Dear All,

Aesthetics cannot be set apart from ethics. And ethics and truth are convergent notions and also their practice or manifestation converges. Even ethics is a kind of truth.

For me aesthetics, the being of beautiful or approaching beauty has been truth.

The main aim of art has been always to find and present the truth. This is the task of science but with other instruments and methodology.

Interestingly, the same things threat both: the commercialisation which falsify and sell the truth of art and science.

The relationship between mathematics and art is ancient, this relationship has been only rediscovered.

"The scientist does not study nature because it is useful, he studies it because he delights in it, and he delights in it because it is beautiful. If nature were not beautiful, it would be not worth knowing, and if nature were not worth knowing, life would not be worth living". Henry Poincare

1.What has mathematics got to do with beauty? Actually, a lot. Physical attraction depends on ratio. Our attraction to another person's body increases if that body is symmetrical and in proportion. Likewise, if a face is in proportion, we are more likely to notice it and find it beautiful.

2. The Golden Ratio (or "Golden Section") is based on Fibonacci Numbers, where every number in the sequence (after the second) is the sum of the previous 2 numbers:

1, 1, 2, 3, 5, 8, 13, 21, ...

The Golden Ratio also occurs in nature, in the patterns we see in sunflowers, pine cones and so on. This is largely because one of the best ways to efficiently pack things tightly together is using the Fibonacci sequence.

3.With computers, we can generate beautiful art from complex numbers. These designs are called fractals. Fractals are produced using an iteration process. This is where we start with a number and then feed it into a formula. We get a result and feed this result back into the formula, getting another result. And so on and so on...

Fractals start with a complex number. Each complex number produced gives a value for each pixel on the screen. The higher the number of iterations, the better the quality of the image.

Dear Marcelo, I often use that quote in my classes. Poincaré is one of the safest sources about the topic.

Math seem to have led the group of sciences in this concern, leaving physics far behind. Would you agree?

The secret behind beauty, as shown by Qefsere, is indeed symmetry - and symmetry can open the door that conducts to chemistry (at large), and to crystallography in particular.

Besides, computing adds the very sense of patterns - hence, of mobile or dynamic behaviors governed by beauty.

Further on, can we claim that health is rooted in beauty? And if so, then how are we going to work out the diffuse continuum disease-health? Or, else, may be this last claim is a bit extreme?

Or does it? Sometimes we happen to see photographs of war events that are by no means beautiful, quite contrary they are ugly and horrifying, yet they contribute to truth.

On the other hand, the majority of legends or fairy tales appear nice (beautiful?) but they have nothing to do with truth, thus also nothing to do with science.

One may like or not, consider beautiful or not, any scientific hypothesis - it's a subjective matter of personal taste. After it is falsified there is no question whether it is true. And this is objective. In the meantime it happens to be called beautiful if it is simple (easy to follow and understand), is expressible as a compact closed-form equation, uses only a small set of assumptions, is highly symmetric and alike.

Talking about personal taste, the trouble merges immediately: whereas traditionally truth has been grasped as "objective" and "universal" (according to mainstream tradition, at least), beauty has been taken to be relative and subjective. Precisely: depending on one' s personal taste or preference. Which makes a little favor to the whole scientific and aesthetic endeavor, for through that way we come to splitting knowledge, one more time, into the "two cultures".

Can' t we go a bit further beyond those traditional assumptions? I believe we can.

Bingo, dear Aria! You made your point. In the ancient Greece - I prefer here to gather both the archaic and classical periods - beauty was relevant - for both the individuals and the (management of) the polis.

Later on, Christians despised beauty and the entire history of truth as a max value was enshrined. We gained truth, probably - by we then lost aesthetics - in the largest and deepest sense of the word.

Beauty was to remain an accessory or subsidiary dimension vis-à-vis truth. Such is exactly the story of encephalo-centrism and logo-centrism.

Can' t we discover that the path of truth is plural and errant, and not sharp and distinct? Plainly said, life is not possible without beauty - in the Socratic sense, for instance.

Is it to say that we measure one's self to their beauty? Or are we talking about the inner person we all have? This "inner" person we have is the creation of what is beautiful, therefore if one's appearance is looked at as beautiful or even desirable, what does the inner self say about that individual? This is the "truth" that we all seek after, our inner self displays what our outer expressions react upon or to. This is the dimension of beauty in its entirety, our inner self depends on how we really are on the outside, otherwise we place a two side lifestyle, one that we see and one that is inside of us, this one inside of us is our truth.

After a long period of reflection that encompasses over 2000 years, we could come rather easily to the conclusion that the dichotomy between truth and beauty is, well, a false dilemma. Real from a historical standpoint; but a mistaken or false one from a reflective point of view - a point that could be named as epistemology or anything else of the kind.

Well! "Truth is beauty, and beauty is truth." Mathematics is based on truths, and therefore mathematics is full of beauties.

Years ago, I read “The art and science of portraiture” by Sara Lawrence-Lightfoot and Jessica Hoffmann Davis (San Francisco; Jossey-Bass; 1997- ISBN: 0-7879-1064-3). It is an inspiring introduction into qualitative social science, precisely by the fact that it manages to create links between art and science, beauty and truth.

Ww could then go perhaps one step forwards. Following up Hemanta, the issue then is about our own capacity to recognize the limitations of physical claims on science in general, particularly when they argue in favor of falseablity, confirmation, contrast with experience and the like as the uppermost values for scientific rigor. Those pretentions, raised up by Popper and the likes are true but only for the classical physical science.

The meaningful of beauty shed new fresh lights on the claims made up by positivist of all kinds.

Carlos, you may be interested in reading Jim March's piece In praise of beauty in the online journal M@n@gement http://www.management-aims.com/PapersMgmt/165March.pdf . My own piece in this journal which deal with serendipitous discovery and the beauty of unexpected deviations from orthodoxy and formula may be of interest to you as well. Truth can be quite ugly but reaching towards it an be an experience of beauty ...

It's a very interesting question.

Somehow, I tried to treat it in a thread on RG, deflecting the problem from the role of "beauty during the creation of a scientific theory", to the role of "beauty during a scientific error" [or an infringment].

For those wishing to read the contributions from several colleagues of RG, I'm putting the link to that discussion at the bottom of this post.

I would remember that S. Freud defined the whole research conducted by Leonardo da Vinci as "conventionally childish," and other times "adolescent." According to Freud, the link between creativity, genius and formal theorizing is at the same level where the totipotent freedom of a child [who "perceives by intuition", and "and continually falls in love with the beauty of what he perceived"], evolves and is promoted onto the *rigor* of the adult, which needs to abandon the stage of intuition, to reach tha stage of "construction".

—g

https://www.researchgate.net/post/What_is_the_definition_of_a_scientific_error_How_is_it_distinguished_from_a_true_infringement2

Besides, we can safely acknowledge, mainly thanks to non-classical logics, that there is no one true. It is, I would argue, the plurality of truths what brings us throughout this path closer to the significance and value of beauty in science. For, provided that we live aside relativism concerning beauty, the very concept of symmetry - and symmetry-breaking -, of patterns, and non-linear dynamic systems permits a larger and broader gate to a feasible encounter from thrush to beauty.

Dear All,

Beauty has more of the element of subjectivity than Truth, especially the scientifically proven ones. The beauty that usually appeals to the human mind is that of "symmetry in form". It may be symmetry in an equation or on the beautiful face of a celebrity. In any case sometimes a little asymmetry put in alongside a huge amount of symmetry like in Monalisa's face seems to have an added value of beauty, although I personally do not find the potarit beautiful. Probably the aspects like name. fame, publicity etc add to the beauty that is perceived in a form.

Such beauty of form however only gives a glimpse of the Truth of the underlying substance that cannot be caught through subject-object interaction. The very wedge between the perceiving subject and the perceived object necessarily hides away the one Truth behind them both, and thereby makes the beauty only partially apparent, which however in our human intelligence we think of being the highest possible, forgetting the limitations of the process of perception.

This argument applies equally well to all that we can conceive of, from art to mathematics, music to philosophy.

Regards,

Rajat

The touchstone, it appears is the believe - hold by some - that we are able to reckon an objective, independent substantial world "out there" - whence a truth about it.

It seems to me that such a claim is highly discussable. By this, the traditional division between objective and subjective claim. That is old wine in old keg, probably.

Even if they are mutually complementary, beauty and truth are human constructs or signifiers, generating discursive practice evidently regulated by “interpretive communities” (Stanley Fish) in the absence of any “metanarrative” (Lyotard) or “transcendental signified” (Derrida), if you like. The complementarity of “language game” (Wittgenstein) embedded in Ontology, epistemology, and axiology (branching out into aesthetics and ethics), the trilogy of philosophy, not excluding in string theory physics, constantly point in that direction.

Dear All

Greater Beauty is recognized in things and concepts that approach closer to Truth.

Thus Truth is fundamental and beyond subject-object duality while Beauty is an effect of Truth that manifests when the object closer to the Truth is perceived by the subject.

Regards,

Rajat

The difference between beauty and truth that is the heart of this question would not be related to the difference between scientific development and social development?

Th. Kuhn already introduced the distinction - not opposition - between the academic community and the scientific community; I mean this just to translate Alexandre's remark.

On the one hand, we have those who produce new knlwedge, and on the other side we have those that help socialize and publicize knowledge. The social appropriation of knowledge is as fundamental as pushing back the frontiers of knowledge.

Well, honestly no new knowledge is produce ever without being permeated, to say the leats, by a strong sense of beauty, I guess.

I do not see any contrast between Truth and Beauty. The most beautiful thing is the universe, wich is the most real too.

The truth often hurts or bothers and beauty can facilitate the acceptance of the truth!

Dear all, can we think then that the age of the splitting between beauty and truth is over? If so, can anyone say the moment when the complementarity or unity of both truth and beauty arose?

Dear All,

Aesthetics cannot be set apart from ethics. And ethics and truth are convergent notions and also their practice or manifestation converges. Even ethics is a kind of truth.

For me aesthetics, the being of beautiful or approaching beauty has been truth.

The main aim of art has been always to find and present the truth. This is the task of science but with other instruments and methodology.

Interestingly, the same things threat both: the commercialisation which falsify and sell the truth of art and science.

The relationship between mathematics and art is ancient, this relationship has been only rediscovered.

Dear All,

Somebody mentioned the portrait of Mona Lisa and expressed his doubt towards its beauty. I can propose him to observe a picture thoroughly. This means that a superficial glance is not sufficient. In addition, one needs a certain practice to evaluate art and also the cultural background may influence the evaluation.

Going back to Mona Lisa, the value and beauty of this picture is not because of the famousness of Leonardo da Vinci, but because the artist wanted to get and record the personality, the feelings, the spirit of a person and also those of an age. By the way, he could find harmony between the woman’s mood and the Italian countryside.

And this is the (fragment of) truth what Leonardo, the artist, scientist and inventor was looking for during his life. We must know, this picture was his greatest fortune!

Thank you dear András. I agree: the relationship between math and art is a recent discovery. Harmony is set at the center, and both truth and beauty are susceptible of being grasp in non-algorithmic terms.

I would say, indeed, that the locus where ethics and aesthetics coincide is harmony. By definition, harmony is not a matter of control, is it?

Dear Carlos Eduardo

The beauty hardly leaves anyone indifferent: emotive, architecting a dynamism of deep inner transformation that generates joy, feeling of fullness, desire to participate for free in the same beauty, of appropriating it, internalizing it and integrating it in its concrete existence. Truth means that which is closely connected to all that is sincere, it is true, is the absence of lies.

Beauty is in the eye of each person

Dear Nelson, thank you very much for your comment.

The real significance of beauty stand in its impact, indeed. Truth, it seems, requires a further elaboration, isn't it?

An yet, a truth that is ugly is not a truth. Let's look at those official reports around us, f.i. And vice versa, a beauty that is not truth is empty: for example all those products of propaganda, adds, and the like.

Would you agree?

The material basis of beauty or ethics cannot, by no means, be discarded. Thank you Imtiyaz.

There is, though, also the cultural side. A tuned balance can help understand better the issues, here as well as elsewhere.

Dear Ida,

Your evaluation is wonderful. Many thanks!

Dear All,

It was me who mentioned Monalisa in this discussion since truly I didn't and still don't find anything beautiful about the portrait. However I fully agree with all the rest of you who have found it to be one of the most beautiful portraits, and surely Leonardo deserves all the credit and more for the same. beauty surely lies partly in the eyes of the beholder, although it is ascribed entirely to the object beheld.

Thanks and Regards

Rajat

Thank you very much Lewis Kausel for the info. on Monalisa. I think if one demystifies the portrait, takes out all the (mis-)understanding that has gathered around it, and then looks at it from one's own point of view, one's own idea of what a beautiful female face should be like, with or without the so-called half-smile etc.etc may be recalling Marlyn Monroe or some such nymph to mind for comparison one will surely find Monalisa lagging far behind in terms of beauty. The enigmatic half-smile with a possible pain underneath no way enhances the beauty. This ia very simple deconstruction which any one can do and the mistaken sense of beauty in Monalisa will evaporate. However, this is not to dishearten or hurt any one who finds beauty in it. each one has a right to have one's own idea of beauty. The same does not apply to Truth of course !

Regards

Rajat

Dear Carlos Eduardo,

To this fine question I must unfortunately give the answer of a historical relativist. Poets in my judgment are experts in the truth/beauty relationship, and their opinions differ from one era to the next. For instance, the Romantic John Keats in "Ode on a Grecian Urn" said "Truth is beauty, beauty truth/That is all ye know and all ye need to know," On the other hand, modernist Federico García Lorca sharply distinguished between the two in his revolutionary drama "El público." The drama turned on the distinction between traditional theatre (Beauty irrespective of Truth) and theatre-under-the-sand (unseemly truth irrespective of beauty), So whether beauty contributes to truth would seem to depend on the Zeitgeist, the spirit of each historical time.

Dear Rajat,

I cannot understand you. If I do not realize something beautiful or delightful, nobody cannot persuade me with some words of it. However, I would like to do everything to recognise somehow the beauty/value of a doubtful art object. I have never used the expression that the most beautiful portrait or art work. The most beautiful art work does not exist. I feel at least like that. Beauty is a cultural phenomenon. The Venus of Willendorf was not formed for the people of the 21st century.

I would like you to mention or show some art work which is really beautiful for you! One should discover other kinds of beauty.

Dear Nelson,

I should repeat your lines: John Keats in "Ode on a Grecian Urn" said "Truth is beauty, beauty truth/That is all ye know and all ye need to know,"

Yes, all ye need to know this!

Dear Nelson, Thank you very much. I do agree in that beauty has a correspondence with a given Zeitgeist. In other words, there is a history of beauty, very much as there is a history of truth.

History is, as we know, the real of change and variation, flux and becoming. Which does not necessarily entail a story of linear succession.

History, dear Carlos, according to Dilthey, consists of a "Realdialektik": the human being, faced with many possibilities, in the course of history tries out one, finds it deficient, then tries out another, finds it lacking, and so on. History is definable as the exhaustion of possibilities. This applies to possibilities in cognition or truth-seeking and to possibilities in aesthetics of the search for beauty. The only fixed rule is that the same possibility never can be assayed a second time. The Holy Roman Emperor tried to revisit Constantine but of course times had changed. Trying to relive history is like trying to restart the Seven Years War.

Dear Nelson, the point is clear. However, it does also make sense that history is an opening of possibilities. And we scan come to the same conclusion, namely "the only fixed rule is that the same possibility never can be assayed a second time". I sincerely think that history is a continuos non-teleological creation of possibilities. Or else, in other words: every generation creates and re-creates anew the horizon of possibilities.

As a geographer I would like to quote a French colleague of mine, Jen-Marc Besse, who said that, reminding the original meaning of the Greek word ethos, that is the dwelling, ethics is a way to make the world habitable. Hence, the basic relevance to this issue of make it possible to aesthetically share the places of our towns and landscapes.

Without hedging our bets against either beauty or truth, in a hubristic zero-sum game, we need to look beyond the binary of beauty and truth, both of which are constructs, if not sites of constructions of arguable realities anyway, to the blurring boundaries between the two, constantly bracing ourselves for the “well-wrought urn” of Keats’ “Beauty is truth, truth beauty-that is all/ye know on earth, and all ye need to know,” breaking down into billions of super elusive Higgs-Boson particles. Any truth claims about beauty or beauty claims about truth attuned to the nuance of the beauty of truth or the truth of beauty are always already subject to slippage, especially as we painstakingly walk the tightrope between falsifiability and verifiability in an infinite regress where singularity dismantles the vestiges of false consciousness inherent in positivism.

I wonder whether it is perhaps useful to frame the question as a cognitive one: what similarity is there between being in a state of awareness/feeling that something is beautiful and the state of knowing that something is true? Could we not plausibly say that there is a certain psychological state associated with each, independent of the objective facts of the matterd - and that these share a similar phenomenology? We might avoid epistemological questions involved with such knowledge by deriving the content of such states from the zeitgeist of the era. Such an answer seems to reflect the opinion of Keats nicely.

beauty is the sensual form of truth. to have a full answer, read hegel's lectures on aesthetics

Dear Carlos !

This is a beautiful, and honest (true) question...

As an anatomist with strong interest in pictorial Arts I often wonder on the mutual influence between aesthetics and science (and the obvious pragmatism of Truth).

I'm afraid that it may have been the interest on the artistic perfection of the human body that brought my scientific urge to study the human body in scientific terms, and to unveil some of the esthetical mysteries beneath the physiological Truth of the Human body. These first steps obviously lead me to commit my life to the struggle against diseases, that can harm ther beautiful perfection of human bodies. Thus I became a physician.

Science is honest and true, and through it, I discover an inherent beauty.

Both are mutually influencial, and both are necessary and complemental. 

Knowledge always entails knowledge of disposition, but beautifull things can be in motion or still, can have symmetry or no symmetry, apparent symmetry or no apparent symmetry, but they do not necessarily bear both beauty and a wholesome disposition or reveal simultaneously their beauty and their disposition.  A recurring element in a formula or discovery, suggestive to predictability, may alure or seduce, but the actual motion in its setting is not so predictable.  I think prediction has some possible realization only when the steps are short and not do not reflect much on ultimate survival.  

Dear friends, please accepot my most sincere apologies. It' s been a long ime since RG did not notify me about many answers and comments on this thread. And, unfortunately, I do no have time enough to browse RG as thouroughtfully as I wish - not even my own questions/answers.

Whence my delay in answering to you.

I remember I read a lomng time ago a quote from V. Woolf (one of my favorite writers) that +/- says: Because truth is such a serious thing I prefer to stick to fiction - meaning that fiction comes closer and in more subtle way to truth than logic or science.

(I strongly think that literature and poetry, f.i., do come closer to truth that classical normal science).

A truth that is truly, deeply and highly beautiful does move people, not because of its btruthfulness, but because of its beauty. Withoutout being a dualist, we can safely think that truth interpels much more our brains and understanding whereas beauty moves our feelings, guts, and emotions.

Would you agree?