I understand the Chakras to be a sort of multi-level skeleton for consciousness intertwining with our physical, emotional and mental bodies. Bodies is the framework used in traditions I have studied. If “I” am something other than my physical body, then why not consider other “bodies” that are other than “I”. The chakras represent realms in which all 3 bodies are involved, dealing with different sets of issues. The lower chakras correspond roughly with Abraham Maslow’s Hierarchy of Needs.

The first chakra deals with maintaining a physical existence, staying alive.

The second chakra deals with relationships, and maintaining the species.

The third chakra is the realm of social interaction, power relationships.

The fourth chakra opens the possibility to unconditioned love’s expression.

The fifth chakra is sometimes represented as connected with “the void”, also with the “inner guru”, an opening to a deep wellspring of understanding.

The sixth chakra opens the possibility of transcending dualities.

The seventh chakra is the realm of Samadhi, subject of a separate post.

One of my teachers, Shyam Bhatnagar, described each of the chakras as having within it its own version of each of the seven chakras. “The 7th in the 3rd” refers to the energy of the 7th chakra as expressed through the 3rd chakra.

We mature through the chakras at a rate of about 6 (women) or 7 (men) years per chakra. So at age 18/21, we’re moving into development of the 4th chakra.


Al hamdu lillAh

Thanks be to God.

I’ve shared time with Sufis. Sufism is normally ascribed to Islam.
Sufism’s fundamental aversion to rigid adherences lead (present tense) to it being unwelcome in some Islamic circles.
That same aversion can sometimes be found in traditions other than Islam,
and those that share that aversion are welcome within Sufism.

Or so is my impression. My exposure to Sufism was at two summer retreats of a particular Mevlevi (referring to Mevlana Jalaluddin Rumi) sufi group, held on rented facilities at Burke Mountain Academy (in Burke, VT), close to the home my wife Bonnie and I found and bought soon after. Group headed by Kabir and Camille Helminski.

The word came to me to add to the end of a message I was writing to the director of a retreat center associated with a (nearby – Barnet, VT – close to the above-mentioned home) Buddhist community about participating in an upcoming retreat. Wanting to end the message expressing my past connections with a Hindu tradition, I used the words Namaste and Shanti. The word Alhamdulillah came to mind. Wanting to make sure that it in fact was saying something I wanted to say in this instance, I looked up its meaning.

“… Alhamdulillah: in theory, it is to be said with a profound sense of love, adoration, and awe of the power, glory, and mercy of God. …”

Yes, the word was just fine at the end of my note. The traditions with which I have my closest connections include divine presence – as expressed with the Muslim phrase used in the title of this post. Buddhism, from what I understand, does not recognize a supreme deity.



For me, a word, no matter what word, can only be an approximation of that which the word is intended to signify/indicate.

Language can attempt to express shared understandings among language-users, but can only be a message

to describe something deeper.

There is a something, for which we at our depths have great longing

We see hints of its passing as we conceive our experience

understandings coming after experience which, when made manifest in time,

is …

before thought about the experience comes to existence.



From the end of a web page on Dharana, Dhyana and Samadhi, I pulled the following quote:

Dharana, Dhyana and Samadhi are, thus, progressive stages of the same process. You may choose different techniques for Dharana and Dhyana as explained in the previous lessons or you may choose just one object for all these three stages. If you practice Dharana, Dhyana and Samadhi on the same object this trio is referred as Samyama. Samyama is said to give the practitioner various Siddhis or supernatural powers. However, a real Yogi ignores such Siddhis and continues his practice further.

Samadhi itself is a progressive step. It further undergoes a series of progressions before a Yogi reach its final destination. These stages or type of Samadhi are explained below:

*  Samprajnata Samadhi

*  Savitarka Samadhi
*  Nirvitarka Samadhi
*  Savichara Samadhi
*  Nirvichara Samadhi

*  Asamprajnata Samadhi

Samprajnata Samadhi: The word Samprajnata is combination of Sam + Prajnata. Sam means “with” and Prajnata means “knowledge with awareness”. Thus Samprajnata Samadhi is a state where there exists knowledge with awareness. This awareness is in the form of reasoning, reflection, bliss and individuality.

Asamprajnata Samadhi is the next stage in which there is no mental activity such as reasoning etc. However, some traces of Samskara or impressions still exist.

Savitarka Samadhi means “Samadhi with reasoning”. In this stage word, its meaning and knowledge of that meaning exists.

Nirvitarka Samadhi is the next stage where mind becomes pure and expresses the object of meditation alone. Thus there is no process of reasoning in Nirvitarka Samadhi.

Savichara Samadhi means “Samadhi with mental reflection” (Sa + Vichara). Vichara is more accurate and subtle than Vitarka. In this stage the object expresses itself as a reflection.

Nirvichara Samadhi means “Samadhi without any reflection”.

All the above type of Samadhi are called as “Sabija” or “with seed” because they involve a seed in the form ones ego or individuality. The final stage is called Nirbija Samadhi which does not involve even a seed. It is total absorption of mind.

In is important to remember that knowing this classification is fine but what is more important is to experience the state of Samadhi. Don’t bother too much about various types of Samadhi and their meaning. Keep practicing with full efforts and you yourself will experience them.

 I plan to add additional material to this thread from the book Sri Vijnana Bhairava Tantra / The Ascent (Yoga Publications Trust).

Enneagram for Meditation

A group of folks have been via-web-meeting every 2 weeks or so to discuss the enneagram. Some weeks ago one of us came up with an enneagram about meditation. The rest of us were challenged to come up with our own version of an enneagram about one’s sitting-practice. The following diagram is what I came up with.

Calm Mind Enneagram
Enneagram for Still Mind Practice

The word samyama (used in my enneagram) was not in my vocabulary until I searched “dhyana dharana samadhi” on Google.  I came to this

Using Computers Since 1965

I was introduced to computers in 1965, and have worked & played with them (outside some time in the Peace Corps, Nepal) ever since. The first computer I used, a Bendix G-15, was old in 1965. It was set off in the corner of the local University’s computer center, away from the newer IBM 1620 and newest CDC  9300 computers (model numbers from the archives of computer evolution). In the same room as the G-15 were a number of analog computers then still in use. They approached problem-solving through modeling differential equations in electronic circuits. A particular arrangement of circuits might represent, for instance, a chemical reaction. The CDC 9300 was a hybrid (last or near-last of its kind) in being able to incorporate analog circuitry along with a digital computer. Its FORTRAN IV compiler was a step up from the FORTRAN II on the IBM 1620.

Entering a program for the G-15 was a matter of typing it onto paper tape on a teletype, then feeding the tape into the computer (tape cartridge can be seen in the top panel of the computer pictured below, held place by the handle across its middle). The main memory was not today’s semiconductor RAM, not even the precursor core (magnetic donuts) technology. It used a rotating drum to hold programs – so hot-shot programmers would place consecutive instructions at an interval apart on the drum so that when one instruction had been completed the next would be just about to come under the read head, all lined up to be read, interpreted, and executed as quickly as possible, rather than waiting an average of 1/2 a rotation of the drum for the next instruction to be available.

I wrote programs in FORTRAN for a small civil engineering company for many years. I maintained & extended both a basic accounting system set up by IBM and the COGO (COordinate GeOmetry) program used by the engineers. I did the legwork to move them from an IBM 1130 to a DEC PDP 11/40 computer running RSX-11D, an early multi-user operating system. The latter never reached its full potential because the computer didn’t have enough RAM (which was quite expensive at the time) to handle multiple users.

I was lured from civil engineering by a “jack of all trades” position at the local university’s (DE, USA) College of Education (from wiring circuits for experimental data gathering to managing a lightly used unix system to working on an Old English Concordance to using the PLATO system). I moved from there to the university’s central computer support organization to be the first person specifically supporting the newly-introduced IBM PC, followed by adding the Apple Macintosh, and later other PCs.

It stuns me to consider the speed of tech evolution, and how it keeps evolving, rapidly. All mentioned above was before ubiquitous computers and the Internet, which have opened up seemingly unending new realms for evolution – for personal interaction, for access to tools and information, and so much more.


Customizing WordPress

I’m working on figuring out various parts of WordPress. Themes are formatting schemes. Lots of pre-defined themes are available for free. I just added one of the more popular ones, will now need to work on customizing beyond changing the logo. Once again, applying the default theme was a breeze.

The Enneagram

The Enneagram is a figure that has been appropriated to model all sorts of things. Most current books on the Enneagram are about a personality model based on the work of Oscar Ichazo of Arica Institute, Chile. Claudio Naranjo was instrumental in bringing his take on Ichazo’s work out of Chile. Many Jesuits picked up the ideas and wrote books, as did others. There may be hundreds of titles by now.

There’s a similar application of the Enneagram, but to body types. Rodney Collin is a source for these ideas. Joel Friedlander and Susan Zannos have written books on this version of the Enneagram.

Another application of the Enneagram is as part of a pantheon of systems – from monads, dyads and triads through to larger systems. John Godolphin (J. G.) Bennett was key in developing these ideas and their application to life situations. He used the term Systematics (also used in Biology, but with a different meaning). Two of his books that are relevant are Elementary Systematics / A Tool for Understanding Wholes and Enneagram Studies. Bennett had ties to Gurdjieff, who introduced the Enneagram to his students.

Bennett’s ideas on Systematics have been applied in business situations. See Saul Kuchinsky’s Systematics / Search for Miraculous Mangement and Richard Knowles’ The Leadership Dance / Pathways To Extraordinary Organizational Effectiveness. Saul died some years ago; go to to contact Richard and his wife. Tell them I sent you.

Here’s a picture of the Enneagram, with a red circle at the top that I added to fit it into the N-Gram diagrams I developed. They are based on the way the patterns of repeating digits in base ten for n/7 (.00, .142857, .99) and n/3 (.00, .33, .66, .99)  are represented in the Enneagram, but with other divisors in addition to 3 and 7, and applied in other bases in addition to ten.

Enneagram with top point emphasis
Enneagram with top point emphasis

The Gurdjieff/Bennett Enneagram is used to model a process of transformation. The sequential steps are mapped clockwise around the circle, starting and ending at the top. A mental approach consistent with the transformation follows the 1-4-2-8-5-7 pattern. Applying the model requires identifying the anchor points (3, 6, 0/9), the intervening steps, and the relevant interrelationships. The process of attempting to use the model as a map can bring clarity to that which is being explored.

Inviting others in, setting up for conversations

So I’m new to a blog. What sort of engagement does it fit?

I live in rural Vermont – moved here a dozen years ago and settled in. I earn a living largely through providing tech skills to local schools and businesses. I’m interested in yoga & related knowledge (ayurveda, nad & swar yoga, tantra, &c), Sufi & Buddhist traditions, and other spirit-traditions.

I initially created this site to hold conversations around Systematics, other systems-related topics, and some mathematical ideas that hold my interest.

Thanks to Tony Blake and a s/core of fellow-seekers, there have been ongoing, though perhaps intermittent, conversations (via deeper-d and earlier online groups) of great interest, generally on topics flowing from the work of John Bennett, particularly Systematics. See web sites and for more on Tony’s work. For more general information on Systematics, see

I met Richard Knowles through the above interests. His book _The Leadership Dance: Pathways to Extraordinary Organizational Effectiveness_ uses the enneagram (9-termed system) in a unique way that I consider to hold great value.

I’ve read much of what Stafford Beer wrote on the “viable system”. The recursiveness of systems in his model intrigues me. That is, the low-level components of a system are themselves (in their own smaller scope) systems. I’ve not found many interested in discussing Beer’s ideas, but would like to.

Reminder to self: put together some words on Bennett and how his ideas have found traction in corporate USA. Sigurd Sr. worked in Organizational Development for DuPont for decades, and shared that experience – the ideas & how they were conveyed & used – with his first child.

I’m going to tag this note with “UniS” – name of a group precursor to deeper_d that I prefer for moniker.

This blog is an unintended consequence

I started this blog not intending to put out some thoughts this way. Nick suggested Word Press as a CMS – content management system for a new web site. My eyes were opened to a whole new way of laying the initial structure onto a web site. Looking into what else could serve as a starting point for a web site, two other CMS programs stand out – Joomla and Drupal. As is Word Press, both are open source.

The CMS is a way to manage content over time. It also provides a base onto which a cornucopia of individual functions can be layered – blogs, bulletin boards, shopping carts, and so on. The work is in getting to know how a particular set of tools works, get to know it in detail, find its stumbly-corners, its strengths. Figure out all the tweaks (settings), what function each provides. Because I’m interested in building web sites, that investment in time and mental energy pays off for the next web site, and the one after that.

I didn’t know that a wellspring of ideas wanting to bubble out would spring forth. So I now have two tasks in “producing” this event called a blog, or web site, or in general, “web presence.” One is getting to know the controls. The other is deciding what to put out there, adding content.

As I write this, I’m realizing that it can be a tool for me to structure whatever’s on my mind, [for instance, going back and putting this paragraph in first person] by putting it out there for anyone to read. What am I thinking about? On what topics would I be interested in engaging in a discussion with another? How do I introduce (mathematical and other) ideas to others that are new to them, how do I share my sense that such ideas may help an interested observer/participant figure out “what’s going on” in our physical, mental and psychic/feeling worlds?

So, less than a week into it, I’ll see where this unintended experiment takes me.


You can find some of what I wrote about a decade ago on N-Grams at . Click on the links for tables to see what N-Grams look like. In my last post I described them as “a collection of diagrams formed using the same mathematical / diagrammatic rules / conventions as the Enneagram, but applied to varying number bases and divisors.” Here are the N-Grams for base ten. Note that the circles for 2, 4, 5, 8 and ten – all with only the prime factors (2 and 5) that make up the base, ten. The circle for 6 is partially gray, because the prime factor 3 generates a repeating pattern, whereas the prime factor 2 does not.

Base Ten N-Grams
Base Ten N-Grams

I’ve corresponded with Shane Roberts who has taken the same idea in a similar direction, calling his diagrams Rotagrams. Shane said I could share his email, (may not be current) systemlover at hotmail dot com. His diagrams include non-repeating patterns, e.g., .125 for 1/8 (base ten) and fractions where the divisor is larger than the number base being used to represent the fraction, mine do not.

Multi-Dimensions & Platonic Solids

Late last century I wrote about three mathematical ideas that hold particular interest for me. (See yesterday’s Math posting for a web link.) All have to do with the basics of number and structure. I went into some detail about ideas,
* the “balanced base 3” about which I wrote yesterday,
* and “N-Grams”, a collection of diagrams formed using the same mathematical/diagrammatic rules/conventions as the Enneagram, but applied to varying number bases and divisors. I’ll say more in another post.

This post is about alternate coordinate systems, in addition to the familiar Cartesian system, where each axis is at right angles to every other axis. The terminology I use is xMy where x is the number of axes and y the number of dimensions being measured. Cartesian coordinates are 1M1, 2M2, and 3M3 in 1, 2, or 3 dimensions. There is a 2M1 system, a 3M2 system and a 4M3 system in which all the coordinates add to zero for any point in space. 2M1 is simply a standard Cartesian single dimension paired with its mirror opposite. 3M2 has 3 axes oriented on a plane from the center of a triangle towards its three corners (or towards the centers of its three sides). 4M3 has 4 axes oriented in 3D space from the center of a tetrahedron to its four vertices (or towards the centers of its four faces). Here is a graphic representing the 3M2 system.

3M2 Coordinate System
3M2 Coordinate System

Coordinates are given in the diagram for points p, q, and y. Point x is precisely between p and q – hence, its coordinates can be determined by averaging the coordinates of p (0,3,-3) and q (2,-3,1). So x is at (1,0,-1).

There are three different versions of 6M3, which I identify using a subscript to the 6, and which I will write here as 6(0)M3, 6(1)M3 and 6(2)M3. The first of these, 6(0)M3 is a doubling of 3M3, each axis pairing with its mirror image. 6(1)M3 has axes oriented from the center of a cuboctahedron (Bucky Fuller calls it a Vector Equilibrium) to its vertices. The 3M3, 4M3, 6(0)M3 and 6(1)M3 can all be easily lined up with the tetrahedron, octahedron, and cube. There are more complex systems, 6(2)M3, 10M3 and 15M3 that line up with the icosahedron and dodecahedron.

Kirby Urner has a different take on what I call 4M3. He named his form quadrays. More info on this can be found at