On the Sumerian division of the circle into 360 degrees

In his brandnew book

Farrell, Joseph P.: Genes, Giants, Monsters and Men. The surviving elites of the Cosmic War and their hidden agendas, Port Townsend, WA, USA: Feral House 2011

the author is dealing – among others –  with problems of ANCIENT MEASUREMENT METHODS, saying something like, that ” there from facts in astronomy the circle should be divided into 366 degrees – at least on Earth -, which however was replaced by the Sumerian system of 360 degress within a circle”.

Well, we might say, that this is just common tale among historians, causing a LOT OF TROUBLE among authors, because they NEVER – even with mathematical STRICTNESS – will be able, to “HARMONIZE”, the NUMBERS in circles derived from orbits of VENUS, MOON and JUPPITER, the orbits of which we have in Babylonian astronomical tables, right down to ancient Greek times of the Library of Alexandria.

Now, we may question, whether HARMONIZATION was the GOAL of the Sumerian system at all, which does not fit into astronomical observations, but – odd enough – by authors normally is seen as SO MUCH PRACTICAL in everyday computation, which we are going to question likewise, at least  inasmuch if seen as GOAL of the system.

Well, our NEW IDEA is LAUGHABLE EASY, and everybody can grasp the genial simplicity behind the Sumerians as follows.

If we have mathematical problems of a very wide range from number theory to geometry, we all know, that things improve DRASTICALLY, if using a CARTESIAN SYSTEM with x,y,z coordinates. The FUNCTIONING of this MERE AUXILIARY CONSTRUCTION is, that it allows DEFINED RELATIONS among OTHERWISE disturbing peculiarities, and from DEFINED ORDER in an AUXILIARY SYSTEM we in today school mathematics or basic mathematics have all this stuff about “ABBILDUNGEN, groups, manifolds,relations,orders” etc. pp.


THE SUMERIANS MADE AN ARTIFICIAL CONSTRUCTION in DIVIDING THE CIRCLE INTO 360 DEGREES – and they did so, NOT, because problems and figures and numbers were intended to harmonzise – which they mathematically NEVER will – but to PLACE BY DEFINED PROJECTION ANY OTHER THINKABLE DIVISION OF THE CIRCLE INTO THIS NEW EQUIDISTANT DIVIDED CIRCLE of their 360 degrees. And they could do so with success, because the DIVISION OF THE CIRCLE WHATEVER is BOUND TO THE INVARIANT ELEMENTS OF SUCH UNIVERSAL SYSTEM, which is just the HALF-DIAMETER and A DEFINED  OPERATION, which is just going around ONE FIXED POINT of the half-diameter ONCE, so to constitute the CIRCLE ITSELF, which by the way our teacher in mathematics did on the school-table very similar to the megalitic people or to any unskilled worker in houseconstructing today – a byside effect of this DEFINITION OF THE INVARANT ELEMENTS OF A CIRCLE being, that the  “circle-constant” PI is NOT NEEDED, and may be introduced later under other mathematical demands.

There was one little word, which cannot go unnoticed, the word “EQUIDISTANT” – which we see in operation, if TRYING TO DIVIDE THE MUSICAL OCTAVE into EQUAL PIECES as well – which in nature DO NOT EXIST. Farrell, Joseph P. in his GIZA DEATH STAR very decisive is hinting to two things,

a) that the ancient Greeks KNEW this socalled “gleichstufig-gleichschwebende Temperatur” ( “equally tempered division of the octave” using 12th root of 2 as ONE DIVISION UNIT and producing equidistant steps of progression )

b) that you normally do not need such an equally tempered musical tone system for MUSIC, but rather for to CONSTRUCT UNIFIED SYSTEMS.

And indeed we have in music the “Circle of Fifths” – as we have in astrological use of astronomy a CIRCLE of the “birth chart” and other astrological charts, which latter is just an ARTIFICIAL METHOD for MEASURMENT – or more tangible: “rough maps” – of the sky.

In other words: With exactly this we imply, that INDEED there might have been in Antique and Sumerian times a DEGREE OF UNIFICATION, produced by very abstract mathematical ideas, that were reinvented only in the last 100 years or so – and RATHER FRUITBEARING – for which we now have 2 KNOWN EXAMPLES from quite DIFFERENT fields of knowledge, that is music and “simple”  star-maps.

In modern mathematics we now would proceed from equidistant rows to Dedekind scission and related construction of socalled epsilon-proximities (or: epsilon-neighbourhoods, something from the manifold-theory) ) – and we apologize, if the professional mathematician would apply even more advanced theories, we as a hobbyist of course didn`t become aware of so far. This is a somewhat complicated approach to question again, why a subdivision of 360 had been chosen, that is: why it might have been chosen beyond its PRACTICALITY in BASIC COMPUTATION OF NUMBERS.

Well, we might say: a subdivision into 360 equal parts is very. very remarkable IN ITSELF  in times of old history we normally see as some sort of “primitive stoneage”. Just imagine the DIFFICULTY to DIVIDE SOMETHING into a MANIFOLD of 360 single pieces at all!  Secondly we may say, that the Sumerian division method was RELATED to grade of COMPLEXITY in APPLIED MATHEMATICS of that rather old history. Because, everything we know from SCHOLARLY ANALYSIS of MATHEMATICS by professional mathematicians – Otto Neugebauer for instance or B. van der Waerden or others –  in times of Egyptian “Papyrus Rhind” – if we are not mistaken here – or in Sumerian cuneiform tablets dealing with DOING maths or in ANTIQUE Greek astronomy, is hinting to an ITERATIVE mathematics based on BASIC computing operations as we have today in our common school-books on maths, plus, we may assume, certain RELATIVELY EASY methods of INTERPOLATION, as were for instance  in use in trigonometrical tables from 19th to mid of 20th century, wandering from NAUTICAL navigation to schoolbooks of secondary education. Thirdly we may hint to the fact, that a subdivision into 360 parts will not only improve calculation with numbers, but will lead to surprising good approximations regardless of the “primitivity of elementary school-mathematics” we normally see as the only possible methods at hand in antique times.

So we see not very clear here, we may put a NEW SUGGESTION, that a division into 360 parts was chosen because of the DEMANDS of mathematics of the time AS APPLIED TO OUR SOLAR-SYSTEM and a PROPER handling of calculations and numbers, but NOT AIMED TO TODAY EXACT, not only because they could not manage to have such exact measurements, but BECAUSE THE INTENDED GRADE OF UNIFICATION for an INTENDED THEORY FOR EVERYTHING in THAT TIME OF HISTORY would NOT NECCESSARELY NEED it! It would not need it, because the interest was restricted and NOT DIRECTED TO DEEP SPACE, at least not under our today horizons of questioning and search in astronomy.

We see not very clear here and may add another possibility: The introduction of the Sumerian 360 degree circle was not only intended as HELP for to solve certain problems of application, but vice versa a RESTRICTION, a PROGRAMMING of the HUMAN MIND, a MIGTHY indirect method of MIND CONTROL, that indeed worked out to the  perhaps PLANNED DEMANDS of the PROGRAMMERS THEMSELVES, because this method not only survived MILLENIA, but even is in use until today – in spite of the fact, that it might be for today scientific horizons a USELESS LIMITATION, mankind however could not get rid of so far! To give an exemple: NOBODY so far to our knowledge ever suggested a division of the circle into 100 or 1000 degrees. NOBODY so far came forward in GIVING UP the concepts based on circles and spheres – and taking a double Giza-Pyramid as CRYSTAL-TYPE MODEL of planet earth – or other heavenly bodies – which, if considering PLATONIC SOLIDS, however MAY have been in place in old antiquity, especially because of the links between pyramids and TETRAHEDRAL structures, see which  play an important role in Richard Hoagland for isntance.

We see not clear here and may add a further observation: It is remarkable IN ITSELF to find in OLD ANTIQUITY something like the IDEAL CONCEPT OF CIRCLE at all. Because if we look to today astronomy we find since KEPLER and COPERNICUS ELLIPSES as MAIN EQUIVALENT of the MOVING of heavenly bodies, to which modern astronomy has added a MANIFOLD – up to 20! –  of OVERLAPPING FORCES, which led to the impression that the ELLIPSE itself is just an IDEALISTIC APPROACH far away from anything “exact”  – and that in REAL there are out there MAINLY DEFORMED ELLIPSES in a MULTITUDE of SPECIAL appearences.

[Indeed in 2015  Buike research has delivered a very short paper “No planetary Kepler-ellipses in our system”, wghich was reexamining datas for excentricity and perihel-aphel-distances as given in Wikipedias, showing VERY IMPRESSIVE CLEARLY that ALL MAIn PLANETS are moving on MINIMAL DEFORMED CIRCLES, which would lead to the question, whether this might have a TECHNOLOGICAL reason?!]

So to say, the today ORIENTATION to EXACT EMPIRICAL DESCRIPTION led to some sort of CONFUSION BY DIFFERENCES IN EACH SINGLE EXAMPLE. In other words: IF WE SEE OLD ANTIQUITY in some way NOT INTERESTED in EXACT DESCRIPTION OF EMPIRICAL FACTS, THIS AGAIN MIGHT BE CONNECTED to the overall specifics in old antiquity to have some sort of UNIFIED SYSTEMS. To put it mathematical: IF WE TAKE THE CIRCLE INSTEAD OF THE ELLIPSE we have introduced INVARIANCE AGAIN, because EVERY ELLIPSOID can be transformed into a circle IF TAKEN ONLY THE SAME CIRCUMSCRIBED AEREA. And very certainly: To concentrate on INVARIANCE instead of detailling variance as we today are used to, is a SURPRISING GRADE OF ABSTRACTION required only for the demands of some sort of  “higher” rational-building.

This would mean, that the division-method of the circle of the Sumerians WOULD NOT BE SUFFICIENT, to build the PYRAMID OF GIZA, for which indeed Farrell, Jospeh P. in his 3 volumes of the Giza-Death-Star asked for QUANTUM-computers (!!!) … which TODAY we are searching for, but it WOULD FIT into an OVERALL LONGTERM STRATEGY, TO PRESERVE KNOWLEDGE AND SCIENCE after all the STRUGGLES, which followed the LAST INTERPLANETARIAN WAR and its near to extinction devastations including the blow-up of the lost planet, that formed eventually the today Asteroid Belt, covering say a span of time from 10 Million years down to 2500 years ago, if at least we take Sitchins reintepretation of the socalled “SECOND war at the pyramids” as referred to in Sumerian tablets into account.

This argumentation would fit into Farrell`s latest book as cited at the beginning of this paper, dealing with those supposed longterm-strategies. Such we would argue, that we have with the Sumerian division of the circle jet another piece of RESTS FROM FORMER FAR ADVANCED UNIFIED THEORIES, with the special characteristis to BRIDGE DARK AGES – but NOT TO DISMANTLE those NECCESSARY TO BE POSTULATED advanced theories of very old.

Not to dismantle is just the reverse of  Plato and other authors from Antique Greece to KEEP SILENCE – which is just the opposite the today NEW hyper-physics does, the appearence of which HOWEVER from view-point of longterm-strategies is INEVITABLE, IF A DEVELOPEMENT WAS FAR ADVANCED ENOUGH – so to say: for better or worse. In CONTRAST to those old times we however may say, that the REAPPEARENCE of Unified Theories in ELABORATED form THIS TIME is done by a MANKIND ASCENDING BY “HERSELF” – the process of ascendence very probably pre-programmed including possibly some security-locks in some way or another installed by WHOMEVER.

If we today CONTINUE this line of developement, it is far from prophecy to see a NEXT Interplanetarian War coming …

But we may close here with the following question, using a traditional language to put our idea, for which we may apologize to the “hardcore” natural scientist:


Or in other words: FOR ENGINEERS especially with the degree of today “enlightnment” it may seem attractive, to “solve” the DIVERSITY of nature by UNIFYING her NEGLECTING quite a lot of “details” to invariance: BUT WHY WAS THE CREATOR SO MUCH INTERESTED IN HAVING JUST THOSE DETAILS DISTURBING TODAY PHYSICISTS – representing PERHAPS quite ANOTHER SORT OF UNITY, quite MORE COMPLEX, than today TRIALS for unified theories???

We – by the way – must not stop in stating, that the Sumerian circle and its division was just an ARTIFICIAL AUXILIARY – but may proceed to the assumption, that if so, the SPHERE OF THE HEAVEN – or ZODIAC –  was an ARTIFICIAL AUXILIARY as well – at least UNTIL those dark ages, that FORGOT, what is preserved in curriculum of geometry until 19th century, which are socalled PLATONICAL SOLIDS, which normally can be INSCRIBED INTO A SPHERE, from which there is a conceptual bridge to the TETRAHEDAL PHYSICS PREVALENT IN SPACE as brought forward by RICHARD HOAGLAND (and referred to frequently by Joseph P. Farrell) …

We may say further: The CIRCLE is NOT the target of this kind of CONCEPTUALIZATION and BUILDING RATIONALS, for what we see in LIVING SYSTEMS and in the UNIVERSE are SPIRALS, which in more recent trials for theories eventually led to theories of VORTICES, which they try to combine with today ETHER-Physics and VACUUM-Physics …

So in the end we see the circle and its division into 360 degrees  rather CRITICAL, in that it MAY have been some sort of GIFT ENABLING mankind to a CERTAIN RESTRICTED DEGREE – and DISABLING MANKIND AT THE SAME TIME from even search for OTHER concepts and divisions, say for circle divisions MORE ADAPTABLE TO OTHER PLANETARIAN SYSTEMS and even OTHER GALAXIES.

This last remark clearly implies, that one of the longterm-strategies NOW IN PLACE ON EARTH, MAY INCLUDE SOMETHING NEAR TO QUARANTINE – set up PERHAPS AFTER the last great interplanetarian war – by WHOMEVER, but a “whomever”, that CERTAINLY must have had at his command HIGHER METHODS and TECHNOLOGIES, than those VERY ADVANCAED PARTICIPANTS of the last interplanetarian war, say on the “administrative level” of our galaxy or “galactical sector” , not just on the level of the planetarian system and its probable “maintenance gropu”!

So EVERYTHING is OPEN – and REMAINS OPEN – for nobody can predict, what MANKIND will do next, what mankind will do THIS TIME and HOW OTHERS would react to that – which even would be of a very restricted importance, because planets and stars in THIS UNIVERSE are COMING and GOING every day, not hindering the universe to show something very disturbing, in that it SEEMS, that there is at work EVERY DAY some sort of “creatio ex nihilo” leading to EVER NEW CREATION as if the universe is REJUVENATING BY ITSELF instead of the dead ends and death-scenarios the OLD concepts in astronomy were suggesting, as was the Zim-Zum-concept in elder HEBREW writings, as for instance dealt with in books of Gershom Scholem, a RATHER “rational” author indeed.

So far our conclusion with regard to the Sumerians may be put like follows:

The Sumerian CIRCLE and the Sumerian DIVISION of circle are not only hinting to UNIFIED THEORIES of some sort aimed to handle variance by INVARIANCE – but with the same token may be seen as hint, that choosing such advanced mathematical concepts was REQUIRED, IF the Sumerians would have had intended to ENGENEER TIME AND SPACE by some UNKNOWN TECHNOLOGY, which may have had implied certain DIRECT MIND-MATTER-BRIDGES, which would imply some sort of what we call today BIONICS, of which we however may have relics in form of TEMPLES, which just do exactly that: that they CONSTRUCT AN IDEAL IMAGE OF COSMOS AND EARTH by use of invariances, which can be ENTERED BY SPIRITED OBSERVERS (or visitors) OPERATING BY USE OF TECHNOLOGY AND MIND SUCH ARTIFICIAL ENVIRONMENT. In other words: the TEMPLE such would become some sort of MIND-MATTER-GATE to OPERATE SPACETIME, that is: some sort of RATHER complicated MASHINE.

WHICH HOWEVER MAY NOT COME NEAR A COMPLETE interpretation, but just may be  a PARTIAL view LIMITED to the LIMITED perception of this today writer!

And ONE of those LIMITATIONS are SPECIAL EVENTS, that may or may not take place in such environments, IF “event” seen as some sort of “behavior of time”, as some sort of “force” inducing effects on ETHER and SPACE.

There is a last observation: ALL THOSE GREAT and IMPRESSIVE TEMPLES of old antiquity are GONE FOREVER. Indeed in Christendom EVERY SIMPLE ROOM can become “conceptualized temple”, a “virtual temple”, which however at best is showing REMINISCENCES only to old very elaborated examples of REAL  temples. In mathematical terms: “every room” enabled somehow to become a “virtual temple” would IMPLY to introduce SOME INVARIANCE of  ROOM or SPACE!!! Question is: WHAT DOES THIS MEAN? DOES IT MEAN, THAT MAN HAS BECOME THE TEMPLE and that THEREFOR any “MATERIAL TEMPLE OF OUTSIDE WORLD AND REALITY” is NOT LONGER NEEDED, “because” it has become “useless”??? And IF so: HAS MANKIND WITHOUT THOSE OLD TEMPLES ENTERED a NEW STAGE OF DEVELOPEMENT under a NEW “PROGRAMMING”??? Say perhaps, BECAUSE of the “Christos-EVENT” and its INDUCED CHANGINGS IN SPACETIME ITSELF caused by “density of time” in the direction from cause to effect as Nikolaij Kozyrev`s theory would postulate – presenting NEW FREEDOM and NEW RESPONSIBILITIES???

follow up 23.04.2012 —

Valery Uvarov, The Pyramids, 2007 – free pdf –  is presenting the following geometrical interpretation of ANYTHING, that can be divided into 12 equidistant pieces: THE RESULT WILL BE THE SOCALLED SMALLEST POSSIBLE PYTAGOREAN TRIANGEL with 5,4,3 or 3,4,5 lengths of sides. He does not stop here but goes on to USE of this special triangle as socalled “Steigdreieck” or “gradient triangle” as in analysis of functions of whatever type, in which geometrical context it suddenly turns out, that the HYPOTHENUSE with lenght of 5 is representing a FREQUENCY in rather strange looking writing! In the next step Valery Uvarov identifies a relation with this hypothesnuse 5 gradient triangle and a frequency of 54 – which he identifies as THE BASIC HEART BEAT OF PLANET EARTH (for which one would need to calculate propper interpolations from Russian UNIVERSAL SCALING research, which however seems at moment under heavy discussion and – sad to say – not free of moral allegations against one of the more prominent exponents from fromer DDR in  this research …)

Well, what might be the MEANING of this?

I may GUESS:


b) The second thing is, that every division on basis of 12 is hinting to SYSTEMS IN SPECIAL RESONANCE WITH BASIC FREQUENCY OF PLANET EARTH – which again is hinting to intelligent SYSTEM DESIGN, this time system-design by SET OF SPECIAL NUMBERS for our SOLAR SYSTEM, and thus hinting to a SPECIAL GROUP of SYSTEM-LORDS of this planetarian system – and by recursio ad infinitum to GOD in his manifestation as “creator of everything” …

I may close this follow up from diverse hints in Uvarov and Nassim Haramein, that there is a PROOF FOR THE EXISTENCE OF GOD (in his manifestation as “creator of everything”) FROM ASTRONOMY and astrophysics of TRUE SET UP and TRUE movement of our solar-system. Or in other words: Our solar system has LOTS of hints – that only due to STATIC models in elder school teachings were camouflaged -, that it NEEDS an Administrator-Group to come INTO existence, plus that it NEEDS an Administrator-Group to STAY into existence – AND NOT ANY REASONABLE DOUBT ABOUT THIS POSSIBLE – and therefor the BEST PROOF for the existence of God, that ever came to my knowledge!

But BEWARE to OVERDUE it – and to offer your doughter to the first and next E.T or Alien, claiming administrator-abilities for marriage … because from Greek mythology and from Old Testament stories of GIANTS with GIANTIC abilities, everybody easily may derive, that they more often showed just VERY humanlike ” weakness in flesh ” …

Well, I have warned you: stick to science and otherwise be on guard!

— xxx—

Addition 2016

In meantime my studies went on and we now may add the following:

In first place the Sumerian 12-60-system to which 360 degrees of a circle belong is a DEDUCTIVE system taken from ONE  REMARKABLE GREAT NUMBER, which is – if I am not msitaken here – 12.960.000.

Secondly we may derive from Uvarov, valery – even if this outhor is heavily debated – the idea, that there might have been astronomical matches, a) 360 days as ANOTHER ORBIT-duration for planet Earth and b) 3600 years  as oribit-duration for this enigmatical “Annunaki-planet” NIBIRU, what ever it might have been.

Thirdly I may hint to the Papyrus Rhind 1800 BC, where we find the METHOD of SQUARING THE CIRCLE, in which is unspoken CUBING the SPHERE, in which is unspoken the TORUS (if derived from square), in which is DOUBLE method for PIXELING , which would have a bearing on today discussions about a HOLOGRAPHIC UNIVERSE “pixelled” in EXTREM SMALL “Planck-Spheres”.

And last but not least: In “”squaring the circle” we have CERTAIn DISCRETE NUMBERS, that would eventually lead to MUSICAL KOMMATA from DIVIDING AN OCTAVE – octave definded as 8 steps or as 8-1=7 steps withouut repetition -, which eventually would lead to a METHOD for UNIVERSAL SCALING especially if searching for THEORIES FOR EVERYTHING. NO JOKING here, there are out there phisicists, that INDEED are trying the OCTAVE as suitable means for to build an universe on FREQUENCIES.

And very sorry: I do not know better AT MOMENT – and have no guarantee, that I will be able to improve in these fields of knowledge, that once were PROTECTED by the socalled 2ANTIQUE SECRECY”, which perhaps NEVER EVER was broken by JUST HUMANS!

Buike Science And Music


About bbuike

- *1953 in Bremen / Germany - since decennia in Neuss / Germany - classical composer (registered since 2005) - scientific freelance writer - registered to German National Library "Deutsche Bibliothek", search "Bruno Buike", with 246 items in 2013 1996-97 - 5000 qm Rekultivierung Obstwiese mit Kleintierhaltung 2004/05 - 3 Wochen Gartenpflege in einem orthodoxen Kloster in Deutschland 2009 - 3 Wochen Katastrophenhilfe Einsturz des Kölner Stadtarchivs 2011 - journey to Przemysl/Poland - and learning of basic Polish vocabulary and reading/pronounciation 2013 University of Tokyo - Conditions of war and peace - Coursera - Certificate 2013, December - after 15 years in mainly Russian-orthodox and Greek-orthodox affairs return to Roman-Catholic church 2014 National University of Singapur, Conservatory - Write like Mozart. Introduction to classical composition - Coursera Certifikate "with distinction"
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