When it comes to modeling real-life phenomena for astrological research, earthquakes are one of the most widely studied.
And why not? After all, the exact time, place, and day are known as well as the strength of the effect (in magnitude).
However, a mapping of earthquake strength to solar system events has proven to be elusive, not to be dramatic, but until now.
Inspired by this Kaggle post, I decided to try my hand at this perhaps age-old problem, and I found that yes, earthquake magnitude correlates with the moon phase at the time of the event. (Moon phase has been looked at quite often but not with the model I will present today.)
First off, I went to https://earthquake.usgs.gov for the earthquake data. (Thanks to Joe Ritrovato for the link.)
I wanted to look particularly at all earthquakes of any depth between Jan 1, 1975 and Jan 1, 2005. Those years were chosen, because a uniform seismograph was finally used through out the world by the mid-1970's, and hydraulic fracturing with its associated quakes was not yet in widespread practice. The search was further restricted to earthquakes of magnitude greater than 5.5, following this system of what counts as a serious earthquake. (Some lower limit to the magnitudes was necessitated by the search limit on the USGS site.)
Here is what my search looked like (be sure to also choose earthquakes only below the fold):
And here is what you will see if you press enter:
If you first choose for the output to be in .csv (spreadsheet) form, then you will get this file:
With this data, we can test a model of how moon phases may correlate with earthquake magnitudes.
Here is my model.
My task was to assign these 8 basic shapes a ranking from one to eight. But how to do that?
My thinking is that the new Moon in Vedic astrology is considered a very malefic influence (malefic is a technical term), and so, I shall assign it the 8. Conversely, the Full Moon is the most benefic, and so, it shall be the 1. What about the other shapes? There is also a standard idea in Jyotish, Vedic Astrology, that the waning shapes are more capable of mischief than the waxing shapes.
So the model is very simple and straight from Jyotish but can be implemented by any observer.
So, what happens if we just set up a correspondence between Moon phase number (from the date for the earthquake) and the earthquake's magnitude?
Over the course of the thirty years of the study and 13,623 earthquakes, is there a correlation?
Yes, there is.
I used the Spearman's rho Rank Test for the group and found a correlation rho of 0.0252 (a measure of effect size) with a p-value of 0.00325.
There you go.
Calculations are below.
If you have the analysis software Mathematica and would like the notebook file itself, here is the download.
Perhaps you are someone who needs tactile data. If so, click to enlarge the earthquake magnitude counts for moon phases 1 to 8 below.
And please do confirm the results (or perform your own tests) with the following digested .csv which contains the date/time stamps of the earthquakes (all in UTC), followed for each by the moon phase ranking, and then the magnitude.
Finally, here is the box whisker plot. The mean diamonds are depicted in pink and show the subtle upward trend from left (1) to right (8). Medians are depicted by the white horizontal lines.
To conclude, a weak but highly statistically significant correlation was found between historic earthquake magnitudes and moon phase ranking. The ranking system has to do with beginner-level general astrological principles about which phases cause the most trouble.
While more work is needed, here a basic scientific hypothesis that has stood unanswered for millennia finally gets to rest its feet for a bit. I am grateful for this sweet birthday present.
By reading the book Cymatics, many of us thrilled to the idea of vibration made visible in that gem of a book from the late 1960's.
With a few lines of code I have decided to plot the equations which go to heart of, and could be said to generate, these beautiful forms.
More motivated me than just the chance to look directly at and witness the imagery. I have seen some claims that the Shri Chakra could be seen from these "tonoscopes".
Could this be real, I wondered? So, I decided to get a handle on the equations (hint: some partial differential equations experience will take you very far) and plot what came out. Here is a good reference for anyone who wants to get a top-down view of the math.
The following are downloadable movies when the first 256 theoretical stationary forms from cross-vibrations on a circular plate or drum are modeled, and after that when a square plate is modeled. They start with the simplest, lowest tones and go to more complex, higher ones.
The blue of any shade denotes initial troughs in the waves that then become peaks, and the light colors of any shade denote initial peaks that then become troughs. Because of this movement, sand would not settle anywhere near either of those cases. That is why the demarcation black lines next to the neutral tan are only where the sand would settle.
Think of these images as topographic maps. The sand is lazy and wants to stay along the black flat lines and not go where it will have to go anywhere up or down (blue-ish or yellow-ish regions).
And here are some links to all 961 theoretical forms in the round plate and all 1121 forms in the square plate. Page through them to see all sorts of cool things
Some immediate thoughts: the beauty is indisputable, and secrets of everything from the Jyotish chart, fractals, design from around the world, and tree bark could be said to reside here. I am also impressed by the variety but stability of the inner blue designs that form.
What is not in these final, complete sets is a stable Shri Yantra. The closest I can see so far is standing wave 763 in the square plate.
Are you starting to see it yet?
However, the "OM Mandala" is said to be occurring with the vocal sonoration of the word "Om", and hence not with these mechanical tones.
If I were to speculate, the intonation would involve multiple overlapping tones (probably three, A + U + M) and hence designs. The exact frequencies would depend on the size of the plates.
The fundamental designs in the movies above are almost yantra-like even in the pure forms and certainly seem capable of forming the overlapping triangles and such of the yantra.
For instance, the circle around the Om Mandala might be formed by M (the first starting image in the movie above), and A could be the set of bigger opposing triangles which does have a representation, and U could be the set of smaller triangles which also does have a representation.
As we are often told as students of Sanskrit, the purity of "Om" would probably have to be just right to sustain a Shri Yantra.
To search for the Shri Yantra, I have plotted sums of three sounds for both the round plate and the square plate up to the 28th image. That is over 3300 jpgs in each linked folder. Have a look in these folders to see if you can find the Shree Yantra.
If it is not in there (I have not looked at them all), then combinations of more complex fundamental images may need to be looked at. This could all be automated fairly easily with AI.
Just to give you a demonstration of how very much things can clean up, here is the density plot of the addition of the first form, the 689th, and the 763rd.
Or how about this image that is from the sum of the lower order first, 52nd, and 55th forms?
It is one thing to say "There is a synchronistic nature to everything sacred," it is quite another to say "And here is the equation".
With this brief demonstration, I hope that you can see that the conjecture of Om forming the Shri Yantra is, at the very least, certainly mathematically possible.
Until I get around to programming the AI and/or getting a better chanting voice, this is where I will hang my hat for now.