-ACANTHOLOGIES-

Things may have many interpretations

Our judgments upon an external stimulation may differ. If we notice a moving shadow, during the night in our backyard, most of us would probably call the police because our experience says that a shadow in the backyard implies a burglar. This is a sign of danger. However, if someone owes a dog and this dog is used to move around the house, then he/she would probably interpret this shadow as the shadow of his/her dog. This is a sign of safety. Things can be interpreted in many ways. The connection between the sign and its significance is unsolicited in theory. In everyday life though, the number and the content of significances that a receiver may apply to an incoming message are formulated by his own physical experience and memory. A medieval man could not perceive a light in the sky as a spacecraft, because he had not memory of such thing. He might choose among a divine message or a star orbiting around the world but definitely would not think about a spacecraft of the New Age..! A thing has to remind us something to get an interpretation. Perhaps this sound clumsy but there is a base. “Remind” means experience, memory and knowledge. Memory is the bucket of meanings and a thing may take several meanings from the bucket.

Space has an effect

Shapes may also get diverse meanings. If we regard the abstract shapes and forms as neutral, then the implications and the interpretations we give to these shapes are subjected to our personal or collective experience. Shapes, initially, are void of our meanings. Someone could say, shapes would be nonsense without human sense. Even more, our sense may create the shapes and then signify them. But human sense is not objective and differs from case to case or time to time. A cross, certainly implies Christianity but also can imply the nearby hospital. A reversed cross though, implies evil for many or an occult religion. Reversing the direction of a simple form can alter the interpretation of its meaning. In fact, when the direction of a shape changes this shape remains intact. Our perception is modified, not the shape. A triangle is a triangle even if we rotate it millions of times. For us though, the “normal” triangle is that one with one of its corners on the top. The rotated version of the “normal” triangle is perceived as a different sign with another suggestion, at the “Traffic Signs Regulations”. But the orientation of the top and the bottom is absolutely human, not universal. If we where bubbles, with only one eye in the middle and it was vital for us to rotate constantly in outer space, then the use of the “normal” and the “reversed” triangle, as two different signs, would be unsafe in our intergalactic highways. Back to earth, we do care about the orientation of a form.

Below are some small experiments concerning how simple drawings are presented in space. The shapes I have made for the following examples are not as abstract and purified as a triangle. I didn’t want these drawings to get completely unsolicited significations. They are referred to real objects and they retain a latent iconographic character. But what if one drawing hides two icons?

1.PIT---DOOR

A MINUS

A ROTATED

A ROTATED TWICE

B MINUS

B ROTATED

B ROTATED TWICE

I’ve made two sketches which I named them: drawing A and drawing B. Once I rotated them, I names them alternatively: drawing A ROTATED and drawing B ROTATED. The drawing A could recall (hmm… I hope you see it, this way...!), something like a gap in the ground, perhaps an open pitfall, which I’m going to call it a pit. So if we would like to decode the meaning of drawing A, we say that drawing A represents a pit. Drawing B could stand for an icon of an open door. The interpretation for drawing B is that B represents simply a door. So, we have: {drawing A=pit} and {drawing B=door}. As you can see the drawing B is made, by hand, as the vertically reversed image of drawing A. Therefore, we can say, the significance we apply to a unique shape may depend on its spatial orientation. If we rotate the two images then we have: {A ROTATED=door} and {B ROTATED=pit}. After rotation, A and B are swapping their meanings (actually, they are swapping their appearance and hence their meanings).
But, what about the memory we retain, of what the two sketches were standing for, before rotation? We remember the initial content of the two drawings. Moreover, A and B are real objects. They are piece of papers where somebody sketched something on them. A and B are objects with images on them, representing a pit and a door respectively. They are objects that have by purpose the character of an image with a specific implication. We can alternatively claim that A ROTATED and B ROTATED are not new images. They are simply the objects A and B rotated and consequently they are nothing more than the images of a pit and a door rotated. So, it could be: {A ROTATED = the rotated object A carrying the specific image of a pit = the rotated image of a pit} and {B ROTATED = the rotated object B carrying the specific image of a door = the rotated image of a door}.

A ROTATED can be either, the image of a door or the rotated image of a pit. B ROTATED can be either, the image of a pit or the rotated image of a door.

I think, a reasonable allegation is going to come up after that. In the beginning we interpreted drawing A only as a pit and drawing B only as a door. Who said that A isn’t already the rotated image of a door and B the rotated image of a pit? Who said that A and B aren’t in a false rotated state that it’s going to get corrected after rotation and reveal the true meaning of the two drawings which will be a door for A (A ROTATED) and a pit for B (B ROTATED). So we have dual interpretations for the state A and B:

A can be either, the image of a pit or the rotated image of a door. B can be either, the image of a door or the rotated image of a pit

Now, some not really necessary but amusing calculations though, describing what is actually obvious, are going to follow (kill your time):
We actually claimed that before the action of rotation which we are witnessing now, somebody has been already rotated the images and what we see now as A and B is the rotated version of a previous state. That’s how I call the state of the objects before the rotation committed by this unknown somebody: A MINUS and B MINUS. If we regard A MINUS as an image representing a door, then {A = the rotated object A MINUS carrying the specific image of a door = the rotated image of a door} and if we regard B MINUS as an image of a pit then {B = the rotated object B MINUS carrying the specific image of a pit = the rotated image of a pit}.
But if {A = the rotated object A MINUS carrying the specific image of a door} and {B = the rotated object B MINUS carrying the specific image of a door} then {A ROTATED = A MINUS rotated twice} and {B ROTATED = B MINUS rotated twice}. We know that {A MINUS rotated twice = A MINUS} because anyway, we are talking about the same object rotated two times for 180⁰ and that means a complete circle of 360⁰ or finally {A ROTATED = A MINUS}. Similarly, we have {B ROTATED = B MINUS}. We said before that {A ROTATED can be either, the image of a door or the rotated image of a pit. B ROTATED can be either, the image of a pit or the rotated image of a door}. So, because of {A ROTATED = A MINUS} and {B ROTATED = B MINUS}, we have {A MINUS can be either, the image of a door or the rotated image of a pit. B MINUS can be either, the image of a pit or the rotated image of a door}.

A MINUS can be either, the image of a door or the rotated image of a pit. B MINUS can be either, the image of a pit or the rotated image of a door.

We can speculate as many previous rotations before the MINUS state as we like. We can also predict eventual future rotations. Always we are going to face, one way or another, the fact of the dual interpretation of one image to be simultaneously the other image reversed. This is because obviously our perception says so and not a calculation. We can say schematically that every time after one rotation, the drawings are exchanging their dual meanings and shapes. (A MINUS ‘gives’ its meanings to B and then to A ROTATED…which is going to ‘give’ its meanings to B ROTATED TWICE and so on… , B MINUS to A and then to B ROTATED and then to A ROTATED TWICE and so on…). As we can guess, the endless rotation of the drawings is simply a loop among two situations (or states of the pair of drawings). These two situations are represented by the condition ‘A and B’ and the condition ‘A ROTATED and B ROTATED’. Every other state will be identical with either ‘A and B’ or either with ‘A ROTATED and B ROTATED’. Every two rotations we have the same state. We need at least one rotation for one single drawing to get signified with both of the double interpretations.

So, If we want to connect potential future rotations with speculated past rotations from a given starting point, then we must admit first that we have only two kinds of starting points. The kind that looks like the ‘A and B’ - and- the kind that looks like the ‘A ROTATED and B ROTATED’. Now, here are some types where we can see briefly which subsequent and preceding states of the drawings are identical from a given starting point:

-The type that connects subsequent and preceding states of the drawings, considering as starting point the ‘A and B’ state, is:
(We accept the following presumptions: each time both drawings are rotated and the drawings have been juxtaposed, as one to be the vertically reversed image of the other)
Drawing A:
{ [image of a pit, the reversed image of a door] = the state of drawing A, 2*n rotations after the starting point ‘A and B’ = the state of drawing A, 2*n times before starting point ‘A and B’ }
{ [image of a door, the reversed image of a pit] = the state of drawing A, 2*n-1 rotations after the starting point ‘A and B’ = the state of drawing A, 2*n-1 times before the starting point ‘A and B’ }
Drawing B:
{ [image of a door, the reversed image of a pit] = the state of drawing B, 2*n rotations after the starting point ‘A and B’ = the state of drawing A, 2*n times before the starting point ‘A and B’ }
{ [image of a pit, the reversed image of a door] = the state of drawing B, 2*n-1 rotations after the starting point ‘A and B’ = the sate of drawing A, 2*n-1 times before the starting point ‘A and B’ }

-For the starting point ‘A ROTATED and B ROTATED’ we have this type:
(We accept the same presumptions as before)
Drawing A:
{ [image of a door, the reversed image of a pit] = the state of drawing A, 2*n rotations after the starting point ‘A ROTATED and B ROTATED’ = the state of drawing A, 2*n times before starting ‘A ROTATED and B ROTATED’ }
{ [image of a pit, the reversed image of a door] = the state of drawing A, 2*n-1 rotations after the starting point ‘A ROTATED and B ROTATED’ = the state of drawing A, 2*n-1 times before the starting point ‘A ROTATED and B ROTATED’ }
Drawing B:
{ [image of a pit, the reversed image of a door] = the state of drawing B, 2*n rotations after the starting point ‘A ROTATED and B ROTATED’ = the state of drawing A, 2*n times before the starting point ‘A ROTATED and B ROTATED’ }
{ [image of a door, the reversed image of a pit] = the state of drawing B, 2*n-1 rotations after the starting point ‘A ROTATED and B ROTATED’ = the sate of drawing A, 2*n-1 times before the starting point ‘A ROTATED and B ROTATED’ }

-Here is a general type for any of the two starting points (we accept the same presumptions):
{ [image1, the reversed image2] appear together at: the state of the OBJECT1, 2*n rotations after the given starting point t₀ = the state of drawing OBJECT1, 2*n times before the given starting point t₀ = the state the OBJECT2, 2*n-1 rotations after given starting point t₀ = the state the OBJECT2, 2*n-1 times before the given starting point t₀ }
{ [image2, the reversed image1] appears together at: the state of the OBJECT1, 2*n-1 rotations after the given zero point t₀ = the state of drawing OBJECT1, 2*n-1 times before the given starting point t₀ = the state the OBJECT2, 2*n rotations after the given starting point t₀ = the state the OBJECT2, 2*n times before the given starting point t₀ }
For every t₀ we set {pit=image1 and door=image2} or {door=image1 and pit=image2}
This is a general type describing: how some meanings -applied to a single form- are going to get separated and distributed -from time to time and between actions- among two objects which represent two spatial orientations of this form and have been set under some specific presumptions.

Well that was two much! All these were a “baggy” way to describe what is obvious.
Every time, each image is, at once, the other image rotated.
Each drawing takes two of the four meanings from the bucket (pit, door, rotated pit, rotated door) simultaneously. We cannot have all the four meanings in one drawing.
Each time after rotation the drawings are ex-changing their meanings and of course their shapes (presumptions: we suppose that each time both drawings are rotated and that the drawings have been set, initially, as one to be the vertically reversed image of the other).
Every two rotations we have the same result.

-In our experiment:
Time matters, because every time period after a rotation, the meanings are opposing these ones before this rotation.
Time matters, because a single drawing can reveal all the four interpretations of the prototype form in two parts. These parts are shared at least among two time periods.
At least a pair of drawings is needed, under specific presumptions, if we need to see all the four interpretations of the prototype form revealed at once.
Space matters, because spatial alternations of a prototype form cause also alternations to our perception and consequently alternations to the interpretations we apply to the form.
Action matters, because in our particular case the action of rotation is needed to modify the spatial appearance of the prototype form.
Action matters, because a single drawing can reveal all the four interpretations of the prototype form, only after one action of rotation is done.
We have two physical objects.
We do not change the arrangement of the physical objects because we do not want to get confused. Each object has to be signified individually and the ‘left to right’ display helps and distributes the four meanings virtually in a horizontal arrangement. The left object has been and always will be in the left. The right object stays to the right.
Each time both drawings are rotated and the drawings have been made as one to be the vertically reversed image of the other
When I say ‘rotation’ I always mean rotation of both drawings for 180⁰.

-Generally:
The prototype form is the induction of a single form with two meaningful spatial orientations.
The prototype form is revealing its two opposite spatial versions, which can be meaningful, in a pair. I call it THE PAIR.
We have UNIT1 and UNIT2 consisting THE PAIR.
By default, the two UNITS cannot take the same spatial version of the prototype at the same time.
A UNIT cannot be without a spatial version.
The UNITS are able to swap their spatial versions of the prototype form.
We have only TWO UNITS and only two spatial versions of the prototype form.
The above statements mean that we have only two combinations of the spatial versions of the prototype. I call these combinations the STATES of THE PAIR.
So, we have STATE1 and STATE2.
We have a bucket of four interpretations: image1, image2, image1 rotated, image2 rotated.
These meanings are distributed among the UNITS in a combination that is unique for each STATE:

THE PAIR .
UNIT1 UNIT2
STATE1: U1:[image1, image2 rotated] --- U2:[image2, image1 rotated]
STATE2: U1:[image2, image1 rotated] --- U2:[image1, image2 rotated]

In our case

THE PAIR of two objects - drawings .
UNIT1 --- UNIT2
STATE1: U1:[image of a pit, rotated image of a door] --- U2:[image of a door, rotated image of a pit]
STATE2: U1:[image of a door, rotated image of a pit] --- U2:[image of a pit, rotated image of a door]

THE PAIR of drawings was a trick to reveal at the same time the four interpretations that we may apply to a prototype form. If we want to reveal at once all the four interpretations of the prototype form, we need two UNITS. In our case, we need two drawings or the two versions of the prototype form at once. In the physical world, one single drawing can reveal the total amount of the interpretations only in a period of time, where at least one rotation (of 180⁰) -of this drawing- has been committed.
Is it possible to make one single image, derived from the prototype form, where all the four interpretations could be applied at once? Maybe yes.
That is a subject for further artistic exploration.

2.SMOKE---WATER

C ROTATED

D ROTATED

The second example is quite the same. We also use a ‘prototype form’ which has at least two spatial meaningful versions. These two versions are again displayed as one to be the rotated(180⁰) image of the other. They are presented as images in a pair of two drawings which I named drawing C and drawing D. We accept the same presumptions as in the first example. There are four interpretations distributed among the two drawings in two combinations (or two states of the pair).
The first combination is described at the ‘C and D’ state as: Drawing C can be interpreted or as smoke coming up from a chimney while drawing D could be water running out from a funnel (well… anyway, I am the maker and I see things that way…!) . At the same time drawing C can be interpreted as the rotated image of water running out from a funnel and drawing D as the rotated image of smoke coming up from a chimney.
The second combination is described at the state ‘C ROTATED and D ROTATED’: Drawing C can be interpreted as the image of water running out from a funnel and drawing D as the image of smoke coming up from a chimney. At the same time drawing C can be interpreted or as the rotated image of smoke coming up from a chimney while drawing D could be the rotated image of water running out from a funnel.
There is always an action of rotation intermediating in between the two states. Each time after a rotation the drawings are ‘ex-changing’ their shapes and their meanings. Every two rotations we have a loop and matching states.
This general type can be applied:
{ [image1, the reversed image2] appear together at: the state of the OBJECT1, 2*n rotations after the given starting point t₀ = the state of drawing OBJECT1, 2*n times before the given starting point t₀ = the state the OBJECT2, 2*n-1 rotations after given starting point t₀ = the state the OBJECT2, 2*n-1 times before the given starting point t₀ }
{ [image2, the reversed image1] appears together at: the state of the OBJECT1, 2*n-1 rotations after the given zero point t₀ = the state of drawing OBJECT1, 2*n-1 times before the given starting point t₀ = the state the OBJECT2, 2*n rotations after the given starting point t₀ = the state the OBJECT2, 2*n times before the given starting point t₀ }
For every t₀ we set {‘smoke coming out from a chimney’=image1 and ‘water running out from a funnel’=image2} or {‘water running out from a funnel’=image1 and ‘smoke coming out from a chimney’=image2}

This scheme describes the second example:

THE PAIR of two objects - drawings .
UNIT1 --- UNIT2
STATE1: U1:[image of smoke coming out from a chimney,rotated image of water running out from a funnel] --- U2:[image of water running out from a funnel,rotated image of smoke coming out from a chimney]
STATE2: U1:[image of water running out from a funnel,rotated image of smoke coming out from a chimney] --- U2:[image of smoke coming out from a chimney,rotated image of water running out from a funnel]

3.SMOKE---WATER --- AND SOME RESTRICTIONS

drawing with the title:”Smoke coming out from a chimney"

ROTATED drawing with the title:”Smoke coming out from a chimney”

drawing with the title:”Water running out from a funnel

ROTATED drawing with the title:”Water running out from a funnel”

Now I would like to provoke a bit the examples 1 and 2 and sabotage the multiple interpretations of the previous drawings. For that reason I’ll use the ‘prototype form’ of the second example. I made two similar drawings. These drawings represent a pair of two opposite spatial versions -which can be meaningful- derived from the prototype form.

We have a drawing to the left:
the drawing with the title:”Smoke coming out from a chimney”

and a drawing to the right:
the drawing with the title:”Water running out from a funnel”.

I avoided giving to the drawings neutral names like ‘drawing A, B, C or d’. Alternatively I gave them well defined titles. These titles describe precisely the content of each drawing and specify their implication. Moreover, instead of using simple line-shading to formulate the smoke part of the left drawing, I used the word “KAΠNOΣ” which means “smoke” in Greek. Also, I used the Greek word “NEPO” which means “water” for the right drawing. Actually, the basic pictographic element, that has been employed to build up the pictures, reassures their own title. No doubt now for the specific implication of each picture.
The two drawings have been set according to the presumptions used in the previous examples. Every time after one action of rotation, the pair of drawings is matching with one of the following states:

-The state1 which can be described as:
‘(drawing with the title:”Smoke coming out from a chimney”) and (drawing with the title:”Water running out from a funnel”) ‘
-The state2 of the pair which can be described by as:
‘(ROTATED drawing with the title:”Smoke coming out from a chimney”) and (ROTATED drawing with the title:”Water running out from a funnel”) ‘

Every time after a rotation, the two drawings seem from a distance to ‘ex-change’ their shapes. But do they really ‘ex-change’ their meanings? Can really the [(ROTATED drawing with the title:”Smoke coming out from a chimney”) made up using the word “smoke”] be also the image of water running out from a funnel? Can really the [(ROTATED drawing with the title:”Water running out from a funnel”) made up using the word “water”] represent an image of smoke coming out from a chimney? Perhaps, the two images at the state2 may be only able to get the literal single interpretations: ‘rotated image of smoke coming out of a chimney’ and ‘rotated image of water running out from a funnel’ respectively. The drawings at the state1 are only what their title says. Perhaps words have the power to guide or instruct our perception. The state1 might be the ‘political correct’ state of the two drawings. In the state2 a conflict may occur between the content of the words/titles and a reasonable interpretation that the shape may get from a distance. Each drawing may have only one interpretation according to the words/titles. But let’s imagine a person speaking a third language who is not aware of English and Greek either. Although he might get suspicious detecting some unknown titles applied to the drawings and words in them, he would more easily fall into the multiple interpretations scheme of the second experiment. Words maybe are able to guide our perception but shapes may have an ‘inter-lingual’ character.

All the writting and images by Rentoumis Dimitrios 2007-2008
Posted 17June2008