Talk:Selector calculus

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I added the pov-stub based on the rather disputed nature of the claims made here. Its not clear to me that this is legit physics/math. See Heim theory and specifically Talk:Heim theory for details. linas 02:28, 8 May 2005 (UTC)

I agree with the above comment. I have a math degree from Harvard, what is written in the article is complete bullshit - tm.

Well, the Harvard man has certainly settled this for us! -eb

EB might be sarcastic, but from the "information" give here it seems that selector calculus is nonsense, mathematically speaking. ---CH 22:35, 5 February 2006 (UTC)

I've also got a solid background in mathematics, the guy from Harvard was apparently never taught how to use abstract mathematics to simulate unknown quantities, aspects or variables. There is nothing wrong here but your interpretation. ---M 20:13, 12 March 2006 (GMT)

Its a good job Newton didn't go to Harvard! 203.118.156.140 09:46, 10 May 2006 (UTC)

Selector calculus.

Infinities, continua, vacuums, and reifying the zero are nonsense. It looks to me as though Heim found an answer to Zeno of Elea. Mathemeticians may not like this development, that does not give them grounds to reject his work out of hand. In fact, the burden of proof is and always has been on those adopting the Platonic approach. 216.207.89.34 19:58, 18 January 2006 (UTC)Don Granberry.

I agree, this is crap. I am nominating it for deletion. ---CH 22:14, 5 February 2006 (UTC)

the smallmindedness above is complete crap. Heim Theory is the only physical theory that correctly predicts particle masses from first principles. take a moment to digest that. There is no other theory that predicts particle masses from first principles!!!!!!!!!!! See article on Heim theory and links. The reason for the selector calculus is that Heim needed to quantize space to solve the singualarity that occurs ar zero radius in general relativity. He could not use traditional infinitesmal calculus so he invented Selector Calculus. Have any other physicists invented mathematics? eh duh... Archimedes, Newton, Dirac, Witten. I therefore nominate the negative comments of the above gentlemenn, and I use the term loosely, for deletion.--Will314159 22:28, 12 March 2006 (UTC)

Censorship

I am not a mathematician or physicist. I am an educated reader who is old enough to clearly remember John F. Kennedy as President.

Deleting this is petulant censorship. Selector calculus may be nonsense. So what? Wikipedia has lots of articles on other unproven, wrong-headed, or silly notions: UFOs, cold fusion, the soul, God, Britney Spears. Nobody seriously proposes deleting these.

Instead of deleting it, it is fairer, and more accurate and helpful to readers, to label it clearly as fringe science or mathematics. Or, merge it into the other disputed articles on Heim. Someone put work into this, and it has value for those looking for information on this type of fringe science or mathematics.

I am now an existence proof for this viewpoint. Before seeing this article, I never heard of selector calculus. Now I know it is nonsense. I have added this fact to my knowledge of the world. This is a good thing.

Label this for what it is. Modify the text. Warn the readers. Then, let them make up their minds on the matter. Don't try to decide things for others.

Thank you.

I disagree that selector calculus is nonsense. As I understand it, Heim assumes space is quantized. Normal calculus is only valid over a continuous range. If the range is discrete calculus fails as follows: for Δx less than the discrete interval integrating from x₁ to x₂ gives a different answer than integrating from x₁ to (x₂ + Δx). A discrete calculus returns the identical (and correct) answer for both ranges. What the article lacks is an example of selector calculus vs Newton/Leibniz calculus for a trivial problem in a quantized space - which would show why it is necessary. Youngbadfrog (talk) 06:49, 23 July 2011 (UTC)

New proposal

1. Merge the "meat" of the article (everything except the introductory paragraph) into difference operator, which is real mathematics.
2. Merge the introduction into Heim theory. (This includes making sure that there is a link from Heim theory to difference operator.)
3. Redirect this article to Heim theory.

That seems fair, whether or not the theory has any validity, unless the article were to be greatly expanded, or if there is some "meat" which is not accepted by the mathematical community. Arthur Rubin | (talk) 23:50, 13 February 2006 (UTC)

(I'm willing to do the first part, if I can get some guidance as to what I need to say in the comments.) Arthur Rubin | (talk) 23:52, 13 February 2006 (UTC)

The "meat" is now copied into difference operator, although we may need to credit the first quotient formula to somebody. Arthur Rubin | (talk) 01:38, 14 February 2006 (UTC)

By real mathematics above, I mean generally accepted mathematics. Arthur Rubin | (talk) 00:04, 14 February 2006 (UTC)

Extending diference calculus to tensors

I'm trying to find some good sources for this. I did discover a couple of interesting comments

• Heim had to go the other way and use the Calculus of Differences and extened it to Tensors which he called Selector Calculus. [1]
• While the mathematics of finite lengths has been developed in the literature (Nörlund, 1924; Gelfond, 1958) the novel feature of Heim’s metronic theory is that it is a mathematics of finite areas. [2]

so it seems we are only half way there. We now have some stuff on difference operators, but have yet to get to the novel part of the theory which is the application to tensors, i.e. a finite version of Covariant derivative. --Salix alba (talk) 01:15, 14 February 2006 (UTC)

OK, you find the application, and I'll tell you whether it's really novel. Arthur Rubin | (talk) 02:00, 14 February 2006 (UTC)

I'm a little concerned about commutivity. Lacking access to Heim's work its dificult to really judge, but the material cut from this page and inserted into difference operator plays fast and loose with commutivity, fine for single valued functions, but not for matricies and tensors which are generally non commutative. --Salix alba (talk) 20:53, 15 February 2006 (UTC)

I see your point. I think it can be corrected for matrix multiplication / tensor contraction, although I didn't feel the need in the difference operator article, but division (aka reciprocal) is almost hopeless. Arthur Rubin | (talk) 02:06, 16 February 2006 (UTC)

I find the second point (While the mathematics of finite lengths … areas.) extremely hard to understand. If Heim's theory is indeed like the finite element method, as the article suggests, then the extension to areas is not new. Two-dimensional elements were already used in the 1942 paper by Richard Courant, referred to at the top of Finite element method. -- Jitse Niesen (talk) 16:00, 16 February 2006 (UTC)

Courant paper 1942. Very Interesting. A paper not accessible to a German soldier during WWII. Heim as a result of an explosion was largely deaf, blind & w/o hands at the age of 19. He invented the mathematics he needed for the physics problems presented. In the way of Newton and Liebnitz. Even as a historical genetic creature, I still don't see the hearburn in certian quarters with Selector Calculus.--Will314159 23:26, 7 May 2006 (UTC)

Bockspur 10th of march 2006

Regardless of the merit of Heim's research or various individual or collective opinions of that work this article seems to be about 'selector calculus'. This article should stand on the internal consistancy of 'selector calculus'. Anything else would be small minded.

Now i don't see much of a description of this 'selector calculus' but it does state that it is equivalent to the finite element method and as long as dx/dt ratio is within bounds then this would pass the smell taste. —The preceding unsigned comment was added by 67.125.184.212 (talk • contribs) 22:26, 10 March 2006 (UTC)

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The man from Harvard misses the point. Heim theory is the Only Physics theory that is deep and broad enough to correctly predict the particle masses from first principle!

There is a problem with General relativity. It fails at the Singularity, that is r=0, to wit; where the radius equal zero. Quantum mechanics solved that for electro dynamics by quantization.

How do you do that for General Relativity? You have to quantize space. You have to do that by using a DISCRETE CALCULUS.

Heim would not be the first PHYSISCT to invent a branch of Mathematics. Archimedes, Newton come to mind. Newton had the problem of showing that the mass of the earth could be treated as existing at a point in the center. To do that, he had to integrate the sphere of the earth as concentric rings and sum the masses up. This is the beginning of Ingegral calculus. Similar problems led to the invention of Differential Calclus. the problems of motions and gravitation gave birth to infinitesimal Calcululs.

The problems of quantization of space has given birth to SELECTOR CALCULS.

Below is the comment I was going to make " Now SELECTOR CALCULUS would not really be a PHYSICAL THEORY, but a MATHEMATICAL TOOL.

It would be analagous to Newton inventing Integral and Differential Calculus as a necessary tool to fully engage his theory of Gravity. For example to be eble to layer a solid ball of mass as first as concentric layers, and then model it all the mass being concentrated at the center. You need integral calculus for that.

As to Heisenberg Matric Mechanics. Von Neumann in his Foundations of Quantum Mechanics showed that Matrix Mechanics and the Schrodinger Wave Mechanics were both examples of an infininte HILBERT Algebra Space.

Later Dirac in his book, did the same thing and introduced the Bra-Ket notation.

Heim because he quantized space avoided singularities by avoiding infinitesimals thus he invented a discrete Calculus. Thus he is on a par with Newton Newton in inventing his own Mathematicsal tools.

The Heim group is working on reworking the Heim Theory by avoiding the Selector Calculus and using standard Calculus Terminology. The key quantizattion occurs at the Christoffel symbol stage. "

And I guarantee you that when Dirac introduce the Dirac Delta function it was not being used in the HARVARD of his day and it did not have a rigorous mathematical foundation. It does today and it is indispensible in Physics and Electrical Engineering.

In Summary, the article should stay, all this stop sign crap should be removed, and I nominate Harvard for deletion. I am only kidding about Harvard being deleted. Just that small mindedness should be deleted.--Will314159 21:34, 12 March 2006 (UTC)

In my opinion the fact that Heim theory claims to predict particle masses is a reason to suspect it, not celebrate it.Rotiro 08:02, 14 April 2006 (UTC)

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The indictment of Selector Calculus based on the Ignorance of it my Mainstream Mathematicians is an Indictment of Mainstream Mathematicians (hereinafter "MM"). The purpose of the Article is to educate the populace about Seclector Calculus including "MM."

Second, the article needs context. Selector Calculus doesn't stand in isolation. It was the key used by Heim in quantizing General Relativity. This led to a TOE. One of the fruits is the prediction or posdiction of the particle masses. The only theory that does this from first principles. String theory does not do this! Another is the space travel extension that has been in the news lately.--Will314159 12:10, 13 March 2006 (UTC)

So, why don't you explain Selector Calculus? For instance, why does it say that it is similar to finite element methods when the description seems to be more similar to finite differences?

I removed the {{npov}} notice as it only seemed to complain that Heim theory is presented as a mainstream theory, which this article does not do. I also removed other parts of which I couldn't make sense. The German-English language barrier is not much of a barrier, "the singularity that occurs when the radius approaches zero in general relativity" should be explained properly, there are no infinitesimals in differential calculus as it does not make sense as at the moment, and the successes or failures of Heim theory are not the subject of this article. -- Jitse Niesen (talk) 12:40, 13 March 2006 (UTC)

I can live with this version of the article. But it probably won't stay NPOV. As I've asked the previous supporter of this article, and I'm asking Will314159 -- explain why this concept differs from difference calculus, and I'll tell you whether that difference is a mathematical difference, nonsense, or no difference at all. — Arthur Rubin | (talk) 13:21, 13 March 2006 (UTC)

i am satisfied with the removal of the NPOV. As I've explained the motivation for Calculus in the past has been Physics. What is a first derivative but velocity, the second but acceleration? etc. Llkewise the motivation for Selector Calculus was the quantization of General Relativity involoved in Heim Theory. Selector Calculus presently is of interest to people interested in Heim Theory and how it evolved. It doesn't matter if Heim could have used something else. He didn't and this is what he invented to further his theory. Is his theory important? What other theory predicts the particle masses from first principles? I am still waiting for the answer. My dog Max, the three legged lab is barking. He wants to go out on the beach and swim. Rubin, Don't you have other things to do? Leave the article alone like it is, puhleasse. Oh I see that the guy that put the NPOV on descrobes hmself as a "Linux hacker." Take Care! Will --65.184.213.36 16:34, 13 March 2006 (UTC) 16:32, 13 March 2006 (UTC)

I am primarily a mathematician -- but there's nothing in this article to suggest that there would be something here that wouldn't be in difference operator. If it wasn't for the disputes, I'd insert the one or two relevant lines into difference operator and change this to a redirect. — Arthur Rubin | (talk) 17:36, 13 March 2006 (UTC)

I wanted to explain my "infinitesimal" calculus remark. Even when I took freshman caluclus in 1968 we used deltas for the domain and epsilon for the range and talked about limits. We understood that "infinitesimals" was just a shorthand way of talking about it, and limits was the rigorous foundation. But sometimes in physics, it was a lot easier to use those dx, dt. And I like to use Newton's fluxion notations. Actually my introduction to calculus was before college, reading a paperback book by a German gentlman, I believe his name was Toeplitz called Calculs, a Genetic Approach. He started with Archimedes, the Arabs and their solution to some sum of square series, Galilieo, Barrow, Huygens, Newton That is my reference. Even though the Selector Calculus may be identical to some other academic method, GENETICALLY, it has an importance of its own in the history of its development and tho the theory to which it relates.--Will314159 17:55, 17 March 2006 (UTC)

Umbral calculus

What's the difference between this and umbral calculus? —Keenan Pepper 21:43, 24 June 2006 (UTC)

There's no assertion in the article which differentiates (sorry) it from difference operator. An umbral calculus link would be inappropriate. — Arthur Rubin | (talk) 15:33, 25 June 2006 (UTC)

A very "shadowy" subject. I stand in the "penumbra of its emanations," legally speaking. Take Care! --Will^(talk) 16:46, 16 July 2006 (UTC)