Goodbye infinity and all that infinite singularity and infinite density descriptions

[Gibsense]

Interesting discussion. Exciting even.
Introducing the Flatlander description was ace (if only I could have done it as well in my post re hyperspheres)
Melding it all together (philosophically not with much backup) I would describe reality as:

• Our universe as a hypersphere (analogy - blowing a balloon up flatlanders on the surface) - surface is 3d
• Time = radial expansion. The time here is a radial expansion not involving travel in a spatial environment. (this assumption gives a realistic Hubble Constant)
• The star in a black hole is at the supposed singularity (nearly)
• The space from a black hole event horizon to its star is time equivalent (reverse of our white hole)
• A feeding Black Hole powers the expansion of the associated White Hole Bubble universe.
• BH>WH>BH>WH. Black Hole via Quantum Fluctuation to White Hole (Observable /Bubble universe/hypersphere)
• Mobius/Klien Bottle, Strip-style Super Universe containing our white Hole + numerous other similar universes (avoids turtles on the back of turtles on the back of turtles) because the white holes contain black holes and so on.
• When we say "Observable Universe bear in mind - 1. It has an event horizon working oppositely to a Black Hole EH. Thereby expanding instead of compressing. 2. 3d space is often described as flowing into a black hole. 3. As per the 'Flatlander Descriptions' you can explore the space 'forever' but it is bounded nevertheless. 4. Information is not 'lost' maybe (the amount of stuff entering the BH comes out in the WH)

Hope this intrusion is useful

 

[Helio]

Here's a quote from Descartes in his Principia philosophiae (1644) that I find interesting:

“We should not try to understand infinity, but consider anything as indefinite, where we find no boundary.” He felt "infinity" views should be reserved for God.

 

[billslugg]

Consider two intersecting lines in a plane. As they are made more parallel, the intersection moves outward. As they become parallel, they no longer intersect. What happened to the intersection point? The lines do not have ends, the intersection point has to go somewhere. The only geometry that can answer the question would be two giant hoops, but then the lines wouldn't be straight.

 

[Classical Motion]

To my way of reasoning, in order for two intersecting lines in a plane to become parallel, the intersection point would have to grow and become a line. A linear parallel intersection.

 

[Helio]

Consider two intersecting lines in a plane. As they are made more parallel, the intersection moves outward. As they become parallel, they no longer intersect. What happened to the intersection point? The lines do not have ends, the intersection point has to go somewhere. The only geometry that can answer the question would be two giant hoops, but then the lines wouldn't be straight.

This looks like a twist in the Zeno paradox. The rate of the outward point’s movement increases exponentially and allows for separation and the turtle will score a touchdown. Calculus allows this.

 

[Atlan0001]

This looks like a twist in the Zeno paradox. The rate of the outward point’s movement increases exponentially and allows for separation and the turtle will score a touchdown. Calculus allows this.

Achilles and the tortoise, SPOL and the traveler. The speed of light may tie the traveler at the finish line but will never beat the traveler to the finish line. Now someone might try to say how wrong that is because light always gets to the finish line first. My answer will be, was it concurrent time, aka a future time that got there first or was it a past history, concurrency, the future history, only arriving at the finish line (on the nose of observation via light and light speed) at one the same time 'with' the traveler?

Someone might say I'm trying to play magical tricks because that light was just emitted at just that time? So it had no time, had only the slightest time, to become a past history, much less light seconds worth of past history . . . much less billions of light years worth of past history. Achilles will never beat this tortoise to the finish line. Asymptote!

Asymptote - Wikipedia

en.wikipedia.org

Atoms squished closer together than ever before, revealing seemingly impossible quantum effects

Using a clever laser technique, scientists have squished pairs of atoms closer together than ever before, revealing some truly mind-boggling quantum effects.

www.livescience.com

Asymptote: Close. Closer! CLOSER! but no cigar! Never a cigar! . . . Though "observational relativity" will always tell a different story, that intersection was/is always reached there at a point, at some point, "at a distance." Always?! More fool observational relativity.

One example of never always, I think:
Position and superposition, asymptotically exist. And never the twain, one!

 

[Catastrophe]

Helio:
“We should not try to understand infinity, but consider anything as indefinite, where we find no boundary.” He felt "infinity" views should be reserved for God."

Or, as I have suggested on several occasions, as its true mathematical meaning of n/zero, where n is any number. Along vaguely similar lines (keeping away from the forbidden 'r' word) use of infinity in any (other) non mathematical context just means immeasurably large, e.g., number.

Apropos of nothing in particular, I have seen it suggested mathematics is at the basis of reality, although I would not subscribe to this personally.

Mathematical universe hypothesis - Wikipedia

en.wikipedia.org

Cat

 

[Catastrophe]

Helio:

The lines do not have ends, the intersection point has to go somewhere.

No, it is a mathematical fiction, so the lines do not "have to" go anywhere.
Alternatively, you can consider infinity - since this has only only a (pure) mathematical meaning. You might think of parallel lines meeting at infinity. It has the same twisted logic as division by zero. In any real sense you cannot do either.

If any really sane civilisation ever exists, it will incorporate general semantics, and 90% of 'normal' communication would be regarded as thoughtless nonsense.

Vide "Science and Sanity" by Alfred Korzybski.

a philosophical approach to language, developed by Alfred Korzybski, exploring the relationship between the form of language and its use and attempting to improve the capacity to express ideas.

Unfortunately we all have some way to go.


Cat

 

[DavidDiamond]

As many of you are aware, I have serious problems in the application of infinity. and related infinite descriptions, to non-mathematical (reality) situations. Here is a post from 2022:




I am delighted to find that serious attention is being drawn to these difficulties by Open University texts published by Cambridge University Press. Here is just a start from what I have been so pleased to read regarding cosmology, and the problems arising from division by zero and like mathematical operations and trying to apply the results to reality.

In the OU text on Galaxies and Cosmology we find:



and





Goodbye INFINITE temperatures and densities etcetera.




I am still reading further and will add as appropriate.

Cat

I propose that the simplest approach to this discussion is to note that 'infinity' can be interpreted as "you can't get there from here." There is no mathematical or reasonable procedure by means of which something that is "infinitely small" can be pumped up to have any finite size at all (I doubt the term "infinitely small" has any useful meaning.) Any universe which is infinite must therefore be infinite in time (pre-existing at any given time) having no t=0.
The implication of the above is that although the observable universe appears to have had a t=0, there must be something more, i.e. our universe must exist within a larger infinite universe, for some value of "universe". Any resemblance between the universe we can see and this 'outer' universe is a subject for speculation only.
The hypothesis that the big bang does not represent t=0 (e.g. some form of the 'big bounce) might change the terms of the above argument.

 

[Helio]

Helio:

No, it is a mathematical fiction, so the lines do not "have to" go anywhere.
Alternatively, you can consider infinity - since this has only only a (pure) mathematical meaning. You might think of parallel lines meeting at infinity. It has the same twisted logic as division by zero. In any real sense you cannot do either.

No. We get to define “parallel” as lines that includes by implication no intersection.

Calculus easily solves Zeno’s paradox. There is no chance a hare or turtle will not cross the finish line by arguing its distance only approaches it fractionally. Calculus serves to support your argument to dump an infinite series when we already have the answer seen in the asymptote.

exists, it will incorporate general semantics, and 90% of 'normal' communication would be regarded as thoughtless nonsense.

Vide "Science and Sanity" by Alfred Korzybski.

Unfortunately we all have some way to go.


Cat

Agreed. But we need only understand the context for each use of “infinite”.

 

[Classical Motion]

Math is our most valuable tool. But it can also be our most deceitful tool. This is because math and physicality are based on different references.

Math works even when the numbers only represent a number. Math is self related plus math is symmetrical. This is why it has so much value........and so deceitful. Never ending up and never ending down. A number line.

Physicality is asymmetrical. It's one way. There is no limit on big. The increasing. But there is a limit on the small. The decreasing. Infinity is one way. Physicality is one way. Plus there is always a handedness with it.

There appears to be an equal number of left handers and right handers. Some kind of handedness principle. I believe there is also some king of motion balance that is at work here. And not necessarily a balance of energy. It might be absolute motion, based on velocity and handedness area(square space). Handedness is hiding something.

But none of this matters with our current light dogma. No progress will be made til this is verified. But it seems to be taboo.

The math of light has got us fooled. And stuck. And hoping math will save us.

 

[Catastrophe]

Helio,

You might think of parallel lines meeting at infinity. It has the same twisted logic as division by zero. In any real sense you cannot do either.

I didn't say you had to. I also said you cannot . . . . . . . . . contrary to definition.

Cat

 

[Atlan0001]

Max Planck was one of those physicists who realized that there might be no limit to the "very distantly" large (the very distantly infinite) or, especially herein, to the "very distantly" small (the very distantly infinitesimal), but that there is very definitely a horizon limit to our relative reach into the small. And that that 'Horizon' limit of lines coming together in intersecting to a superposition point of otherwise always paralleling lines has substantiality (such as the "Planck heat" and the other "Planck units") all its own in the natural scheme of things.

 

[Helio]

Helio,



I didn't say you had to. I also said you cannot . . . . . . . . . contrary to definition.

I'm unclear on what you mean by "contrary to definition". If lines are deemed to remain separate from one another then it isn't contrary to the definition. So I must be missing something.

IMO, if the context of a claim includes an asymptote that is demonstrable in nature's behavior, then the use of "infinity" is not unreasonable since it is more interesting than having to explain, or remind, people what an asymptote is. I see the reasonable use of "infinity" to be hyperbole to add emphasis more than the valid mathematical certainty of it.

You've made some effective arguments, however, against the use of infinity, especially regarding a BB singularity. There is no physics nor example in nature's behavior to support such a definitive claim. One could argue that there is a degenerative limit in size, as we see for white dwarfs and neutron stars, which may be true for stellar BHs, thus preventing singularities. I believe both claims are not science but supposition.

 

[Catastrophe]

Helio,
Quote

I didn't say you had to. I also said you cannot . . . . . . . . . contrary to definition.

I'm unclear on what you mean by "contrary to definition".
Quote

Too simple to be understandable, so badly put by me!
You cannot say they meet, because that would be contrary to their definition.
Obviously too briefly put to save time Apologies.

***********************************************

Regarding Zeno - according to Google' brief intro:

In the arrow paradox, Zeno states that for motion to occur, an object must change the position which it occupies. He gives an example of an arrow in flight. He states that at any one (durationless) instant of time, the arrow is neither moving to where it is, nor to where it is not.

Coming back to my comments on use of (meaningless) words, if Zeno (if he did) had not said "one (durationless) instant of time" there would be no paradox.

If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion.[17]

— as recounted by Aristotle, Physics VI:9, 239b5

He seems to insist that the arrow moves in discreet jerks, moment by moment, but then asks 'what if both instants are the same'?
If both moments are the same, then the arrow still remains motionless.
If they are continuous then there is no space between them to move.

We can all make up our minds as to whether Zeno is best remembered for meaningless garbage. Of three paradoxes, this is the one known as Zeno's Paradox.

I am not sufficiently interested to check on the others. Any offers?


Cat

Note, for clarification (he says via Aristotle)
"If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion."

No. Zeno states that for motion to occur, an object must change the position which it occupies.
If it is motionless at both instants of time and they are the same instant, then the arrow is still motionless.
If it is motionless at both instants of time and they are continuous, then there is nothing between the two motionless instants to allow them to have moved. Hence it is not in motion.
Where is the slip in Aristotelian logic?

 

[Atlan0001]

Someone is watching an old movie on the t. v. between the bordering vertical sidebars of the t. v. The scene is one of the actor constantly arrowing down the road unmoving in the middle of the screen, but the road and all the scenery is passing left to right continuously between the unmoving sidebar horizons of the set. The actor is traveling, always in one place, on a large Carousal of passing scenery going round and round. The scene is he is arrowing in motion down the road and the scenery is still. The reality is the scenery is in motion moving right along and he is on a treadmill fixed in place between unmoving horizons.

Is he in motion through a motionless universe? Or is the universe in motion between horizons and he gets no closer to the horizon of it than 300,000kps and 14-billion light years from it, or is everything in motion (left to right, fore to aft of the traveler) but the horizon and his fixture to it (the universe's constant set / reset centering of him)?

Stephen Hawking set up essentially the same scene in his 'A Brief History of Time' with a centered "Life Zone" of the universe between fixed horizons and life forever migrating the universe's eternally revolving evolution to stay centered in that Life Zone center horizon of it.

 

[Helio]

Helio,
Quote

I'm unclear on what you mean by "contrary to definition".
Quote

Too simple to be understandable, so badly put by me!
You cannot say they meet, because that would be contrary to their definition.
Obviously too briefly put to save time Apologies.

***********************************************

Yeah, we define parallel lines as never meeting, but this is a strict definition. In GR cosmology, if space is "closed" than the lines will be bent by space given enough distance. In this case, the strict definition, I suppose, will not serve us when many billions of light years are important. But, as engineers, when is that?

Regarding Zeno - according to Google' brief intro:

If Mr. Zeno were to join our discussion, we would both likely pounce on him because he's doing what we oppose -- abusing the use of "infinity" by claiming a paradox. If a runner travels 10km/hr, then it doesn't matter how one slices the 10km, the runner will not struggle with endless fractions of distance. His use of infinite slices of distance is not juxtaposed with the infinite slices in time, such that the velocity of the runner remains constant. They did not have a formal math to address this, but we now have calculus.

I'm just guessing, but perhaps he was just teasing people with his math game. They didn't have Xbox or television back then for entertainment. [The arrow story is a little more interesting, admittedly.]

Coming back to my comments on use of (meaningless) words, if Zeno (if he did) had not said "one (durationless) instant of time" there would be no paradox.

Yes, time slices are part of any velocity, which he dances around, apparently.

He seems to insist that the arrow moves in discreet jerks, moment by moment, but then asks 'what if both instants are the same'?
If both moments are the same, then the arrow still remains motionless.
If they are continuous then there is no space between them to move.

We can all make up our minds as to whether Zeno is best remembered for meaningless garbage. Of three paradoxes, this is the one known as Zeno's Paradox.

Wiki shows several different related "paradoxes" presented by Zeno. But calculus (Lim--> 0) easily solves them all. But this is true only for asymptotes, which isn't a problem for using "infinity" unless it is used not to argue an asymptote but to argue a paradox.

I am not sufficiently interested to check on the others. Any offers?


Cat

Note, for clarification (he says via Aristotle)
"If everything when it occupies an equal space is at rest at that instant of time, and if that which is in locomotion is always occupying such a space at any moment, the flying arrow is therefore motionless at that instant of time and at the next instant of time but if both instants of time are taken as the same instant or continuous instant of time then it is in motion."

No. Zeno states that for motion to occur, an object must change the position which it occupies.
If it is motionless at both instants of time and they are the same instant, then the arrow is still motionless.
If it is motionless at both instants of time and they are continuous, then there is nothing between the two motionless instants to allow them to have moved. Hence it is not in motion.
Where is the slip in Aristotelian logic?

Galileo's Relativity has another way of seeing this. Using the arrow's inertial frame, it isn't the arrow moving but the atmosphere that is passing around it.

 

[billslugg]

If two non-parallel lines are made to be parallel, the point of intersection moves away at a faster and faster rate. At the point where the two lines separate, the distance is "infinite" BUT so is the velocity "infinite". An infinite velocity cannot be localized to a discrete location. So that resolves it. Stick with me for more handy tips.

 

[Catastrophe]

Thank you billslugg.

Helio, this is where I was earlier, when parallel lines first cropped up.

Of course I was assuming flatness. I am well aware, for example, that in a curved system, a triangle can have three 90 deg angles - the old Earth triangle description of 90 deg at a pole and two 90 deg angles at the equator

Cat

 

[billslugg]

The way I always resolved the parallel line conundrum was picturing the far ends looping around and connected to the rear ends. Sort of like two giant hula hoops. So maybe mathematics defines that space is curved. Or it could be that there is an edge to the universe and the two lines separate at that plane.

 

[Atlan0001]

"Superposition":

Definition of SUPERPOSITION

the placement of one thing above or on top of another; especially, physics : the combination of two distinct physical phenomena of the same type (such as spin or wavelength) so that they coexist as part of the same event… See the full definition

www.merriam-webster.com

 

[Helio]

The way I always resolved the parallel line conundrum was picturing the far ends looping around and connected to the rear ends. Sort of like two giant hula hoops. So maybe mathematics defines that space is curved. Or it could be that there is an edge to the universe and the two lines separate at that plane.

I think that is a helpful way to see flat space vs. open of closed.

 

[billslugg]

Another way out of the connundrum might be that the precision with which the intersection can be defined falls apart at some extreme distance because of Heisenberg uncertainty or perhaps quantization.

 

[Helio]

Another way out of the connundrum might be that the precision with which the intersection can be defined falls apart at some extreme distance because of Heisenberg uncertainty or perhaps quantization.

And the anisotropy will spoil the angle.

 

[Atlan0001]

I see something here I can relate to but what surrounds it to make it so is beyond me, at least for the moment!:

Affine connection - Wikipedia

en.wikipedia.org

And:

Definition of AFFINE

a relative by marriage : in-law… See the full definition

www.merriam-webster.com