Yes, John, I agree with you. I think it is more important for fundamental science did not even a problem a "black hole exists or does not exist", but an adequate model of the Universum as a holistic process of generating structures in eternity and time. This requires a "crazy" new ontology, which will give a new heuristic for the fundamental knowledge.
Regards,
Vladimir
Tom,
Why would zero be even or odd?
Eckard,
It was when I did try imagining a point that that I couldn't get around the contradictions. No matter how small, if it didn't have some dimensionality, then how are we to "see" it having existence?
I am sorry for my ignorance, but numbers are an organizational tool, reflective of an infinitely complex reality. They can be either units of measure, or individual entities, ie, pebbles, because there is no platonic form.
No, I'm not an expert and haven't made any claims otherwise. Does this mean that interested observers such as myself should be excluded from discussions about the nature of physics, when such devices as blocktime, multiworlds, dark energy, inflation, etc, are invoked to solve the many problems? People like Tom might think I need to learn enough to understand why these many fixes are valid, but my suspicion is there is more jury-rigging than anyone cares to consider. People such as myself are only the vanguard of skepticism.
Regards,
John M
Vladimir,
First it will take the realization that when observations don't match theories, simply adding a patch is not good science in the first place.
Regards,
John M
Proof that zero is even is as easily looked up as everything else I've been telling you.
Tom,
I appreciate that this year the Nobel Prizes in physics and in chemistry honored ingenious work. Nobel himself decided against a prize in mathematics, and the Committee did also prove prudent in 1912 and 1921.
Nonetheless I confirm from my engineering perspective the importance of Euler's equation, and without overestimating myself, I maintain that Dedekind's relapse into pebble-like numbers deserves a scrutiny. What about Lorentz transformation, I know this message, and I will try and look for mistakes.
While Vladimir is correct when he mentions that pre-mathematical intuition often led to progress, I am skeptical concerning guesswork that is based on any kind of teleology including theology. I am sure, you will share this view of mine.
John C,
Sometimes I fear I got you wrong. What do you mean with "a Euclidean point in the midst of oo"?
Eckard
Tom,
So in what amounts to a base two system, not flipping the switch at all is equivalent to switching it on and off however many times.
What does this have to do with anything multiplied by zero is still zero?
I certainly am not making any claims to mathematical proficiency, but I still see space as the basis of geometry and topology, not a product of it. I really am not above being convinced otherwise, but you haven't yet managed to do it.
Regards,
John M
The Abhas Mitra eternally collapsing object is a very interesting parallel to Mersini-Houghton's Hawking radiation ECO. In both papers, the dragon that is a black hole is made to eat his own tail by the underlying physics that defines the dragon.
Mitra argues that as the dragon accretes matter, particles of matter eventually get small enough to collapse due to their own self gravity. This limits the infall of matter to somewhat short of the event horizon and the particles are then trapped in eternal recycling loops. This explanation is pure GR and is a juxtaposition of the two diffeomorphic limits of GR; the event horizon and the Planck scale. That particle collapse precludes the formation of anything like a black hole and ends up recycling the accreted matter in an eternal recursion that is an ECO. The dragon is destined to eat his tail for eternity.
The accreting black hole of Mersini and Houghton shows that particles of accreted matter also get smaller and smaller, but before the Planck limit, particles radiate as matter/antimatter pairs by the well-accepted Hawking mechanism and that radiation likewise precludes formation of a black hole. They do not deal with the recycle issue, but presumably some of that radiation does recycle.
Thus we have two really nice examples, one GR and the other QM, showing the inconsistencies associated with the common idea of a black hole. Neither model deals with the angular momentum, which is a further complication that nevertheless is a very important consideration.
It is intriguing that the concept of a boson star is also an eternally recycled object. A boson star is pure energy as a QM concept or knot that seems to be able to exist under certain circumstances in our universe, but has never been observed. The synthesis of these ideas offers a potentially useful way to finally get GR and QM back together and talking to each other again. They have simply been apart too long.
"So in what amounts to a base two system, not flipping the switch at all is equivalent to switching it on and off however many times."
No.
"What does this have to do with anything multiplied by zero is still zero?"
It doesn't, because the statement is completely false, as you would know had you read the references I gave you.
"I certainly am not making any claims to mathematical proficiency,"
Yes you are.
" ... but I still see space as the basis of geometry and topology, not a product of it."
So what? That's totally irrelevant.
"I really am not above being convinced otherwise, but you haven't yet managed to do it."
You apparently are above being convinced otherwise, or you would not spurn the learning resources you are given.
John,
Jonathan Dickau, who in my opinion has as much talent for honing in on a subject as you have for driving it away, said in the beginning of this exchange: "Dr. Mitra's main thrust is that we cannot just ignore when various Math quantities go to infinity, and must examine the Physics there more carefully."
Do you agree?
Nicely done, Steve.
Tom,
I see you similar to Cauchy in that he lost all but one of his students. At least you lost me. While your stuff is easily understandable by means of e.g. http://physicsinsights.org/lagrange_1.html , I cannot see how it relates to my seriously meant claim that singularities in physics are mathematical artifacts of pebble-like numbers. Doesn't deliberate distraction indicate lacking arguments?
Eckard
Tom,
It seems even the technology is conspiring against my education. For some reason that download came up blank.
To give a brief observation of the title though, doesn't the speed of light limit how much information from the global context into the local event limit what can be known of the input, which limits the effectiveness of least action as an effective tool?
Regards,
John M
Eckard,
I'm not trying to win a contest. There are many methods of applied mathematics that aim for the same goal. You write, "I cannot see how it relates to my seriously meant claim that singularities in physics are mathematical artifacts of pebble-like numbers."
You may be serious with your claim, yet it isn't true. A physical singularity is space collapsed to a point, which so far as we know is a physical impossibility; it certainly isn't analogous to a pebble. Cauchy, Dedekind, Weierstrass, Weyl, Brouwer -- were all essentially analysts who appreciated the value of the infinitely small, to help lead us to an understanding of the limits of the finitely large. Those limits are determined by boundary conditions -- the challenge to foundational physics is to replace arbitrarily chosen boundary conditions with a mathematically complete theory that generates its own boundaries. In quantum foundations, that leads to such discrete models as the many worlds hypothesis; in classical physics, it leads to analytical frameworks that accommodate continuous measurement functions.
"Doesn't deliberate distraction indicate lacking arguments?"
I suppose it does. My arguments have always been based on well known mathematics.
I'm sorry, John. I should have saved it as a PDF. Attached.Attachment #1: The_principle_of_least_action_means_that_there_is_no_barrier_between_local_events_and_global_structure.pdf
I think this is pretty good, too.
Eckard,
What is confusing to me is why you seem to see things as if it is common for others to see numbers as being the value only (pebble-like) rather than the accepted concept of 'place : value' being dependent on the dimensionless interval between places on the number line being a constant. We can illustrate a number line with a calibrated interval, but it's really as dimensionless as is a Euclidean point. I think John Merryman has difficulty with that composite concept of numbers, but that may arise from his experiencing a form of epilepsy. Maybe I'm just sloppy, but I really don't care how many angels dance on the head of a pin. I'm having enough challenge catching up with math that most here consider routine. :-) jrc
Argh.
https://www.youtube.com/watch?v=xz7jLnWcxMs
Yes, excellent Steve..
This emphasizes the point I've made about Quantum-Classical convergence, in comments above. The two contenders will instead be seen as two sides of the same coin, but it may take a while. I think there is too much politics involved, however, so it required someone like Hawking to comment before certain evidences became admissible, but finally the logjam is broken and progress is occurring.
Regards,
Jonathan
Tom,
While I'm not conversant on the details, I don't have any issue with the general idea. There are infinite/endless feedback loops feeding through every event and they all interact. I find the classic paradigm to be reductionistically mechanistic. Remember I spend my life dealing with animals and this does seem intuitive to me. It just seems that modeling it within the framework of linear rationality creates its own conceptual feedback loops which legitimately take a lifetime to internalize.
It is not that I seriously do not respect this commitment, but from the point of view of an outsider, there is seeming evidence of missteps along the way, leading to the various previously mentioned patches and extrapolations. We have certainly argued them repeatedly and I realize you are not going to give my side of the debate anymore consideration than if I were to declare the moon made of green cheese. So it does seem moot to continue.
John C,
I do have some appreciation of numbers as different categories of abstractions. A title of one of my essay entries was "Comparing Apples to Inches." Much of the conflict between Tom and I has to do with me not accepting spacetime as a physical reality, rather than just a mathematical model. I see measures of distance as measures of space as a real dimensionality, while measures of duration being of actions occurring within this spatial void. With the resulting relations similar to that between pressure or temperature and volume.
I also have to say my limited interneting time is being consumed by trying to follow the increasing pace of world events. The temperature is rising.
Regards,
John M
