studiot

That's the whole point, there are no gaps in the real number line.

Architecturally this is called passive cooling. Here are some links. https://en.wikipedia.org/wiki/Passive_cooling How India's lattice buildings co...How India's lattice buildings cool without air conFor centuries, India’s architecture featured intricate lattice structures. Now, as modern architects search for better ways to keep buildings cool, it’s making a comeback.

The point is that polar coordinates will completely fill the plane or 3D space with the radius at infinity. David's problem is that he has used a boundary - the circle he wishes to fill. So you need to be able to describe that boundary in polar coordinates to use the method and further since he is filling a disk, the outer circle radius is constant. That means we can start with a single line of that radius and sweep it around one end in infinitesimal steps, remembering that a line has no width. As the radius sweeps around and angle of delta theta it covers all points in a sector bounded by the infinitesimal arc of the out circle. Summing all these goes to an integral as delta theta goes to zero.

It can be done if you rearrange your dots. The trick is to use polar coordinates not cartesian ones and arrange you dots (which in the limit have zero diameter) in radial lines and then consider the angle between each line, taking the limit as that angle tends to zero. You might also find the six circles and seven circles theorems interesting, along with Steiner chains. (they do not fill all the circle.) You may like to know that the radial method is part of the mathematics of s orbitals in quantum mechanics.

Despite the social media hype the presneter, Ella Al-Shamahi, is not Lara Croft2. She actually makes some very subtle points and questions. It is also true that some of her explanations have alternatives, but the story she tells does hang together in the large. Now that there have been 2 episodes that weave in lots of modern scientific analysis techniques, without baby explanations of radiological and other dating methods. Actually the dataing method I found most interesting were the growth 'rings' in teeth, not one I had heard of. Also interesting is the paleoclimatology evoked to explain why H Sap moved out of Africa and into Saudi and thence through S Asia to Indonesia and on to Australia. But yes the episodes are overlong because of the money wasted on CGI and dramatic music and repetition of clips where something useful was said or shown. Unfortunately that tendency is increasing and common to many programs these days. However you are under no obligation to watch it or expose yourself to the danger that you might learn something.

Not sure where to place this but anyway is anyone else watching the New BBC series about the evolution of Homo Sapiens. There are 5 separate 1 hour programmes in the series, of which the first has already been shown on BBC2. The presenter is a paleoanthropologist and interestingly a woman. I say interestingly not in a disparaging way but because there is a noticeably softer approach from previous 'hard sicence' programmes with male presenters. This programme is also bang up to date with much new material and hypotheses about the evolution of our species. As such it may well be of interest to all those who have been arguing about this subject recently.

Interesting. thanks. +1

The various terms associated with 'eigen' come from the German and are attributed to Hilbert. They are mathematical terms concerning linear mathematics so we have eigenspace, eigenfunction, eigenvalue, eigenvector and eigenstate. The german word eigen means 'proper' and can be used for several puroposes in linear mathematics depending upon what they are applied to. These words have pure mathematics meanings realted to the solution of equations, but also have specific physical meanings when applied to physical systems. The physical systems may be 'classical' or 'quantum' mechanics or even statistical. The first two replies here give some examples from classical and quantum physics. https://math.stackexchange.com/questions/26662/eigenvalues-and-eigenvectors-in-physics In pasing I note a sprinkling of downvotes, which I see no reason for and only serve to discourage someone who is 'doing their best'.

Diagrams can be very useful and informative. Do you mean portrayals of real world things like an internal combustion engines and abstract concepts like the carbon cycle or the hydrological cycle ? videos have their uses but still graphics can be studied more easily. I myself post a lot of sketches compared to some.

Depends what you mean by visuals. And also why you are 'adding' them.

Why is everyone so hung up on 'particles' these days, without any proper understanding of what they mean ?

Glad to hear it. +1 The moral of this is that you can't be expected to know all the tricks at once or without a lot of practice, so if you need help ask a question about what you wish to achieve.

First a question. How old is the child or are the children you have in mind ? There is no general answer to this question, every child is different with different needs and these needs change as the child grows eventually to approach adulthood. So for instance some forcing is necessary. This is the reason mothers (and hopefully fathers) hold their your child's hand tightly, when waiting at the roadside to cross. The younger the child is the more likely it is to be suddenly distracted. Sometimes this does not matter, but no one want their child run over. Parents should also offer a chance to try out all sorts of different activities and passtimes and be prepared for any given child to like some and dislike others. So you buy say some roller skates for birthday or christmas, and they are used a few times then forgotten. Do they like dolls or dogs ? Swimming or reading ? and so on. You can reinforce the likes and quietly drop at least some of the dislikes. But is is also necessary to discourage antisocial or other desireable behaviour, especially watch out for cliques that try to override adult guidance. Hope this is helpful.

Not sure I understand any of this but I do agree there are too many distractions in some modern cars. FYI the incident with the fire engine occurred in 1968 or 69 as I was walking my dog.

Considering the nature of the spam, I was wondering if it was not directed at SF at all. I wondered if it was simply to increase the mentions of certain organisations referred to and thereby increase the web footprint of those organisations. Somebody paid those spammers.

Yes indeed I am focused on the Google AI as it pushes itself in front of me every time I do a Google search, which I used to (and still do) do quite frequently. I do not go seeking AI answers however. The only time I tried CHATGPT it returned rubbish and I have no idea how to access the others, not that I want to. It does concern me, however, that the Google summary headline which used to be often really good has become so untrustworthy since the AI. No one needs and AI to find a train from Exeter to Somewhere and the old system worked perfectly well and did not tell me I had to change trains at the starting point. Indeed so as a general principle. But you are quite incorrect about this. The red instruction is not really directed at those stationary at the traffic light. They are a positive direction to any approaching vehicle to stop the vehicle (at the stop line). No question that is a positive active command, that of changing what you are doing. Yes sometimes drivers cooperate to clear a path, sometimes the emergency vehicle will actuall drive the wrong on the wrong side of the road, or the wrong side of bollards etc. But it is interesting to watch the difference in the way ambulance, police and fire vehicles approach a situation where the traffic signals are against their passage. The ambulances definitely slow down to a walking pace and 'feel their way' through the junction. The police and to a lesser extent the fire engines just go barreling on through and expect others to get out of their way. Their victims may not be standing by the side of the road, waiting to cross in their turn, they may already be partway across, obeying the traffic signals appropriate to them. I once watched a fire engine do exactly that to try to cross the London North Orbital Road ( a very wide important and heavily trafficed high speed road) whilst the traffic light was red to the fire engine as it approached. The result was a powerful side impact on a sports car that was correctly crossing along the North Orbital. Apart from sending the sports car spinning down 50 yards or so to block one direction of the North Orbital, it left the fire engine stuck immobile right in the middle of the junction itself.

I think you guys do a great job and definitely deserve a chocolate biscuit.

Get an AI on the job. 😄😁☹️

How often does the blood transfer service receive 999 calls ? What % of ambulance blue light journeys are transfers to a better medical establishment and therefore not recorded on the 999 system ? What % of police 999 calls are about a life threatening incident ? Here is another ridiculous answer (although it does also contain a valid one in part) Question travely by train from exeter to Addingham Yorkshire. The A! has highlighted a correct start but then says changes in Both Exetr and York ! Foresooth.

Do you not think these statistics are misleading ?

I don't since ChatGPT started of with an incorrect statement. Stopping when a light is red is a very positive and active statement or instruction; it is most certainly not a negative or passive one. The second run through was a better consideration so whould we always ask an AI twice for its best answer, like the postman who always knocks twice ? But thank you for that work in progressing the discussion. +1 Yes that is a good point, but not quite correct as it is certainly not without consequences. It is true that emergency travel under the blue light laws allows emergency responders to break traffic regulations. But they retain a duty of care. It is interesting that there are 2 - 10 deaths (mostly pedestrian) by police cars per year in the UK. As compared to a very much lower incidence by the fire service and mostly zero by the ambulance service. Especially as the last two services are more likely to be travelling in a life and death situation as compared to the police.

Good morning all. Traffic signals were first introduced in 1868, following the railway practice of red/green semaphore arms. Lights came later and the first 3 color lights were introduced by the americans in1929 in the Motor City. I don't know about the legal status in other countries, but I would imagine all those deriving from the British legal system would have the same definition whicvh currently stands thus. Note that green means "You may go, if your way is clear" That 'if' is the legal version of mathematical if and only if. In Britain you can be prosecuted if you proceed when you way is not clear. Indeed we have several further traffic signals trying to control the simple fact that people simply ignore the condition and there are further specific offences related to these. This is despite the fact that you would always have failed your driving test if you did not give this complete answer to the question about green. (All signs, lights, directions, instructions on boards, or on the road are officially called signals following the semaphore days). Hopefully that is the information you require, but remember this topic is about LLMs and other rule based systems and my issue was about their reaction to being fed on contrary and conflicting information. Here is another really bad 'mistake' by AI, demonstrating a total lack of understanding, even of plain English. In this case the answer is worse than just dangerous it is life threatening as the AI direction directs vehicles through a green traffic light and straight across a pedestrian crossing which may also be green. The manouvre suggested is possible but prohibited for that reason.

Thanks for the reply. But you are missing my point. The red light rule is pretty clear and most humans obey it so there is little or no tension between the rule and the action. But The green light rule is very often disobeyed by many if not most humans so there is considerable tension bewtween the rule and the action.

This may just be a good theme for a SCiFi horror - but how does any 'robot' resolve the tension between clear cut rules as you describe and how humans actually act as must be descibed in any large scale 'learning' input, as Otto has described. This was the reason behind my question to @Otto Kretschmer about the traffic lights. The vast majority of human activity conforms to the red light rule. Whereas a large proportion on humans disobey the green light rule. Note I do not know the 'answer' to this - It is a genuine point for discussion.