Replies: 24 Comments
on Wednesday, February 27th, walt said
Marjan, I don't know. Perhaps...especially if you knew the language of math. But I think even Rajinder, mentioning subliminal self, suggests that we do seem to grasp beauty whether we consciously grasp the math or not.
Rajinder, I'm patiently awaiting your next blog.
on Tuesday, February 26th, Rajinder said
Walt,
Although I dont entirely agree with you, I believe you have frog-leaped a number of conceptual steps to allude to what the pragmatist Dewey referred to as 'aesthetic experience'. I want to consult this in my next blog entry if you dont mind.
Marjan,
You have rightly pointed out the problems of painting using mathematics as 'paint' rather than as a tool. One important focus ( outside of the concerns of this blog entry) is on the process of the painting. I THINK, with mathematics as a constant companion - so mathematics, if nothing else, is a deeply personal way for me to work out the world around me. ...so I challege you to 'sift through the layers of paint to discover a labyrinth of idea and histories, both universal and personal, embedded within'.
But I am hoping for something else. ( Caveat: The following rant might be too simplistic and as a consequence trivialise and introduce errors). You know when you add 7 and 5, 7+5=12, you have an a priori proposition. You do not need to consult experience for the answer. Nor is the answer in the definition of 7 or 5. Kant said that you just know and that this is a synthetic apriori proposition.
What if I were to place lots of 7s and lots of 5s and lots of pluses on my canvas? I am getting you to think about the 12s. Maybe? Now, what if I place all the mathematics for my interpretation of 'beauty' on my canvas. Will you somehow sum up a particular conception of beauty in your head? What if I give you clues, as in, I paint a beautiful woman with the maths? What happens then?
Now what if I place several mathematical interpretations of beauty on canvas? Will your "subliminal self" come to play?
In my blog entry I explained that Kant's synthetic a priori truths would not allow us to conceive of a non-Euclidian geometry. There are many alternative to Euclidean geomtry out there. Much of these numerous mathematical combinations would be useless and cumbersome. The true work of the mathematician consists in choosing among these combinations so as to eliminate the useless ones. How do you do this? It is felt rather than formulated.
Poincaré suggested that the choices of mathematics is made by what he called the "subliminal self." Mathematical solutions are selected by the subliminal self on the basis of "mathematical beauty," of the harmony of numbers and forms, of geometric elegance ( perhaps something that Walt was referring to?). It is this harmony, this beauty, that is at the center of it all.
My paintings are beautiful paintings of beautiful people about beauty, both physical and mathematical. And perhaps the mathematical equivalent of lovely might even act as the perfect sieve to reveal a new dimension to this supreme force of human experience affecting real and lasting transformation in us. Art and maths are but languages through which we attempt to understand that which is ineffable. ( from my press release...sorry).
on Tuesday, February 26th, marjan said
Walty
Just as I was getting off the plot, I took the bus and ended up here again. If I knew more about mathematics, would I be able to see the complex formulae in the work?
on Tuesday, February 26th, walt said
And while one need not know how the engine works to drive a car it doesn't hurt to know a little about how to maintain it properly. But if one does know a lot about how a car works they will certainly have a deeper grasp of the mechanical beauty of the device and if they are in fact a master mechanic and engineer they might be able to build a better more energy efficient and environmentally friendly car.
Sorry Rajinder...I don't mean to lay so much extra baggage on you...making mathematical paintings is more than enough for now. You don't have to solve the worlds problems at the same time.
on Tuesday, February 26th, marjan said
Thanks, Walty!
That makes sense and of course is applicable to most of the world's population and somehow the premise(s) purpose(s) of this blog escape me still, although interesting. One obvious questioning point is when using mathematics to produce an aesthetic object, it is already an 'a posteriori' experience and the other being that people who e.g. use a canvas, already are using mathematics for the simplest composition but to a different degree (whether consciously aware or not). I'm not too keen on logical leaps in other's thinking, because I can do those myself.;)
I think I should get off the pot. I don't mean that 'pot'(one has to be careful these days!).
Thanks again, Walty.
on Tuesday, February 26th, walt said
Marjan, our senses are pre-wired to work on a binary system of recognition, a mathematical system of contrasts. It isn't what happens after we've experienced but the fact that our visual system is binary before we experience a thing. Not a philosophical use of the words at all. But if it makes you feel better how about substituting the word pre-cognitive in place of apriori. Pre-cognitive mathematics. I think we're hardwired as a species for mathematics notwithstanding those of us who for whatever reason are not willing or able to learn the language. It's like driving a car. You don't have to know how an internal combustion engine works to put the key in the ignition and drive the car.
on Monday, February 25th, jose said
My intent was not to put East up against West or even suggest that they are separate or in any way superior to one another, Rajinder, and please forgive me if my comment made you feel in any way that I was claiming so. Not at all, for me East/West/North/South form a unity.
Indeed, as you say, philosophy of mathematics is not a subject that is consulted widely, least of all by me, and I fear I am quite unable to put forward any theory I might favour. If at all I would confess that eastern thought interests me more than western thought, but then again I have to admit that my investigations and interests have not been in the field of mathematics but more of psychology and dialectics which I found to be more pragmatic and useful in the end than the many theories I had to digest in University. As a matter of fact, I think my aversion to Kant and other renowned thinkers of the so called west, and thus my incapacity and unwillingness to uphold their ideas or investigate further along the lines they open [although Heidegger did have a strong influence on my becoming an artist], has to do with my reaction to this period when the superiority of the Judaeo-Christian world-view was forced upon me. It was something I could not accept at the time, and still find difficult to swallow. Regarding mathematics again, and picking up on what Mark said below, I think that if through your method you manage to convey the emotion you feel when faced with the beauty mathematics reveals to you than you will have done a good job indeed.
on Monday, February 25th, marjan said
Walty
Can you please explain this to me, because it makes no sense whatsoever. It's doing my head in. Aesthetics is by definition based on the senses, which are by definition 'a posteriori' (even when imagined)....
on Monday, February 25th, walt said
Rajinder, our orientation to patterning is how I see a connection to apriori mathematics...we see by contrasting light and dark patterns, color contrast, contrast in locations in space, size, textural relationships etc. I see this as apriori mathematics in that even when we are not congnitive of the how it is that we see it is still kind of a binary system in which we judge by certain contrasts...on/off,Light/dark, bigger/smaller, in front of and behind, up/down, left and right...our photo-chemical optical process makes these contrasts very quickly so we can locate ourselves in space and time. While we may use these visual cues emotionally they carry far more than only emotional weight. They are become a visual language. In this I see a connection to the mathematics to which I think you refer. And of course this begins to get to aesthetics...and as well to the idea that Mark refers to as overthinking the process in that we hardly recognize the process at times even when we are in the middle of it all.
Am I getting warmer?
on Monday, February 25th, Mark said
Not saying what has been said befor here in regards to mathematics is wrong. In fact it might all be more then correct. Maybe too it is my own lack of mathematical knowledge that makes me say this. BUT, is this not just over thinking it all to an extream??? Art is emotion, creating comes from emotion. Now if math is emotion so be it, but I see math (not numbers) as a means of calculated ends. Cetainly even when one creates there is an amount of calculation to reach an end, but for me it more emotion then calculating. My two cents.
on Sunday, February 24th, Rajinder said
Marjan,
I was not dismissing Ellen at all. The possibility of an explanation in mathematics is the very basis of my thesis. And patterns provide the potential for knowledge. Without patterns we wont be having this discussion at all.
Jose,
Kant's explanation and my interpretation of it is but one potential explanation for the place of mathematics beside aesthetics. It appeals to me. Philosophy of mathematics is not a subject that is consulted widely and if you find an alternative that appeals to you, I hope you will share it with us. Access to the finer details and interpretation of the philosophies of the East is as yet obscure. In the East, we tend not to have much use for categories e.g.I am from the East and you are from the west. We see everything as one seamless union of things..or at least I think that is the case having lived my life away for the most part.
on Sunday, February 24th, marjan said
Now that I've had a quick peek at memory lane, you are dismissing Ellen's comment which is based on patterns in mathematics. An enormously important part of mathematics.
Walty is going the 'a posteriori' path, and I'm in between the two, except that I don't believe in anything ' a priori' in the first place and that is because of sound logic.
All that is sort of by the way, whilst I find this blog enormously interesting, I can't see why or how your process of working actually shows itself in your work (except in symmetrical patterns).
Now, I remember why I couldn't force myself through Kant at college....
on Sunday, February 24th, Rajinder said
Ellen,
I think we have to be a little cautious about what we call mathematics. Although mathematical concepts came originally from natural objects, mathematics is done in the mathematical world of ideas and not in the real world of objects. If mathematics tells us something about the real world, it is wonderful but it is not mathematics.
Numbers are concepts. The number four for instance does not exist anywhere but in the mind. We start with natural numbers in mathematics and build abstract objects that live in the mathematical world using axioms, rules of mathematics and the law of logic. The absolutists believe that we we discover mathematics like we discover stars and the creationist believe that mathematics does not have existence beyond those who create or study it. Much of what is mathematics cannot remotely be considered natural and is far removed from the real world.
Mathematics provides us with the arena within which the other is allowed to emerge in its otherness. There may be an underlying maths premise to everything as long as we accept that in all of mathematics, we are fee to choose our axioms arbitrarily and develop their logical consequences regardless whether our system is self-evident and useful or otherwise.
on Sunday, February 24th, Ellen said
On a purely visceral level: the heartbeat is math; the pluse is math; every function of the body- instinctual or premeditated can be broken down into mathematical relationships. Sorry if I'm being simplistic, but does not this beg the question: What is it that humans (or for that matter nature) do that does not have an underlying math premise. Of course, Rajinder, I am in no way trying to deminish your meticulous planning of your work through the conscious use of carefully considered mathematical relationships. All I mean is that we all use math in one form or another: it is undeniable that the heart must beat in a certain count to keep us alive.
on Sunday, February 24th, walt said
Rajinder, thanks for the followup. So let me see if I have this right...the math, as equations, is painted with numerals and symbols into the image having been worked out separately? Here I am only trying to build a picture of what the work looks like since it is hard to see it in past photos posted on the previous blog. You are very correct in stating that math is not a spectator sport. But the deeper elements of art in general are not particularly understood by the common passerby either so it seems important that I grasp what it is you are trying to do.
I've been through the education and have read and tried to grasp, at least in brief, much of the philosophy of aesthetics as Jose has mentioned of the western world. While much of it does seem peripheral, it does at least set certain parameters for how we understand what we are seeing and or doing...parameters being the outside boundaries the peripheral nature is an apt description. The parameters don't always get to the guts of the thing itself. The guts are experiential...visual art is by its visual nature experiential. It is the experience of looking and processing that makes it work or not. If that experience has power we are shaken, if not we turn and walk away. And by power I do not mean the more common shock art but that visceral, emotional responce that can touch or even shake one to their core.
on Sunday, February 24th, Rajinder said
Walt,
My goodness..you sound like the voice in my head..it is a little freaky ;-). What follows is a mind-dump with little to no editing.
I owe you a response from the last blog entry. I am glad you have brought it up here.
In the early stages of my painting process, I single out certain qualities of my subject-matter that I want to work with. I work out ways of trying to describe an ineffable quality or a value like say a woman's beauty using mathematical techniques. I call it the aesthetic content of the image. This becomes the prime concern of my mathematics and the 2nd stage of my painting process. Once I have worked the mathematics, I build the shape on my canvas using whatever scrap of mathematics I have generated. You see where I am going?
My concern is with metadialogs. My hope is that my paintings will engage my viewer in parallel trajectories of interpretions/recognition that through the geometries of our minds and the terrain of our subconcious, the parallels will coincide at a point of revelation at the cutting-edge of our understanding.
I use the best mathematics possible as you would use the best materials for your paintings. I am not concerned with perspectives or fibonacci numbers. I develop my own interpretations in mathematics, at times using methods and techniques beyond those that are commonly available. My paintings are based on my believe that our Reason is not the ability to read the text of what you called Das Ding and Sich, not even to reduce Nature to text, but Nature's ability to define Reason. To define us!Mathematics provides the means.
The big question mark lies in the aesthetic 'frequency bands' that we are tuned to. I have too much resting on apriori(s) and intution. Because I go thru the maths, and I work it into my painting, the eventual 'wallop' for me is more then the sum of its parts. I dont know if anyone can experience this without going thru the process. Mathematics unfortunately is not a spectator sport. You need to work thru it. Sometimes even reading it is not enough. But perhaps.. there is a chance that the beauty in the concatenation of the numbers and symbols and the meaning that they aspire to placed layer after layer in the construction of an image, a quality of which it describes in innovative ways, might lead to something.. a personal understanding, a private revelation.
on Sunday, February 24th, Odette said
Rajinder,
I have seen your work and I liked it very very much.
I do agree that there is a connection between maths and art... when I read the title of your blog the first thing that came to my mind is Fibonacci.
on Saturday, February 23rd, jose said
Rajinder, I have absolutely no doubts that mathematics play a very important part in our work as artists, be it intuitively and, as Walt suggest, an apriori sense of it, or consciously and thus knowingly resorting to it to create things with a particular intent, the most striking and elevating examples of which I find in Islamic [especially Persian] ceramic patterns, that somehow come across like maps of the labyrinth between the heavens and us. Kant, however doesn't do it for me, never did, kept me too busy in my mind and forgetting the rest of me and so I decided to let go of him – as a matter of fact I find most of our western philosophy looses itself in thought without ever reaching conclusions or solutions that are in any way useful to the people its philosophers are living amidst. I find it curious that you, a man of the East – from where a fundamental breakthrough in mathematics reached us in the West [the notion of zero], and indeed many other interesting insights have yet to be even acknowledged by our stuffy professors – should call on Kant.
on Friday, February 22nd, walt said
Rajinder, I'm still not sure HOW you have thread mathematics into your imagery. Are the shapes due to the processing of some equation or equations? Or are you interpreting a given shape, color, texture as mathematical symbols or equations? I guess the question is: which comes first the chicken or the egg? (And maybe you have answered this already. If so forgive my inability to understand the language of mathematics in this instance.) I suppose there is yet another variation on the possibility in that the math is a separate dialog (a meta-dialog) that may or may not concur with the imagery. Again please forgive that I do not speak the language as readily as you. But I have a sence that the human mind grasps certain mathematics apriori and unconsiously therefore intuiting an image without understanding the mathematics involved in seeing, picturing or translating the image. And unless there is something else to be grasped... doing the math simply slows down the process of recognition, interpretation and emotive response by adding, shall we say, a third rail to the process.
Recognition, however, is not exactly the same as creating or constructing as in the artistic process of making an image. And of course in the making one uses a certain level of geometry along the way. But again, given the number of mathematically untrained artists who make perfectly believable and aesthetic faces (or other images) without consciously comprehending the mathematics involved...in fact, when those mathematics are explained such conscious information often chokes off the ability...it seems a moot point as once the image is achieved it becomes das ding an sich Kant speaks of does it not? It becomes a thing itself.
on Friday, February 22nd, marjan said
Rajinder, thank you for taking the time to explain further. Reminds me to brush up on my Kant....
Unfortunately, also, I am only vaguely familiar with Turing, because of the Turing Test and Searle's 'Chinese Room Argument.'
I gather that the fascination with Goedel is not only the Bach's fugues (I found all that too far-fetched), but the certainty of specific uncertainty(ies), which is (are) also being disputed. Mathematics has always seemed to be me as pretty patterns, a beyond of 'phenomanology' display of symbols of objective truths. So, yes, I have thought about it,but not necessarily found similar or same aesthetic value, perhaps mainly because I understood mathematics better in music (another language of certain and specific grammar...).
on Friday, February 22nd, Mark said
As soon as you used the word 'Math' my brain shuts down. Not sure I understand what you have said, my stupidity I am sure, but if you mean that art, the aesthetics of art, are organic moods and feelings and the need to express, then I got you. If you mean that the aesthetic of art can move others in ways they may not have thought of, I got you. If you mean that math is at the root of all this, here I am lost, but I do not disbelieve you. Yet I think even if true, one does not need to understand your idea to create or enjoy the creation. Sorry if I got it all wrong.
on Friday, February 22nd, jose said
Rajinder, you have started to explain to us what you put forth in your first blog in a manner that a person unkowledgeable in maths, such as myself, can start to grasp. I look forward to more.
on Friday, February 22nd, Rajinder said
Marjan,
Philosophy of mathematics and my struggle for brevity conspire to make the last two paras of my article almost unreadable. You are right. I am sorry. It is futile at best to do a good job of it in two paragraphs.
Kant's wonderful philosophy, one interpretation of which I have tried to summarise above, gives us an account as to how poetry and mathematics are true theoretical counterparts.Mathematics is like poetry because of what they achieve. We know this about mathematics particularly today when we suscbribe, for instance, to the possibility that Godel and Turing's famous results are an indirect reflection of the fact that human understanding is intepretation. In mathematics and as it is in poetry being is expressed as the authoring of its expression.
I am not saying that mathematics should not be perceived as aesthetic. On the contrary. Mathematics is aesthetics. But have you not wondered why? Perhaps Kant's is one possible rational explanation.
on Thursday, February 21st, marjan said
Forgive me, but I can't quite see why mathematics shouldn't be perceived as aesthetic (in rare cases synesthetics see numbers in colours etc. anayway...) and you somehow totally lost me with the connection with a priori Kantian premises. Aesthetics is the opposite of anaesthetic. So somehow reason only follows. There is no rational reason not to see or seek aesthetic pleasure in mathematics. I'm lost in what you are trying to say.
Mathematics has been part of cultural semiotics for centuries, even if at times and moreoften it refers to objective truths, so I really don't follow... Please, explain, thanks.
