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.

That said, it can be very difficult to figure out the latest wrinkles in political usage. Why for example, has the phrase "pregnant women" been replaced by 'pregnant people"? The last time I looked it up, men do not get pregnant — Bitter Crank

It's only a matter of time.

I consider the Paradox an aberration that results from collapsing one dimension to a lower dimension in certain circumstances and insignificant although bizarre. But Wolfram claims that this crops up in Feynman diagrams. It goes to the very nature of lines and points. — jgill

No, I think it is significant and general. — apokrisis

One way of perceiving the sum of all paths in Feynman's path integral for paths that consistently move towards a target is to have the particle pass through a series of finite parallel plates, each with "portholes" where the particle pops through, from one plate to the next in a system where both the number of holes and the number of plates increases without bound, with plates being squeezed closer and closer together.

A path then is zig-zag, roughly like the original diagonal paradox except with random configuration. If all possible paths of this type arise, then there will be some with lengths growing towards infinity that are nevertheless contained in a closed and finite environment and go from left to right, let's say. Like the sequence of contours in my note. One meter or infinite meters? The "same" path. :chin:

I may be wrong, but I have come to the conclusion that the only way to be politically correct towards liberal morals and aesthetics is to not be rigid at all, to not offend and to be 'open-minded' towards everything that does not violate state laws.

I repeat that I may be wrong, but this is what I take modern liberalism for: lack of models & aesthetics that first of all are politically correct (aesthetics which try to include as more qualities as possible, so none might feel excluded and no model may dominate). — Eros1982

That's an interesting assessment of American liberalism. But you haven't stated what comes next under that rubric: condemn those who do not follow this prescription.

"Most notably Hilbert's paradox of the Grand Hotel, but also the following:

Gabriel's horn
Galileo's paradox
Ross–Littlewood paradox
Thomson's lamp
Zeno's paradoxes
Cantor's paradox
Dartboard paradox"

The Diagonal Paradox can be extended in principle to any curve in 2D. For example, a circle of radius 1 has a circumference of 2pi, but if I apply my system of sine curves to the circumference I find that as they converge uniformly to the existing circumference, their lengths tend to infinity. Hence I am staring at what appears to be the simple circle I began with, but I now have one with infinite circumference, and hence infinite area.

Thus infinity is everywhere in plane geometry where it shouldn't be.

I consider the Paradox an aberration that results from collapsing one dimension to a lower dimension in certain circumstances and insignificant although bizarre. But Wolfram claims that this crops up in Feynman diagrams. It goes to the very nature of lines and points.

It's not science. But it's speculating or philosophizing about scientific results.

I hypothesized in my post to jgill [a calculator that can't calculate beyond 5 would display 5 (the arbitrarily large number) for both the queries 2 + 3 = ? and 3 + 29 = ?]; he asked, paraphrasing, how can a finite brain grasp infinity. — Agent Smith

I did? I'm old. Maybe I was closing up shop for the night. :chin:

I just proved an interesting result demonstrating a sequence of sine contours on the interval [0,1] that not only converge uniformly to the line from 0 to 1 while growing towards infinite length, but converge in this way along the interval [0,1] all the way down to the point (0,0) while becoming infinite in length. I mention this only because there is interest in the relationship between 0 and infinity and somehow combining continuity and discreteness.

I'll give details if requested. :cool:

I always thought from my experience that maths types were invariably into classical music. It was the physicists who scaled peaks. — apokrisis

I knew Lester Germer, a multi-dimensional person. He was a fighter pilot in WWI.

My oldest and best climbing friend ,Dave Rearick, was a math prof at the U of Colorado.

I believe that the majority of the harms that death visits on a person are post-mortem. Why? Because the ante-mortem harms seem relatively insignificant compared to the harmfulness of death — Bartricks

↪jgill
You clearly don't understand the case I have made at all. — Bartricks

And thankful of that I am. :roll:

This thread has opened the door to a BIG NUMBER theory, a BIG BANG theory companion!

Oops, looks like there already exists such a Theory :sad:

At what time are the harms of death visited upon us? They are visited precisely when death itself is visited upon us and not a moment earlier or later. . . . Not later - because after death we are beyond the harm of losing life and its benefits, having already lost them. — Cuthbert

:up: Pretty much says it all, unless one wants to speculate about surviving death in some form. That would be a thread to which Houdini might contribute - or not.

Perhaps, it is why philosophy seems to be so much of an area for heated debate . . . — Jack Cummins

Amongst the philosophical minded. :smile:

:clap: Eloquently said!

That differs from how I find 'classical' is used. I find that 'classical' mathematics means all and only those results that can be formalized as theorems of ZFC with classical logic. And classical logic means the first order predicate calculus including the law of excluded middle. — TonesInDeepFreeze

Well, that's interesting. I learned something. Thanks. Classical analysis of course means more or less what I said, going back to Weierstrass and Cauchy - and I forgot, the study of special functions - but in foundations classical has another meaning.

Wiki:

In the foundations of mathematics, classical mathematics refers generally to the mainstream approach to mathematics, which is based on classical logic and ZFC set theory.

:cool:

But maybe you didn't mean that you don't use those sets. But that you do use them, but you don't use the extended real line with its points of infinity? As instead you simply deploy the fact that the reals are unbounded? — TonesInDeepFreeze

The basic set theoretic structure of the reals underlies almost everything I have done, but I haven't used infinity as a "point" (nor the axiom of choice). Infinity is a limit in the language of calculus.

(3) What is the difference you have in mind between classical and modern? Ordinary contemporary analysis is classical analysis. — TonesInDeepFreeze

Classical means the tools of analysis like limits, differentiation and integration and all those entail. Nitty gritty. Actual specific results vs broad generalities. The more modern you get the more abstract the subject becomes with broad generalities and topological arguments. It's vague to an extent.

Hard & Soft Analysis