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John Michell: Explorer of Dimensions

A Cooperative Effort

 

Secret Academy

Secret Academy: we can't give it away
It is quite some time since the Secret Academy has been lost in the rat-maze of the World Wide Web. Here it is resurrected by the popular demand of my fan. The web site was first posted around the year 2000 and was about the only site that dealt exclusively with the subject of ancient metrology. There are now many sites that do this very thing and the impact of the Secret Academy on these subsequent sites is exactly nil, ignorance rules ok. The “we can’t give it away” is now reduced to “I can’t give it away.” The main man died in April.
                 I am referring, of course, to John Michell the most underrated true historian of our or any other age. He is remembered only for his scattier pursuits and eccentricities but his true genius is known to very few. He founded the modern search for the precise values of the ancient units of measurement and the methods of their application in the monuments of antiquity. What he found, circa 1980, became the basis of our studies for the remainder of his life. Other towering intellects of the past Newton, Galileo, Jomard, Petrie and Stecchini to name but a few, have been absorbed in the same quest. Only John succeeded in laying the foundation of the structure of metrology and it has been my privilege and joy to help complete the task.
                 The measurement system of the ancient world is the greatest monument to the cognitive power of humanity and is older than any recorded civilisation. The word “system” is singular. There is only one system of measurement throughout the pre-metric world; culture to culture, continent to continent; the similarities of the national standards, both in their structure and method of use so far out weigh their differences that the only conclusion that can be reached is that all of them had referred to the same “canon of order”.
                 In fact, the existence of such a refined system of reference is such an anomaly in the field of historical research that it may be regarded as inexplicable within the paradigm of our present knowledge about the past. The universal measurement system should not exist granted our preconceptions about the origins and development of humanity. It is as though a technically advanced device such as digital computer had been found in a prehistoric tomb. Then similar devices subsequently found at opposite ends of the world.
                 However, it does exist in all its refined detail and it will be explained in the pages that follow. Firstly, a brief background article explaining my relationship with John will serve as an introductory piece to both of us and to the structure of metrology. It was written recently for an on-line publication as a memorial essay.

John Michell, Explorer of Dimensions

My name is John Neal, most often called Nosh. No one of academic or literary consequence would know who I am but for the influence of John Michell. He was a polymath with the most eclectic range of interests possible. This enabled him to both to relate to and to converse knowledgably with anybody he met, within minutes of meeting he was a close friend.

Secret Academy: John Neal and John Michell
John and me in a crop circle c 2002, I am the short one

We met in 1967 during the acid revolution. All of the youth at that time came from a background of wartime austerity, rigid short-back-and-sides conventionality and Lord’s Day Observance type orthodoxies. Suddenly we were having visions and pigging into every powder, pill and mind expanding substance we could lay our hands on. Things would never be the same again and the world was irrevocably altered, consciousness, art, fashion, music and more subtly — the sciences, entered new dimensions.

At this time, worldwide, there was an extraordinary amount of UFO activity, this was something that I experienced very vividly and my companion at the time was a gentle giant of a man, a bass guitarist called Honk, from Cardiff. He knew John and that he had recently written a book on the UFOs; we therefore hied off pell-mell to John’s house in Powis Terrace where he introduced me to the man who would become the greatest influence on the remainder of my life. “The Flying Saucer Vision” had come into being in typical John fashion, he had lost the complete manuscript on a train and it had to be entirely rewritten. He may have been the smartest man in the world but he could out ding-bat the best of them.

Our interest in heavenly phenomena we realised was to remain a mystery; but it was the parallel works of others that made us look downwards instead. One in particular, Aimé Michel had written about something he called “orthotenies” and these were straight lines across the landscape along which there had been UFO sightings; they connected prehistoric sites, he claimed. Now, this was something we could get our teeth into, archaeology and landscape geometry, bliss. John was already familiar with the works of Alfred Watkins, principally “The Old Straight Track” wherein he had proposed that sites of antiquity were connected by straight lines that he termed leys and old roads and tracks followed these alignments.

Another major influence on John at that time was “The Canon” by William Stirling. This is a work written c 1897 that concerns the cabbala and the expression of canonical numbers that are codified in ancient religious texts through the structure of the words and phrases —the Hebrew letters being numbers as well. John understood ancient Greek and saw parallels in the Greek texts of the Christian scriptures, the science known to their Gnostic authors as gematria. Out of these studies arose his most influential work “The View over Atlantis” which was the book that inspired our generation of (not so gullible as you may think) youth.

Although shot through with woeful inaccuracies which precluded serious academic acceptance, the main thrust of the book kept its integrity of purpose. The existence of the leys was substantiated by a follow-up work — “The Old Stones of Lands End” during the research period he took along to Cornwall some of his raggedy-arsed mates. The research material that was gathered was submitted to statisticians of the Royal College who concluded that such alignments were not coincidental (“so there!” he said).

Secret Academy
Gaby Nasmith, John, Christopher Rudman, Jake Hemming, Linda Wroth,
John Neal and Lizzie Benzimra at Boscawen-un stone circle, Cornwall 1971

Now into his stride, one sublime work followed another “City of Revelation”, “Dimensions of Paradise”, “Twelve Tribe Nations”, “At the Centre of the World” (my favourite), “Who Wrote Shakespeare” and these are just the principal ones. Countless others, many smaller works, articles, his regular column in the “Oldie”, pamphlets and reviews; charming, witty, endlessly humorous, a veritable cascade of enthusiasm and inspiration. In addition there was his huge volume of artwork, poetry, magazine and publishing ventures, yet you never saw the bugger doing it. He loved company and would stay up as long as whoever could last the course, drink glass for glass, smoke joint for joint and imbibe anything put before him. When his company staggered off into the night or pitched forward onto his table (with luck), then he would get to work. In another age he would have been be burned for witchcraft for his mysterious productions.

Having had the privilege of a classical education, that invariably stands its recipient in good stead, he absorbed much of the Platonic logic that so profoundly affected his well-informed point of view. However, in his management of situations it was Socrates he most resembled. When people confronted him for an opinion on, or an explanation of something he had claimed, he would craftily turn the tables and first elicit what was their opinion, then take issue with them. As well mannered and mild as he was, if he felt affronted he could deliver the most lethal retort. Once, when a publisher had foolishly sent him a highly illustrated book to review, in the text the author had been scathingly contemptuous in his references to John’s own considered views. His reply to them was the most withering invective that I have ever witnessed the final sentence of which read: “I sincerely hope that your contemptible little book moulders upon the shelf and is a reproach to you in your old age.” That’s my boy.

Often enough we were separated for very long periods and enormous distances and, incredibly, always seemed to be quite independently struggling to resolve the same historical enigmas. How many people do you know who put in hundreds of man hours in trying to resolve the precise length of the royal Egyptian cubit? With neither one of us knowing the other was similarly engaged. The problem for both of us was that there was nobody to consult, it is lost knowledge.

My own tentative solution to the problem had to be abandoned when we were reunited, about 1980, after four years absence in America. It concerned the linkage of time periods with linear units and is of no concern here but this was the pivotal point for us both although it took another ten years to come anywhere near full resolution. This concerns what John considered to be his –to a lesser extent, our- greatest discovery. Indeed, once in the late hours after a long struggle resolving a knotty metrological puzzle concerning temple dimensions, when the blindingly obvious answer came to us he threw down the calculator and exclaimed “Christ Nosh, do you realise what we have here? It beats hollow any discovery ever made in any field of archaeology.” I am inclined to agree with him, but I would, wouldn’t I?

We were ideally suited to collaborate. He soared on the wings of almost divine inspiration and I am the pragmatic sceptic with a state of the art built in bullshit meter. Between us we resolved the enigmas that had been puzzled over by towering intellects of the past — namely the structure of ancient metrology. The first and most important breakthrough came with his 1981 publication “Ancient Metrology”.

John Michell: Ancient Metrology

This rather small book for the first time in history precisely indentified the lengths of certain units and elaborated upon the reasons for the subtle differences in these individual units. I tried to elicit from him exactly how he had come to his conclusions but he simply did not remember. My own methods, on the other hand, require that each piece of data is first regarded as hypothetical, enough corroboratory pieces of the same nature is then regarded as a proposition. Enough mutually supportive propositions may only then be regarded as the general theory. However, if the correct answer is initially arrived at through inspiration, it only needs to be verified. After all, inspiration is precisely how Dmitri Mendeleev arrived at the arrangement of the periodic table.

Right dear reader steel yourself — that was the easy bit. If the nature of John’s great discovery is to be understood, we must delve into the realm of number. This is where most people fade away, John and I always sought our “third man” and when we thought we had him, he never stayed the course. This is why I published under the logos of The Secret Academy and the motto is “We can’t give it away”. This epithet became part of our personal language that was mostly numerical. Whenever we discovered a juicy and pertinent fact concerning our studies we would finish our explanation with “can’t give it away”.

The problem is that although the subject is complex in the extreme, it obeys simple rules it is therefore not complicated. Exactly like music which is the art it most resembles, from a finite series of data points there is a seemingly infinite number of arrangements. Additionally, academic acceptance of the system is precluded because of the source of the information; academe is very stuffy and hates anything that originates from beyond its closed doors. The vast majority of conservative academics also abhor, anything termed a “discovery” especially in historical studies. In the case of John, he is branded as a dreamy mystic. This is a case of give a dog a bad name, rather like the man who takes a pee and is charged with indecent exposure. Whatever his magnificent accomplishments may be, it is all that people remember him for.

Prior to John’s discovery no ancient measuring unit had ever been precisely defined, all had to be expressed between plus minus parameters. This is because of the variations that they are all subject to, and had erstwhile been regarded as either slackness in their maintenance or belief that the historic systems had been arbitrary. This had led to a general averaging of the units by historians; which practise further cloaked the astonishing beauty of the complete structure of metrology. The variations are deliberate.

Taken from John’s “Ancient Metrology” the following list of units in two values of each has been simplified down to the foot values expressed in English feet:

  Tropical Northern
Roman .96768 .9732096
Polar .987428 .993071
Greek 1.008 1.01376
Royal Egyptian 1.145454 1.152
Ancient Jewish 1.3824 1.390299

He termed the lesser values Tropical because they were regular fractions of the geographic degree of the earth at 10º and the longer values were termed Northern because they were compatible with the degree at 51º. The difference between the two values is the regular unit fraction 175 to 176.

This initial exploration of historical measurement is important on many grounds. The principal reasons are that this is the first time related measurements have been grouped into a single classification terminology. Secondly absolute and exact values are established. Thirdly a geodetic, or earth related, relationship is proposed. This means that just as the decimal or modern standard units were devised through the medium of a detailed survey of the globe — so must the ancient standards have been created. As preposterous as this may sound to modern thought processes which looks upon our ancestors with a patronising attitude, there is in fact nothing outlandish in this statement. All of the instrumentation necessary to conduct just such a survey was available in the very remote past.

Although Ancient Metrology was a small book much important information was packed into its slender form, including how the measurements made sense of the dimensions of monuments such as Stonehenge and the Great Pyramid. At Stonehenge for example he established that the vitally important width of the lintel stones was 3.4757485ft and for want of a name, termed this a sacred rod (because we are talking exact values numerically arrived at it is permissible to use such large numbers of otherwise meaningless decimal points). He also instituted such essential geodetic data as the ancient establishment of the vital earth polar and mean radii; polar radius as 20854491ft and mean as 20901888ft. The polar is ten million sacred Jewish cubits, for example, and the mean is another unit fraction at 441 to 440 of the polar. Although all this was new and vital information, John had barely scratched the surface but there the subject became stymied for around twelve years.

When I researched the matter, with slowly increasing intensity over these intervening years, I was struck by the way in which John had reached his conclusions from such a small data base and limited reference field. Such was the man’s inspired genius that he had made more headway than respected and established scholars who had devoted a lifetime’s work to such ends. It became obvious that John was correct in his assumptions; it also became obvious that his Ancient Metrology was merely the tip of the iceberg. After wearing out a few calculators, when the subject began to crack it all unfolded with heart stopping suddenness. It was like seeing glory, waking up with a precious jewel, looking straight into the holy of holies at the heart of the temple. It was as though John had found the key to the door and with his customary good manners let me enter first, and we couldn’t give it away.

Starting with John’s brief list I noticed that the royal Egyptian values were out of line with measures that they were more compatible with; such as the Greek foot of value 1.008ft is the unit fraction 7 to 8 of the royal Egyptian 1.152ft. Not only was this a more correct arrangement but the new reduced column could be extended to all of the national values and the blank left by the movement of the royal Egyptian in the Northern column could be similarly filled by an increased value and be a further verified value. Each column is separated by the fraction 175 to 176.

    Tropical Northern
Roman .9621818 .96768 .9732096
Polar .9818181 .987428 .993071
Greek 1.002272 1.008 1.01376
Royal Egyptian 1.145454 Secret Academy 1.152 Secret Academy 1.1585829
Sacred Jewish 1.1374545 1.3824 1.390299

Several pertinent facts concerning metrology in general became immediately apparent with this rearrangement; they must be briefly outlined, sorry, I know this bit hurts like hell. Firstly, I saw that this method of viewing the data showed a fractional integration across national systems that had been missed by researchers. It had been missed because they had used the wrong classifications in their comparisons. This unit fraction expression is exactly how the Egyptians, Greeks and Romans conducted their day to day calculations. They could not express a fraction such as say, five eighths, because only one eighth could occupy the eighth position. It would have to be expressed as one half, plus one eighth. It is well known that the Roman measures relate to the Greek as 24 to 25 and the Roman to the vanquished Belgic people’s measure was 8 to 9, now I was looking at the previously unknown integration of the Greek to the Egyptian as 7 to 8.

Secondly, it enabled correct identification of the modules that John had invented terminology for. The module he termed polar was in fact common Egyptian measure because the common is six to seven of the royal Egyptian and this becomes apparent with the corrected column placement. Also the measure he had found at Stonehenge of 3.4757485ft and termed a sacred rod was in fact the more prosaic three royal Egyptian feet. Thirdly, the values he had claimed for the Jewish sacred feet were far too long to fit the description “foot”. The error came in dividing the sacred cubit of 2.0736 feet by the conventional one and a half which is the cubit length. This sacred cubit is a two-foot cubit, or dupondia, and when so divided is a foot length of 1.0368ft and is then immediately identifiable, usually called a common Greek foot (36 to 35 of the regular Greek values). Ok, you can relax a bit now, not much more of all that.

With my vastly increased data base to that that had been used by John, the discoveries along this route of unit fraction integration piled in almost as fast as I could record them. I isolated what were the distinct feet measures of twelve national systems and saw that this was a general rule and all of them showed the same level of integration and the same variations in their measures. In other words, throughout the world the people, from remote antiquity, had all used the identical system. This terminology, Egyptian, Greek, Roman, Assyrian, Sumerian, Aztec, Japanese etc was redundant. All these national terms were merely those measures the bureaucrats had selected from a wide choice of values to be the national standard for social regulation.

It must date from the far mists of time, because in historical times these disparate people were not even aware of each others existence; yet they used the identical measurement systems. From the long distance, or itinerary measures of leagues and miles, the intermediary furlongs and stadia, the standard modules of fathoms, paces, yards, cubits and feet right down to the sub divisions of digits and inches, exactly the same methodology. From the early days of John’s researches he said to me of these cultural similarities (that did not relate at that time to measurements as such): “They had perfected standardisation of culture which enabled them to endure for perhaps thousands of years. It was accomplished by reference to the ‘canon of order’ and that canon governed all of their stylistic artefacts, architecture and arts for example. The differences in the various cultures, Chinese, Egyptian etc are merely differences in style, all referred to the identical canon.”

What had been found in the measurements was mirrored in the monuments that had first attracted us to research the megaliths and the ley system. It is universal, there are no national boundaries. The leys were stripped of their sloppy “energy lines, man” image that had precluded serious academic consideration. The remnants of the great culture that had inspired us from the beginning were very obviously mark points, the remains of the great global survey. Obvious, if you have long distance alignments, you must first survey them. The forgoing has been much condensed and there is vastly more corroboratory evidence for these claims.

Secret Academy: John Michell
John measuring the Greek marble at the Ashmolean

It is small wonder that such high concepts are hard to communicate; strangely enough it was John who proved quite resistant in his acceptance of this vastly expanded system that was initially his own discovery. I had to perform a confusing mutation from pupil to teacher (only in the realm of metrology), and at times be quite firm with him, giving him bollockings that he took with very bad grace. “I thought I was being forward proposing just two variations of each measure, now we have eight, oh dear, dear me” and so forth. He clung to the narrow paradigm of his own limited field and had to be prised out of it with the most surprising difficulty. The above picture of John in the Ashmolean, for example, we took it in turns to measure both the foot length and attempt to assess the overall fathom of the outstretched arms. As the anatomical foot is one seventh of the overall height, there had to be a harmonic in the two measures. The differences in the individual foot measures are far too small to be certain of, but the harmonic must be the correct one. He insisted that the value of the foot was his .96768ft but this throws out the final solution, shown below.

Secret Academy: Roman Foot

It took a very long time for him to fully absorb the expanded metrology but when he finally did, circa 2003, he attacked the delicious problems it throws up with all his old relish and enthusiasm. He gave it its final form by devising the most thorough integrated table using a progressive series of unit fractions that embraced all of the measures both known and potential. When I did the classification on this table many of the modules had to be marked as “unidentified” but in the fullness of time with much additional research, all were found to be valid. There are nineteen separate “feet”, anything less than the least is a half cubit, and anything greater than the largest moves into other modules (remen, palimpes, cubit etc).

It is important because as John stated in his introduction to Ancient Metrology: “A tradition which has been accredited by many learned men over the centuries is that the ancients encoded their knowledge of the world in the dimensions of their sacred monuments. If that is so, any attempt to elicit that knowledge must be preceded by study of ancient metrology, for to interpret any set of dimensions it is of course necessary to establish the lengths of the units of measure in which they were originally framed.” Knowledge of metrology adds a whole new dimension to archaeology. His greatest discovery is indeed the measurement system that was there since the foundation of the world. The whole subject, because of the necessity for a different mental attitude that it is vital to adopt, is very difficult to communicate and it may take a very long time to be acknowledged and generally embraced. But if it is ever accepted it will be his most lasting memorial and the one that he was proudest of as an accomplishment.

John Neal, London July 2009

John Neal, Secret Academy

John Neal. Born 1941 studied agriculture and grew fascinated with the old systems of measurements then still in everyday use. Keenly interested in archaeology and at an early age read Maud Cunnington’s account of the digs at Woodhenge wherein she claimed to have deduced a regular unit of measurement not dissimilar to the English foot; regarded ancient forgotten people as highly civilised thereafter.

Author of “All Done With Mirrors”, “Measuring the Megaliths”, “The Structure of Metrology”.

Photograph by Palden Jenkins

Contact John Neal: johnneal@secretacademy.com

A Cooperative Effort


If what follows is to be understood the reading should be accompanied by a calculator in order to verify what is being stated.  Any values taken from metric examples have been converted to English feet at 3.2808427ft to the metre.  The whole edifice is only visible from the viewpoint of decimal feet.  Researchers in the past have most often used English inches to express the values; this occludes the pure numbers that are expressed almost as much as the decimal system.  Metrology could never be understood expressed in the modern SI units for the simple reason that the important numbers are lost and these numbers are expressed in feet.  There is no provision in a metre for a third subdivision.


John Michell
John beneath his iconic portrait painted
by Maxwell Arnfield c 1970

After many years of study it was the uncertainties of the clear definition of the modules of metrology that precluded progress; having John’s absolute values was the single virtue that permitted any advancement in the investigation.  However, there were other values of the same modules that were very closely known that did not conform to his model.  In many cases these could be exactly defined by another a unit fraction link, that of 440 to 441 to the modules pinpointed by John.
            The best known examples are the Greek and Roman feet of which there are multitudinous examples.  The interesting thing is that because John had exactly defined the greater values then these lesser values could, for the first time, also be exactly defined because of the virtue of unit fraction relationships.  For the Greek foot John gave 1.01376ft, then the 441st part less is 1.0114612ft and this is the most commonly quoted value for this module; and his value of the Roman foot of .9732096ft reduces to .9710027ft and this is the commonly accepted value of the Roman foot.  They had never before been defined with this clarity and exactitude.  Once again, because of the unit faction integration of metrology, once any value has been exactly determined, all others may be exactly expressed and this is what had never been previously possible in this field of historical research.
            Progress continued to be made by following this line of enquiry, the best example of which is the value of the royal Egyptian cubit, probably the most scrutinized historical measurement.  John had defined this as 1.718 18 recurring feet.  This was the value given by Petrie from his examination of the Great Pyramid, however even he could not be exact, having to give his value as 20.620 ± .005 inches, whereas Michell’s value is 20.618 18 recurring inches.  If this value is reduced by its 441st part then it is the eminently rational 12/7 English feet, 1.7142857ft and there are numerous examples of royal cubits of this length.
            Berriman too had seen a way to arrive at Petrie’s value.  He envisaged the royal cubit as being the radius of a circle that has a perimeter of 129.6 inches.  He thought its perimeter number being sexigesimal (6 to the power of 4 = 1296) was significant.  It is.  Had he used the universally accepted pi ratio of 22/7 he would have precisely identified the cubit defined by Petrie and more exactly by John Michell, of 1.7181818ft.  However, he used true pi and arrived at a fractured number for this cubit and this is very surprising; for it was Berriman who stated that the Great Pyramid had been constructed to this pi ratio of 22/7.
            A great deal about the structure and function of metrology may be deduced from these simple facts.  Berriman’s solution to the cubit identification was numerically identical to that of Petrie whose solution was exactly ten times greater.  A circle of 129.6 inches, more properly 10.8ft, has a diameter 3.436363ft, two royal cubits.  The King’s Chamber in the Great Pyramid, the measurements of which defined the cubit for Petrie, is exactly 34.36363ft long or 20 royal cubits, and the perimeter around the walls and to the underside of the inserted floor, he established, was 108ft.  Petrie stated that this was the pi ratio and that this ratio and this cubit framed the overall construction design for the whole pyramid, 440 in the base side and 280 for the height.
            This is how the foundations of metrology that had been laid by John began to expand into its far greater scope and significance.  Many examples of length were found to flesh out the overall structure of metrology and the range of values for a single module, all related by the connective links of the ratios 175 to 176 and 441 to 440; simplifying the identification to eight values and taking the example of the Greek feet they may be arranged into a table as so:

Root Reciprocal Root Root Canonical Root Geographic
.994318 1 1.00571426 1.0114612
Standard Reciprocal Standard Standard Canonical Standard Geographic
.996578 1.002272 1.008 1.01376

            The first line is appended Root, the second Standard.  These modules increase by the 175th part horizontally and the 440th part vertically, they increase from the English foot to achieve acknowledged values of the Greek foot.  The Parthenon foot, for example, is very clearly given as 1.01376 which is the 440th part greater than the Attic 1.0114612ft.  Because we are viewing the base measurement as the English foot, the above table is also the formula numbers by which all other modules may be classified.  It is apparent that the English foot is one in the series of the Greek feet. 

            As can be seen, I have had to ditch the terminology of Tropical and Northern of the two values 1.008 and 1.01376 as identified by John, and formulate identification terminology that suits the nature of the modules in the light of the expanded range.  The next step was to bring in all the other national feet into an integrated whole and all of them are subject to the above variations.  One well known ancient module is often known as the lesser foot and its variants are as so:


Root Reciprocal Root Root Canonical Root Geographic
0.894886 .9 0.915143 0.910315
Standard Reciprocal Standard Standard Canonical Standard Geographic
0.896920 .902045 0.9072 0.912384

Once the “Root” value is established the unit fraction links become visible, the value .9ft is the Assyrian foot as defined by Oppert from measurements taken at Khorsabad, all these values then take the defining term “Assyrian” and the variants are termed this plus the variant term.
            Terminology is one of the principal occluding factors in the study of metrology because what is essentially the same foot attracts a whole plethora of designations and this Assyrian foot is often referred to as the lesser foot, but also as Italic, Oscan-Italic, Oscan-Umbrian, Campanian, neo Babylonian, Lydian, Basque and Mycenaean and this is by no means all of the terms.  Therefore these terms may be discarded by calling all of them “Assyrian” with their classification appellation because it is the Assyrian, at .9ft that displays the direct link to the English foot.  For example, the Mycenaean foot as identified by Stecchini is given as .910315ft but the Mycenaean title is here discarded and it is termed Root Geographic Assyrian.
            Actually these eight values are simply the “core” values and the true structure is “grown up” metrology but these are sufficient to illustrate the principals.
            My next task was to isolate as many national feet as possible, identify their Root values and display their unit fraction integration in tabular form.  This was a process the value of which I had learned from Stecchini who portrayed it as so:

  Mycenean 15 9  
  Roman 16   24
  Greek   10 25

However he was not using the Root values but the Root Geographic values and I was able to expand his integration as so: 

  Mycenean 15 9 5    
  Roman 16     24 8
  Greek   10   25  
  Belgic     6   9

Then by taking twelve of the national values the table looked like this in terms of unit fractions:

Secret Academy: Unit Fractions

John then took up the subject again and perceptively noticed the prevalence of square numbers in this arrangement, 4, 9, 16, 25, 36, 49, 64 etc and found how to arrange the values in a descending order as so:

column 1. First eleven are fractions of the common Greek foot of 1.028571

1/2          .514285                 3              ½ common Greek foot

2/3          .685714                 4 8          10 digit palm length of Sumerian foot

3/4          .771428                    9 15                     ½ common Greek cubit (12 digit span, 9inch dodrans)

4/5          .822857                       16 24                ½ Sumerian cubit                                               

5/6          .857142                            25 35           ½ royal Egyptian cubit                      

6/7          .881632                                   36 48                    not identified (6 to seven of common Greek)

7/8          .9                                                    49 63               Assyrian foot

8/9          .914285                                             64 80          Iberian foot

9/10        .925714                                                    81   99                 not identified (six to seven of Belgic)

10/11     .935064                                                         100 120         not identified (six to seven of Sumerian)

11/12     .942857                                                           99 121         Samian foot

                .953281                                                    80 100                lesser Roman foot

                .964285                                             63 81          not identified (six to seven of Nippur foot)

                .979591                                        48 64               common Egyptian foot

35           1                                                35 49                    English – Greek “Olympic” foot

36           1.028571                                 36 48                    common Greek foot

                1.05                                               49 63               Persian foot

                1.066666                                           64 80          Foot of Persepolis  

                1.08                                                           81   99                 greater Belgic foot

12/11     1.090909                                                        100 120        Sumerian foot

11/10     1.1                                                                     99 121        Saxon foot

10/9        1.111111                                                   80 100               archaic English foot

9/8          1.125                                                   63 81         the foot of Nippur

8/7          1.142857                                       48 64              royal Egyptian foot

7/6          1.166666                                 35 49                    Russian ½ arshin

6/5          1.2                                     24 36           Roman remen or 20 digit “palimpes”. 

5/4          1.25                              15 25                Greek/English 20 digit “pygon”

4/3          1.333333                  8 16                     16 inch module widely used by English speaking people

3/2          1.5                          3 9          English-Greek 1 ½ foot cubit 

2/1          2                              4              English-Greek 2 foot cubit

column 1.  Last eleven are multiples of the English foot

           
           Two values, the Common Greek foot and the English foot (or Olympic Greek) are pivotal to the whole arrangement.  In the first column the top series of numbers are the unit fractions by which the modules relate to the common Greek foot and the bottom set show their fractional relationships to the English foot.  The second column is simply all of the modules both proven and potential expressed in decimal English feet.  The final, offset column, displays how the modules all relate by “square” numbers to the modules above and below.
            This table also makes clear the limitations of measures that may be termed mathematical “feet” as distinct from other modules, they are the emboldened values.  The values that are less than the smallest foot (the Assyrian .9ft) are half cubits.  Throughout the ancient world these half cubits are also termed feet, they may be termed “natural” feet as they conform to the proportionate lengths of the human foot.  Right up until 1923 when the Maltese adopted metrication, the half royal Egyptian cubit of .857142ft was the official foot standard.  There was a similar standard in Britain known as the Welsh foot which was identical to a Saxon half cubit at .825ft.

            In order for this table to fit together in this symmetrical form certain of the values had to be taken as a different variant than those in the original table of integration.  The Sumerian foot is taken as 1.090909ft instead of the accepted 1.097142ft where it is 24 to 25 of the royal Egyptian of 1.142857ft.  These shifts are perfectly legitimate because the unit fraction linkage is maintained, but at 20 to 21 instead of 24 to 25.  Similarly the Root Roman foot of .96ft at 24 to 25 of the English/Greek becomes at .95238ft — 20 to 21.  There is little doubt that this is the case because the Roman foot, from antiquity, is reckoned at having a ratio of 9 to 5 with the royal Egyptian cubit, it would then be calculated from what can only be termed a lesser Root.  It is also accepted from antiquity that it is 24 to 25 of the Greek (Strabo in his Geographica states that the Greek stadium is 600 Greek feet and 625 Roman feet).  The above makes clear how these seemingly incompatible equations are made to be correct through the exact differences in the individual units. 

            The table above was the final stride towards an understanding of metrology, it was hard won.  John would often have protracted telephone conversations with me trying to distinguish the values that should be used in the series.  It was his final contribution and was the cementing link of all that gone before.  After some 40 years of study it brought a sort of closure to the subject, it was complete.

 

Secret Academy: John Michell Secret Academy: John Michell

John Michell about the time he took up the study in the 1960s and on the right still at it shortly before he died. 

Photographs by Louise Hogeson and Steve Marshall.