studiot

You don't seem to have read my post#4. How would you use gaussian elimination to solve that system? These equations and their solution are not special and are taught in high school.

Don't worry, understanding a (stress) tensor is the easy part, you only need to duck out if someone asks you to calculate one. It's simply a posh word for several things happening at once (together), like if you squueeze an orange around the middle it gets longer the other way and eventually bursts if you squeeze hard enough.

Neither Nature, nor our thought processes are exclusively sequential. For example in Nature the stress tensor is an example of many different things (nine in 3D) acting together in a connected way. Man models this by using a matrix representation, that is non sequential. In Man's thought processes we look at an engineering drawing and (some) can appreciate the whole subject at once, without sequentially working out the botoom, sides , top etc.

Spring here too, so it's raining. Directdude, let's here from you.

Just to add to what Janus has said. It is not necessary for all the variables to appear in all the equations for them to be simultaneous, or for you to be able to solve them. Here is an example. s = ut + 0.5ft2 v = u + ft v2 = u2 +2fs f = (v-u)/t s = 0.5(v+u)t These are 5 equations with 5 variables, s, t, u, v and f which describe motion uder constant acceleration. They are simultaneous, even though t is the time variable, they all apply together. It is indeed necessary to have N equations for N variables, to be able to find a unique solution, if such a solution is possible. But N equations may not be sufficient since a solution may not be possible, even with N equations. Having more than N equations or less than N may also lead you into trouble since you may then have a choice of multiple solutions, even an infinite number. I would advise you to lay aside the issue of linear v non linear until you have thoroughly understood the meaning of simultaneous equations.

Thank you for your reply, Ed. I agree with much of what you say, but I think things are a tad more subtle and complicated than that. We can discuss the meaning of DC v AC in another thread after we have determined what the OP actually means. I think that the difference between DC and AC is off topic here. I am not sure the OP himself is quite clear about his idea since post#1 contains some contradictions and as both you and I have pointed out the subsequent diagram is not complete. My objective is to get directdude to think further about his idea and try to lead him to make his own discovery about the implications of what he is proposing. I am holding my discussion of transformers until after the proposed circuit details are cleared up. I hope the snow has not reached you neck of the woods.

Good morning Ed, Where is DC defined as a two wire system? See Externet's comments, post#7 Further a supply is only alternating if it changes polarity. The point is that the OP specified 'switching' between two negative supplies. Each negative supply must have a reference.return wire so that makes 3 or 4 wires. Since there is no polarity change, it is simply DC pulsed from one level to another. Thank you direct dude, for your diagrams. They do not indicate polarity or wiring so I am still left guessing. If you combine the two supplies to form a two wire system then you will end up with zero if the two supplies have the same voltage.

Edit I realise I said 'normal' friction. Of course I should have said 'ordinary friction' to avoid any misunderstanding that I meant in a normal (perpendicular) direction. The friction acts in the usual direction, at right angles to any 'normal' forces.

If you mean something different from what I drew, please post a proper diagram to show what you do mean. I cannot make anything new out of your post 5 (ask for help achieving this if you need it)

Agree totally with Klaynos, but here is some extra info. The surface (in this case the water - air interface) has a surface energy / surface tension that is disturbed by a vessel cutting through it. This is the source of the increased resistance at the surface (klaynos : wave drag) not normal friction between the hull surface and the water, which is obviously still present when submerged. Submarines submerge to lower resistance to motion. Hydrofoils raise up to take as much hull area as possible out of the interface.

Look carefully at the OP proposal. It will work with a (suitable) transformer. It will not be subject to greater resistive transmission losses than other systems: That is not its problem. What the OP is describing looks something like this.

I have separated your post into two parts. Part (1), The description of your proposal. This is properly called two level or bi level direct current or unidirectional current. Some might also call it a biased square wave. It does not have two phases. Part (2) Your support reasons and proposed advantages. Such a system is extremely inefficienct for power transfer, but is used for signal purposes (hence the square wave terminology) Transformers to handle square waves are quite diffeently constructed from those for sine waves. The radiated interference signal from sine wave power sources is bad enough, but square waves would be sunstantially worse.

Which is exactly the point I was trying to make in another thread. Thank you for phrasing it better than I did.

What do you mean by "the ensemble of all such vector spaces" please?

Hello Huestan and welcome to SF. You say you were educated in Canada, but going for UK citizenship. This is important because the career trajectory for Engineers in the UK , and the USA is quite different. In Europe it is different again. I am not quite sure how the Canadian system works, but I believe it has characteristics of both the UK and the american systems. In the UK the institutions that control the engineering profession are not part of the State. They are private organised by the professions themselves, and success in state examinations does not guarantee professional progression, as it does in Europe. In the USA there is the State test of Professional Competence, which is above academic or professional institutions. The UK system is to aim for what is known as Chartered Engineer status (or Incorporated Enginner as the next step down). This staus is above any academic or state qualification. So your first goal should be to look at each system and decide which path you want to follow. Of course it is possible to convert from one to the other if you move and work elsewhere.

First I would like to thank both wtf and Xerxes for the large amount of hard work and thoughtful interesting material they have put into this. Perhaps unfortunately this has introduced the issue of 'what is a set?', which was not the subject of this thread, interesting though it may be. Indeed I would support the contention that that issue deserves a thread of its own. I think it was Xerxes, though I cannot locate it at the moment, that offered a link to Professor Weiss's lecture notes and thoughts on the subject of what constitutes a set. These notes use Richard’s paradox to exemplify what is not a set, in his definition. In my original post I did not specify any particular definition or restriction on what might constitute a set. Indeed the fact that we have so many words for an assembly of objects suggests that there are many (some subtle) shades of meaning. So we use Aggregate, agglomerate, collection, class, group, assembly, category and many others. Now during my working life I was an applied mathematician, which means I was interested primarily in obtaining answers by fair means or foul. I have more time now to lift the covers and look underneath and this is what I was attempting in starting this thread. To an applied mathematician, restrictions of set definition based on Zermelo does not cut it. Rather it introduces severe difficulties, for example the set of all men or all men in Denmark or whatever as heavily used in actuarial mathematics. In fact an effect I have noted is for restrictions to be stated at the beginning of something, a course, a book, a development of theory etc and then to be forgotten later when attempts to apply that theory outside the domain of definition are made. Zermolo’s theory is like this and placed somewhere in the middle of the pecking order of set generality. In particular it was developed for and strictly is restricted to sets with numbers as elements. This does not prevent it being useful sometimes elsewhere. I cannot put this idea of generalisation v restriction more clearly than Professor Phillips. This is extracted from his Analysis, Cambridge University Press. So to the original post. Although zero elements imply total properties = elements times available properties = 0 I am still not sure about this as I said in post#8.

Because of the language difficulty I suspect tomjin means something different from us for many of the terms he is throwing about. Since this thread is about constants everyone should agree first what that means. Then I suggest that the words isotropy and homegeny are examined because I think tom is mixing these concepts.

Why only feedback, Mike? Why not feedforward? https://www.google.co.uk/?gws_rd=ssl#q=feed+forward+error+back+propagation

Whyever not? Frequency (actually phase) pulling into sync of linked oscillators is a well observed and documented phenomenon. The flashing of fireflies is one classic example. https://www.google.co.uk/search?hl=en-GB&source=hp&biw=&bih=&q=frequency+pulling+of+linked+oscillators&gbv=2&oq=frequency+pulling+of+linked+oscillators&gs_l=heirloom-hp.3...1875.13860.0.14391.41.17.1.23.5.0.219.2032.1j14j1.16.0....0...1ac.1.34.heirloom-hp..22.19.1827.6S54l699au8

As a bystander this seems to me to be developing into classic trolling. DFTT.

Actually you need time to pass for other processes than movement or motion, for example spontaneous radioactive decay. You could still measure time passage (or lack of it) by these means.

+1 for research and detail, arc. Just to add something about Martin Gardner. He was responsible for the book Fads and Fallacies in the Name of Science (now in the Dover catalogue) "Examines various cults, quack systems, frauds, delusions which at various times have masqueraded as Science. Accounts of hollow earth fanaticslike Symmes; Velikovsky and the wandering planets; Bellamay and the theory of multiple moons from the list of topics are relevent here.

This whole junket is clearly a plug for Nigel Molesworth books. https://en.wikipedia.org/wiki/Nigel_Molesworth At least they offered a semblence of humour.