Random musings about mathematics

[exchemist]

So all that ad hominem was used to affirm my position and rudimental understanding of what "bending" of space and its underlying "causality" means?
In that case I thank you.

I also find a certain irony in the fact that I always need to defend the concept of a mathematically ordered universe, which you constantly try to falsify.

Please note that by definition tensors are mathematical objects that are causal to the bending (warping) of space. By that logic, it is you who seems to have a limited understanding of the underlying "implicate order", as in Bohmian Mechanics.

I find little synopses like the following as interesting and pertinent to deeper understanding of the nature of spacetime and how Bohm's reality of the "explicate order" becomes manifest.

I call that discussion of a topic, rather than quoting textbook rote as is so desperately clung to in these "discussions", which does nothing to further support the contention that space can be bent, warped and "contorted" and WHY!

Moderators are allowed to comment on the behaviour of forum participants, so to that extent they are allowed to make ad hominen comments, surely? That seems to be what is happening here.

As a mere reader, rather than a moderator, I have to tell you that if you try to wrench this thread onto your pet obsessions with Tegmark's mathematical universe or Bohm's "implicate order" metaphysics, I'll report you again for hijacking. The thread subject is whether or not space can be said to be bent, warped or contorted, i.e. "curved" rather than "straight", not your pet metaphysics.

I would however be genuinely interested in any evidence you can produce that the cause of curvature of space is a matter of "great debate", as you claim in post 239. My limited understanding of GR is that the cause is the energy and momentum of entities, esp. rest energy, i.e. mass. I've not heard of anything beyond that, but then I freely admit this isn't my field. So if you have a relevant reference or two showing this debate, I'll be intrigued.

But it must be relevant. Stuff on microtubules, quorum sensing or differential equations (about which you have no bloody idea whatsoever), not acceptable, OK? .

 

[Write4U]

I would however be genuinely interested in any evidence you can produce that the cause of curvature of space is a matter of "great debate", as you claim in post 239. My limited understanding of GR is that the cause is the energy and momentum of entities, esp. rest energy, i.e. mass. I've not heard of anything beyond that, but then I freely admit this isn't my field. So if you have a relevant reference or two showing this debate, I'll be intrigued.

I'll do my best in the spirit of Occam and Einstein (Everything should be made as simple as possible, but not simpler. ~Albert Einstein)

This is just a little taste that presented itself right away. The difference between a smooth and granular spacetime fabric seems to be a major obstacle to any reconciliation of the current theories.

Theory of Relativity and Quantum Mechanic​

By Tayyaba Imam, February 19, 2023

Space time continuum​

General Relativity describes space as continuous, while Quantum Mechanics views it as quantized or granular. Einstein’s 1915 theory of General Relativity explains gravity as a continuous force that shapes the geometry of spacetime. In contrast, quantum mechanics regards forces as discontinuous and made up of ‘quanta’. As a result, there is no equivalent concept of a gravitational field in conventional quantum mechanics, unlike the other three fundamental forces.

Nature​

Relativity considers objects as indivisible masses in space-time, while Quantum Mechanics views matter as probability waves rather than localized particles. Relativity predicts definite outcomes, but Quantum Mechanics provides only probabilities. When applying Relativity to the scale described by Quantum Mechanics, the results are not meaningful.

​

Clash of Titans

The Theory of Relativity deals with the laws of gravity and large-scale structures of the universe. At the same time, Quantum Mechanics explains the behavior of matter and energy at the atomic and subatomic levels. However, they are incompatible with each other in their predictions for the behavior of particles at these very small scales.

Theory of Relativity and Quantum Mechanics - Scientia Magazine

In a world where time warps and particles dance to the tune of probability lies the intersection of two of the greatest theories in physics:

scientiamag.org

Einstein proposed that gravity is, in fact, the curvature of the space-time fabric.

Question (for sake of simplicity): What is the toroidal universe theory?

Why is this Wholeness incomplete? Turn this geometric slice 360 degrees and we get a toroid that satisfies all questions regarding the evolutionary continuance of the universe while maintaining conservation of energy in a closed system.

Toroidal Function -- from Wolfram MathWorld

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the associated Legendre functions of the first and second kinds (Abramowitz and Stegun 1972, p. 336): for n>m. Byerly (1959)...

mathworld.wolfram.com

This is a representation of the hypothesised toroidal Universe, or "donut theory" of the Universe. Such a Universe cannot really be visualised this way, as donuts have two dimensional surfaces, and the proposed toroidal Universe would be curved not just through space, but through spacetime.

ESO Supernova

supernova.eso.org

And is that not what we are discussing? Curved spacetime?
It would answer the age-old question of "what came before". Itself, it was there all along just with somewhat different properties.

 

[DaveC426913]

And is that not what we are discussing? Curved spacetime?

No.

 

[Write4U]

And is that not what we are discussing? Curved spacetime?

No.

OK, let me rephrase;
Is that not what we are discussing? The proposition that it is a "fallacy, Space can be bent, warped, etc, etc?"

Counter arguments are not allowed? How can a discussion take place when arguments for or against cannot be presented?
"No" is not a discussion. It is a rejection that is meaningless without context.

 

[DaveC426913]

"No" is not a discussion.

Neither is spamming reams of trigger-word inspired articles.

Discussion is not really what you're interested in.

... meaningless without context.

That must be frustrating for you.

You know what else is meaningless without context? Spammed reams of articles related only by trigger-words.

 

[Write4U]

You know what else is meaningless without context? Spammed reams of articles related only by trigger-words.

And you know for a fact that I do not read the material before I quote it? Based on what evidence, pray tell!

And as far as trigger words are concerned, do you have a different approach to gaining available knowledge? One that is not based on some conceptual trigger word? I could accuse you of spamming Einstein because of his trigger words. It's just that those trigger words are used by everybody and are therefore allowed as reference.

I suspect that you are being hypocritical because you don't know how to answer some of my questions about those newer and therefore "verboten" trigger words that accompany the advancing knowledge and science at more fundamental levels and scales.

But that is how science advances. With new technologies come new discoveries. With new discoveries come new perspectives and vocabulary (trigger words).

I make no secret of my limited knowledge, but that was a matter of circumstance, not inability to understand sophisticated concepts.
I may not know the symbolic maths, but I can almost always understand the accompanying narrative and in science it is the underlying concept (trigger word ), like "wave function" and "relativity" that guides the inquiry.

With my example of Einstein's man-in-the-box, it was me who discovered the error contained in the end of the clip, demonstrating that I do read or follow an argument to its conclusion and think about it critically. If I don't agree with it, I don't quote it. Seems reasonable, no?

Of all the years I have posted here, there have been very few instances where I needed actual correcting in conceptual understanding, if not in just plain semantics., like using new "trigger words" that may seem unfamiliar today. But give it time, those words will become rote like "quantum" that bridge the gap between physics and mathematics.

DaveC426913:
Discussion is not really what you're interested in.

Oh that's just not fair. I beg for discussion with copious quoted tidbits, only to have the door slammed in my face.

 

[DaveC426913]

And you know for a fact that I do not read the material before I quote it? Based on what evidence, pray tell!

Where did I say that?

I suspect that you are being hypocritical because you don't know how to answer some of my questions about those newer and therefore "verboten" trigger words that accompany the advancing knowledge and science at more fundamental levels and scales.

Is that what you are doing? "advancing knowledge and science at more fundamental levels and scales"?

By Googling?

I make no secret of my limited knowledge, but that was a matter of circumstance, not inability to understand sophisticated concepts.

The problem is you don't seem to know how to converse.

A: "Can space be physically bent?"
B: "Here's five pages of links and quotes that have to do with curved space!"
A: "Great. What's your point?"

This is not how conversations work.

I may not know the symbolic maths, but I can almost always understand the accompanying narrative and in science it is the underlying concept (trigger word ), like "wave function" and "relativity" that guides the inquiry.

What you don't seem to understand is what to do with those underlying concepts in a conversation.

There is a term for this: it is called an infodump.

You think that infodumps of stuff you've Googled is a substitute for any kind of constructive thought. Here, I mean thoughts beyond frivolous ones like "Hey, what if a square is just a kind of circle? Maybe circles should be enfolded and unfolded to include all shapes, including quorum sensing microtubules."

This is why I keep mocking you as a bot; you go through the robotic motions of reading and writing but never seem to really make a point.

I don't know less offensive ways nudging you toward more constructive discussion. We'ved all tried.

Maybe a less offensive way to analogize it: You act like an intrusive librarian.

A bunch of us are in a discussion in the hall of about subject X.
You step out of the library with a truck loaded with every book that has the word 'X' in it, bursting in on the conversation.
"Great", we say. "Um. Was there some wisdom you wanted to share about the specific issue we're arguing over?"
"Oh no. I have my own thoughts that have nothing to do with yours; but I thought you might benefit from the entire library of information on it."
"Yes, we know how libraries work. Thanks
"Let me read to you the first chapter of each of these." :sits down, opens a dozen books:
"Er, hey, you guys want to grab lunch?"
"Lunch?", you say. "Here's take-out the eat-in menus for every restaurant in a three mile radius!"
"We're ... going down to the caf."
"Forget the cafeteria. MondoWok on Fifth is better. Look at this menu. They have Lobster puddin'"

Does it make a little more sense how an entire truck of every book on X is not really helpful?
Does it make a little more sense how infodumps are not really substitutes for conversation?
Does it make sense how dragging a discussion off to your own personal agenda is highly intrusive?




Infodumps and missing-the-point-of-a-conversation are hallmarks of those on the autism spectrum. Have you ever been tested?

(Serious question. I'm not being facetious here. I mean, what if you are and no one knew it? We'd all have egg on our faces.)

There are tests online, but I can't vouch for any particular one. There may be many fake ones. Be sure to find one associated with the national health service of your country. And be sure to check that it is targeted for your age group. Adult and children tests are different.

 

[Write4U]

Is that what you are doing? "advancing knowledge and science at more fundamental levels and scales"?
By Googling?

Advancing my knowledge and yes, the internet is as good as any library, if used judiciously.

Infodumps and missing-the-point-of-a-conversation are hallmarks of those on the autism spectrum. Have you ever been tested?

Yes, I have been tested and no, I am not autistic.

 

[DaveC426913]

Advancing my knowledge

I thought you meant knowledge outside your own.

You know, if advancing your own knowledge is the primary goal, that can be accomplished by reading quietly to yourself. Blasting it all over the forum and annoying other members does not really further that goal.

and yes, the internet is as good as any library, if used judiciously.

Well, you could use some knowledge advancing on that "judicious" part.

Maybe try restricting yourself to, say one giant infodump article per page per thread. That's one more than the average.

 

[Write4U]

A few quotes and a link is info-dump? I call that research to broaden the scope of the inquiry.

As I have made clear on several occasions, when I research a subject I look for common denominators that tie seemingly disparate subjects together under a larger universal umbrella, a common theme that yields a deeper understanding of how natural phenomena relate to other natural phenomena.

This mode of research was advanced by David Bohm who observed that science has become fractured by specialization and that prediction was recently confirmed by Sabine Hossenfelder who complained that today only commercial specialization is rewarded with grants, stifling deeper more subtle general aspects of scientific knowledge and application from dedicated research.

Else you get a "discussion" like: https://www.sciforums.com/threads/entities-and-attributes-in-science.165979/, which leads nowhere except frustration and ill-will.

Question: Is the Universe a bottle with energy or stuff in it? If so, is space curved inside the bottle? Is space "emptiness or stuff" ?

Is the universe made of energy and matter? If so: where did the matter come from?

Matter and energy are the two basic components of the entire Universe. An enormous challenge for scientists is that most of the matter in the Universe is invisible and the source of most of the energy is not understood.

What is the universe made of? | Center for Astrophysics | Harvard & Smithsonian

Matter and energy are the two basic components of the entire Universe. An enormous challenge for scientists is that most of the matter in the Universe is invisible and the source of most of the energy is not understood. How can we study the Universe if we can’t see most of it?

www.cfa.harvard.edu

 

[Write4U]

Yes. You do. That's your agenda (see post 250, where you confirm this). It is counter to the goal of any particular poster's thread. Any particular thread is asking a specific question, defined briefly in the title and clarified in the OP.

Sorry if I misread the depth of the questions. I'll keep it in mind.

 

[Write4U]

Sorry if I misread the depth of the questions. I'll keep it in mind.

p.s. I had my own threads, but they were closed (hijacked) for being too complicated, apparently.

 

[DaveC426913]

I'll keep it in mind.

Historically (and it has been a looong history) you have not, in fact, kept it in mind. You'll forgive us if we don't hold our collective breaths.

 

[exchemist]

I'll do my best in the spirit of Occam and Einstein (Everything should be made as simple as possible, but not simpler. ~Albert Einstein)

This is just a little taste that presented itself right away. The difference between a smooth and granular spacetime fabric seems to be a major obstacle to any reconciliation of the current theories.

Theory of Relativity and Quantum Mechanic​

By Tayyaba Imam, February 19, 2023

Space time continuum​

Nature​

Clash of Titans

Theory of Relativity and Quantum Mechanics - Scientia Magazine

In a world where time warps and particles dance to the tune of probability lies the intersection of two of the greatest theories in physics:

scientiamag.org

View attachment 6818

Einstein proposed that gravity is, in fact, the curvature of the space-time fabric.

Question (for sake of simplicity): What is the toroidal universe theory?

Why is this Wholeness incomplete? Turn this geometric slice 360 degrees and we get a toroid that satisfies all questions regarding the evolutionary continuance of the universe while maintaining conservation of energy in a closed system.

Toroidal Function -- from Wolfram MathWorld

Toroidal functions are a class of functions also called ring functions that appear in systems having toroidal symmetry. Toroidal functions can be expressed in terms of the associated Legendre functions of the first and second kinds (Abramowitz and Stegun 1972, p. 336): for n>m. Byerly (1959)...

mathworld.wolfram.com

ESO Supernova

supernova.eso.org

And is that not what we are discussing? Curved spacetime?
It would answer the age-old question of "what came before". Itself, it was there all along just with somewhat different properties.

There is nothing here to indicate the “great debate” about the cause of curvature which you claimed exists. As I thought, you just made it up.

 

[Write4U]

There is nothing here to indicate the “great debate” about the cause of curvature which you claimed exists. As I thought, you just made it up.

This does not seem to profess agreement of particle behavior between the theories. AFAIK, the difference of the wave function and the straight line of a particle is an obstacle. A wave function of necessity includes a complex curved path on top of matter, which is incompatible with the concept of a particle that @ C acquires mass and must follow a straight linear path.

Any curvature in a photon's trajectory is caused by the apparent relative distortion of space, not by its own actual trajectory.
Is that not what the man in the elevator demonstrates?
Does space inside the moving elevator bend as the elevator accelerates, while the particle follows a straight path?

Clash of Titans
The Theory of Relativity deals with the laws of gravity and large-scale structures of the universe. At the same time, Quantum Mechanics explains the behavior of matter and energy at the atomic and subatomic levels. However, they are incompatible with each other in their predictions for the behavior of particles at these very small scales.

If they were compatible then both would yield the same prediction which they don't. Bohm solved that problem with the simplest possible solution. A particle is always a particle that rides a larger Universal Pilot wave function that follows the Schrodinger equation and is deterministically predictable.

Question: Is the concept of "duality" not self-contradictory? Can anything "Be and Not be" at the same time?
Or is that superposition or just a product of human imagination?

 

[exchemist]

This does not seem to profess agreement of particle behavior between the theories. AFAIK, the difference of the wave function and the straight line of a particle is an obstacle. A wave function of necessity includes a complex curved path on top of matter, which is incompatible with the concept of a particle that @ C acquires mass and must follow a straight linear path.

Any curvature in a photon's trajectory is caused by the apparent relative distortion of space, not by its own actual trajectory.
Is that not what the man in the elevator demonstrates?
Does space inside the moving elevator bend as the elevator accelerates, while the particle follows a straight path?

If they were compatible then both would yield the same prediction which they don't. Bohm solved that problem with the simplest possible solution. A particle is always a particle that rides a larger Universal Pilot wave function that follows the Schrodinger equation and is deterministically predictable.

Question: Is the concept of "duality" not self-contradictory? Can anything "Be and Not be" at the same time?
Or is that superposition or just a product of human imagination?

No evidence here of your supposed "great debate" in science about the cause of the curvature in space.

Your post is, as they so often are, quite irrelevant to that issue.

And no, I'm not interesting in going down some irrelevant rabbit hole of yours to do with quantum gravity, nor in trying to explain to you what Einstein's thought experiment about the elevator means.

 

[exchemist]

I thought you meant knowledge outside your own.

You know, if advancing your own knowledge is the primary goal, that can be accomplished by reading quietly to yourself. Blasting it all over the forum and annoying other members does not really further that goal.


Well, you could use some knowledge advancing on that "judicious" part.

Maybe try restricting yourself to, say one giant infodump article per page per thread. That's one more than the average.

Interesting that Write4U has been tested, or so he says, for autism. If true, that suggests his annoying behaviour here is also apparent in other spheres of his life.

 

[James R]

Write4U:

Why is it necessary in every thread in which you post for several other posters to have to try yet again to educate you about what it means to post on topic?

Why is it necessary for you to repeatedly tell us all how you're a Big Picture thinker who wants to gather all the threads about every subject in the world and smoosh them all together into a grand mash of vague notions and superficial definitions?

Look...

I also find a certain irony in the fact that I always need to defend the concept of a mathematically ordered universe, which you constantly try to falsify.

This is not relevant to the topic of the current thread.

.... it is you who seems to have a limited understanding of the underlying "implicate order", as in Bohmian Mechanics.

This is not relevant to the topic of the current thread.

I find little synopses like the following as interesting and pertinent to deeper understanding of the nature of spacetime and how Bohm's reality of the "explicate order" becomes manifest.

This is not relevant to the topic of the current thread.

I call that discussion of a topic...

It is not the topic of the current thread.

The difference between a smooth and granular spacetime fabric seems to be a major obstacle to any reconciliation of the current theories.

This is not relevant to the topic of the current thread.

Einstein proposed that gravity is, in fact, the curvature of the space-time fabric.​

This has already been noted, earlier in this thread.

Question (for sake of simplicity): What is the toroidal universe theory?

This is not relevant to the topic of the current thread.

Why is this Wholeness incomplete? Turn this geometric slice 360 degrees and we get a toroid that satisfies all questions regarding the evolutionary continuance of the universe while maintaining conservation of energy in a closed system.

This is not relevant to the topic of the current thread.

It would answer the age-old question of "what came before". Itself, it was there all along just with somewhat different properties.

This is not relevant to the topic of the current thread.

AFAIK, the difference of the wave function and the straight line of a particle is an obstacle. A wave function of necessity includes a complex curved path on top of matter, which is incompatible with the concept of a particle that @ C acquires mass and must follow a straight linear path.

This is not relevant to the topic of the current thread.

Bohm solved that problem with the simplest possible solution. A particle is always a particle that rides a larger Universal Pilot wave function that follows the Schrodinger equation and is deterministically predictable.

This is not certainly not relevant to the topic of the current thread. It is also another transparently blatant attempt by you to try to shoehorn in yet another iteration of your Bohm worship obsession.

Question: Is the concept of "duality" not self-contradictory? Can anything "Be and Not be" at the same time?

This is not relevant to the topic of the current thread.

Or is that superposition or just a product of human imagination?

This is not relevant to the topic of the current thread.

Get it?

 

[James R]

A few other matters:

So all that ad hominem was used to affirm my position and rudimental understanding of what "bending" of space and its underlying "causality" means?
In that case I thank you.

I have made no ad hominem attack on you in this thread. I have merely asked you to post on topic.

As DaveC said, if you want to talk about a different topic start your own damn thread.

Let's be clear, though: this does not give you license to try to override my decision to close your microtubule thread, however. Nor does it give you license to start a blog on sciforums in which you ramble about any old thing that pops into your head about any of the only three topics you ever seem to be able to post about.

I also find a certain irony in the fact that I always need to defend the concept of a mathematically ordered universe, which you constantly try to falsify.

You're being deliberately obfuscatory here. If it is your contention that the universe is made of mathematics, then all I can say is that, so far, you have done next to nothing to defend that hypothesis. You can't even suggest how mathematics could produce a single physical effect, let alone create a physical object, or anything like that.

If, on the other hand, you're trying to accuse me of saying that the universe cannot be described using mathematics then you're making a false accusation, because I have said the exact opposite on many occasions.

Are you just pretending you can't remember any of the numerous previous discussions you and I have had about the matter, or can you actually not remember them? If it's the former, then you're a liar and you ought to stop that. If it's the latter, why don't you just come clean about your memory impairment, so that we can all make allowances for it in future discussions with you?

Please note that by definition tensors are mathematical objects that are causal to the bending (warping) of space.

How could a mathematical abstraction possibly cause the warping of physical space?

For a change, don't try to skip this question. Try to answer it. Be honest.

After all, it's the same question you've been unable to answer for years now. Why don't you just give up on this hopelessly flawed idea that mathematics causes physical effects?

By that logic, it is you who seems to have a limited understanding of the underlying "implicate order", as in Bohmian Mechanics.

By the logic of you being wrong about something, that shows that I have a limited understanding of another thing that is irrelevant?

How does that work, Write4U?

I call that discussion of a topic, rather than quoting textbook rote as is so desperately clung to in these "discussions"...

Now you're dissing textbooks that don't support your mad notions?

You don't need no edumacation? All you need is an imagination? You're running with that cry of the crank?

p.s. I had my own threads, but they were closed (hijacked) for being too complicated, apparently.

Tell that lie again and I will issue you with another warning, Write4U.

The reasons a couple of your threads were closed were posted in those threads at the time of closure. Those reasons did not include "Write4U posts stuff that is too complicated."

Go back and refresh your memory if you honestly can't recall why the threads were closed. It's all on record.

And if you can recall, then stop telling knowing lies.

 

[Write4U]

This is not relevant to the topic of the current thread.

This is not what I post as information related to the OP. I post these in response to your off-topic ad hominems!

How could a mathematical abstraction possibly cause the warping of physical space?

How could 1 +1 = 2 ?

It is not the maths that are causal. Causality is a mathematical process in essence.
To say that causality is a physical process is true, but meaningless without a quantifying measurement (mathematical function) of the values.

It is the same as saying that an orbit is a function of Time, which is also not a physical but an abstract mathematical measurement.
A function of time describes how one quantity varies with respect to time. In physics, this can refer to the position of a moving object, the temperature of a heated substance, or the voltage in an electrical circuit. Functions of time are crucial for analyzing dynamic systems and predicting their behavior over time. They can be represented graphically or algebraically, and understanding them is essential for fields such as physics, chemistry, astronomy, and engineering.6

Determinism is a mathematical function.

In summary, determinism is a characteristic of functions that ensures consistent and predictable behavior, making it a key concept in both mathematics and computer science.23

In mathematics, computer science and physics, a deterministic system is a system in which no randomness is involved in the development of future states of the system.[1] A deterministic model will thus always produce the same output from a given starting condition or initial state.

In physics​

The trajectory of a projectile launched from a cannon is modeled by an ODE that is derived from Newton's second law.

Physical laws that are described by differential equations represent deterministic systems, even though the state of the system at a given point in time may be difficult to describe explicitly.

In quantum mechanics, the Schrödinger equation, which describes the continuous time evolution of a system's wave function, is deterministic. However, the relationship between a system's wave function and the observable properties of the system appears to be non-deterministic.

Deterministic system - Wikipedia

en.wikipedia.org

Universal physical constants interactively obey universal mathematical constants. It's really not that complicated.

List of physical constants - Wikipedia

en.wikipedia.org

List of mathematical constants - Wikipedia

en.wikipedia.org

Now you're dissing textbooks that don't support your mad notions?

No, I am not. This is a perfect example of you deliberately misinterpreting what I actually am saying.