joigus

Agreed. It's so easy to see in most of this the hallmark of human beings projecting their own feelings of guilt, inadecuacy, etc onto the external universe in some sense. It's obviously a crude sense of the need for reciprocity. Something like "I've taken too much from you, here's something back". In the most sinister version it involved sacrificing children, like the Phoenicians did.

Enjoying the moment leaves little time for praising. I'll try not to. 😄 Now that you mention praising, I've always wondered why gods almost universally demand praising. If there ever was a clue that gods are made up, that's it. Gods are designed with visibly human vanity.

Wasn't Avi Loeb also involved in an alien-intelligence explanation of sorts of asteroid Oumuamua?

Well, human hallucinations and so-called AI hallucinations are different things. Same word does not imply same concept, or that the analogy should be pursued necessarily, although it could be interesting. I'm not sure if AI is relevant when talking about gods and their arguable "behaviours". Hallucinations, particularly in the way of hearing voices or seeing visions, must have existed for a very long time among us humans. How these hallucinations were "socially channeled" so to speak resulting in some kind of evolutionary advantage (unifying decision making has been suggested as a possible advantage) is a synergy that must have taken place at some point during the upper Paleolithic. It is entirely possible that AI-generated hallucinations might end up encouraging new religions in the future. Especially among ignorant people who are likely to succumb to the fascination of these tools. Who knows.

Explanation is overrated, at least in the usual sense in which most people dabbling in physics use the term. More often than not, when the dust has settled from all the explanationatory attempts, new simplifying and unifying principles emerge that seem to carry little explanatory power, turn out to be considerably more abstract, but prove themselves in the end much more powerful when it comes to calculating, and thereby predicting with great precision a plethora of phenomena. Well-known examples are the principle of stationary action (or "least action") and the principles of symmetry that other members have mentioned. This is a fundamental tradeoff that today we suspect to be inescapable. If you think about it, why would one want to "explain" GR or quantum mechanics in terms of mechanistic models, in the way of little gears and levers, fluids, etc, that act microscopically? Rather, one would expect that the deepest a theory is, the more far-removed from immediate intuition it is bound/likely to be. In other words: Why would Nature "model" its basic workings as simplified replicas of what the denizens of a little planet can picture in their immediate sensory perceptions? Also, it is a symptom of someone who doesn't understand modern physics that they tend to disregard the power of symmetry principles. The successive reformulations of the gauge principle during the 20th century from Weyl to Yang and Mills is a good cautionary tale in this regard. Oh, and Newton and Einstein do not need unifying. Newton is the weak-field, low-speed limit of Einstein. as @KJW has pointed out.

Angel messengers are just cultural derivatives of Middle Eastern mythologies (cherubim). Dreams and visions have to do with the workings of the brain.

Worshipping is deeply wrong. Worshipping is incompatible with questions. If I had any inkling of a god, I would batter it with questions before any worshipping took place. But my feeling is gods could do nothing about that because imaginary beings are incapable of actual actions.

Thank you for the pointers. Things like \( i^{i} \), \( e^{i\pi} \) or \( \left( -1 \right)^{\pi} \) I tend to see as kind of trivial (perhaps wrongly). But I didn't know about the other ones.

I'd be very surprised that only very light element and iron (which has never been involved in superconduction of any type) were the only ingredients of no less than superconductivity at room temperature. That's a very tall order. Your extraordinary claim truly deservers extraordinary evidence. No problem. I tried to react quickly.

No.

Of course. I tried to imply it: This sounds a tad more complicated than what I mean by an "interface" in IT. As I understand, an interface is barely a computer version of a translator. A piece of software/hardware that speaks both languages. But then again, I'm not an expert on AI by any means. I do remember having studied simple code widgets to generate neural networks many years ago (back in the '90s). As soon as I learned you had to reassure the system, in a manner of speaking, of what is right and wrong as an answer, my initial interest lost considerable momentum. This code was supposedly good at recognizing letters in different typographies. The world has changed a lot since then.

That's a fair point. If you just dropped a solar system somewhere in the universe at random (equal probability of dropping it anywhere), I suppose there would be instances (like, eg, if you do it close to the rim of a big cosmic void) where the mass, radiation, etc distribution would not look isotropic, nor would it look homogeneous. In fact, it would look highly "non-so". In that sense, that vantage-point factor in it cannot be overlooked. We might have been fortunate (or unfortunate, as the case may be) that things look more or less uniform from here.

The word I'm having problems with is "indeed"... 🙂

Why would it do any of those things? There is a good rationale at present to ascribe DE to the energy of the vacuum in QFT. The cosmological constant in Einstein's field equations is independent of the distribution of matter in the universe, and does not depend on time or place --thereby the name: cosmological constant. AKA dark energy.

I was wondering the same thing. Given the modular nature of these technologies (from what I gather), an important challenge that comes to mind is whether and/or to what extent, and efficient interfacing between the language-handling and the maths-handling modules can be achieved. Fatal mistakes can happen at any level, and you wouldn't want your maths module to carry out a calculation to perfection, only to find the LLM operating with the outputs failing to see the significance of a particular result. That's what human minds achieve to almost perfection, given the necessary conditions.

Agreed. It's perhaps worth nothing that whenever you have a "bulk" behaviour in physics that's complicated (or in fact non-solvable), a first-order approximation that manages to qualitatively describe things reasonably well is some kind of coarse graining that averages over any local features. One example is mean-field approximation in magnetism.

No, you're not learning. You're not learning anything at all this way. At least from this particular discussion. In a manner of speaking, you're trying to learn Chinese poetry without having studied Chinese first. If you persist, you're doomed to failure. I think most of us have kinda taken to you because you're so nice and respectful, as well as passionate about science. If you want to write Chinese poetry, you first: 1) Learn simple sentences and instructions in Chinese, like: "Hello", "can I have a bowl of rice?", 2) Then learn Chinese nuances, idioms, double-meaning, collocations of words, and so on. 3) Once you have all that mastered, the universe is the limit, and you can now aspire to create new tropes, alliteration, humour. Does it make more sense this way? Last time I told you something like this it felt like I was shooting you with neutrinos.

Please, don't answer with edits to a previous post, as it would produce a ripple in the causal fabric of space-time. ;) I didn't say it was... And more than likely it isn't.

At least this isn't another AI-generated manifesto.

Elementary operations between transcendental numbers will likely produce at least an irrational. But it's a case study.

And \( \pi^{\pi} \) is likely irrational, but we don't know...

No, no, no. You're fudging big time. And you need to understand dimensional analysis. Energy doesn't couple to curvature in GR. Energy sources curvature, by way of Einstein's field equations: \[ R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c⁴}T_{\mu\nu} \] Well... only those components of curvature contained in the Einstein gravitational tensor. Yes, you're trying to fudge, because --as @swansont told you--, for any pair of numbers p and q, you can always fix r so that p = rq. So you're doing the fudging of all fudges. Of course, saying that \( G=\frac{c⁴}{8\pi\rho} \) is wrong in almost every way. For starters, it's dimensionally incorrect. The dimensions of Newton's constant are, \[ \left[G\right]=MLT⁻²M⁻²L²=M⁻¹L³T⁻² \] This you can get from Newton's universal law of gravitation. OTOH, the dimensions of your RHS are, \[ \left[\frac{c⁴}{8\pi\rho}\right]=L⁴T⁻⁴M⁻¹L³=M⁻¹L⁷T⁻⁴ \] So you have a mismatch. Einstein's field equations tell you, \[ R_{\mu\nu}-\frac{1}{2}Rg_{\mu\nu}=\frac{8\pi G}{c⁴}T_{\mu\nu} \] Now, the LHS has dimensions of curvature (although it's not the whole story about curvature; it leaves out the Weyl components). But sure enough it has dimensions \( L^{-1} \). And indeed: \[ \left[\frac{8\pi G}{c⁴}T_{\mu\nu}\right]=M⁻¹L³T⁻²L⁻⁴T⁴ML²T⁻²L⁻³=L⁻² \] Please stop trying to dive before you've learned to swim, or else you'll sink. @studiot , @KJW , @swansont , @MigL , @Phi for All , @Markus Hanke , and myself, are just trying to help you. You should be diving into dimensional analysis, balancing chemical equations, proving trigonometric identities, learning vector algebra and the like. PS: Please refresh the page for LateX display

I see. But massive objects that are at rest relative to each other also experience gravity. Furthermore, gravity satisfies the equivalence principle, so all objects experience the same acceleration, irrespective of their state of motion (relative velocity with respect to anything). It seems difficult to explain these features with a theory that puts relative velocity with respect to some "ripples" at the source of forces. Besides, we already know that the only way (consistent with the principles of either classical mechanics or quantum mechanics) that a fundamental force of Nature can depend on a relative velocity (known as magnetic) is: \[ F=k\boldsymbol{v}\times\boldsymbol{B} \] where \( k \) is a constant and \( \boldsymbol{B} \) is a vector function of position and time. This is known popularly (and a little bit incorrectly perhaps) as "Feynman's proof of Maxwell's equations", as divulged by Freeman Dyson, and revisited by others. See, eg, https://arxiv.org/pdf/hep-ph/0106235 for a later review. It is entirely possible that I misunderstood something in the key idea, of course. PS: Please refresh the page for the maths to display correctly.

Nothing stands still. Motion is relative. Galileo knew this already.

I was reading some angry comments by a member whose thread has been closed hours ago. This person wrote a saying in a language other than English. A language spoken by quite a number of people in the world that I couldn't understand. While using Google Translate in order to ascertain any possible precise nuances of the sentence, I've been led to ponder on how much of what we say might be lost in translation when we use such tools. Here's the result of my experiment taking a sentence in vernacular English as a seed and Hawaiian (how vernacular, I don't know) as target language in the first part of an obvious loop: Input in English: "Shut up, bitch!" Translation to Hawaiian: "E noho mālie, e ka wahine!" Input in Hawaiian: "E noho mālie, e ka wahine!" Translation to English: "Be quiet, woman!" I somehow find hard to believe that GT would produce anything like the inverse loop here. This is mostly an observation, but any reflections are welcome.