Define an artist. — Brett

One who produces art.

I'm still fascinated by the concept of accidental art vs art. If I sketch an image that is pleasing to the eye, but I had no intention of creating art, that image is not art. However, if I sketch the same image, thinking, "this will be art", then it is. Heady stuff, indeed! :roll:

Plus without a background in metaphysics you'd be unlikely to recognise it for the proof that it is. — Bartricks

I know I am lacking the credentials, but please display this "proof." Others here may very well be metaphysicians and may be eager to process this information. Thanks. :nerd:

A god's existence can be proved, and God's existence can be shown to be more reasonably believed than not — Bartricks

Support this far-reaching pronouncement with a logical argument. Apply your favorite tool of reason, please.

But patterns are nothing more than what humans perceive is beautiful, regardless if infinite chaos can be contained in a mathematical system — Gregory

It might be best to avoid referring to mathematics in this regard. Mathematical chaos theory is a fairly well-defined, logical and coherent area of inquiry. It has to do with iterative systems in the complex plane initially. What does "infinite chaos contained in a mathematical system" really mean? I can generate chaotic behavior in a mathematical context by formulating a complex function and iterating it over regions of the plane. I suppose that's what you're getting at.

Experts on whether a god exists or not are metaphysicians, for it is a topic in metaphysics — Bartricks

You haven't proven that there are actual experts on the existence of god. You simply assert that if they do exist they are metaphysicists. I would concur, since in my opinion there are no experts in this regard.

So, if I had thought,"I'm going to do art" the first time and did exactly the same procedure, that first image would have been art? This is a tad more complicated than putting a brush to canvas. In my case the "brush" has a "mind" of its own.

Who else is an expert on it, then? — Bartricks

It doesn't follow logically that anyone is such an expert.

'Art is an expression of human consciousness. And art work is information about an artists consciousness and subconsciousness'

I'm no artist but it sounds good to me. Perhaps, . . . information from an artist's . . .

However, there is a way to "represent" all the the logical operations of set theory ONLY in terms of the objects and arrows of a category — Mephist

OK, now I see a real "use" for category theory. Nice presentation.

For example, many mathematical ideas are expressed as music, rhythm, harmony, etc.. This is a completely different way of expressing mathematical ideas, distinct from putting symbols and geometrical figures on paper — Metaphysician Undercover

You don't use symbols to express music? Well, one can play an instrument by ear I suppose.

Unless they are in areas like medical science, where experimental results frequently are in conflict, particularly over time. Then what do you do?

I was curious about post WWII art, so I searched. Here's an example of what came up (www.widewalls.ch):

"Art always responds in some way, and so the vantage points from which to observe it were polarized as well, which gave birth to a vast number of concurrent streams. Therefore, we can see the most obvious difference between the tendencies toward abstraction, suggested by the pro-democratic American high-culture, and the European post-war art, which fell under the slight influence of figuration and realism, propagated by the Soviet Union. And then, there was everything else in between: Pop Art, which employed aspects of mass culture (unlike Abstract Expressionism), Fluxus, as a Dada-derived anti-art nihilist movement, Art Brut or Outsider Art if you want, new realism in France, and all the other forms of realism, which emerged in Great Britain, Socialist Realism in the Russian Soviet Republic, etc. It seems that the post-war dunghill was a very fertile ground to start from, and lucky for us, some of the most ingenious artists were eager to make new history. Let’s see which of the paintings from this era of ambivalence and post-trauma could be the most pertinent ones, from today’s point of view, and take a quick survey of the most iconic artworks made in our recent history, in times of crisis which we cannot fully understand, but we could perhaps compare it to the crisis of our own."

↪Pfhorrest
You should defer to experts as a general rule, so long as they are talking within their area of expertise.
But when they're not, then you shouldn't. — Bartricks

Sounds reasonable. I think that pretty much sums it up. :cool:

I have not looked yet, but from your description of it being a computer program with the unintended byproduct being aesthetically pleasing, I would say it was originally not art, just aesthetically pleasing math, but that anything you create now with the program with the intent that it should be aesthetically pleasing would qualify as art. — Artemis

Thanks. But you should look.

And you are correct that I had no intention of creating art; what began to appear intrigued me, however. And being intrigued I experimented with different mathematical concepts and formulae. What then appeared seemed to me to be art, but it differed little from what inspired the process. So, non-art the first "accidental" time, but art afterwards?

Whether or not I consider it art is of little or no consequence. I have enjoyed experimenting and seeing what appears. I have several theorems that predict convergence of the procedure at many points in the plane, but the "art" comes up when I avoid implementing the theory.

The scientists, engineers, and others who use the mathematics force the existence of conventions which form the artist's medium. Then the mathematicians work with the existing conventions, and those conventions are a pollution to the notion of "pure mind art". — Metaphysician Undercover

"Conventions" ? Can you be more specific?

Although the physical sciences have influenced quite a bit of mathematics, the intervention in the artistic process of mathematics as a medium that necessarily pollutes "pure mind art" is debatable. How does pure mind art make it to the public domain? Must it always involve sculpturing with one's bare hands? Or painting with colored oils that are extracted from plants? Or wait, for a novelist, does it entail writing out one's work with a pencil?

Intention to create something that is aesthetically engaging in some way. — Artemis

Is intention necessary? What of my images? Have you looked? You seem well versed in art matters. Please comment.

↪jgill
I do not follow your meaning. I think we do indeed know art when we see it. Or rather, we know it when archaeologists see it.

So, some seem to think you only know something when you can define it, as if somehow reality were made of definitions.

I think we already have - via our reason - the understanding that the definitions are seeking to capture — Bartricks

What meaning? I agree with the , "know art when . . . " statement. Maybe that tells us art is only "definable" by one's subconscious? I'm not sure about your "reason" comment. Does reason lead to understanding in this context? I would guess not.

jgill You are an artist. I bet by varying the formula you could learn to control the patterns / colours produced. — Pop

Thanks for replying, but by gaining control I would inevitably reduce the complexity of the imagery; I've tried, but with poor results. The subconscious has more latitude.

The discussion seems to have steamed up about hypotheticals.

Come on Bartricks and Artemis, take a look. It goes to whether art must be intentional. A real, concrete example!

To expand the discussion a bit, I have written many math programs over the years in connection with my interest in infinite compositions of complex functions in the complex plane. In another forum (now deceased) there was minor controversy over whether imagery produced from this mathematics - and virtually unpredictable - was a kind of art, like fractals. One prof of anthropology insisted the imagery was indeed art, a product of my subconscious, and thus influenced my mathematical discoveries or creations below my levels of awareness.

Form your own judgments. What do you think? :

https://www.coloradomesa.edu/math-stat/documents/CoupledContourSystems.pdf

https://www.coloradomesa.edu/math-stat/documents/AWeakEmergenceNote%20.pdf

Just a comment from a personal perspective in an academic environment: for years before Fermat's Last Theorem was validated, math departments would receive putative "proofs" by novices. Sometimes these were well-reasoned, with current math concepts and procedures, but usually the full professor to whom they were addressed would pass them on to a graduate advisee with the instruction, "Find the mistake." And they always did.

Tulsi. You see what a dreamer I am — fishfry

It's a minor issue in the big picture, but, having served in the military years ago, I would prefer a CIC who has had some military experience. I like Mayor Pete and I like Tulsi (particularly since she demonstrates she can still do pushups! :smile: )

But I suspect Trump will pull it off after a disastrous performance by Biden in the final debate.

Thanks for the link! I keep learning things on this forum. :cool:

Mathematicians just dream up their axioms and principles for no apparent reasons, just because they are beautiful or something, so that the mathematical principles are somewhat arbitrary in this way, pure mind art. — Metaphysician Undercover

Lots of wiggle room in that "something." "Pure mind art" is good! :cool:

all attacks on religion would also apply to any subdiscipline in mathematics — alcontali

Category theory maybe. :smirk:

In conclusion, is chaos theory all bunk? — Gregory

You are referring to something other than mathematical chaos theory, which is not bunk IMO.

I understand art as an expression of human consciousness, and art work as information about the artists consciousness — Pop

I would extend that to include the artist's subconscious as well.

.. . . believe that mathematical principles are always developed for purposes, goals, ends, and therefore . . . — Metaphysician Undercover

Certainly some sort of goals, but not necessarily physical ends. To a large extent it's curiosity about "what comes next?"

Whew! Thought you were coming after me. I'm a retired mathematician who hasn't kept up with the highly abstract areas in a number of years. So I learn stuff about modern set theory from members like fishfry. I also still dabble in minor research, so I may quibble with comments about that topic.

However, I don't have much patience with arguments about foundations of math if the poster seems to have only a minimal knowledge of math.

I have no expertise in philosophy, although I may seem confrontational when I encounter words or concepts that appear to be poorly defined. :cool:

But now I am too curious: which theorems did you prove? — Mephist

I write math notes now as a hobby. Here's a couple :cool:

https://www.researchgate.net/publication/319057086_A_Primer_on_the_Elementary_Theory_of_Infinite_Compositions_of_Complex_Functions

https://www.researchgate.net/publication/324017489_A_Short_Note_Compositions_of_Linear_Fractional_Transformation_Forms

May I ask you a question? How does one come to know this material and not have heard of measure theory? — fishfry

Where does measure theory (surely not taught in high school) intersect any of this? I've used it in various integration processes, the most interesting being functional integration. And Feynman constructed his sum of paths integral in more or less that concept.

there is no definition of the "meaning" of a theorem, and many mathematicians (starting from Hilbert, I guess) think that there is no point in trying to identify the "meaning" as something different from a list of symbols. — Mephist

This must be a significant difference between what you do and what a research mathematician does. Recently I've proven theorems related to compositions of functions in the complex plane, and with each I have a deep feeling, a strong sense of meaning, about the result and how the result comes about. A lot of geometrical mental imagery coupled with the essence to which the symbols point - much like reading literature and realizing all those symbols describe something that stirs the imagination.

However, my theorems are not profound - strictly what Wikipedia calls "Low" interest! :cool:

Probably you think that I completely missed the "meaning" of what a mathematical proof is — Mephist

What you have said about proving mathematical theorems may be the way computers see the process, but most theorems are not proven by computer programs. I don't see the connection to anything I have encountered in theorem-proving. But I am retired and way behind the times in really abstract math. Maybe the world has changed in my absence. Maybe not. I appreciate your efforts to explain, however.

"I agree that that's not all."

Which has to take a prize as an understatement. Is most of your experience in computer science?

And then topos theory is abstract sheaf theory — fishfry

Thanks for saving me the effort of looking it up. That one sentence is enough for me. :brow:

but we do multiply by the product xy which is (-infinity)(+infinity). Is this where the problem occurs? — TheMadFool

Maybe so. :roll:

Yes, of course practically all "normal" proofs are short and all the computing power needed is a pen and a peace of paper. But in reality all computations can be considered to be proofs, right? You reduce an expression in a normal form following some rules (if it's a multiplication between integers the "proof" can be made automatically with a calculator). — Mephist

It depends upon what you mean by "short." Or "normal." In the area I'm most familiar with theorem proofs vary from a few lines to a number of pages in length. And a short proof may be of an extension of a theorem which required many pages of reasoned articulation. I would rather use a pencil than a pen, however, so I can erase my errors or scribbling along non-productive paths of thought!

When you say computations can be considered proofs I'm not sure where you are going. Proofs of what? And "reduce an expression in a normal form" - what's that? Mathematical proofs are rigorously reasoned arguments in logic in which concepts and relationships play significant roles.

There are occasional exceptions in which computers are essential, like the Four Color Theorem in combinatorics. And then mathematicians attempting to verify the overall presentation of proof and conclusion are stuck with verifying computer algorithms and assuming the computers running them do not produce computational errors.

"The correspondence between topology and logic instead, that's one of the most popular and ideas of today's mathematics!"

I'll have to check this out. I've been out in the pasture too long I guess. :worry:

Perhaps there is a little confusion about the symbols ${{0}^{+}},{{0}^{-}}$

They usually refer to approaching zero from the right (through positive numbers) or the left (through negative numbers).

. . . but mathematics need computations for proofs. — Mephist

I have conjectured and proven lots of theorems - some quite challenging - that do not require computations beyond basic inequalities and a little arithmetic of complex numbers. However, creating examples and imagery in the complex plane usually requires programming skills and a computer. So, even if not for proofs, computations are necessary in many areas of mathematics. :cool:

Just when I think I've seen the most :scream: math ideas presented on this forum, I am pleasantly surprised :smile:

(fishfry: how did you post that graph? Are you a forum subscriber?)

. . . all physical experiments are calculated with integrals over open sets. — Mephist

Huh? :roll: Really?? all?

One way to define "constructive physics" is simply to say, "it uses constructive mathematics". But definitions of the latter sometimes arise principally from avoiding the LEM. Another tack is to avoid non-computable numbers. Or simply to state that experiments must be conclusive in a reasonable finite amount of time. I'm not sure what you two are referring to here. But I haven't read all the thread.

This is a big, big controversy in current physics — Wayfarer

I'm aware of that. But I wonder if string theory might be considered a metaphysical subject amongst philosophers who are not necessarily scientists/mathematicians? And if so, if experimental evidence did arise, would this, technically, be considered metaphysical actuality?