Art and Science (Fine Arts and Mathematics, Mathemartics Conference, Samos, April 2007)
Art and Science (Visual Arts and Mathemartics, Mathematics Conference, Samos, April 2007)
Mihalis Papadakis
Sculptor
Sculptor
26/4/2007
Art and Science
(Visual Arts and Mathematics [1])
(Visual Arts and Mathematics [1])
“A society with no Art would not be capable of having Science”
(EVALT ILIENKOV, 1924-1979)[2]
(EVALT ILIENKOV, 1924-1979)[2]
Today, for common sense –and unfortunately not only for common sense- every reference to the relation between art and science directly leads to electronic art products. This commenced mostly due to the appearance of photography, which supposedly replaced the “Portrait” and the “Landscape”. The truth is that photography created a wide audience – client, which would not have the ability to be a client for the “Portrait” or the “Landscape”. Many theoretical scientists support that photography democratized Art. A similar situation appeared with the development of the industrial production of wide consumption goods, which created an aesthetics that was, and is, determined by the limitations of technology abilities. This type of aesthetics, named massive culture, is expressed by works of Applied Art in Art Rooms.
I will not be concerned with this big issue here, though.
My aim is to discuss, if it is possible –even as a suspicion- that something deeper is happening in the relation between Art and Science that concerns the process of knowledge itself as well as Logic.
Art is the ability of a person to create images-objects, where Relations and Forms-Shapes of his/her sensory and creative comprehensiveness are recreated, in a natural or imaginary place.
Mathematics is the science that studies Forms-Shapes and the Relations of objects of comprehension and imagination of a person, in a natural or imaginary place.
The former creates, visualizes, the latter studies. The study of the Standard is inhered in the creation, the same way as the image of the Standard, at which the study refers, is inhered in the study.
Art creates its objects as combinations, where all the senses participate, so that even its imaginary objects contain, not only the forms of vision, but the meaning of forms of other senses as well, from where synaesthesia, quality is produced.
Mathematics analyzes and produces its objects, number, point, function and sum, as attributes of quantity.
The former deals with quality, which contains quantity, the latter deals with quantity, as a determination of quality.
Due to the fact that Forms in Art cannot exist irrespective of their natural body (their material) – that they cannot exist only as images in the thought, that is to say–, many people believe that its Forms are not clear abstractions, but mostly the result of the effort to reproduce more or less exactly natural or notional forms. This confusion is further strengthened by the incorrect use of the word “imitation”.
The absorption of Mathematics only to the quantitative attribute of objects provides the convenience to use the symbols of this attribute in the simplest, non-combinative, abstractive form (e.g. the number). This creates the wrong conviction that the symbols describing mathematical images are only mental, and that Mathematics express mental attributes.
In order to be able to see which “the role of Art as a means of conducting a research” (R. Penrose) can be and “artists do a part of our research for us”, as Feigenbaum complements, our effort should commence from the ontological matter of the objects of Art and Mathematics, as in both cases we have to do with abstractions.
The question should be framed as follows:
Are Art and Mathematics two different kinds of the abstractive ability of thought? Or is there a causal nexus between them, such that they demonstrate two different phases of the same abstractive ability?
As I support the “causal nexus” answer, I believe that an ontological analysis will help change the attitude of Art towards Mathematics and the contrary, and find ways of creative collaboration, to the account of both, as well as of knowledge.
The truth of Shape
In order for the Forms, Shapes and Relations to become objects of Mathematics, a developmental procedure of abstractive thought should precede, until the point, when distinct objects in the natural world become universal images-shapes-symbols, with which thought produces its universal notions.
A “first phase” –schematically, we could say- in the developmental procedure of the abstractive thought is [3] the discovery of the relation between the particular shape of an object and the attributes of another object. For over a million and a half years sapiens was experiencing the truth of this discovery through the tool.
In order for his comprehensiveness, though, to obtain the ability needed by this phase to produce mental shapes by natural objects, natural factors, like the standing position, the hand morphology etc., that favor the use of objects as tools, should comprise the natural background of this type of behavior towards the environment. The natural objects, that he occasionally uses, attract more and more his attention and he processes them up to the point that they become factors determining his behavior.
They are no longer objects helping him occasionally, but stable objects ensuring his survival.
Tool production becomes a special and necessary activity that affects the natural partition in the old group and the social organization thereafter.
Tool: Formalism of knowledge
No matter how primitive we consider the stone tool, it should by necessity, even from the first phase of its use, contain the attributes of three at least factors imprinted on its shape: a) the attribute of the group (sum) of natural objects, on which it should work, b) the attribute of the abilities of the hands of the subject-user, of their functional form, as well as of the force, that he has (another sum) and c) the elements of the relation between the subject-user and the natural object, in size and force, of the two sums, towards the maximum result with the minimum energy loss (function of sums to the aimed result, built on the “principle of economy”).
Energy loss for the creation of tools, so that their use is constant, was not, as it is not, an easy case. The tool is not made each time for a different natural object, but for groups of natural objects with common features. The above general, but necessary, factors create the images-shapes in mind, which contain the concept of sums and functions, as attributes of the truth of the shape. This truth is confirmed by the survival of man, who transmits it, transforming to a universal truth. When, though, this truth becomes universal, it is stereotyped-that is to say, random forms of the material body of the tool are deducted-so that the Shape that shows formalistically the composition of the attributes of the factors that ensure its success, is “cleared”. That is to say, its abstractive expressions become Abstraction. Under this approximate procedure, the person obtains conscience (knowledge) of these factors, so that he can “describe” them on the form-shape of the tool. The shape of the tool is the image of a developing analytical and combinative thought, as well. This tool formalism comprises the coding of a transmitted knowledge as well, before it takes the form of a “stereotyped proposal”.
Image
The “second phase” –schematically again-, the one that distinguished homo sapiens sapiens from other sapiens, was the discovery that it is possible for his relations with the natural world to be imprinted with the use of the shapes of an “image-representation” [4] isolated, though, this time from the material body and the functional use of the tool. The image-representation, that first appears 40000 years ago, is an ability only of homo sapiens sapiens,[5] the man of today. With the creation of the image-representation, man makes a critical step regarding his abstractive thought. Having learnt how to handle shapes with the use of the tool and having learnt to trust them as images of truth, he uses them for a wider, by the direct effect, analysis of his relations with the natural objects that surround him.
The image-representation becomes the image of the concept itself in the thought, where it obtains its “name”. Concepts, produced by the tool, have “names” that describe the relations of the collective subject sapiens with objects. With the image-representation, the concept of the image of the object reveals attributes and relations more and more general than the ones of the first “subjective” relations. With the image-representation, man’s thought starts to understand the concept as an independent unit (the concept itself) and gives it a “name” (number etc.), that together with the other respective “names” provides the thought with the possibility to work creatively, creating relations, that do not directly depend on experience. Art handles its images exactly the same way, as images on their own. This change in thought becomes another level, another quality, regarding the relations of man with his world.
The ability of Abstraction
Let us take a simple example: The image-representation of a bison, consciously, is not a copy of the shapes of a particular bison. This would be senseless, regarding the practical problems that would be faced. An image-representation of a bison in a deep cave, painted under the light of torches, is the image of the experience of the subject, which is done by memory. Memory is selective and abstractive, because it is an impulsive evaluation mechanism. If we want to recall the image of a standard, with which we had an experiential relation, this image appears composing different phases of the experience, having as a result for the image of the memory to be in a way a symbol of the experience of the standard as well. This way, though, it becomes highly interesting. The image-representation becomes a representation of the general attributes of every bison. From this representation it strikes out, it deducts-without aiming it (it does not remember them)-special characteristics of the units of the species and shows common characteristics of every bison in total. The apparent inability to copy becomes the ability for Abstraction. Whereas, then, it describes an experience of the past, the abstraction leads him to the repetitive (stable) characteristics, where it reveals the possibility of the representation to correspond to a future experience. The whole procedure of representation does not start with the idea of abstraction. Abstraction is the necessary element that is taught by the procedure of iconography. The aiming of the image-representation towards general, stable attributes (abstraction) belongs to the nature itself of the image-representation. Art teaches, necessarily, abstraction, not only to the one that doesn’t know it, but to the one that does not recognize it, as well.
Parenthetically, we must explain that abstraction in Art, on the other side, has to get over rational convenience. Abstraction in Art derives from synaesthesia and Intuition. Knowledge does the illustration of the implications of Intuition, which at times provokes the limits of rationalism, an object of Art. This is considered, usually, as an irrational excess. The intuitive approach of the Unknown is presented deceitfully as “intuitive knowledge of the non-knowledgable”. That is to say, as an ability of knowledge of another nature, Faith. Logic, though, is not a closed system; it should continuously study the laws and its rules, because its Standard is the Infinite. This is what Art reminds intra-historically and with knowledge.
Meter and “Assessing”
Assessments, that sapiens did empirically for the long interval of one and a half million years through the tool pass into the image-representation, so that their existence and function is visualized. The image-representation is an assessment in a way.
By painting a bison again and again in different situations, man conventionalizes more and more the image (abstraction) and learns to handle it as a symbol so that he can describe assessing situations, relations and future tactics. At the same time he learns to handle the points, the lines and the shapes as elements of a “language”, by which his abstractive thought conceives and renders the image of essentialities of natural objects and situations. Freedom given to him by the non- functional use of the image-representation and his trust towards the truth of shapes create the impulse for him to draw intellectual tactics and imaginary object relations. He learns to see the concept of the total in the image-representation of the bison. A total (sum), which is expressed by the representation of the one, can now be assessed as the size of One. Since all the members of the total are in general similar to the one and are defined by it, One can become the Meter of the total. So, he uses the image-representation in its intellectual form-form of thought- as a Substance-Standard of the unit, with which he assesses (measures) the natural mass.
As far as the tool is concerned, the assessed side, which exists on its shape, is directly connected to the aimed result. So, the concept of “assessing” cannot be autonomous from the shape.
In the image-representation imagination is released [6] from the production of a direct effect. This gives imagination the opportunity to transfer its assessing side to more complicated relations and shapes and to be involved with the representation of this side as well.
Throughout the course of artistic creation evolution, man surely exercises his eye in other assessments as well. Roughly we can say that the seasonal, lunar etc cycle is related to the biological cycle of plants, animals etc. Findings aged 35.000 years more or less refer to a kind of quantitative records, and the few samples that we have definitely do not correspond to the knowledge that man should have then for the representation of quantities and for calculations. Nevertheless, with the drawing ability, the conditions are created, so that man learns to think with mental images and symbols. The element of quantity, which is one of the two essential attributes of things (the other one is quality), is impossible not to have attracted his attention. Besides, the quantification of shapes is a function of the ability for the creation of the image-representation. Nevertheless, drawing ability is a prerequisite, temporally as well, for the awareness of quantity. This can be seen by the fact that Mathematics, as a science, start from geometrical shapes. Their language, until today-despite the complaints of mathematicians-suggests energy.
Step in thinking
The procedure of creating shapes, visualizing abstractive thought, starts with the form of the shapes of the tool. The shapes of the tool are in a way the “childhood phase” of the drawing procedure, where the direct need to define the general attributes of the natural environment of man, from where he draws his existence, rules. The environment and man’s aims are categorized empirically to attributes that are drawn in the forms of the survival tools. Thinking begins from the simple identification of sums. The combination of sums gives him the possibility to describe more specific situations. Those, which are called “specific”, until the point when “specific” starts to have an existence, independent of the intentions of the subject. The drawing of a bison is the first combinations of abstractions, in order to represent situations (“specific”) on their own. Like this, though, the drawing of forms of thought, becomes an end in itself. This is a step in mentality, a quality change in the relations between man and the environment. How many thousands of years have passed, in order for the constants of star combinations in the sky to be transformed from orientation tools to a Universe itself, besides man’s conveniences?
Composition and Harmony
The proportion and the symmetry that necessarily coexist in the tool become basic attributes of the shapes of the image-representation, ensuring its truth.
By the image-representation, homo sapiens sapiens cultivates the creative ability of his thought in order to detect, though the chaotic images of his experience, essential ideas and their functional forms, giving him the possibility to orientate.
The creation of images-representations, which describe more complicated facts (hunts etc.), brings about limitations that already existed in the nature of drawing itself, e.g. the “principle of economy”. Irrespective of the natural limits (e.g. how big or small the available surface is) the procedure of representing itself demands putting limits to the functional space of the drawn objects, so that the representation can project the meaning, for which it is created. As a result, the meanings of proportion and symmetry are transferred by the different shapes to the whole representation and appear as the attributes of composition and harmony.
The Beau
Right at the beginning, the shape of the tool could exercise a kind of charm, an aesthetic satisfaction (quality determination for the feeling created by vision, when the image of the object activates the “images” of other senses registered in memory as well). The charm that the shape can exercise on man is so powerful, as the power of the truth of the tool, which coincides with its survival. The image-representation “inherits” this power of the truth from the tool, a truth that charms, and augments it. In non-rational thinking, this power of the image seems autonomous, magic, a power-fetish. Something similar to the fetishism of the “language” in Mathematics.
The feeling of the Beau (as a concept later) derives from the feeling of satisfaction, which is created in man, when the representation that he created is revealed to him as true and charms him. By the way, due to the fact that man creates the representation, he imagines, many times, that even the truth that it contains is subjective.
The “Beau”, as a determination of aesthetic satisfaction, can be similar in Mathematics, as a criterion for the truth of mathematical suggestions. They reveal, though, this way –correctly- the deeper meaning-essence of this determination, which is: the utmost economy in the visualization of the most general possible truth. The same attribute of the Beau stands in Art, as well, only in Art it should first charm the senses and then the mentality.
Conclusion
With the image-representation, homo sapiens sapiens (the man of today) obtains a huge historical benefit. The benefit to think his thought and the means (the language), by which it is expressed.
This conclusion is drawn from my claim that in the field of the abstractive procedure of thinking, Art takes the place of abstraction, which connects the Standard to mathematical abstraction: Standard - Aesthetic Abstraction - Mathematical Abstraction - Standard (see table).
Feigenbaum condenses in a way the above as follows: “Art is a theory on how the world looks to people. It is obvious that no one knows with detail the world that surrounds us. What artists have accomplished is that they have realized that there exist only a few significant things in life, and they are searching for which those are. Like this they are conducting a part of my research for me”.
If we suppose that with the above I managed to support with some adequacy my claim that Art and Mathematics are related with a causal nexus, then the collaboration between them can be accomplished and can promise a lot for both.
-------------------------------------------------------------------------------- [1] In the present text, with the word “Art” I am referring only to Visual arts, and between Sciences I choose Mathematics, not only for text economy, but also because in Visual arts we have the materialistic form of abstraction, while in Mathematics –at the other end- the most clear form that abstraction can take in the intellect. For this reason, perhaps, the Mathematics (the most philosophical science according to Plato) is not only a science, but a tool of analysis, prediction and proof for other sciences.
[2] From his book: Technocracy and human ideals in socialism, adapted to become a phrase.
[3] The use of the present tense, like below, wants to suggest that the same procedure, as a procedure, is present also today, not only in the development of the knowledge of the child, but in the way that an adult can obtain new knowledge.
[4] With the term “image-representation” I mean only paintings and portable sculptures, which homo sapiens sapiens had been creating and exchanging between his groups.
[5] It is noteworthy that Neanderthal, who lived together with homo sapiens sapiens for 4000 years in Europe and shared the same tools with him, did not show any kind of interest on artistic products. It is estimated that maybe this ability of homo sapiens sapiens gave him head over Neanderthal, who was superior as far as natural formation is concerned, what brought him to harmony with the natural environmental conditions.
[6] Imagination is a general ability of the thought, which functions throughout the graduations of the world’s mirror in the thought. The release of imagination from the need and its appearance as an independent ability creates the deceitful idea that it exists only in the thought that is freed of need, and especially in the thought of artistic creation.
I will not be concerned with this big issue here, though.
My aim is to discuss, if it is possible –even as a suspicion- that something deeper is happening in the relation between Art and Science that concerns the process of knowledge itself as well as Logic.
Art is the ability of a person to create images-objects, where Relations and Forms-Shapes of his/her sensory and creative comprehensiveness are recreated, in a natural or imaginary place.
Mathematics is the science that studies Forms-Shapes and the Relations of objects of comprehension and imagination of a person, in a natural or imaginary place.
The former creates, visualizes, the latter studies. The study of the Standard is inhered in the creation, the same way as the image of the Standard, at which the study refers, is inhered in the study.
Art creates its objects as combinations, where all the senses participate, so that even its imaginary objects contain, not only the forms of vision, but the meaning of forms of other senses as well, from where synaesthesia, quality is produced.
Mathematics analyzes and produces its objects, number, point, function and sum, as attributes of quantity.
The former deals with quality, which contains quantity, the latter deals with quantity, as a determination of quality.
Due to the fact that Forms in Art cannot exist irrespective of their natural body (their material) – that they cannot exist only as images in the thought, that is to say–, many people believe that its Forms are not clear abstractions, but mostly the result of the effort to reproduce more or less exactly natural or notional forms. This confusion is further strengthened by the incorrect use of the word “imitation”.
The absorption of Mathematics only to the quantitative attribute of objects provides the convenience to use the symbols of this attribute in the simplest, non-combinative, abstractive form (e.g. the number). This creates the wrong conviction that the symbols describing mathematical images are only mental, and that Mathematics express mental attributes.
In order to be able to see which “the role of Art as a means of conducting a research” (R. Penrose) can be and “artists do a part of our research for us”, as Feigenbaum complements, our effort should commence from the ontological matter of the objects of Art and Mathematics, as in both cases we have to do with abstractions.
The question should be framed as follows:
Are Art and Mathematics two different kinds of the abstractive ability of thought? Or is there a causal nexus between them, such that they demonstrate two different phases of the same abstractive ability?
As I support the “causal nexus” answer, I believe that an ontological analysis will help change the attitude of Art towards Mathematics and the contrary, and find ways of creative collaboration, to the account of both, as well as of knowledge.
The truth of Shape
In order for the Forms, Shapes and Relations to become objects of Mathematics, a developmental procedure of abstractive thought should precede, until the point, when distinct objects in the natural world become universal images-shapes-symbols, with which thought produces its universal notions.
A “first phase” –schematically, we could say- in the developmental procedure of the abstractive thought is [3] the discovery of the relation between the particular shape of an object and the attributes of another object. For over a million and a half years sapiens was experiencing the truth of this discovery through the tool.
In order for his comprehensiveness, though, to obtain the ability needed by this phase to produce mental shapes by natural objects, natural factors, like the standing position, the hand morphology etc., that favor the use of objects as tools, should comprise the natural background of this type of behavior towards the environment. The natural objects, that he occasionally uses, attract more and more his attention and he processes them up to the point that they become factors determining his behavior.
They are no longer objects helping him occasionally, but stable objects ensuring his survival.
Tool production becomes a special and necessary activity that affects the natural partition in the old group and the social organization thereafter.
Tool: Formalism of knowledge
No matter how primitive we consider the stone tool, it should by necessity, even from the first phase of its use, contain the attributes of three at least factors imprinted on its shape: a) the attribute of the group (sum) of natural objects, on which it should work, b) the attribute of the abilities of the hands of the subject-user, of their functional form, as well as of the force, that he has (another sum) and c) the elements of the relation between the subject-user and the natural object, in size and force, of the two sums, towards the maximum result with the minimum energy loss (function of sums to the aimed result, built on the “principle of economy”).
Energy loss for the creation of tools, so that their use is constant, was not, as it is not, an easy case. The tool is not made each time for a different natural object, but for groups of natural objects with common features. The above general, but necessary, factors create the images-shapes in mind, which contain the concept of sums and functions, as attributes of the truth of the shape. This truth is confirmed by the survival of man, who transmits it, transforming to a universal truth. When, though, this truth becomes universal, it is stereotyped-that is to say, random forms of the material body of the tool are deducted-so that the Shape that shows formalistically the composition of the attributes of the factors that ensure its success, is “cleared”. That is to say, its abstractive expressions become Abstraction. Under this approximate procedure, the person obtains conscience (knowledge) of these factors, so that he can “describe” them on the form-shape of the tool. The shape of the tool is the image of a developing analytical and combinative thought, as well. This tool formalism comprises the coding of a transmitted knowledge as well, before it takes the form of a “stereotyped proposal”.
Image
The “second phase” –schematically again-, the one that distinguished homo sapiens sapiens from other sapiens, was the discovery that it is possible for his relations with the natural world to be imprinted with the use of the shapes of an “image-representation” [4] isolated, though, this time from the material body and the functional use of the tool. The image-representation, that first appears 40000 years ago, is an ability only of homo sapiens sapiens,[5] the man of today. With the creation of the image-representation, man makes a critical step regarding his abstractive thought. Having learnt how to handle shapes with the use of the tool and having learnt to trust them as images of truth, he uses them for a wider, by the direct effect, analysis of his relations with the natural objects that surround him.
The image-representation becomes the image of the concept itself in the thought, where it obtains its “name”. Concepts, produced by the tool, have “names” that describe the relations of the collective subject sapiens with objects. With the image-representation, the concept of the image of the object reveals attributes and relations more and more general than the ones of the first “subjective” relations. With the image-representation, man’s thought starts to understand the concept as an independent unit (the concept itself) and gives it a “name” (number etc.), that together with the other respective “names” provides the thought with the possibility to work creatively, creating relations, that do not directly depend on experience. Art handles its images exactly the same way, as images on their own. This change in thought becomes another level, another quality, regarding the relations of man with his world.
The ability of Abstraction
Let us take a simple example: The image-representation of a bison, consciously, is not a copy of the shapes of a particular bison. This would be senseless, regarding the practical problems that would be faced. An image-representation of a bison in a deep cave, painted under the light of torches, is the image of the experience of the subject, which is done by memory. Memory is selective and abstractive, because it is an impulsive evaluation mechanism. If we want to recall the image of a standard, with which we had an experiential relation, this image appears composing different phases of the experience, having as a result for the image of the memory to be in a way a symbol of the experience of the standard as well. This way, though, it becomes highly interesting. The image-representation becomes a representation of the general attributes of every bison. From this representation it strikes out, it deducts-without aiming it (it does not remember them)-special characteristics of the units of the species and shows common characteristics of every bison in total. The apparent inability to copy becomes the ability for Abstraction. Whereas, then, it describes an experience of the past, the abstraction leads him to the repetitive (stable) characteristics, where it reveals the possibility of the representation to correspond to a future experience. The whole procedure of representation does not start with the idea of abstraction. Abstraction is the necessary element that is taught by the procedure of iconography. The aiming of the image-representation towards general, stable attributes (abstraction) belongs to the nature itself of the image-representation. Art teaches, necessarily, abstraction, not only to the one that doesn’t know it, but to the one that does not recognize it, as well.
Parenthetically, we must explain that abstraction in Art, on the other side, has to get over rational convenience. Abstraction in Art derives from synaesthesia and Intuition. Knowledge does the illustration of the implications of Intuition, which at times provokes the limits of rationalism, an object of Art. This is considered, usually, as an irrational excess. The intuitive approach of the Unknown is presented deceitfully as “intuitive knowledge of the non-knowledgable”. That is to say, as an ability of knowledge of another nature, Faith. Logic, though, is not a closed system; it should continuously study the laws and its rules, because its Standard is the Infinite. This is what Art reminds intra-historically and with knowledge.
Meter and “Assessing”
Assessments, that sapiens did empirically for the long interval of one and a half million years through the tool pass into the image-representation, so that their existence and function is visualized. The image-representation is an assessment in a way.
By painting a bison again and again in different situations, man conventionalizes more and more the image (abstraction) and learns to handle it as a symbol so that he can describe assessing situations, relations and future tactics. At the same time he learns to handle the points, the lines and the shapes as elements of a “language”, by which his abstractive thought conceives and renders the image of essentialities of natural objects and situations. Freedom given to him by the non- functional use of the image-representation and his trust towards the truth of shapes create the impulse for him to draw intellectual tactics and imaginary object relations. He learns to see the concept of the total in the image-representation of the bison. A total (sum), which is expressed by the representation of the one, can now be assessed as the size of One. Since all the members of the total are in general similar to the one and are defined by it, One can become the Meter of the total. So, he uses the image-representation in its intellectual form-form of thought- as a Substance-Standard of the unit, with which he assesses (measures) the natural mass.
As far as the tool is concerned, the assessed side, which exists on its shape, is directly connected to the aimed result. So, the concept of “assessing” cannot be autonomous from the shape.
In the image-representation imagination is released [6] from the production of a direct effect. This gives imagination the opportunity to transfer its assessing side to more complicated relations and shapes and to be involved with the representation of this side as well.
Throughout the course of artistic creation evolution, man surely exercises his eye in other assessments as well. Roughly we can say that the seasonal, lunar etc cycle is related to the biological cycle of plants, animals etc. Findings aged 35.000 years more or less refer to a kind of quantitative records, and the few samples that we have definitely do not correspond to the knowledge that man should have then for the representation of quantities and for calculations. Nevertheless, with the drawing ability, the conditions are created, so that man learns to think with mental images and symbols. The element of quantity, which is one of the two essential attributes of things (the other one is quality), is impossible not to have attracted his attention. Besides, the quantification of shapes is a function of the ability for the creation of the image-representation. Nevertheless, drawing ability is a prerequisite, temporally as well, for the awareness of quantity. This can be seen by the fact that Mathematics, as a science, start from geometrical shapes. Their language, until today-despite the complaints of mathematicians-suggests energy.
Step in thinking
The procedure of creating shapes, visualizing abstractive thought, starts with the form of the shapes of the tool. The shapes of the tool are in a way the “childhood phase” of the drawing procedure, where the direct need to define the general attributes of the natural environment of man, from where he draws his existence, rules. The environment and man’s aims are categorized empirically to attributes that are drawn in the forms of the survival tools. Thinking begins from the simple identification of sums. The combination of sums gives him the possibility to describe more specific situations. Those, which are called “specific”, until the point when “specific” starts to have an existence, independent of the intentions of the subject. The drawing of a bison is the first combinations of abstractions, in order to represent situations (“specific”) on their own. Like this, though, the drawing of forms of thought, becomes an end in itself. This is a step in mentality, a quality change in the relations between man and the environment. How many thousands of years have passed, in order for the constants of star combinations in the sky to be transformed from orientation tools to a Universe itself, besides man’s conveniences?
Composition and Harmony
The proportion and the symmetry that necessarily coexist in the tool become basic attributes of the shapes of the image-representation, ensuring its truth.
By the image-representation, homo sapiens sapiens cultivates the creative ability of his thought in order to detect, though the chaotic images of his experience, essential ideas and their functional forms, giving him the possibility to orientate.
The creation of images-representations, which describe more complicated facts (hunts etc.), brings about limitations that already existed in the nature of drawing itself, e.g. the “principle of economy”. Irrespective of the natural limits (e.g. how big or small the available surface is) the procedure of representing itself demands putting limits to the functional space of the drawn objects, so that the representation can project the meaning, for which it is created. As a result, the meanings of proportion and symmetry are transferred by the different shapes to the whole representation and appear as the attributes of composition and harmony.
The Beau
Right at the beginning, the shape of the tool could exercise a kind of charm, an aesthetic satisfaction (quality determination for the feeling created by vision, when the image of the object activates the “images” of other senses registered in memory as well). The charm that the shape can exercise on man is so powerful, as the power of the truth of the tool, which coincides with its survival. The image-representation “inherits” this power of the truth from the tool, a truth that charms, and augments it. In non-rational thinking, this power of the image seems autonomous, magic, a power-fetish. Something similar to the fetishism of the “language” in Mathematics.
The feeling of the Beau (as a concept later) derives from the feeling of satisfaction, which is created in man, when the representation that he created is revealed to him as true and charms him. By the way, due to the fact that man creates the representation, he imagines, many times, that even the truth that it contains is subjective.
The “Beau”, as a determination of aesthetic satisfaction, can be similar in Mathematics, as a criterion for the truth of mathematical suggestions. They reveal, though, this way –correctly- the deeper meaning-essence of this determination, which is: the utmost economy in the visualization of the most general possible truth. The same attribute of the Beau stands in Art, as well, only in Art it should first charm the senses and then the mentality.
Conclusion
With the image-representation, homo sapiens sapiens (the man of today) obtains a huge historical benefit. The benefit to think his thought and the means (the language), by which it is expressed.
This conclusion is drawn from my claim that in the field of the abstractive procedure of thinking, Art takes the place of abstraction, which connects the Standard to mathematical abstraction: Standard - Aesthetic Abstraction - Mathematical Abstraction - Standard (see table).
Feigenbaum condenses in a way the above as follows: “Art is a theory on how the world looks to people. It is obvious that no one knows with detail the world that surrounds us. What artists have accomplished is that they have realized that there exist only a few significant things in life, and they are searching for which those are. Like this they are conducting a part of my research for me”.
If we suppose that with the above I managed to support with some adequacy my claim that Art and Mathematics are related with a causal nexus, then the collaboration between them can be accomplished and can promise a lot for both.
-------------------------------------------------------------------------------- [1] In the present text, with the word “Art” I am referring only to Visual arts, and between Sciences I choose Mathematics, not only for text economy, but also because in Visual arts we have the materialistic form of abstraction, while in Mathematics –at the other end- the most clear form that abstraction can take in the intellect. For this reason, perhaps, the Mathematics (the most philosophical science according to Plato) is not only a science, but a tool of analysis, prediction and proof for other sciences.
[2] From his book: Technocracy and human ideals in socialism, adapted to become a phrase.
[3] The use of the present tense, like below, wants to suggest that the same procedure, as a procedure, is present also today, not only in the development of the knowledge of the child, but in the way that an adult can obtain new knowledge.
[4] With the term “image-representation” I mean only paintings and portable sculptures, which homo sapiens sapiens had been creating and exchanging between his groups.
[5] It is noteworthy that Neanderthal, who lived together with homo sapiens sapiens for 4000 years in Europe and shared the same tools with him, did not show any kind of interest on artistic products. It is estimated that maybe this ability of homo sapiens sapiens gave him head over Neanderthal, who was superior as far as natural formation is concerned, what brought him to harmony with the natural environmental conditions.
[6] Imagination is a general ability of the thought, which functions throughout the graduations of the world’s mirror in the thought. The release of imagination from the need and its appearance as an independent ability creates the deceitful idea that it exists only in the thought that is freed of need, and especially in the thought of artistic creation.
Mihalis Papadakis
- Technoculture: Applied Aesthetics as a Substitute of the Work of Art, Arta 30/11/2013
(To be translated soon)
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