MigL

Are you now saying there are no actual boundaries ??? The problem is that boundaries define the discrete domains. IOW, no boundaries >> no discreteness. So which is it ???

@Eise can speak for himself, but I don't think you've got it straight and may be over-reacting. I believe he is addressing people, and we do get quite a few, who consider themselves Philosophers, and think they are making deep enlightened 'logical' statement, but in effect, don't have a clue what Philosophy entails. As a matter of fact, we run across so may of those people in SFn, that most of us in the Sciences and Math considered Philosophy a 'crackpot science', before Eise explained the purpose and reach of actual Philosophy. That is how I read the statement

That's usually done by techniques like separation of variables, which usually involves making some 'simplifying' assumptions about the system in question. The solution to the partial differential Hydrogen atom comes to mind, as two of the variables are easily separated due to spherical symmetry considerations. This is essentially what is being discussed; exact solutions to N-S may only be available if simplifying assumptions can be made. Otherwise, it's numerical methods by computer.

And others have pointed out that discreteness also leads to problems. Do you intend to address those issues, or will you just keep ignoring @studiot 's inquiries about boundaries between discrete domains ?? And how do these discrete domains interact with each other if there is nothing on a smaller scale to carry information between domains ?? The Planck scale is not necessarily where space-time becomes granular/discrete, but rather where distances and durations in space-time cease to have meaning.

I have learned something from this thread ... @joigus used the word 'celerity' in his post, and when I quoted him, I assumed the auto-correct on his phone had over-reacted, and 'corrected' celerity to velocity. ( I thought celerity might have something to do with being celery ) Turns out celerity is a term meaning rapidity or swiftness of motion/action. My apologies for assuming error of others, instead of my ignorance. ( learning is a humbling, but joyful, experience )

Not sure if anyone else has noted that whenever @Time Traveler is asked a particularly 'difficult' question, his answer always includes highlighted text, and it begins with "Thank you for the sharp and critical counterarguments" or "I appreciate you holding my feet to the fire". Almost as if he poses your questions to an AI, then copies and pasts the AI's reply here. Who are we really having this discussion with ??? I will repeat; misapplying a model always leads to inconsistencies, especially when trying to explain processes that the model doesn't take into consideration. Take for example Newtonian corpuscular theory of light, which fails with the process of diffraction. Or Huygens wave theory which falls apart for the photoelectric effect. Yet both were 'right' in their particular domain of applicability. The appropriate model follows the observational evidence, and so we have quantum particles of light, not waves or classical corpuscles. There are no observations of the Planck scale, nor any indicators of space-time discreteness ( correct me if I'm wrong and then this thread is valid ), so why try to force-fit observational reality into an incomplete/inappropriate model, and then be surprised when infinities and paradoxes appear ???

I always wondered how rice was a staple for so many ( Billions ) of people, when the areas where it is grown are so limited, as compared to grain. World production for grain is almost 5 times greater that that of rice, 2.5 Billion metric tons vs 500 Million metric tons ( milled as opposed to @TheVat 's unmilled ) in 2026. I guess that leaves about 300 Million metric tons of milling byproduct to be used for construction.

Reality is always real. Our modelling sometimes, does not fit that reality. Oh, good Lord ! Relativistic Navier-Stokes Equations ?!?!

Probably because we continuously tell young people that they should involve/engage with Politics. We are failing to push them towards more involvement with Science. Young people see Science interests as 'nerdy', not as a discipline that teaches and re-enforces critical thinking.

Of course. The mathematics are 'constructed' to model reality. As often happens, when you use the wrong model to make predictions, you are led to absurd results, or 'paradoxes', which are not evidenced in reality. If you use the model which 'fits' reality, you avoid the problems resulting from trying to fit reality to an unsuitable model. The model we currently have of the Planck scale is not one where granularity becomes evident, rather it is where/when our concepts of dimension, distance and time, become undefined. Any other predictions you are drawing from the model are unsupported. But I am glad you found a kindred soul in Anton Rize. I'll leave you two to discuss it further with AI.

Both Math and Physics treat time and space as continuous, in such applications, rather than discrete, sliced up, pieces of time and/or space. If we did not, an arrow would never move, because at each instant in time, it is stationary, in its flight; like snap-shots of its flight. ( another so called paradox, that arises from confusion, and appropriate use of, continuity, discreteness, and what happens at the limit )

The Greeks were fond of siscreteness/granularity/atomicity. Did you really need AI to realize that the ( so called ) paradox arises because of a confounding between continuity and discreteness ? ( and there may yet be confusion, not understanding, on your part )

The effect @exchemist mentions is responsible for the longevity, and 'self healing', of 2 Millenia old Roman concrete. But apparently coal ash can be used with similar effect as volcanic ( Vesuvius ) ash ... or rice husks.

Would that not take all the fun out of sex ? ( you're not 'incel', are you ? )

But Italy has been part of the EU for a great many years. I would think that the 'softening' of G Meloni's policies, are due to electoral wishes as she's coming up for re-election no later than Dec 2027. She may also have seen 'the writing on the wall' after her infatuation, and subsequent quarrel, with D Trump. As for V Orban in Hungary, he was simply a corrupt grifter in the D Trump style ( although on a much smaller scale this being Hungary ), whose people finally got tired of it; I wonder when, and if, the Americans will do the same. Not very informed on the Polish situation. Anecdotal reports of reduced, bot related, social media divisive/disinformation posts are coming in from all over. Even related to the Alberta separation issue in Canada. No formal investigations/studies into the matter as of yet.

After many years of working in the chemical industry, being part of the 'fire brigade' and the possibility of having to wear respirators or supplied air, I finally have the opportunity to grow a 'goatee' now that I've retired. I trim it every other day, as I like a 'neat' appearance ( unlike Clint ), unfortunately there is a large amount of gray in it, and with my poor eyesight, trimming is quite a chore. Its been two weeks now and it's growing in nicely, especially once I start adding a little color. My advice ? Trim as often as you need, and keep skin dry/oil free to prevent ingrowing. Tre pain/irritation will 'make a man out of you'. I'm also thinking of shaving my head for further effect.

Now I get it. It's no wonder D Trump is pis*ed off at Ukraine and Zelinisky. He was counting on the Russians to undermine the mid-term elections. Oh well; on to plan B.

Actually the Nobel Committee should let it be known that if D Trump resigns from the Presidency, they will award him the Peace Prize, as his resignation would greatly increase the prospects of World peace and stability.

This is getting tiring; especially the wide spaces absent of text in your posts. ( I spend more time scrolling than reading; or is that an example of 'nothing' ) People are giving you real world examples, and you counter with "but suppose ... ". Reality is not in your head, it is out there for everyone to observe objectively.

Notice that A Nobel died in his villa in Italy, but he left the administration of the Prize named in his honor, to a Norwegian Committee. He must have known if he had left it to Italians, they would soon embezzle all the money, and there would be nothing left. ( I'm joking )

For those not familiar with Navier-Stokes, they are a set of equations describing fluid motion. In the simplest terms, they are an application of Newton's second law of motion to a fluid, taking into consideration all internal and external forces acting on that fluid. Further assumptions allow more simplifications, by considering only an incompressible fluid with constant density/viscosity, as this video derives The next video will attempt to demonstrate various methods of solving Navier-Stokes equations. I'll take understanding ( even if I can't solve ) over AI solutions any day ...

Donald Trump was 'slighted' again, and did not receive the Nobel Peace Prize. Even after having 'stopped' 8 wars 😄 😆 🤣 . And I'm sure we'll hear plenty about it over the next few days. The Peace Prize went to Navanethem Pillay, a South African Jurist, and former UN High Commissioner for Human Rights. D Trump will no doubt, start insisting that he deserved it more, and pressuring her to give it to him. Ironic actually, as Navi's lifelong efforts to promote peace, international law, and ensure that war crimes, crimes against humanity, and genocide are prosecuted, is arguably the exact opposite of what D Trump has done.

Of course. Challenging you to bring some sanity to this thread. Thank you.

No. Time is time. It is converted into an orthogonal 'distance' by multiplying by the speed of causality, c , and making it complex, to facilitate its usage in the interval between events. That's the problem with people who think they are Philosophers, as opposed to reall Philosophers who actually understand the purpose of Philosophy ( such as @Eise ). The workings of the world around you cannot be based on models built solely in your head, they need to be grounded in observational evidence, otherwise they are 'beliefs', with no base in reality.

November 2nd can't come soon enough ...