A student and I were discussing the charts of birth, renunciation, and enlightenment for the Buddha, Siddhartha Gautama. These charts are amazing and worthy of many blog posts, a goal for another time. They are sourced from *Buddhist Astrology*, a really excellent book.

Perhaps I can just say for now that witnessing a Great One's chart is like They are right there, in front of you.

What I want to focus on here is the Jyotish of the Four Sights. I can not do the topic justice, but I would like to add a bit to the discourse.

The basic idea is that Shrii Gautama saw as a young man four sights, "four holy messengers", that led to his enlightenment: 1. an elderly man, 2. a sick man, 3. a dead man, and 4. a saddhu (holy man/monk), in that order.

Some say he saw them all at once, a day before renunciation. Others say that he saw them at different times. Based on the birth chart of the Buddha, I am inclined to think that the sights happened at different times and also not right before the renunciation chart took place. The order of the sights also makes sense from the birth chart.

Rather than showing you about that, I want to show you here the more important themes raised by the sights themselves. Let's begin by seeing where the themes of one through four are in anyone's chart:

Perhaps I can just say for now that witnessing a Great One's chart is like They are right there, in front of you.

What I want to focus on here is the Jyotish of the Four Sights. I can not do the topic justice, but I would like to add a bit to the discourse.

The basic idea is that Shrii Gautama saw as a young man four sights, "four holy messengers", that led to his enlightenment: 1. an elderly man, 2. a sick man, 3. a dead man, and 4. a saddhu (holy man/monk), in that order.

Some say he saw them all at once, a day before renunciation. Others say that he saw them at different times. Based on the birth chart of the Buddha, I am inclined to think that the sights happened at different times and also not right before the renunciation chart took place. The order of the sights also makes sense from the birth chart.

Rather than showing you about that, I want to show you here the more important themes raised by the sights themselves. Let's begin by seeing where the themes of one through four are in anyone's chart:

Some interesting patterns immediately emerge.

First, these four stages of spiritual development are all squares, at ninety degrees, to each other, and if we use the Buddha's Virgo lagna as the ascendant of the chart, all of the four houses are the tamasic fixed signs.

Moreover, they represent the four aims of life which I have written about before: dharma, artha, kaama, and moksha (but interestingly, not in that standard order and not in the order of fire, earth, air, water like the zodiac).

Only the dharma bhava (ninth house) is not a dussthana.

Perhaps in the Gautama's super-high awareness, He saw that if we are tamasic, fixed, in some way, and we are, that the four aims of life could indeed still be fulfilled, but in the order of the sights, by being aged, sick, then dead, then a saddhu, or one could go straight to the latter, to dharma, straight to being a renunciate where age, sickness, and death (all three of which He experienced in that order and at the proper periods according to his birth chart) are for another day.

Just some additional thought structure from the Buddha's amazing life and appropriately*amazing* charts.

]]>First, these four stages of spiritual development are all squares, at ninety degrees, to each other, and if we use the Buddha's Virgo lagna as the ascendant of the chart, all of the four houses are the tamasic fixed signs.

Moreover, they represent the four aims of life which I have written about before: dharma, artha, kaama, and moksha (but interestingly, not in that standard order and not in the order of fire, earth, air, water like the zodiac).

Only the dharma bhava (ninth house) is not a dussthana.

Perhaps in the Gautama's super-high awareness, He saw that if we are tamasic, fixed, in some way, and we are, that the four aims of life could indeed still be fulfilled, but in the order of the sights, by being aged, sick, then dead, then a saddhu, or one could go straight to the latter, to dharma, straight to being a renunciate where age, sickness, and death (all three of which He experienced in that order and at the proper periods according to his birth chart) are for another day.

Just some additional thought structure from the Buddha's amazing life and appropriately

I have posted a few times here about a rich dataset that I have.

Data were obtained from Stanford's SNAP data repository of Amazon.com reviews that gave daily misspelling rates; astronomical data were from Wolfram's Mathematica software and its astronomy resources.

Here is what the dataset looks like. Click on each picture to enlarge.

Data were obtained from Stanford's SNAP data repository of Amazon.com reviews that gave daily misspelling rates; astronomical data were from Wolfram's Mathematica software and its astronomy resources.

Here is what the dataset looks like. Click on each picture to enlarge.

Each of the 5296 rows represents a sequential day in a 14.5 year span of Amazon review misspelling rates during Jan 1, 2000 to Jul 1, 2014.

Across the top are the labels. In each column is a simple, stable, linear function of the right ascension (i.e., the astrological Tropical degree) of the planet, moon, or star at midnight at the start of that day in London, UK. Retrogressions of the planets are also included.

The final column is the log of difference of the misspelling rate of the day from the 27-day SNIP baseline. (The Moon's right ascension completes its cycle every 27 and change days. That is the shortest cycle for any of the right ascensions.) Thus, it is the data over time minus its background noise. The following is a graph of this column's data over time.

Across the top are the labels. In each column is a simple, stable, linear function of the right ascension (i.e., the astrological Tropical degree) of the planet, moon, or star at midnight at the start of that day in London, UK. Retrogressions of the planets are also included.

The final column is the log of difference of the misspelling rate of the day from the 27-day SNIP baseline. (The Moon's right ascension completes its cycle every 27 and change days. That is the shortest cycle for any of the right ascensions.) Thus, it is the data over time minus its background noise. The following is a graph of this column's data over time.

SNIP stands for Sensitive Nonlinear Iterative Peak-clipping algorithm. This method preserves any cyclic patterns -- such as the planetary placements and retrogressions -- while discarding "background noise" in the data, which would tend to obfuscate the patterns. The SNIP method is not subjective. It comes out of processing signals within spectra and is unprejudiced. Note that the SNIP method comes from signal processing and tends to preserve cyclic behavior in spectra.

For today's study, the data for the first 80% of days were developed into a training group, and that of the subsequent 20% of days were isolated as a test group.

What was doing the training and testing? They were done entirely by an automated machine learning (AI) algorithm from BigML.com called DeepNet. DeepNet* was applied to the training set of the first 80% of days. This DeepNet was then tested or evaluated on the last 20% of days. The DeepNet is a hands-off technique offered to anyone for free.

The chart below displays ridiculously good results as given in the usual AI industry way: the error rates for predictions for the 20% test group by DeepNet (in green) is dramatically smaller than other standard methods of prediction, in gray, which are based on the mean (average) rate of the training data or an approach assuming random chance. Moreover, the strong R-squared suggests good correlation of predicted misspelling rates to actual values only for the astronomical data of the DeepNet.

For today's study, the data for the first 80% of days were developed into a training group, and that of the subsequent 20% of days were isolated as a test group.

What was doing the training and testing? They were done entirely by an automated machine learning (AI) algorithm from BigML.com called DeepNet. DeepNet* was applied to the training set of the first 80% of days. This DeepNet was then tested or evaluated on the last 20% of days. The DeepNet is a hands-off technique offered to anyone for free.

The chart below displays ridiculously good results as given in the usual AI industry way: the error rates for predictions for the 20% test group by DeepNet (in green) is dramatically smaller than other standard methods of prediction, in gray, which are based on the mean (average) rate of the training data or an approach assuming random chance. Moreover, the strong R-squared suggests good correlation of predicted misspelling rates to actual values only for the astronomical data of the DeepNet.

Let me summarize my take: *future* misspelling rates in Amazon reviews were successfully *predicted *using only basic **astronomy** data when compared to random values or when the average (mean) value was repeatedly applied. Moreover, similarly there was a fine fit of correlation of the model's predicted values to the actual values as shown by the R-squared.

Here are the DeepNet fields in order of importance.

I am not even sure what to do next, but in case you do, here is the spreadsheet.

fullamazonmisspellingdata.csv |

Please let me know what is up, and please reference this post if you use the data set.

* For an instructable on exactly how I did this, see here. Note that a linear split was used.

]]>* For an instructable on exactly how I did this, see here. Note that a linear split was used.

An AA rating is "Data as recorded by the family or state". The expectation of many researchers is that AA data is of the highest accuracy possible and can be used freely. In the following, I show statistically that it is extremely unlikely that the AA rating charts altogether are accurate. I will be considering charts of people only and only those born at or after 1930.

From here on, I will try to state things as explicitly as possible.

The common assumption (the

One behavior of accurate birth data is that the minute of birth is evenly distributed. That is to say, a birth time of 8 minutes after the hour is not expected to happen much more or less than a birth time of 9 minutes after the hour, for example.

The following is a simulation of a uniform distribution so that you you know what its plot looks like.

As you can see, there is variation, but no bar is wildly higher or lower than another bar. On the whole, the bars are even, more or less.

The statistical test that I will be using to test a match of the Astro-databank data to a discrete uniform distribution is called the** Pearson's chi-squared test**. If its result is less than 0.05, then the data is generally considered unlikely to be from that distribution.

For example, in the randomized computer simulation above, the test statistic is 57.6489 with a p-value of 0.525436 which is consistent with it belonging to the discrete uniform distribution.

For the minutes of charts of people born after 1930 in Astro-databank with the highest AA rating, do they fit a discrete uniform distribution?

No. For a sample taken from the first 13,056 such charts (the largest practical one for the limits of my computer), the** test statistic** **is ****63.7**** and the resultant p-value is ****7.18058*10^-10**. Again, any p-value less than 0.05 is generally considered statistically significant. Thus, the alternate hypothesis is supported.

As a comparison to the above graph of an even distribution of birth minute, look at the graph for the AA charts:

The statistical test that I will be using to test a match of the Astro-databank data to a discrete uniform distribution is called the

For example, in the randomized computer simulation above, the test statistic is 57.6489 with a p-value of 0.525436 which is consistent with it belonging to the discrete uniform distribution.

For the minutes of charts of people born after 1930 in Astro-databank with the highest AA rating, do they fit a discrete uniform distribution?

No. For a sample taken from the first 13,056 such charts (the largest practical one for the limits of my computer), the

As a comparison to the above graph of an even distribution of birth minute, look at the graph for the AA charts:

While Astro-databank remains an invaluable overall tool for researchers, birth minute in Astro-databank, generally speaking, is not useful.

Calculations and source files are below.

accuracy_unlikely_1.nb |

urls3b.mx |

data3.mx |

[Postscript: for those who would like to see the data only for people who are born at or after 1980, here you go. P-value is 3.30016*10^-22. So, the situation is even worse.]

]]>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:

query_5__any_depth.csv |

With this data, we can test a model of how moon phases may correlate with earthquake magnitudes.

Here is my model.

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.

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

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

There you go.

Calculations are below.

If you have the analysis software *Mathematica *and would like the notebook file itself, here is the download.

earthquakes_usgs_2.nb |

To those unimpressed by the correlation rho of 0.0252, this MiniTab post is an easy-to-read explanation of why that is not necessarily worrisome. The post then describes doing an F-test as the next step to look at significance when one has a low rho. Here are the results of the F-test.

DF SumOfSq MeanSq FRatio PValue

Model 7 2.86487 0.409267 2.37283**0.0201455**

Error 13615 2348.32 0.17248

Total 13622 2351.19

From G*Power, effect size is 0.0349025, alpha is 0.05 and beta is 0.9500295. Thus, these results can be considered interesting and significant enough for further study.

DF SumOfSq MeanSq FRatio PValue

Model 7 2.86487 0.409267 2.37283

Error 13615 2348.32 0.17248

Total 13622 2351.19

From G*Power, effect size is 0.0349025, alpha is 0.05 and beta is 0.9500295. Thus, these results can be considered interesting and significant enough for further study.

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.

usgs_earthquake_data.csv |

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.

]]>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".

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).

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.

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.

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, 32nd, and 370th 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.

]]>With this brief demonstration, I hope that you can see that the conjecture of Om forming the Shri Yantra is, at the very least,

1 medium-large butternut squash

4 - 6 oz. goat cheese

2 - 3 oz whole walnuts

1/2 - 1 oz rosemary sprigs

3 to 6 tbsp. ghee

1/2 lb. of dates

Preheat oven to 395 degrees.

Slice off the ends of the cleaned squash. Then, slice the squash in two longways, and then for each half generated, slice in half again.

Clean out seeds and strings. You may want to save them. (See postscript.)

Arrange the squash pieces in a baking dish. Dollop the ghee on them. Align the rosemary sprigs on top. In the sides of the dish, add walnuts.

Bake for 45 to 55 minutes in the oven. While it is baking, de-pit the dates and crumble or cube the goat cheese.

After the 45 to 55 minutes of initial baking, pull the squash pan out and add the dates and cheese. Return to the oven for 5 minutes only to melt the cheese, or you can just let the dates and cheese stay firm without this last melt.

Serve!

P.S. You can toast or bake the squash seeds and extra walnuts separately with a bit of ghee and salt and pepper for 10 minutes for a fun snack for the next day or as part of hors d'oeuvres for this meal.

Accordingly, my assistant drew up a table of all Super Bowls so far and their event information.

I then drew up each chart and made a prediction. These were then checked against the real winners.

I should preface by saying that I am a football agnostic. I do not know much about football, only watching socially for a few minutes here and there and receiving the good-natured teasing of friends for knowing so little.

I want to admit that I have seen some games at some times, enough to develop the model, yet I feel I can judge these past charts fairly, truly without any

Thirty five out of forty five Super Bowls were evaluated correctly. (Five early Super Bowls did not have recorded start times available.)

Final 2-sided p-value is 0.0002.

To do this project even more fairly, I would recommend the following:

- just using the charts and the names of the teams (no identifying "birth data" of the charts)
- employing a reader who knows nothing about football (this will be hard and I would have to teach them the technique first)
- no access to internet while the reader is performing the test (I did not use it)
*OR*you can just have the reader read for future games (presumably including regular league games). This was obviously not possible for this study.

There is no money in it, and my clients actually don’t like it.

They ask me why I do it. These are intelligent well-educated people, but they tell me they come to astrology because they are sick of science. ("One year coffee is good for you, one year it is bad for you…")

The work of astrological science is lonely, scary, and frustrating and really tough on me physically.

I do it instead out of love, out of passion, out of honestly wanting to know the answer.

That is why I say it is a hobby for me. I think that is a good thing.

I went to college full-time at fifteen, actually being able to emancipate based on my scholarship stipend. Some of my friends were getting PhDs at that age from schools like Harvard and Princeton.

One thing united us in order to work so hard and give up so much, so young. We all shared an immense personal love for science, actually being in love with Mother Nature Herself.

Then, 5 or 10 years later, we all made it into the profession, the industry, of science, and we almost all dropped out.

Research into fundamental astrology returns my gaze back to Mother Nature, and it is that worship which is really why I do it, and yet I certainly do keep all the numbers real. You must, to get really close to Her.

So, even though I do a particular methodological approach which is very big data and AI oriented, using pretty advanced mathematics, I do it for intensely personal reasons, and actually as an artistic expression, I feel.

The methodologies that I would like to see at large in the future of astrology research would be ones that would speak to our fact-based culture as a whole, and maybe along the way, some money could be sent toward astrological researchers, because a need of society at large is met, some pressing practical societal need is answered.

Richard Feynman once said: “People who wish to analyse nature without using mathematics must settle for a reduced understanding.”

So, I think we have to increase our mathematics chops, even if we are doing hermeneutics, perhaps learning from all the good work happening in the digital humanities in the past decade.

We also have an opportunity to go beyond what even regular science provides society, and that is to do our work with love, for love.

It is not just an opportunity, it is a necessity, for astrology is and we are psychology and medicine and football games and politics and money and families, everything altogether, and that is love. I know it is.

Click on image to see the presentation from The Kepler Conference for Astrological Research, Jan 2017.

[Edit: a crazy further reduction in RMSE was achieved by finally using a neural net. The quick write-up of that can be seen here.

A full journal article was just approved for publication (March 2018). It will be referenced in the bibliography.]

To hear the audio of the misspellings, download the original file**below **and mouse over on the second red graph.

[Edit: a crazy further reduction in RMSE was achieved by finally using a neural net. The quick write-up of that can be seen here.

A full journal article was just approved for publication (March 2018). It will be referenced in the bibliography.]

To hear the audio of the misspellings, download the original file

kepler_2017_mercury_retrograde__presentation.pptx |