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Howell - possible phenomenological origins of Puetz's "Universal Wave Series" (UWS)?

"... History never repeats itself, but it rhymes. ..."
"... History never repeats itself, but it rhymes. ..."
"... History never repeats itself, but it rhymes. ..."(?Benjamin Disraeli, not Mark Twain?)

Table of Contents


Stephen Puetz, at the Progressive Science Institute, Honolulu, HI, USA, conceived of the "Universal Waves Series" (UWS), which is by far the most [broad, deep, stunning, insightful] concept that I am aware of for relating periodicities of phenomena across [physics, astronomy, geology, climate, weather, evolutionary biology, history, crops, financial markets,etc]. A great many of the [known, reported] periodicities are described by the UWS as a "factor of 3" series, where each successive cycle is 3 times [more, less] than it's predecessor in the series. These extracted periods are the same across phenomena!

This, of course, raises the huge question "WHY is the UWS able to describe periodicities so near-universally?". Puetz has speculated on a number of "causes" in his [book, paper]s, mostly based on fundamental physics or geological processes, but so far these are difficult to prove (see the section below).

The approach that I have used on this webPage is to ask whether an approximate "Space-Time" correspondance at all scales would yield the UWS. Specifically, the UWS is a log-log scale of [time, cycle].

Do UWS cycle (spectral) peaks also imply a corresponding generalized log-log relationship of time with respect to [length, mass, energy, etc]?
This is easily seen for some simple situations. For example, the exponent 3 in the expression : Volume of a sphere = 4/3*pi*radius^3, implies (loosely) a factor of 3 on log(length) scales. However, I'm far more used to deriving equations specific to the [system, condiitions] being modelled. It's "comfortable" to think that, for a spherical system, measurements related to volume relate back to length to the power 3. Likewise, measurements related to surface relate back (very roughly) to length to the power 2. But I would assume that cycles would smear out for many different systems, leaving not much of a cycle signal.

A natural first set of exponents (number bases : like [nibble, byte, word, hexademimal, octal, etc] in computers) would be the [low, simple]est : [2,3,6,12]? The discussion begins in the next section below.
Frankly, I am not offering anything new, and one might consider my "Space-Time" commentary to be a [version, variation] of Glenn Borchardts [vortex, infinity] concepts in [3][8], and the work of others.

Is Stephen Puetz's UWS, along with its companion [double, half] wave series, a far more [profound, substantial, meaningful] aspect of "Space-Time" than General Relativity (GR)? I don't know that, but it lingers as a thought. It's certainly far more [simple, intuitive, beautiful, real & pervasive] than GR. It's not as applicable to the time-travel, wormhole] fun of sci-fi [films, books], which hold promise that we can somehow [fix, escape] our big blunders, or out time-manouevre adversaries. But UWS also opens up perhaps equally fascinating and far more pragmatic flights of imagination, and that may make for better entertainment if that is what you are after. It may also be useful to your life, unlike the GR time-travel. The UWS also evokes the ancient Mayan system of 20+ calendars, which contains similar periodicities over a more limited range of phenomena, and although I didn't invate, comments have alluded to similarities between the [MayyaChinese] calendars, and perhaps that is common across even societies that never came into contact.

Note that throughout this webPage I use the terms [period, cycle] interchangeably.

Basis of Space-Time concept

My [simple, cheap, flawed] assumptions are that [time, length] are intricately related in a very general sense, and that they somehow share the same integer series (exponent basis) across dimensionality as approximately dictated by geometry. The inverse of the integer series also applies. I'm not comfortable with these assumptions, but let's see if a justification can be built.

dimensionality shorthand comments
zeroD : [d,t]^0 "prime dimensionless ratios" (Poirier)
two fundamental laws cannot share the same PMDs
square root : [d,t]^0.5 intra-Birkeland current, radial to axis of current (Donald Scott)
linear : [d,t]^1 string (Fourier series)
planar : [d,t]^2 drum (Bessel functions)
spherical : [d,t]^3 sphere (?spherical functions?)

harmonics : Obviously, an integer series assumption is grossly inaccurate, as is it's application to a wide range of specific [phenomena, problem specifics]. This is mentioned in Puetz [book, paper]s.

Puetz "turning point distribution principle" : It seems that this concept is more for explaining how UWS cycles can contribute to a change in [state, phase] of a system, which is act the harder part of time series prediction. But it doesn't seem to be a basis for why the UWS exists in first place?

To what extent might these long-know processes, or others that I have missed, occur in natural systems, leading towards the UWS? Do they depend on dissipative processes? Do these process lead to cycles according to "primary log-bases" like [2,3] that are [dominant, cleaner]?

As of 18Apr2022, I have yet to search the literature more deeply for examples of this "primary log-bases" tendency.

Table of cycles: Puetz's Universal Wave Series (UWS)

A partial table is provided in Puetz - Universal Waves Series tabTable, from 2014.txt, although keep in mind that the periodicities are adjusted slightly as more and more data is analysed in Puetz's journal publications since Puetz's 2009 book on the subject. Puetz does thorough statistical analysis of results, maintaining strict quality standards for decig if j=know data fits into the sies. Many of the key mathematics for the statistical assessments were developed by Puets, although he does [refer to, discuss] standard methods as well.
(The following images are from the Puetz financial newsletter, see references below)

prime dimensionless ratios (Poirier)

intra-Birkeland current, radial to axis of current (Donald Scott)

string (Fourier series)

drum (Bessel functions)

sphere (?spherical functions?)

Hypothesized causes of the UWS (Puetz, Borchardt, Condie)

p52 of [4], Puetz noted that all his UWS cycles up to the publication of the book in 2009 "... relate closest to either gravitational or electromagnetic forces. Nothing can be found related to eithertrong nuclear force or the weak nuclear force. Neverthelless, neither force should be completely discounted as a potential factor in modulating these cycles. ...". As I note in the section "General Relativity (GR) Space-Time", and since ~2010 elsewhere on my website, I am NOT fond of [GR, QM, dark [matter, enegy, [strong, weak] nuclear force]. I do retain them in the context of "multiple conflicting hypothesis".

Glenn Borchardt collaborated with Puetz in [3]. He emphasizes vortex motion and his "concept of infinity" from 2004 to partially explain Puetz's UWS. Very insightful in relation to modern astronomical papers (finally!? - mainstream is catching on), in [3] he suggests that dark matter is simply baryonic matter that is difficult to observe.

Most recently, in a paper co-authored with Kent Condie of the New Mexico Institute of Mining and Technology, Socorro, NM, USA[4], Puetz hypothesized causes for a number of geological series. While and these were assessed, definitive cusions cannot be drawn : Perhaps zero point energy, and a host of other ideas can provide a very different conceptual basis, as well.

Glenn Borchardt

Glenn Borchardt certainlys a different way of looking at things than I do, and that helps me in strange ways at strange times. I think mostful to me is his concept of infinity, which to me is like my "multiple conflicting hypothesis" practice. Both are ways to reduce my tendency to become locked too tightly to [concepts, ]. It's not easy to be open-minded, not matter how easy it may be to claim that.

I don't have time (18Apr2022) to ito more detail, but [8], [3] are good starting points, as are the other [paper, book]s he co-authored with Puetz and colleagues in the references below.

Life in the plane of a Z-pinch

Benoit Mandelbrot fractals: "The misbehavior of markets"

Benoit Manderot stressed that "... the true power of fractals arises when these are used with time as a fractal dimension ..." ([1]. The book provides a wonderful analysis of the fractal nature of [commodity, financial] markets. Note that Puetz also worked with collaborators on a fractal analysis of geological data from a [fractal, UWS] perspective.

A stunning part of the book discusses Mandelbrot's follow-up analysis of Alfredo Pareot's constant wealth distributions across [history, geography, society] - regardless of [religious, politicial,economic] * [beliefs, structure, processes]. So much for so much of sociology and political science!

Another interesting historical analysis is described by ?South African team?, who relate Nile river flooding as related to solar cyccles over a ?1,100? year timeframe. Apparently, the Egyptians used that as one factor in deciding taxation rates for each year?

Fractional Order Calculus (FOC)

I will have to think about this later...

General Relativity (GR) Space-Time

I am NOT a fan of [GR, quantum mechanics (QM)], although these concepts have been fantastically successsful in [theory, practice]. Far less am I enthusiastic about dark [energy, matter, etc]. I DO retain them as part of a conceptual ecosystem of "multiple conflicting hypothesis", which indeed requires that overwhelming mainstream scientific beliefs (religions) are retained including those back in history (eg Ptolemic planetary motions). These are wonderfully creative ideas, with beautiful mathematics, but they are carried as unquestionable religions, defended fiercely by their [priest, disciple]s, to the ruin of many good scientists who dare hypothesize differently.

For a FANTASTIC analysis of the conceptual failures of GR, the origins of the mistakes, why it has been so successful, and a more accurate conceptual framework, see
Stephen "". From the start of relativity theory with [Poincare, Lorenz] (at least that's the earliest that I am aware of, although I suspect that it goes back farther) many other [scientist, amateur]s have come up with a wide variety of analysis coming to the same conclusion, plus there is a great deal of data analysis as well. These alternate analysis cannot are "right", nor are any necessarily "right", but I think many make very strong points.


See my previous incomplete musings Howell - comments on Puetz UWS, the greatest of cycles, human implications for a few other references, albeit not all relevant to this webPage. That link provides a very incomplete listing of my initial thoughts about Puetz's UWS back in 2015, when I first ran into it.

[1] Puetz, Stephen J., Prokoph, Andreas, Borchardt, Glenn, Mason 2014, Evidence of Synchronous, Decadal to Billion Year Cycles in Geological, Genetic, and Astronomical Events: Chaos, Solitons & Fractals, v. 62–63, p. 55-75 [].

[2] Stephen J. Puetz 2009 "The Unified Cycle Theory: How cycles dominate the structure of the universe and influence life on Earth" Denver Colorado USA, ISBN: 978-1-4327-1216-7

[3] Stephen J. Puetz, Glenn Borchardt 2011 "Universal Cycle Theory : Neomechanics of the hierarchically infinite universe", ISBN 978-1-4327-8133-0

[4] Stephen J. Puetz(a), Kent C. Condie (b) "A review of methods used to test periodicity of natural processes with a special focus on harmonic periodicities found in global U – Pb detrital zircon age distributions" Earth-Science Reviews 224 (2022) 103885 a Progressive Science Institute, Honolulu, HI 96814, USA b New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA
(a) Progressive Science Institute, Honolulu, HI 96814, USA
(b) New Mexico Institute of Mining and Technology, Socorro, NM, 87801, USA

[5] Puetz SJ, Prokoph A, Borchardt G (2015). Evaluating alternatives to the Milankovitch Theory. Journal of Statistical Planning and Inference, in press, uncorrected proof.

[6] 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.

[7] Stephen Puetz "Universal Cycle Theory Financial Newsletter" Honolulu, Hawaii E-mail:

[8] Glenn Borchardt 2004 "The Ten Assumptions of Science: Toward a New Scientific Worldview" New York: iUniverse, Inc. ISBN: 0-595-31127-X

[9] X. Liu, X. Yuan, C. Xia and X. Wu, "Analysis and Utilization of the Frequency Splitting Phenomenon in Wireless Power Transfer Systems," in IEEE Transactions on Power Electronics, vol. 36, no. 4, pp. 3840-3851, April 2021, doi: 10.1109/TPEL.2020.3025480

There are a huge number of other analysis relating [physical, human] processes to astronomical time series, including ancient calendar systems. Here I list only powerful books by Sacha Dobler :

[20] Sacha Dobler 2018 "Solar History: The Connection of Solar Activity, War, Peace and the Human Mind in the 2nd Millennium" ISBN: 1730722873

[21] Sacha Dobler 2020 "Solar Behavior, how solar and geomagnetic conditions shape human history, the self-destruction attempt of the West and the new Golden Age" personal publication, ISBN 978-3-033-08224-3

[22] Sacha Dobler 07Sep2021 "Hormonageddon - How Chemical and Electromagnetic Influences weakened the Human Character in three Generations Paperback" personal publication?, 146pp, ISBN-13: 979-8472232999