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I wonder, is it in fact useful? When? Where?

I think @StringJunky is implying a necessary condition for a phenomenon to be emergent, not a sufficient one.

I dunno, this concept is a work in progress for me. Just musing: could entropy have something to do with your examples not being emergent?

Geostationary orbit is equatorial https://en.wikipedia.org/wiki/Geostationary_orbit The tilt is why it won’t block the sun except when the sun is lined up over the equator

You can't reverse engineer an emergent phenomenon and, conversely, you can't predict the outcome of an emergent phenomenon from its component parts. Ultimately, emergence has a strong unpredictable element about it.

Orion should be visible from London. Your sky chart may not be for your location or the right time of the year.

The quality (not qualification) or characterisitc of being emergent applies to a phenomenon, not to an equation. However I think that since emergence only occurs in special circumstances, these special circumstances need be incorporated in any description or specification of an emergent phenomenon. As a for instance, my earlier example of arching action. Despite the antiquity of the arch, we do not have an 'equation' to this day that properly describes arch action, although we understand it. Furthermore arch action only occurs in particular circumstances.

Trying to challenge me? I think we can talk about emergence when following condition applies: The phenomena can be described without knowing or needing from what they exactly emerge. A few examples: the gas laws of Boyle and Gay-Lussac: without knowing that gas is made of flying around particles these laws cna be fixed empirically (but not explained, of course, then we have to get to statistical mechanics, assuming smallest particles bouncing around) One of my favourite examples: traffic jams. These can be mathematically described without knowing if we are talking about horse cards, diesel or gas cars And yes, of course, free will. The problem of free will and determinism can be decided without reference to the brain, neurons and neurotransmitters. Just take determinism for granted, and ask if in a determined world free will is possible. That simply means that neurologists have nothing to add, if you take determinism for granted. The exact details are of no importance. About time as an emergent phenomenon I have nothing to say: ask Carlo Rovelli, or Lee Smolin... It is of course highly speculative. But a fact is that all our established theories can work very well without knowing if time is emergent or not. Wow, 4 weeks later. Sorry....

Sorry for neglecting the forum for such a long time. It is a stressful time (corona (homeoffice) and stress at work), and I seldom have the peace to do more 'thinking' for this forum. Here an observation about this topic: I wonder if it is really so astonishing that math is so effective describing the world around us. In my opinion we need only two aspects of nature to more or less guarantee that we can use math to describe it: regularities in natural phenomena, to begin with simple phenomena like the yearly rising of the Nile, sun sets etc. I cannot imagine a regularity that cannot described mathematically. If somebody can, please give an example. the existence of 'natural kinds', like water molecules. Simply said, if you acquired knowledge about one water molecule, you know it is valid for all water molecules. Life would would be impossible without these. So just add the smallest bit of anthropic reasoning (if above aspects of nature would not be the case, no observers could exist) and your are done. No?

That depends on what you mean by 'thrive'? If it destroys the ecology that was there before, it's not only wrong, but eventually fatal. Two things: 1. Distinguish types of 'farm animal'. I have no problem with horses kept for riding or pulling; sheep and llamas kept for wool, cows and goats kept for milk, hens or geese for the eggs. (The male offspring would still have to be killed young because of the feed, tending and grazing, as well as the rivalry among them, so they wouldn't have much to thriving time.) I'm not sure old cows and sheep would be very palatable, but I suppose you could eat them once they've had a long and happy life. I do have a problem with animals bred and kept for no other reason than to be killed young, for their flesh: pigs, steers, waterfowl, turkeys. But my aesthetic objection to breeding and raising animals in order to be killed, even if humanely, is the lesser of the problems. 2. Keeping farm animals in conditions that I could describe as "a good life" is a whole lot less economical than factory farming. It's just not commercially feasible in the world as we find it. (I can imagine changes that would make it feasible, including wide-spread permaculture, but the current economic structure does not encourage alternative methods. I think the movement started half a century too late.) The biggest obstacle of all is the sheer number of humans demanding a meat-heavy diet. To meet that demand, you need to produce on a scale that's impossible to sustain through humane and ecologically sound farming practices. If the demand were reduced by 90%, we could manage. (Though there still remains the problem of all those billions of carnivorous pets.) I had not previously made a moral argument. I do have convictions on the matter, and do grapple with compromise. I have not found a way to live in the world without compromises, some of which are uncomfortable.

This Zeno paradox is deeper than any of the others and was not properly answered for 150+ years after the others. The other Zeno paradoxes rely on sequences of integers and their reciprocals. This one relies on something deeper. The solution came after it became necessary to integrate many functions that could not be integrated by the Riemann integral, commonly taught in high school today. As you likely know, the Riemann integral is the sum of lots of small rectangles that make up the area under a curve. In fact it is the limit as the width of these rectangles ten to zero. But Zeno's question is what happens when that limit is reached ie the width is zero? The generalisation the the Riemann integral was introduced by Lebesgue (1875 - 1941) adn this ushered in what today is known as measure theory. https://en.wikipedia.org/wiki/Henri_Lebesgue The other approach to this issue was also developed in the first half of the 29th century by Paul Dirac and is known as the Dirac Delta function.

I'm a bit unclear on how earth/moon would cast shadows large enough, at that distance, to much restrict the visible area. Especially if the Webb is following a system that's in orbit around the sun, which is shifting the star field for it anyway. Wouldn't the sunshield itself also impede the view in that direction, and again the star field would shift throughout the year such that no area would be blocked for long? Also: how does an "orbit" around a libration point use less fuel than nudges at the point itself? I'm sure it does, but there's something counterintuitive about it.