Virtual Experimentation [A Virtual Space-Time Travel]

Jean-François COLONNA
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CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641, École polytechnique, Institut Polytechnique de Paris, CNRS, France
france telecom, France Telecom R&D

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[Real Numbers don't exist in Computers and Floating Point Computations aren't safe. [Les Nombres Réels n'existent dans les Ordinateurs et les Calculs Flottants ne sont pas sûrs.]]
[Please, visit A Virtual Machine for Exploring Space-Time and Beyond, the place where you can find thousands of pictures and animations between Art and Science]
(CMAP28 WWW site: this page was created on 10/23/1997 and last updated on 11/14/2023 17:52:45 -CET-)

[en français/in french]

Keywords: Anaglyphs, Art and Science, Artistic Creation, Autostereograms, Celestial Mechanics, Computer Graphics, Deterministic Chaos, Fractal Geometry, Intertwinings, Mathematics, Natural Phenomenon Synthesis, Numerical Simulation, Physics, Quantum Mechanics, Rounding-off Errors, Scientific Visualization, Sensitivity to Rounding-Off Errors, Software Engineering, Stereograms, Texture Synthesis, Virtual Experimentation, Virtual Space-Time Travel.

Science and Techniques translate into mathematical language the behavior and the shape of studied systems; a model consists of a set of equations relating the characteristic state quantities of the system under study, such as space-time coordinates, velocity, temperature, or again pressure. These equations must be solved analytically (according to the possibilities: let's recall to mind that the N-body problem cannot be solved in this way for N greater than or equal to 3) or numerically in order to validate the assumptions and to make predictions. The most of the time, thanks to faster and faster computers, these computations create very large amounts of numerical results.

We define a Virtual Experiment as the association of the equation solving (according to some initial values and boundaries conditions) and of the result analysis. Eventually, this cycle repeats itself many times, in the same way that a laboratory experiment does, when perturbing the initial conditions, for example... It is noticeable that this last type of scientific investigation (historically the first one...) requires more and more numerical processing, in particular when the measures are too numerous or occur at a too high frequency (in particles colliders or in telescopes for example). Thus rise a common problem to numerical and laboratory experimentations: the result analysis.

Except for some exceptional cases, the produced results are too numerous to be red alpha-numerically. For example, when studying the two-dimensional turbulence , it is not uncommon to compute ten millions of values for each time step, and when conducting experiments on elementary particles with high energy accelerators, more than one million of values can be measured in less than one second! Thus, the situation would be desesperated, if the techniques of Computer Graphics would not have made great strides, especially in the artistic field as well as in the entertainment.

Vision (ie. the sense by which the qualities of an object constituting its appearance are perceived) is probably at the origin of insatiable mankind's curiosity and of scientific research. It is the most "advanced" natural way to catch close and distant environments. With his eyes and visual cortex, man can extract complex colored patterns from a moving, changing and noisy context. Thus it is a natural idea to use the whole sense of sight for result analysis; The numerical results will be displayed to users (scientists or engineers) as animated pictures, and then exploited by their eyes, and maybe tomorrow with the help of pattern recognition systems as it is common today in the picture processing field. Picture is a tool for synthesis: it provides a global presentation of results. It will facilitate the comparison between "natural phenomena" (measures) and their simulations (numerical results). It will generate concrete representations for abstract concepts.

Generally, these visualizations will be arbitrary ones; but they will facilitate experiments in domains like pure mathematics . Microscope has shown us the infinitely small, telescope, the infinitely big and computer, providing that we are developing adequate and accurate models, is going to open our eyes to "new universes": maybe, a new Copernician revolution is just starting... Computer Graphics enables us to watch at modelized phenomena that are too fast , too small or again too far (in space-time) to be shown directly by other instruments. But moreover, it enables us to access or to manipulate laboratory inaccessible phenomena. The dream comes true: we have acces to the (virtual) space-time travel machine!

Thus, a travel from the infinitely small to the infinitely big becomes possible: we can reach the Quantum Mechnanics World , or the most abstract structures , or again imaginary worlds reflecting our own Reality and finally, cosmic scales that defy our imagination .

Computer Graphics is one of the best way to concile (or, better, to reconcile) today Art and Science . As a matter of fact, techniques needed to produce realistic documents, ie. misusing human senses are highly scientific (ie. make use of mathematics, fluid dynamics, hierarchical systems,...). Moreover, Scientific Visualization is a communication tool: then it must be "optimized"; thus, it must abide by great (and old...) artistic laws about proportions and chromatic harmonies . Today, Computer Graphics is a mature technique. Thus, it can be used by scientists as a really productive tool. But it requires consideration: it is very important to put scientists on their guard against non informative aestheticism: "beautiful" and "informative" are not synonym !

In more general terms, most of our today Science and Techniques rely on computers; unfortunately and despite our beliefs, theses machines are unreliable and bounded. Their unreliability finds its root in the way programs are written; their limit (in the scientific context) comes from the very simple fact that real numbers cannot be represented and manipulated inside a digital machine ! The consequence of these two negative properties is that this fantastic tool must be used very carefully; unfortunately, the today tendency is to replace the cogito ergo sum with a "computo" ergo sum...

Copyright © Jean-François COLONNA, 1997-2023.
Copyright © France Telecom R&D and CMAP (Centre de Mathématiques APpliquées) UMR CNRS 7641 / École polytechnique, Institut Polytechnique de Paris, 1997-2023.