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joigus last won the day on September 17

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About joigus

  • Birthday 05/04/1965

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    Biology, Chemistry, Physics
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    Theoretical Physics
  • Biography
    I was born, then I started learning. I'm still learning.
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  1. It's joigus. Hello. Sorry, I don't speak French. And I didn't make any mistakes. This is a divergent series. =(1+2+...+)mp/2 If you're implying a different summation rule (Borel summation), or re-ordering, you should say so. What summation criterion are you using? No. My expression checks for units of mass. I bothered to check. It it were as you say, it wouldn't. And it does. I didn't write mP*tP anywhere. Check it out. It's a finite sum, by the way, so it should be no problem. ?? I mean, no ordering criterion or Borel transform should affect it. Are we on the same page?
  2. I don't think your formula is correct. What you're essentially doing (if I understand you correctly) is adding up \( \frac{m_{P}}{2} \) a certain number of times, \[ \frac{m_{P}}{2}+\cdots+\frac{m_{P}}{2} \] and positing that this amounts to Hubble's mass*. Let's call that \( m_{H} \) for brevity if you will. How many times are you adding up half a Planck mass? As many as there are Planck times in a Hubble time. So, what you're saying amounts to, \[ m_{H}=\frac{1}{2}\frac{t_{H}}{t_{P}}m_{P}=\frac{1}{2}t_{H}\sqrt{\frac{\hbar c}{G}}\sqrt{\frac{\hbar G}{c^{5}}}=\frac{1}{2}t_{H}\frac{\hbar}{c^{2}} \] In other words, the "Hubble mass" is proportional to the Hubble time. For starters, I don't think there's any reasonable definition of a Hubble mass that can be related to the expansion parameter. The amount of mass that's trapped within a Hubble radius is the amount that happens to be there due to the whole expansion history of the universe, and should in no way be assumed proportional to time. Keep in mind that the expansion parameter, in the FLRW models can have in principle any time-dependence that you want to postulate. It can be accelerated, decelerated, oscillating, etc. *I'm assuming that by "Hubble mass" you mean the mass of the universe within a Hubble radius. What I'm trying to tell you is that the amount of mass in there is nothing to do with the Hubble "mechanism".
  3. That's a bunch of commited students though... Commited to do Seppuku if you fail.
  4. I think the answers that you got here are more than enough to go by. But let me try and add a very strong inkling that the quantum must be more fundamental. There is a well-known result of formal (mathematical) quantum mechanics called Ehrenfest's theorem, which tells you that whatever evolving quantum configuration reproduces classical physics at least for the expected values. So classical mechanics is somehow in the guts of quantum mechanics. But there is no way that you can get the quantum with all its peculiarities from classical mechanics. The closest you can get to that is very vague, but it does exist. It's called the Hamilton-Jacobi equation. Some people like to say that, had William Rowan Hamilton spent one more sleepless night, he may have surmised something like quantum mechanics was plausible. But I think that's an overstatement. How would he have figured out the need of a fundamental constant like \( \hbar \)?
  5. I couldn't agree more. That doesn't mean definitions are free from responsibility to be useful. 👍
  6. Consider me a ramshackled old monument* that needs your attention from time to time. And is very thankful for it. The uses of the present continuous that I can remember are, 1) Pointing out, reminding, or plainly informing the listener about the activity the speaker is involved in at the time of speaking: I can't talk now, I'm working 2) Pointing out, reminding, or plainly informing the listener about a future activity the speaker already --at the time of speaking-- has made arrangements for. It's impossible for me to attend, I'm seeing the doctor at that time 3) Pointing out, reminding, or plainly informing the listener about an annoying habit they indulge in: You're always talking back to me To which I would add: 4) Quite deliberately using function 2) for emphasis, when the speaker is only signaling their firm intention: I'm not talking to you anymore! And that much is what I remember, although there may be other, literal of figurative. But English is very rich indeed, and what it may lack here and there in grammatical structures, it makes up for in creativity. I've always been a fan of, I must be going** *Maybe not a monument, and just a piece of work. **Top that! A modal with "be going"
  7. LOL. Thanks. Yes, I took a quick look at the Wikipedia page, but I couldn't figure out, was he a terrible teacher? To @StringJunky: Going over your example I realised it's perfectly OK to use perfect future tense in some cases. What threw me off the tracks in the particular example was the combination of the action (making cakes, rather a short-term action), the time adverb "once", and the use of the perfect future. The overall effect of this accumulation of elements results, to me, in a very unnatural sentence. Again: "Once I make another cake, I will have possessed three cakes" I'd rather say: "Once I make another cake, I will have three cakes" What I mean is, frequency adverbs, as well as time adverbs, strongly constrict the tenses. E.g., "I often visit old monuments" Is OK. But, "I'm often visiting old monuments" is awful, from the point of view of good English grammar. Perfect? This largely depends on the state of the apple.
  8. It doesn't make sense to me, which doesn't mean it doesn't make sense. What does it mean to add half Planck's mass from one to the ratio Hubble's time/Planck's time? I can't make heads or tails of it. Where did you get it from? Mmmmm. I think I have an intuition of what you're trying to do there... Think Hubble-to-Planck units. Also, what's the purpose? I'll get back to you. In the meantime, perhaps someone can answer.
  9. Thank you. I know. I possess an almost inexhaustible patience, but I don't own it. I can own a car, or a house though. They are always on my mind. I will have owned them all by the end of 2022. But I will have never possessed them. I was once trying to explain this to a student who insisted that gerunds are nouns.
  10. You're right. It makes perfect sense. It's just that I rarely ever hear or read that use of verbs denoting possession. And I'm wondering why that is. I've searched on Google, and I get about 3'900'000 occurrences of "I will have owned," and 393'000 of "I will have possessed." It is perhaps relevant to say that most of them --and the first pages of them-- are from grammar sites, and not real language in use. But let me add that that doesn't necessarily mean there's anything wrong with them. Perhaps it's something people are less likely to say for some reason. To take an extreme example, "my dog funded the project" is a perfect from the grammatical and syntactical point of view, though it's unlikely that we would ever hear or read that anywhere. I can't say I'm familiar with his work... Perhaps for good reasons...
  11. English verbs... Who needs them. The answer is everyone! I like to think about English verbs in different degrees of "malleability". They go all the way from modal verbs --which I like to think of as verbal particles, rather than "real" verbs--, going through stative verbs --reflecting status, rather than "fixed for all time", at least in my understanding--, down to ordinary action verbs. But the most important difficulty with this categorisation --with any categorisation perhaps-- is that these qualities change with time and with how people --with special focus on native speakers-- actually use these things. Language changes, and if people somehow agree that it's OK to say "I'm loving it" --never mind McDonald's"--, then it's OK to say "I'm loving it."
  12. I'm sure there's a gif of the gaps too. There's a gif for everything!
  13. Your examples and your explanations are pretty good too, Studiot. And you're always willing to help, which is priceless. But the truth is some academic material out there focuses on producing contorted expressions that only contribute to complicate things much more than need be. Language is not mathematics, and I see students suffer every day on account of some expressions being too artificial; and other times too formal. Language should be learnt by impregnation, not by "problem-solving" techniques. I'm very much willing to hear native-English speakers tell me if "I will have possessed whatever" is an expression they would use in any conceivable context, because, if it is, I will gladly include it in my toolkit. Please, fill me in on this one, cause I'm always willing to learn. This is not past perfect; it is present perfect: https://www.oxfordlearnersdictionaries.com/grammar/online-grammar/present-perfect-simple-and-present-perfect-continuous Past perfect is I had eaten the apple. It's used to express a past event or situation with reference to an event or situation that happened further back in the past.
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