The One means that there is no other One, it is Unique and Simple. It is composed only of itself and it is Alone and All-one (everything and everyone) — Illuminati

I am very old. I apologize, but when I read something like this I tend to fall asleep. Is this supposedly enlightening? Is there a Zen moment of Aha!! ? Why do you write something like this over and over? Does meditation help making this pronouncement astounding?

Finally, why is this on the forum page and not in the Lounge? Moderators?

Very appropriate. It was trying keeping up with the many non-properties of nothingness.

Speculations about the nature of space go far beyond the well defined parameters of mathematics. You are on a mystical journey.

As a mathematician, how would you formally account for the emergence of spatial structure within an entity that is dimensionless? Specifically, how can space, as a relational or metric construct, arise from a foundational state that lacks extension, orientation, or measurable attributes? — Illuminati

The origins of space and time are speculations, not facts. A mathematical "space" is a set of "points" and some sort of structure. With two points one may get a measure, I suppose. The transition from the sort of foundational state to what we experience in the real world lies not in the realm of mathematics to the best of my knowledge.

The closest I can come to what you seem to be talking about is the essential singularity e^(1/z) in the complex plane. In every neighborhood of z=0 the function takes on any value an infinite number of times, save perhaps one such value. Sounds like a mystical phenomenon doesn't it?

Carry on. Beyond my bailiwick.

This is not about mathematics or arithmetics as each number was explained in a philosophical manner. — Illuminati

True enough. Like the Zen definitions, perhaps.

From this perspective, Zero is equated with “nothingness,” in its
primal manifestation as Chaos - that is, as a universal, unlimited
unity without form, prior to the emergence of any differentiation.
Thus, Chaos is not merely the opposite of Order, but a state of
absolute potential unity, where no distinction has yet arisen.
In this logic, Zero is - meaning it is the opposite of non-being. — Illuminati

I realize this is a kind of divine interpretation of one and zero, but tossing chaos into the mix is rather unpleasing to a mathematician. Nevertheless, continue with your rapturous presentation.

From an infinite composition of complex functions arises "Reproductive Universe". Entirely unpredictable - an example of weak emergence.

There is an interesting mathematical model of cause/effect in compositions of functions.
$f\circ g(z)=f(g(z))$ like a force field where one function starts the movement, then another function causes further movement, etc. Over and over again the process can be written
${{F}_{n}}(z)={{f}_{n}}\circ {{f}_{n-1}}\circ \cdots \circ {{f}_{1}}(z)$. In certain settings (certain Banach spaces) this process approaches a limit as n grows larger and larger, provided there is what might be called a hidden "guiding principle" of each function and that the sequence of these converges as n grows.

I've mentioned before this relates to theology as well, for de Chardin's "Omega Point" might be so interpreted.

Mathematically, this is both a sufficient and necessary condition for convergence to a "final effect".

Perhaps a philosophical idea lurks herein. Otherwise, what I see is an endless word game being played. But pay no mind and continue.

Farmer's work begins before the rising sun and ends after the last vestiges of sunset. The only security they have comes from their own efforts, while in the big cities, social democrats pound the drums for large unions like the UAW, while looking down on flyover country as they commute from coast to coast. There is a tendency for city dwellers to think the country folk beneath them, with jokes and demeaning comments. Why should it be surprising that farmers move to the party that supports individual efforts and responsibility?

In my case, my father being a university professor of course presented a professional path that appealed, and when I took up climbing those free summers were a huge motivating factor. I was a USAF officer for a short while, and could have remained in the service, and could also have taken a civilian job based upon that education and experience, but I got married - and that, I admit, just seemed to happen - an almost wistful push from a societal breeze.

My point is a very shallow one: when young we seem unaware of the finiteness of life as well as the force exerted by our social surroundings. As we age unawareness smoothly slips into trepidation, especially if we have obligations.

Nice thread. Welcome to TPF.

At the same time, the idea of ​ temporality and being-to-death remains attractive for my research. In this idea, I see Heidegger's attempt to describe the very inner tension that makes a person act. Decomposing temporality into a sense of possible one's own death and ignorance (the unknown of the purpose of existence and the consequences of any choice), I tried to express this "inner tension" in simple language — Astorre

Finally, at the age of 88, with some medical problems,I have begun to understand this conjecture. But, at a younger age, like many if not most of my peers, this line of thought would be beyond my horizon. I doubt it even roamed my subconscious.

Have others here experienced this sort of finitude?

. . . but just states that if society already treats 16 year olds as adults for other purposes, then to be consistent, they should also be allowed to vote. — Hanover

OK, kids, let's head to the liquor store! And let's permit consensual sex for girls at that age. Oh. and let's bring back the draft, this time for 16 year olds.

Can uncertainty and finitude be considered the true primary causes of existential choice? — Astorre

To what extent does an an individual's recollection of an existential turning point in their lives support or negate this pronouncement?

I became what I consider an "existentialist" in the early 1960s after reading Sartre's book and realizing that an activity that I had found compelling but which held no attraction to those I socialized with could become an intricate part of my life and have "meaning" simply because I decided that it should. That revelation shaped my life, and still does at age 88.

"Finitude" played no role in my decision. Not once did it arise in my deliberations, although I suppose I might have been a little less compelled were I immortal. Heidegger's concept seems to me absurd. "Uncertainty", however, existed in my choice of a professional career - I was fortunate to have several options. To what extent would each of these interact with the activity to which I had given meaning? Which of these alternatives would be most "meaningful" itself? It turned out that choice went well in both regards.

I would like to read of others on this forum who went through similar experiences. To what extent does psychology intersect with philosophy here?

In mathematics one's imagination leads to new concepts or ways to prove existing conjectures. Then the application of logic finishes the job.

Many of us came here as refugees after being thrown into the ether when our old home was invaded and closed down to us — Sir2u

I was on a superb climbing forum (supertopo) for several years until it shut down. Topics like Zen and consciousness along with climbing discussions. Quite varied. I've enjoyed this forum, especially mathematical threads, having been a practitioner for eons.

I’m pretty sure “liberal” can’t be described in zeros and ones — Fire Ologist

Lib = 12 9 2 = 1100 1001 10

:nerd:

Consider the phrase, "I am politically nonbinary." — David Hubbs

It means my politics cannot be described in zeros and ones. Big deal. :nerd:

Fascinating idea to be sure, but, if spacetime structure contracts to a single point, for which descriptions of events is complete insofar as there wouldn’t be any more events to describe, wouldn’t that suffice as the end of spacetime? — Mww

It would just take spacetime closer and closer to alpha without ever reaching the point of completion. The component of time would shrink, but not collapse.

Just doodling with a theorem of mine in Banach space. Pay no heed.

Time ends with the end of the last relational intelligence; spacetime ends after the last formulation of a mathematical model of a relativistic continuum. — Mww

Which sparked my interest since I am or was a mathematician. I can model the far future in an imaginative way by considering the passage of spacetime as a series of cause/effect steps, say at Planck time rhythm.

Suppose each step is a function operating on the previous effect and all this takes place in some enormous but closed environment. And suppose each function "contracts", brings things a tad closer together. Then, under certain mathematical assumptions, as time moves ever forward, if at each step there is a thing that does not change (a "fixed point"), and these things converge to a specific thing (call it "alpha") as time marches on, the entire structure of spacetime contracts to that singular alpha.

This may conflict with entropy, since objects seem to be moving apart, but maybe not.

Which means no "end" to spacetime, but eventually all is taken to the vicinity of alpha.

Teilhard De Chardin calls alpha the "Omega Point", towards which everything moves.

Who da fuck is that? — RogueAI

AI with too much makeup.

these details will for now remain veiled. — Kizzy

What a shame.

Not necessarily. My old Democratic party (I registered in 1958) is sick unto death. I hope it recovers.

Thanks. I see I have neglected to reply to the one in question. :yikes:

What are the other pros and cons? — Banno

How does one find the replies he/she made in these PM conversations? All I can find are the incoming messages.

Speculation in the sciences and mathematics has become the fashionable version of philosophy and those who explore those realms of thought, the modern philosophers. How much more can be said of ontology without bringing in to play artificial intelligence?

As a retired mathematician I have seen the shift to foundations over the traditional ideas and simply extending knowledge in an envelop of heritage. Beyond the two basic forms of "infinity" - all I ever employed - are abstractions that appeal to a large number of math devotees. Here is an example: Unimaginable Infinities

Dear Vera, Rest in Peace. A sad time.

Logical form or syntactic structure does not have to issue from inborn powers in our brains, nor does it have to come from a priori structures of the mind. It arises through an enhancement of perception, a lifting of perception into thought, by a new way of making things present to us

(Robert Sokolowski - The Phenomenology of the Human Person)

Nicely said. We watch and learn.

IMO logic arose from observing the relationships between physical entities. Cause and effect and so on. But I admit to being very shallow on the origins of logic, and avoid "being"and other vague concepts.

This is the same problem with space as there may be with time.
The Planck length is the smallest unit of length, approximately equal to 1.616 x 10^-35 meters.
In a sense, our measurements of both space and time may be fundamentally flawed, in that, as there is no position in space, there may be no moment in time. — RussellA

Actually, the Stoney scale is roughly 1/10 the duration of the Planck scale in time measurements. These are simply units of measurements, not ultimate bounds in a some philosophical sense. If you were to ride on that photon as it traverses a Planck length, time would vanish completely for you.

I have wondered why certain physical facts about time have not entered into these discussions. For example, as you stand on the side of the road and someone passes you in a car going 60mph, time is measured infinitesimally slower for them compared to you. And someone drifting above you in a balloon measures time infinitesimally faster than you. In the calculus of physics an instant of time is a limit concept, not an established fact.

As a math prof I would give them a short written quiz. Or, I would discuss the topic with them, one on one, and discover how well they understood it.

This might not be appropriate in polite society. :cool:

It's how we are raised. As a child my family moved from city to city every two to three years, so I became conditioned to leave the past behind. One place for three years to graduate from high school, then college two years here then two years there, USAF two years and two years, grad school, teaching, etc. before finally moving in middle age to the house where I have resided for forty years.

Nostalgia is a distant concept. As is identity linked to a particular place or dwelling. Forgive me, but I think I will avoid Kundera.

Jan, hello and welcome. The need or exploitation of details depends upon the topic. Discussions of the classical notions of "being" may veer off into assorted details since the subject is not well defined, but when occasionally a topic in mathematics is introduced the necessity for details arises due to the subject's highly defined structure, whether one agrees with or disputes accepted qualities.

Can you tell I was a mathematician?

This seems to suggest the only reliable description of time requires a conscious observer, right? — Hanover

Just nit picking, but "reliable description" implies conscious observers. If no observers then reliable description is meaningless.

I'll get around to watching these. I assume Wolfram is still promoting his ideas about Cellular Automata as a foundation for science and math. I bought his enormous book when it first came out, but flamed out of reading it after several hundred of the thousand pages or so. It did encourage me to write several computer programs and experiment developing the patterns he alludes to.

It became a joke at scientific cocktail parties that almost everyone had a copy, but no one had completed reading it.

Thanks for bringing to my attention. But I must admit, going on 89, that having turned off the sound I fell asleep part way through. It seems like it's a discussion about the origins of calculus where the limit definition is given in terms of infinitesimals, called monads or whatever by Newton and Leibnitz. Weierstrass and Cauchy improved upon it by introducing epsilons and deltas.

Non-standard analysis is the modern version, but is not a popular approach in universities.

Symmetry (function)

↪jgill
how do you know is the same distance — Danileo

23 steps out, 23 steps back.

Comes from

${{e}^{i\theta }}=\cos (\theta )+i\sin (\theta )$
and
${{e}^{z}}=1+\tfrac{z}{1!}+\tfrac{{{z}^{2}}}{2!}+\cdots$

Is a poetic way of relating the important numbers of math, pi, e, i, 1, and 0.

↪unenlightened
yea approximate symmetry rules the world, but pure symmetry is not, as everything is affected by particles symmetry is impossible — Danileo

In mathematics, metric spaces are sets of points and a measure of distance between them: d(x,y)
such that d(x,y)=d(y,x), symmetry. In the real world, is the distance between my front door and my mailbox the same as the distance between my mailbox and front door?