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.

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

It would be possible in principle to set out on a deterministic process of mechanically identifying every possible idea, though as that space of possibilities is likely infinite this process would likely never finish identifying all of them. — Pfhorrest

Each irrational number is an "idea", so this process cannot exist.

possibility of doing math involving two-dimensional quantities (which is all complex numbers are) — Pfhorrest

Complex numbers and complex variable theory are more than simply doing math in two dimensions. For example, (x,y)->(u,v), u = 3x + 4/y, v=x-y does that.

Admittedly nit-picking, but clear concise arguments need to be accurate.

In mathematics there is no strong consensus on creation vs discovery. But a practitioner may create a mathematical object and then discover its properties. It makes little to any difference in practice. I always consider it a kind of exploration.

And thus we finally learn why we assume the world is mathematical. It's been a long journey, but we have reached the end and may celebrate. :roll:

Scientifically, it's a well discussed theorem. Alternative universes. Parallel universe. The multiverse. String theory. Etc — Outlander

Not really a "theorem", but entertaining speculation. However, discussing these ideas gets one nowhere. Train to become a Lucid Dreamer or follow the instructions for the Art of Dreaming by Castaneda. You will be shocked and amazed with the actual experience, and then you can do the speculating.

Whoops! I misread this as "The Impact of the Natural Athlete . . ." and I thought, sounds interesting and a discussion I had not been aware of.

Nevertheless, I have wondered about the idea of distorted time when near death. ( "HIs life passed before his eyes . . ." ) Here is a bit of nonsense I posted a couple of years ago, and it includes speculations about mathematical formulae comparing one's perceptions of intervals of time as one ages. I'll do a simple one later for the near-death interval that somewhat reflects what you describe. That could be tricky since the trend during aging is the other way.

As for the "timeless" notion, that is quite a conjecture. Something to ponder. :cool:

An Elementary Note: Playing with Complex and Distorted Time in C

Clearly, even after all of that, and sixty years of mathematics, you still can't provide an example of two things that are exactly the same? Sophistry always works this way. — JerseyFlight

Yes. Pitiful isn't it? I feel so ashamed. :cry:

Sans quantity, no maths. — javra

Generally speaking this is not entirely incorrect regarding numbers. Euclid's Elements - first four books, basic point-set topology, elementary geometry, !st order Categories in Category theory are counterexamples. But numbers or quantities are lurking everywhere in the math galaxy.

Infinite causal chains and the beginning of time

All your concerns will be addressed here. :cool:

Metaphysician Undercover has posted numerous times on this issue. He should chime in.

To be a mathematical supernaturalist you simply need to hold to the position that numbers are more than human symbols — JerseyFlight

Oh oh. How embarrassing. Guess I qualify. :yikes:

It always gives me a laugh when I meet a mathematical supernaturalist — JerseyFlight

Having been in the math game for sixty years I feel deprived not meeting such a colleague. I am sure had I done so I too would have chuckled. :cool:

My argument is that this is pretty much exactly the situation professional philosophers are in — Hippyhead

Perhaps a "professional philosopher" would comment on this. Heloooo out there . . . do any such members exist? Please speak up. :meh:

Hopefully this thread can go back to its original focus. Sorry for the diversion. :sad:

I only wish to tell you that with your background, every single thing that's been discussed on this forum that you think is beyond you, is actually trivially within your capabilities and knowledge. — fishfry

Fair enough. When I speak of a topic being "beyond me" it's a cop-out for not having the mental energy at my age (83) to study it, or just a complete lack of interest. I appreciate your comment.

Every so often, however, something a bit out of my purview will intrigue me and I will make an effort to understand it. For example, a couple of years ago the notion of a functional integral sparked my interest, having read of Feynman's Sum of All Paths concept. My brief exposure to the concept fifty years ago was shallow and uncompelling.

That was a delightful exploration, starting with the basic Wikipedia definition, and I wrote a short math note about functional integrals in spaces of complex contours. I enjoy writing math programs, especially graphics, and I came up with some nice imagery. That was fun.

I should not be making dismissive comments about set theory. You, fdrake, Nagase, and a few others have clearly explained ideas in this subject, and it is a powerful link between math and philosophy, and a vital part of the mathematical galaxy. I apologize, and if I slip up in the future you should nail me!

Most of my research efforts have been in classical analysis, very basic dynamical systems in the complex plane, trying to determine convergence/divergence of certain sequences. At one time this was a popular topic, but modern analysis has moved the focus more toward algebraic systems and generalizations.

But I remain attached to the old-fashioned, nuts and bolts, stuff. For example, my latest efforts concern the iteration of linear fractional transformations (f(z)=(az+b)/(cz+d)) when the attracting fixed points are functions of time and are no longer "fixed". Like predator and prey, do the iterates "catch up" with the roving attractors? Modern theory dealing with LFTs is more geometrical and algebraic.

OK. Enough rambling. Thank you for your comments.