joigus

Sure. When this topic surfaced before, I remember we went over the difficulties of interstellar travel too. People tend to forget how bleak outer space is, how incompatible with human life, or any kind of life for that matter, and the sheer vastness involved. I more or less tried to include aspects like these in my camel analogy.

Agreed. On a related line of reasoning: And, Connecting to my previous argument, you're giving one particular reason why you never find camels in the North Pole: Why would they bother? In few words, it's an argument from silence, and although that doesn't rule it out necessarily, it should make us be weary of its rationale. It is my understanding that Fermi himself didn't pursue it very much at all. I get the feeling that there can be no blue potatoes. My firm belief is based on two recurrent experimental facts, One: Every time I see a potato, it's not blue Two: Every time I see something blue, it's not a potato But that may just be because in this part of the universe all potatoes are non-blue. As to erasion, that's more of an argument from noise.

Ok, this discussion is well over my head, but the reason I asked whether the rock was constantly affected by water was precisely motivated by the colour. You seem to rule out the possibility that the greenish colour be due to microscopic mats? I know I'm probably thinking of the obvious. A geologist's pick would settle it, of course. As to local knowledge, againg probably thinking of the obvious, I always try to get as many information leaflets, brochures and such from the local tourism office. Surprisingly enough, you sometimes find some valuable specifics about the geological history of the area, botanicals, etc. I'm sure you know all these things and just didn't get the chance to settle this then and there.

Ok. Thank you. That's a tad more information than I needed. Unfortunately I won't be able to pay you a visit any time soon. I'll take a look at the most significant bits when I get the time. Also, if you don't mind my saying, I would advise you to lower down a bit your expectations of getting credit. Most of these series have been summed and understood centuries ago.

Ok. I'm not gonna say much here, but I'd bet DT would rather have had a hall packed full of crooks now (the Thomas Mathhew kind, if you know what I mean). Now, that was a bloodbath.

Poodles are delicious. I find them much softer than mastiffs. And much easier to catch...

I've heard it's been raining cats and dogs last night in America...

Ok, I went back to your square, but on second thought I can't make sense of it. I thought I understood (crudely) what you were trying to do. Now I see you're dividing the square into pieces that actually overlap, so it's not a partition of the square really. It's something else. So I went to a completely analytical POV, ignoring the picture. I see no proof of convergence yet. Maybe you provided it before on some other thread, but I missed it. In purely analytical language, what you're saying is that, \[ \sum_{n,m=2}^{\infty}\frac{1}{n^{m}}=1 \] which, yes you're right can be proven, as the partial sum satisfies, \[ \sum_{n=2}^{k}\sum_{m=2}^{\infty}\frac{1}{n^{m}}=1-\frac{1}{k} \] So, yes, you're absolutely right AFAICT. But I still don't understand your square, I'm sorry. I had to interpret it purely analitically, with no pictures. PS: I tried to relate it to Riemann's zeta function, but I fell back to an infinity-infinity indeterminate, \[ \sum_{n,m=2}^{\infty}\frac{1}{n^{m}}=\sum_{m=2}^{\infty}\left(\zeta\left(m\right)-1\right) \] as I told you your method seems to indicate. The way to go is to build the partial sum Anyway... I'm a bit tired to do hard math now. That was fun.

Lol!

Sorry, I made a mistake here. Both sides have n-dependence. I'll get back asap.

Seems like the water is battering on that rock. Is that correct? Beautiful picture, by the way. Oh, I see you already said it.

When? How about proving convergence? No. We can't see that because that doesn't make any sense. 1/n is a term of the harmonic series, while 1/(n+1)+1/(n+1)2+1/(n+1)3+... is an infinite series. Therefore, the RHS either diverges or is a number, and has no n-dependence. You're saying that \( 1/n = \pi²/6 -1 \) (see below: Basel problem). No. What you're doing here is use the partial decomposition trick, \[ \frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1} \] So you've split a convergent series as the difference of two divergent series. On the LHS you have the famous series in the Basel problem, which converges to \( \pi²/6 \) so what you're saying is, \[ \frac{\pi²}{6}=\infty-\infty \] which, of course, is totally meaningless. I meant PFD (partial fraction decomposition) before.

I'm relieved that someone appreciated the pun! Yes, it seems the most sensible idea that some kind of cutoff mechanism has to be applied at short distances/large momenta. For some reason GR cannot be taken as is at infinitely short space-time scales. I hear lots of noise in the direction of complexity and gravity. I wonder if there's something to it or it's just more fuss.

Ok. You haven't provided any proof of convergence yet. On the LHS you have the square of a divergent series. So that bit certainly cannot be equated to 1. On the RHS you have an infinite sum of different convergent series. Taken one by one, they are all convergent (as per comparison test), as far as I can see. But, mind you, you have an infinite sum of infinite sums! I think you may have found an interesting relation, which I would call "improper identity"? Certainly, not an equation. Sometimes, divergent series, upon further examination, can be found to be quite interesting, perhaps through a singularity or pole of a well-known function, etc. One famous example is the improper identification 1+2+3+... = -1/12. These identites rarely mean what they say; they mean something rather more abstract and sophisticated. Professional mathematicians are experts at getting robust proofs from arguments like this. Why don't you try getting in touch with some expert in analysis in academia? As to originallity, don't put too much stock in it. It is said that every discovery has been discovered before. And please, do not name it after yourself. That's frowned upon in the academic world.

You should take a look at exchemist's beautiful picture here then. Isn't it gneiss? Oh I certainly would. Gone are the times of just a couple of fellows defending their idea against everybody else. Theorists today enlist in armies, complete with headquarters and all. I'm personally neutral in all this, btw.

Yep! I was thinking of the geometric given that two sides of a triangle in no way can be seen as a symmetric counterpart of the third. But this one is simply brilliant and brilliantly simple. After all, the 'recoil' is never instantaneous, and you would have to rephrase/generalise to discuss curvature, or a triangle with smooth vertices.

I take it that you see this as a nail in the coffin then?

Who would suspect at least two members of these forums have actually been pelted with salt.

LOL, for a while I was thinking of writing "I'm sorry, MigL". But I was sure you were going to comment anyway. No, I agree that maybe it's just a tack in the sole, as suggested in the headline. I'm no expert on LQG, I must say. But I've observed that some high-profile champions of the theory have spent some time thinking hard about extensions of the principle of SR (like doubly-special relativity, and such). There must be a compelling reason why these people have found worth their while thinking about it. Sometimes it's about how natural a hypothesis seems to be. I think it's been observed in the past that you could reasonably try to save any crazy idea (and I'm not saying LQG is crazy) by introducing more and more ancillary hypotheses. As to "landscape", that's just a word I loaned from an experimentalist talking about this. I think it woud be better to say "the region of parameters". Very shrewd counter-criticism, btw.

LQG (loop quantum gravity) predicts the minutest dependence of the speed of light on frequency, which would be best detectable on large populations of high-energy photons with very long astrophysical paths. A good candidate to test this would be a very far away (=> very early) gamma ray burst. GRB 221009A stepped forward some years ago. From: Stringent Tests of Lorentz Invariance Violation from LHAASO Observations of GRB 221009A Although this doesn't totally do away with LQG, it seems to rule out a vast landscape of the LQG parameter space. The somewhat less hyped version of these news is that we are a tad surer that LIV does not occur in Nature.

1. No 2. Yes 3. Depends 4. Neither 5. Yes 6. What?

None of this proves any healing intention or "purpose" in an ant's hypothetical "mind", which is the point we're discussing. Same with the ant megalopolis. You might want to call them architect ants, but that would just be a figure of speech.

I know what biologists mean when they say "proofreading". I was referring to people who take these metaphors for what they're not and argue that it somehow implies there's an intention at work there. Same goes, I think, for terms such as "ant doctors". "Ant doctors" is shorter to say than carbohydrate-driven release of metapleural secretion" or something like that. That's what makes these particular ants (all of them) "doctors". There's nothing more going on there.

It would have been shorter like this. The "arguments" remind me a lot of those of intelligent design: "Something like this is so amazing that I can't see how this could be possible unless some kind of design is involved". "Ant doctors"... We should take these words with a pinch of salt, along with "God particle", "theory of everything" or "DNA proofreading". Those are just colourful terms, conveniently antropomorphized for the sake of mnemonics. From: https://indianapublicmedia.org/amomentofscience/ant-doctors.php Scientific source where the "ant doctors" are explained: https://www.nature.com/articles/s41467-023-43885-w

The next step would be a mob of people with multiple-personality disorder?