studiot

Duality appears again and again all over maths and science - It is very common. In Science we have positive and negative polarities, north and douth poles, many related to direction like upstream and downstream, forwards and backwards etc.... In Maths we have the Dual Space, left hand and right hand (this has been further developed in molecular theory as Chirality) So yes you could fit something in there.

Welcome back the ghost of Bishop Berkely. https://en.wikipedia.org/wiki/George_Berkeley We already have something like this called infinitesimals. https://en.wikipedia.org/wiki/Infinitesimal

Last time I did any programming it was called a seed for input to a stochastic or iterative process. My apologies it should have been improper rotation. https://en.wikipedia.org/wiki/Improper_rotation

Hang in there bro, I really am trying to help. I have a real respect for draftsmen who can do such things so much better than I can. Did you know that a century ago nearly all technical design and calculation work was solved by draftsmen ie by graphical techniques ? There was even an italian mathematician, named Cremona, who published a textbook called the graphical calculus. From you last few posts I can see that your normal English is perfectly good. Since I have not understood what you are trying to express I really don't know if it is something I don't know. So I am trying to open up known areas of Science in case it is something related to your notions. Then we can get on the same page. So you mentioned rotations and relativity. Did you know there is a link in what are known as 'forbidden rotations' I only find it a waste of time drawing attention to something like that if there is no response, either "Yes I already knew that" or "No, I hadn't heard of that, tell me more" Either way that progresses the discussion.

It is really difficult to answer you since you are mixing and muddling many definitions in the scientific dictionary. Counter rotation is not an inverse, just as the operation of subtraction is not an inverse. There is such a thing as an additive inverse in set theory (and group theory) but these terms refer to a single unique set element only, not to set operations. Not necessarily. In Differrential Geometry there is such a thing as torsion. Here the radius is zero. It is even more difficult to answer if you fail to address points made to you. We are taking notice of what you write and are trying to make something of it, but it is up to you to help.

Hello, You have an over determined system that is linear. There are no unique solutions to this situation however The branch of mathematics dealing with this is called Linear Programming ( There is also non linear programming for non linear equations). The method identifies a 'convex hull' in the variable space, bounded in the linear case by lines or flat surfaces / hypersurfaces depending upon the number of variables. The over determined system is turned into a determined system by introducing additional constraints to identify the optimum maximum or minimum solution. Probabilities are dealt with by adding weighting coefficients to the equation matrix. https://en.wikipedia.org/wiki/Linear_programming

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Let us just take one concept at a time huh ? Surely the phrase infinity unit is self contradictory? We have come a long way since the ancients contemplated 'infinity'. One particular property of infinity that was only discovered in modern times was that of self similarity between an infinite set and any subset of it. An infinite set is one where there exists a bijection (one to one correspondance) between the set itself and any subset of it. The transitive property further means that there exists a bijection between any pair of subsets. This is a simple example of self similarity. When applied to lines this mapping means that there exists a bijection between any line segment and the whole line or any other line or line segment. I understand what you are trying to do with your rotation, but you do not need the loop structure. The loop actually adds something extra which place the loop in another area of maths - That of Symmetry and Group theory. It should also be noted that we now distinguish more than one 'infinity' , although that said, even the ancients distinguished two kinds.

I am not familiar with the type of diagram you are drawing - does it have a name ? Structure ? What structure ? Perhaps you could briefly explain what you understand by einstinian relativity or just what aspect or part of it you need. Then we could move on to how it relates to your structure.

In the UK, folks like myself and exchemist will probably have battery operated ones either bought or handed out free by the fire brigade. As they are battery operated, these present no maintenance safety issues. If, however, you live in rented property, there was a change in the law back around 2000 to make mains operation a requirement (for the landlord) .Clearly there need to be an off switch for maintenance purposes.

We visited Becky Falls over the weekend, which is largely made of heavily weathered Dartmoor granite. The white rock at the top of the picture is a good example - Dartmoor Granite looks just like weathered and crumbling concrete with a greyish white colour. The banded black rock is a chunk of hornblende/amphibole with quartz banding which can be found in odd places around the gorge. The individual drinks carton in the middle is there for scale. I wonder if this has any similarity to @exchemist strata?

Remember that Aluminium is amphoteric. So its interaction with what you are cooking must take that into account.

I gave up reading through other folk's code (and correcting it) thirty years ago. Please write something in English (the language of this forum) and please keep it short. Then we might get some idea as to where you are going with this.

Mass induces gravity to infinity that extent to quantum harmonics/quantum pseudo harmonics (speculative). It's a transition from quantum realm to classical realm...we can predict with certainity the position of earth on its orbit, however where is earth if you narrow down to it's center of gravity(it's singularity)? Anyway,lots of temptation to go off topic(TOE). I really can't see the relevance of your reply to my comment. Sorry I missed a word out whilst editing. "you can't when it is at that somewhere." should read "you can't tell when it is at that somewhere." Did you notice that little word "if" in your quotation from Wikipedia ? What if you don't measure it ? And what do you understand 'probability' to mean ?

Yeah choose file is step 1 to upload them to SF Step 2 is to make them visible to others by placing them in your post. Don't waste posts like this. You only have 5 in your first 24 hours as a new member. After that you can post freely.

Asking Brian Cox about it is a good notion, but put it in writing to him. From the fact that you have approached BC, I deduce you are somewhere in the UK. Unless you live somewhere like the Isle of Lewis, you are probably within few miles of a University. Go and ask in the Physics dept. They won't bite. I remember when I was 12 I made the common mistake about cloud reflection and wrote to Patrick Moore about it. He was delighted to reply and explained the greenhouse effect beautifully when he wrote back. You could also make a general statement and ask for some advice on it by private message (PM) to someone here. Some have benefitted from that route in the past. Finally you may have noticed you have reached your posting limit for your first 24 hours as a new member. Don't worry you will be able to post freely after that.

Really ? The difficulty QM has that with that statement is that you can't when it is at that somewhere.

Can you not post .jpg or other acceptable format that I don't need to down load ? You can place pictures in your post by placing the cursor where you want the picture and the clicking on the thumbnail at the bottom of the text entry editor.

Sure, why not? It is called partitioning. Remember that the product mn (n2 in this case) is the count of elements and is called the order of the matrix But both matrices are planar arrays. This technique was much used in the days when computers were no powerful enough to handle large arrays in one go. Does this help ?

You didn't say if you understood this, because it is exactly what you said, writ differently, and with some additional information justifying why you computer can do this.

The short answer is no, you cannot in general add the dimension of array to the dimension of the element. Each has its own separate and usualy different dimension. This is perhas easier to see with planar (2D) matrices such as the jacobian matrix or the del operator matrix. Here elements of 1, 2 or 3 ( or more) D are incorporated in these matrices. If you can understand this statement that this must be the case since the array maps Rn → R and both have the same cardinality.

Rock ? You started by asking about partly saturated soil. I very much doubt that the cost of 100m of 2 - 3 inch pipe in igneous rock would be economic. However limiting factors are twofold. Unless you live in Iceland or NZ your output water would be in the 16oC range so not a great deal of temperature different to drive the heat exchange. The actual rate of takeup would be limited by the pipe material - probably plastic. But stainless steel has a relatively low conductivity as well. In Mordredland you may also be fighting permafrost. You still haven't said much about where you are coming from.

I agree +1 to SJ for finding that manual. I note you can also save as a pdf. I sometimes use a free image extractor forpdf files to get a jpg. Also many scanners some with image file format convertors. Perhaps you could post a pdf ouput file to experiment with (if the forum doesn'y lik dotpdf, add dottxt to the end for stripping out) ? https://www.google.co.uk/search?q=pdf+image+extractor&sca_esv=566487c1e8374dca&sca_upv=1&source=hp&ei=VqDtZqylJ9yxhbIP7aiHgAw&iflsig=AL9hbdgAAAAAZu2uZoCAb3C3E79D7cebrT8kXpZbiBbE&ved=0ahUKEwisqMie9tGIAxXcWEEAHW3UAcAQ4dUDCA8&uact=5&oq=pdf+image+extractor&gs_lp=Egdnd3Mtd2l6IhNwZGYgaW1hZ2UgZXh0cmFjdG9yMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBRAAGIAEMgUQABiABDIFEAAYgAQyBhAAGBYYHjIGEAAYFhgeSOAnUABY8SNwAHgAkAEAmAFxoAGTDKoBBDE4LjG4AQPIAQD4AQGYAhOgAvkNwgIOEC4YgAQYsQMYgwEYigXCAhEQLhiABBixAxjRAxiDARjHAcICCxAuGIAEGLEDGIMBwgILEAAYgAQYsQMYgwHCAgsQLhiABBjRAxjHAcICCBAAGIAEGLEDwgINEAAYgAQYsQMYgwEYCsICBxAAGIAEGAqYAwCSBwQxNC41oAflcg&sclient=gws-wiz

By whom? Walt Disney of course. 😀

Excellent idea identifying your level of expertise. I wasn't aware that anyone offered a 'bac' in such anarrow field. Generally the bac requires a spread of subjects. Modred is 110% correct in saying the Physics is the dominant partner here, not Mathematics. Relativity is merely couched in mathematical terms for convenience of expression. I think that full explanation here is a job for @Janus who does the best ones. Meanwhile a few comments on the Physics. There are two types of mass, inertial as Mordred has mentioned, and gravitational. These two types have heen distinguished since the days of Newton. Happily they have the same values using appropriate equations. Thre are also several types of Relativity. There is what we call Galilean or Newtonian Relativity Einsteins Special theory of Relativity this may be understood at high school level Einsteins General Theory of Relativity which requires some more advance maths to properly understand it. This is the one you are speculating about. Physics in the guise of quantum theory) requires that space cannot be empty. It also requires that whatever is in it alters the mathematical structure from a simple orthgonal coordinate system imposed, not by Physics, but by us, to a more complicated one. I do agree with you that there is no 'stretching' involved - perhaps you have been looking at those awful trampoline pictures that should be banned. I said whatever is in it since quantum theory has no requirement that the something be mass, although it does describe how the mass works. The whatever includes energy which also also change the coordinate system. These last two comments have been the focus of intensive research over the last part of the 20th century and into this current one.