studiot

When I first saw the OP I thought it was a deep question. On second thought I realise that it is actually much deeper than I first thought. TheVat made a worthwhile distinction between concrete and abstract nouns This is one of the advantages English has over Mathematics. So to discuss your question, let us consider two well defined sets. 1) The set of people born on or after 1950. 2) The set of people born on or after 2050. The first set has a specific finite number of members. This number is given (measured) by the natural or counting numbers, otherwise known as the positive integers. Note these does not include zero. We show these in set notation by listing between curly brackets (braces) thus {1,2,3,...}. The three dots at the end (ellipsis) denotes indefinite continuation. The second set has no members and is called the empty set or the null set. Thus we denote the empty set {}. This is very important to show that there are no members. Note also that it is not the number zero. Create as many copies of the null set as we need. Then collect them together, grouped in sets within a larger container set. { {{}}, {{},{}}, {{},{},{}},...} Which corresponds to our set of natural numbers {1,2,3,...} So we have constructed as many counting numbers as we wsih for nothing ! That is almost enough set theory for our purposes but there are two theorems we need that I will state but not prove. 1) There is only one empty set. 2) The empty set is an (honorary) member of all sets. The first theorems comes into play with the issue of moving the box. Suppose I form my box from the curly braces with nothing inside and send it to you over the net. I have moved an empty abstract box and, so long as there is no data corruption along the way, it is still empty at your end. Mathematically the question of what is in your box is answered by theorem 1 which says that it must be the same nothing as there is only one empty set. In case you think this is rather arbitrary, smart ass even, there is a definite application in Engineering and Physics in Fluid Mechanics and other places. In Fluid Mechanics there are two formulations of the equations of fluid motion depending upon your viewpoint. An abstract box with abstact walls is constructed in the imagination and suprimposed within the flow. View 1 considers the flow flowing through the box, which is fixed in position, size and shape, in and out through the walls. It is known as an Eulerian analysis. The flow into / out of the box brings with it physical variables such as momentum, energy, mass, force on the walls and so on. This causes changes in other properties such as density etc. https://alldifferences.net/difference-between-lagrangian-and-eulerian-approach/ View 2 considers the box to move with the flow and is called a 'with the flow analysis', or Lagrangian analysis In some flow patterns the flow can actually be at a standstill ie there is no flow. These are called stagnation points. They appear directly in front of obstructions to the flow and other places. If the box is located at such a stagnation point it enclose zero momentum since there is zero motion. Don't forget that the spark plug gap can actully be zero (nothing) if the electrodes are touching. This is a different nothing from the what is in the space between them, since there is not even space between them. Time is not the same as space and considering the quantity of space within the box must involve a relativistic calculation, due to the problem of defining simultaneity.

How can you reassure us we are not helping to bust a patent or copyright ?

I agree. Most of the 10 pages of this thread have involved (sometimes overheated) semantic arguments over definitions. The actual OP question was answered quite quickly and simply several times. +1

Since we are leaning towards (computer) applications, rather the the pure Math of Analytical or Algebraic Geometry i would recommend the any/all of the following books. The first three are particularly applicable to CAD, meshes and so on, The last (Cundy) is a fun book about the practical side of making physical models of Mathematical objects such as polyhedra, the cone that runs uphill and many more.

I would have said it is slightly (perhaps a great deal) more than that. Taking your system and its environment and the dividing boundary, awareness, consciousness whatever i expect to involve some sort af back and fore, to and fro process across that boundary. So information passes across the boundary, is examined on one side, causes information to flow back and so on in some sort of regenerative process. The blue tree, kelp and so on are simple clear cut questions, to simple to be up to the job IMHO.

Indeed, it depends on which side of the cutlery one reside's An aquired taste means we have to learn to live with it, not that we like it... Old spots forever. 🙂

Start here for mesh modelling of real world solid objects. (if a T Rex is real world 🙂) https://en.wikipedia.org/wiki/Coons_patch

Have you a particular example in mind ?

Sigh. You seem more interested in holding a mud slinging match than discussion. Let me try again. Here is your entire post that is in contention I replied to parts of this and for convenience quoted only those parts I was replying to. I note that when you when you responded you did exactly the same. I responded to that reasonable question about my previous post in the same reasonable manner as my reasonable answer to the member who prompted that discussion in the first place. You don't think the internet can become self aware, yet you later describe great danger in its doing so. Why bother if it can't become self aware. You then go on to a long list of things (not a phrase but a whole paragraph BTW) that one could look for in the activities of 'the internet'. I picked two of them out to comment on, as the two I can prove already applies to Windows 10. The rest I did not respond to as I have no evidence. The fact remains that you picked this particular part of my post to quote and directly accused me of mockery on the basis of it, when I have at no time until now quoted that part of your post. I take it as obvious you were referring to that misquote of yours since you associated other answers to other parts of my post within your own reply. You done that and obtained a conclusive response from Windows 10? I believe that you just mocked me and/or my input. Please don't do that again. The problem of AI/internet awareness and the dangers related to AI (aware or not) are very serious. I repeat I did not include the red part of your postings in my replies or associate any of my comments with it. But what you have failed to pursue in all this is the validity of my comment about Windows 10,

I thought joigus commanded us to think deep thoughts.

Sadly the king of jong only stopped by long enough to make his post, but has been to busy with his subjects to come back to us peasants, but +1 for an excellent comment.

Perhaps the only thing more bloody minded than Windows 10 is the ScienceForums quote function, which certainly distorts quotes by its new habit of 'rolling them up'. A piglet can become excellent bacon or a destroyer in the cabbage patch or even an actual danger to human life.

Thanks for the support, but Dan does have a point about the dangers made in his second sentence. Lots of things are dangerous in our world and we need to best organise our society to deal with them. Some things are even dangerous but necessary which are the hardest to approach.

This is not a thread I feel I can usefully contribute to, so I feel honoured to be involved by reference. I suppose this is because of my propensity to respond to questions where members demand binary, black or white, answers by suggesting that when I look at nature I find many more than 50 shades of grey.

How so ? You made a very specific statement with a subject a verb, an object and a conclusion. Like Windows 10 does already ? Yes I picked this out of your post because of its specifity and made the totally correct observation that Windows 10 already does both the stashing and the initiating/refusing of tasks. So it would not be a new phenomenon to watch for it is already happening. The question mark at the end was in invitation to discuss further if you wished. Your response was to quote a totally different part of your post To which I had not responded and then claim that There can be no mockery in my totally true statement about Windows10, which was the only one I made in that post you took unwarranted exception to. I am sorry if you misconstrued those simple words, had I actually been rude I would apologise.

No the distance increase very slightly as you are further from the centre of the earth. But this is the physical or actual distance your would measure with a tape measure. For this reason all map distances are calculated at a standard ditance from the centre of the Earth - Sea level is normally used. So if you were 50 yards above sea level and measured 100 yards to another object, also 50 yards above sea level you would say that your reduced distance (reduced to sea level) is just under 100yards. The difference is not significant below an elevation of about 1000 feet above sea level, unless you are doing some very advanced surveying.

For the benefit of overseas members, B & Q are a large DIY chain that have been running a heavy advertising campaign under the slogan You can do it.

Was there anything you wished to discuss here ? You were not interested in discussion in your last thread on the same subject.

In order that a quadric through 9 given points may be determinate:- 1) No four of the nine points may lie on one straight line 2) No more than six may lie in one plane 3) No more than 5 may lie on one conic.

You done that and obtained a conclusive response from Windows 10? I believe that you just mocked me and/or my input. Please don't do that again. The problem of AI/internet awareness and the dangers related to AI (aware or not) are very serious. If you simply react to what others write and do not read it carefully enough you are likely to knee jerk to the worng conclusions. I did not say this. I did say Like Windows 10 does already ? Windows 10 does both of these things. If you don't know this just ask. But no I do not consider W10 to be self aware, just a bloody nuisance.

Let us suppose that we have declared the probability of some event E to be exactly 1, the question arises what do we mean. So P(E) = 1 Interpretation 1. (a priori interpretation) E must always occur. Interpretation 2. (empirical interpretation) E has always occurred. This does not imply that E will occur in the future Interpretation 3 (subjective interpretation) We think E will occur But does not imply that it must occur. As regards the Monsoon, the example refers to the discovery of one Gilbert Walker, Statistician and Director of meteorological observatories in India. At that time the Monsoon was widely regarded as being related to solar activieies, in particular the cycle of sunspots. Walker collected vast amounts of data in India and also had access to data from across the British Empire. Walker offered a discovery of amazing scope. Not only was the Monsoon unrelated to the sunspot cycle, it was related to the pressure and temperature halfway around the world. He could not explain how pressure and temperature in the Western Pacific affected rainfall in the Indian Ocean. But his calculations showed that it did. He named this connection the Southern Oscillation. https://en.wikipedia.org/wiki/Gilbert_Walker

No it is an initiation rite for newcomers. 🙂 Oh and did I say welcome ?

It's very complicated because of the cross products (xy, xz, yz) in the general equation. Surfaces have a general equation f(x,y,z) = 0 The equation you refer to is called a quadric and the surfaces are called quadric surfaces. Obtaining a parameterisation means obtaining three equations x = f1 (u,v) y = f2(u,v) z = f3(u,v) So that each RHS only contains the parameters u and v and each LHS only contains one of the coordinates. For 3 dimensions there are many more possibilities than for 2 so the surfaces are often split into further sub categories, each with its own parametrisation. As with 2D to eliminate the efects of the cross products you would normally perform a coordinate transformation first. These are purely analytical methods, I was preparing a detailed explanation, but this often takes me some time so here are five references to be going on with. Sensei mentioned computer methods which work on a different plan and the last reference is about that. https://opentextbc.ca/calculusv3openstax/chapter/quadric-surfaces/ https://www.win.tue.nl/~sterk/Bouwkunde/hoofdstuk3.pdf https://tutorial.math.lamar.edu/classes/calciii/parametricsurfaces.aspx https://www.researchgate.net/publication/241165348_A_Simple_Method_for_the_Parameterization_of_Quadric_Surfaces http://staff.ustc.edu.cn/~dengjs/files/papers/47 mu23.pdf What sort of college course has this stuff as a pre requisite ?

I make such a distinction, in fact I distinguish 3 types of probability.

Whilst I agree that there are vested interests in every branch of History, and none more so than in Political History, I see you are missing the notion that a historian in an uninvolved country, or from an uninvolved time, can dispassionately examine the availbale data and present balanced conclusions. IOW you seem to be suggesting that say a modern South American could have no valid opinion on the Celtic expansion in Europe 4,000 years ago ? I would also point out that the thread is entitled Military History/History and you made a sweeping statement about all forms of History. As to the data, many nations have something like the UK 40 year rule where top secret papers are not released until 40 years after the events. So anything inside that time frame must include a goodly measure of speculation. So I repeat my observation that The more remote (in time and place) the chronicler is from the events the more objective she can be.