Are there Physics and Mathematics Texts for Holistic Learners

[Jarvis323]

Wow! Thank you all for your great insight.

IMO, it may just simply be that some require intuition or motivation more than others, maybe in part because they need it to maintain interest and focus, or maybe simply because of the way that their brains try to put pieces together and organize information.

Whatever the case, it's surely true that a student needs to have focus to do well. They have to be paying attention. I just need some 'help' with this or my mind will wander; I will find myself pondering abstract philosophical concepts, trying to work out mental experiments, or working out the details of some invention or potential project. I think these same qualities that I think make the thinker, day dreamer, and problem solver, are very beneficial for a mathematician, but potentially detrimental to the beginner student in a linear, and ridged educational path. No doubt, math requires this to some extent as things are built on layers of foundational axioms, theorems, formulas, algorithms and concepts.

You need to wade through a lot of tedium to get to the level where you can productively daydream up coherent and useful mathematical inventions. It's not a lack of love for mathematics that is holding me back, it's more my dislike for tedium and inability to force the aim of my focus arbitrarily. I love mathematics, particularly abstract mathematics, especially the type which requires little background knowledge, but lots of ingenuity and cleverly structured logical deduction.

I don't buy this "mathematics is an art" view. Art is bound up in culture and perception, and has an instrinsic freedom. The mathematician is constrained by what is ultimately true by well-defined criteria, whether the result is rigorously proved or not.

A writer, poet, artist or composer can create whatever he or she likes, but inescapably $\sum_{n = 1}^{\infty} = \frac{\pi^2}{6}$ - there is no choice and no artistic freedom. Mathematics is beautiful, but it's not an art.

If mathematics were art, you could submit a blank piece of paper as your mathematical thesis and demand a PhD for it, following the theme of John Cage's 4'33":

If mathematics is not an art, just because it is a reflection of something real or inflexible, then is photography also not an art? Is non-fiction writing not an art? It's my opinion that the process of bringing together select pieces and then building a beautifully, and logically structured representation of something true, and then communicating it elegantly, and moreover, assigning it some truth based conceptual meaning, is altogether perhaps one of the most creative and artistic endeavours of all; mathematics may be the purest and richest art we have.

 

[vanhees71]

Well, that's a delicate question and not easy to argue about. I think doing mathematics and also the natural sciences is to a certain extent also comparable to the work of an artist. You need ideas and intuition to figure out something new. It's a creative endeavor. Of course the rules are much stricter for math and for natural sciences you have to make observable predictions and test these predictions in experiments. So in some sense you also have to be more focused than an artist who is completely free in his expressions, but you also must not be so focused that you cannot find something new.

 

[PeroK]

If mathematics is not an art, just because it is a reflection of something real or inflexible, then is photography also not an art? Is non-fiction writing not an art? It's my opinion that the process of bringing together select pieces and then building a beautifully, and logically structured representation of something true, and then communicating it elegantly, and moreover, assigning it some truth based conceptual meaning, is altogether perhaps one of the most creative and artistic endeavours of all; mathematics may be the purest and richest art we have.

So, we now have three possibilities:

1) Mathematics is not an art.
2) Mathematics has some artistic elements and may be considered an art.
3) Mathematics is the purest and richest art we have.

Atlhough, I think if you went along to the Arts Council and looked for funding for a PhD in Mathematics, you might come away empty handed! I also like the idea of taking a class at the London Royal College of Art and teaching them differential equations! You wouldn't get away with that, for the pure and simple reason, that mathematics is not art. How could you teach mathematics (as an course in Art) at an Art College? It's absurd.

It's all very well for mathematicians and physicists to convince themselves they are artists - anyone can do that. Everyone is an artist in their own eyes.

The real test is to persuade others that you are artists. To be truly an artist, you would have to persuade the wider public and bodies who support and fund Art. To get people to attend maths lectures purely for the aesthetic pleasure of seeing someone paint (incomprehehensible) equations.

I believe the argument that maths is the purest and richest art would cut no ice outside a maths and physics forum!

 

[micromass]

So, we now have three possibilities:

1) Mathematics is not an art.
2) Mathematics has some artistic elements and may be considered an art.
3) Mathematics is the purest and richest art we have.

Atlhough, I think if you went along to the Arts Council and looked for funding for a PhD in Mathematics, you might come away empty handed! I also like the idea of taking a class at the London Royal College of Art and teaching them differential equations! You wouldn't get away with that, for the pure and simple reason, that mathematics is not art. How could you teach mathematics (as an course in Art) at an Art College? It's absurd.

It's all very well for mathematicians and physicists to convince themselves they are artists - anyone can do that. Everyone is an artist in their own eyes.

The real test is to persuade others that you are artists. To be truly an artist, you would have to persuade the wider public and bodies who support and fund Art. To get people to attend maths lectures purely for the aesthetic pleasure of seeing someone paint (incomprehehensible) equations.

I believe the argument that maths is the purest and richest art would cut no ice outside a maths and physics forum!

So something is only an art because other people think it's an art. I don't accept that definition.
I don't consider somebody an artist because he gets good criticism or funding from famous people. Rather, I take the following definition: "Art is the most individual expression of the most individual emotion". Meaning that art is very personal. You don't consider math art? Fine, then don't. But I do, and that's what art is about: individualism.

 

[vanhees71]

I vote for 2+3) :-))).

 

[PeroK]

So something is only an art because other people think it's an art. I don't accept that definition.
I don't consider somebody an artist because he gets good criticism or funding from famous people. Rather, I take the following definition: "Art is the most individual expression of the most individual emotion". Meaning that art is very personal. You don't consider math art? Fine, then don't. But I do, and that's what art is about: individualism.

"Art is the most individual expression of the most individual emotion"

I don't recognise that at a defining characteristic of mathematics, I'm sorry to say.

Would you, say, quite happily debate whether Riemann or Beethoven was the greater artist?

 

[micromass]

"Art is the most individual expression of the most individual emotion"

I don't recognise that at a defining characteristic of mathematics, I'm sorry to say.

Would you, say, quite happily debate whether Riemann or Beethoven was the greater artist?

I don't believe in somebody being "greater" than others. I consider Riemann and Beethoven both to be extremely skilled artists, whom I both enjoy a lot. You wouldn't consider Riemann an artist. Fine with me. Then don't. But I do. And I don't think you can reason about art. It's something you feel or not.

 

[PeroK]

I don't believe in somebody being "greater" than others. I consider Riemann and Beethoven both to be extremely skilled artists, whom I both enjoy a lot. You wouldn't consider Riemann an artist. Fine with me. Then don't. But I do. And I don't think you can reason about art. It's something you feel or not.

But, you can reason about mathematics and there lies the difference! Most of modern art, I would say, is a confidence trick - of sorts. That's why I would be reluctant to consider maths and science as arts and why I posted the piece by John Cage. You can't publish a blank sheet of paper and call it maths, but you can submit a blank score and call it music!

If you say "General Relativity" is a work of art, I think you are saying it's one man's emotional response to the cosmos. And in a way it is. But, I would see that as stretching a point.

Also, if maths and science are arts, I'm not sure what isn't art. Is there anything that you would definitely consider not to be art?

 

[micromass]

but you can submit a blank score and call it music!

To consider your own argument, would an Arts college fund you for a blank score? Do you think they should? If you went to a music concert and they wouldn't playing because their score was blank, would you be satisfied? Apparently the people at the John Cage concert were, but I sure would be quite angry. I don't think a blank music score is art.

Mind you, art is personal. If you say a blank music score is art, then all power for you. But I'm not very interested in that kind of things anyway. So for me personally, it's not art.

I don't see what this discussion is good for really. Art is something personal. Nobody is going to like the same things. You're of the philosophical opinion that there are some pieces of art that everybody must consider to be a masterpiece. I'm not of that philosophical opinion. So arguing about this is pretty senseless.

 

[Jarvis323]

Also, if maths and science are arts, I'm not sure what isn't art. Is there anything that you would definitely consider not to be art?

Consider the comparison of Beethoven and a garage punk rock band. Which of these would you consider a more pure art? How about the difference between a sheet of randomly placed characters and a formatted page of meaningful text? How about an avant guard painter compared to a theoretical physicist? Is pure randomness art, or does art require some meaningful ordering? If art is something personal, does it not have that effect because you are an organized being and there are some things which ring true, or meaningful to you based on your organization? Maybe art is usually fuzzy enough that you don't know what exactly it means, but it has an effect. Some part of your mind sees something coherent in it. In a way, you could consider what we typically call art, a form of mathematics by where the expression is sufficiently vague and the axioms sufficiently general that it can be assigned many different meanings, and does not make any specific single statement. The way I think about it, the purest end of this spectrum is mathematics based on simple and clear axioms, and the most diluted end of the spectrum is pure random noise.

In essence the argument I am making is that nature is the true source of art, and there is no more pure description of it than mathematics. The purest artist is then one who more purely expresses the patterns and organization in the natural universe.

 

[PeroK]

To consider your own argument, would an Arts college fund you for a blank score? Do you think they should? If you went to a music concert and they wouldn't playing because their score was blank, would you be satisfied? Apparently the people at the John Cage concert were, but I sure would be quite angry. I don't think a blank music score is art.

Mind you, art is personal. If you say a blank music score is art, then all power for you. But I'm not very interested in that kind of things anyway. So for me personally, it's not art.

I don't see what this discussion is good for really. Art is something personal. Nobody is going to like the same things. You're of the philosophical opinion that there are some pieces of art that everybody must consider to be a masterpiece. I'm not of that philosophical opinion. So arguing about this is pretty senseless.

Okay, no problem, although I'm sure I never said half those things you ascribe to me! The John Cage piece I posted to show the absurdity of much of modern art, which I described as a "confidence trick". I could have posted a Rothko, Jackson Pollock or an extract from Ulysses instead.

I thought this debate was quite interesting, because I think the initial "maths is art" debate starts by imagining it's putting maths on some sort of pedestal of undoubted value and quality. But, in fact, works of art have only a subjective value.

In general, maths and science have a well-defined, instrinsic value; whereas, art has (only) subjective value. That might be the critical difference.

A blank sheet of music is art, because essentially art has no rules. It's not my opinion: Cage's work is out there on the concert schedules; Rothko's work was at the Tate Modern a couple of years ago. Ulysses topped a poll of the greatest novels of the 20th century.

 

[gleem]

In general, maths and science have a well-defined, instrinsic value; whereas, art has (only) subjective value. That might be the critical difference.

I would bet that scholars would disagree with you on the value of art to a society. Not a monetary value of course. It has intrinsic value and runs deeper than that of science and math. Man can (has) live(d) without science and math but it seems he cannot live without art. I would say that math and science stem from the same origin as art, the need to create and find fulfillment.

 

[PeroK]

I would bet that scholars would disagree with you on the value of art to a society. Not a monetary value of course. It has intrinsic value and runs deeper than that of science and math. Man can (has) live(d) without science and math but it seems he cannot live without art. I would say that math and science stem from the same origin as art, the need to create and find fulfillment.

I didn't mean that art has no value - far from it - but the criteria by which art is judged are necessarily subjective (in terms of the quality of the art). Even a simple example like doing an English Literature degree as opposed to a maths degree. Is David Copperfield a classic? Or, Rebecca? There's no right and wrong answer. Whereas, Maxwell's equations are objectively one of the peaks of 19th century physics.

 

[gleem]

but the criteria by which art is judged are necessarily subjective (in terms of the quality of the art).

This tread has migrated to math as art. G. H. Hardy (British mathematician) said "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.". So we have some math documented of no practical use.

The term 'art" is is often taken too narrowly. Mathematics is sometimes interpreted as just being mechanical going from one step to another according to some plan, like staking bricks one upon another. Frank Lloyd Wright "stacked bricks" and artfully so. Are not His buildings considered art? Art is the conscious use of skill and creative imagination to be appreciated for their beauty or emotional impact . Doesn't mathematics have that affect on at least some of us ?

From Paul Lockharts book "A Mathematician's Lament"

So let me try to explain what mathematics is, and what mathematicians do. I can hardly do
better than to begin with G.H. Hardy's excellent description:

A mathematician, like a painter or poet, is a maker
of patterns. If his patterns are more permanent than
theirs, it is because they are made with ideas.

So mathematicians sit around making patterns of ideas. What sort of patterns? What sort of
ideas? Ideas about the rhinoceros? No, those we leave to the biologists. Ideas about language and culture? No, not usually. These things are all far too complicated for most mathematicians' taste. If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful. Mathematicians enjoy thinking about the simplest possible things, and the simplest possible things are imaginary. . . ."

 

[PeroK]

This tread has migrated to math as art. G. H. Hardy (British mathematician) said "I have never done anything 'useful'. No discovery of mine has made, or is likely to make, directly or indirectly, for good or ill, the least difference to the amenity of the world.". So we have some math documented of no practical use.

The term 'art" is is often taken too narrowly. Mathematics is sometimes interpreted as just being mechanical going from one step to another according to some plan, like staking bricks one upon another. Frank Lloyd Wright "stacked bricks" and artfully so. Are not His buildings considered art? Art is the conscious use of skill and creative imagination to be appreciated for their beauty or emotional impact . Doesn't mathematics have that affect on at least some of us ?

From Paul Lockharts book "A Mathematician's Lament"

Let me ask you then. Is there any human endeavour that is not art?

 

[gleem]

Let me ask you then. Is there any human endeavour that is not art?

Art is more than pictures, statues, vases certainly it includes music, poetry, literature, and architecture. Anything done creatively and skillfully and appreciated by other for its execution can be considered as art. why not conversation, not necessarily for content but for engagement. or debate (not political) for tactics. So yes many other human endeavors can be considered art. What is not art? To me activity following mundane procedures is not art, Certainly most human activities are not art.