Mathematics is commonly classified by philosophers as a form of art — Metaphysician Undercover

You and I have our differences, but here I am more or less in agreement. Mathematics is a practice, a device used by the sciences, etc., but mathematicians would largely agree it is a kind of art, requiring imaginative progress - the canvas upon which I apply my mental brush is the complex plane.

As for failure in mathematics, le mieux est l'ennemi du bien.

I am a leftie democratic socialist Mr Gill, I hope that does not lower your opinion of me too much. — universeness

Wife & I are still registered Democrats. You might be surprised at where we would agree on politics. For example, I have always felt there should be free education all the way to professional degrees and PhDs, and there should be free health care for all. I firmly support Medicare and Social Security, along with defined benefit retirement plans. The USAF made me a meteorologist at the U of Chicago, free of charge and fully financially supported, then, later, the GI Bill helped with my terminal degree. :cool:

But our country's immigration catastrophe and a few other issues, like overly liberal law and order policies, pull us to the moderate right at times.

OK. So much for all that. My opinion of you is very, very high, Buddy ! :smile:

This is huge — Wayfarer

It will be overturned by the Supreme Court. I know you think it is justified for this person, but even some Democratic strategists are calling it a step too far. A Democracy in which one cannot vote for a popular candidate of a major party because the reigning opposing party won't even allow his name to be penciled in on the ballot?

Hey, I love Bret Baier ! :cool: — jgill

I just learned who that is and I hope this is fake news. :joke: — Jaded Scholar

My wife and I usually vote moderate conservative these days, and we both enjoy the evening news with Bret. A tilt to the right, but maybe less than CNN's tilt to the left. The Fox commentators is another matter. Hannity and his ilk are way off my radar.

It's a program/programming language that is basically C, but combined with some Java to build higher-l — Jaded Scholar

I meant the complex plane, C. Not a programming language. And I'm actually talking about

${{F}_{n}}(z)=\underset{k=1}{\overset{n}{\mathop{\Re }}}\,{{f}_{k}}(z)={{f}_{1}}\circ {{f}_{2}}\circ \cdots \circ {{f}_{n}}(z)$ , $F(z)=\underset{n\to \infty }{\mathop{\lim }}\,{{F}_{n}}(z)$

And going the other way, as well, in physics (mathematical) research? A contour in C looks like $z(t)=u(t)+iv(t)$ , t = time.

Oh, man. If Trump would just employ the mechanism most of us have that mediates between what pops into consciousness and what comes out of our mouths . . .

What a choice upcoming. I cannot forgive Biden for ignoring the border crises.

I'm glad that the only thing I've ever experienced on this front is when physicists semi-jokingly check the room for mathematicians before writing (Δx)² ≈ 0 or sin(θ) ≈ θ for θ<<1. — Jaded Scholar

Hey, I use that. The wiggle makes it true. :smile:

Your discussion with Uni is the best thing I have seen on this site.

turn this site into something akin to fox/fake news — universeness

Hey, I love Bret Baier ! :cool:

Just off the top of your head, can you think of instances where complex functions are composed? I appreciate your comments about string theory and spin in that subject, in particular. I'm looking into compositions of contours in C and I have wondered about compositions of strings.

Physical impossibility is admittedly just a possibility for us; we are epistemologically limited, so we don't know with certainty whether anything is physically impossible or not — Janus

We are limited by what we do not know that which we do not know. What is beyond our realm of perception is to some extent beyond our realm of conception. As my late algebra student, my Corgi, Jake, would attest.

It seems professionals in science or math become uncomfortable in this environment. My own experience is my first thread about the diagonal paradox, to which there were some negative replies going beyond mere analytical comments to what seemed personal attacks. But, at least in those days science or math topics were not relocated to the Lounge.

At that time there were a couple of grad level math people here, but after a while they experienced the fatigue of constantly arguing with members who were minimally acquainted with the subject, but held strong views against accepted perspectives. When the competent are belittled by the unknowledgeable the former tend to move on to other conversational pastures.

I'm so old I don't really care. When MU pops up with his highly literate arguments about mathematics I indulge and appreciate his perspective if I can. But I also know that if I open my TPF mouth about QT I wander into unknown territory and my thoughts are trivial.

If those who wished to argue science were Gentlemen, like you my friend, or Ladies, some of those who left might have stayed. But this is all conjecture. And philosophy is all about argument.

The mathematics supporting quantum mechanics is entirely logical. But, although there are various metaphysical interpretations of QM, are there metaphysical analysis of this particular math structure?

The metaphysics of mathematics seems to be the existence of a mathematical object in a mathematical structure. Not the structure itself.

If quantum theory becomes philosophically stable at some time in the future all this stuff that spins off its mysteries will probably become scientific ectoplasm.

I just heard a pin drop. :yawn:

Is risk vs reward a proper philosophical subject? I don't see much here to indicate it is. The world is full of stories of those who have succeeded in risky ventures. We learn from these tales, and they may help us as we toil away at life. But, is there a philosophy of risk taking?

What did Aristotle have to say?

Hunter is becoming legendary. An Errol Flynn for our political age, sailing the American Main. Like Trump, the more he is pummeled the more he is admired. Pay attention, GOP !!

Yes. Impeachment effort seems ridiculous. Especially since Trump leads in the polls.

Prepare yourselves for a second Trump term as President. Borderless Biden has been asleep at the switch too long. Financial crook or senile elder?

There is no Purpose Fairy flying around at night, dispensing reasons to live. You have to find your own. — Vera Mont

:up:

Try to come to grips with existentialism. There must be something that gives you pleasure. Discover paths that lead from that activity, even if it is an activity hardly worth mentioning to others. Use your imagination to illuminate and create value with obscure discoveries. What is tiny can become big.

The interplay of different kinds of risk you report sounds scary. My inner OSHA supervisor is trying to steer me in the other direction. — Paine

Alex Honnold starred in the Oscar-winning film "Free Solo" and became the world's most famous rock climber. He epitomizes a certain justification of controlled risk in the climbing community, although he lost several sponsorships in the process. His spectacular accomplishment was supported by considerable practice and an innate ability to confine emotion to allow near physical perfection - a degree of calmness not seen often in that community or society in general.

I propose "curmudgeonlogy". — wonderer1

Finally, A breakthrough on TPF, an original philosophical path that must have the amateurs and professionals here salivating! I can imagine dust blown off ancient texts searching for what Aristotle had to say on the subject - if anything at all. :cool:

Intervention by means of a mean old person . . . — Paine

the roster of mean old people — Paine

What's with this categorization? Is there a name for a philosophical study of "mean old people"?

The philosophy of risk should be the psychology of risk. As a former rock climber for over fifty years I have observed the interplay between physical risk and reputational risk.

but you do wonder why they don't incorporate a 'maths module' based on something like Mathematica, — Wayfarer

This should work for definitions and examples and evaluations of certain complicated computations. As to reasoning and the guess work that goes into problem solving I'm a little pessimistic. How do you program creativity? I am currently looking into compositions of contours in the complex plane, and finding ways to compose that violate standard usage of the term as well as more conventional approaches. Mathematica is a machinery for what I come up with. Just a trivial example.

There's no middle ground between existing and not existing. — RogueAI

There's the problem, whether regarding the moon or a quantum particle. Were philosophical terms defined more clearly some threads would vanish. Exist physically, or exist metaphysically? One or the other or both or neither? Then there are those damned probability waves, always collapsing like snowcones on a summer day just because we stare at them.

The moon shows a tendency to persist when we look away.

So mathematically, you can create an nth dimensional array, and such an array would exist in reality, but cannot be geometrically displayed in 3D — universeness

Done all the time: n-dimensional vector spaces. I think the Hilbert space ( a special kind of vector space) in quantum mechanics may be infinite dimensional. Then some kind of linear operators are defined on it.

If pushed, would a mathematician be willing to say something such as 'well you could think of the 'imaginary number line,' as in a sense, 'wrapped around' every coordinate in a standard 3D coordinate system, such as (x,y,z), or (x,y,z,t), t being time — universeness

Sure. There are no limits to how bizarre math can become. This doesn't seem so outlandish.

Some physicists, like Smolin would say that string theory is done — Metaphysician Undercover

:up:

Spacetime, therefore, is not all there is to reality. — Wayfarer

Would you want this on your tombstone? :smile:

No matter matter who, the important difference is Unlike topological dimensions, the fractal index can take non-integer values, indicating that a set fills its space qualitatively and quantitatively …‘

-Fool — Bella fekete

I'm not following you. But that's OK, I am not a philosopher.

Here is what I think is a very good way to look at these two planes — Metaphysician Undercover

An entertaining and fanciful philosophical abstraction of a bit of mathematics. But we are looking at two lines, not planes. The real axis and the imaginary axis - producing the complex plane. :cool:

This comparison is actually grounded on an inverse topological layout — Bella fekete

I take it you use "topological" loosely, like some use "fractal" - both well-defined mathematical terms.

That series of conjectures is more convincing than not even by the progression within this here forum, of the con-foundation of intended disposition — Bella fekete

??

I don't know if you can accurately say that is "the world". Isn't it more like two distinct perpendicular worlds, the world of real numbers and the world of imaginary numbers? — Metaphysician Undercover

It's a world in which a being embodies the characteristics of two genres, the rational and the imaginative. A bit like mankind.

Thanks for the links. Particularly the one concerning a reduction of ST dimensions to two at quantum scales.( I continue to dabble in the complex plane where the world is two dimensional.) :cool:

I must say I find most of this fairly much incomprehensible — AmadeusD

We need not objectify the self so that we share definition completely. — Vaskane

A clue

But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

What makes these "problems" unsolved and real? :chin:

But when you approach these problems, Zeno's paradoxes for example, and the irrationality of pi and the square root of 2, with the attitude that these problems have already been solved, you do not look at them as real problems — Metaphysician Undercover

Work-arounds were in existence 3,600 years ago and have improved over the eras since. And, yes, 2,600 years ago there was considerable dismay among the ancients. You have confirmed what is seen frequently here that when one turns philosophical on an issue one goes back in time to see what the Greeks had to say, and to join them across the ages in their despair.

I would think intuitionism might appeal to you. But even there the obvious imperfections are swept into a corner and allowed to exist.

Out of curiosity, are you an old guy like me, middle aged, or a "youngster"?

Just filling in space until JS reappears. :cool:

I am not a mother, but I was "Mr. Mom" back when this was either a joke or something seen as suspicious or wrong. — Fooloso4

For darn sure women's lib changed my experience of being a woman. I crashed from being a Mother Goddess to "just a housewife". — Athena

I supported Womens' Lib and that resulted in me becoming "Mr. Mom" - a single parent - for a while. But life moved on in unexpected but welcome ways.

Don't look back. Something might be gaining on you.

I think I have mentioned before, but I wrote a Wikipedia page on an obscure mathematical topic a few years ago. Recently, when I asked chat about that topic it replied with the first paragraph verbatim from Wiki. I guess I was flattered, but it is a low priority math topic. :cool:

As noted, I've used ChatGPT since day one, it's become very much part of my day-to-day. — Wayfarer

I use the Bing version of AI chat, but it's been disappointing. On some historical issues it simply reprints paragraphs from Wikipedia. Two days ago I asked about a fatal accident that had occurred in a nearby community, and it came back apologetically with no results. I then Googled the accident and it came up on top of the first page.

Moreover, one of the reasons for modern mathematics no longer being merged with the field of physics is that - as I also mentioned previously - assumptions and value judgements about physicality or "reality" are outside the field of mathematics, which is now primarily directed with finding and fleshing out any and every mathematical system we can think of — Jaded Scholar

Some time back on this forum I mentioned that October of 1958 when I started a postgraduate curriculum for the USAF at the U of Chicago I found that the mathematics department would no longer offer courses to the physics department, the latter offering all physics math courses. The rift went beyond the obvious differences in notation and symbolism (which I find annoying and distracting) and probably had something to do with differing attitudes about proofs. And the foundational stuff about mathematical systems.

I am an old guy, and when I go to one of 26K pages on math on Wikipedia I'm not sure what is being discussed. Even most of modern complex analysis seems foreign.

I enjoyed reading your rebuttal to MU. Amusing and entertaining, unlike so much on the forum that rehashes and compares what classical philosophers had to say.

Born in Alabama. Naturalized Coloradan. High Prairie.

What happens when an observation is made is that those probabilities ‘collapse’ into a precise measurement. — Wayfarer

An analogy I've used before is that a differential equation (like the Schrodinger equation) may have a multitude of solutions, one of which suits the experiment being performed. Upon measurement one of these is determined to be be correct. No "collapse". But my analogy may be incorrect.

.there’s no mention of the word ‘fractal’ anywhere in it. I don’t think it supports the argument you’re making — Wayfarer

Pop science usage seems to be anything that is wiggly and is wiggly upon magnification. Mandelbrot's creation carefully derived in the complex plane is another matter. Maybe other pop usages as well.

No evidence our cells are intelligent?!!! — ken2esq

OK, this guy is legit. A lot depends on how intelligence is defined, at least for me. Do cells think as well?

The Levin Lab:
We work at the intersection of developmental biology, computer science, and cognitive science. Our goal is to understand degrees of intelligence at multiple scales of biological, artificial, and hybrid systems; we use these insights to develop interventions in regenerative medicine.

In high school in the 1950s in Atlanta I had a course in civics. Is that what you were talking about? Also world history. But emphasis was on science and math. I was a major in high school ROTC, and our Army officer in charge, a captain, was an alcoholic. Baby steps toward a Military Industrial Complex?

The fractal nature of our biology doesn't quite work the same way. — Vaskane

Thanks. I learned something.

Abstract

Fractal geometry allows structures to be quantitatively characterized in geometric terms even if their form is not even or regular, because fractal geometry deals with the geometry of hierarchies and random processes. The hypothesis is explored that fractal geometry serves as a design principle in biological organisms. The internal membrane surface of cells, or the inner lung surface, are difficult to describe in terms of classical geometry, but they are found to show properties describable by fractal geometry, at least sectionwise and within certain bounds set by deterministic design properties. Concepts of fractal geometry are most useful in characterizing the structure of branching trees, such as those found in pulmonary airways and in blood vessels. This explains how the large internal gas exchange surface of the lung can be homogeneously and efficiently ventilated and perfused at low energetic cost. It is concluded that to consider fractal geometry as a biological design principle is heuristically most productive and provides insights into possibilities of efficient genetic programming of biological form.

https://pubmed.ncbi.nlm.nih.gov/1767856/