joigus

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?

You just deny what I say, or express skepticism about it. I don't see many arguments, or counterexamples, or the like. That's just gainsaying. Doubtful, for the reasons I just pointed out. I did want to be more helpful as to the constants of Nature you were talking about, but I'm sorry I didn't understand. I do believe you were trying to make an argument there. Maybe if you care to rephrase...

Illusion of design, as I've argued --only forgetting to explicitly mention evolution, as @Eise reminded me of. Delusion of design is your banner. At this point this is just gainsaying, and I've made my case, so I think I can leave it to rest.

That was exactly the metaphor I was thinking of. Oh, but it was on my mind all the time. Selective pressure is what makes the process drift away from Laplacian probability (which is what most people think of when they say "random"; Laplacian probability = all outcomes are equally likely). And "the process" is, of course, a very slow one of filtering structures that are better adapted to pass on their genes from the ones that are not so efficient. The snippet is from Gödel, Escher, Bach if I'm not mistaken, right? Yes, it does illustrate the illusion-of-design concept very nicely.

This is a straw man, as I didn't claim that something "suddenly appears" at the nth step of induction. (See my words in Italics at the end of paragraph below, or re-read carefully what I said before.) Ergodicity, pressure, temperature, chemical equilibrium, planetary formation, ecosystems, degenerative syndromes, differential cell development, protein synthesis, chaperonin-regulated protein function, embyonic development, feedback mechanisms, viral population dynamics, animal behaviour, population equilibria... and all that. IOW, everything except the raw summary of the fundamental laws of Nature. None of these things can be seen in the raw equations of physics. They appear somewhere along the huge buildup of complexity from the elementary particle to swarms of billions and billions of them. But it's not like: "Now!, the adding of one particle has made it because..." It's gradual, rather. OK. I didn't claim to have answers for everything. Although it's not really so much that I have no answer for it. I never have answers for questions I do not understand. Here I have to put my foot down. Either we agree on what you mean by random, or we stop talking about this. Otherwise I might be talking about an elephant, and you be talking about a mouse --in a manner of speaking. Non-random is just a limit in a sequence of probability distributions of decreasing entropy. A probability distribution with entropy equal to the natural logarithm of the number of states is very random. A probability distribution of 10-100 entropy (just a small fraction of unity) is almost deterministic. Only at zero entropy we are at the non-random (deterministic) realm. So again, what do you mean by random? Living things have somehow "managed" to exploit regions of very, very low entropy (very non-random in that sense). Ok. If you wan to open that can of worms, it's ok. Only be aware it is a can of worms. Scenarios in which constants of physics may be changing in a much, much wider context could make a universe in which life, consciousness, etc can arise actually in an inevitable way. The possibilities are endless. Remember Haldane: IOW: What meta-conditions could make what we see as a formidable coincidence actually inevitable? This should give you pause. One man's coincidence is another (better informed) man's inevitability. If there is no mind (as a thing separate from matter) certainly there can be no mind using my mind. As Schopenhauer said, man can do what he wants, but he cannot want what he wants. Can you choose what mind you will have tomorrow at 10:30? Nah. It doesn't make sense. Mind must arise from something physical. There is enough mathematical leeway for me to think that mind is something that arises physically. The simple-minded mechanistic view of the universe is long dead and gone. Modern science does not claim full understanding. I'm assuming by "materialism" you mean that. "Pattens of behaviour in matter" is vague enough that it can include pretty much everything, so I cannot see how it could be weak. Not precise is OK, but not weak. Let me put it this way: Life (and mind, as a consequence) finds its way by following its grove. Only it is a much more intricate grove than the one found by planets and asteroids. Impossible to see by just solving an equation from any simple statement of principles.

A brain can build purpose. A neuron can't. Purpose = "intention", "aim", "meaning", etc. What you're doing here is stretching the meaning of the ordinary word to take it outside of the specific sense in which scientists and philosophers of science use it. For you it's just a synonym of "function". In that sense, of course neurons have purpose, because you use it to mean "function". No. It's not just a question of power. It'a question of different patterns, laws, and correlations arising, which a bunch of tens of neurons cannot even begin to accomplish. You tell me. I sense a big teleological explanation coming up. Random is not just anything. It has to be consistent with patterns of quantum noise. The die analogy was just that; an analogy. Here I don't understand what you say. Maybe that's why I don't get your point. What does this have to do with purpose in ants? The constants are representations of a material universe? I cannot make sense of that. Dimensionless constants are what they are 1/137 is not a representation of anything. Had it had a very different value, there would be no mind in the sense of a part of the universe trying to make sense of the whole universe. I did: You are a dualist. Your question only makes sense if there are two different realities. Namely: matter and mind. What we call mind comes from patterns of behaviour in matter. I'll answer that when you answer this: When the Earth turns around the Sun, who is doing the computing? How does the Earth know where to go next?

This made me laugh. Which goes to prove how weird I am.

Neurons have no purpose. "Supposedly" is a word that doesn't help very much. Supposedly, many things could be true. "Inanimate" is not really a scientific category. It has meaning in common language, but the distinctions are blurred when one gets to the level of individual cells. The point was not that neurons can give rise to power purpose, btw. Rather, it was that billions upon billions can, while only dozens can't. Therefore something qualitatively different arises when really big numbers accrue. Orders of magnitude matter. The very same way that a hundred ants would do nothing like an ant megalopolis. You misunderstand "random". A weighted die is random. It only has a different odds (probability distribution) than a fair one (Laplacian probability). You, as many people, let me say, misunderstand "random". Neurons do not conform to Laplacian probability, they are very particular to special configurations. That's why they can tell one from the other. Otherwise they wouldn't play their role and our ancestors would have been eaten by the lion every single time. Many people talk (very loosely) about "random" meaning "Laplacian probabilities" or "the probability of all outcomes is the same". I suspect you also do. I said "I assume" so I wasn't characterising anything. But point taken. Ok. You disagreed with the question "what do you mean?" Here: Referring to: (My emphasis.) IOW, "makes a universe" not "makes a mind"... IOW, Stephen Hawking meant (very clearly) "make a universe", not "breathe life into inanimate matter", as you seem to suggest by his trope "breath fire" into the equations. No, as I recognize no mind. But your dualism is apparent now. Modern science does more than just evoking emergence. It runs simulations of fungi or ant colonies solving the travelling salesman's problem in real time. There are also explicit theoretical models of it in other contexts.

It's certainly not. But being human is particularly misleading in this respect: How can mind be contingent? It must have been there all along.

Does any one of your neurons have a whole map of your purpose in life? Are 86 billion neurons more than two? Yes? OK, then more than two neurons bumping into each other can give rise to purpose. "Randomly" is just a misinterpretation on your part. Glial growth occurs in correlation to "regularities your neurons bump into" rather than being a one-off event, as you seem to suggest. "Breathe fire into" is just a metaphor. What do you mean? Didn't you understand my qualifications in that sense?: No. I assume --and this is just a wild guess--, that's what you are saying. Actually, that's what you are saying. Here: I'd rather say "the universe is made of matter and mind" is (most likely) just an illusion. Let me be fastidiously clear: What I mean is that ants building a megalopolis display a behaviour that's not programmed in each and every one of their genetic codes separately, or even their brains and the chemicals in their organic fluids. No matter how clever a programmer might be, no matter how subtle and seasoned in reading code, he or she would be totally unable to read into any of those things the elaborate and intricate result of an ant megalopolis, just by reading the code. It's just not coded there. That's emergence for you.

Well, it depends on what it means "to beat". If it means "simpler", it's possible that the program inside an ant's brain and endocrine system can be tackled by just a handful of code lines in the equivalent computer program. I actually don't know, so maybe that's an interesting talking point.