The Sandorian Grove - Tag: toth diagram    
 Hitlist of the major flaws in Human Thinking11 comments
picture16 Nov 2009 @ 00:24
Gotamo Siddharto,aka the 'Buddha', was said to have proclaimed 2500 yrs ago that at the root of the confusion of human Beings we would find the misunderstanding about the true relationship between 'cause and effect'.

This is an interesting statement, in especially considering that 'cause and effect' is a polarity, a pair of complementary opposites, two-sided, in Pali, literally 'dukkha' (commonly mistaken for 'suffering', cp my rantings in the Purple Notebook on that subject). That means it would have been included already in his "3 negative properties of Universe". Leaves the case that Gotamo perceived 'cause&effect' as a super-polarity on top of his 8-fold path of 'oba-odus' (see Polar Dynamics 1 on that).

In any case, true to his Vedic heritage of his times, he expressed these 3 negative properties as a triad of 'doshas', the negative qualities or imbalances of the 'positive' triad called 'Gunas:

1. Every manifestation is two-fold (sabbe dhammaa dukkhaa)
2. Every manifestation is unstable (sabbe dhammaa aniccaa)
3. Every manifestation is non-identity (sabbe dhammaa anattaa)

One could now contemplate that the 3 flaws ('doshas') could well be an 'axiomatic system' of the failure in human thinking, consideration, and ability to conclude and deduct.

Let's look at more 'modern' thinkers and tinkerers: flaw #3 was expressed in its own way by Count Alfred Korzybski, founder of 'General Semantics', famous for the sayings "the word is not the thing". "the map is not the territory", etc.

Flaw #2, the concept of "semper flux", "nothing is permanent" was reflected and solutioned by Korzybski very well in his 'time binding' concept.

Flaw #1 is not very broadly known or used, at least not explicitly. Besides some secret modern Gnosticists, it was only Hegel to consider the 'pairs of opposites' as a central problem in philosophy. His followers promptly 'sequentialized' it in to separate issues: thesis,antithesis, and synthesis by introducing a timeline. The 'dialectics' has been too much distorted to serve as a criterium for assessing the flaws in the thinking of modern man.

Hubbard had a clear view of this concept but only a limited handling. He expressed the concept of the Gunas triad as 'doingness, havingness, beingness' and saw the basic relationship to 'goals' of humans but his resulting 'GPM handling' (Clearing Course) was so flawed that it produced serious problems.

So, let's see a tentative hitlist of the 'Major Flaws in Human Thinking':

1. Misunderstanding of the Cause&Effect relationship (Gotamo)
2. Improper Identifications (Gotamo, Hubbard, Korzybski)
3. Distorted time (Korzybski)
4. Polarizations (Gotamo, Patanjali, Hegel, Nordenholz)
5. thinking in 'absolutes' rather than 'relatives' (Korzybski, Hubbard, NLP usage of absolutes like 'to be', 'always', never,' etc..)
6. Thinking in Singularity/Solipsism (aka the Yaltabaoth Syndrom)

did I forget something?
aah, nothing new from academix since Adorno.. (who was chewing upon Hegel)
;-)  More >

 Buying my own paper from over 18 yrs ago...3 comments
picture5 Oct 2009 @ 15:05
By now nearly 6 years ago, my ex threw out most of my books (some claim she burnt them), including the legendary "Proceedings of the 4th World Conference on Robotics Research 1991/1898" which contained a paper of mine. Lost forever?

Far from it - thanks to the miracles of the Internet, my paper of more than 18 years ago resurfaced. offers all 11 pages of it for precisely 18 bucks (one dollar per year?) as a pdf for download or shipped in printed form in 24-48 hours, see [link] . The best parts, its colorful diagrams, are missing, 3 empty pages at the end are staring at me instead.

Of course, you can also buy the entire "Proceedings" of this legendary world conference, hosted in 1991 by the Carnegie Mellon University [link] for the modest sum of 132 greenbacks. A prophetic work, indeed, going at the same time backward and forward in time, spanning 103 years, and, according to vendor, first published in June 1988 by the Society of Manufacturing Engineers [link] , three years before I presented the article: "Software Development Concepts For Intelligent Control Of Concurrent Processes". Some time-traveling in the style of JD Flora [link], for sure.

Now, seriously, the power of documentation via the Internet extends itself backward into time. If this trend continues, we will see Cesar's ORGINAL 'De Bello Gallico', annotated by himself and his ghostwriter(s), perhaps published by Thomson Reuters under the heading 'Science' with subheading 'War'. Who knows?

For now, I still need to recover a thesis of mine from 1979, burnt by my mother in 1985, presenting a 'Meta-Parser for Compiler-Compilers', a precursor to my 'ConCur' system, precursor to the Toth diagram [link] , for the bold project of my mentors Wirth and Piloty to create a computer language to create computer languages and to model the world as such once and for all! (see Digital Physics [link] ). But, don't worry, I let Tony Smith [link] fight it out with Wolfram & Fredkin.

In any case, I bought my own paper back today and it feels strange to read my predictions about the future of computer programming languages. 19 years ago already ahead of today.

(see for example [link] that I RT-ed (retweed or re-twittered?) some days ago after receiving the link from Lionel [link])

Well, well, well...  More >

 The Solfeggio Scale on the Toth Diagram20 comments
picture3 Aug 2009 @ 18:35
Little Anthony wasn't satisfied with the tuning of our guitars and retuned all of them the other day. With just a bit more than 2 years in this world, he didn't conform with our self-set musical standards. A good time to think about tuning (once again) and see where it may lead us.

Mathematically the base of 440 Herz in 7-stage tonal system is a bit strange, quite chaotic, some say. But what else is out there?

Well, there is the Solfeggio scale (not to be confused with the Solfège method!), of course, and I took the opportunity to tune down from 440 Hz to 417 to get in range. The result was a real mind opener (or should I say heart opener?)

In any case, hearing is believing but unfortunately not a lot of music exists (yet) that is based on this tuning and some that do exist have some errors, like some videos on that promote the concept as a meditation tool.

Of course, after playing a bit on the newly tuned guitars and bass, one of the first things that I checked out was the claim that the chords that seem more harmonic would be within the same numerical 'group' of tones, namely:

1. 174 417 741
2. 285 528 852
3. 396 639 963

Wow! That IS interesting. Magick ;-) Check out the diagonal sums too ;-)

Next step, you guessed it, let's look at where the frequencies would be on the Toth diagram (see drawing)! To allocate them without further own meditation/contemplation, I used the existing descriptions from the Internet, and lo'n behold, here they are:

(Solfège name / binary number / frequency (Hz) / descriptions by others)
... 285 Quantum Cognition
UT 396 Hz Liberating Guilt and Fear
RE 417 Hz Transmutation, Undoing Situations and Facilitating Change
MI 528 Hz Love, Transformation and Miracles (DNA Repair)
FA 639 Hz Connecting/Relationships
SOL 741 Hz Consciousness Expansion, Awakening Intuition
... 852 Hz Returning to Spiritual Order

We identify the Ifa prime energy (Odu) for 528 as Otura and immediate recognize the next nodes as a clockwise progression as a wheel within the fourfold wheels of the Toth diagram: Otura, Irete, Ogbe, and Oyeku. We can chip in the remaining Odus even without a description of Solfeggio fans as Oturupon (963 Hz) and Ika (285 Hz). For the latter 'quantum consciousness' is an odd description as in Ifa it is the sacred energy of birth (and death).

Then we'll have:
(binary number / Ifa name / frequency (Hz) / descriptions by others)
4. Ika 285 Quantum Cognition
5. UT Ofun 396 Hz Liberating Guilt and Fear
9. RE Oshe 417 Hz Transmutation, Undoing Situations and Facilitating Change
13. MI Otura 528 Hz Love, Transformation and Miracles (DNA Repair)
14. FA Irete 639 Hz Connecting/Relationships
256. SOL Ogbe 741 Hz Consciousness Expansion, Awakening Intuition
0. Oyeku 852 Hz Returning to Spiritual Order
2. Oturupon 963 (?)

Back to the harmonic triangles: the missing corner of the first triangle must have a frequency of 174 or 1074 since all frequencies of the Solfeggio scale are 111 Hertz apart. Note that the sum of individual numbers needed to maintain the phenomenon of equal sums is PRESERVED either way: 1+7+4=1+0+7+4=12 (the other triangles add up to 15 and 18 respectively). This is a very interesting property of the sums of 111.

The ninth energy node (Olodu), we could speculate, could be on the OUTER wheel of the Toth Diagram.

Let's look at the properties of the harmonic triangles that are complete:
Ofun-Irete-Oturupon are all describing spiritual qualities, and Ika, Otura, Oyeku are on the emotional and basic life side, the side of what I came to call the 'soul side'.

The triangles are composed of two Odu nodes of a basic wheel in sequence PLUS one Odu node of the 'super wheel of manifestation', Ogbe, Oyeku, Ofun, and Oshe.

The subgroups that produce harmonies are triangles within the wheel, namely:
1. ?, Oshe, Ogbe
2. Ika Otura Oyeku
3. Ofun Irete Oturupon

OK, let's look at the binary code:

1. ? 1010 1111
2. 0100 1011 0000
3. 1010 1101 0010

Obviously, (2.) results from (1.) by adding a binary '1' and (3.) from (2.) by adding 2 (binary '10'). Therefore, if the internal math would be consistent, the missing Odu node would have the binary code of 0100 minus 1 and that would be 0011 which is Owonrin, the upper left node on the Toth diagram.

Owonrin is characterized as 'form' in contrast to 'essence' (irosun), slow or frozen flow in contrast to energy bolts, mental images in contrast to 'movies', giving permanent shape to things. The frequency (174 or 1074?) would result in moods of creative contemplation, imaginery, phantasy, but easily also slowing down energies, in this sense relaxing. Owonrin, in 'classic Ifa' is the bridge between 'will' and 'physical manifestion'.

As a temporary final note, the 'sound of creation', as a chord, would be 'Owonrin-Ogbe-Oshe', (174,417,741 Hertz), and whoever knows Ifa good enough, knows the above combination very, very well. The Universe is a woman, one might conclude from the above, if it wouldn't already be clear enough. The 'sound of silence' (oyeku) together with the 'sound of the heart' (otura) results in life (Ika, which, as a name, also contains the root of literally 'heart'): 285, 528, 825 Hz. Finally, the great harmony of the spirit would be the wisdom of Ofun, the relations within the world (Irete), and the ethics and sovereignty of the spirit (Oturupon) as 396, 693, and 963 Hz.

Hmm, time to get back to the noise-making toys, eh.. tools, and play with that after playing enough with numbers for now :-)

PS: Aug 6th: I corrected the binary writings of the odu since I goofed. And found that the math is not as clear for the first column. It is still Owonrin (as I happen to know through other sources) but one doesn't arrive there by simply subtracting 1. I left it there because it is still fascinating. I also made the graph a bit clearer since several people wrote me that they couldn't see the basic loop. You can look at the Toth diagram description earlier in this BLOG to verify the sequence. In itself it is quite amazing, lending credibility to BOTH the Toth Diagram and the Solfeggio Sound Theory.
Also, dear reader, check out the sound files Mortimer made (see the 'comments').  More >

 Linking the Toth Diagram to Traditional Sacred Geometry5 comments
picture23 Jul 2008 @ 14:57
Before going more in depth and height of abstraction, I want to demonstrate how the Toth Diagram links into Traditional Sacred Geometry (see picture).

The importance of making this link is not to create new paradigms but to enrich the existing ones by adding the quality of energies in its constructing points, elevating the tetrahedron construction from a fancy geometric structure to a meaningful tool.

With the help of Buckminster Fuller's Tensegrity paradigm, and the mirrored-down structure of the 'second binary split' or 'level of four', we can demonstrate that each and every point in the Toth Diagram and the corresponding tetrahedra is clearly defined and MUST assume its position.

(With the help of the Concur Principle we can also construct maps for the higher (lower?) dimensions which created those, in especially the 'Level of Four', in Ifa called the 'four types of ashe', the four cosmic powers whose flows are breathing in life into the creation. We will see that the nodes of the Toth Diagram not only represent a cellular automaton but that they are the nodes of a waveform system as already demonstrated in one of the pictures in the last article.

For now, if you remember...  More >

 The Toth Diagram28 comments
picture19 Jul 2008 @ 21:22
The Toth Diagram

A binary. balanced graph with a depth of 4 levels will have 16 end leaves. If, as postulated by Steingrubner (1988), new branches rotate at 90 degrees with every binary split and we then make a cross section at the bottom level, we arrive at a diagram that I want to call the Toth diagram, in honor of my grandfather Janos Toth.
It is a cross section of a graph following the Concur Principle (Steingrubner, 1990) which postulated that a perfect model of an entire Universe can be represented as a balanced binary graph and that the very same model also represents all possible events within that Universe if it were to be used as a finite state autamoton (postulating a structural identity of "object" and "method"). Furthermore, all laws of that Universe are enclosed in the transitions of the unfolding levels as an LLR grammar. The rotation at every level serves, amongst other reasons, is required to satisfy the orientation rules of basic fields in nature such as found in the laws of electromagnetics. It is with these rotations that one arrives from the originary binary code sequence at a 3-dimensional graph, the Toth diagram. The strength (or weight) of nodes in ConCur is determined by the length of their vertices, adding a movement in time, a 4th dimension. If regular, it could be compared to a "pulse" of the represented Universe.
It was not until the late 90's that I encountered the vast knowledge contained in the Ifá. philosophy. Only the qualitative descriptions of the basic primal energies in Ifá, the sixteen "olodu", convinced me finally that in fact also our own Universe can be modelled as a Concur Graph of degree 4. To qualify as a complete model, it must contain an "axiomatic system" that leaves no part of the model unclassified. Already Philip Neimark ([link]) had arrived in the 90s at a condensed description of the sixteen Ifá principles or energies but to extract a more precise description that would satisfy as an "axiomatic system" took some more years during which I received much help and inspiration from Edward Dawson who then co-authored the book "Polar Dynamics 1" which, with all its pluspoints and drawback, still is the only book published that makes a serious attempt to "rationalize" the profound wisdom contained in traditional Ifá which until then was never systemized comprehensively.

Some time after the publication of "Polar Dynamics 1", the importance of the four fundamental progressions of energies, the "olodu wheels" became apparent and it was included as an addendum to the Italian version of the book "Your Personal Archetype", the first comprehensive and intelligible collection of today's archetypes based on the analysis more than one thousand individual life paths, authored by Sandor, Dawson, and Miranda.


What was still missing,  More >