Here is Puetz's analysis of Wheeler's  Table of civilization collapses
http://www.billhowell.ca/miniProjects/Puetz%20&%20Borchardt/Puetz%20&%20Borchardt%202011%20p503%20Table%20of%20civilization%20collapses.jpg

Compare it to the "27Sep09 The Sun and civilisations - Echos of the 2012 end of the Mayan calendar Great Cycle of 5,126 years?" link below.  Of course you used some earlier graphs in your book "Grand Phases on the Sun".   Pages in the web-directory below explain some of Puetz's statistical tests.  I'm impressed with Puetz's work, but still not entirely comfortable that even his work is enough for real "quasi-cycles", and it lacks the shear conceptual power and results of Paul Vaughan in Vancouver (he doesn't do any of this anymore, as far as I am aware).

I've photographed several pages from Puetz's book, and posted them to my web-site :
Puetz & Borchardt web-directory
http://www.billhowell.ca/miniProjects/Puetz%20&%20Borchardt/

Puetz's "Universal Wave Series" is a fascinating approach to cycles, the only equivalent I'm aware of is the 20-or-so calendar system and how they used that, but I assume that all ancient civilisations may have had something similar.  Western civilisation isn't much good at this, and maybe that helps avoid the [mental, social] disease of "cyclo-mania".  But it does lead to laughable blindness.

Puetz's statistical modelling is top class - far beyond what I normally see even in science.  He has also been mathematically inventive (collaborating with some professor).  He uses extremely tight test levels, and is careful to reject "success" when his models come close.   Most of the "quasi-cycles" I run into don't really fit into his UWS series, but perhaps his future developments will lead to a much broader basis for explaining many other cycles (still UWS is quite successful over time scales and subjects!).  There is no sign that he has applied fractional order calculus, though, and that is something I expect even if essentially no-one is doing it - apart from Paul Vaughan in Vancouver.

I'm just reading through Borchardt's "neo-mechanics".   It's wildly different from modern physics, and probably much closer to "natural philosophy" as physics was known before ~1905.  [Loose, full of assumptions, approximate], the neomechanics leaves me a bit uncomfortable, but at least he's not a wild as [big bang, black holes, dark [energy, matter], general relativity, quantum mechanics, etc].


Bill Howell
Volunteer firefighter, Member of Hussar Lion's Club & Sundowners
1-587-707-2027     www.BillHowell.ca
P.O. Box 299, Hussar, Alberta, T0J1S0



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From "Howell's Blog"  http://www.billhowell.ca/Howell%20-%20blog.html

• 27Sep09 The Sun and civilisations - Echos of the 2012 end of the Mayan calendar Great Cycle of 5,126 years?
  

http://www.billhowell.ca/Civilisations%20and%20sun/Howell%20-%20radioisotopes%20and%20history.jpg

Here is a revised, high-detail chart relating the sun-barycenter hypothesis for solar activity to the rise and fall of civilisations. Radioisotopes carbon 14 (C14) and berylium 10 (Be10) are used as proxies for solar activity. (Note: slight upgrade 04Oct09 - put in radial graphs and table of climate/temperature periods).

It is interesting to note that the Mayan Great Cycle period of roughly 5,126 years is one-quarter of the Mayan Grand Cycle of 25,630 years, which is approximately the precessional cycle of the Earth's axis, which is one of three cycles commonly associated with Milankovic cycles (Earth orbit eccentricity (~100 ky and 400 ky), Earth axis obliquity (40+ ky) and precession (26 ky)).

• 08Dec2015 Howell - The Greatest of cycles : Human implications? - 

I'll fix the link another day...

• ... draft document in prep - posting within a day or two ...
  Here is an [initial, random, scattered] framework of human-related "quasi-cycles", as background thoughts to the work of Puetz, Prokoph, Borchardt, Mason 01Apr2014 (see my 07Dec2015 posting below). I use the term "quasi-cycle" as complex natural cycles tend to be non-stationary, meaning that they do not always adhere to a fixed pattern, and that is one of many excellent points on the reliabilitities and errors of analysis that Puetz etal bring out far better than the vast majority of scientists.
  (first posted 08Dec2015, random, scattered framwork document, 06Oct2016 - oops added the file&link)

• 07Dec2015 Alert! awesome, beautiful paper! : Puetz, Prokoph, Borchardt, Mason 01Apr2014 Evidence of Synchronous, Decadal to Billion Year Cycles in Geological, Genetic, and Astronomical Events - It's rare that I put an "Alert" on a posting, but this one may deserve it. Based on Glenn's neo-mechanical assumptions (the 10 Assumptions of Science), and at odds with several "Great Religions" of modern scientists, this paper provides a breath-taking model for [astronomical, geological, genetic, climate, etc] cycles from 57 ky to 14 Gy - a vastly greater span than I've seen before. Furthermore, the concept seems likely to be extensible to much shorter times-scales. For example, authors do discuss sunspot cycles, and I'll take a wild guess that this will work at least down to semi-annual timescales, but likely to tiny fractions of seconds (ad-inifitesimal?).
  
  • Puetz, Stephen J., Prokoph, Andreas, Borchardt, Glenn, and Mason, Edward W., 2014, Evidence of Synchronous, Decadal to Billion Year Cycles in Geological, Genetic, and Astronomical Events: Chaos, Solitons & Fractals, v. 62-63, p. 55-75
  • Puetz SJ, Prokoph A, Borchardt G (2015). Evaluating alternatives to the Milankovitch Theory. Journal of Statistical Planning and Inference, in press, uncorrected proof.
  • Puetz SJ and Borchardt G (2015). Quasi-periodic fractal patterns in geomagnetic reversals, geological activity, and astronomical events. Chaos, Solitons Fract (2015) 81:246-270.
  Comments:
  • The Bill Howell in the acknowledgements is NOT me. Apparently he is a friend of Glenn Borchardt's, possibly a geologist.
  • Both Prokoph (one of the authors) and Paul Vaughan do great wavelet transform analysis. Vaughan (see elsewhere on my website) does what I consider to be the best modelling of short-term climate (<=150 years) of anything that I've seen in detail. It will be very interesting to see the application of Puetz etal to timescales <57 ky, and whether Paul Vaughan will have important critiques of, and contributions to, that analysis.
  • Although the Borchardt's underlying concept is based on fractals, I don't think the authors have addressed "fractional order calculus", a growing topic of interest to me. Paul Vaughan has addressed that in his own way.
  • Human [history, markets, etc] effects are of interest to the authors.
  (first posted 07Dec2015, incomplete quick comments)