- Introduction
- Basis of concept
- Table of cycles: Puetz's Universal Wave Series (UWS)
- 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)
- Glenn Borchardt
- Life in the plane of a Z-pinch
- Benoit Mandelbrot fractals: The misbehavior of markets
- Fractional Order Calculus (FOC)
- References

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.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.

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.

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?

**sympathetic resonance**:

"... Sympathetic resonance or sympathetic vibration is a harmonic phenomenon wherein a passive string or vibratory body responds to external vibrations to which it has a harmonic likeness. The classic example is demonstrated with two similarly-tuned tuning forks. ..." (wikipedia)**frequency splitting**:

"... The frequency splitting phenomenon (FSP) is a critical issue in wireless power transfer (WPT) systems. When the FSP exists, the load power will sharply increase and can be dozens of times of the power obtained at the resonant frequency if the driving frequency varies from the resonant frequency, which seriously affects the system safety. ..." (Liu etal [9])**frequency scavenging**:

"... Energy harvesting (also known as power harvesting or energy scavenging or ambient power) is the process by which energy is derived from external sources (e.g., solar power, thermal energy, wind energy, salinity gradients, and kinetic energy, also known as ambient energy), captured, and stored for small, wireless autonomous devices, like those used in wearable electronics and wireless sensor networks. ..." (wikipedia)

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

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 :

- Internal causes - "... There has been considerable discussion about the causes of the low-frequency LIP (and zircon events, with the most direct information coming from experimental and numerical modeling related to mantle plumes and to the supercontinent cycle. ..."
- Deep mantle hypotheses - In recent years, the rapid evolution of numerical computing provides a means of simulating complex processes for convection with temperature-dependent viscosity, subduction, plume generation, and convection with compositional variation.
- Lithospheric-activated hypotheses - Lithosphere-activated events are generally related to short-lived phenomena in the lithosphere or uppermost mantle. The most common models are those related to the sudden breakthrough of slabs stored in the MTZ resulting in slab avalanches.

- External causes
- Periodic asteroid/comet impacts
- cycles in the density of dark matter
- climate cycles as postulated by the Milankovitch Theory
- Solar activity harmonics

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.

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?

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.

[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 [ http://dx.doi.org/10.1016/j.chaos.2014.04.001].

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

[3] Stephen J. Puetz, Glenn Borchardt 2011 "Universal Cycle Theory : Neomechanics of the hierarchically infinite universe" www.outskirtspress.com, 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.

http://www.sciencedirect.com/science/article/pii/S0378375815001901

[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.

http://dx.doi.org/10.1016/j.chaos.2015.09.029

[7] Stephen Puetz "Universal Cycle Theory Financial Newsletter" Honolulu, Hawaii http://www.uct-news.com E-mail: contact@uct-news.com

[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 https://www.amazon.ca/Solar-History-Connection-Activity-Millennium-ebook/dp/B07JQJTF6C/ref=sr_1_1?dchild=1&keywords=Sacha+Dobler+%22Solar+History%22&qid=1591938819&sr=8-1

[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

18Apr2022 initial posting

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"... 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?)