The most common impossible object is that which makes us see three dimensions when there are only two —depth where there is only length and width—. However, there are other examples that bring diversity to the matter. In sum, a series of visual and cognitive paradoxes which seem to invite us to expand the limits we ordinarily allocate to our perception.

three_hares_by_cidaq-d4viy42

The notion of the impossible object, in practice, is relatively remote. As well as some elementary examples (such as drawings that are made of three dimension objects on a flat surface; for example a cube), stands out especially the Three Hare motif, an emblem that beyond its symbolic and esoteric implications, is also, and probably not coincidentally, an optical illusion: there are only three ears for three animals that, on their sides and forming a circle seem to have each their pair of ears, but while the eye observes each animal in relation to the others, we can appreciate they all have at the same one and two ears, which they share but also belong to each. Following this format, the Three Hares where especially popular among Medieval Christians, especially in western England (there the motif is present in many churches) and some regions in France and Germany.

In modern times the Swedish draughtsman Oscar Reutersvärd found in this idea an ideal vehicle to express his artistic anxieties. Since the mid 1930’s Reutersvärd was nicknamed the “father of the impossible object”, in a large measure because his work led some geometric hypothesis to the very limits of their own logics, finding original shapes that overflow our thoughts, defy them, and question what we consider the borders of reality to be. Reutersvärd’ story, by the way, is interesting since he was dyslexic and had cognitive spatial problems, which was not enough to deter him, from becoming a renowned artist, aided by his family’s encouragement and his own perseverance.

ascending-and-descending-escher

Taking the latter into account, it is more likely that when referring to impossible objects, no-one has reached the genius or variety that the Dutch M. C. Escher did. His talent has been rewarded with the immediate recognition of his works. Indeed: Escher’s oeuvre bares a seal of its own, that of ludic authenticity that made him extremely well know, almost a pop artists avant la lettre.

One of the most distinguishing features of Escher’s impossible objects is that the inherent surprise of geometric invention adds details that accentuate, paradoxically, the confrontation between reality and unreality. Escher places the impossible object in the mock innocence of a daily scene to make the viewer believe that it fist perfects and limply in his reality: when whoever observes it believes it, soon finds out that he is in an improbable world, in a disproportionate world, in which the possibility of impossibility results, at the very least, unsettling.

In the palace that I imperfectly explored, the architecture had no purpose. There were corridors that led nowhere, unreachably high windows, grandly dramatic doors that opened onto monklike ells or empty shafts, incredible upside-down staircases with upside-down treads and balustrades. Other staircases, clinging airily to the side of a monumental wall, petered out after two or three landings, in the high gloom of the cupolas, arriving nowhere. I cannot say whether these are literal examples I have given; I do know that for many years they plagued my troubled dreams; I can no longer know whether any given feature is a faithful transcription of reality or one of the shapes unleashed by my nights. (Andrew Hurley)

The description of Borges’ City of Immortals emulates both the spatial features and the mood and the spell that certain of Escher’s impossible objects exert on those who are willing to participate in the game they suggest. On the other hand, the relationship between the Argentinian and the Dutch man is not at all granted (but, very blessed none the less), since they both share a certain metaphysical curiosity for regions in which Western logic, in many of its expressions, brushed against the absurd but also with absolute meaning (The Mexican writer Adriana González Mateos has explored the liaison between the two in Borges y Escher: un doble recorrido por el laberinto, 1998).

Perhaps the best examples of this way of conceiving the impossible object are two more or less contemporary lithographs: Ascending and Descending, and Waterfall, the first from 1960 and the latter from 1961. When we observe them, we accept the challenge they offer —following the flow of the water, and imaginarily climbing and descending the staircases— and the sudden illusion of the geometric space is revealed at once, but at the same time, the unending horizon of possibility.

mc-escher-waterfall

The space is limited, but within these limits there seem to be no limits whatsoever, or at least, that is the paradox that Escher’s creations suggest: impossible objects which, however, are possible.

And is the world, not essentially, geometry?

.

The most common impossible object is that which makes us see three dimensions when there are only two —depth where there is only length and width—. However, there are other examples that bring diversity to the matter. In sum, a series of visual and cognitive paradoxes which seem to invite us to expand the limits we ordinarily allocate to our perception.

three_hares_by_cidaq-d4viy42

The notion of the impossible object, in practice, is relatively remote. As well as some elementary examples (such as drawings that are made of three dimension objects on a flat surface; for example a cube), stands out especially the Three Hare motif, an emblem that beyond its symbolic and esoteric implications, is also, and probably not coincidentally, an optical illusion: there are only three ears for three animals that, on their sides and forming a circle seem to have each their pair of ears, but while the eye observes each animal in relation to the others, we can appreciate they all have at the same one and two ears, which they share but also belong to each. Following this format, the Three Hares where especially popular among Medieval Christians, especially in western England (there the motif is present in many churches) and some regions in France and Germany.

In modern times the Swedish draughtsman Oscar Reutersvärd found in this idea an ideal vehicle to express his artistic anxieties. Since the mid 1930’s Reutersvärd was nicknamed the “father of the impossible object”, in a large measure because his work led some geometric hypothesis to the very limits of their own logics, finding original shapes that overflow our thoughts, defy them, and question what we consider the borders of reality to be. Reutersvärd’ story, by the way, is interesting since he was dyslexic and had cognitive spatial problems, which was not enough to deter him, from becoming a renowned artist, aided by his family’s encouragement and his own perseverance.

ascending-and-descending-escher

Taking the latter into account, it is more likely that when referring to impossible objects, no-one has reached the genius or variety that the Dutch M. C. Escher did. His talent has been rewarded with the immediate recognition of his works. Indeed: Escher’s oeuvre bares a seal of its own, that of ludic authenticity that made him extremely well know, almost a pop artists avant la lettre.

One of the most distinguishing features of Escher’s impossible objects is that the inherent surprise of geometric invention adds details that accentuate, paradoxically, the confrontation between reality and unreality. Escher places the impossible object in the mock innocence of a daily scene to make the viewer believe that it fist perfects and limply in his reality: when whoever observes it believes it, soon finds out that he is in an improbable world, in a disproportionate world, in which the possibility of impossibility results, at the very least, unsettling.

In the palace that I imperfectly explored, the architecture had no purpose. There were corridors that led nowhere, unreachably high windows, grandly dramatic doors that opened onto monklike ells or empty shafts, incredible upside-down staircases with upside-down treads and balustrades. Other staircases, clinging airily to the side of a monumental wall, petered out after two or three landings, in the high gloom of the cupolas, arriving nowhere. I cannot say whether these are literal examples I have given; I do know that for many years they plagued my troubled dreams; I can no longer know whether any given feature is a faithful transcription of reality or one of the shapes unleashed by my nights. (Andrew Hurley)

The description of Borges’ City of Immortals emulates both the spatial features and the mood and the spell that certain of Escher’s impossible objects exert on those who are willing to participate in the game they suggest. On the other hand, the relationship between the Argentinian and the Dutch man is not at all granted (but, very blessed none the less), since they both share a certain metaphysical curiosity for regions in which Western logic, in many of its expressions, brushed against the absurd but also with absolute meaning (The Mexican writer Adriana González Mateos has explored the liaison between the two in Borges y Escher: un doble recorrido por el laberinto, 1998).

Perhaps the best examples of this way of conceiving the impossible object are two more or less contemporary lithographs: Ascending and Descending, and Waterfall, the first from 1960 and the latter from 1961. When we observe them, we accept the challenge they offer —following the flow of the water, and imaginarily climbing and descending the staircases— and the sudden illusion of the geometric space is revealed at once, but at the same time, the unending horizon of possibility.

mc-escher-waterfall

The space is limited, but within these limits there seem to be no limits whatsoever, or at least, that is the paradox that Escher’s creations suggest: impossible objects which, however, are possible.

And is the world, not essentially, geometry?

.

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