Art, Mathematics, Science and Technology Interactions
Matjuska Teja Krasek, B.A.
Among other things, my artistic research work is connected to different kinds of symmetry (symmetry operations), Penrose tilings, Penrose rhombs, quasicrystals, the golden mean as an element of symmetry, Fibonacci sequences, etc. With the help of reflection, imagination and intuition I try to glean new relationships, new levels of structure, new and different kinds of order in these elements and structures. On the other hand, through some perceptually instable (ambiguous) compositions I wish to emphasize the principles of the way our cognitive system works - not solely our visual apparatus, our brain and mind, but the entire process of perception (as a whole) as well. I find computer graphics as a very useful and attractive medium for creating artworks and technology itself as a link in a braid where science, math and art interact.
Nature is a veritable treasure house of diverse patterns and humans, as one of its creations, are no exception. It is possible to encounter the same patterns in numerous variants, in different spaces and different periods. Periodic structures in liquid crystals are similar to the wavy sand dunes in deserts; circular shapes of planets are repeated in the shapes of raindrops; spirals can be found in galaxies, in snail houses, plants, etc. Repetition of geometric shapes in Nature makes one think that in the centre of space, time and matter lies mathematics.
Fig.1 M.T. Krasek, Emotions from Arcturus
We may also think, on the other hand, that the whole of mathematics originates within ourselves, within our minds . Whether mathematics has existed forever, or whether it is but a product of man's thoughts and has therefore existed only since the appearance of mankind is a question to which there is no answer yet. Maybe it is not so important whether mathematical principles exist because we search for them, or because we find them .
Humans as a biological pattern move within Nature, explore it, learn about it and try to reveal the principles governing it .
Perceptions strive to balance and symmetry or, to put it differently,
balance and symmetry are both characteristics of perception. They are
put into effect whenever external conditions allow for it. Balance and
symmetry are also the main characteristics of the principles governing
the material world, be it atoms or complex organic compounds. This
aspiration for order and balance is therefore a biological and a
psychological need of man .
Artists and Scientists Walking Hand in Hand
Researchers explain processes in nature, creators either transform Nature or create something new on the basis of their knowledge, feelings, intuition, and imagination. Complex processes of perception, classification, comparison of patterns and their arrangement into new patterns of a higher order take place in our brain's neuronal network. Our brain creates an inner virtual image of the world around us, which enables us to more or less effectively act in all spheres of our lives.
Fig. 2 M.T. Krasek, Double Star GA
In our brain there is no division into sciences and arts, but a complete
image of the way we understand and perceive the world around us. The
division is formed as comprehension leaves our brain and is focused on
individual aspects of the world within and outside. Most neuronal
patterns, which had been formed on the basis of sensory stimulants, are
preserved in the form of sensory images, be it visual or otherwise. Re-
collection and connection of these images is taking place in a process
called imagination. Imagination is an explicit creative ability of our mind
and brain, which fundamentally defines every creation, be it artistic or
scientific, of new knowledge. 
It is therefore a human trait common to both artists and scientists to look for principles, order, beauty and harmony; there are indeed many ways of searching, and especially of presenting that which we have found . In one of his essays late physicist David Bohm wrote that
… a scientific spirit is necessary, not only in what is commonly
called “scientific research”, but also in art and in every phase of
life, and that without this spirit, human actions are continually in
danger of deteriorating into a mere response to illusion, leading to
conflict and destruction. 
Therefore an artist needs a scientific attitude to his/her work as the scientist must have an artistic attitude to his/her.
Fig. 3 M.T. Krasek, Stars for Donald
The golden mean, Fibonacci sequences, fivefold symmetry, self-similarity, and inward infinity are just some of the characteristics that are found in nature, art, and science. All these are present in Penrose aperiodic tilings and three-dimensional quasicrystals .
They can be explored and presented through artworks as well. With the help of reflection, imagination and intuition we can try to glean new relationships, new levels of structure, new and different kinds of order in these elements and structures .
Both artists as well as scientists need to work hard to successfully realize or introduce the concept of symmetry, which can help us analyse, create, classify, recognize and understand.
Fig. 4 M.T. Krasek, Quasicube V
Art has a lot to contribute to help spread the awareness of symmetry in the broader sense of the word - “one that relates to harmony and proportion and ultimately to beauty” , individual kinds of symmetry, and symmetry as a connecting link between various disciplines.
Spreading awareness and knowledge about symmetry, of golden mean as one constant which unites the opposites into a new whole on different scales for example through works of art can be very simple and effective, especially when one takes advantages of new technologies.
It is a well-known fact that a text may easily be forgotten, but images persist and are remembered; this is how our brain works. Works of art can therefore help spread the awareness of symmetry . And we can use various tools for that. We can use very simple, classical ways of representations or new sophisticated computer software techniques of today.
Fig. 5 M.T. Krasek, Sunset
The symmetry concept should by all means be incorporated into our educational systems. Different generations, and especially those to come, should be exposed to symmetry in its broadest sense of the meaning. It is only in this manner that we can help the young to become creative adults, to perceive more than meets the eye in things and events around them . The task of both artistic and scientific disciplines, as said by the late Slovene artist, art theorist and philosopher Milan Butina, is the same here:
...to teach future scientists and artists to observe the world within and
outside, and thus to perceive the inner images of both worlds in order
to use them to shape man's world. 
We can act in this manner now and wish our actions and influence will have an effect on future
generations in the way they’ll use the technological achievements solely to benefit mankind.
Fig. 6 M.T. Krasek & C.A. Pickover, Infinite Curl 5
Computers, or computer/human hybrids, will surpass humans in
every area, from art to mathematics to music to sheer intellect. I do
not know when this will happen, but I think it very likely that it will
happen in this century .
Is this the future we generate these days? Are we very enthusiastic about it and how much do we look forward to it?
1. Krasek, M. T., Spreading Symmetry Through Artworks. In Symmetry 2000, Hargittai I., Laurent T.C., Eds. (Wenner-Gren International Series, London: Portland Press, 2002), p. 522.
3. Ibid., p. 521.
4. Butina, M. O slikarstvu. (Ljubljana: Debora, 1997), p. 59. (In Slovene, Engl. translation of the quotations in ).
5. Ibid., pp.53, 54.
6. As in .
7. Bohm, D. On Creativity. Nichol L. ed. (London, New York: Routledge, 1998), p. 29.
8. Krasek, M. T., Sharing some common interests of M.C. Escher. In M.C.Escher’s Legacy: A Centennial Celebration. Schattschneider, D., Emmer, M., Eds. (Heidelberg: Springer, 2003), p. 200.
9. As in , p. 525.
10. Hargittai I., Hagittai M. Symmetry: A Unifying Concept. (Bolinas, California: Shelter Publications, Inc., 1994), xv.
11. As in , p.526.
12. Ibid., pp.526, 527.
13. As in , p. 59.
C.A. Sex, Drugs, Einstein, & Elves:
Sushi, Psychedelics, Parallel Universes, and
the Quest for Transcendence. (Petaluma, California: Smart Publications,
2005), p. 242.