perform the split actively, and transforming what initially was passivity into a splitting activity.The field ranges from the distinction between passive and active nihilism, and Nietzsche's ambivalent attempt to overcome both with his notion of the 'ewige Wiederkehr des Gleichen' ('Eternal Recurrence of the Same') to Freud's 'fort/da' and obscure aspects of Žižek's (death) drive.

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The aspect change, as described here, seems to provide an interesting model for the analysis of relevant -and this means irreversiblechanges, especially for irreversible, eventful changes provoked by the appearance of something new (what we described as a second aspect).In order to apply the inversional as well as splitting aspect change, I will very briefly try to read the Paulinian conversion and his subsequent position between Judaism and Christianity, as well as his notion of the hōs mē, as developed by Giorgio Agamben, through the Kippbild model.
As is well known, Paul was a devout and even fanatic Pharisee who combated Christians before he converted to being one of them: '[…] circumcised on the eighth day, of the people of Israel, of the tribe of Benjamin, a Hebrew of Hebrews; as to the law, a Pharisee; as to zeal, a persecutor of the church; as to righteousness under the law, blameless' (Phil 3, 5-6). 14The Damascene Conversion, as described by the Acts of the Apostles, was a splitting event, an eventful encounter with Jesus Christ.This dramatic encounter, however, was not an encounter with something completely new: he already knew the other side of the distinction and had a name for it.The described Damascene Conversion was more than simply crossing the boundary of a distinction and naming the other side, and presumably more than a simple inversion, since with his conversion, Paul not only saw, in terms of the inversional model we described earlier, Christ and the Christians 'as figures', as subjects; becoming Christ, he also perceived them from their own side, as victims of persecution.Paul switched to the position of the persecuted without becoming a persecutor of the former persecutors, without simply inverting the hierarchies.
The term 'conversion' is, however, somehow problematic: Paul converted to an abject side -something that nowadays might recall the term 'perversion' -rather than to a well-established and more or less respectable institution.In order to maintain the richness of what happened here, one might try to combine both terms (conversion/perversion) in order to mutually enrich them.At the same time, he converted in an unfolded field that was not yet developed (there were already Christians, but there was no real Christianity yet, let alone an organized church).
The very problem of understanding Paul consists therefore exactly in the uncertainty as to what extent we can already imagine the conversion as a movement towards something new, inasmuch as it rather consisted in the split and change (relativization) of a given situation (what after the split appears as Paul's 'Judaism' before).And this is exactly the reason that the splitting aspect change is so interesting here.As I have tried to show, the occurrence of something new (a new aspect) is inherently connected to the split and relativization of the former condition.Indeed, according to Paul, the messianic event consists in a split of all former positions and identities in themselves.After the event, everything is 'as if not', hōs mē.
What I mean, brothers, is that the time is short.From now on those who have wives should live as if they had none; those who mourn, as if they did not; those who are happy, as if they were not; those who buy something, as if it were not theirs to keep; those who use the things of the world, as if not engrossed in them.For this world in its present form is passing away.(1 Cor 7, 29-30.)As Giorgio Agamben has developed it in his book Il tempo che resta (2000), hōs mē is the best definition of messianic life.The consequence of the messianic event is a radically different identification of one's situation.This extends to ownership structures, professions, intimate social systems, and institutions like matrimony.Each state is split and brought into tension with itself.For Agamben, hōs mē is the formula of this split.'The messianic vocation is the revocation of every vocation.' 15The hōs mē is thus, if we follow Agamben, anything but a happy, liberated con-dition.Quite the opposite, it is the condition of intensity and inner tension that follows from the occurrence of a messianic event. 16 Relating to Paul himself, his 'Christianity' would not simply consist of the choice of something new, a new identity that at this time has not yet been established.(Paul never speaks of Christianity.)Neither would it simply consist in the split of a given situation, the split of 'Judaism' itself (because what is called 'Judaism' after Christianity is the product of a relativization and of a retroactive change).Rather, we have here the very connection of both: the split of an intactness (what retrospectively appears as 'Judaism') through an event, something new.'Christianity', especially in this initial state, but to a certain extent to this day (since it never followed the temptation to get rid of the 'Old Testament'), is not simply something completely different from 'Judaism', something that could be isolated from it, but rather the apparently paradoxical -but via the model of the aspect change, nevertheless understandable -connection of something new that splits and relativizes a former condition.
The Kippbild model can thus provide a model that overcomes a deep tension between the main current philosophical interpretations of Paul: while Agamben -and this holds even more for Jacob Taubes 17 views Paul as belonging essentially to Judaism and tends to interpret Paulinian Christianity as the consequence of the introduction of a split in the Jewish tradition, Alain Badiou, another major contemporary philosopher who wrote a book on Paul, 18 on the contrary tends to view Paul exclusively as the militant subject of a new event and its consequences. 19Somehow similar to Marcion, who wanted to strictly separate Christianity from Judaism and thus represented the eternal Christian temptation to create an identity isolated from Judaism, Badiou is much more interested in Christianity as the beginning of something completely new, rather than as something that from the very beginning was connected with 'Judaism' by splitting, relativizing, and in this sense somehow producing it.This is not the place to unfold all the possibilities that arise the moment we try to adapt the aspect change to Paul's conversion as well as to his contemporary interpreters.I just want to suggest that the Kippbild model, by providing the occurrence of something (the second aspect) that comes simultaneously 'out of the blue' and 'out of the duck/ rabbit' (out of a given condition, which the second aspect retroactively splits and relativizes), and by providing something we initially experience rather than perform, offers a very interesting new possibility for interpreting Paul's Damascene Conversion in a way that covers opposite interpretations: yes, Paul indeed converted to a new condition, but this condition introduced a split into the former whole at the same time, relativizing it, and in turn this new condition cannot be isolated or fully embraced without reducing it again.One formal reason that Paul keeps provoking tensions after two thousand years may lie in the complex interconnection between the split and relativization of a given situation and the decision in favour of, or conversion to, something new.In doing so, Paulinian Christianity seems to radicalize both: the split and tension, and in consequence the 'messianic' hope of overcoming it.In this reading, the hōs mē might be understood as a deeply split situation that creates nostalgia for the lost integrity, and an absurd messianic hope of overcoming an insuperable and painful split.
In his demarcation against social democracy, Walter Benjamin described the messianic time opposed to an empty and homogeneous future, in which every second could be 'die kleine Pforte, durch die der Messias treten konnte' ('the small gateway in time through which the Messiah might enter'). 20In the demarcation against a totalitarian misunderstanding of particular aspects into lost wholes and orthodox forms of self-particularization by playing aspect-blind, and in the demarcation of death-driven approaches that try to convince us that there is no loss and no hope, but only an endless, non-teleological repetition -which in turn, however, is conceptualized teleologically as the overcoming of a teleological religious tradition -one could similarly say: living in a split condition means living a life in constant and persistent tension, and in the hope of a (messianic) redemption that will persist through the impossibility of its being thought of.

13
The so-called Rubin vase got its name from the Danish psychologist Edgar Rubin, who described it in his book Synsoplevede Figurer(Visual Perceivable  Figures) in 1915.Fig.3istakenfrom this book.In a footnote, Rubin refers to a vase he once allegedly saw in a cabinet of curiosities, where the 'gag' of the aspect shift was applied.See Edgar Rubin, Synsoplevede Figurer: Studier i psykologisk Analyse (København: Gyldendal, 1915), p. 31.In this context, he mentions Lillien Jane Martin, a female pioneer in psychology who had presented the picture 'King of France and Family' (Fig.2in this paper) in a publication shortly before Rubin's book came out.See Lillien J. Martin, 'Über die Abhängigkeit visueller Vorstellungsbilder vom Denken.Eine experimentelle Untersuchung', Zeitschrift für Psychologie und Physiologie der Sinnesorgane, I. Abteilung.Zeitschrift fürPsychologie, 70.3-4 (Leipzig: Johann Ambrosius  Barth, 1914-15), pp.212-75 (p.214).One might thus be sceptical about the story of the cabinet of curiosities and suspect that this was invented by Rubin in order to claim priority of his own 'discovery'.4 I develop a similar, but more detailed inquiry of the figure of Paul through an interpretation of Pasolini's script 'San Paolo'.See Luca Di Blasi, 'One Divided by Another: Split and Conversion in Pasolini's San Paolo', in The Scandal of Self-Contradiction: Pasolini's Multistable Subjectivities, Traditions, Geographies, ed. by Luca Di Blasi, Manuele Gragnolati, and Christoph F. E. Holzhey (Vienna: Turia + Kant, 2012), pp.189-207.5 As I will show in the second section, however, the aspect change of the duck-rabbit is much more complicated and differentiated than it might here appear.6 Kasimir Malevich, 'From Cubism and Futurism to Suprematism: The New Realism in Painting', in Art in Theory 1900-1990: An Anthology of Changing Ideas, ed. by Charles Harrison and Paul Wood (Oxford: Blackwell Publishers, 1992), pp.166-76.7 At least in the case of Luhmann, there might be a possibility of connecting his later thoughts to the aspect change.There is a connection (at least with regard to content) between the figure-ground distinction as analysed by Rubin and the figure-medium distinction as described by Fritz Heider a few years later.Luhmann, in turn, adopted the distinction of form and medium and reconceptualized it with the notion of form developed by Spencer Brown.See Niklas Luhmann, 'The Paradox of Form', in Problems of Form, ed. by Dirk Baecker (Stanford: Stanford University Press, 1999), pp.16-26.8 See George Spencer Brown, Laws of Form (New York: Julian Press, 1972).9 Referring to Wittgenstein, Fabian Goppelsröder mentions the importance of the very instant of the aspect change as a special moment between 'seeing' and 'seeing as': 'Dieser Moment der ent-schärften Perspektive auf Welt ermöglicht eben jene Erfahrung der Unsicherheit zwischen den Aspekten, in welcher das "Sehen" noch nicht wieder zu einem "Sehen als…" fokussiert ist.Dieser Moment ist der Moment des Übergangs, des Aspektwechsels selbst.'See Fabian Goppelsröder, Zwischen Sagen und Zeigen: Wittgensteins Weg von der literarischen zur dichtenden Philosophie (Bielefeld: Transcript, 2007), p. 80.For scientific and experimental approaches to the interval between one aspect and the other, see for example Jürgen Kornmeier, Wahrnehmungswechsel bei mehrdeutigen Bildern -EEG-Messungen zum Zeitverlauf neuronaler Mechanismen (Freiburg: Fakultät für Biologie der Albert-Ludwigs-Universität Freiburg, 2002).10 Ludwig Wittgenstein, Philosophical Investigations (Philosophische Untersuchungen), trans.by G. E. M. Anscombe, reissued 2nd edn (Oxford: Blackwell, 1997),