which is that the behavior of a small percentage of the world population is responsible for most problems. — Xtrix

I assume you mean by "small percentage of the world population" the highly civilized nations (HCN), to which millions flee, desperate to be admitted, for the promises of a better life. Are you saying the HCNs both create most problems but solve many problems?

Were it not for the HCNs life would be barbaric with early deaths from disease and injuries. Look at the American Indians.

Therefore, is what is needed for better philosophy actually a fasting and detoxification of thought? — Xtrix

I like this. In order to improve philosophy, don't do philosophy.

Non-thinking is relevant to mathematics as well. Long retired, I still conjure up math notes and post them as a hobby. But in doing so I may be harming the subject. arXiv.org receives hundreds of papers a day, every day of the year. Much of this activity is polluting thought and contaminates what is pure, creating a swamp of diversity that drags the discipline into incomprehensible sludge.

You have a lot of patience. The "vagueness" principle apokrisis advances might work better. It would parallel the actual history of math.

The interval would be made so small that the length of the line was the same size as the width of the line - both being now effectively zero. — apokrisis

A line in turn would be arrived at as the constraint on the quality of “plane-ness”. Squish the 2D plane from either side and the limit of its compression becomes how a 1D line arises. — apokrisis

The sequence of contours of the form ${{Z}_{n}}(t)=t+i\tfrac{1}{\sqrt{n}}Sin\left( 2\pi tn\sqrt{n} \right)$ demonstrate convergence to both an infinitesimal straight line (on the x-axis) and the origin, 2D down to 1D down to a point. $t\to \tfrac{1}{\sqrt{n}}$ and $n\to \infty$ with ${{Z}_{n}}(t)\to 0$.

Oh oh, I almost forgot $\text{Length }{{Z}_{n}}(t)\to \infty$. You can ignore that I suppose :cool:

Whoops, mistake.

Space is a concept (opinion) that has reality existence as an immaterial existent. — val p miranda

It seems like you are just playing with words. Suppose your idea is accepted. What difference does it make besides a brief discussion in a faculty lounge? Is it really worth the effort?

Time, however, is a concept and it can be defined as what clocks measure, but time is not limited to this definition. — val p miranda

As a concept, time is the measurement of motion. — val p miranda

See the difference between these two concepts of "time" val? — Metaphysician Undercover

In math, time = t. So simple.

So in this view, you start from a material vagueness or everythingness - a quantum foam of possibility - and this then reacts with itself to become a more limited and stable arrangement of somethingness. Existence evolves in a least action or path integral fashion where everything cancels down to whatever definite form can stabilise the situation and make for an orderly Universe unfolding in dissipative fashion in an emergent spacetime.

I find this somewhat hard to understand, but it seems sensible enough. — noAxioms

It's poetic as well.

In the philosophy of mathematics, I am not a scholar, but I have read many books and articles. In mathematical logic and set theory, I'm not a scholar, but I have a good handle on the basics through taking courses and careful study of several textbooks — TonesInDeepFreeze

Hey, I'm a fan. You have my respect. :cool:

I used to pick up bits of modern math knowledge from @fishfry before he departed.

Why do we need to order the curves? — keystone

If you want to start with curves (or continuous objects) in order to derive points you need a systematic way of talking about them. If you plan to assemble contours or curves by gluing together tiny straight lines, then you are doing nothing more than is done when one calculates the length of a contour in complex analysis.

But I guess what you are really interested in is potential infinity and its kin. So my comment is what difference does it make how you deal with that? We've had posters here who spend years working up what they consider astounding revelatory articles, only to be more or less ignored. They become so enraptured with their ideas they get caught in that spiral in which the more effort you exert the more you think your product is of value, losing their objectivity.

But if you enjoy your project as a personal challenge, have at it. I have certainly been in that boat!

If what exists exists in space and if space is an existent then space exists in itself. If it exists in itself it cannot be the same as itself. — Fooloso4

Maybe it is. A possible definition of space. :snicker:

All bijections are injections. So you're confused to begin with

The reason old-fashioned terminology is not so bad. One-to-one onto, etc. Bourbaki may be to blame? Just nit-picking, ignore me.

Can you explain what you mean by 'catalogue all continuous curves'? — keystone

When math starts with points that are then assembled into curves, there is a way of describing those points on the real line, identifying a point with .5 for example. If you are starting out with curves or geometric figures you need to be classify them, order them somehow, for you then wish to create points by intersections I suppose. You need rigorous definitions for curves, then an axiomatic structure. All of which seems far-fetched. But who knows?

I believe that calculus is more closely aligned with this parts-from-whole approach than it is with the conventional whole-from-parts approach. — keystone

How would you catalogue all continuous curves? That would be a starting "point". In order to have derivatives and integrals you would need some kind of function derivable from a catalogued example. Sorry, but the whole approach sounds absurd.

(I had no way of knowing that, out of the blue, you would be using category theory) — TonesInDeepFreeze

Nowadays it's an extremely popular rabbit hole, complete with patios, restaurants and theaters. Doesn't do anything for me. Both Category theory and K-theory arose in the mid 20th century. I've mentioned before that one of my instructors from a half century ago was at a talk about the latter when the lecturer started entertaining comments and questions from the audience, became so annoyed with the flack he was receiving, he practically yelled, "Just believe me and I can prove anything!!"

Well, not in mathematical analysis.

Those solutions are true for parabolas and yet the line this object traces is a straight line. — Agent Smith

Nonsense. Start with $\frac{{{d}^{2}}s}{d{{t}^{2}}}=-32$ and use the height of 100 and initial velocity of 0 and solve & compute. You are confused because the formula becomes quadratic, like that for a parabola. I think you delight in raising hackles . . . :cool:

Yes sir! But what happens when understanding the foundation of the universe is "the task at hand"? — Metaphysician Undercover

Good luck with that. :roll:

Couldn't there be something wrong with both? — Agent Smith

No

I recall starting a thread on how irrational numbers could be the smoking gun that there's something seriously wrong with mathematics and the universe itself. — Agent Smith

There's nothing wrong with math, so it must be the universe. I wouldn't put anything past that sucker!!!

Now think about an irrational ratio such as that expressed as pi, and you'll get a glimpse at the problems which pervade mathematics. — Metaphysician Undercover

It'll take more than a glimpse for me. I know, I know, pay no attention to the man behind the curtain. :cool:

The "Butterfly Effect" is an example of order emerging from chaos. — Gnomon

No, just sensitive dependence on initial conditions.

I can't speak to the standard axiomatization of analysis, but the informal definitions that us engineers were taught didn't use sets — keystone

If it's any consolation I was a math major at two big state universities in the 1950s and I can't recall of ever studying any aspect of foundations beyond skimpy material on rationals and irrationals and the continuity of the real line. As a freshman at Georgia Tech I was placed in an experimental course in introductory calculus that began with epsilons and deltas - very confusing at first. The engineers had it much easier, as I learned when I moved back into the standard curriculum. But when I started grad school at another university in 1962 one of the first required courses was an introduction to foundations using Halmos' Naive Set Theory and the Peano Axioms. It was quite illuminating.

The player has free will to make the shot. The little routine is part of the shot. Not an argument against free will. Now, an argument can be made is it his subconscious governing his actions and setting in motion the shot, but does getting commands from one's subconscious violate free will? The decision still arises from the individual, just not the conscious part.

That's the extent of my knowledge of free will.

Now that is math for you, try explaining that! — Pantagruel

Haven't a clue. It's Greek to me.

I consider it ironic that deterministic actions like following a routine are necessary proof for free will. If you set out to follow a routine or rules and it was impossible it would be evident that you didnt have choice — introbert

Yesterday I listened to a discussion on NPR of the role of rituals in life. They talked about watching a basketball player about to take a shot. If the player goes through a mini-ritual most spectators think he will make the shot, as opposed to a player who doesn't. I don't think this behavior has much to do with free will.

Could be. I just look at the math of the thing, which doesn't seem like Magick.

I don't think this successfully detaches the observer from the event, do you? — Pantagruel

There's your philosophical wiggle room! Have at it. :cool:

The role of measurement, perhaps. — jgill

Can you amplify this? — Pantagruel

An experiment is performed. A machine registers the outcome. This is when the "collapse" occurs. An hour later a scientist reads the measurement - his reading doesn't mystically create an answer. Mathematically, a superposition means a variety of possible answers arising from a solution of an equation. One is correct.

If I am wrong a physicist on TPF can correct me. :smile:

I admit, I am wrong at times!

And modeling only highlights the role of consciousness in creating the scientific view of reality, a paradox that emerged rather conspicuously in the observational phase of quantum physics. — Pantagruel

The role of measurement, perhaps.

There's no mention of other universes in the theory. The theory posits only that an isolated system evolves according to Schrodinger's equation. The cat being dead is a valid solution. It being alive is another. — noAxioms

"Superposition" is essentially linearity with regard to solutions of Schrodinger's equation. When modelling a physical phenomenon mathematically, frequently a differential equation is involved. These equations might have multiple solutions, linear combinations of one another. When a measurement is executed the proper solution crops up. In general, a math equation might have superfluous solutions.

For example, drop an object from a height of 100 feet. How long before it hits the ground (ignore air resistance)? Answer from acceleration due to gravity is t=2.5 and -2.5. Obviously the answer is t=2.5 seconds.

So time has a fundamental grain determined by c. A moment or duree is the completion of a change. And the Planck scale is the size of the smallest such moment. — apokrisis

Food for thought.

Wiki:

Definition of the second
In 1968, the duration of the second was defined to be 9192631770 vibrations of the unperturbed ground-state hyperfine transition frequency of the caesium-133 atom. Prior to that it was defined by there being 31556925.9747 seconds in the tropical year 1900.[18] The 1968 definition was updated in 2019 to reflect the new definitions of the ampere, kelvin, kilogram, and mole decided upon at the 2019 redefinition of the International System of Units. Timekeeping researchers are currently working on developing an even more stable atomic reference for the second, with a plan to find a more precise definition of the second as atomic clocks improve based on optical clocks or the Rydberg constant around 2030.

In a flight of philosophical fantasy, the sequence of contours that converge uniformly to the line segment [0,1] but increase in length toward infinity might approach a boundary point between two worlds. In one, the length is 1, in the other infinity. As one stares at the paradox one looks directly into the many-world environment. :cool:

Exactly my first experience with Castaneda's Art of Dreaming many years ago. Stephan King describes an alternate reality in one of his books in which an onion is pulled from the ground and someone a mile away smells it. — jgill


Take that <whatever you call these people>! — Agent Smith

In to the sauce again, AS? My comment was made on a different thread. :roll:

Many that claim a NDEs say things seem realer than real. — TiredThinker

Exactly my first experience with Castaneda's Art of Dreaming many years ago. Stephan King describes an alternate reality in one of his books in which an onion is pulled from the ground and someone a mile away smells it.

A moment in time – a durée - thus is an irreducibly complex object. It combines rotation and translation to create the emergent thing of a "fundamental time step" — apokrisis

?? Bergson's time intervals? What? Rotation & translation = the two spools? :chin:

So, at least as far as I can tell, saying 'potentially infinite' is not yet, at least, a formalized notion but rather a manner of speaking — TonesInDeepFreeze

I had never heard that expression in a mathematics discussion before joining TPF.

Should be on a physics forum, but what the hell . . .

What surprises me about our math-phobic friends on TPF, is that philosophy majors usually love the esoteric. You would think they would revel in knowing more about mathematics than the Great Unwashed. — Real Gone Cat

Yes, they certainly like to talk about what Kant meant or how Aristotle would know, but math is more precise, with less room to wiggle. :nerd:

As if the leminscate stands for that thing like the golden arches stand for a hamburger stand. — TonesInDeepFreeze

:lol:

I had to look up Paul Erdos, to see that he is famous for his work on Ramsey theory. Seems like Erdos was very socially active. Is he responsible for the famous notion "six degrees of separation"? Or was he just paranoid about aliens? I see you can still earn money by solving Erdos' problems. Have you ever managed to get any reward? — Metaphysician Undercover

I don't know about the six degrees or aliens. I met him once and talked with him briefly at a meeting in Hungary years ago, but I am not in that select group of mathematicians who have "Erdos numbers". He stayed with my advisor for a week long ago as he traveled around the world, giving talks and working with colleagues. Universities supported him on his visits to their campuses. He lived out of a suitcase and shopping bag and, while his mother was alive, stayed at her apartment in Budapest on and off.

Their is a curious parallel in the world of climbing. Fred Beckey, who died in 2017, was the most prolific climber in American history. Like Erdos he lived a vagabond life, sleeping on the sofa of whoever he was visiting. I knew him slightly and we bouldered together occasionally. I suppose there could be something like a "Beckey number" earned by doing notable climbs with him. :cool:

↪Agent Smith
This is actually false. There are plenty of accounts of people ‘going to hell’ then when they recover from their ‘brain death’ they try and turn their life around. — I like sushi

It would be nice to see some references here.

↪jgill

Do they say anything about this life? — TiredThinker

I think that is a very good question, one that might be answerable.

That doesn't surprise me at all. I've had numerous discussions in this forum with mathematicians, and I've already been well exposed to the absurd ontology which seems to be exclusive to that cult. — Metaphysician Undercover

Yes, we're a wicked bunch intent on the corruption of the intellects of youth in order to bring them to the alter of our Satan, Paul Erdos RIP. All bow.

NDEs don't occur after brain death. So they tell us nothing about an afterlife.