Art, Mathematics and Basketball

The word “beautiful” is very complicated and yet we routinely apply it successfully to a wide range of situations. We all know what it means to say a painting is beautiful (though that description has fallen out of favor in the modern art world). Most of us also know what a beautiful smile is. Those of us who watch sports know what the announcer means when they say that a basketball player has a beautiful jump shot. In mathematics or physics, a proof can be described as beautiful. And a contemplation in a spiritual text can be beautiful as well. The list goes on…

Does the word have the same meaning in each of these situations? Why do we all understand each of these uses yet see that the things being described are quite different and may have nothing more in common with each other than their “beauty”?

Ludwig Wittgenstein, arguably the most important philosopher of the 20th century, had an interesting explanation. He believed that we used “language games” to describe the world. He used the word “games” to imply that there are rules and conventions surrounding various subjects that we all understand. We have to evaluate the meaning of words within the language game in which they are being used. So the word “beautiful” in the sports, spiritual, mathematical or art language games is used and understood within the context of each game with its unique set of rules and conventions.

He also said that the use of the word in differing contexts bears a “family resemblance” – it is not identical across language games any more than two members of a family are identical. Yet we usually can tell that two people are members of the same family, just as we implicitly understand that a beautiful jump shot in basketball bears some resemblance to a Mark Rothko painting. We know they are both “beautiful”.

What other kinds of “language games” can you think of in which we routinely use the word beautiful? I think you’ll be amazed at the variety and complexity of this word and the number of “games” in which we use it…

7 responses to “Art, Mathematics and Basketball

  1. I love the way this image is both beautiful and mathmatical and evokes something about the dynamics of basketball as well. I can’t imagine a better image to illustrate your commentary here.

  2. I never could clairly explain to myself why I have an instinctive abhorrance for the geometrical paintings…Is it my savage, expressionist streak? Is it my dislike of mathematics? (irrational all that, I grant you)

    But I know I’ve always prefer curves (ok, curves also are geometry, but there is something MORE with curves…) to straight lines… I try also to ordonate the chaos in my paintings and probably I even use some geometrical or mathematical elements too (like the Fibonnacci serie)… But I always wondered if there isn’t a connection, a causal connexion between abstract painting (which, at a very profound level is not satisfactory, not fulfilling) and the suicide of artist, supposedly very succesful (at least financiarely) like Mark Rothko and Nicholas de Stael… Each of us, and I think susan can confiorm this, doing this abstract thing, arive at something more or less figurative, natural…

  3. Danu

    I find that what I like is to try to have geometric elements in with other more organic elements, whether that is a textural background like in this image, or with other shapes that are more curved. One of the reasons I add the curved marks with an ink pen in these is also to break up the hard lines of geometry.

    I admit I’m a little more left brain oriented (according to the Vancouver Art Institute brain test) so I actually like working with geometric shapes and patterns.

    I hope you’re wrong about a connection between abstract painting and suicide!

  4. Wow, what a great discussion is going on here! Not the kind of discussions I have with my bulls on the canvas all the time…
    And to be honest, I don’t know where and how I should enter this dialogue, although it is really exciting my brain…

    As always I have a big problem with the left and right brain parts stories, as my own brain seems to be made of a very porous stuff where everything seems to circulate in all directions without any boundary classified as left and right or up and down or whatever.
    I am BASICALLY a mathematician, I mean I am a mathematician with “corps et ame”, and some say that I am a painter too, so I guess mathematics and Painting are quite close. I always called maths “The Abstract Art par excellence”.
    Personally I use a lot of mathematics in my paintings even if they don’t look geometrical, straight or curved lined. i use maths “to order” my paintings, order all the relationships between the elements of my paintings. I am hardly aware that i am doing it, because having done intensely maths since I am a child, it is simply a reflex for me to order everything, above all to put all element in ordered relationships to each other. Also elements like shadows and lights for example.

    Perhaps Danu is right that abstract painting “at a very profound level is not satisfactory, not fulfilling…”, and it is a great remark, but I totally doubt the connection to suicide. I have lived almost all my life in a Big Abstraktum, and I loved it there! And anyway, I can’t understand why somebody could kill himself because of the way he paints. He could suicide because he has no success with that, yes, but not because of his art itself.
    By the way, i love Nicholas de Stael, and what a great house he had in the Provence…

    I read Wittgenstein many many years ago, and if I remember well I loved it. i am not sure I would still love it today. when I read what you write about his language games, Bob, I find it today too unnatural, too sophisticated, too intellectual.
    I think i use myself the word “beautiful” in each case with exactly the same meaning: something which touches my soul, in such a way that everything else around stops existing for some seconds. It is a reaction beyond rationality and emotionality for me.

    Sorry, I must go now!

  5. Miki – Happy to have you join the fray!

    The brain “divide” is certainly a gross generalization – everyone has to use large amounts of both aspects to do anything, but I do think many of us have a leaning, a tendency to approach problem solving a little more one way or the other. And painting is a form of problem solving at some level.

    I don’t agree that abstract painting is somehow less fulfilling than more representational art. That I think is not a good generalization. It is very personal – for some I’m sure it is true, for others not at all. I find it interesting, for example, that most artists I’m aware of, as they progress in their craft, if anything tend to become more abstract in their work. I think it is less usual to trend the other way. I wonder why this is?

    I like your definition of “beautiful” – it seems to apply to any context in which the word is used, whether art, sports, science, etc. It raises another question for me – why does this happen? Why does everything stop, as you say? It’s not just that what you see is unique because you see a lot of things that are new but not beautiful. Oh well, maybe it is beyond words – that’s certainly what Wittgenstein said! One of his objectives in his study of language was to identify what we could meaningfully talk about and what was beyond the mind, language, etc.

  6. I think you are right, Bob, that abstract painting is not less fulfilling. I have also noticed, like you, that many artists progress to abstract. But I have noticed too, that when they have reached a certain level of abstraction they come back to “normality”, at least if they live long enough!
    I can in fact only speak about my own experience with myself. I have started with “abstract” simply because I started naturally, having received one day a water colour box as a gift. I was unable to draw anything which looked like something real, so I just made colour compositions, with some fantasy shapes and lines. As I gradually became better in drawing I became more realistic in my style. Then came a point when I got really bored to “repeat” nature and my style automatically started to change nature, to make all kind of transformations to the real elements. always more, until they were beyond recognition. As I was there I got bored again and felt the urgent need to paint realistically again… and so on.

    My painter’s life is really such a sine wave between the two extremes of totally real and totally abstract. In fact I believe that most of the painters would be like that if they would get bored as quickly as I do and paint as fast as I paint, (I am quite a painting turbo machine when I start!).
    And of course it depends too from the personal need each of us has “to know”, to really reach the very bottom of the things, to try to find the last truth. I am not like that, this bottom does not exist for me, knowledge has an incredibly complicated and fascinating space time structure.

    I believe that there is nothing about which we could not speak if we tried. The only problem is that the language does not develop as fast as our thoughts, perceptions, experiences, etc., and we can’t speak about some things it is just because the appropriate words don’t exist, or because we don’t feel the need to speak about them. When I find something really beautiful, most of the time I simply say “Wow!” with shining eyes and it is enough for me and the people who are close to me.
    But yes, I was fascinated by Wittgenstein language studies, as I am myself very interested in everything touching language. By the way I always considered myself mathematics as a language, and it was for me and for a long time the most appropriate way to express myself.

    Strange, I don’t believe at all that painting is “a form of problem solving”. Well, I know that some people go into painting as a therapy form against all kind of problems. But if they then go on, if they find taste in it, I think they paint just because they love it, because it is exciting, fulfilling, etc. I am sure that many personal problems can be solved with painting, but I don’t believe that this is the reason why one paints….

    Anyway, only personal thoughts about your great themes, Bob, always only based upon the own experience…. and as I am a quite weird person, I won’t surely generalise!

  7. Interesting metaphor! My artistic path as a sine wave – I love it! I, too, get bored doing one thing and then migrate to something very different. And then, after a while, back again, though usually I bring something from where I’ve been to that next stage so there is this evolution rather than a pure oscillation.

    Math is a pure form of language. In fact, Wittgenstein went through 2 distinct phases. In his early phase (his Tractatus) he “proved” that symbolic logic (ie mathematics) was the only language that could meaningfully picture reality. In his later phase (his Philosophical Investigations) he refuted himself and advocated the primacy of natural language (in the context of “language games”).

    When I referred to “problem solving” in painting, I was speaking more generally, not about personal problem solving. Rather, at each stage of a piece of art we are tackling an artistic problem – where to put the next line, how to create the balance as you say. These decisions are a form of problem solving. Our natural tendencies apply to this type of problem solving (as well as to how we solve our personal problems!).

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