joigus

@MigL is right. More to the point. Almost infinite is nonsense. If someone gives you an "almost infinite" number, multiply it by 10^10^10...^10 and it's "almost nothing" no matter how big it looked.

Thanks a lot to both of you. Expectations are very important is the main idea that I wasn't aware of. I forgot to mention that the classes are taking place as teleconference, due to Covid-19. As to the big things is seems I've somehow got it right. Maybe it was intuition. As to the little things it seems that his family already are taking care of everything that's not under my control. I wasn't aware of this. I see. This particular boy is so keen on understanding things, that I don't need to press him at all. He often says, "don't tell me; I want to figure it out by myself!" That's not always a good idea... Yes, he might. He's very intelligent. I just hope he doesn't ask me what time is...

With the exceptions of occasional crackpots, the selfish, the unkind, and the uncouth; and on rare occasions, the sheer lunatics that come and go, most of the members of this community are giving me an enormously valuable environment to exchange ideas. Teaching has been a great pleasure for me for many years. Now, for the first time, I'm tutoring a boy that suffers from Asperger's syndrome. After a month now, I must say that it's been one of the most gratifying teaching experiences I've had so far. Things are going pretty well, good results keep coming, and everyone involved seems to be happy. We've started with maths. Every time he shouts “now I understand it!” is priceless. But he's emotionally vulnerable, and also gets quite anxious when he misunderstands something and gets embroiled in the wrong calculation. The verbal feedback is somewhat wanting, because he stumbles over words and speaks too quickly for me. So sometimes it takes me a while to realise what he really means. Any experience that any of you may have to share with me, any tips and directions, will be greatly appreciated. Especially heads-up when it comes to physics, which I'm kind of dreading.

I personally don't abide by what maybe @Eise would call a shallow reductionism. I consider myself a reductionist in the sense that I think that what molecules do in people's brains, however complex, determines what they think, feel, believe, wish, and finally do. And those things must have been set in motion by what they have seen, heard, thought, felt, believed, wished, and finally done, in full circle, before that, reflected in the behaviour of the molecules in their brains, which have registered somehow in their states the previous experiences. I don't think that saying that what people wish, or think, feel, believe, wish, and finally do determines what the molecules in their brains do. There is a fundamental asymmetry in the explanation, if nothing else. I think that it's the workings of the molecules what gives rise to actions, feelings and decisions. It's very awkward to me, to say the least, that it's the other way around. I don't think that's what @Eise is saying though, I must clarify. One thing is what molecules determine with their behaviour and a very different thing is the system of concepts that we need to describe it (rest potentials and activation potentials, membrane processes, homeostasis, and so on.) An atom alone is not engaged in homeostasis. It wouldn't "know" it is. It's the fact that there are many atoms, that they are what they are in the proportions that they are, and that they are combined in the precise way the are, that determines my wishes, beliefs, and course of action. My wishes determine nothing in what an atom does. Or maybe concepts can be twisted so that you can express things as if they do, but it's the most uneconomic way of describing things. I just hope we don't agree just because we've had similar upbringings, @vexspits. I've always envied the Protestant/Jewish/atheist upbringing because of the tradition of rational criticism. But it's been a long time since I freed myself from my Catholic upbringing. At a high price family-wise, of course. But when you dislodge yourself from such amount of nonsense, the momentum you gain is truly amazing. The truth is that the more we talk about this, the more points of agreement I find with you, at least as to a working definition of free will. Being able to act according to your wishes and beliefs is good enough for me. I would throw in things like fear, or reckoning, etc. But... It's possible that our sticking point is just about the role that emergence plays in all this. It seems to me that you contemplate emergence as something that stands on its own, independently of what @iNow calls "the components." I find it very difficult to see, as you seem to do, a mechanism levitating logically on top of other substructures that we know to be there and be sub in a meaningful way.

My guess would be that they wouldn't, because R3 is special in that covectors are isomorphic to vectors. In Minkowski I've seen them used, but that's because you've got spacelike and timelike, and the derivative by the invariant parameter must preserve the genus, so you would have the timelike element plus a Frenet-Serret spacelike triad. Spacelike go their own way, while timelike keep the isomorphy between 3-vectors and 3-covectors, so that Frenet-Serret would still be useful. But that would be just my guess...

My guess would be cerebrorum malleus.

3Blue1Brown is a very high quality channel for maths, IMO. And Mathologer. Mathologer is especially rigorous while intuitive at the same time. I don't remember if they have anything on infinitesimals or geometry, but I'm sure they have.

True. But that is in GR. In Newtonian gravity fields can be ascribed to point sources or densities of mass, and studied separately to a certain extent. Also true. In GR frames of reference are local, not global ("global" is preferable to "non-local," for what I think you mean) "non-local" being generally reserved for other concept in field theories. Namely, couplings or interactions of the form, \[\varphi_{1}\left(x\right)\varphi_{2}\left(x+d\right)\] with \varphi_1 \varphi_2 being any field variables. Fields are better looked upon as distortions of space-time, rather than as a property of matter. "Matter" in modern field theory (QFT) rather being considered as excitations of fields. Most fields (Yang-Mills fields) requiring an "internal variable" (independent of space-time) and gravity being peculiar in the sense that these "distortions of space-time" are felt the same by all matter and radiation (equivalence principle.) That's why gravity can be considered as a distortion of space-time itself, while Yang-Mills fields are excitations of these internal variables that can be studied in terms of their space-time projections. All are local fields, and none are strictly linear. Even electromagnetism in QFT (quantum electrodynamics) has non-linear effects at sufficiently high energies.

My interpretation of the question was more along the lines of @swansont, rather than @Markus Hanke's. Although I think Markus is totally right in his qualifications. And the reason is that the user said "how do gravitational fields interact," using the plural for "gravitational fields." The moment you consider different sources of gravitational field and ask yourself how they combine, it seems to me that you must be taking a Newtonian approach. Something like, \[\boldsymbol{g}=\boldsymbol{g}_{1}+\boldsymbol{g}_{2}\] In GR there is no useful way that I'm aware of in which you consider the gravitational field as made up of individual gravitational fields that can be tagged.

You're both welcome. A couple of things more. First, I just wanted to add that Fermi was no idiot, of course. But the assumptions he made date back to 1950. We know much more about planets now. Something we know now, for example, is that the Earth-Moon system is far from typical. The Moon is an unusually large satellite and has a rather bigger than normal stabilizing effect on the Earth's tilt. To the point that astronomers are starting to look upon the Earth-Moon system as a binary planetary system, rather than a standard planet and its small satellite or group of satellites. The huge tidal effect that the Moon has on the Earth is believed to have played a major part in the origin of life at least during the first billion years, stirring the chemicals dissolved in water and thus triggering volume reactions (much quicker and efficient) rather than surface effects. https://www.space.com/12464-earth-moon-unique-solar-system-universe.html Another factor is the presence of outer giants like Jupiter and Saturn, for billions of years playing the role of shuttles for asteroids from the Kuiper belt, etc. Water and amino acids in the asteroids are also thought to have been very important. In case any of these factors were found to be essential to the appearance of life, it could be a basis to estimate the number of solar systems in the Milky Way that satisfy similar conditions. Would other different sets of conditions be just as good, or maybe even better? I don't know. I don't know if anybody knows. Drake's equation came later than Fermi's argument (in 1961). Actually, I think Drake's equation is a more promising ground for estimating the chance of there being intelligent life forms, among other things, precisely because, although ambitious, it's a much less assuming parametrization of the probability, rather than an equation or a "closed" calculation. There is room for re-estimating the factors as we learn more about the phenomenology of galactic (or extra-galactic) solar systems. Plus the last factor is, if I'm not mistaken, the probability that a civilization will be able to send signals, rather than travel to Earth, which significantly increases the odds. Fermi was concerned with interstellar travel, AFAIK. The detection of signals with a message in them will probably be the first evidence, if there ever is one, of some form of intelligent life besides us in the universe, rather than the flight of UFOs. But here's the bad news, IMO: Take a look at this table with time gaps separating the appearance of new levels of organization: First prokaryotes (from Earth's formation): 1 billion years First eukaryotes (from prokaryotes): 800 million years First multicellular eukaryotic organisms (from single-celled eukaryotes): 2 billion years First intelligent life (from multicellular eukaryotes): 700 million years Average for the appearance of a new level of organization: 1.125 billion years Now suppose there's a planet out there with something like eukaryotes (cells with a nucleus). You're going to have to sit there waiting for 1.1 billion years for you to see anything interesting to happen if the above table is anything to go by. That's the problem.

Yes, but the author also says, The limbo picture is the one lingering in my mind. Also, I fail to see what the coronavirus has to do with coal in and of itself. Many other industries have been affected by CoVid19. In the energy department, oil, for example. I find the article wanting in the causal analysis.

No, sorry. I wasn't clear. Fermi was skeptical of the possibility of intelligent life in the universe that would be in principle technologically capable of interstellar travel. So in that sense, Fermi's comment must have been critical or skeptical of that possibility. While we were talking, I've searched for references to the origin of Fermi's mutterings, and it seems to have been an informal conversation of which it is by no means totally clear what he meant: https://en.wikipedia.org/wiki/Fermi_paradox#Original_conversation(s) Then it seems that he got involved in somewhat more serious calculations and estimated the probability of interstellar travelers to be negligible. One of his arguments apparently was that the Earth is a typical planet, which we know for sure not to be true, for example.

When Fermi said that he wasn't in his finest hour, I think. It would be sad that he were remembered mostly by that. It's very easy to rebut: Stay in the North Pole for 10.000 years looking for camels. After that time, you haven't seen camel number one. Conclusion: Camels don't exist, because otherwise they would have reached the North Pole by then. When you're heavily constrained in your observation, it's easy sometimes to forget that there are correlations in your observation methods, accessible places to look, etc. Fermi's argument is called argument from silence, and it's very well known to archaeologists and historians to be seriously flawed. It is very likely that someone caught something informally muttered by Fermi and poorly thought out, IMO, and then went nuts with it. The argument from silence can sometimes be used --with extreme care-- if you are reasonably sure that your observation method is not biased. Another example: Marco Polo didn't mention the Great Wall of China. That doesn't mean it didn't exist back then. Edit. Another example: Aliens in the opposite spiral arm of the Milky Way could think, "I'm sure there's no life in the Milky Way besides us, because otherwise they would be here by now." But, wait, there's us, isn't there? You can think of tens more examples like these...

Thanks a lot, Mordred.

You're mixing too much, too sweepingly, too loosely, too vaguely, too disconnectedly, too ambiguously, too ambitiously, and too pointlessly, IMO.

Thanks a lot. How can I ever respond in kind? Would you rather have a rep point or a recommended read? I don't think I can recommend you a read that will surprise you... @MigL tells me I hand out rep points like they're candy. I hope it's not me going at it again, @studiot. +1 I'm very loose with rep points. It's better than being loose with guns, I suppose.

Can you sketch some kind of rough holographic dictionary in your picture of matrix objects and strings? Bulk/surface, etc... I'm not sure what your intention on this forum is. Do you want to ask any questions, or do you want to explain your ideas, or do you want to give them some publicity? Or do you want people to tell you what they think about your ideas? Do you want to elicit questions, corrections, collaboration? The more down-to-Earth you get, the more feedback you're going to get.

It's the algebra of real numbers. It's not "some form" of special algebra. If you can point to what the problem is with @Strange's explanation: Maybe I can try to make it simpler. But I think you should really go over the steps. It's really all down to multiplication and division of real numbers.

Sorry. If it's not too much trouble, I really want to understand your argument. The way I see it, there are two problems related to the cosmological constant. Or, if you wish, a problem in two steps. One is: 1) Why is it that QFT predicts such a large value (about 10120 times its measured value.)? And then: 2) Why is it that its actual value is so small and why that particular value?

Good point. +1 It is believed that the impact was so considerable that it actually sent ripples of seismic activity around the world. If the world was going through an especially traumatic seismic/volcanic episode or series of episodes, it would have been the last straw. Some renowned paleontologists --although not many, I believe-- can't still bring themselves to believe the impact was the main trigger of the catastrophe. I cannot claim I've made any calculations, but a meteorite the size of Mount Everest hitting the ground at 10 Km/s in an oblique trajectory near a seismically active area on a shallow sea, sounds to me like could be enough to do it. The main suspect as to the seismic activity was the formation of the Deccan traps (very far from the impact) and also the mid-Atlantic ridge, pushing America and Eurasia/Africa apart. I'm waiting for someone with expertise to tell us about what they think could have been the culprit. Plus a summary of the chain of events.

"Yes and no" doesn't bode well with standard logic. Yes and no is the empty set of propositions. As soon as you get out of the empty set, give me a call. Maybe I can help. He doesn't mean anything remotely similar to the derivation function. That's more like what they mean. At no point does @ALine write the words "well defined." This is your imagination speaking. You seem to assume lots of things that neither you nor others have written about. Say you want to see how, (A ==> B) <==> (Neg B ==> Neg A) A: I'm Italian B: I'm European Obviously: A ==> B (if I'm Italian, them I'm European) Let's see that this is equivalent to Neg B ==> Neg A I'm not European ==> I'm not Italian Is that intuitive enough?

I totally agree with this +1. I also concur with Swansont that it looks like you've proven 1=1 there. I'm not sure. I'd have to go over the details. I do have an argument of why the cosmological constant gives the order of 10120 times bigger than it should be when you apply QFT. It has nothing to do with the coupling constants, as Mordred suggests. Maybe I'll talk about it some day in Speculations so that everybody can slap me in the face openly for getting sloppy. Or maybe I won't have the guts. It's to do with how incredibly many particles you're producing when you take the Mp cutoff seriously (you plan to actually go to Mp collision energies.)

Down to basics, I think you're sniffing around the idea that, (A ==> B) <==> (Neg B ==> Neg A) For the particular statement, A: f(x)=f(y) B: x=y So if you find any occurrence of x=/=y (Neg B) and f(x)=f(y) (A); you've proven f not to be injective or one-to-one. Is that it?

OK. I'll let Studiot press you for more data, but AFAICT, you're trying to keep too many things constant. Enthalphy is useful for processes at constant P, in which case the change in enthalpy can be identified with the heat (isobaric,) but those processes are not at constant T, in general. If you keep P, T, n constant, V is determined and thus constant too (by the equation of state,) and there goes your process. Also, a detailed specification of which processes you would like to compare would be very useful, if not absolutely necessary. The more specific you are, the better answer you're going to get.

. I've got a wonderful anecdote about Fermi. He was to be thesis advisor of a young researcher. One of the questions he asked: How many barber shops are in Chicago? Now, that's devilishly clever. (Just to compensate.)