I like very much your question, Victor. I agree with you in that the solar system can be explained as a SOC. That, descriptively is in fact what happened early on n the history of our Galaxy.

As to the equation, right now I do not have the ingredients. Yet, as you know, being a SOC the solar system does exhibit a power law property. Hence...

Thank you, Carlos, for your answer. And what about galaxy? I read elsewhere that large scale structures of our universe exhibit power law too so they may indicate SOC, but i also do not find any equation describing galaxy's equation of motion. Best wishes

I remember having read about in E. Chaisson's book "Cosmic Evolution".

Besides, as we know, the epistemological entailment of SOC is that we do not need "ad hoc" arguments any longer; f.i. external, superior, creationist, and the like.

The issue raised by your question can also be retailed to a twofold aspect, thus: on the one hand, the arrow of time, and correspondingly, the measure of the solar system (or the galaxy)'s complexity. Though and marvelous questions, as they are.

Thank you, Carlos, for your answer. You made a sharp remark, which reminds me to another question: provided we can generalize SOC to the universe, does it mean that SOC excludes God as the Prime Mover? What do you think? Thanks

SOC as well as self-organization are probably the most radical conceptual tools that do not need of causality. And yet, causality was a cornerstone in the entire history of mankind since the Greeks. This means that complexity science is a radical cultural and scientific shift, in that it does not work and is not based on causality - whatsoever.

In other words, the traditional stand between subject and object is not necessary in complexity theory, whence the autonomous and external assumption of a subject on and upon an object becomes groundless.

We are, it seems, in the midst of a conceptual and theoretical revolution, indeed.

One answer is No, because planetary orbits *do* have characteristic scales, so the notion of criticality in that context isn't appropriate. On the other hand, one may ask whether in the manifold of *initial conditions* the notion might be of some use, since planetary systems with more than two bodies are, generically, chaotic. However, once more, the issue is what concrete insight could one derive from such a statement, i.e. in a way that isn't tautological but could make some predictions, that could be checked by simulations. It isn't obvious.

Dear Stam, thank you for your answer. What i initially meant is whether the stochastic differential equation associated with SOC can lead to testable prediction with respect to solar system. Best wishes

Dear Carlos, thank you for your answer. Perhaps you are right that the cause and effect arguments need revision, but if we compare with the original experiment, that is the sandpile, then one can ask: who will add more sands into the sandpile in order to trigger avalanches? So it seems to need a subject as Prime Mover. Best wishes

The problem is that planetary orbits, in the two-body approximation, are integrable, so the only way stochastic aspects *might* enter the description is in the case of chaotic dynamics.

thank you, Stam, for your answer. Best wishes

Right Stam! I agree with you. The solar system and our galaxy, to take up Victor's comments and answers are chaotic systems; or rather, close to the edge of chaos. Entropy out there - especially in our galaxy as far it we know about it, largely reigns.

Now, @Victor: the idea of a Prime Mover sends us back to Aristotle and the Aristotelian tradition. Whence there is no room any longer, at all, for your question about SOC and power laws.

Dear Carlos, thank you for your answer. Allow me to clarify what i meant before: is it possible to think of SOC as physical process underlying solar system, but at the same time still gives room for someone who triggered its creation at the beginning? Thanks

Dear Victor, I got your point the first time you ask it. Now you are kindly re-phrasing it.

SOC and self-organization - closely related to each other - have the merit that they provide new insights and tools that enable us to think far beyond causality.

As we all know, causality only works as a scientific explanation:

a) Under controlled circumstance, and

b) At the local scale or level.

Complex systems are intrinsically not controlled and causality is extremely poor to explain complex behaviors. No matter how you think or conceive of causal explanations.

For the first time in history (since the ancient Greeks) we are liberated, to some extent, from having to think causally. Isn' t that great?

Thank you Carlos, for your answer. I got it, but I think the question of whether SOC is responsible for origin of the Universe remains an open question. best wishes

@Carlos, with regards to this discussion on SOC, I just posted a different but related question concerning possible application of SOC in prediction of human behavior. Your comments are welcome. see the question at https://www.researchgate.net/post/Is_there_connection_between_Self-Organized_Criticality_and_Human_Cognition#share

Thank you very much Victor. I'll be glad to participate. Kind regards

@Carlos, thank you so much for your comments and best wishes

@David, thank you for the reference. Best wishes

Dear Carlos and others, thank you so much for all your answers. Allow me to upload a pdf file summarizing this discussion. best wishes

My study of spatio-temporal planet distribution revealed it to be log-normally distributed. The orbital resonances arising due to the particular type log-normal distribution found are close to Fibonacci ratios such as 1:2 2:3 5:8 8:13 etc. Spin rates were also found to relate to these ratios.

In order for the ratios to be maintained, the eccentricities of the orbits required lead to precessionary rates of planet pair conjunction cycles which also relate to each other in simple ratios. eg Earth-Venus 1200yrs, Jupiter-Saturn 2400 years and Neptune-Uranus 3600 years. Multi-planetary periods converge around the periodicities found in carbon 14 and beryllium 10 solar proxies. A hypothesis that planetary orbital periodicities and the resonance they generate are affecting solar variability is further supported by an analysis of spin and orbit rates of Venus, Earth, Mercury and the Sun's various latitudinal bands.

See my profile for links to the papers if this sounds like it might be useful to you.

@Roger, thank you for your answer. I will find your paper soon. Btw, have you taken a look at a paper on planetary resonance in Pattern Recognition in pHysics journal?

Hi Victor, yes, I wrote two of them and acted as editor for the PRP journal special issue. I hope you can find the time to have a look at the attached paper

Article Pattern Recognition in Physics The Hum: log-normal distribut...

@Roger, thank you so much for your paper, i will take a look at it soon. Btw, if it is true that there is planetary resonance, then is it also true that there should be a planetary wave model? Or a wave model of solar system? Thanks

Titius Bode 'law' is a heuristic rather than a law because there is no underlying physical explanation for it and it fails quite badly for Pluto by a factor of nearly 100%.

Th average error for Bode's law is 15%.

By looking at orbital and planet pair conjunction periods (connected to distance by Kepler's 3rd law), I have been able to reduce the error to 2.5%, although a derivation is not yet found to connect the fundamental observation of the log-normal distribution of planets with the specific resonances the pairs are close to.

Regarding a wave model, what we have found is that a simple model using 5 planetary orbital periods and their harmonics can generate a curve which matches the 14C curve to around R^2=0.7, thought to represent past solar activity levels. The model in its latest development achieves a match to 265 years of sunspot data to a Pearson value of R^2=0.9. See R.J Salvador's paper in the special issue on my profile page for more details.

@James. Thank you for your answer. Yes Titius-Bode law is interesting, but it misses several planets, and it lacks theoretical argument. So that is why i asked about wave model of solar system. Thank you anyway.

@Roger. Thank you, i will try to find the Salvador's paper that you cited. Best wishes

Victor,

You can download the whole of the special edition of PRP I helped edit from my profile, or Just Rick Salvador's paper on the 1000yr solar model vs 14C here:

http://www.pattern-recogn-phys.net/1/117/2013/prp-1-117-2013.pdf

@Roger, thank you so much for the url. I will take a look at this file soon. Btw, since i have heard that PRP journal has been stopped, allow me to suggest you to consider a new journal called INternational Frontier Science Letters (IFSL) published at http://www.isfs.org.in. Best wishes

@James. Thank you for your answer. Yes i agree with you that there is something universal going on. In 2004 i published a paper where i applied Bohr's quantization of angular momentum to describe planetary orbits of both inner and outer planets in solar system. Of course, we should treat inner planets as a different system compared to outer planets, so we should use different quantum numbers. The result is very interesting: not only that i explain planetary orbits in better way than Titius-Bode law, but i can also predict three more planetoids beyond Pluto.

At the time of my paper, no planetoids beyond Pluto were discovered, but several months after my paper then the three new orbits predicted by my paper were found by astronomers one by one. May be that discovery is just coincidence, but i think there is something universal with Bohr's quantization of angular momentum. The question now is how to explain Bohr's quantization from the wave equation perspective.

Ps: i can give you the link to my 2004 paper, should you be interested. Best wishes

@Roger. I have taken a look quickly at Salvador's paper that you cited, and it seems very interesting. Allow me to ask a question: i read that sunspot cycle since 2008 indicates that the sun is going to enter a minimum, does it mean that there will be global cooling trend within the next few years? If you can answer that question, please let me know.

Second question: with regards to your paper, i am preparing a book draft discussing alternative model of cosmology. Should you be interested to contribute in this book, then please kindly let me know your email address so i can send you my book draft, so you can take a look. Best wishes