studiot

Thank you for offering this excellent example to enable us to take this thread deeper into the base of Mathematics.. So let us see what it can tell us before I ask a pertinent question. A general 'string' has what I will loosely call 'ends' for the moment. You mention an 'infinite string' Well the string ...111111 has one definite end as it starts (on the right) with 1, using one meaning of infinity, that of unending, it goes on forever, adding 1s on the left. So we say this particular string which we describe as infinite has only one end. Firstly are you aware of the ellipsis? That is the three dots both KJW and I have used ? It simply means that there is more but we haven't attempted to write it all. Useful shorthand. Since you want to look into the philosophy of things What, in your opinion, is the most basic operation or activity in Mathematics ? You did not take me up when I suggested that there are at least four different types of number in maths; are you not interested ? Once we have established the basics, we can move on to proof and its meaning because you have that incorrect in both maths and science - those two disciplines have significant significant differences in meaning.

Let's start here shall we. My dog is more intelligent than any AI yet constructed. It is not (perhaps yet) possible to train an AI to sniff out a whole range of substances that dogs can easily and naturally. So by running to an AI summary you are missing out on the important points being made on examples that are specifically designed to follow your desire to only work with mthas realting to the material world around us. MyQM comment has direct realw orld consequences, it is not some esoteric maths. The maths models the real world, not the other way round. Having said that it is suprising just how often the real world and the theoretical mathematical one follow the same path and at the sme time comforting. Thank you for telling me your understanding of the infinite. Religeous considerations have no place in mathematics,, and your appear to control and limit your progress in this matter. If you wish to pursue religion then I will have no further interest in this thread. This is despite my know;edge that a reasonable value for Pi is clearly stated in the Old Testament (and presumably the Torah) although not quite as good as the value in the Rhind Papyrus. Yes you have got an inkling of the idea here, although zero is indeed a number and the basis not all other numbers, rather than one. But you are hampered because I think you do not understand what a number (itself) is. In fact there are at least four types of object we call 'number'. And they are all as different as chalk and cheese. Further they obey different rules. Do you wish to learn more or do you wish to preach at me again ?

Jayant Narlikar was one of the co founders of the Steady State alternative to the big bang theory of cosmology. Although currently out of fashion, the big ban v steady state saga is reminiscent of the wave v particular theories of light which also see sawed back and fore in popularity. BBC NewsJayant Narlikar: Remembering the Indian scientist who cha...Jayant Narlikar who died at age 86, was dedicated to science education and shaped a generation of Indian researchers.

I put a lot of effort and that last post and , in genera, my posts link to each other to build up concepts. So it would be helpful to both of us if you read them through several times as I see you have either missed important parts of the content or have some misconceptions. So thank you for the response but please answer the questions, they are all designed to point to particular points of importance. I know the scottish dancing attachemnt was showey eye candy, but it was only meant to lead to another point. Actually if you look at the history of mathematics you will find that in all the early civilisations geomtry prereceded arithmetic and indeed progress was held back in most for thousands of years because of unwieldy symbolisations. That is why it is important to answer my introductory question about 1 and 2 and oneness and twoness. There is much more to discuss about symbols, did you notice I had introduced the word 'labels' ? Proper consideration would carry forward the i j k discussion where they are labels or indexes, and their relation to the square root of minus 1 is coincidental. This is because, as I said earlier their arithmetic is not your normal arithmetic where A time B gives the same result as B times A. Instead in their arithmetic A time B does not necessarily give the same result as B times A. This is vitally important in the real world because it is the reason for the Heisenberg Uncertainty Principle in Quantum Mechanics. More simply the use of plus and minus as directions in electrical circuit theory as explains the difficulty that arises because the directions for current and voltage are necessarily opposite. The rotating arm is a real world mechical object. There is no graphic plot needed for this. You cannot relate rotation angle to a point (such as 0). I did not suggest that. You must relate it to a line. Back to scottish dancing. That was from a chapter entiltled an infinity of curious arithmetics. An infinity. OK so what do you think infinity means, that you do not like it ? Here are some simple arithmetics presented as tables. The first is concentional algebraic substitution of the effect of replacing x by (-x). The second is just a similar letter substitutionT The third is purely symbolic using geometric shapes. But they are all the same

OK so let us start to offer some reasonable justification and explanation. First question. What do you think ' - ' (or +) or '1' or 2 or 12 are or mean in mathematics ? Many folks with insufficient background and even some who should know better fail to fully appreciate that these are symbols. They represent a mathematical concept so it can be manipulated and discussed. So 1 represents oneness - whatever that is - it is not oneness itself 2 represents twoness - whatever that is - it is not twoness itself and so on. + and - are even more tricky because not only are they just symbols, they do multiple duty, representing different mathematical concepts. Writing +90 or -90 may mean different things in different contexts. Yes they can represent the operation add 90 or subtract 90. But I am going to use the meaning 'signed numbers' also called positive and negative numbers in ordinary arithmetic. This is similar to positive and negative in electricity. But it represents direction not an arithmetical operation. So let us step into the real world and consider a rotating arm, exactly one unit long, fixed at one end to a pivot. as in Fig1 Since the arm is free to rotate in either direction I will label one direction positive or + and the other direction negative or - Then let us add two axes and set the pivot to the origin and align it along the first axis as in fig 2 Now let us swing the arm through exactly 90o in the negative direction. Call this operation multiplication by some as yet unknown number 'r' as inFig3 It can be seen that the free end of the arm now aligns with the -1 on the second axis Now swing the arm another 90o in the engative direction and note the free end now aligns with -1 on the first axis. So considering only the free end of the arm its starts of at position +1 and after being multiplied twice by 'r' it ends up at position -1 (actually I have called the operation multiplication but it is really something more subtle called composition in the arithmetic of 'operations') Algebraically we can write r2 (1) = -1 r2 = -1 r = √-1 So here is an example of the construction and meaning of 'i' in the real world operating on real material objects alone. But the arithmetic is not the arithmetic of ordinary numbers, it is the arithmetic of operations which is similar to, but not the same as that of ordinary numbers. and i is not a symbol for an ordinary number. But it is not imaginary either, that was a really unfortunate name from history. Here are two pages from the second chapter (called an infinity of arithmetics) of an interesting book on modern maths It is fascinating how many different operations in the real material world follow this pattern. This example is about the mathematics of Scottish Dancing.

If you have two or more generators of any type in parallel there will be a difference in their voltage output. This will result in a reverse current circulating in the parallel loop. Whether this is significant will depend upon the nature of the generators and their voltage difference. I have posted the relevant mathematics on this site at least twice now in other threads.

Congratulations, you have just discovered my point that there is no closed formula for this activity. It is a process. Philosophically there are two complementary processes. Analysis and Synthesis. It is many times simpler to measure something that is actually there (Analysis) than to create a desired something that is not yet there (Synthesis). Much Engineering is composed of the latter.

So you can put numbers into that formula, take a tape measure or whatever, and walk out onto the hill and point to a spot ? How ?

From the numbers and positions of the diodes I guess that the solar cells are grouped and the diodes are set to protect a group rather than individual cells. Are they bypass diodes or are they set to prevent fully illuminated cells form trying to pass current through shaded (and therefore lower voltage output) cells. Some better circuit diagrams would help.

I really don't know what that long thread is about because you seem to be preaching not just listening and discussing. In particular here is a real world engineering problem that does not satisfy your specification. You are to dig out part of a steeply sloping hillside and build a heavy reinforced concrfete box reservoir in the space. In order to support the new weight several lines of prebored piles are to be installed raking at 1 : 4 along the front or outer floor of the reservoir. Regardless of where each borehole starts on the hillside, the pilecap has to end up in the right place just at the underside of the reservoir floor to correctly distribute the load to the floor reinforcement. What closed formula can your AI pal offer to locate the drill point for each pile ?

There you are a much better coherent post and folks are already starting to off help and explanations. +1 to KJW. Thank you too for that post +1 also for encouragement. I think I now have a pretty good idea of where you are coming from. Now please don't misunderstand this next bit it is not a personal criticism, nor is it a criticism at all. It is an acknowledgement that folks are different and think differently,. I think perhaps that when you come across something that interests you, your mind suggests all sorts of loosly associated matters and that you started here by listing a great many of them for help. Now that I realise that this thread could become really productive. So well done for looking into i j k and finding the Miller indices. We can use this to look at the idea of indices as labels next post and start to work through your worries (hopefully others will chip in more and more) including you difficulties with infinity and electrical calculations with imaginary numbers.

Let me add to what swansont and markus have said, by asking Do you know what a functional is ? Why do you say that T is the kinetic energy density, not the kinetic energy ? never mind what "would be behind the tear or break" what does your system 'strain' into or what is behind that strain in your words ? In simple terms do you know what strain is ?

Thank you for your response. Actually there is a whole lot more to i, j k than this, which has dfinite solid connection to things like crystals and mineralogy and other applications. I wonder if you are hankering after this sort of approach, that used to be called practical mathematics. Here is a page from such a book an I wonder if you would post your reaction to it because if I am correct in my guess then you would enjoy this approach. What do you think ? The book is a british book published by Odhams called Mathematics in Theory and Practice

I should check your facts with the natives before posting next time. The relevant current body is Natural England and the relevant term is ancient woodland. It is however true, as exchemist says, that human occupation of the British Isles has led to a steady deforestation over thousands of years. Requirements for building, wars, farming clearance, sightlines (the Romans did a lot of this) and more have all played their part. These have been only partly offset by deliberate (re)planting, which has occurred only sporadically, for example the New Forest, by order of King Henry VIII.

Interesting use of emergent. Thank you. +1

Dare I use that phrase "with you there bro" again without starting another forum war ? +1 😄

Was all this meant to be a response to my request ? After all you did ask for responses. Which perhaps is why you have started with a most unfortunate title in maths. The use of the word 'Real' has very very special meaning in maths so I highly recommend you change your title as you clearly mean something different. Since you seem to have difficulty with infinity I suggest you look at the branch of mathematics called Concrete Mathematics. This has proved to be a very useful concept in modern everyday applied maths. https://en.wikipedia.org/wiki/Concrete_Mathematics

One step at a time please. No one want to respond to a wall of text. So pick one on the points where your system is different from conventional maths and we can discuss it.

+1 to joigus for doing the unpaid work of technical checking and proofreading a technical document that contained material that had no business to be there, free and gratis.

Wow, not respectful ? from someone who has clearly not read the rules he or she signed up to. I asked very respectfully for a summary instead of a link offsite (which are prohibited in the format you have provided on this site ) What I asked for would at least put you on the right side of the rules here. As I do not know what an electromagnetic vacuum is, conventional or otherwise I asked specifically as I do not wish to guess or discuss at cross purposes. If you are going to be that touchy you will not fare well when the mods read this thread. Good night.

And what would the electromagnetic vacuum be please. Can you summarise what the conventional features are and how your proposal differs.

Yes I did read it it but No I did not understand it. I would say from the responses of other members many are in the same boat. Not understanding is the reason I asked for a slowdown and agreement on basic definitions so thank you for referring me to that rather deficient Wiki article about solids. But at least I know where you are coming from on that now. And since this is your show we can use that definition of solid as opposed to any other, That is all I was initially asking for. Can we discuss the meaning of the term model without all that histrionics ? You didn't answer my query about observables v observations so I still don't know if you understand the term observable. You are also clearly incorrect in your use of the term data. Data is a wider term than observations (or observables) all of which have their particular place in the scheme of things.

It did also bring to mind the problems that came with the post war Orlit and Airey houses buit with prefabricated pos and panel construction. 640 × 481 I know the panels or planks were set hardened concrete, but after decades joints leaked, letting in the water and wind. The panel construction allowed diferential movement. I don't know if the layers of printed concrete will suffer the same in time

The programme was on 8pm to 9pm this evening on BBC. The section of video was a few minutes about half way through. Being in England you should be able to get it on iplayer.

Just seen an interesting bit of 3D printing on the TV programme about the current Chelsea Flower Show. They were using fine concrete as the print material, and the print machine was 2 - 3 times the size of a human. The result was a hollow cellular wall.