User talk:Eric Kvaalen

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Changes in tropical year[edit]

About your question concerning the statement in Tropical year: "Aggravating this error, the length of the tropical days (measured in terrestrial time) is decreasing at a rate of approximately 53 s per 100 tropical years."

The day can be measured conceptually as the mean time for the sun to return to the same position in the sky for an observer at a fixed location on the Earth. The official definition changes from time to time to suit the instruments and mathematics in use, and tends to be redefined at intervals of 20 to 80 years. The day can also be defined in terms of 86,400 seconds of time as kept by atomic clocks. There is a theoretical definition of a time scale named Terrestrial Time (TT), which is implemented by adding 32.184 seconds to International Atomic Time. It is not possible to precisely calculate the difference between mean solar time and Terrestrial Time; it must be found by observation.

Throughout human history, calendar days have been a count of observed solar days, not days measured by atomic clocks. The calendar in widespread use around the world, the Gregorian calendar, approximates the tropical year. Thus, indirectly, we measure tropical years in observed solar days. But astronomical calculations are carried out in TT (or sometimes other time scales that can be transformed to and from TT with great precision). So the 3 days, 17 min, 33 s that (according to Holford-Strevens) the Gregorian calendar would be behind the Sun after 10,000 years was calculated using TT. But since the Gregorian calendar counts observed days, not TT days, the problem will be even worse. Jc3s5h (talk) 12:11, 28 April 2011 (UTC)

Thank you for the response. But my original question was "What is meant by 'tropical day'?" Surely it is not "the mean time for the sun to return to the same position in the sky ..." because that could be a year (or never, if one is stringent enough)! Maybe you mean "to return to the same azimuth" or "from midday to midday". And I don't think that is called a "tropical day", since the word "tropical" has to do with the sun "turning" at the tropic of Cancer or Capricorn. Maybe you meant to write (in the article) "Aggravating this error, the length of the tropical year (measured in solar days and seconds) is decreasing at a rate of approximately 53 s per 100 tropical years." Can you give me a quote from your reference source for this figure? Eric Kvaalen (talk) 06:28, 1 May 2011 (UTC)
I've reviewed the source, and it turns out the phrase should have been "tropical year" rather than "tropical days". Also, the position of the decimal point was wrong, it should have been "0.53 s" rather than "53 s". I have corrected the article. Jc3s5h (talk) 15:56, 4 May 2011 (UTC)
Thanks. I'm still not convinced it's correct though. I think it means the length of a tropical year as measured in solar days and seconds, not Terrestrial Time. That the earth's period could be changing that much in real time (Terrestrial Time) seems too much. Could you provide the actual quote? Eric Kvaalen (talk) 11:51, 5 May 2011 (UTC)
I have sent a photo of the passage by email. Another source says the same think. According to McCarthy and Seidelmann (2009, p. 18, full bibliographic details in article)

The tropical year can vary by several minutes from year to year because of the motion of the Earth's perihelion, the secular increase in the rate of precession, and the periodic actions of the Moon and planets on the Earth's orbit. Averaging over time gives us a specified value for a mean tropical year. The precession rate is increasing, so the length of the tropical year is decreasing by 0.53 seconds per century.

The conventionally accepted value of the tropical year is 365.242 189 7 days, or 365 days 5 hours, 48 minutes and 45.19 seconds. An accurate expression calculating its length in days in the distant past (Laskar, 1986) is

365.2421896698 - 0.00000615359T - 7.29×10-10T2 + 2.64×10-10T3

where T is in Julian cenuries of 365.25 days measured from 2000 January 1 Terrestrial Time (TT).

Since TT is the only kind of time mentioned in this passage, and because UT1 is so hard to work with because it is irregular and unpredictable, I feel confident all the times quoted in the passage are TT. The conventionally accepted value of the [mean] tropical year agrees with the value on page C2 of the 2011 Astronomical Almanac. On page C1 that publication states "Mean elements of the orbit of the Sun, referred to the mean equinox and ecliptic of date, are given by the following expressions. The time argument d is the interval in days from 2011 January 0, 0h, TT." It goes on to say on page C2 "The lengths of the principal years at 2011.0 as derived from the Sun's mean motion are...." Jc3s5h (talk) 14:03, 5 May 2011 (UTC)


Thanks for the scan and the reply. The book you scanned (I assume that's Blackburn & Holford-Strevens) says that the length of the day is increasing by 0.0015 seconds per century. Since it was 86400 seconds in 1900, then (continuing to use T to mean the number of centuries measured from 2000 AD), the length of a day is 86400+0.0015×(T+1) seconds. The tropical year, as of 2000 AD, was 31,556,925.445 seconds, and currently shortening by 0.53 seconds per century, so it is approximately given by 31,556,925.445−0.53×T seconds. Combining these two, we find that the length of a tropical year in days is approximately
(31,556,925.445/86400.0015 − 0.53×T/86400) / (1 + 0.0015×T/86400)
≈ (365.2421863 − 6.14e−6×T) / (1 + 1.74e−8×T)
≈ 365.2421863 − 6.14e−6×T − 6.35e−6×T
This shows that the expression you quote above from Laskar has the term − 6.14e−6×T (approximately) but doesn't have the last term which takes into account the fact that the day is getting longer. That's pretty strange. Do you have the reference to Laskar? I don't find that formula in his 1986 paper referenced in Tropical year.
I concede that your sources do mean that the length of the tropical year (in absolute seconds) is presently decreasing. I didn't realize it was such a large effect. But I notice that the equation of Laskar (if you copied it right) shows that the year will start getting longer in a few thousand years, due to the cubic term in T.
Eric Kvaalen (talk) 15:01, 7 May 2011 (UTC)
Yes, the scan is from Blackburn and Holford-Strevens.
I will need some time to think about all your questions, but let me point out where I think the terms can be found in the Laskar (1986) paper. In Table 5, page 64, notice the list of terms for ecliptic longitude (λ) for Earth. This gives the expansion for longitude, while the form of the equation in McCarthy and Seidelman is for the length of the tropical year, which is the time required for the longitude to increase by one revolution. So Laskar's expression would have to be differentiated to give the rate of change of longitude and solved for the time required to change λ by one rotation (2π or 360°). Also the time units would have to be changed from 10000 julian years to the mixed time units in McCarthy and Seidelmann (julian centuries and days). As partial confirmation of this idea, consider the t term in Table 5 for Earth, 628307584918000×10-10 = 62830.7584918. If we ignore higher-order terms we would expect λ to increase by 2π when one year passes, which would be an increase in t of 10-4. So Δλ for 1 year ≈ 62830.7584918×10-4 = 6.28307584918 which differs from 2π by only 0.0017%.
I agree with your results, approximately. First, I used somewhat different values; based on a graph on page 54 in McCarthy and Seidelmann I used a rate of change of day length of 1.7 ms day-1 century1-. Also, the graph indicates that when using the linear approximation to day length, 1 UT1 second = 1 SI second in 1820 (This is because TT is a successor to ephemeris time, which was computed based on the work of Simon Newcomb, who relied on observations beginning when telescopic observations began and ending in the late 19th century.) The equations got a bit messy, and my memory of how to do series expansions is a bit rusty, so I just put the equations into OpenOffice Calc and did a numerical differentiation. That showed that the length of the tropical year at 2100 will be shorter than the tropical year at 2000 by about 1.2×10-5 day.
I do not find it surprising that Laskar left out the term to convert from SI seconds to UT1-seconds-of-date. There is considerable uncertainty in the length of the UT1 day at various times in the past and future, and astronomical equations of motion always use SI seconds because that is the unit that is compatible with the laws of physics that the equations of motion are based on. So by giving the length of the tropical year in SI seconds (or the equivalent) Laskar lets the reader employ whatever advances may have occurred in correlate UT1 to TT after Laskar published, or lets the reader plug the results directly into equations of motion.
For the length of day graph on page 54, McCarthy and Seidelmann cite Stephenson, F.R. and Morrison, L.V. (1995) Long-term fluctuations in the earth's rotation: 700 BC to AD 1990. Philos. Trans. Phys. Sci. Eng., 351, 165-202. I have not found a free source for this paper. Jc3s5h (talk) 21:29, 7 May 2011 (UTC)

Hill sphere[edit]

"...will eventually fling the moon into either the planet's Hill limit, or the planet's Roche limit. Which of the two depends on..."

"I don't understand what you mean by the moon going into the planet's Hill sphere. It's already in the planet's Hill sphere -- otherwise it wouldn't be a moon."

What I meant is the moon approaching the Hill sphere boundary from the inside--moving from the inside of the Hill sphere to the outside. You can visualize a sort of a "habitable zone" for moons in the shape of a thick spherical shell surrounding the planet, with the inner radius at the Roche limit, and the outer radius at the Hill limit*. The moon can exit this shell through the inner surface, or through the outer surface. Freederick (talk) 14:02, 29 July 2011 (UTC)

*Actually, according to this article the moon would probably be sufficiently perturbed to be shed even if it merely approached the hard limit of the Hill sphere.
Sorry to have taken such a long time answering: I was AFK on vacation. I took the liberty of placing this response here, as keeping track of responses on NS comments can be a pain. :-) Freederick (talk) 14:02, 29 July 2011 (UTC)

Three-phase traffic theory[edit]

Thank you very much for your very important comments. We applied some changes to the abovementioned article based on your comments. In our changes, we have tried to answer on your remarks „Clarify“ made through the text (3 times). Please check whether our explanations are clear and prove whether section “Criticism of the theory” that you have written is still valid in relation to recent publications: 1.) The article by Hubert Rehborn, Sergey L. Klenov, Jochen Palmer, "An empirical study of common traffic congestion features based on traffic data measured in the USA, the UK, and Germany"] Physica A: Statistical Mechanics and its Applications, Volume 390, Issues 23–24, 1 November 2011, Pages 4466-4485. 2.) The article by R.-P. Schäfer et al, "A study of TomTom’s probe vehicle data with three-phase traffic theory"]. Traffic Engineering and Control, Vol 52, No 5, Pages 225-231, 2011). 3.) The Chapter 10 of the book (Kerner, 2009) in which a detailed criticism of two-phase models with a fundamental diagram has been made. 4.) Section 5.2 in the article arXiv:1012.5159 (http://arxiv.org/abs/1012.5159). — Preceding unsigned comment added by Blueshifting (talkcontribs) 15:22, 17 January 2012 (UTC)

On the Number of Primes Less Than a Given Magnitude[edit]

Hi, I raised a question over on the Mathematics Reference Desk regarding a passage that you originally added [1] several years ago to the article "On the Number of Primes Less Than a Given Magnitude". Any comments/insight you have would be appreciated; thanks! —SeekingAnswers (reply) 16:36, 24 August 2012 (UTC)

Algebraic structure[edit]

The reason "algebra over a field" and "associative algebras" were cleaned out was that "algebra" was taken to mean "associative algebra," as it is in most contexts, and it seemed senseless to include all the special cases. That said, recently some edits have been made to "algera over a field" that might help your recent edits be incorporated. Stay tuned! Rschwieb (talk) 01:31, 30 October 2012 (UTC)

Well, you could say that since fields are rings, the article did include algebras over fields. But although I don't insist that all the kinds of algebras for which there is a Wikipedia article be mentioned, I do think algebras over fields should be, since they include such important cases as the real numbers, the complex numbers, and the quaternions. Eric Kvaalen (talk) 16:55, 30 October 2012 (UTC)
I agree that if we have an article on an important topic like that, then it's worth weaving in a wlink to it. If you check out the latest edition of algebraic structure, you can see my attempt to seamlessly incorprorate the links. Rschwieb (talk) 17:12, 30 October 2012 (UTC)

initial context-setting[edit]

Hello.

You began an article with this:

In a Lorentzian manifold, a null hypersurface is

One problem with this is that the phrase "In a Lorentzian manifold" does nothing to tell the lay reader that mathematics is what this is about. Another is that the title phrase should not be italicized. One should italicize a term when writing about the term rather than using it to write about what it refers to, but the latter alternative is operative here. I changed it to this:

In differential geometry, a null hypersurface of a Lorentzian manifold is

Michael Hardy (talk) 20:11, 20 November 2012 (UTC)

All right, I'll try to remember! Eric Kvaalen (talk) 10:30, 23 November 2012 (UTC)

Race and intelligence article[edit]

Thanks for your attempt to restore some of the removed content in race and intelligence, but it will take more effort than that to avoid ArtifexMayhem removing whatever you add. The section you tried to restore (and this section, which he also removed) had been in the article for years, and presumably he will allow it back if someone proposes a new version that gets consensus. You seem to have some interest in restoring the section, so would you like to try that? BlackHades tried to once but got burned out, and I can't do it on my own. Akuri (talk) 08:20, 4 April 2013 (UTC)

Gospel of Matthew[edit]

Your edits to Gospel of Matthew are rather major, and as you can see I disagree with them (although unfortunately the edit summary doesn't give me enough room to explain my reasons at length). I suggest you put your arguments on the article Talk page. PiCo (talk) 12:39, 8 May 2013 (UTC)

I'm sorry about the time you put into your edit - I know it seems harsh. I'll put the two edits side by side on the Talk page and explain the reasons in detail. PiCo (talk) 09:31, 13 May 2013 (UTC)

I have added to PiCo's comments here. My specific concern is the deletion of the two reliable sources you cited without discussion. You may want to take issue with deletion of the article content they were supporting as well, but I'll leave that up to you. Ignocrates (talk) 03:07, 25 May 2013 (UTC)

Eric Kvaalen's work should never have been deleted. I agree with Ignocrates but note the good will admission about being 'harsh'. - Ret.Prof (talk) 04:04, 26 May 2013 (UTC)
I added some material to your edit. - Cheers Ret.Prof (talk) 05:26, 3 June 2013 (UTC)

Leonora Piper[edit]

I suggest you read older material that is available on line about Mrs. Piper *Evidence for the Supernatural by Ivor Lloyd Tuckett, Kegan Paul, Trench, Trubner Limited , London, 1911 first edition, 409 pages, 2nd edition shorter and abridged, [2] The Mediumship of Mrs. Piper, Appendix Q, pages 321-396 Kazuba (talk) 04:43, 3 June 2013 (UTC)

Chembox[edit]

Hi I started his discussion. Since you suggested new parameters recently maybe you want to take part.--Saehrimnir (talk) 05:50, 22 July 2013 (UTC)

Move reverted.[edit]

Greetings! I have reverted your move of Thiokol to Thiokol (company). Per Wikipedia:Requested moves#Requesting controversial and potentially controversial moves, a community-based consensus must be developed "if there is any reason to believe a move would be contested". In this case, the page that was moved was at that title since 2005, and had hundreds of incoming links, making it highly likely that the move would be contested. Furthermore, WP:TWODABS indicates a preference against disambiguation pages with only two links, if one of them can be considered the primary topic. This is because the disambiguation function can be served just as well with a hatnote on top of one of the pages, without having to take the extra step of creating a new navigation page. Cheers! bd2412 T 14:17, 6 December 2013 (UTC)

Well, for me, the primary meaning of Thiokol is the substance, not the company. The company is not even called that anymore. Eric Kvaalen (talk) 16:52, 6 December 2013 (UTC)
I suspect that if the polymer was more significant historically, the article would be more substantial. bd2412 T 17:07, 6 December 2013 (UTC)

Lift-induced drag[edit]

Eric, thanks for your latest comments and questions at Talk:Lift-induced drag. (See your diff.) Rather than post my thoughts on the article Talk page, I have posted them on my sandbox - see User:Dolphin51/Sandbox. Feel free to add your own responses, comments or questions on my Sandbox.

I will try to respond to the remainder of your questions in coming days. Dolphin (t) 06:48, 11 January 2014 (UTC)

Ways to improve Denjoy–Carleman–Ahlfors theorem[edit]

Hi, I'm ColonelHenry. Eric Kvaalen, thanks for creating Denjoy–Carleman–Ahlfors theorem!

I've just tagged the page, using our page curation tools, as having some issues to fix. The article needs to be dumbed-down a little so non-math people mighat have a chance at learning something. Further, you might want to consider incorporating the short proof by Dov Aharonov (1981), or the articles by Heins (1948) or Skeath (1965).

The tags can be removed by you or another editor once the issues they mention are addressed. If you have questions, you can leave a comment on my talk page. Or, for more editing help, talk to the volunteers at the Teahouse. ColonelHenry (talk) 06:26, 27 January 2014 (UTC)

Ambiguity[edit]

Hi! Could you specify more details for the ambiguity you've mentioned in apparent molar property for multicomponent solutions?.--5.15.63.70 (talk) 05:54, 19 February 2014 (UTC)

Done. Eric Kvaalen (talk) 18:25, 1 March 2014 (UTC)

Gibbs free energy[edit]

Please take a look at Wikipedia_talk:Chemical_infobox#Template-protected_edit_request_on_5_February_2014. It looks like your request for "Gibbs free energy of formation (deltaGf)" does not function. Maybe I can fix it. -DePiep (talk) 17:07, 1 March 2014 (UTC)

Yes, please! Eric Kvaalen (talk) 18:25, 1 March 2014 (UTC)
Please take a look at the demo Chembox and the questions there. -DePiep (talk) 19:39, 1 March 2014 (UTC)