User talk:Bo Jacoby

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[edit] Root-finding algorithm

Hello, and welcome on Wikipedia. I have some questions about your addition to root-finding algorithm. I don't remembering seeing this method before, but that's does not say much as I never really studied the numerical solution of polynomial equations. Do you have some reference for this method (this is required for verifiability)? Is there some analysis; for instance, does the iteration always converge, and is anything known about the speed of convergence? Just a small remark: we sign our contributions on talk pages, but not in the articlesthemselves; see Wikipedia:Ownership of articles#Guidelines. I hope that you continue contributing. Please drop by at Wikipedia:WikiProject Mathematics and feel free to ask me any questions on User talk:Jitse Niesen. Cheers, Jitse Niesen (talk) 22:20, 12 September 2005 (UTC)

Hello Jitse. Thank you very much for your comment on my article on root-finding algoritm. You request a reference for verifiability and some analysis, and you ask whether the method always converge and what is the speed? I agree that such theoretical stuff would be nice, but alas I have not got it. I have got a lot of practical experience with the method. It was taught in an engineering school in Copenhagen for more than 5 years, and the students implemented it on computer and solved thousands of examples. I have not got any nontrivial reports on nonconvergence. So much for verifiability. Does the method always converge ? The answer is no for topological reasons. This is why. Consider initial guess p,q,r,s converging towards roots P,Q,R,S. For reasons of symmetry the initial guess q,p,r,s will converge towards Q,P,R,S. Both solutions are satisfactory, but they are not the same point in four-dimensional complex space. Consider f(t)=(1-t)(p,q,r,s)+t(q,p,r,s), 0<t<1. This line joins the two initial guesses. Note that the iteration function, g, is continuous, no matter how many times we iterate. We don't iterate an infinite number of times. Let A and B be open disjoint sets such that A contains (P,Q,R,S) and B contains (Q,P,R,S) and such that g(f(0)) is in A and g(f(1)) is in B. But no continuous curve can jump from A to B. So for some value of t, 0<t<1, g(f(t)) is outside both A and B, and so the method does not converge everywhere.

I do not think that this immature argument belongs to a wikipedia article.

However, I believe that the method converges 'almost everywhere' in the sense of Lebesque, but I have no proof. Nevertheless, the question of convergence is not the right question to pose. As you only iterate a finite number of times, you will not necessary get close to a solution even if the method converges eventually. So, the method is good for no good theoretical reason! The solutions are attracting fixpoints for the iteration function. That's all.


Bo Jacoby 07:12, 13 September 2005 (UTC)

[edit] Please vote

Hello. Please vote at Wikipedia:Featured list candidates/List of lists of mathematical topics. Michael Hardy 23:01, 14 October 2005 (UTC)

[edit] Mathematical notation style conventions (non-TeX should match TeX as much as possible)

Hello. Please note the differences between the first and second versions of each of the following:

ln(-1) is a solution to ex=-1.
ln(−1) is a solution to ex = −1.

(Proper minus sign instead of nearly invisible hyphen. Spacing on both sides of "=".)

If x=it is
If x = it is

(Spacing.)

ex=eit is a point on
ex = eit is a point on

(Spacing.)

from point 1 (=1+0i) to eit.
from point 1 (= 1 + 0i) to eit

(Spacing. Italicizing i BOTH times, not just the second time.)

at the point -1 (=-1+0i). So eiπ=-1.
at the point −1 (= −1 + 0i). So eiπ = −1.

(Proper minus sign. Spacing. Italicizing i BOTH times. Digits, inclduing "1", should not be italicized in non-TeX mathematical notation; neither should punctuation, although that point doesn't arise here.)

And so ln(-1)=iπ
And so ln(−1) = iπ

(Proper minus sign. Spacing. Consistently italicizing i.)

Michael Hardy 19:36, 3 November 2005 (UTC)

Thank you very much ! Bo Jacoby 07:27, 4 November 2005 (UTC)

[edit] Hot & Cold Photons?

I've left some comment on the thermodynamic evolution "Talk Page". Let me know if you have suggestions. Thanks:--Wavesmikey 04:38, 26 November 2005 (UTC)

[edit] why the difference in notation?

Consider the expression

\ {n \choose i}p^i(1-p)^{n-i}

Fixing (n,p) it is the binomial distribution of i. Fixing (n,i) it is the (unnormalized) beta distribution of p. The article does not clarify this.

Bo Jacoby 10:02, 15 September 2005 (UTC)

This is mentioned only implicitly in the current version, which describes the beta distribution as the conjugate prior for the binomial. You could add a section on occurrence and uses of the beta distribution that would clarify this point further. --MarkSweep✍ 12:50, 15 September 2005 (UTC)

I don't see what makes you think the article is not explicit about this point. You wrote this on Sepember 15th, when the version of September 6th was there, and that version is perfectly explicit about it. It says the density f(x) is defined on the interval [0, 1], and x where it appears in that formula is the same as what you're calling p above. How explicit can you get? Michael Hardy 23:07, 16 December 2005 (UTC)

... or did you mean it fails to clarify that the same expression defines both functions? OK, maybe you did mean that ... Michael Hardy 23:08, 16 December 2005 (UTC)

Yes, precisely! Bo Jacoby 16:54, 31 December 2005 (UTC) See Inferential statistics, where the same simple expression is used for deductive and inductive distributions, and where the limiting cases are: the binomial distribution, the beta distribution, the poisson distribution and the gamma distribution, and, of cause, the normal distribution. I find this unified approch very attractive. Bo Jacoby 09:58, 4 January 2006 (UTC)

[edit] Mathematical notation conventions

Hello. Your comments at talk:normal distribution inspire this comment. In editing mathematics articles, you may find it useful to bear in mind the difference in (1) sizes of parentheses and (2) the dots at the end in these two expressions:

Z(t)=(d/dt)\log(\int{e^{xt}f(x)dx})=\mu+\sigma^2t+...
Z(t)=(d/dt)\log\left(\int{e^{xt}f(x)dx}\right)=\mu+\sigma^2t+\cdots

Michael Hardy 23:56, 8 January 2006 (UTC)

Thank you very much. I totally agree. Please feel free to edit on the spot. Bo Jacoby 07:52, 13 January 2006 (UTC)

[edit] Reference

"Bo Jacoby, Nulpunkter for polynomier, CAE-nyt 1988" — could you please write out "CAE-nyt" in full? Is it a journal, a technical report, something else? I have no idea where to find this reference. Thanks. -- Jitse Niesen (talk) 11:26, 11 January 2006 (UTC)

"CAE-nyt" = 'Computer Aided Engineering News', a periodical for "Dansk CAE Gruppe" = 'Danish CAE Group'. I can fax the article to you if you are interested in history. For mathematical reasons you need not read it, because the explanation in the WP-article is better than that of the old article. Bo Jacoby 08:00, 12 January 2006 (UTC)

I found the method from scatch, but I don't know who was the first one to do so. I gave a lecture to 'Dansk Selskab for Bygningsstatik' on December 10th 1991. My lecture was published and a reference to that publication is now added to the WP-article. After the lecture I had some correspondance with Jørgen Sand. He says that the method is the Durand Kerner method, and he gave the following reference, which I have not checked.

Terano, T., el al (1978): An Algebraic Equation Solver with global convergence Property. Research memorandum RMI 78-03, Tokyo.

For topological reasons strict global convergence is impossible, but the method converges almost everywhere, and the convergence is fast. Bo Jacoby 07:49, 13 January 2006 (UTC)

Excellent. I found some references to articles about the Durand-Kerner method. I'll check them when I have some time and see whether this is indeed the same method as described in Jacoby's method. -- Jitse Niesen (talk) 13:53, 13 January 2006 (UTC)
Ohh. I had to look. Cool. How about some pictures of the basin of attraction for this solver? We have those famous pictures of the basin of attraction for the Newton zero finder; I wonder how this compares. In particular, its not clear to me how/why the initial guesses can end up in different basins. linas 05:46, 31 January 2006 (UTC)

The space C4 contains 24 open basins of attraction, one for each permutation of the four roots of a degree 4 polynomial. I don't know how to make a picture of that. If an initial guess p,q,r,s is in one of the basins, then q,p,r,s is in another basin. Bo Jacoby 07:33, 31 January 2006 (UTC)

[edit] Style remarks

Hi Bo. I have a few style remarks. First is that one should make variables italic, so x instead of x. Second, per the math style manual one should not force PNG images if inline, so one should write an instead of a_n\, which is an image. These are small things, but they are good practice to follow. :) Oleg Alexandrov (talk) 01:17, 21 January 2006 (UTC)

Thanks, Oleg. You've got a point. I need to find out how to make a little not-equal sign in 'math'.

x=0 \,, x \ne 0, x = 0, x?0  ?

Without 'math' it can be done, but then the font is different:

x = 0, x ≠ 0

I'd like if the same variable takes exactly the same typographical shape thoughout the article. Bo Jacoby 05:49, 21 January 2006 (UTC)

In short, the math display on the web sucks. :) Oleg Alexandrov (talk) 06:17, 21 January 2006 (UTC)

[edit] One more style remark

Hi Bo. Just one remark. Writing links as Ordinary_differential_equation#Homogeneous_linear_ODEs_with_constant_coefficients is not a good idea, as they mess up the diffs, as you can see here. Then it is hard to see what changed. I will fix that right now, but a tip for future reference is to remove the underscores. (And by the way, I don't know if it is a good idea to link to sections to start with; those section names can (will) change eventually, and then the link breaks down. But I see, it does not hurt either). Oleg Alexandrov (talk) 00:23, 24 January 2006 (UTC)

Thanks. Its a very good tip. But why didn't you like my other edits to root-finding algorithm ? Please note the Wikipedia:Simplified_Ruleset point 9. Take your time to produce what we agree is a step forwards, rather than to make what I must consider a step backwards. For example I don't think that the words: 'Much attention has been given' belong in an encyclopedia. Bo Jacoby 10:32, 24 January 2006 (UTC)

[edit] Splitting circle method

I noticed this comment of yours. I created the article after stumbling across the algorithm's name, but didn't write an explanation as I couldn't figure out much from the sources I found. I created a stub anyway in the hope that someone with more knowledge in this domain will be able to expand it. If you could, the work would certainly be appreciated. Fredrik Johansson - talk - contribs 11:11, 24 January 2006 (UTC)

Thanks to this I read about Jacoby's method. That's a quite interesting algorithm, and remarkably simple to implement. Though it evidently works, it would be nice to have an online reference outside of Wikipedia for verification purposes. You don't have a website where you could put a description? Fredrik Johansson - talk - contribs 11:31, 24 January 2006 (UTC)
Hi Fredrik. Isn't it remarkable that an algorithm 'evidently works' ? Alas my references are all to old to be online. A new website would basicly contain the same information as the WP-article. Look at Talk:Root-finding algorithm for some discussion. There is not much more to be said. Try it and convince yourself that the problem is solved. Bo Jacoby 13:35, 24 January 2006 (UTC)
There's no problem, just an opportunity to make verification more convenient for future readers. Fredrik Johansson - talk - contribs 15:58, 24 January 2006 (UTC)

[edit] n-ary operations

I haven't looked at your edit to function (mathematics) on this point, but there are such things as n-ary operations, no matter what the abstract algebra article may say... Randall Holmes 22:40, 29 January 2006 (UTC)

I agree. But the group operation is an example of a binary operation, and not of an n-ary operation for n>2. Bo Jacoby 23:08, 29 January 2006 (UTC)

[edit] Query

  • JA: Bo, I moved your question to the end (I gave warning in the edit line), as it's best to put new talk at the end, or else people tend to miss it. I'm writing a reply as we speak, well, not just this second, but in a second. Jon Awbrey 15:04, 3 February 2006 (UTC)

[edit] Combinations

Hi. Some of your changes to the Combinations page removed info that is relevant, without making it really clear that the material was moved to another article. IMO - it would be better to have a complete, self-contained article on combinations, or to move all of the info to binomial distribution and then have combinations redirect there. Just my $0.02. dryguy 19:20, 8 February 2006 (UTC)

Surely the information is relevant, but it is also stated in binomial coefficient, so it does not need to be repeated everywhere. A link is sufficient. Bo Jacoby 10:44, 9 February 2006 (UTC)
Sorry, I mis-typed. I meant to say move to the binomial coefficient article. In any event, my point was, that some of the info that was moved was highly relevant to the combinations article, and probably best belongs there. If the duplication bothers you, why not pick one of the two articles and place all of the combinations info in one place. I think that the combinations article is now a bit too thin. It could either be restored, or the remaining info moved to binomial coefficient with combinations redirecting to the binomial coefficient article. dryguy 13:32, 9 February 2006 (UTC)
There is a discussion going on regarding merging of the two articles, as you also suggest, but not everybody is in favour of a merge. The present cleanup is a compromise. I don't mind at all that an article is thin, if it contains a definition and a link to more detail in another article. The concept of 'combination' is equivalent to 'subset', so there is not much to be said, I think. Bo Jacoby 14:30, 9 February 2006 (UTC)

[edit] Multiset

Hello. Please note my recent edits to that article. Michael Hardy 00:40, 9 February 2006 (UTC) Thank you, Michael. Bo Jacoby 10:31, 9 February 2006 (UTC)

[edit] Style

Bo, just one remark, and I may have said it before. Per the math style manual, variables should be italic. Thanks. Oleg Alexandrov (talk) 16:02, 8 March 2006 (UTC)

[edit] Ordinal fraction listed for deletion

An article that you have been involved in editing, Ordinal fraction , has been listed at Wikipedia:Articles for deletion/Ordinal fraction . Please look there to see why this is, if you are interested in it not being deleted. Thank you.

[edit] Note

You may want to take a look and comment at Wikipedia talk:WikiProject Mathematics#Problem editor.

The moral of the story is that please modify articles only on topics you are very sure about, and only when you have good published references for whatever you are writing.

Also, if a couple or more of editors tell you to drop something, then drop it, especially if you are not completely sure you perfectly understand the topic at hand. Oleg Alexandrov (talk) 05:09, 17 August 2006 (UTC)

[edit] Exponentiation

I moved your comment about the article to Talk:Exponentiation because discussions about article content belong on article talk pages. I assure you I don't have any personal grudge with you. The article Kepler's laws of planetary motion seems much improved due to your editing. CMummert · talk 14:17, 12 January 2007 (UTC)

Thank you! Bo Jacoby 15:31, 12 January 2007 (UTC).

[edit] Mathematics CotW

I am writing you to let you know that the Mathematics Collaboration of the week(soon to "of the month") is getting an overhaul of sorts and I would encourage you to participate in whatever way you can, i.e. nominate an article, contribute to an article, or sign up to be part of the project. Any help would be greatly appreciated, thanks--Cronholm144 17:46, 13 May 2007 (UTC)

Thanks! Bo Jacoby 18:04, 19 May 2007 (UTC).

[edit] definition of a subgroup

A subgroup is a pair (S, *) closed under the operation * and selection of unity, which is what we call a 'nullary operation". This means that the only unity allowed in the construction of a subgroup is the unity of the group. --VKokielov 18:37, 4 June 2007 (UTC)

By the way, 0 is never part of the multiplicative group of a field. --VKokielov 18:42, 4 June 2007 (UTC)

Thanks. The pair ({0},·) is closed under the operation of multiplication · . The element 0 satisfies 0·x=x for x in {0}, because 0·x = 0·0 = 0 = x. The group ({0},·) is not a proper subgroup of a larger group of complex numbers, but still it is a group. It is isomorphic to ({1},·) . Bo Jacoby 22:18, 4 June 2007 (UTC).

[edit] thanks

Thanks for such a precise and detailed answer to my question about statistical significance on the Talk:Standard deviation page. Luzhin 17:13, 23 July 2007 (UTC)

you are welcome, my friend. Bo Jacoby 20:24, 23 July 2007 (UTC).

[edit] Please don't use Wikipedia for self-promotion

Howdy, I noticed the little disagreement over at Wikipedia:Reference_desk/Mathematics#What_is_the_addition_equivalent_of_a_factorial.3F and it struck me as odd than a mathematical disagreement would get people saying "please take it elsewhere." In looking into this further, I came across things like Wikipedia_talk:WikiProject_Mathematics/Archive_16#Problem_editor and Wikipedia:Articles_for_deletion/Ordinal_fraction. It appears there has been an ongoing problem for quite some time with you trying to promote your own nonstandard notation. I'm not much of a subject matter expert in this field, so I can only go by what other people have written, but do you agree with this assessment? I must remind you once again that editors are expected to cooperate with each other, and this includes observing Wikipedia's policies and guidelines. Friday (talk) 18:56, 6 August 2007 (UTC)

[edit] \cdots on Negative binomial distribution

Does the Negative binomial distribution article really need product dots between each variable? I've never seen it written like this is statistics books, or many other articles.--Vince | Talk 07:55, 2 November 2007 (UTC)

no, it is not strictly necessary, but it makes the formulas safer to read, and it makes no harm. It avoids confusion where f(k) does not imply multiplication while p(1-p) does imply multiplication. Bo Jacoby 23:53, 2 November 2007 (UTC).

[edit] Durand-Kerner-Weierstrass method

Thank you for considering my proposed change regarding subscripts. I believe the two formulations are equivalent. I found the alternate slightly easier to implement for arbitrary n, as each iteration relies only on results from previous iterations, rather than the iteration in progress. This makes it easier to halt iteration if changes fall below a specified precision.

May I impose on you to comment on the suitability of this algorithm to polynomials with complex coefficients?

John Matthews JMatthews 09:01, 2 November 2007 (UTC)

Thanks for your comment. The two formulations are not quite equivalent. In the original case the newly computed values of the approximate are used as soon as possible. In your formulation they are not used until after the loop. Both formulations provide useful algorithms. The original formulation is the one consistent with the numerical example.
Regarding the halting condition: You do not want the computer to loop infinitely at any rate. So in very exceptional cases you must stop the iteration even if the roots have not been found with the specified accuracy. How many iterations are you prepared to perform in that case? Why not use the same number of iterations in the normal case? So don't bother testing against a precision, but iterate in the normal case the same number of times as you iterate in the worst case. Have a nice day. Bo Jacoby 09:18, 2 November 2007 (UTC).
Thank you for this thoughtful analysis. In this particular case, I am implementing a generic procedure. The user may have instantiated the code with a more or less precise numerical type, depending on space and time constraints. I'm not sure I see the value in iterating beyond the useful precision of the specified type. John Matthews JMatthews 11:54, 2 November 2007 (UTC)
Congratulations! If you skip the change condition the program becomes slower in average, but not in the worst case. Once users have grown accustomed to fast response they complain over slow response. Don't create an expectation that you cannot maintain. Bo Jacoby 11:55, 8 November 2007 (UTC).


Hi John. You will find that the 'old' version of the algorithm is slightly space-saving as only one version of the variables p,q,r,s is needed.
Yes, I see this. Of course, for a given polynomial order, n, each iteration takes O(n2) effort, while the array copy takes only O(n). It is still an appealing optimization. John Matthews JMatthews 19:06, 4 November 2007 (UTC)
You will also find that the criterion for halting the iteration loop is a little complicated, involving first the computation of a size of the last step taken, and secondly an emergency break preventing the program from looping infinitely in exceptional cases. If you try to solve x2+1=0 using real initial guesses the algorithm will loop forever. That's why real initial guesses are avoided. But no matter which initial guesses you choose some equation exists that remains unsolvable using these initial guesses. So, theoretically, you cannot safeguard against the infinite loop. That's a hard fact of life. So you must stop the program after a finite number of iterations. If your experiments show that the roots usually have stopped moving after 5 iterations, you may choose to limit the number of iterations to, say, 20. Having done this you may contemplate the cost and the benefit of performing these 20 iterations every time. The cost is the time of doing 15 needless iterations in the normal situation, and the benefit is the simplification of coding the halting criterion. It may seem insensitive and brutal and un-gentlemanlike to keep beating on roots after they have stopped moving, but actually it makes no harm or pain. Have fun! Bo Jacoby 00:22, 3 November 2007 (UTC).
My exit condition looks at both max_count and change. The former is O(1); latter is only O(n). I'm looking at scaling max_count as a function of n, now. Yes, it is indeed fun! John Matthews JMatthews 19:06, 4 November 2007 (UTC)
Yes, and the program becomes clearer if you simply omit the change part of the exit condition. You need the max_count part anyway. If one exit condition is sufficient then the other one is unnecessary from a logical point of view, if not from an optimization point of view. For sufficiently small values of n the algorithm is fast no matter what, and for sufficiently big values of n the algorithm is too slow no matter what. So why complicate the program for the sake of the intermediate values of n only? Scaling max_count is a good idea. I believe that max_count=7*n is sufficient, but I am not sure. It depends on the 'typical' equations to solve. Your report will be interesting. Bo Jacoby 12:26, 6 November 2007 (UTC).
I'm getting excellent results up to order 38 with the floating point precision I have available. Optimizing the max_count parameter proved unreliable, and the exit condition is really quite simple. Rather than reference my site, I'll post a link here. Thanks! John Matthews JMatthews 18:29, 7 November 2007 (UTC)

[edit] please comment on recent edit at Negative binomial distribution

In this edit you essentially rved an edit I made. I'd appreciate it if you started a discussion of it on the talk page. Also, your edit comment makes little sense to me. Pdbailey (talk) 13:56, 25 January 2008 (UTC)

Hi, I generally like to keep comments in one spot, so I replied to you over on my talk page. I'm only posting here because I don't know if you know that this is usual and that it is customary to watch a talk page that you post on. Pdbailey (talk) 17:39, 26 January 2008 (UTC)

[edit] power of one

Thank you for commenting on my edit to exponentiation and correcting the content.
I know I have add inappropriate content AFTER my edit. However, I did NOT correct back because I want to wait somebody for correcting this. QQ (talk) 06:17, 25 February 2008 (UTC)

My friend, I do not understand. Do you expect me to do make some corrections ? Bo Jacoby (talk) 14:46, 25 February 2008 (UTC).

[edit] Quick personal question

Howdy, your posts are almost always fluent English, but I noticed a weird grammar mistake in your last talk post. Since I have been writing assuming you are a native speaker, I wanted to catch myself before I made a mistake in how I read your posts.

The specific thing is that you said you were "willing to work against consensus" which normally means "willing to sabotage/counteract/fight consensus", as in, an enemy of consensus, not a friend.

It is important to both you and I, that I know if you are a (near) native speaker, because I believe you may be acting uncivilly and disruptively, but this is based on the assumption that you are completely comfortable with the language.

In other words, I need to know whether the failure to communicate is just a simple language barrier.

I guess in either case, it would be helpful to know:

  • Do you think I am listening to your side?

or more negatively:

  • Do I seem to be ignoring you on the talk page?

My intention is to listen to you carefully, find every possible thing that you say that could help the encyclopedia, and then ensure that Oleg sees that they are helpful too (and similarly from Oleg to you). JackSchmidt (talk) 16:03, 26 February 2008 (UTC)

No, I am a Dane and not a native English speaker, and yes, I do make mistakes in grammar. I should have written, "willing to work towards consensus" - that was a very bad mistake. I'll fix it. I do intend to act civilly and to cooperate. Yes, I think you are listening to my side, and no, you do not seem to be ignoring me on the talk page. Thank you very much for being careful on these matters. Bo Jacoby (talk) 21:34, 26 February 2008 (UTC).
Ah, I am very glad to hear I was mistaken too. I apologize if I said anything rude, was impatient, or otherwise irritating. :) Now when I read your talk comments, it is very easy to see you trying very hard to work together with people who do not yet agree. A few more people have joined in the discussion, so I am not at all worried that it will work out.
We now have the two extremes laid out clearly for people to examine, your van der Waerden/Bourbaki approach (which are probably ancestors of all algebra on continental Europe, so who can argue!), and Arthur Rubin's very precise statement, but with 5cm parentheses!
It may not be possible for everyone to agree which single formula is best, but it should be easy to include both (with fixed tex). I think the summation with "informal" limits (i+j=k) is easier for young students (well American students at least) to read, and a "purer" notation is better for the formal definition.
Thanks again for being patient. It can be very hard for people to communicate, both in formulas, and in words. JackSchmidt (talk) 22:02, 26 February 2008 (UTC)

[edit] Dash to minus

Thanks for catching it twice! I restored your fix, and left this note on Silly Rabbit's talk page too. JackSchmidt (talk) 19:18, 28 February 2008 (UTC)

[edit] x+2=x+2

As in ZFC, objects are not typed in NF.  --Lambiam 08:11, 1 April 2008 (UTC)

[edit] Compressibility misunderstanding

Thanks for catching that! what I mean to say was more along the lines of losing "compressibility effects"... so something like when you have a shock wave/blast wave and the gas loses its "ideal-ness" and compressibility effects come into play. (along with changes in chemical composition and whatever else). As far as formatting goes, I dont know if it should be left as is or adjusted to fit the other sections that are in the article or somehow rewrite that portion of the article so that the formatting is uniform. I'm not sure what to do with it. I'm trying to keep that section as clear as possible because its an area of great disagreement (cause no one does their homework). Thanks for the help! Katanada (talk) 23:07, 2 April 2008 (UTC)

[edit] Product of Planck constant and Gravitational constant

Hi Bo Jacoby: Would you look at "Talk:Black hole electron", Item 9, "Quantum-gravitational effect" when you have some time. Clearly, the product of h and G is a constant value. We will know this product value when the L1 wavelength (and/or Planck length) value is more precisely known. We need to know if any correction factor is needed in the equation: (L2) squared = (L3)(L1). This is clearly defined in the article. Any correction factor that may apply must be very small. If you have interest in this, let me know on my Talk page. DonJStevens (talk) 15:12, 13 April 2008 (UTC)

Hi Bo Jacoby: The one second Schwarzschild radius that you described is interesting. With frequency 5.48x10 exp 85 rotations per second, the wavelength (c/frequency) would be 5.47x10 exp -78 meter.

Some theorists expect that photon energy has an upper limit, so that the expression "photon energy equals h times frequency" has an upper cut-off limit. As photon energy approaches Planck mass energy, wavelength approaches Planck length and time per cycle approaches Planck time. The values length and time then become either quantized or uncertain so that the (E=hv) expression, at some high energy level does not apply. In my opinion, this is probably correct. DonJStevens (talk) 18:27, 14 April 2008 (UTC)

Hi Bo Jacoby: Some things in nature are clearly quantized by limits; electric charge, electron mass, muon mass, impedance of space, velocity of light and so on. The acceleration limit is fixed at (c squared)(1/radius). Photon energy is fixed (has a charge acceleration limit) because alternating current required to generate a continuous em wave cannot be less than one charge per 1/2 cycle and the front to back dimension of a minimum segment of the continuous wave cannot be less than one wavelength. For a continuous wave with minimum radiated energy, exitation current will be (2e) times frequency. Then (h)(frequency) will equal (2e) squared, times frequency, times impedance. With some algebra, we find frequency divided by voltage equals (2e) divided by (h). This is the Josephson junction frequency to voltage ratio. The charge acceleration is (c squared)/radius, where radius is wavelength/2 pi. Acceleration increases linearly with frequency and exitation current increases linearly with frequency. DonJStevens (talk) 14:42, 16 April 2008 (UTC)

Hi Bo Jacoby: As photon wavelength is shortened (frequency increased; energy increased) three significant energy levels are attained. The electron Compton wavelength is first 2.426·10−12 m, next is 1.213·10−12 m. This second wavelength has energy equal to the mass energy of one electron plus one positron. As wavelength L is shortened ever more a wavelength is found that has energy determined either by the Planck constant or the gravitational constant. E = hc/L and also, E = Lc4(1/3πG). This wavelength is L=(3πhG/c3)1/2 = (2π)(Planck length)(3/2) 1/2. This wavelength is related to the electron Compton wavelength in a specific way. I expect (can't yet prove) that the L1 photon wavelength is the upper energy limit photon wavelength. DonJStevens (talk) 14:27, 19 April 2008 (UTC)

Hi Don. I edited your text above for readability. Why should there be an upper limit for photon energy? There is no energy, nor wavelength, determined by the Planck constant. How should the gravitational constant be related to the Compton wavelength? Bo Jacoby (talk) 16:00, 19 April 2008 (UTC).

Hi Bo Jacoby; When the wavelength of a photon is known, then its frequency is known and its energy is known. E = h (frequency). The frequency equals (c)(one second)/ wavelength. E = (hc/wavelength)(1 sec). The photon wavelength that has energy equal to one electron mass is h/mc or 2.426x10 exp -12 m. This is electron Compton wavelength. The gravitational constant defines a photon sphere radius (or photon orbit radius) value for any gravitationally collapsed mass. Radius = 3Gm/(c squared). When the radius (or circumference) is known, then its mass (and mass energy) is known. Radius (c squared/3G) = m. Radius (c exp 4)/3G = E . We need to translate from electron Compton wavelength to photon sphere circumference in order to use either the Planck constant or the gravitational constant (or both of these constants) to specify electron mass. The applicable gravitational time dilation factor at the photon sphere radius is needed to perform the translation. The idea of an upper limit for photon energy is not new. It is based on a maximum energy density value. When photon energy is great enough to cause limit space curvature, then no greater energy density (no smaller wavelength) is possible. DonJStevens (talk) 21:05, 19 April 2008 (UTC)

Hi Don. Assuming a single photon makes a black hole. The radius, r, of that black hole is computed from the mass, m, by r = 2Gc−2m. The mass is computed from the energy, E, by m = c−2E. The energy is computed from the frequency, ν, by E = hν. The frequency is computed from the wavelength, L, by ν = cL−1. So r = 2Gc−2m = 2Gc−4E = 2Gc−4hν = 2Gc−3hL−1. (Note that Lr = 2Gc−3h is an area). What prevents it from being a big black hole (r>>L)? Where does the electron mass enter into the calculation? Bo Jacoby (talk) 06:30, 20 April 2008 (UTC).

Hi Bo Jacoby: I like your equations because they follow the logic used to define the Planck length. You said r = 2Gh/(c cubed)L. The L value relates to a circumference. The particle turns around twice to complete a spin cycle so the L value is 2(2pi r) or (4pi r). You will find that when L is equal to (4pi r) then the radius is required to be equal to the Planck length or (hG/2pi c cubed) exp 1/2. The Plack length computation explains how constants can be used to define a critical length value. A critical length based on a gravitational photon orbit radius, 3Gm/c squared rather than 2Gm/c squared is larger than the Planck length by the factor (3/2) exp 1/2. The proposed critical circumference is 2pi(Planck length)(3/2) exp 1/2. This circumference length can be directly related to the electron Compton wavelength by analyzing gravitational time dilation. The electron as modeled by Burinskii does not have an event horizon. It is a gravitationally confined (naked) ring singularity. It has some but not all of the properties predicted for a black hole. DonJStevens (talk) 16:40, 20 April 2008 (UTC)

Hi Don. I don't think the L value relates to a circumference. It is the wave length of a photon moving with the speed of light. It is not orbiting like an electron around a nucleus. I have no information on the theory of Burinskii. The Compton wavelength of the electron depend on the mass of the electron, and this mass does not appear here, so I do not understand where the Compton wavelength comes into the picture. Bo Jacoby (talk) 20:32, 20 April 2008 (UTC).

Hi Bo Jacoby, A different starting point may be more useful. The electron, separated from an atom, with no displacement velocity has the property of "spin". It has the angular momentum value h/4pi so it seems to spin like a top. The full description of spin is more involved but we can analyze it as a thin ring spinning at light velocity. Then mcr = h/4pi. The r value is h/4pi mc. This radius provides a circumference equal to 1/2 of the electron Compton wavelength. It must turn through two revolutions to complete a spin cycle. If this spinning ring is gravitationally collapsed to the radius value 3Gm/c squared (where m is the electron mass) the energy density is just right so that self-gravitational attraction (space curvature) allows the blueshifted electron Compton photon to chase its tail in a circular path. With gravitational collapse, angular momentum remains constant and total energy (mass energy) remains constant. This allows the circumference to relate to the electron Compton wavelength. Theory predicts infinite blueshift (time rate, zero seconds per second) at the Schwarzschild radius but not infinite at the photon orbit radius. DonJStevens (talk) 22:23, 20 April 2008 (UTC)

Hi Bo Jacoby, Here is a little more of this story. Notice that two radius values are defined. Radius = h/4pi mc and radius = 3Gm/c squared. The ratio of the smaller to the larger is r/r. This defines a size ratio, about 1.051x10exp -44 to one. The square root of this size ratio is the implied blueshift ratio at the electron mass photon orbit radius. Gravitational time dilation will shorten space to match time dilation. The blueshift ratio is square root of (r/r) or 1.o25x10exp -22 to one. This is equal to the ratio 2pi(Planck length)(3/2)exp 1/2 divided by 1.213x10exp -12 meters. The photon with wavelength 1.213x10exp -12 meters, when gravitationally collapsed, can materialize a pair of electron particles, each with a photon otbit radius 3Gm/c squared. DonJStevens (talk) 18:23, 22 April 2008 (UTC)

Hi Don. It is difficult for me to follow. Partly perhaps because your formulas use nonstandard notation. You talked about a cutoff frequency of photons. Then you talk about the electron. Why does the electron enter into that question? The electron spin is usually not interpreted classically as a thin ring spinning at light velocity. The Compton radius involves the charge of the electron while the r value h/(4πmc) does not. Where does the Compton wavelenght enter into the game? A photon materialize into a positron-electron pair, but that has nothing to do with gravitation. A photon does not have an orbit radius. So, I do not follow. Have a nice day. Bo Jacoby (talk) 19:36, 22 April 2008 (UTC).

Hi Bo Jacoby; A growing number of theorists are concluding that the electron must be gravitationally confined. This is not a new idea but studies by J. Wheeler, B. Greene, A. Burinskii and others have added evidence supporting this concept. This will continue to be evaluated until we find a way to merge general relativity and quantum mechanics. I appreciate your communication with me and wish you the best. DonJStevens (talk) 14:33, 23 April 2008 (UTC)

Hi Bo Jacoby; Though you may not wish to follow this (your choice), I concluded that I must reply to your question: Where does the electron Compton wavelength enter into the game? I will write the applicable equations and then define each value. L1/L2 = L2/L3 = L4/L1 = (L4/L2)exponent 1/2

L1 = 2pi(Planck length)(3/2)exp 1/2

L2 = 1.213x10 exp -12 meter

L3 = (2pi)squared, times (c) times one second

L4 = 2pi(3Gm/c squared), where m is electron mass

From the L or length definitions, it is clear that (L1/L2)squared is equal to L4/L2. Then L2 is equal to L4(L2/L1)squared. With L2/L1 equal to L3/L2 a substitution is made.

L2 = L4(L3/L2) exp 2

The electron Compton wavelength is 2(L2) or 2(L4)(L3/L2)squared. When L2/L1 is equal to L3/L2, the applicable G value must be very close to 6.6717456x10 exp -11. DonJStevens (talk) 16:31, 26 April 2008 (UTC)

Hi Don. To improve readability, please use subscripts and superscripts like this: L1 and 10−12. Bo Jacoby (talk) 21:25, 26 April 2008 (UTC).
Hi Bo: Good suggestion. L1 = (L2)2 divided by L3. This allows L1 to be very precisely determined. The product of h and G may then be precisely determined. DonJStevens (talk) 13:09, 27 April 2008 (UTC)

Hi Bo Jacoby: The relationship between photons, electrons and angular momentum is well described in the paper "Is the electron a photon with toroidal topology?" (1997). You can see this if you search for it by title. If you don't see this, let me know: I will help. DonJStevens (talk) 16:30, 4 May 2008 (UTC)

[edit] Nu vs theta for true anomaly

Hi Bo Jacoby, I changed θ (theta) to ν (nu) in the Kepler's Laws article because it denotes 'true anomaly', a parameter denoted universally by ν (nu) in all the other literature I've seen -- including other parts of this same article.

True anomaly is the angle PCL, where P is the satellite perifocus, C is the center of mass of the large central body (planet or sun), and L is the current location of the satellite, measured along the orbit plane. This same angle is already denoted as ν in several other places in the same article. In fact, the article as it stands has a lot of repetition that should be merged and removed. The derivation from Newton's laws should be merged into the rest of the article.

If I have misunderstood the meaning of the "angle formerly referred to as θ", i.e., if it is something other than the true anomaly, then please explain and accept my apologies. Karn (talk) 03:27, 7 June 2008 (UTC)