On an uncrowded roadway I might turn the driving over to "George", who is a part of me. Sometimes George takes over when I back out of the garage and a few minutes later I wonder if he closed the garage door. Generally, George and I get along fine.

But George is not God.

I've got plenty of nothing — magritte

and nothing's got plenty of me!!!! :party:

How can a sphere be unbounded? — Gregory

Riemann sphere

↪Gregory
But maths treats infinity as a "discrete" whole. You have infinities of many different "sizes". — apokrisis

This certainly seems to be true of areas of math concerned with sets and/or foundations, and probably valid in other areas of modern, abstract mathematics including analysis. Although in my subject of classical complex analysis a specific point on the Riemann sphere identifies with infinity, I've never had to deal with a discrete whole infinity and think of unboundedness in the complex plane instead.

I believe that even when some middle phase is very evident and visible, but it gets traversed, there has to be some explanation as to why it gets traversed — SaugB

It is a victim of the momentum of time itself. Whatever that is! I suppose if time has a kind of mass, then the expression is not completely bonkers. :cool:

The Planck scale is the birth of the dialectical contrast between the reversible and the irreversible as an actualised physical reality. So Bergson was right about durations. Or if we are to talk about point-like "instants", then we have to recognise that they must already have this internal dialectical structure. An instant already marks the point where irreversibility AND reversibility have just entered the world as "a thing". — apokrisis

This certainly gives Planck time a new spin in my thinking. I've assumed it had more mundane characteristics in terms of light traveling a tiny distance and the four universal physical constants. I assume your first sentence above refers to an inability to measure below certain limiting dimensions.

So, how do we attribute existence to that traversed thing, ie, in our example, the orange between the yellow and the red? — SaugB

And how do we attribute existence to the moment in time at which that color exists? Does time flow in a continuum of instants? Or does it exist only in intervals? Bergson argued that time as we live it is in duration (durée réelle), and time for science is a matter of instants - allowing for the freezing of time for purposes of calculations, like instantaneous velocity. So the existence of "a traversed thing" is equivalent to an instant of time.

Peter Lynds had a paper published in the Foundations of Physics Letters some time back in which he proposed there are no instants of time. Some physicists thought his ideas were profound, while most others considered them rubbish. This discussion of time is analogous to dialectics concerning the existence of irrational numbers.

There is new evidence that the so-called laws of physics aren't even constant throughout the universe. You're part of the old school, which is just now beginning to get bumped out. — JerseyFlight

The possibility that certain constants in those laws might vary a bit in space and time does not mean physical principles are endangered. There remains quite a bit of orderliness in nature.

. . . what if symmetry isn't part of the equation, what if we are discovering chaos? — JerseyFlight

We must stay calm. :gasp:

Thanks. Wish I knew more about modern physics.

I took a year of physics in college 65 years ago and of course used some of the elementary ideas in calculus courses I taught. The group SU(2) is as close as I get to contemporary physics as it concerns 2X2 matrices of real or complex numbers. The multiplication of 2X2 matrices corresponds to composing two linear fractional transformations, and I have long explored infinite compositions of LFTs. Apart from that it's Greek to me! :cool:

And if that space is made of, say, unitary matrices instead of ordinary numbers, you can make something like a special unitary group, in which you can build structures identical to the physical stuff that makes up our universe — Pfhorrest

Maybe a reference would help.

I suspect that these were more likely middle-class than working class — unenlightened

In the late 1940s Joe Brown and his companions initiated the British era of working class climbers, and those I met in the 1980s and 90s who were living on the dole were largely, but certainly not entirely, from that class.

If one visits some of the poorer areas of NYC they might find unemployed young men exercising and playing basketball during the working day. Well, before the virus struck! A leisure class, but not an appealing one.

The comment I made initially is not original. It was coined by one of the California climbers of the 1960s - perhaps Eric Beck - about dirtbaggers and elitists of that era. I was a member of that climbing generation and climbed and camped with one of those dirtbaggers from a working class background who is now a billionaire. Another colleague and friend from a humble background became almost literally Royal Robbins: Spirit of the Age.

I've known a few climbers too in N. Wales, and they climbed the slate quarries for fun, precisely because they were not the children of the quarrymen who climbed them with drills and explosives for a living. — unenlightened

Your reasoning here leaves me bewildered. When you are so confident about motivations, you should know something about the world to which you refer.

Leisure: "opportunity afforded by free time to do something."

If one is on welfare, with no job, this might apply. I have observed this in young British men who are addicted to the sport of climbing. They pool their resources for housing and food and pursue their dreams. (However, my observations are dated having been from the 1980s. Thatcher's government might have made this less likely).

Many aspects of the universe are orderly. We invented math to model these features. Why does this orderliness exist? Good question. :chin:

At either end of the social spectrum there is a leisure class. :smirk:

Stanislaw Lem at one time suggested what he called an "ergodic theory of history" in which some events have such historical momentum that even eliminating a principal participant would have little effect on the outcome. The other extreme, of course, is the "butterfly effect".

On the one hand, you rightly say that my algorithm will in the end find every idea that humans will ever express — Tristan L

How do you define "the end"? :chin:

It might help if members gave their real names, as on Quora. It's cowardly to be nasty when hiding behind a cardboard avatar. And yes, I know there are excuses for doing so, but it's still seems a bit chicken-hearted.

. . . mathematicians, and philosophers don’t have to worry that they’ll be out of work soon — Tristan L

:cool:

So The Expansion Of Giza And The Sphinx, Is Interlocked With The Dimensions Of Earth's Square Perimeter, Hence The Bottom Of A Pyramid Is "Square". — The Grandfather Of Philosophy

The Egyptians had a simple formula for the design of a pyramid: Imagine the height to be the radius of a circle, then form the square base to have the same perimeter as the circle's circumference. This may or may not have actually been used! :cool:

I've read the article - well, more or less - it's 26 pages long and repetitive and I skimmed over some sections. The principle thesis seems to be that at the very last instant before final termination of consciousness at death, there is a kind of freezing of time, and consciousness distorts the perception of time's passage to an extreme, so that one is caught in a kind of photographic hologram that is unchanging for all time as an artifact of consciousness. External time proceeds, but one's internal perception is drawn out in a seemingly endless period - all within fractions of a second in real time.

The author can correct me if necessary.

I do not find anything like what I would consider a "proof" of this phenomenon. Having an interest in the nature of time I find the concept intriguing, but nothing beyond rather bizarre philosophical speculation.

As for questions 1) and 2), I don't subscribe to a religious after-death existence, so I'll not comment on a possible correlation. And I don't see any value for society unless the hypothesis becomes a belief and the comforts of a supportive cult emerge.

I don't have that much experience with academic publishing, and none in this area. If anyone knows more about this - what's the deal here? How common are such journals? — SophistiCat

Thirty years ago a colleague at the University of St Andrews and I created something similar as a means of communicating new information about certain mathematical topics. For some time we accepted abstracts and research notes, lightly "peer reviewed" or refereed by the two of us. For about ten years we published the journal once a year, supported by our respective institutions and sent free of charge to participants. After I retired the journal was taken over by another colleague at another university as an on-line only format. The journal still exists, but the generation of mathematicians who contributed is depleted to such an extent that its existence is marginal and inconsequential.

These publications may exist as means of communicating material that is fairly speculative, and not suitable for the more rigorous and formal journals - those that print more for popular academic pursuits.

Another journal comes to mind: Foundations of Physics Letters. A bit more sophisticated than the efforts I have described. Nevertheless, even with putative more stringent refereeing some real doozies are printed, like Peter Lynds' article on the nature of time: Peter Lynds and Time

The journal passed away. :cry:

Publishing in a well-accredited refereed journal in math takes more effort by the author to conform to specific requirements, and the refereeing process is usually more rigorous. Also, the topic should somehow fit into the general areas of interest at the time. But this does not preclude questionable refereeing. I have seen this up close.

I know little about journals in the social sciences, but my impression is that levels of rigor may be less. Fake Papers in the Social Sciences

By the way, I do have a theory of linear time, but that’s a wholly different matter. — Tristan L

Have you discussed this in another thread? If not, perhaps you could begin one on the subject.

But my philosophy probably falls somewhere in the space of a skeptic physicalist. — Malcolm Lett

Careful of that Phi function. It's a doozy to compute! Welcome. :cool:

Oh dear. No leeway for us really old guys? Frank and I are both 83. :worry:

(Comment posting is malfunctioning)

Is this a reply to my question? If it is, it mustn't have escaped your notice that this ambiguity is within a given language and not a result of translation from one language to another. — TheMadFool

I was referring to my previous post:

Compounding this situation is that even in a discipline there may be differing definitions of a single word. For instance, in math, varieties can mean several (but closely related) things in abstract algebra, and duality can mean various things. — jgill

The meetings and conferences I attended were in English and I never noticed a problem with languages.
I was referring to your post:

As far as I know, although scientific language is a subset of ordinary language, all words used in science are given precising definitions - no room their for ambiguity — TheMadFool

Wiki: "In mathematical contexts, duality has numerous meanings[1] although it is "a very pervasive and important concept in (modern) mathematics"[2] and "an important general theme that has manifestations in almost every area of mathematics".

Varieties in algebraic discussions.

From Stackexchange, when asked, What do mathematicians mean by "form"?

" 'Form' doesn't really mean anything on its own. It's a historical label that got attached to a few things and then got attached to a few other things by analogy. Forms are usually like functions, but not quite, or something. I wouldn't worry too much about it. – Qiaochu Yuan Jul 20 '16 at 7:36
It would be interesting to track down specific first occurences (of "differential form", "modular form" and the like). For example, in Classical Invariant Theory, "form" more or less meant "homogeneous polynomial". I'm ready to believe that this meaning was influential in the naming of differential forms, or modular forms, but a serious historical inquiry would be necessary to establish that..."

Different authors use terms their own ways at times. I recently used "form" while discussing linear fractional transformations in a specific context, but others haven't.

Things are not quite as precise and tight in the general math community as one might suspect. But inside a particular sub-discipline they usually are.

. . . all words used in science are given precising definitions - no room their for ambiguity, my friend. — TheMadFool

In math, as I have mentioned, there can be ambiguity regarding a word. Once it's placed in context such ambiguities may disappear.

So you are becoming more "you" in a sense. — apokrisis

Practices like Zen allow one to understand that one's "I" is an artifice. And the experiences of the Art of Dreaming (Castaneda) allow one to experience that "I" as an isolated and powerful sense of pure will.

But the strangest experience I had was to awaken in the dream state as another person entirely, with the feelings and gestalt of that person, in an old house in Ireland. It was quickly over, but the sensation of being another remains. It's indescribable.

When we engage in a demanding physical and/or mental activity we can momentarily lose the sense of self and become immersed in the flow. I've had this happen when working on a math theorem or doing gymnastics or rock climbing. Or simply driving along an empty highway, letting "George" react.

Identity is indeed strange.

↪jgill
My mistake - I should have written Euclidian plane rather than configuration space. — RussellA

What I meant was that in this context each of the points {A, B, C, D} in the unit square [0,1]X[0,1] corresponds in a one-to-one manner with a point in [0,1], and we've seen that these points cannot be counted or determined by an algorithmic output. That's all.

Where do victims of violence or accidents fit into this scheme? An instantaneous death would mean no natural afterlife? You probably address this in your article, but I forget.

Esperanto?

Compounding this situation is that even in a discipline there may be differing definitions of a single word. For instance, in math, varieties can mean several (but closely related) things in abstract algebra, and duality can mean various things.

. . . and you start an unending process of adding to a list of infinite decimal expansions new infinite decimal expansions that aren't yet on that list, you would eventually get to the infinite decimal expansion of that. No? — Pfhorrest

When you say "eventually get to" I take that to mean in a finite number of steps. The sequence S(n)=1-1/n does not eventually get to 1, but gets pretty darn close in a large but finite number of steps. In your process you apparently use the Cantor notion of replacing a digit at each step (or a set of digits?) - I'm not clear on this. There are an infinite number of digits in sqr(2)-1.

I suggest you move on to other aspects of creativity, rather than get entangled with this issue. Others are more knowledgeable of transfinite math than me.

OK. Once one goes into transfinite set theory, Zermelo's Well-Ordering theorem (used in the Hahn-Banach theorem, e.g.) , etc., one can presumably do lots of things. In connection with a listing of "ideas" I suppose there is some relevance. Sorry I brought it up. I live in a simpler, more naive world in which the set (0,1] does not include its greatest lower bound.

That process of course . . . any given real will eventually be included on the ever-growing list, — Pfhorrest

Suppose you start with .1111... and end up in a finite number of steps at sqr(2)-1. How do you do this? Just curious.

I take it then that we can thus start with a list of any size, even just one item long, and continually generate new numbers that aren’t on it to add to it. — Pfhorrest

Step by step? An algorithm? If so, then you are generating all the real numbers and counting them as you do so. Perhaps you refer to an uncountable algorithm? Is there such an animal? :chin:

Considering four elements A, B, C and D spatially located in a "configuration space" , an algorithm could list every possible instantiation of these four elements within the space. — RussellA

Suppose your space is the interior of a unit square in the Euclidean plane and A, B, C, and D are points in that space. Please demonstrate such an algorithm.

you could start with a list of any one real number, diagonally generate new one to add to that list, diagonally generate another new one, and so on, and mechanically spit out new real numbers without end like that. — Pfhorrest

What is a "list of any one real number"?

Sometimes it's all hat and no cattle. :roll:

There is no algorithm that will eventually spit out every possible irrational number? — Pfhorrest

Wouldn't that be tantamount to counting them? A Turing machine algorithm?

When one is young ten minutes may seem like an hour, but when one is old one may think ten minutes have passed when, in fact, an hour has. In a perfect world the passage of time would be perceived accurately at all ages. Here is a simple function relating the measured passage of time, t, with the perception of that passage, T, according to age. Lamda is time of death and t=0 is the beginning of life. T=T(t) has meaning in this sense when differentiated: dT is perceived passage and dt, actual passage.

Very near the end of life the curve shoots up dramatically, representing that short period when one feels that conscious time goes on forever, while measured time is minute. This is only an elementary mathematical analogue of the metaphysical ideas in play on the thread.

$T(t)=t\left( 2-\frac{t}{\lambda } \right)+\frac{\varepsilon }{\lambda -t}$, $dT=\left( \frac{2}{\lambda }\left( \lambda -t \right)+\frac{\varepsilon }{{{\left( \lambda -t \right)}^{2}}} \right)\cdot dt$