joigus

I sympathize with your qualms at https://www.scienceforums.net/topic/72263-is-nature-playing-fair-with-krauss-object/ as well as as expressed here. But something far more immediate than what professor Krauss foreshadows in the interview you quote is the fact that the surface of last scattering really is about to disappear behind the kinematic horizon. "About to disappear" as compared to the age of the universe. So it seems that Nature doesn't care too much about what's devoutly to be wished by us. I will confess something to you that's relatively private and only laterally scientific. In the Summer nights, when I'm alone looking at the starry dome, I like to think that somehow we they will find out that all the information that we've lost they will have lost, all the information that we're loosing as we speak, will be possible to salvage. One thing that gives me hope is that every major mathematical model that we use involves analytic functions. Maybe those beings Krauss talks about will pack more mathematical/observational punch than we do. Maybe they get to exploit the mathematics in combination with super-duper-high-precision observations to the point of being able to extrapolate where they can't see and cross-check back in the visible universe by analytic continuation arguments. I wish that were to be true, even if it's just to satisfy the curiosity of remote-future virtual minds running on computers. This is the expression of a hope, rather than a conviction, but a reasonable hope at that, I think.

+1. Don't forget this is the philosophy forum. Conjectures are as enthusiastically embraced by some as vehemently opposed by others.

A piece of feedback?

That seems as a reasonable solution. Why don't you propose that to Oxford? I would come out to support you in the end. 👍 I think some distinctions must have a historical reason... Edit: I also think some old-school lexicographers are overly obsessed with keeping old structures. I'd like to look at language more as an evolving structure, and pay more heed to what the modern use is. But the fact that some of these old structures are an issue in exams is painfully real. Students are required to say "I'm well" instead of "I'm good" although the use of the word has clearly changed in the speakers' minds. There are many other examples.

This is what I would like to do. It's the simplest solution and it seems generally accepted by most native speakers. My problem is better illustrated by Oxford Dictionary: There's one more "different meaning" (I don't see that much of a difference). But then you come across this: https://www.oxfordlearnersdictionaries.com/definition/english/belief?q=belief For that one I've got "data" vs "datum," but English has a love-hate relationship with Latin words. Yes, it's like there is some nuance I can't quite wrap my head around (as to why do you need the distinction). An example of the uncountable use, to me, could be: "[...] on matters of religious belief" An example of the countable (I think, would be): "People have conflicting beliefs about the subject" It's kind of confusing (to me, at least) to use have same words with very close meaning, and with different grammatical character. There must be a nuance, but I can't quite put my finger on it.

Hi, again. I'm kind of obsessive-compulsive linguistically. Plus I have a (small) problem. My question has to do with the grammatical splitting of English nouns into countable/uncountable, that has little to do with meaning. I understand most people take a stance much more utilitarian than mine. That really resonates with me. But, I've met problems with words like "input" or "advice" before. When you are under the obligation of teaching your students proper English, and you know they're going to be judged by the level of it, this trivial matter kind of crosses some line. "Input" and "advice" are uncountable. So, if you want to refer to one, let's say, instantiation of the concepts, you use formulas like using a determiner of sorts: "I'm going to give you a piece of advice" or, "Let me give you some input" What would be a natural companion for "belief"? In a slightly different use of the word, it acquires the countable character to mean "a particular item of belief." Then the plural becomes "beliefs." I know that to be valid in British English. Is it also in American English? But let's say I want to avoid that. One thing that concerns me both as teacher and as speaker is to develop a trick that doesn't require to stop and think about grammar while you're speaking or writing, so that the language flows more naturally. Let's say I want to find a trick to avoid using it as countable by using a determiner. Somehow, "a piece of belief" doesn't sound right to me. "A sample of belief" doesn't do it for me either. "A point of belief" or "a belief issue" somehow sound better... Another option is to completely forget about the distinction between "belief" as countable and "belief" as uncountable.

I don't want to be a nitpicker, but Hawking's radiation is not a theory. It's an extremely clever mix-and-match semiclassical calculation, using QFT in curved backgrounds, that predicts a radiation spectrum for a black hole. The thing about GR is that it's extremely solid. As Markus has told us (I wasn't aware of it) there is an exact solution of GR that includes the possibility of Hawking radiation (which historically was obtained using a living-dangerously kind of mixed reasoning!). I don't think GR is completely free of problems. The most obvious one is the existence of singularities. If you want to improve GR, you must think in a perpendicular direction, so to speak. IOW, you must look for proper generalizations, rather than denial. Another source of confusion: The Penrose diagram that you're showing patches up space time to have a BH that has a birth, as the Schwarzschild solution is eternal. So Penrose's patching up plugs in the history of the collapsing star in the past, which is not present in the Schwarzschild solution. I'm also very interested in this: How?

I'm not sure about the sufficiency of some of your definitions. For example: I would include within my belief system the absolute conviction that life of another human is to be respected under all circumstances. That no human should kill another human. Is that something that I hold "as true" following your definition? But then I may have an almost irresistible compulsion to kill somebody at some point in my life because they committed an act extremely harmful, painful, unfair and gratuitous to me or to someone I love. So there you are; there are conflicts, which you are always avoiding with your definitions. The ability to decide is constrained in manifold ways. It's not like an arrow pointing in one direction. As I said before, there's fear, doubt, reckoning of chances to win or lose, foreseeing of consequences, and probably hundreds more... I don't think it's a simple matter of following the arrow.

Whenever I remember my dreams, it's about beautiful women who want me and doors that instantly connect parts of my world that are far away, and I get from one to the other in an instant. Once I dreamt I was explaining an idea I'd had to Leonard Susskind. I'm pretty sure none of that is in my future. I'm single, frustrated theorist and I hate to travel long distances. So based on my experience I'd say dreams are about your feeling of incompleteness, rather than the future.

You're most welcome. Very interesting topic, by the way.

I'm not aware of this.

Another good point. +1 I was thinking about the albedo effect too. Only 15 % of solar energy would be absorbed. Good point about CO2 too. +1. How would this wanderer planet have captured so much water would be another issue, I suppose. Wanderer planets are very much an astronomical unknown at this point. Would they keep their magnetosphere and seismic activity intact? I haven't thought about it and I don't know what's known. But then, connecting with Studiot's point, I suppose, why conceive of an unlikely event (formation in a different solar system's accretion disk) that puts a black box as to the origin and only connects with later events? Is seems contrary to science general tendency of assuming the simplest explanation first.

One way of defining cosine is as proportional to the horizontal projection of what you call B in your figure. The segment B would be the one that sweeps the angle. That's why it's zero. The sine of 90º is 1, on the contrary, because the vertical projection of B is just B. The post does answer your question, although it may be difficult to see because it's moving. Take a look at the horizontal projection of the triangle when it goes through 90º.

Indeed. More things: Did the Moon come with it, as a package deal?

I'm not a monotone speaker, although one of the best teachers I had at university was a real drone. I mostly use some mime to teach, as a visual aid. Very general teaching tips those you're giving me. Can be applied in lots of cases, me thinks. Although I once had a student who suffered what was announced to me as some kind of geometric dyslexia. I'd never heard of such a thing. We had to circumvent anything that was visual. I can hardly remember a more difficult teaching experience than that. I don't think I did very well TBH. Going back to my student, which I will name A. A couple of days ago we started dealing with optimization problems. We got stuck, as the problems require separation in two very different steps. The 1st one for insight (setting the problem's variables, relating them and writing down the function in terms of one final variable); and the 2nd one, more mechanical, taking the derivatives and solving for the stationary point, etc. Now, there came my mistake. I should have paid more attention to @iNow, because I didn't chose the problems very carefully beforehand, which should have been in a progression from less to more difficult, especially when it comes to insight, which is the most difficult part. Unfortunately both problems were also "mechanically" difficult. Something quite amazing then happened, because A told me after having been pointed out by me what the mistake and the reason for his confusion were, that we'd better turn page and go for another problem (without having properly finished them at all!!!) I said to myself "what the hell?" But then what @iNow and @naitche told me must have resonated in my mind, because I suddenly relaxed about it, thought "what the hell!" and offered him two more problems, much better suited for a warming-up stage. It worked wonders! I just wanted to tell you, people, that your advice has been priceless. Thanks a lot. And A thanks all of you too, I'm sure. It's as if A were telling me: 'don't you remember what these people have told you, you idiot? All your contributions are helping me a lot. As A would say, Follow meeee?

+1. Thank you. That's a great answer.

That's what I think. Art and/or symbolism certainly imply intelligence. But I would make the further qualification that first hints only too reasonably come later than the real thing. The excavations of Homo naledi (335,000–236,000 years ago) at the Rising Star cave in South Africa have shown that, very likely, a stray cousin of ours that looked very much like an upright ape and didn't use tools or made any kind of art, seemed to go to the trouble of carefully placing their dead in an almost inaccessible dead end of a cave where no other fossils of animals have been found. My suspicion is that some "human" attributes go farther back than we dare to postulate. Cautiousness is mandatory, of course.

I think the key words (e.g., for a Google search) here are "theory of mind" and "anthropology." IOW: Humans at some point started to realise other humas also thought and try to guess what the other human was thinking, in order to extend prediction to the context of the human mind itself. Some scholarly sources: https://evolutionaryanthropology.duke.edu/research/3chimps/research/theory-of-mind#:~:text=Theory of Mind,that differ from our own. https://www.youtube.com/watch?v=j-bUEgalv-8 https://www.youtube.com/watch?v=TFTe3z5ISGo

+1. I act according to my wishes and belief. What happens when my wishes and belief point in different directions? What do I do then? Where does the stream go?

Sorry, I understood G⁰ is a constant function with respect to pressure, but does depend on T. From what I understand in chemistry this is the usual thing[?]. Actually, @Matthew99 does write d/dT of G⁰ in his OP. I lately follow prof. Susskind's notation. He's an American, but uses A for Helmhotz's. Ich bin ein Physiker

Yes, I started out thinking it was a next-to-trivial problem with the increments of the thermodynamic equations. Now I suspect that the problem is subtler. I haven't had the time to go over your last post in detail yet, but the fact that you do power series expansions in T checks with one of my intuitions. Very schematically, and from a purely mathematical POV, I see two possible sources for the discrepancy. One of them is that maybe you cannot interchange the "reactants-to-products" deltas with the T derivative. My comment, was in that direction. And look at what @Matthew99 is doing here: (re-edited for brevity and to clarify the point) Now, can you so "cavalierly" do that? I'm not so sure anymore. The other possibility I see (that really would cover everything) is that you need a more general expression for the Gibbs free energy involving moles and chemical potentials. I'm striving to understand the chemist's viewpoint from my rather simplified physicist's viewpoint. In statistical mechanics the be-all end-all of all thermodynamical formulas is actually Helmholtz's free energy. If you have a 1-phase system its expression is, \[F=U-TS\] This comes from what we call the canonical partition function. But when you're considering different molecular species that could be exchanging components, you really must use the full-fledged macrocanonical partition function. Because these thermodynamical variables are related by Legendre transforms, the alteration of one induces redefinitions in the other. Consequently, your expression for the Helmholtz free energy and the rest of the TD potentials would no longer depend on just P,V,T, but would have to include the chemical potentials and the moles that are being exchanged. Now it would be, \[F\left(P,V,T,\mu,N\right)\] This possibility would require me (or anybody else who shares this "insight" and has the same toolkit) to go back to the macrocanonical partition function, derive an expression for the entropy with additional constraints for the stoichiometric coefficients, derive all the potentials, and finally derive the expressions for the delta G in terms of specific heats and formation enthalpies. I'm in two minds about trying that.

No, no. I don't really have a position. I'm striving to find one. I don't agree with John Searle as to AI, so I'm not sure I'd agree as to free will. I'm more with Daniel Dennett as to AI, so... But Eise has shown me very clearly that I was (unwillingly) misrepresenting Dennett as to free will, because I didn't completely understand his points, so I must take some time to try and understand it better. Once I do that, maybe I develop my own position. Or maybe I will keep drifting, who knows. 👇

Free as in "free fall." Talk to you later.

Thank you, @iNow. +1. @Eise, please do carry on. I'm thinking about more arguments to offer you (I'm designing a toy-model scenario for you to discuss) and I'm doing my homework on Daniel Dennett and free will. Plus reviewing all the previous arguments.

Sorry, I wasn't able to look at the picture with any degree of closeness without my eyes hurting --it's quite blurry. Now I can intuit what it is about. I think I'm on to it. It took me a while to realize what you meant. I think the problem is quite subtle. There must be a mathematical reason why you can't exchange the "operators" \[\triangle_{R}\] which compares two phases of the thermodynamic system that are coexisting and, \[\left(\frac{\partial}{\partial T}\right)_{P}\] which obtains the infinitesimal change by T in an infinitesimally small reversible change (we physicists use the word "irreversible" in a different sense). The most "suspicious" expression is the second one, in which you use an integral. Unless someone comes up with the answer I'd love to keep thinking about it tomorrow, when I find the time. Does that make sense? PD: Of course, when you write: \[\triangle_{R}c_{p}=\sum_{J}\nu_{J}c_{p,J}\] you mean, \[\sum_{\textrm{products}}\nu_{j}c_{p,j}-\sum_{\textrm{reactants}}\nu_{i}c_{p,i}\] right? Just one caveat: You're trying to solve a logical contradiction between 2 expressions, one of which involves an approximation. It could take some time.