Shifting Sun-Earth-Moon Harmonies, Beats, & Biases

Paul L. Vaughan, M.Sc. – October 2011

This post has no introduction, per the author’s request, start with the graphs. A PDF of a more complete paper is linked at the end. – Anthony

Motivation

One purpose of this article is to direct the attention of sensible observers to a serious oversight in the mainstream quest for understanding of multidecadal solar-terrestrial relations (section I).

Another is to ask the community to start thinking carefully about what can be learned from rotating multivariate lunisolar spatiotemporal phase relations shared by Earth Orientation Parameters (EOP) and terrestrial climate records, while seizing the same opportunity to highlight critical omissions in “classic” works on alleged solar-barycentric terrestrial influences (section II).

These data exploration notes are volunteered in support of ongoing publicly collaborative multidisciplinary research.

Audience

The diverse audiences addressed might not be the ones preferred by some readers. Addressing rotates priority across a spectrum of functional numeracy & orientation.

Format

Volunteer time & resources are limited, so presentation is skeletal & informal.

Conclusion

The majority of recent multidecadal terrestrial variability is due to natural spatiotemporal aliasing of differential solar pulse-position by terrestrial topology over basic terrestrial cycles including the year.

It’s not the deviation of solar cycle frequency from average solar cycle frequency that’s of practical significance from a terrestrial perspective. Earth, the receiver, has no clock locked to the average solar cycle length, so the pulse-position modulation is differential.

These observations depend on neither the success nor failure of CERN’s CLOUD experiment.

Details

Vaughan, P.L. (2011). Shifting Sun-Earth-Moon Harmonies, Beats, & Biases.

Vaughn Sun-Earth-Moon Harmonies Beats Biases (1MB 25pp PDF)

Best Regards to All,

Paul L. Vaughan, M.Sc.

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October 17, 2011 7:38 pm

Great post again, Paul. The comprehensive processing of a broad range of data, the results, and the explanations of the mathematical techniques are impressive and thought-provoking, as are your questions. It’s a solid addition to your previous posts from Nov-Dec, then in the spring,
As with many others, it’s going to take some time for me to adapt to the techniques you’ve, assuming that I can find sufficient time to get into them, one step at a time.
A couple of points/questions are of special interest to me (at first thought – other items will probably bubble up with time). There is NO need to answer, there’s lots of time for me to mull these over on occasion:
– How the contribution from “ocean sloshing” (a slang term – but NOT referring to circulation, which brings other connotations) might compare to the presumed shifting of the Earth’s shells.
– The phase change around 1929 (and several other comments) seem reminiscent of historical and geological references to the possibility that strong, rapid changes in the Earth’s axis/ crustal movements may have occurred in the recent past (in particular 12 ky BP, 1500 BC and 700 BC, very approximately).
– Explanations of torsional effects at a distance within the solar system, especially if related to physical processes that are not the typical 1/r^2 relationship, but perhaps even approaching first or zero order relations.
– Geomagnetic and cosmic ray manifestations of what?
I also enjoyed many of the posts, including (not exhaustively):
62. Ninderthana: October 15, 2011 at 5:35 pm personal interpretation
63. Werner Brozek: October 15, 2011 at 5:45 pm angular momentum in the solar system
64. davidmhoffer: October 15, 2011 at 5:53 pm Ernst Beck historical comments about 1929 reversal
77. davidmhoffer: October 15, 2011 at 8:12 pm morlets, Chandler, lunar orbit tides & climate
90. Richard Holle: October 15, 2011 at 11:21 pm http://research.aerology.com/natural-processes/solar-system-dynamics/ – I’ll have to look at this later..
91. rbateman: October 15, 2011 at 11:27 pm reminder of Piers Corbyn..
93. AusieDan: October 15, 2011 at 11:29 pm financial market reference (Harry S. Dent?)
96. Bernie McCune: October 15, 2011 at 11:54 pm Chandler R&D experience
121. ecliptic: October 16, 2011 at 7:54 am historical cycles
137. Peter Plails: October 16, 2011 at 1:56 pm past Corbyn & Vaughan postings
140. Paul Vaughan: October 16, 2011 at 2:58 pm further details and explanations
154. davidmhoffer: October 16, 2011 at 9:46 pm further details and explanations
157. aposticon: October 16, 2011 at 10:52 pm pendulum waves – fun video I’d seen before
Anyways, I’ll only be able to look at this post once a week or so. Luckily, “persistence” is a great strength of sites (like WUWT) for those of us who can only occasionally get to the material. Thanks to Anthony Watts for accommodating work like this…

October 17, 2011 8:16 pm

Norman Page says:
October 17, 2011 at 2:09 pm
I think a good empirical correlation comes first
If you fish around long enough and look at enough things there will be correlations just be chance. None of the correlations examined are ‘good’. And for the ones that some think are good mechanisms must be found. There are enough claimed ‘good’ correlations to go around. Begin to look for mechanisms for those. As Paul would say: “Tip: check if there is a coupling and if there is enough energy available”.

Paul Vaughan
October 17, 2011 8:50 pm

Holle (October 15, 2011 at 11:21 pm) “many years of work”
Started in late November 2007. Easily found the 6.4 year framework right away (in local weather records) and wanted to understand.
“Richard Gross (NASA EOP expert) was the first to suggest a redirection of my focus from the solar system to lunisolar cycles. Physicist Piers Corbyn (WeatherAction.com) efficiently pointed directly at specific lunisolar cycles. Physicist Ian Wilson highlighted hierarchically-historic solar system shaping of lunisolar cycles. Their collective influence demystified coincidences (bottom-panel) on the following graph: […]” – p.16

October 17, 2011 9:33 pm

Watch what happens when we have a Synod conjunction with Jupiter on 10-29-2011 when the moon is maximum south declination. There should be a larger than usual meridional surge of warm moisture coming off of the equator into the mid-latitudes having some intense interaction with the Mobil Polar Highs that will be forming the other half of the lunar tidal bulges in both hemispheres.
These patterns are what got me interested in wanting to understand WTF was going on, back in 1983.

Paul Vaughan
October 17, 2011 10:13 pm

@Baa Humbug (October 16, 2011 at 6:54 pm) “Might it not been better to delay the article until you had the time to respond to questions?”
Can’t imagine when such a time will ever again arise. Those days are in the rear view mirror.

Howell (October 17, 2011 at 7:38 pm)
Thanks for stopping by Bill. Good to ‘see’ you. Much appreciated.

Paul Vaughan
October 18, 2011 6:34 am

Peter Plail (October 16, 2011 at 1:56 pm) “[…] Magnetic process […] […] Magnetic effect that is one of the tools that Paul feels Piers uses in his predictions.”
Some kind of misunderstanding/misinterpretation.
(Tip: Ask Piers for his views on Svensmark.)

Louis Hissink (October 16, 2011 at 2:49 am) “I suspect that an electrical engineer might spot a few familiar relationships in Paul’s graphs – which basically suggests explanations might be forthcoming if the plasma model was assumed, rather than the standard one.”
Beware confounding.
“The majority of recent multidecadal terrestrial variability is due to natural spatiotemporal aliasing of differential solar pulse-position by terrestrial topology over basic terrestrial cycles including the year.” – p.10
Note that temperature is not singled out. Geomagnetic aa index shows the same patterns. Beware confounding. Bear in mind parallel processes also affected by lunisolar cycles (e.g. QBO) & solar cycle acceleration/deceleration. (And don’t forget the year!! [Too much anomaly-think…])
The mainstream confusion is due to the spatiotemporal version of Simpson’s Paradox. Models that are “physically correct” by current mainstream standards are at best a topological distortion of reality since they make false assumptions about the spatiotemporal framework.
No amount of “physics” [especially today’s] can compensate for such fundamental misconception. They’ve misinterpreted the data. Hence the spectacular logjam on the river of mainstream enlightenment. Might as well call it Simpson’s Logjam.
The mainstream NEEDS help from spatiotemporal aggregation experts.

Paul Vaughan
October 18, 2011 6:50 am

G (October 16, 2011 at 8:59 am)
If you think I’m pushing a barycentric theory, you might want to consider the possibility that you’ve interpreted the message backwards.
Your comment reminds me of a similar misunderstanding in an earlier discussion where a commenter thought I was pushing the idea that LOD drives terrestrial climate.

October 18, 2011 7:21 am

Paul Vaughan says:
October 18, 2011 at 6:34 am
The mainstream NEEDS help from spatiotemporal aggregation experts.
Nonsense
Paul Vaughan says:
October 18, 2011 at 6:50 am
Your comment reminds me of a similar misunderstanding in an earlier discussion where a commenter thought I was pushing the idea that LOD drives terrestrial climate.
All those misunderstandings stem from your inability to communicate.

E.M.Smith
Editor
October 18, 2011 10:37 am

:
FWIW, I looked at the impact or potentials for impact from the way the circumpolar current gets shot through a jet where Antarctic Peninsula and S. America come together.
Your post makes me wonder if that’s a key point for the lunar tidal cycle having an impact.
As the N/S tidal swing makes the depth at that ‘jet’ vary, there ought to be an increase / decrease cycle in the amount of cold water shot up the West coast of South America (the excess that doesn’t fit through the ‘jet’ constriction). There could also be other places where there are secondary effects (like the tendency for the ‘jet’ to stir the S. Atlantic into a spin).
It’s all a ‘thought of the moment’ hypothetical… but an interesting thought of the moment.
We’ve got the potential driver (lunar position), the visible effect (N. / S. Hemispheric tide variation with the long cycle lunar shifts) and the potential amplifier (Drake’s Passage).
Might be interesting to look for correlations between the temperature of the ocean off of Chile and lunar cycling… and maybe check the depth / velocity profile at Drakes Passage for similar cycling.
Wonder if anyone has a grant for that… I’ve always wanted to see Patagonia 😉
http://chiefio.wordpress.com/2010/12/22/drakes-passage/
FWIW, I’ve not read the detailed article yet. The posting was enough to fill my buffers for a few days. My interpretation of what I think the article is representing, in as concise (and thus more wrong) terms as I can make it, would be:
The first chart is Atmospheric Angular Momentum, vs Length of Day vs Neutron Flux. But done as “morlet wavelet power”. That is, given a varying function where is the power in it located. See:
http://en.wikipedia.org/wiki/Morlet_wavelet
for an over view. It’s just a way to find ‘where is the bulk of the action’ in something that’s a bit chaotic.
So that chart shows that the Air is moving in sync with the Length of Day (i.e. changes in the earth rotation rate) that are in sync with solar changes (via the proxy of cosmic rays).
I’ve looked at some of the LOD changes vs solar changes correlation before, and looked at a variety of potential causes (including some rather brain bruising looks at the potential for Spin Orbital Coupling at a macro level between planets and sun). What this chart shows is a very clean correlation of the powers and motions. Hard to make that go away… or ignore it.
In short, it argues that “The Sun Rules, CO2 Drools…” and the author makes a case that we can’t know what the CO2 contribution might be until the other effects are accounted.
The Chandler Wobble chart will need a bit more thinking. For now, it looks like it is at least showing a spike in position right on top of the 1930′s Dust Bowl and drought / heat spike. I think the rest of it is saying “solar / lunar positions influenced or at least correlated with it”. More of of a ‘sun and moon rule the earth’ evidence.
Looking at it a bit more, the 179.3 year yellow lunisolar cycle CosLS line is, I think, the “punch line”. It shows a nice long period cycle that directly overlays the cold 1800s into the warmer present, and is now ‘rolling over’ into a new drop. There is a minor dip in x and y period rate of change right on top of the ‘cold 70s’ and I’d take that whole mix to mean that the CosLS dominates longer term, but a change of ‘rate of change of period’ can have a ‘blip’ introduction. The conclusion from this would be that with CosLS headed down for many decades, we’re headed into significant cold (and any ‘blip’ on top of that would be a ‘year without a summer’ in the north…) That x’ power and y’ power are now plunging in a downtrending CosLS is “bad news”. IFF I’ve interpreted this correctly. Mechanism? The Chandler Wobble changes how much the earth is tilted toward the sun and can easily have an impact on arctic temperatures and AO state (that drives Russia and Canada into frozen or warms them from time to time) and via them, can make the rest of us quite cold too. AO is the Arctic Oscillation: http://www.cpc.ncep.noaa.gov/products/precip/CWlink/daily_ao_index/ao.shtml In essence, the position of the north pole matters and the Chandler Wobble changes it. The Chandler Wobble has a strong connection to the lunisolar position cycle. Sun and Moon rule, CO2 drools, when it comes to weather and climate impacts (accepting for the moment the broken definition of climate as ’30 year average of weather’). Also changes is wobble might slop the oceans around.
The ‘colored carpet’ graph is showing SOI Southern Oscillation Index of ocean state vs time.
http://www.cgd.ucar.edu/cas/catalog/climind/soi.html
With what looks like a clear oscillation in state in sync with the ‘cold’ period in the 1960s-1970s and the warm period recently. It looks to me like there might be a decade or two lag between the state change and impacts on average land temps, but that would take a bit more ‘think time’ to evaluate. What’s clear is an ocean oscillation driving in sync with temperature cycles (and, via the prior graph of AMO, in sync with the lunar solar positions…)
The final graph shows a near identity between ocean temps (all of them, in two sets) and the “solar cycle acceleration”. Done as Morlets, it’s comparing the power at a point in time in the ocean changes to the power at a point in time in the solar cycle changes and finding that “they all go together when they go”.
The net conclusion is that you must now show how CO2, as driver of climate, is able to run backwards into controlling the power and position of the sun and the moon… Or accept that the sun and moon changes are driving climate changes. Possibly via changes in the earth wobble and rotation rates.
At least, that’s my interpretation of it.
I think it’s interesting work, but would really benefit from a ‘de-jargon preprocessor’… Maybe then we could check the assumptions and the reasoning that connects that to the conclusions.

wayne
October 18, 2011 12:32 pm

Paul Vaughan:
I haven’t been through all of the comments yet (time limited) but many who are criticizing your work clear know not what they are looking at. On a first pass over you PDF it is clear that this has to do with a very special area of gravitational interplay between the gravitational fields of the eight major planets and the sun and moon.
I would ask one thing of you though, could you also supply a brief summary description of the equations you are using such as (PP being planetary period) (PP1*PP2)/(PP1+PP2) and other equations you use over and over through your work. I and others don’t have the time to take a course on harmonics right now but would love to look a bit deeper in your contentions. Some links would do. Keep it light at this point.
It is well known that the current periods of the planets has much to do with these tiny gravitational tugs between each other over billions of years as periods and for sure probably has it’s imprints on each planet’s climate cycles.
Please try to explain a bit more on what Morlet analysis is, assuming 2pi, or 10pi, this has to do with complete rotation interval harmonics of influence but I have never delved into elliptic harmonics at this depth though have spent quite a bit of time in the past with gravity in solar system simulations. Supplying this would greatly help many here understand just what you are saying within without being experts in this area.
Also, when you show a graph oscillating between 1 and -1 can you also give some indication of the scale?
Keep it up.
-wayne

George E. Smith;
October 18, 2011 12:32 pm

“”””” Janice says:
October 17, 2011 at 7:34 pm
George E. Smith; says: “There are so many sources of reliable presentations of fundamental Physics, that anybody who wants to learn it can access information from the very people who discovered the physics in the first place. If you can learn about electro-magnetism from James Clarke Maxwell himself, or Atomic Physics from Max Born; why waste your time with dubdubdub.flybynitephysics.com”
True, Maxwell and Born are good for studying classical physics, but that does leave out quantum mechanics, eh? And quantum mechanics bottomed out about in the 60′s, which is where string theory rears its somewhat ugly head “””””
Well Janice, now you have me totally bamboozled; so I went back and reread my original post, and I am still totally bamboozled.
Could you please point out for me, just where in my post I excluded Quantum Mechanics; or for that matter String Theory, or anything else.
Well I suppose it is reasonable to presume that perhaps I was suggesting the exclusion of dubdubdub.flybynightphysics.com, although I never did that either; just asked why waste one’s time on it.
As for string theory, I had a very interesting discussion about that, with another Physicist over a beer, and some Kobe beef sandwiches, at a home barbecue. Well we also discussed parallel or multi-verses. Mind you he’s far more knowledgeable than me on Physics; he has one of those Nobel Physics Prize things, that some scientists get; and his is one of the real ones; not like that of our energy Czar, who got his for something somebody else discovered decades earlier; but politics intervened; well like the Einstein situation all over.
But I digress, this Nobellist observed that the more unprovable ones claims are, the more absurdly exotic they can be.
As for me, “string” theory strikes out on the first pitch. Anything that wiggles, can’t be fundamental, since it must be made up of more primitive things that can move relative to each other.
Quarks might be fundamental, and this chap knows quite a bit about those; maybe more than anybody else.
But do tell where I offed Quantum Mechanics.

Agile Aspect
October 18, 2011 3:22 pm

No introduction?
Okay, then that leaves the mathematics.
Since there are infinite number of wavelet representations, I’m always curious as to why you choose the Grossmann-Morlet wavelet for your time-frequency wavelet or packet?
For instance, why did you choose a wavelet with fix basis instead of one with an adaptive basis? Is the entropy of the signal constant?
If one looks at the form of the Grossmann-Morlet wavelet, it’s essentially the FFT of a gaussian.
If one assumes the signal is not 2*PI periodic, then the FFT which is will respond as if there was abrupt change in the signal.
I also noticed one of the references in the PDF was a reference to M. Mann regarding regarding his use of wavelets. It appears Mann and company are using Slepian wavelets and SVD.
Would you care to comment on how their use of Slepain wavelets and SVD relates to your use of the Grossmann-Morlet wavelet?
Have you posted the code for your version of the Grossmann-Morlet wavelet?
Note, Mann and company do provide a descent introduction to the wavelets they’re using. You could learn great deal regarding presentation from that paper.
And where are the spatio temporal results?

Lazarus
October 18, 2011 6:26 pm

A practical joke – surely?
Even if somehow it actually makes sense to some boffin somewhere what is clear from the comments is that Watts certainly hasn’t got a clue any more than than the rest of us. He must have been told it was something that supported the ‘skeptic’ position and cast doubt on ‘the consensus’ and just went with it.
It also confirms that he doesn’t have a clue about science in general and just posts things that he assumes confirm is biases.

October 18, 2011 6:34 pm

Lazarus,
Anthony Watts didn’t write this article.
Why don’t you submit an article – written by you. Based on your obvious lack of comprehension, I’m sure it would be fun and easy to deconstruct.

October 18, 2011 6:59 pm

E.M.Smith;
As the N/S tidal swing makes the depth at that ‘jet’ vary, there ought to be an increase / decrease cycle in the amount of cold water shot up the West coast of South America (the excess that doesn’t fit through the ‘jet’ constriction). There could also be other places where there are secondary effects (like the tendency for the ‘jet’ to stir the S. Atlantic into a spin). >>>
Beck was on the same page in regard to the above, but he was looking at it from the perspective of CO2 concentrations. As the momentum (for lack of a better term) of the water is changed by the moon’s orbital phases, areas of large spinning tracts of water would be created which in turn would play havoc with downwelling and upwelling. Beck shared with me that he had identified several areas on earth where this could be demonstrated to occurr. One was in the North Atlantic but the “big ones” were south hemisphere, but I don’t think he specified where. His point was that not only would that result in changes regarding how water currents redistribute heat, but also that the amount of CO2 absorption (in areas of cold water) but also outgassing as cold (CO2 rich) water is moved to warmer areas causing it to outgas CO2.
Beck was pretty confident of this being a driving force of both temp variations and CO2 variations and was corresponding in depth with a colleague (never said who) that was doing further research. Beck’s own focus was the ice core data which he believed exhibits a 200 year resolution rather than a 30 year.
Incidently, if you break the GISS temp record down by lattitude, the warming bubble in the 1930’s is MUCH more pronounced in the SH than the NH. Given the much larger percentage of water surface in the SH, and constriction points like the one you mentioned, any change in the moon’s orbital phases would in theory be much more pronounced in the SH. Given the correlation with the temp record, that appears to support both Beck and Vaughn (if we’re interpreting Vaughn correctly).

October 18, 2011 7:19 pm

Paul Vaughn;
If you think I’m pushing a barycentric theory, you might want to consider the possibility that you’ve interpreted the message backwards.>>>
Is it just impossible for you to respond with something as simple as what you ARE pushing? If you put the same amount of effort into answering questions as you do in explaining that you don’t have time to, and actually answered some straightforwardly instead of snark like the comment above, you might find the results rather positive.

Paul Vaughan
October 18, 2011 8:44 pm

Paul Vaughan
October 18, 2011 8:45 pm

(October 18, 2011 at 7:19 pm)
Patience David. Working for a living.

Ben
October 18, 2011 11:00 pm

Did the Cliff’s Notes version come out yet?
Or at least the Geek Speak to English translation?

Lazarus
October 19, 2011 1:52 am

Smokey says:
“Anthony Watts didn’t write this article.”
I know he didn’t write the article. Everyone here does. Someone called Paul L. Vaughan, M.Sc.apparently did. Do a google scholar search for this name and any of the sciencey sounding stuff in the article and you will find absolutely no scientific publishing history at all. Search for the combination of the words ‘rotating multivariate lunisolar spatiotemporal phase relations’ and the only google hits you get are on WTFUWT.
These are real words but used in the context of ‘Shifting Sun-Earth-Moon Harmonies’ it looks more like trying to push Morphic fields or Young Earth Creationism, and appears to be just another example of pseudo-sceptics willing to latch onto anything that supports their beliefs because real science generally does not.
“Based on your obvious lack of comprehension, I’m sure it would be fun and easy to deconstruct.”
I’m certainly admitting I can’t comprehend this post, are you claiming too? Please do enlighten us all. From the posts above it looks like none of commentators has any idea either but are too polite to suggests that Watts has been well and truly pawned.

October 19, 2011 2:01 am

Lazarus,
Quit trying to change the subject. Write your own article… if you’ve got the cojones… and we’ll have fun deconstructing it. I’m betting you won’t. Prove me wrong! ☺

Lazarus
Reply to  dbstealey
October 19, 2011 3:00 am

Why are you desperate for me to write an article? What on? Shifting Sun-Earth-Moon Harmonies?
You are welcome to de construct anything on my blog but I doubt you’ll find me writing or even linking to anything approaching the gibberish of ‘rotating multivariate lunisolar spatiotemporal phase relations’ and asking unqualified and gullible people to ‘think about it’.

rbateman
October 19, 2011 3:12 am

Within the last year or so, some circular phenomenon noticeable in EUV have been spotted on the Sun.
Look closely: http://sdo.gsfc.nasa.gov/assets/img/browse/2011/10/18/20111018_001344_1024_0193.jpg
Dead center on the Solar Equator, then about 1/2 sol. radii outward starting at 2 O’clock postion and ending at the 7 O’clock position. The phenomenon, as far as the Sunspot Regions 11314, 11319, 11316, 11317 and 11321 indicates, is rotating as a unit clockwise. See http://fenyi.sci.klte.hu/DPD/2011/20111018/index.html
and ftp://fenyi.solarobs.unideb.hu/pub/DPD/data/gDPD2011.txt for relative motions.
Very odd behavior, indeed.

October 19, 2011 6:13 am

rbateman says:
October 19, 2011 at 3:12 am
Within the last year or so, some circular phenomenon noticeable in EUV have been spotted on the Sun.
Perhaps some of those ‘rotating multivariate lunisolar spatiotemporal’ thingies are showing themselves…

Paul Vaughan
October 19, 2011 6:21 am

Special thanks to Ninderthana for contributing to the discussion.
Assuming sampling’s uniformly balanced across all forms of symmetry isn’t remotely sensible. No “energy” ‘s needed to misinterpret the effect of shape, size, orientation, magnification, & aggregation on perception of spatiotemporal pattern, only lapse in human cognition & judgement. For the most obvious example, continents are hemispherically symmetric neither meridionally nor zonally.
Current mainstream models are at best a topological distortion of reality, as they are based on data misinterpretation, laced with untenable assumptions, and contextually ignorant of spatiotemporal constraints.
Best Regards.

Paul Vaughan
October 19, 2011 7:07 am

Janice,
Bearing in mind that there are other warm pools, you may find the following article of particular interest:
Zhou, YH; Yan, XH; Ding, XL; Liao, XH; Zheng, DW; Liu, WT; Pan, JY; Fang, MQ; & He, MX (2004). Excitation of non-atmospheric polar motion by the migration of the Pacific Warm Pool. Journal of Geodesy 78, 109-113.
http://202.127.29.4/yhzhou/ZhouYH_2004JG_PM_Warmpool.pdf
Keep this geometry in mind when reading Bob Tisdale’s articles (GS, IPWP, KOE, SPCZ), while noting the asymmetric multivariate fractal dimension in the climatology animations [ http://wattsupwiththat.com/2011/10/15/shifting-sun-earth-moon-harmonies-beats-biases/#comment-768741 ], and while considering the section I.7 elaboration [ http://wattsupwiththat.com/2011/10/15/shifting-sun-earth-moon-harmonies-beats-biases/#comment-769231 ].
Tip: Keep eye on Chinese research and more generally accumulating effects of increasing differential between China’s math education system & inferior counterparts of West.
Regards.