My work on QR passed three essential Phases:
I started with the chemical processes through which macroscopic phenomena are formed by the interactions/combinations of different
atoms. The first QR exhibition in
in 1971 was exclusively devoted to this purpose. It was divided into two sections:
First Section represented the 92 naturally existing atoms. Each atom was represented
by a selection of its characteristic visible
line spectrum, i.e. its strongest and most sensitive lines. The size of each spectral line
was made proportional to its frequency, according to the well-known equation:
E = h v (where E is the energy of the spectral line, v is its frequency and h is Planck’s constant).
Second Section represented combinations
between different interacting atoms showing the molecules of some familiar macroscopic phenomena, in terms of their characteristic
spectral lines. For example, water was depicted as the spectral equivalent of the chemical process defining its formation, H2O (i.e. as an interaction graphically represented by the
colour equivalent of a selected group of Spectral lines , between two atoms of
Hydrogen and one atom of Oxygen). Among other examples represented (in the Exhibition)
were: Salt, Sodium Chloride (NaCl); Ethyl
Alcohol (C2H5OH); Clay (Al2O3.2SiO2.H2O); Sugar (C12H22O11);
and even a composition entitled: Neo Human-Being 98% ( H200O81C30N4Ca).
lasted throughout the Seventies.
|Spectral lines structure of the H Atom - a detail - 1987
In the eighties,
my work changed its direction by focusing on the analysis of the structure of
the atom. This transition from molecular
to atomic structure manifested itself in a change of artistic language.
In PHASE 1,
only selected visible spectral lines
were involved. These were translated into colour areas and treated as the distinctive colour characteristics of atoms/molecules.
In PHASE 2
both visible and invisible spectral lines
were involved, and were treated as the essential structural units of atoms and space-time.
Because of this change
of direction, my artistic work in Phase 2 (and subsequently in Phase 3) has generally been executed, as black on white drawings.
The drawings represent the spectral
line series as wave lengths and are used as straight lines with different sizes.
There are six spectral line series
in the H Atom. They fall within different regions of the electromagnetic spectrum: The Lyman series in the ultraviolet region;
The Balmer series in the visible region; the other four series ( the Paschen, Brackett, Pfund and Humphrey) fall within the
infrared region of the electromagnetic spectrum. Consequently, with the exception
of the Balmer series which are represented by the different colours of visible light,
all other spectral series of the H Atom are invisible and are represented as black lines in the drawings.
These drawings are to me (as the mathematical equations
are to a mathematician) a means of verifying the reality of the artistic structural solutions as well as grasping their possible
deeper meanings and implications.
However, there are two sets of interconnected problems associated with the formulation of these solutions: artistic and scientific. Both are the necessary product of the penetration of the atom by modern science. They are :
necessity of creating a new artistic methodology appropriate to the visualization
and representation of atomic-quantum phenomena.
controversial interpretations of the new scientific facts associated with the new deeper atomic- quantum level of reality.
The Artistic Problem:
The penetration of the atom by science presented a
new unprecedented challenge to modern artists: how to carry out (as creative individuals) through indirect perceptual experience, their artistic investigation into the structures and processes of atomic-quantum
level of nature. Such an investigation had to be indirect and dependant on the findings of modern science and technology. Therefore it demands a new methodology completely at variance with the methodology of their predecessors
(since the cave artists of upper Paleolithic age) who had investigated the familiar
objects/things of macroscopic phenomena, with which they had interacted through direct
perceptual experience. Some modern artists have spoken of investigating atomic structural processes through the investigation
of macroscopic structural processes. Many more, however, have become more involved
in creating technological devices in the name of art. The majority however have continued and even extended the scope of the
largely free and unrestricted tradition of twentieth century art.
QR looks at this problem from a different viewpoint. It sees the uniqueness of our age in this new form of relation between humans & nature, or the new form of perceptual activity.
By going beyond macroscopic reality to atomic-quantum reality humans are going beyond traditional level of perception to a
new deeper level. The old perception of mass-object-form, is being gradually negated
and replaced by a new perception of energy-process-structure. This is a unique
unprecedented change. It applies equally to art. The old artistic creativity was on the level of mass-object-form. The new
artistic creativity is on the level of energy-process-structure. And this has
created a real possibility for the unification of art and the new science.
The methodology suggested by QR was developed as we
have seen on the basis of atomic spectral line series, energy-levels, wave functions, electrons and the unity of atomic and space-time structures. I call it a methodology of “aided senses” instead of the hitherto existing methodology of “unaided
The Scientific Problem:
The prevailing theoretical
framework in quantum physics (i.e. quantum mechanics) did not make things easier for artists either. Rather, it made it difficult
if not impossible (with its concepts of probability & indeterminism) to represent or picture atomic-quantum phenomena.
And this made the problem even more exasperating to those artists who may have contemplated picturing the processes of atomic-quantum
However, some scientists
took a different or even an opposite position, allowing for the representation or visualization of atomic-quantum phenomena. Einstein, as far back as the Forties of the last century asserted his “(belief) in the possibility of giving a model of reality which shall represent events
themselves and not merely the probability of their occurrence ”. A number of other scientists including Planck, De Broglie,
Schrodinger, D.Bohm, etc.. held generally similar views. Roger Penrose, in a recent work published 2004, emphasized that “It
would be a pity to feel that one must necessarily rely merely upon a pictureless, unvisualisable
formalism in order to make headway with the description of quantum actions”.
In other words, there
has always been, within the modern scientific community, an important current unwilling to accept the prevailing view or calling
for a theoretical framework allowing representation, description or visualization of atomic and quantum “events”
or “actions” . This is a hopeful indication as far as art is concerned.
For, description, representation and visualization are, essentially, in the very
nature of art.
The only viable solution
is a form of an art-science interdisciplinary
cooperation. Modern artists and scientists must interconnect, even more so, than the artists-scientists of the Renaissance. They must find ways to work together to
create what maybe termed a new scientific
art or an artistic science appropriate to the new civilization humans hope
to build in the 21st century.
The main developments,
in my artistic work, in the eighties, were outlined in two interconnected texts:
A. A slide–illustrated lecture on QR : “ A Representation
of the Spectral Line Structure of the H Atom”, at the Whitechapel Art Gallery
Lecture Theatre, London,
5 April 1987. The text was published in the Constructivist Forum,
Issue 6, 1987 - London.
B. A lecture on “An Artistic Representation of the Structure
of the Hydrogen(H) Atom : Quantum Realism”, at a Symposium on ARTE E TECNOLOGIA,
organized by the Gulbenkian Foundation, Lisbon,
from 17-19 Dec.1987. (Published with other contributions in a book-form in 1993, by the same Foundation).
Both texts underlined an equivalence principle of atomic structure and the system of energy-levels and Spectral lines. I applied this principle to the
Structure of the H Atom according to the energy-level diagram for Hydrogen (by Walter Grotrian).
However, in both texts,
the essential problem was how to reformulate the basic elements of different scientific interpretations dealing with the mechanics of atomic systems into artistic terms. My graphic analysis followed at first the familiar lines of the Bohr H Atom with its atomic orbits, Spectral lines
and electronic jumps. Later, I had to follow the far more complex ideas of quantum
and wave mechanics, with their uncertainty relations, vectors and wave functions. This made it necessary to work out a number of procedures and ideas for a new artistic methodology concerning among other things the mode of distribution of the spectral structure of the atom,
energy-levels, the relation of wave functions & electrons and of atomic & space-time structures. This artistic methodology maybe outlined as follows:
1. The structure of space-time is subject to the same basic principle
as atomic structure. The drawings sheet is initially divided into horizontal lines according to the squares of the natural
numbers, i.e. 1,22, 32,42……etc. They represent the lines on which the different
positions of wave function amplitudes are located. The exact positions of amplitude points (or,
wave function points) differ according
to the number of the spectral series and wave lengths of the spectral lines.
2. The size of the individual spectral unit is made according to its wave length (rather than its
frequency, as was the case in Phase 1). Art deals primarily with qualities
i.e. colour , form, relations, proportions, spatial
dimensions etc. In short, all such aspects relating to the concept of beauty
as an absolute, which has been the preoccupation of a great deal of art particularly,
since the time of the Greeks.
These qualities are
revealed through the wave lengths and structures of the spectral line series. On the other hand, the frequency of the spectral
lines is an indicator of energy-mass, which is primarily the preoccupation of science.
3. The structure of the Grotrian diagram is one of parallel
lines (vertical & horizontal).
made, at first (in the case of the Bohr H Atom) the spectral lines of each series
converge at a point on their common energy-level
to indicate the probable position of the electronic jump at that level. Later,
all spectral line series, (as directed light units), were made to converge at
a point on energy-level No.1, representing the probable position of the central electronic point, in its relation with wave functions. All of this meant linking the electron mass with the energy associated with the different converging (or
directed) spectral lines or light units
according to Einstein’s principle of mass-energy interchangeability.
4. I made use of the theoretical possibility, which allows
for an infinite number of energy-levels and spectral line series beyond the
atom . I wanted to show the H Atom with its single electron as the simplest structural order of matter existing within a totality of a universal structural wholeness.
This implied a picture of the H Atom in a universal multi-dimensional
space expressed in terms of complex spectral line series (or units of light).
Each spectral line unit within these series represents a directed wave length
or light unit, linking the universally complex diversity of the different Schrödinger
wave function points on the various energy-levels throughout the universe,
with the central potential electronic
point on energy-level No.1.
also meant to show how the electron potentially extends beyond the atom to the whole universe.
5. On the other
hand, both previous texts (particularly the sections dealing with the fine structure
of the spectral lines of the H Atom)
touched upon a question suggesting the possibility of an artistic/graphic solution to the very
important but problematic relation between the electromagnetic and gravitational fields. A number of drawings made between 1987 –
1996 served to strengthen the viability of this suggestion. (One of the drawings
was incidentally published as an illustration to my text at the Gulbenkian’s Symposium in 1987).
show that when the fine structure of the spectral
lines of the H Atom is added to the spectral line series of the H Atom, we
get a surprising graphic result: with the exception of the first, the Lyman spectral
series, all other spectral series,
beginning with the second Balmer series,
show new complex structures suggesting space-time curvature.
only lead to the conclusion that a gravitational field is created alongside the
electromagnetic field associated with
the electron, beginning with the Balmer spectral series. The drawings therefore,
should also be seen as a graphic/artistic illustration confirming Einstein’s
great insight in his theory of general
relativity, which reduced gravitation to the geometry of space-time curvature, associated with a material particle.
The curvature revealed itself in the drawings when
the fine structure of the spectral lines of the H Atom was added to the spectral line series
of the H Atom.
6. This means that the drawings comprise two types of lines, electromagnetic and
gravitational. Only the first type
of lines, i.e. electromagnetic wave lengths, are measurable.
|Spectral lines structure of the H Atom - 1990
“The universe is not only stranger than we think,
it is even stranger than we can think”
Since the late Eighties, I became gradually more preoccupied
with the structure of the electron.
Nature eternally exists and develops as a totality of interconnected and interacting levels. The
source of this developing existence, lies
in nature’s structural reality. That was what defined the starting point
of my artistic work on QR, i.e. the structural interconnection between atomic and molecular/macroscopic levels of reality.
The same applies to the structure of the electron, which provides the intricate connection between the atom and the deeper
universal system of wave functions.
In other words, just as the atom is a system of electrons, energy-levels and spectral lines, the
electron itself is also a system of wave functions and energy-levels extending throughout the universe.
The electron, therefore should be conceived both as a structural
element of the atom itself, and equally, as extending deeper beyond the atom
as a universal system of wave functions.
A proper artistic description/visualization of this deep
universal system which represents the wave function structure of the electron, is
possible if, (1) It is treated within the framework of the Lyman spectral series of the H Atom. Or, (2) that a new interpretation
is given to the velocity of light(c) as an absolute.
From the point of view of humans, the velocity of light
(c) has only a fixed, constant value of 299792 km/s, which is the product of
the wave length of light multiplied by its specific frequency.
From the point of view of light itself, in its complex
relations with this universal system of wave functions, the velocity of light (c) should be treated as if light is composed
of different spectral units. Each unit represents the difference between the values of an energy-level and the position of
the electron (on energy-level number 1), within this universal system of infinite energy-levels and spectral line series. Each unit moves as a directed straight line (towards the electron) rather than as
a periodic process of a given frequency (v). All of these spectral units, irrespective of their lengths/sizes, should be treated
as equaling the value of the velocity of light (c). From the point of view of
light such directed spectral units should be regarded as representing spectral wave lengths having frequency equaling one. Therefore, they are identical, in that they all represent the value of
the velocity of light (c) i.e. the distance that light travels between two energy-levels.
From the point of view of humans, the velocity of light
(c) is the distance covered by light between any 2 space-time points.
the point of view of light, there are only quantum jumps from an energy-level directly to the electron. The distance covered by each quantum jump equals (c). Time is a human invention.
|Spectral lines structure of the H Atom - 1994
I began my artistic work on QR since mid 1960s , by synthesizing
- An old
concept going back to Heraclitus, who spoke of the world as in a process of change (or, “in a state of flux”)
- A modern
concept formulated by Einstein on the interchangeability of mass & energy.
The synthesis led finally, in the nineties, to a graphic/artistic
solution depicting the world as a system or as a structure of energy units corresponding to specific spectral wavelengths, and based on a new conception of the
velocity of light(c).