Will we actually turn ourselves into Venus? — Xtrix

That would require a lot of neoliberals having absolute power to push industries not complying with climate goals. — Christoffer

Oh oh. Put on your mask when flying through those clouds of sulfuric acid.

Universal cooperation is a pipe dream. Also the idea that we can quickly de-carbonize is a fantasy it seems. The "political" part of the problem is the promulgation of impossible targets, — Janus

I agree. Best to do what we can, and prepare for the inevitable. If I were to be around for the next couple of hundred years I suspect Colorado will become like current day Las Vegas environment, largely vacated as people pack up and move to Canada. Miami may survive as a kind of Venice.

As an Independent searching for the illusive middle ground my choice would be Harold Ford, Jr

Please settle on an icon. I'm dizzy watching them come and go. :gasp:

There is no point at infinity in the complex plane. That point is by definition outside the plane. To allow it in is to break the rules of the structure. There is no north pole in the Reimann sphere — Metaphysician Undercover

This is why zero, like infinity, has no place within ordinal numbers, and must be excluded. — Metaphysician Undercover

I admire your certitude. It must be nonplussing to watch the world of science evolve using a flawed intellectual mechanism. :confused:

Both S and T are indeed sets of numbers that are generated by the formula to the right of the ":" symbol. The summation symbol is just shorthand for plus after plus .....

Perhaps you might just stick with the archaic terminologies of infinity (potential & actual) and avoid "bounded".

This is an essay in philosophy, not mathematics. Don't worry about it. It's your project. I'm still unsure of what PoR is, other than a sort of linear process that goes from previous to following. I'm not your target readership. I have enough trouble trying to keep up with a very minor PoR in a certain low interest math topic. :cool:

If all I see is symbols, the me that is trying to learn, screams and runs away. Does that make sense? I would like to break through that barrier and be able to understand the language of symbols. — Athena

Interesting you should say that. I still do minor research and write short notes. Just last night I was dabbling with my current project and the thought came to me, All I'm doing is moving symbols around. The create/discover part of the process was missing. :chin:

Later: An idea came to me and now the symbols have meaning. :cool:

Climatologists do speak with such confidence, just not in their scientific papers. https://www.google.com/amp/s/www.nytimes.com/2016/09/04/science/flooding-of-coast-caused-by-global-warming-has-already-begun.amp.html — Benkei

Paywall restricted.

↪jgill

It is mind-blowing if you're into that stuff, but I'd say it's not at all surprising — Metaphysician Undercover

One of the strangest elementary features of the complex plane is the point at infinity. No matter which direction you go, if you keep moving outward, like beyond an expanding set of circles centered at zero, you approach a "point" at infinity. This is "true" since whatever is out there corresponds via projection to the north pole of the Riemann sphere. :cool:

Moderators: How do I eliminate multiple posts?

T is countable, infinite, bounded above and below.
This one is confusing me a bit, as I don’t see how it is bounded above. — Bob Ross

Bob, when one expands the sequence:

${{t}_{2}}=1+\frac{1}{{{1}^{2}}},\text{ }{{t}_{3}}={{t}_{2}}+\frac{1}{{{2}^{2}}}=1+\frac{1}{{{1}^{2}}}+\frac{1}{{{2}^{2}}},\text{ }{{t}_{4}}=1+\frac{1}{{{1}^{2}}}+\frac{1}{{{2}^{2}}}+\frac{1}{{{3}^{2}}},\cdots ,\text{ }{{t}_{n}}=1+\sum\limits_{k=1}^{n-1}{\frac{1}{{{k}^{2}}}}\lt\infty$

a line segment from the interval [0, 3] inclusive would be a bounded finite — Bob Ross

The real numbers constituting [0,3] are uncountably infinite, but the set of these numbers is obviously bounded above and below. This would of course be a finite line segment.

the problem would be that any “unbounded” f(n) one could provide is bounded to the, in toto, concept of that two-dimensional spatial graph. — Bob Ross

No. S is unbounded above, and if one plots a graph of the terms of S (vertical axis) vs n (horizontal axis) one would need a piece of paper having infinite dimensions. However, the sum of that series diverges so slowly that the sum of the first 6,000,000 terms is less than 21 !

This does not sound like MAYAEL — L'éléphant

I agree. I wonder if his TPF account was hacked?

In the Euclidean or complex plane what happens in the vicinity of zero can be far more mind-blowing than MU imagines. In the complex plane the function $f(z)={{e}^{\frac{1}{z}}}$ exhibits a bizarre behavior in that, for any complex value, w, and within any tiny circle centered at zero, there exists an infinite number of values of z such that $f(z)=w$.

Edit: Whoops, gettin' old. There are two points that are exceptions: zero and infinity.

Zero is an essential singularity of this function.

Oh dear! What can you tell me about the 1960s-1970s math education failure? — Athena

New Math

As an Asst Prof in the early 1970s, I had a colleague whose office was a couple of doors down the hall. He was a retired Army colonel with an MA in math, and he taught some of the remedial and freshman courses. One day, early in the semester, he burst into the department chair's office, red in the face and clearly angry,"What is this shit!? Why prove a*0=0???" We were using Vance for College Algebra and there it was in chapter one. I was less vocal, but I too found it ridiculous to toss bits of math foundations into a more or less utilitarian course.

Proof: a*0=0

Note in the Wiki piece that Time magazine called New Math one of the 100 worst ideas of the twentieth century. :cool:

Most mathematicians seem to just take zero for granted, with zero understanding of what "zero" means. — Metaphysician Undercover

How true. It means nothing to me. :sad:

Perhaps I didn't read far enough, but the person mentioned that believed negatives were greater than infinity was John Wallis, who actually did accept them, but thought so because dividing by 0 gives infinity, and going smaller would have to mean going past infinity. Strange indeed. — Jerry

You are correct. This is revealed on page 253 from a work by Wallis in 1655. My reference is later in the book, page 593, concerning what Euler thought in 1750+.

It seems we accept negative numbers now on a similar footing as whole numbers, but complex numbers are still pretty hotly debated as to whether we should consider them as real as the real numbers. — Jerry

Good point. Apokrisis mentioned this in a previous post, regarding Penrose's fascination with complex numbers.

Is there no insight to be gained by understanding why the idea of a negative eluded such minds for so long? — Jerry

A very good question. Might this understanding help in current studies in QM? Are there blind spots in our conceptual apparatus that prevent us from comprehending quantum entanglement?

On the other hand, would this be yet another philosophical journey into the past, analyzing what others did centuries ago, but with no relevance to the modern world?

I wouldn't count on broad support from the mathematical community for such a quest.

Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity. — jgill

Can I ask you where you got this from? — Real Gone Cat

Mathematical Thought From Ancient to Modern Times, Morris Kline, Oxford University Press, 1972

The first culture to do math with negative numbers was the Chinese and they didn't have the concept of 0. I wonder what their definition of negative numbers was — Agent Smith

Actually, the Hindus about 628 introduced negative numbers to represent debts. Positive numbers represented assets. Euler, in the latter half of the 18th century still believed negative numbers were greater than infinity.

(I can't wait to see all the action when you guys move on to FRACTIONS :scream: )

Inflation isn't important and isn't a problem. — Xtrix

Tell that to my fellow senior citizens on fixed incomes. :roll:

The takeaway from negative numbers is that one should stay positive about them. Don't despair, just add a minus here and there. As if they care!

So, it's called the Inflation Reduction Act because it was cut down so much from the original bill that would have been the Inflation Enhancement Act?

The terminology (i.e., potential and actual) are misleading (as a potential infinite is not merely potentially limitless in content) and, therefore, this distinction shall be hereon depicted as “bounded” vs “unbounded” infinity.

Here are commonly accepted concepts and notations:


$S=\left\{ {{s}_{n}}:{{s}_{n+1}}={{s}_{n}}+\frac{1}{n},\text{ }{{s}_{1}}=1,\text{ }n=1,2,3,4,... \right\}$


$T=\left\{ {{t}_{n}}:{{t}_{n+1}}={{t}_{n}}+\frac{1}{{{n}^{2}}},\text{ }{{\text{t}}_{1}}=1,\text{ }n=1,2,3,4,... \right\}$


$I=\left\{ r\in R:0\le r\lt1 \right\}$


$Y=\left\{ q\in Q:0\le q \right\}$


$X=\left\{ 1,2,3 \right\}$


S is countable, infinite, unbounded above but bounded below.
T is countable, infinite, bounded above and below.
I is uncountable, infinite, bounded below by its greatest lower bound, which it includes, and above by its least upper bound, which it does not include.
Y is countable, infinite, bounded below by its GLB, which it includes, but unbounded above.
X is finite and bounded above and below.

I suggest either using "bounded" and "unbounded" in their proper sense or defining other words to express what you mean. For example, S and T could be called something like scripted infinities, whereas I and Y would be unscripted infinities. But other mathematicians might disagree. If one has any math training it is disconcerting to read your definitions.

Rolling dice and recreating a biological being are not comparable. Sorry, I'm not convinced. Maybe others are. Kind of a blend of metaphysics and quaisi-probability.

Superposition by definition means that the two states measurably interfere with each other . . . — noAxioms

It doesn't seem so outlandish if one sticks to the mathematics: solutions of Schrodinger's equations are linear combinations of one another. One of these crops up upon measurement.

Do you want to provide some of those categories on the chance of conceiving me? — Athena

My dear lady, that was done long ago. Regardless of categories. :cool: — jgill

OH come on. I was looking forward to a better answer. — Athena

:smile: :smile: :smile:

My favorite math professor loves math and he gets so excited when he talks about it. He makes comments such as "cry for the joy" of the math principle he is talking about. I don't think he needs anything else in life other than his joy of math and sharing it — Athena

I'm not sure I've known a colleague becoming that euphoric, but it is a really good feeling when understanding dawns. It's mostly a game of exploring concepts. But I only taught at the college level and know little of techniques used in K-12. However, the modern math movement supported by university mathematicians during the 1960s and 1970s was a failure - I ventured into it when I taught a freshman algebra course. For a few very motivated students it worked well.

As to motivation, part if not most may have to come with genetics, like musical talent.

If you have an infinite number of universes in continuous space that are the size of our observable universe, that means that inflation will inevitably end up creating indiscernible copies of our exact universe — Count Timothy von Icarus

This is like monkeys typing Shakespeare. It doesn't seem impossible, but "inevitable" is a stretch.

Do you want to provide some of those categories on the chance of conceiving me? — Athena

My dear lady, that was done long ago. Regardless of categories. :cool:

Wikipedia Mathematics Articles

I'm of the opinion that magick should be taught in public schools. — Bret Bernhoft

The word "Magick" was coined by Aleister Crowley as he developed his religion of Thelema. It means true magic in the archaic sense and not parlour tricks. How would you teach a topic for which there is no evidence it exists in the physical world?

I've avoided Castaneda because I've read that the books were largely shown to be fictitious — Noble Dust

Yes, that may be so, but when one avoids the drugs and reads carefully there are jewels of wisdom there. His instructions for what he called the Art of Dreaming are spot on and worked on my first attempt, providing an astounding experience that has stuck with me for half a century.

Currently I am reading Born to Climb: From Rock Climbing Pioneers to Olympic Athletes, by Zofia Reych. A beautifully written account of one of the fastest growing leisure sports and a young woman's journey along an existential path.

What should I live for or how should I live? — rossii

It would help if you would say where you are in the spectrum of ageing: twenties, thirties,...

When I was in my twenties, evading the Union Army as it burned Atlanta, I became an existentialist, realizing there is no divine purpose to life. One must create meaning. It then becomes a task to do just that and one begins the search having a purpose.

Lemonics improves with age. Amazing, something that gets better the older you are! :cool:

So what are your thoughts here when one direction looks to track the "deep maths" of Nature and the other choice may be just unphysical pattern spinning? What do we learn if this is the case? — apokrisis

Motivations vary in the mathematical community. What is common, however, is the drive to explore, sometimes with regard to the mysteries of nature, sometimes within the discipline itself. I'm a spinner.

But am I right that you argue the complex plane has lessons in terms of the physics of chaos - patterns of convergence~divergence? — apokrisis

I don't know about the physics of chaos (other than my experiences as a meteorologist ages ago), but the patterns that appear as examples of weak emergence are fascinating.

what would happen if physics were re-written in the language of intuitionistic mathematics? Would time become “real” again?

Since computations are done on computers with computable numbers and functions, isn't that already the case? The notion that a non-intuitionistic approach damages the idea of time seems ridiculous. A purely philosophical tragedy.

But Gisin points out that intuitionistic mathematics could offer a natural way out of the deterministic lockup.

I've never known a fellow mathematician who claimed to be an intuitionist. The fact that all functions from [0,1] to R are continuous from that perspective is quite unappealing to someone who came up in classical analysis. (Yes, it depends on the definition of "function"). Equating the flow of time with adding more digits to a number seems a bit absurd, at least for me.

Zoom in on your complex plane with its pattern of curl, and do you start to lose any sense of whether some infinitesimal part is diverging or converging? — apokrisis

The complex plane itself doesn't have a pattern of curl. It's a vector field based on a complex function that does the job. I have zoomed in up to 10,000X to display fascinating objects purely from curiosity. In the vicinity of an attracting fixed point, no matter the magnification, one sees convergence. It's just a matter of how one writes the computer program.

One can ask again whether maths made the right pragmatic choice even if Peirce is the metaphysically correct choice? — apokrisis

I admire Peirce for his thoughts on nonstandard analysis. I once toyed with the idea of teaching a real analysis course from that perspective, but gave it up when a friend at a larger university did just that, with poor results. I find it a bit amusing that when one looks at the standard graphical depiction of a mathematical Category, one sees Peirce's Triangle.

. . . almost everyone has a problem with your views of infinity. Now we may all be wrong, and you may be correct. But is it necessary at this time to focus on the infinite as such, or can this be shelved or stated another way that allows your readers to focus on the first premise they can readily accept? — Philosophim

:up:

In India, it seems religion and math went hand in hand. — Athena

That's an amazing article on Indian mathematics on Wikipedia. Ramanujan, of course, was one of the great geniuses in math. When I was a math prof I would be asked occasionally to teach the survey course in mathematics history - a task none of us relished since no one had the necessary background. It would have been an enormous help had Wikipedia been available!

How do you guess mathematics might have evolved had it not been for the Romans and Christianity? Or, is it the teaching of math to school age kids that you think should be different? My wife is a retired HS English teacher and she made the same remark about coming up with the right answer without going through all the steps when she was a student. :smile:

↪jgill

I put a lot of effort into these posts. If you don't have anything substantive to add, please go to a different thread. — T Clark

Sorry. I was feeling frivolous after reading the sandwich vs hotdog thread. :sad:

Ogg Eep did in 100,000 BCE — T Clark

Alley Oop, perhaps?

You guys need to stop joking and start chomping away at this mouth-watering question at the heart of philosophy. :chin:

Thanks for the link. Nice paper. I have Penrose's massive book, but have only read bits and pieces. The rotation/translation bit makes sense, although my knowledge of modern physics is weak. I have, in fact, done a fair amount of research involving Moebius (or linear fractional) transformations (that crop up in these physics discussions), but going the pure analysis direction in the complex plane rather than the geometries coming off the Riemann sphere. A non-terminating continued fraction - a kind of analogue of an infinite series - can be perceived as an infinite composition of such transformations (as can a series).

(We were speaking of fixed points before. I introduced the idea of accelerating the convergence of limit-periodic CFs through the use of attracting fixed points of LFTs back some years ago.)

. . . exemplifies a confusion which lies at the heart of philosophy — hypericin

Wow! That came out of nowhere. :yum: And to think some say that philosophers only look backward.

The mystical and math go very well together and I think the Western mind is biased and this bias is like blinders that limit the consciousness of the Western mind. — Athena

There are about 24,000 math topics on Wikipedia, many if not most by "Western minds". That doesn't sound like the Western mind is terribly limited.