I once was naive enough to consider this a new idea. See
http://www.ulrichmutze.de/art.html
Who does what? I agree that science should contain some element of art. But needs it to contain mathematics?
This is a natural idea for everybody involved in sciences which make heavy use of mathematics. There are however very important activities e.g. in life sciences, in which mathematics plays a minor role, if any. The truely heroic enterprise of finding out how the body of animals manages it to built cholesterol is an example.
Agent-based models, cellular automata's and similar simulation tools are changing the way of understanding those kind of phenomena, they are supported by the conceptual framework of complexity theory in general. This is not only true for biology, which at least had the aid of chemistry, but for psychology and social sciences. ¿How can complex patterns emerge from simple rules? Theres the answer: complexity.
(Spanish)
Bueno, el echo de que las imagenes obtenidas sean "funcion" de alguna fuente de información,
con parametros cualesquiera, daría la pauta de que estas haciendo matematicas, en efecto
la manera en que representas la salida de tal funcion (en tu caso, en una imagen bidimensional),
es tu elección, pero en el fondo no son mas que datos. Bien, Que es el arte visual (en este caso)?:
Supongo que no hay en todo el planeta alguien suficientemente capacitado como para juzgar como no
artistico tu trabajo. Podría, talvez incurriendo en el error, definir el arte como una manifestación,
de la manera elegida, de un estado emocional, de una idea, un reflejo de la realidad en la que subyace
el artista; en fin estas manifestaciones y sus formas son infinitas, por esto tu trabajo es artístico
pues en el fondo tratas de manifestar un pensamiento, una dirección al espectador, como intentando
crear un corriente artistica novedosa. Ahora, excluir a las matematicas en este proceso, me
parece que no es correcto, estas "impregnan" la realidad, sus componentes y las interacciones entre ellos.
Crees que las ciencias de la vida estan menos influenciadas por esta área cientifica? Yo creo todo lo contrario,
es en estos sistemas extremadamente dinámicos y complejos donde, justamente, la dinámica de estos esta regida
por leyes matematicas, quizas muy complejas y lejanas a nuestro conocimiento, pero aún asi, allí estan.
Bueno, como no manejo bien el idioma ingles, puede que no haya dado con certeza la cuestion que planteas,
pero bueno, este escrito es a base de lo que alcanze a interpretar.
Desde ya mis saludos cordiales, mis disculpas si no he entendido bien el topic, atte. Luis F.
Creo que por ratos se olvidan que la matemáticas es, después de todo, un lenguaje y que la ciencia no es una verdad, es una aproximación a la realidad. La matemática es una forma de describir un fenómeno, no el fenómeno mismo. Lo interesante de la simulación es que logra describir cosas que la matemática no puede -ecuaciones diferenciales sin solución, agentes, redes, algoritmos genéticos- de una manera lógica pero no analítica, lo cual le brinda mayor flexibilidad y capacidad a costa de la introducción de cierto grado de error. Aun así, la brecha entre la ciencia y el arte es una linea delgada, ambos son producto de la creatividad, la inspiración y la técnica, solo que la ciencia exiger rigor y comprobacion.
Imagina que de repente abres tus parpados y observas un objeto moviéndose de derecha a izquierda hasta perderlo de vista. Es tu cerebro, el cual de una manera mas difusa, en mayor o menor medida, almacena ese "evento" de forma matemática. Si fueses pintor, y quisieras recrear tal evento, al tratar de recordar, tendrías por ejemplo, la descripción de este de manera muy matemática, recordarías, entre otras cosas: la dirección del objeto, cuán rápido se movia segun tu criterio, el objeto en sí mismo, su forma bajo una descripción mas o menos geométrica, etc; en fin si tu cerebro almacena todas estas "pistas" para simularlo en cierto sentido en el pensamiento, puedes obviamente reproducir una imagen en una pintura de lo que recuerdas, quizás si te haces ajeno al "realismo" de lo representado, estarías pintando algún tipo de abstracción de la realidad, dónde con abstracción refiere a justamente abstraerse del lenguaje estricto de la observación y su trascripción que representa parte o por entero el evento en un lenguaje diferente. Bueno en fin, lo que quisiera destacar es que en fin nuestro cerebro tiene, para cada cual, un lenguaje para poder entender la realidad, este en el fondo tendrá, podría decir, "mucha matemática" y en fin de cuentas no podemos desprendernos de este lenguaje, si porsupuesto trasformarlo para recrear una situación.
Al final, somos máquinas muy sofisticadas, a tal punto que nuestra propia escencia "mecanicista" se va diluyendo cuando crece la consciencia que tenemos. En el momento que piensas: "puedo escapar a la causalidad universal que define cada instancia de mis historia?", bueno es ahí donde te vuelves un tanto mas consciente de tu individualidad, y al final pasarás a pensar que no estas "suelto" sino que eres parte de algo mucho mayor, etc etc. Bueno esto ya es un aspecto mas filosófico y podemos estar años hablando y replateando en busca de algo que a priori nos supera.
Estoy viendo que me fuí demasiado del tema, pero a veces es necesario "escabar mas profundo" para encontrar una aproximación, almenos, de la verdad que buscamos.
Un abrazo, atte. Luis F.
Having once learned Latin at school, I get a bit of the content of this contribution and I'm sad not to get enough for really understanding it. Please try to refain from using non-English languages whenever possible. Thanks, Ulrich M.
however i used http://translate.google.com and it was: The statue which on a sudden out of the frankincense, parpados Abreu y un objeto moviéndose observe the out of the izquierda derecha from the spear out of the perderlo Vista. Thou art the brain, el cual a male as one of the Bounce Manera, en mayor medida, O hands of Meno, almacena ese "inevitably" of the form of matemática. If fueses Pinto, y quisieras Such to recreate the event, out of the al tratar remember, tendrías por ejemplo, la, ye that out of the description of the Manera muy matemática, recordarías, entre otras cosa: la dirección del objeto, rapid cuán you that he removed the criterion, segun, en el objeto the Almighty and Merciful mismo, of its own form of description, one a male bajo O Meno of geometric, etc.; See, if you end almacena todas summer of the brain "the baker" They do simularlo en cierto sentido en el pensamiento, obviamente puedes reproducir en imagen a single one of which speak of the pintura recuerdas, if the Quiz you haces al ajeno "realism," out of the representado speak, estarías pintando algún Type of abstracción de la realidad, con dónde abstracción refiere from the abstraerse justamente del lenguaje de la estricto y su trascripción the observance of which part of the O representa el por entero en un lenguaje the event diferente. En Buenos Fin, quisiera destacar lo and behold, which you are endeavoring to portray the brain nuestro how many instances, prepare for carcasses cual, un lenguaje para entender la realidad down to the foot, that ye make tendrá en el Fonda, podría Decius, "held in much matemática" Behold, the end of the y cuentas no podemos desprendernos out of the lenguaje, ye that, if porsupuesto trasformarlo prepare to recreate one of situación.
Al final, somos muy sofisticadas máquinas, from the Punto which nuestra Such combat statistics escencia "mecanicista himself" to VA diluyendo crece cuando tenemos la conscience which. Behold, a moment of which El piensas: "puedo escapar a la Universal causalidad which web page hit counter carcasses out of the urgency and the history of dis?", Buenos Ai, you are un donde vuelves you so much the feeling of a male you individualidad, y al final chance to repay my pasarás and from the no está "suelto" allows OWNER and out of the cold is held in much part of the mayor, etc., etc. Buenos ya let it be you are a male un PAY ATTENTION filosófico Años y podemos esta hablando y en replateando out of the brushwood and the cold is the a priori us above it.
Estoy viendo me, which I have been demasiado del Tema, their steps from the art necessarily veces "escabar depth of a male" They do one encontrar aproximación, almenos, and de la verdad buscamos.
Un abrazo, atte. Luis F.
This is an impressive demonstration of the usefullness of todays automatic translation (in)capabilities!
Yes, :), in really is not Latín, is Spanish: (Here one traslation:)
He imagines that suddenly you open your eyelids and observe an object moving from right hand to left side up to losing it of sight. It is your brain, which in a more diffuse way, in major or minor measurement, stores this 'event' of mathematical form. If you were a painter, and you would like to recreate such an event, on having tried to remember, you would have for example, the description of this one of a very mathematical way, would remember, between other things: the direction of the object, how rapid it was moving according to your criterion, the object in yes same, his form under a more or less geometric description, etc; in end if your brain stores all these 'tracks' to simulate it in certain sense in the thought, you can reproduce obviously an image in a painting of what you remember, perhaps if you become foreign to the 'realism' of the represented, you would be painting some type of abstraction of the reality, where with abstraction it recounts after exactly the event is abstracted of the strict language of the observation and his trascripción that represents part or entirely in a different language.
Good in end, which he wanted to emphasize is that in end our brain has, for everyone, a language to be able to understand the reality, in the fund it will have this one, he might say, ' a lot of mathematics ' and in account end we cannot get rid of this language, and of course transform this, to recreate a situation.
In the end, we are very sophisticated machines, to such a point that our own escencia 'mechanicist' is diluting when there grows the conscience that we have. In the moment that you think: ' I can escape to the universal causality that defines every instance of my history? ', good it is there where you become somewhat more conscious of your individuality, and in the end you will happen to think that you are not 'free' but you are a part of anything much major, etc etc. Good this is already a more philosophical aspect and we can be years speaking and re-silver-plating in search of something that to priori overcomes us.
I see that I went away too much of the topic, but sometimes it is necessary ' " deeper ' to find an approach, of the truth for that we look.
A hug, atte. Luis F
I agree that math (or logic/computation now a days) is the most desired language to describe reality, however, I think it would be a mistake to state that nature behaves mathematically, because that would imply that there is a natural language and that that language is equal to the one created by the Occidental culture. I think anyone who has been in a laboratory would agree that it would be more precise to state that: 1) nature behaves, and 2) that the description of math/logic is a good APPROXIMATION to that behavior. And that is not always the case, chaotic phenomena can be described in a general form, but no approximation is good enough.
Even not being a mathematician, I agree with Cristian GARCIA.
I think too that mathematics are a mean for our brain to undersatnd universe and nature laws; but narure exists independantly of the methods we use to understand it.
And perhaps, if our brain was more powerfull, we could use others systems than mathematics to describe universe.
Best regards
Didier
A readable contribution to these questions by an outstanding mind is the paper by E.P.Wigner enititled
The Unreasonable Effectiveness of Mathematics in the Natural Sciences
to be found (among many other places) at
http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html
I agree with chaos and complexity is art, one of the most beautiful area of mathematics and general science.
Some concepts of the nature could operate under logic/computation (mathematical) laws, when all dimension scales are considered. Still nature has its self hidden language not totally accessible to human brain yet. Perhaps combination of right knowledge, laws, and modeling reasoning into systemic approach could help to a pathway for understanding nature language, and discover one of its formalism facets. Even Nature language and its dimension scales is an art ….
Edward, logic is not the same thing as math; I think that it would be safe to say that math is a type of logic. Normal computers are based on boolean logic and with it they can perform, as you say, discrete mathematical operations such as counting. Math on the other hand uses deductive reasoning to obtain analytical results. The point is that its not always possible to obtain those analytical results, especially true with non-linear equations. With computation, however, its possible to approximate to those results at the cost of some error, this is true at least for numerical solutions of differential equations, other simulation techniques like cellular automata's dont include error (its also true that they are not trying to resemble some analytical form).
The problem with chaos is not computation, that is, even if you could have infinite computational precision there would still be some underlaying empirical problem: initial conditions. An infinitesimal difference can make a huge difference, that is the principal of chaotic systems, so the problem is that there's never a precise enough measurement, since any measurement includes error (however small), that error is going to lead the system to a totally different result as time progresses (butterfly effect).
On chaos:
http://www.youtube.com/playlist?p=PL101C8D7AB73427D7&feature=mh_lolz
And probably, to my mind, biological system and life mechanism functions as this.
Adaptation to environnemental conditions for organisms are difficult with linear equations because they couldn't adpat in real time to external coditions, and often for a "reaction" to changing external condition, they respond with intervention of a threshold that permit them to return at initial conditions for homeostasy after.
So, catastophic theory as René Thom's one permit more esaely to explain biological functionning.
regards
Didier
The Master Petar Deunov said in his lectures and talks that the Divine World is MATHEMATCALLY made (constructed)! The Master Petar Deunov is the adept of the involution and the evolution as a supreme and basic manifestation of the absolute, as a general law of universal life dominating everything.
Can scientific data be art?
The Master Petar Deunov is amongst the most famous personalities in Bulgarian history and spiritual culture. The principal subjects in his lectures and talks are: man's place and role in the Universe, in Nature and Society, the spiritual understanding of Culture, Ethics, Psychology, Medicine, Music etc.He gives exercises for breathing, meditation and concentration. He founds the Paneurythmics, which is played nowadays in USA,Canada, France, Russia, Kongo and other countries in the world.
Can scientific data be art?
I once was naive enough to consider this a new idea.
Edward, I agree with your first remark. Your second remark looks to me like a severe misunderstanding. Actually, to be chaotic (or to show chaos) is a property of the dynamics (or, what means the same, of a dynamical system). That exactly known initial conditions (and only those) determine the orbit (not only give a probability for an orbit) is what also is called determinism. Most of the chaos discussion is on deterministic systems.
Your third remark uses a very uncommon notion of math: boolean logic is a (small) subdiscipline of math, but not a math in itself. It is not uncommon to speak of several different mathematics such as Constructive Math, Intuitionistic Math, Discrete Math. Also the idea is old to build 'the whole of mathematics upon logic'. As far as I know, one needs at least predicate logic of the first kind for such an enterprise. The resulting building shows strange features that I'm tempted to classify as ridiculous. The point is that one has to appeal to axioms (instead of constructions, algorithms) to get hold of the natural numbers, and nevertheless one allows natural numbers to be used in the very beginning when introducing the principles of predicate logic. I think we live in a extremely interesting epoche in the evolution of Mathematics. I guess all elements that have to be brought together to build an universal and practicable math are there, but building the edifice has just started. I'm convinced that the final version has to have the structure of a software, to which math textbooks are the documentation.
Can scientific data be art?
Scientific data are logical and precise data hold by mathematical models or laws, or induced /generated by other data or developments. Computational modeling was able to reveal that data processing with smart methods usually display an exciting and interesting screening of conclusion/ finding/ response/or data reaction ……. for example by fractals …. A rousing art drawing……
Dear all,
since term ‘chaos’ is commonly understood as disorder or anarchic release by non scientists, non mathematicians or inexpert personnel; I suggest a more understandable and accepted terminology to term ‘chaos theory’ for example ‘random’ or ‘uncertainty’ or ‘nonlinear dynamics’ theory …etc..…
What are your thoughts??? ……………. Yet some administrative staffs don’t comprehend that scientific contributions could be genuine and viable in this field, and others admit it as dangerous!!!! …….So many of them disallows authors’ congresses participation for this discipline………
It is in doubt..................
Can scientific data be art?
It is only by a beginner's (mine) mishandling of the ResearchGate system that my contribution to that already existing topic became the seemingly foundational contribution for this topic. Actually my contribution is not on scientific data but on data generated by computations designed to debug my own C++ programs. Certainly Fairouz Bettayeb's 'Can scientific data ...'-contribution is on true scientific data.
Fairouz Bettayeb's 'Dear all'-contribution
At least the specific point concerning the role of exactly known initial conditions that was brought up by Edward Yesid Villegas needs to be discussed within a defined notational framework. Here it would make no sense simply to assume 'nonlinear dynamics', or theories encorporating randomness or uncertainty.
From time to time I allow myself any sort of 'political incorrectness' and in such a mood I would come up with an additional reason for disallowing peoples' participation in chaos-related congresses: that most of chaos theory is elaborated hype and will share the fate of cybernetics, synergetics, and other world explaining, paradigm shifting 'theories'.
I agree with you Ulrich when you point on the exact role of ‘initial conditions’, perhaps which needs emphasis and more discussions. Maybe we have to find the more accurate terminology to chaos that includes nonlinear dynamics, randomness and uncertainty…. and shifting theories.
Sure the term “chaos” is more fashionable or ‘people’ and in some case promotional. But still interesting and serious congresses share good knowledge and experiences in this fashionable science, that could be missing due to the term ’chaos’ by developing country's researchers…....... In these countries, some research institutes and may be ministry of higher education and research central administration, are still governed by non scientists, and the term ‘chaos congresses’ is scared and usually none accepted.
I agree with you Ulrich when you point on the exact role of ‘initial conditions’, perhaps which needs emphasis and more discussions. Maybe we have to find the more accurate terminology to chaos that includes nonlinear dynamics, randomness and uncertainty…. and shifting theories.
Sure the term “chaos” is more fashionable or ‘people’ and in some case promotional. But still interesting and serious congresses share good knowledge and experiences in this fashionable science that could be missing by developing countries researcher's due to the term ’chaos’ ….. In these countries, some research institutes and may be ministry of higher education and research central administration, are still governed by non scientists, and the term ‘chaos congresses’ is scared and usually none accepted.
That the name 'chaos' in some countries is an obstacle for acceptance by research administration instances is an interesting statement which I would never had taken into consideration. This is the beauty of discussions in an international community, as ours, that unexpected facts can be brought up. That the selection of names in research fields influences the way in which the public looks to that research field became evident to me when the high energy physics community was confronted with the introduction of names such as 'quarks', 'strangeness', 'charm', 'beauty',and 'truth'. I remember that many colleagues formulated uneasiness with these names since they were felt to carry a touch of infantilism. This seemed, however, mainly a European concern. On a world-wide basis the effect of this terminologic decision seems to have been 'promotional', to use your term, Fairouz.
I would like to add an historical remark to the topic 'sensitive depenence on initial conditions' which is the starting point of 'chaos theory'. It is a classical result, that orbits defined by differential equations depend in a continuous, and even differentiable, manner on the initial conditions. For a precise statement see e.g. E.L.Ince: Ordinary differential equations, Dover 1956, paragraph 3.22, pp. 68-69). A remark to this book: The dover-edition is an unaltered republication of an edition in 1926 and thus belongs to the pre-Bourbaki epoch of mathematics. My first academic teacher in Mathematics, Erhard Heinz, recommended this book warmly as containing many times more interesting stuff than the more abstract modern textbooks, which were arround in 1964. As Heinz pointed out with an inscrutable mix of humor and indignation, the formulation mentioned above is correct but the argument is erroneous in a subtle way. This is to illustrate that what math has to say on 'dependence on initial conditions' seemed to be canonical and unsuspicious. The student was not made aware of the fact that strange things like the 'butterfly effct' are still possible, and happen in surprisingly simple systems. Continuity, often seen as the exact expression of the ancient principle 'natura not facit saltus' does not exclude the butterfly effect. Mathematicians may see themselves confronted with difficult problems. Physicists can help their imagination by mentally inspecting Galton's board, clouds of molecules, turbulent fluids. Computational physicists know how to build models of these phenomena that show exactly this 'sensitive depenence on initial conditions' and, hence, all the features which general chaos theory considers. A concrete study by myself is
http://www.ulrichmutze.de/articles/pdsb7.pdf
For turbulent fluids a simple-minded model needs a lot of particles and therefore much storage space and execution time. So for solving real-world engineering problems non-simple-minded models have been developed. Their sophistication should not convey the impression that simple Newtonian mechanics of mutually interacting particles would not be sufficient. This can be seen in parallel to the fact that in practical optics today simple-minded ray tracing is by far superior to the beautyful Seidel theory. In celestial mechanics there is no longer a practical need for analytical theories of orbits, such as Brown's analytical theory of Moon's motion.
Fascinating discussion - brings back fond memories of when "Schönheit im Chaos" first came out. To say "thanks" for this thread (and to link back to the original question), I'll offer the following URL to an exhibition of scientific data which was presented at an art museum a few years ago: http://archive.nyu.edu/handle/2451/14870 . To me, this answers "Can Scientific Data be Art?" with a resounding 'yes'. (Full disclosure: Prof. Bromage & I are related.) -- Mike Campbell
Sure Ulrich some terminology could be misunderstood by neophytes.....
Perhaps inverse problems approach could be interesting to initials conditions dependence and sensitivity in engineering problems ????
Thank you Michael. Creation is absolutely an art. Understanding this art essence and formalism could help to understand something new from the nature hidden language and spirit.......
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