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I was introduced to computers in 1965, and had a continuing interest (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 dustbin of computer evolution). In the same room as the G-15 were a number of analog computers still in use. They approached problem-solving through modeling systems in electronic circuits.
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. The main memory was not 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 quick as possible.
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 moved 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 (from wiring circuits to managing a lightly used unix system to working on an Old English Concordance). That evolved into a job supporting those using the newly-introduced IBM PC and then Apple Macintosh and later 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 led us to seemingly unending new realms for evolution – beyond the hardware and the range of tasks it could automate to catalyzing the transformation of many aspects of society.
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 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 www.centerforselforganizingleadership.com/ 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 (.oo, .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
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 www.duversity.org/ and www.toutley.demon.co.uk/ for more on Tony’s work. For more general information on Systematics, see www.systematics.org/pmwiki/pmwiki.php.
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.
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 www.solbakkn.com/math/n-grams.htm . 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 I’ve corresponded with Shane Roberts who has taken the same idea in a similar direction, calling his diagrams Rotagrams. Shane has a web page at www.myspace.com/systemlover and said I could share his email, systemlover at hotmail dot com. His diagrams include non-repeating patterns, e.g., .125 for 1/8 (base ten), mine do not.
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 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 www.grunch.net/synergetics/quadrays.html.
I add the (trademark) because the phrase is claimed (along with “prana calendar,” “inner tuning” and other phrases) by Shyam Bhatnagar, who along with his one-time close companion Harish Johari were important influences in my life. I will not go into detail, but have been disappointed in how Shyamji has led his personal life, and have broken ties I once had with him. I still hold in high value the ideas to which he introduced me, some experiences for which he was a catalyst.
He uses the term “micro-chakras” in the context of human development. Each of the seven (major) chakras has within it a sort of miniature version of each of the seven chakras. These 49 stages are further divided by the three major nadi-s (or channels – left, right and center – named ida, pingala, and sushumna respectively) through which they manifest, forming 147 micro-chakras. The micro-chakras take center stage in turn as the human organism develops. In the first year of life, energy goes down the right channel, then takes the next 42 or 49 years to go up the right channel (6 years per chakra for females, 7 years per chakra for males). Trauma in one’s life can form blocks in the then-developing micro-chakra.
I see correlations with this model of human development and Abraham Maslow’s “hierarchy of needs” (no reference at hand). We start with a need for grounding, security (first chakra), then for relationship to family and friends (second), then ego and power (third), unconditional love (fourth), and so on.
I recommend the book Chakras / Energy Centers of Transformation by Harish Johari (Destiny Books, 1987) for extensive detail on the chakras and their meanings. It refers to the topic of this post to some degree in the descriptions of the “behavioral characteristics” of each of the chakras.
I (and many others) know Harish as Dada (“older brother”). He wrote many other books – on yantras, breath, ayurveda, Hindu myths – some child-oriented, massage, cooking, gems, numerology, and more. He was a master artist. Among other media, he used layered watercolors with washes between layers. He drew from classical sources to express the gods and goddesses that were often the subject of his paintings. His voice is available on CDs and other media.
Dada and Shyamji have sung sounds that can carry the listener to rarely-visited realms in the seas of the chakra energies.
Some of those who were close to Dada formed Sanatan Society, which has .org and .com web sites.
Publisher Inner Traditions has produced many of Dada’s books, and in 2009 a book by Shyamji with co-author David Isaacs, called Microchakras / InnerTuning for Psychological Well-being [Includes CD of InnerTuning Sacred Sounds].
I have Shyamji’s book. I find myself unable to listen to the CD, nor delve into the text, for personal reasons. However, I do believe its description of [ the components of the being known as "human" and their development through a life ] has great value.
The usual way mathematicians discuss number bases 2 and larger (call base “b”) has them with digits that range in value from zero to b-1. Base ten has values 0 to 9; base two has values 0 to 1. Some years ago I hit on the idea that for base 3, using digits with values -1, 0 and +1 (rather than 0, 1, and2) more closely corresponds in some ways to the working of the world. Values are “on target” or to one side or the other. For numbers expressed in this system, there is no difference between rounding and truncating a number.
A few years ago I ran into Abhijit Bhattacharjee of India via the web. He has a site at www.abhijit.info/tristate/tristate.html with much more information on this idea. In his bibliography at http://www.abhijit.info/tristate/biblio.htm Abhijit says of Donald Knuth:
In 1981, in his book “The Art of Computer Programming”, Vol 2: Seminumerical Algorithms. Second Edition. Reading Mass: Addison-Wesley, pp 190-193 calls it the “prettiest number system of all”…
I now realize this is where I first encountered the idea, as this book was text for a programming course I took in the 1970’s.
Here’s are diagrams representing the “standard” and balanced versions of base 3. Each step lower in a diagram represents adding one more digit of precision to a number. In the upper diagram, all numbers that begin with “0.1…” are equal to or larger than 0.1. In the lower diagram, the value 0.1 is the precise middle of all numbers that begin with “0.1…”.
 Diagram, two forms of Base 3 In the first form, the descending lines from a single point represent the digits 0, 1, or 2. In the second form, the descending lines represent the digits -1 (to the left), 0 (vertical), or 1 (to the right). To get a feel for how this works, here’s how one would count from -5 to +13 in balanced base 3, using “<” for a digit with value -1, and “>” for a digit with value +1: <>>, 0<<, 0<0, 0<>, 00<, 000, 00>, 0><, 0>0, 0>>, ><<, ><0, ><>, >0<, >00, >0>, >><, >>0, >>>. In these three-digit numbers the first is the 9’s place, the second is the 3’s place, and the third is the 1’s place. So the first number in this sequence, <>> represents (-9)+(+3)+(+1)=-5.
At www.solbakkn.com/math you can find more on this topic. It also includes information on N-Grams, and a pointer to information (in a PDF file) on Dimensionalities, two other math topic of interest to me. Eventually I plan to move and expand information about all three math topics on this site.
If I weren’t relatively adept in social situations, I might be said to lean towards Asperger’s. I tend to take things literally, and love to explore the underlying structure of my world. Over the years I’ve explored extensively the ideas of Bucky Fuller (Synergetics), Stafford Beer (Viable System Model), and John G. Bennett (Systematics), among others.
Various spiritual/self-development traditions have been part of my life. I believe our life is a gift, and our implicit task in this life is to find a way to use our being and the circumstance containing us to “good ends.” That includes exploring the measure of “good.”
I’ve found help in “working on self” in a variety of traditions beyond the Christian tradition in which I was raised. These include Hindu (chakras as a model for levels of human consciousness, various branches of yoga, ayurveda, and more), Sufi, and Buddhist traditions, and the “Bennett branch” of what Gurdjieff brought forth.
My thanks to Nick (springercartographics.com, cartotalk.com) for pointing me towards Word Press. Getting this site up and running was a breeze, with the help of web host bluehost.com. I told bluehost I wanted to “apply” Word Press to systalk.org, and in minutes, the site was ready to go. I’m absolutely amazed how easy it was. I’ve edited this paragraph a few times, re-posted, and re-loaded the web page to see the update. And I’m doing all this on a slow dial-up connection! So different from using godaddy’s site (yawn) to redirect dns for systalk.
The interface for administering the site is clear and easy. If Web Press is indicative of where the web is going, I think it’s ready for yet more magnitudes of change – a lot more people will be using the web for a lot more purposes, as a tool for expression as well as a source of information. I’m using and administering my own web site, not relying on Facebook or some other corporate medium.
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