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Shaun 
Posted: Mar 30 2009, 05:32 PM

Dozens Disciple Group: Admin Posts: 1,115 Member No.: 3 Joined: 2August 05 
This should interest all those researching ancient measures  the author connects up the old Saxon foot with other measures in a fascinating study.
You can download the article in pdf form from the DSGB site. Rollrights 
Dan 
Posted: Jul 7 2009, 03:27 AM


Dozens Disciple Group: Members Posts: 1,463 Member No.: 19 Joined: 8August 05 
So why didn't he just standardize on the Saxon foot? Seems it would have made things easier. 

Ruthe 
Posted: Jul 7 2009, 07:11 PM


Regular Group: Members Posts: 360 Member No.: 47 Joined: 27February 06 
I imagine somebody will give us chapter and verse, but I imagine there were conflicting requirements. The Roman influence probably still held a lot of support with its 12 inches to the foot, the palm of 3 inches, the hand of four inches, the span of 9 inches and the digit of 3/4 inch (16 digits to the foot). The new foot retained these relationships whereas the Saxon foot would require more changes to make it the standard. Don't forget that it was the Romans who popularized the division of units into twelfths, simply because of the greater divisibility versus tenths. This was perpetuated throughout Europe, with national versions of lengths equivalent to the foot that differed marginally from country to country and even area to area, but with the same subdivisions. This was also enshrined in later monetary systems implemented initially by Pippin and then his son Charlemagne, resulting in the livre of 20 sous and the sou of 12 denier. Have a look at my avatar, the Roman pocket abacus. The second column from the right is for unciae, so there are five beads in the lower slot and the bead in the top slot has a value of 6 uncia allowing for counting from 1 to 11 uncia. The first column was for fractions of an uncia. Anyway, the change of the rod probably involved far less disruption than using the Saxon foot as the standard. Anybody who wishes to add or correct me on this, please do, I would prefer the correct detail. 

dgoodmaniii 
Posted: Jul 8 2009, 12:18 AM


Dozens Demigod Group: Admin Posts: 1,927 Member No.: 554 Joined: 21May 09 
That's pretty slick, Ruthe. I think I'm going to have to build such an abacus soon. It's not as powerful as a slide rule, of course, but I rarely need the extensive capabilities of such, and it would require a lot less precision to build. (I have calculators, of course. I've just always been fascinated by mechanical, nonelectrical devices.) 

Ruthe 
Posted: Jul 8 2009, 03:29 PM


Regular Group: Members Posts: 360 Member No.: 47 Joined: 27February 06 
The picture of the Roman abacus is that of a reproduction made from an image found on a Roman column frieze. Columns 3 to 9 are an example of a biquinary abacus where the beads in the lower slots counted as one of that column's value while the bead in the top slot had a value of 5. The symbols in the gap between the upper and lower slots indicate that the value of each column was 10 times that of the column to the right, starting with ones in column 3 and going up to millions in the last column. This demonstrates that although the Romans had no written form for zero, they did recognize the significance of a zero value in each column represented by no beads moved to the counted position which I assume was the centre gap between the lower and upped slots. This then shows the Romans used a decimally based, place value system for performing calculations. A further characteristic that becomes evident, is that Roman written values could be easily transferred to the abacus and likewise the result of calculations transferred back to their written notation. As examples, a value of 5 (Roman V) was just the single bead in the top slot of column 3, and values of 50, 500 etc (Roman L, D) the upper bead in columns 4,5 and so on. This abacus is said to have been in use around 50AD and was approximately 120 mm x 80 mm or 5" x 3 1/8", making it marginally wider but no longer than my Sharp calculator. In other words, the world's first pocket calculator!!!! 

jim 
Posted: Apr 23 2012, 10:20 AM

Regular Group: Members Posts: 164 Member No.: 641 Joined: 20April 12 
Gosh it's been years since I posted this and I guess I have just let things go due to work etc.
I am not a math person but became interested in ancient problems when researching the Saxon or Drusian or Indus valley foot 13.2 inches. The cube root of 2. Did the ancients know and use the cube root of 2 ...... 1.25992? I came to believe they probably used the approximate 1.26 and that would surfice. There is a remarkable coincidence, I think, with the approximate for pi 22/7 and the approximate of the cube root of 2 ie 1.26. Imagine a cube with a side equal to the approximate of pi 22/7. Imagine you wanted to double the cube approximately ok use the approximate for the cube root of 2. 1.26 22/7 x 1.26 = 3.96 39.6 inches is the old Saxon yard see the essay. The old English Tun 39.6inches a side, see the essay. look I hope this may interest someone and if anyone wants to do this by construction. Then divide a line into 25 even parts and add 6.5 giving 31.5 and you have 1.26. I am sorry if this is not correct math but as I said I am not a math person. Jim 
icarus 
Posted: Apr 24 2012, 01:52 AM

Dozens Demigod Group: Admin Posts: 1,913 Member No.: 50 Joined: 11April 06 
Jim,
How ancient is ancient? If we are talking before 1 AD only some cultures were decimal. Positional notation was not common among societies, especially less than the radix point. If the "ancients" converted the cube root of 2 to any ratio, perhaps it was 5/4. The Romans may have expressed it as 1 and 3 uncić, and going back further the Babylonians would have a shortened sexagesimal form of 1:15,35,42,56,48,23,53,42,43,42,47,05,40... Again, maybe only 1:15, since they were fond of regular numbers, and 1,15 is regular. If the cube root of two was known, it would seem 1.26 may be too "decimal", and folks would've used 5/4 sooner than (5/4 + 1/100). 
Shaun 
Posted: Apr 24 2012, 09:07 AM

Dozens Disciple Group: Admin Posts: 1,115 Member No.: 3 Joined: 2August 05 
1,15 ... as 5/4, or the next approximation as 91/72, with the true value between the two, 91/72 being slightly over.

jim 
Posted: Apr 24 2012, 11:35 AM

Regular Group: Members Posts: 164 Member No.: 641 Joined: 20April 12 
I think the Indus Valley could be considered ancient and so when I read this reference I considered it important. I imagine the sample rule mentioned is available to study. It is remarkable how near this early decimal system of Germany and Britain is the double of the modern decimal metric system. Had it not been unhappily driven out by the 12 inch foot, we should need but small change to place our measures in accord with the metre.’ Phillip Rush and John O’Keefe state in Weights and measures. ‘The northern foot (13.2 inches) derived from the early Indus Valley civilisation in northern India.’ From “The Roots of Ancient India”, The Archaeology of Early Indian Civilisation, second edition, revised, by Walter Fairservis Jr. (page 291).; ‘… linear measurement was apparently well standardised. Mackay by good fortune found a piece of shell marked in regular fashion and quite clearly intended as a rule. Nine divisions remain, and from circular markings at two placed five units apart it would appear that a decimal system was in vogue. Each division is approx 0.264 inches wide, or a fiveunit total of 1.32 inches. Thus a foot in the decimal system would be 13.2 inches, which fit into a widespread system of the ancient world. Similarly Vats and Wheeler provided evidence that a cubit was also used. Thus both the smaller and larger units of measurement were used in building and presumably to lay out fields.’ Jim 
Shaun 
Posted: Apr 24 2012, 02:03 PM

Dozens Disciple Group: Admin Posts: 1,115 Member No.: 3 Joined: 2August 05 
This is mentioned in other texts, the implication being that the circumference of the Earth was known in ancient times; but the correspondence to the metre suggests also that the circumference was divided as today  first into quarters, and then decimally into metres.
Most measures in the ancient world reflect the fact that the circumference was divided sexagesimally (by sixties). 
jim 
Posted: May 25 2012, 09:25 AM

Regular Group: Members Posts: 164 Member No.: 641 Joined: 20April 12 
Hi
I hope some of you find this interesting. It was for me but not being into math I have often wondered if anyone would be interested. How to double the volume of a cube by construction by changing its shape. I am sure you guys would be pretty good at this but here is one way which I have found and published in a local magazine many years ago. Turn a cube into a pyramid and in the process double its volume exactly. I was looking at the three pyramids of Giza and noticed that the third pyramid Mycernius was approximatly 1/10th the volume of the Great pyramid. I had used the measurements give by I E S Edwards who wrote the Pyramids of Egypt. Edwards gave the base length of the third pyramid as 356.5 feet which differed quite significently to Flinders Petries measure. Never the less I persisted and decided to use a combination of the numbers 3456 so made 356.4 Imperial feet as the base of the third pyramid. I had already noted that this number times 3 equaled the diagonal of the Great Pyramid. I thought to myself 'What if the architect of the pyramid had intended building a cube on the base and not a pyramid so just for the exercise I decide to treat the base of the third pyramid as the base of a cube. The volume of such a gigantic cube 356.4 cubed = 45,270,270.14 cubic imperial feet and by doubling this 90,540,540.29 comes close but does not exactly equal the volume of the Great pyramid. As I said earlier I had noticed the base of the third pyramid was 1/3rd that of the diagonal of the Great pyramid. 356.4 x 3 = 1069.3 imperial feet for the diagonal of the Great Pyramid. This renders a base of 756.0385704 and 756 feet is commonly used to denote the base of the Great pyramid. And so I started from there and wondered how to find a height that would deliver a volume twice that of the imagined cube. By trial and error I dived the base of the third pyramid by 3 ie 356.4 divided by 3 = 118.8 and multiplied by 4 = 475.2 imperial feet, and so this would become the height of the imagined pyramid. This did not equal the actual height of the Great Pyramid but would have reached the base of the capstone, which Agathachides said was 4 cubits in height. In any case this method doubles the cube exactly by changing its shape. Try it with cube of base 1 and volume 1. 1 x 3 =3 = diagonal of pyramid. side = 2.121320344 1 divided by 3 and multiplied by 4 = 1.3333333333 hgt of pyr Volume = 2 I would really enjoy some feed for someone not into math at all really. Jim 
wendy.krieger 
Posted: Jul 20 2012, 10:30 AM

Dozens Demigod Group: Members Posts: 2,432 Member No.: 655 Joined: 11July 12 
Unfortunately, the rollright system fails to observe the obvious fact that 'hundred' means six scores, so a mile would be 1200 fathoms or 1440 paces, ie 12 furlongs of 120 paces of 10 shaftments.

jim 
Posted: Jul 23 2012, 11:14 AM

Regular Group: Members Posts: 164 Member No.: 641 Joined: 20April 12 
Hi Wendy
I corresponded with R D Connor for a time and I would like to quote a portion of one of his letters. Connor 9th January 2002 'I quote from Philip Grierson's English Linear Meausres, University of Reading 1972, p6. [Peoples are supposed to have been] addicted to borrowing the weights and measures of other people, however remote from themselves in time and place. Thus Flinders Petrie  I choose deliberately a great name, that of one of the creators of modern archaeology  is ready to assure us that the Parthenon and Stonehenge were alike constructed to a foot of 11.68 or 11.69 inches, derived from the Egyptian remen of 19.161 inches while the builders of neighbouring Erechtheum preferred to employ the North Syrian or Phoenician foot of 11.09 inches. ................ Such beliefs and inferences belong, in my opinion, to the realm of fantasy.' Connor was not impressed with suggestions that measures can be found by reference to ancient monuments such as the Great Pyramid. I quote Connor ' This I do not subscribe to but at the same time I must say that my forthcoming book on the Weights and Measures of Scotland show a great inter  dependence of French, English and Scottish metrologies than I had expected.' I had put to him that the Mile is constant 4800 5000 5280 7200 all equal 6336 inches and are a part of the very same system. The foot equals... The Indus Valley or Saxon or as you have said the Rollrigh 13.2 inches The Roman 12.672 inches Imperial 12 inches 7200 is in fact a span of 8.8 inches Jim 
jim 
Posted: Jul 24 2012, 10:22 AM

Regular Group: Members Posts: 164 Member No.: 641 Joined: 20April 12 
After this letter from Connor I decided to have another look.
I decided to isolate the Roman and Greek measures. When the Romans arrived in Britian so did the Greeks and both carried their own measures. The Greek foot of 12.15 inches is well known and as Connor was discovering, if there is a need to trade, then measures must marry. And so it is evident the Greek and Roman is in agreement ie 24:25. Just as the old Saxon measure is in agreement 24:25. The Geek foot 12.15 inches and the Roman of 11.664 inches are this ratio. Incredibly 5000 Roman feet = 4800 Greek feet. The very same numbers are seen in the old Saxon measure. 5000 feet of 12.672 inches = 1 mile 6336 inches 4800 feet of 13.2 inches = 1 miles 6336 inches The Greek and Roman measure contain the very same numbers as the old Saxon measure. And confusions compounded upon another with a mile of 4860 feet. Where did this evolve? Simply it is the Roman and Greek measure converted to the imperial foot. A much deeper question is the possibility that these measures have a common Root. And I carnt forget the foot of Olympia which prof Connor proudly measured for himself. 12.6 inches. Jim 
davidk 
Posted: Aug 25 2017, 07:03 PM

Casual Member Group: Members Posts: 132 Member No.: 1,157 Joined: 25October 15 
The common root could be the imperial foot, If it represents the number 100 so 0.12 of an inch represents one then we can divide the variosus feet you have identified by 0.12 to see what numbers are represented,
11.664 = 97.2 12 = 100 12.15 = 101.25 12.6 = 105 12.672 = 105.6 13.2 = 110. 97.2 + 2.8 = 100 ( 2.8is a lunar number) 101.25 / 1.25 = 81 or 9 x 9 105 / 5 = 21/20 to the base 105.6  100 = 5.6 a lunar unit (this is 52.8 x 2) 110 100 = 10 and the 10/11 ratio as expected. So it is possible that the foot represented 100 units within these systems. 
davidk 
Posted: Nov 10 2017, 03:17 PM

Casual Member Group: Members Posts: 132 Member No.: 1,157 Joined: 25October 15 
Hi Jim
congratulations on having your paper accepted by the European Association of Archaeologists very recently. August/September 2017 meeting at Maastricht in Holland. Since you wrote it in 2006 it is testament to your preseverance that you have promoted it for so long and finally have been accepted by the Scientific Branch of the Association. This should send out notice to anyone interested in these units of ancient measure.( noting 10x11x12) Jim's unit is accepted now as extremely ancient and 4 x 1320 = 5280. Have you had any feedback in Australia as a result? It seems to be good times since Plimpton 322 has been decoded and the paper is excellent, a huge breakthrough in our understanding of ancient mathematics and its unusual complexity. As far as i am aware you are the only researcher who has recorded the area of the stone circles as containing astronomical information. It is a unique position to be in and i hope the dozenal demigods and disciples take note of this. Pi as 22/7 is the translator but also fibonacci pi that you are promoting. Also the Greek foot as 12.6 inches and this ties in exactly with my findings in respect of the Greek foot. If the imperial foot is a metric unit representing 100 units then it is 8.33333r units to the inch. 12.6 x 8.333r = 105. this is the ratio of the Greek/Roman foot to Thom's megalithic foot as 102/105 = 0.971428571 102 / 8.3333r being 12.24 x 8/3 = 32.64. The unit is identified in Anne Macaulay's book 'Megalithic Measures and Rhythms' In my book 'proving the megalithic yard' this 100 unit length of the foot is explored as above and is part of the proof. i have not got involved with the Sarsen circle but 0.971428571 x 100 is a suggested circumference by several metrologists.Also it has been suggested it is one day so one week is 97.1428571 x 7 = 680 exactly 10 of Thom's megalithic rods. Your unit 1320 x 34/33 = 1360 half of 100 megalithic yards. Also this fibonacci version of pi seems to work with the actual circumferences as follows Aubrey circle 89760 x 3.14181818181r = 282009.6 /144 = 1958.4 / 144 = 136. Another Thom unit. So 144 x 144 is the identified square. Or 6600 x 3.141818181r = 20736/144 = 144/144 = 1. This is a dozenal website it just does not get more dozenal than this. to quote 'The Origin of Numerical Systems and the Manipulation of Pi and Other Mathematical Constants. Our ancestors appear to have manipulated numerical systems based on their understanding of natural numbers. The imperial is a naturally occurring system of number based on the doubling of base two and multiplying by the sequential primes from three to eleven and removing base 7 through the design of Pi used within the system. Pi is used as 1760/560 or initially as 22/7. The system Thom discovered is designed exactly the same way but the primes are taken to base 17, removing base 13 through the design of Pi. Pi is used as 1632/520 or initially as 40.8/13. ' 
davidk 
Posted: Dec 20 2017, 10:53 AM

Casual Member Group: Members Posts: 132 Member No.: 1,157 Joined: 25October 15 
Having the paper 'From the Rollrights to Stonehenge' accepted by the Association of European Archaeologists is a huge step forward for the 21st century metrologists investigating the design of the ancient stone circles.
The Saxon foot 1.1 English feet is the unit of translation to produce astronomical information in the perimeters and diameters and possibly more importantly the areas of the circles and ellipses. This is a stepping off point into the past that has been considered and accepted and can be used as a focus to drive futher investigations. There is a problem at Stonehenge in that many investigations pluck the diameter and circumference seemingly out of thin air. It is important to set a standard for the Saxon foot to be used against, when investigating Stonehenge, and it involves sorting out the wheat from the chaff, in respect of completed and recorded Stonehenge investigations. Professor Mike Parker Pearson has co authored a paper that identifies the diameter of the first phase of Stonehenge the Aubrey circle as 285.60 imperial feet. He is the current person in charge of all work at Stonehenge so this can be considered reasonably reliable evidence. This diameter is also confirmed to the findings of Professor Alexander Thom in the 1960's amd 70's. He confirmed that the circumference was required to be in whole numbers often expressed in units of 2.5 of the base unit. Thom also confirmed, based on an investigation he supervised but did not carry out, that the diameter of the postholes from centre to centre was 283.60 feet giving the radius of the postholes as 1 imperial foot exactly. It is important to realise that Thom was given 'carte blanche' to investigate Stonehenge, this is how highly his work was rated at the time. So the baseline for further investigation is set. Use the Saxon foot against a diameter of 285.60 English feet and use pi as 22/7 remembering that there is a possibility that units of one English foot are held within the design. This starting point is based on well researched and recorded findings and is well know to all archaeologists but not necessarily clarified until now. Applying the use of the Saxon foot to the diameter produces a strange decimal number 285.6 / 1.1 = 259.6363636r. It is important at this point, to introduce one of the 'rules' for further investigation. Explain your decimals. This is possibly the worst way to engage a reader with a theory on Stonehenge. They simply did not do decimals. They probably used fractional maths as 22/7 indicates. Fractions certainly offer a better understanding of the reasoning applied to the design of the circles. So 259.63636363636r  what is it as a fraction because these recurring decimals can always be expressed in fractions? But the starting point is also decimalised as 285.60. This can be overcome by making the English foot represent 100 units so 28560 is the starting point. The diameter is then expressed as 28560 / 110 in Saxon feet. So now it can be multiplied by the Pi approximation of 22/7. 28560/110 x 22/7 = 628320/770 = 816. This is the base unit in the system discovered by Thom. So the Aubrey Circle is 816 Saxon feet. Dividing by 2.5 or 5/2 gives 3264/10 and this is an expession in Thom's megalithic yards. In terms of astronomical units the Nodal cycle of the Moon is 6800 days and this divides by 2.72 the unit Thom has been repeatedly challenged against and has now been cast aside by the whole of the archaeology profession. 6800 / (272/100) = 2500. Thom never made this link in his work but it is there at Stonehenge without question using bona fide evidence that is reliable. This starting point was established in my first book but without the Saxon foot, and what an enormous difference it makes!! The theme throught the book is without Thom's work we have no starting point for investigation. The starting point is now redefined as the circumference of the Aubrey circle is 816 Saxon feet using a unit accepted as ancient by the European Association of Archaelogists. The units held in the circumference can be expressed as 330 imperial feet x 272/100 imperial feet = 89760/100 imperial feet or 300 Saxon feet x 272/100 imperial feet = 816 Saxon feet. The dreaded decimal places disappear and the explanation becomes very simple using the imperial base 12 system. So the acceptance of Wakefield's paper signifies a turning point and a reference point that needed to be established. My first book is sold out except for a few copies in my local bookstore at Scarthin Books, Cromford, Derbyshire. A second print run is not being considered. The book lays out a methodology for the investigation of the Stonehenge first phase the Aubrey circle. The Sarsens came much later. When written the link between the imperial and Thom's system had not been established despite countless hours of computer modelling. It is ironic that when it was discovered it was a simple 33/34 relationship. I hope you like the front cover of this bookhttps://www.amazon.co.uk/StonehengeProving...ords=megalithic if you look inside the book it says front cover of stonehenge if the megalithic yard did not exist no Stonehenge 
davidk 
Posted: Dec 20 2017, 09:59 PM

Casual Member Group: Members Posts: 132 Member No.: 1,157 Joined: 25October 15 
104 and 103.6
these work with the two versions of Pi 104 is base 13 so works with 408/130 103.6 is base 7 so works with 220/70 408*220 = 89760 the Aubrey circle the numerator is 130 x 70 = 9100 so using fractions produces meaningful information, 89760/9100 This is 3.142857143 x 3.138461538 = 9.863736264 not really much to go on. Also pi can be restated in fractional form 22/7 can be 1760/560 and 408/130 can be 1632/520 1760 is a mile in yards and 1632 is half a megalithic yard in inches. Thom's diameters must be base 13 to work with Pi as 1632/520 and the imperial must be base 7, 7 x 13 = 91. 91 is cancelled out at the Aubrey circle to give 897.60. 104 x 1632/520 = 326.4 the megalithic yard 103.6 x 22/7 = 325.60 and this is 29.60 x 11. So the Aubrey circle diameter at 285.60 is a faily complex numerical mixture. It produces 897.60 imperial feet using 22/7 and also the megalithic yard appears as well even though 22/7 is used. This means base 17 must be in 285.60 and it is as 3 x 17 = 51. 285.60/51 = 5.6 feet and this is the imperial diameter to give 17.60. So base 17 in the diameter is simply carried to the cirumference whereas Pi as 22/7 converts 5.6. So the diameter of 285.60 can be broken down further since 51 can be divided by Thom Pi 51 / Thom Pi = 16.25 so the diameter is based on the same arrangement as the circumference but in reverse ie tthis time Thom Pi is used. None of this can be chance and the measurement of the diameter by Thom and then Parker Pearson are seemingly spot on accurate but the design is even more complex but not gone into yet. this is the reason the circumference is 330 x 272 and any number of permutations can be arrived at 13.2 x 6800 Imperial x Thom 13.6 x 6600 Thom x Imperial 26.4 x 3400 27.2 x 3300 52.8 x 1700 54.4 x 1650 Two systems entwined and working together to produce astronomical information using the imperial foot. The Saxon foot works in exactly the same way. If the foot is 100 units all the decimals disappear. So if the Aubrey 89760 is multiplied by the cancelled out denominators 56x52 then 2912 is the result or 8 years of 364 days. 89760 x 2912 = 261381120 this is 2 to the power 10 x 3x5x7x11x13x17 so both types of pi are engaged as 1632/520 and 1760/560 as base 17 and 13 and base 11 and 7. 