exchemist

I remember decomposing the wave function into radial and angular parts, certainly. But tell me, if the packing density of spheres is independent of radius, how can the packing of circles not be? Or have I perhaps misunderstood your earlier response?

I recall from chemistry that the packing density of close-packed spheres is a fixed proportion, irrespective of the radius of the spheres. On that basis I think I would expect the same to apply to your 2D problem. Though I agree if one reduces the radius so that it ->0, one would seem to have a conundrum, since spheres of infinitesimal radius would, at least intuitively, seem to fill the space completely. Perhaps a mathematician can help.

In principle yes, especially if painted matt black. This is known at the Stack Effect: https://en.wikipedia.org/wiki/Stack_effect You can also get help from any ambient breeze by mean of the venturi effect, with a suitably shaped cowl on top, to create a slight pressure drop at the top when the breeze blows. And then there are these rotating cowls that spin in the wind and create suction by means of the design of their blades. My neighbour has those at the top of his 3 storey house.

Well exactly..........

No, you are way off. Have a look at this table of ages in the Levant: https://en.wikipedia.org/wiki/List_of_archaeological_periods_(Levant) The Book of Samuel, in which the story of David and the Palestinians (=Philistines - the Arabic for Palestinian is "Filistin", there being no "p" sound in Arabic.) occurs, is through to have been written about 600BC. So late Iron Age, bordering on the historical periods (i.e. when people started to write history down). The Israelites would have fought the Philistines with spears with iron tips and with swords. A sling would have typically been used by shepherds, who could not afford expensive weapons, to keep wolves etc off their flocks.

Aha, thanks. I see these started to be released towards the end of last year, perhaps in response to the "stochastic parrot" criticism of LLMs. Evidently they are expected to be less crap at maths and other problems requiring reasoning, presumably including scientific problems. So far so good. But I see, according to the Wiki article, they use even more computing resources, between 10 and 100 x what a "simple" LLM uses. So even more disastrous for the energy economy and the climate.

What makes them slow down?

The point, in this case, is that the up-front investment is gigantic.

I am very sceptical that the demand for space tourism or these completely undeveloped ideas like space art, music, ballet and sport (!?) would justify such a massive engineering exercise. What would be this low gravity medical treatment you have in mind? So-called microgravity, in Earth orbit, has some applications but that is because one is in free-fall, equivalent to zero-g. Mars has ~40% of Earth gravity. What medical procedures would benefit from that?

I notice this is about "reasoning" models. But also they mention LLMs. Is there such as thing as a reasoning LLM, now, or are these reasoning models distinct from LLMs?

That is superficial and wrong. Christianity has generally been supportive of science and indeed many early scientists were clerics or people with religious training. There have been a handful of incidents e.g. Galileo's house arrest for espousing Copernicus's heliocentrism (although Copernicus was a cleric), and the c.19th kerfuffle - among some Protestants - over the age of the Earth* and Darwin's ideas. But that's about all. For much of its history, modern science has been broadly seen as revealing the handiwork of the Creator, not opposing religion. The "Conflict Thesis" was dreamt up by two academics (Andrew Dixon White and William Draper) at the end of the c.19th - shortly after the (temporary) Darwin controversy - and is now discredited: https://en.wikipedia.org/wiki/Conflict_thesis Regarding Man being in the image of God, this has been explained already on this thread, not least by me, yet you seem unable to grasp the point. There is no conflict between Man being, as he undoubtedly is, a hairless ape and him being in the words of Genesis, made in the image of God. Go back and read the thread again. It's about Man possessing an immortal soul and being (or becoming) morally aware. Nothing to do with what physical shape his body is, or how he evolved. *Cardinal Wiseman gave a series of lectures in Rome in the 1840s about science and religion, in the course of which he showed the new discoveries of the age of the Earth were not in conflict with scripture. (In light of the Galileo affair, the Catholic church made sure it did not again make the mistake of opposing scientific discovery.) https://books.google.co.uk/books?id=4BMPAAAAIAAJ&printsec=frontcover&source=gbs_ge_summary_r&redir_esc=y#v=onepage&q&f=false

It's not a matter of taking sides. Science does not conflict with sensible versions of religion. If you think I am not discussing science, why don't you take a look at the posts I have made in the last couple of weeks?

What would be the point of settling Mars, in your opinion?

Both St Matthew and St Luke's gospels have Jesus making a joke about this, saying John the Baptist came, not eating nor drinking and you say "He is possessed!". And now I come, eating and drinking, and you say "Look, a glutton and a drunkard!". In other words, there's just no pleasing some people.

Yes, the creationist often makes the error Cardinal Newman warned against, of treating absence of a current scientific explanation as evidence of God's intervention in Nature. Newman quite reasonably observed that the Christian who builds his faith on that (what Prof. Charles Coulson was, much later, to refer to as "The God of the Gaps") is liable to having it destroyed, as science advances! However those creationists to whom I have pointed this out tend to brush it off, possibly because they nearly always are evangelical Protestants, who would rather die than concede that a Catholic cardinal had a point! 😄 What does Webb look for? I imagine spectra of key species in the atmospheres of planets, but I wonder what those would be. Free molecular oxygen might be one, but photosynthesis may not have developed in life elsewhere so one can't rely on that. Simple gases like ammonia and methane are widespread, so presumably not those.

Yes, I quite agree with both of you that it is a false argument to suggest that a low probability event is equivalent to an impossible one. I'm less sure I follow you in your comments about the evidence for life arising naturally. We have no theory of abiogenesis as yet. We have plenty of evidence that modern life forms arose from earlier, simpler ones. One can reasonably extrapolate that back to the idea of some original life form or life forms, which were the first to be "alive", but we don't have any actual evidence of the existence of these. All we have to go on is the commonality of much biochemical architecture across all modern life, which might suggest evolution from some common ancestor. I think it is important in arguing with creationists (not "theists", please note, as plenty of theists accept life can have originated without special supernatural intervention) not to overstate the evidence. One thing I find creationists often don't understand is that science, being evidence-based, does not pretend to have all the answers already.

In what context?

Perhaps it’s not quite as daft as it sounds. You think you know a subject, but the more you delve into it the more you come to question what it is really about. But I was glad this Edwards guy seems sharp and to have a sense of humour, still. Sometimes modern academics can seem po-faced, strait-laced and serious. Unlike my Physical Chemistry tutor, who died last year. He used to muck about on Concorde before it entered commercial service (researching its effect on the ozone layer), used to drink far too much, once tried to get my then girlfriend into bed, broke into the cathedral at 2 am to play the organ, got the physical chemistry lab computer to play Handel’s “Arrival of the Queen of Sheba”……etc. I only found out, in the college report, that he was actually involved in the design of the cathedral organ when it was revamped. A bit of a headbanger, really, but certainly enlivened college life.

Just read the annual report for 2024 and was depressed to read, first of all, the Dean's report, which was full of the trendy, dull, corporate-sounding platitudes that I tend to think indicate a 2nd rate mind. I was resigning myself to the idea that this is what academic institutions have become nowadays when I started reading the report on the college in 2024, written by the college theology tutor, Prof Mark Edwards. What a relief. The donnish sense of waspish humour is still alive after all, I'm pleased to say. I quote one passage that amused me: ...we have welcomed two new Canon Professors, Andrew Davison as Regius Professor of Divinity and Luke Bretherton as Professor of Moral and Pastoral Theology. Professor Davison, a former undergraduate in Chemistry at Oxford, has written with distinction on the sacraments, but has also become known as an expert on Science and Religion; his recent study, "Astrobiology and Christian Doctrine", explores the possibility that intelligent life has more than one chance of survival in the universe. Some fear that it is now breathing its last in American universities, but Professor Bretherton's welcome return to his native England took place before the impending exodus. He has written six distinguished books, of which five are about political theology; the fact that he waited until the fifth before asking "What Is Political Theology?" suggests he has already mastered the Oxford approach to teaching. I must admit I was tickled by the suggestion that this guy wrote four learned books before sitting up and asking himself, "WTF am I talking about?" 😄

This is also true of all manner of skills a child learns, from multiplication tables to French vocabulary, or sport. There is a certain amount of hard work needed to achieve mastery and the child has to realise that. Fortunately, children are quite good at that sort of thing and generally do understand and accept it without a great deal of “forcing”.

Not sure about that. I think small children are very open-minded, as they have not yet learnt when to be sceptical. I don't really think a young child has to be taught to be open-minded. I suspect it how to teach critical evaluation and scepticism without it leading to closed mindedness, incuriosity or cynicism that is the challenge.

Yrs, but I think one should raise them to be critical as well as open-minded. There are far too many credulous people in today's world. And with the internet it is more crucial than ever to be able to sort reliable information from rubbish. One important thing to do as a parent, I think, is to lead by example by displaying curiosity about the world: taking an interest in as wide a range of things as possible, be it things in nature, stories, other people and so on. I think the ability to take an interest in things, to be curious and keen to apply one's mind to whatever one encounters, is vital, whether it be serious analysis of a situation or an idea, or just amusement. Seeing the funny side of things is very helpful in life. And then make sure they go to a good school, where their minds will be expanded, encouraging them to think, not just get good grades in exams and (also important) one where they will pick up the habit of enjoying physical activities. This will develop habits that will help keep them healthy in mind and body in later life. (I sometimes think that teaching me to enjoy singing and the feeling of fitness I got from rowing have been more important in my life than everything academic that I learnt. My son also got used to being fit at school - now he climbs mountains for leisure.)

Children can be the image of their parents.

Yes, and it is interesting how that picture of God evolves in the Old Testament. At the start, he is just the God of Israel, just one among many, though supposedly superior to the gods of other tribes and nations. At some point this changes to a belief that the other gods are mere idols, i.e. fakes, and there is only one god.

I’m British and I ‘m not clear what you mean by the green light rule either. Can you elucidate?