All Done with Mirrors

Having delivered a lecture on the history of weights and measures at the Oxfordshire County Museum at Woodstock on 1st November last year, Vivian Linacre visited the Ashmolean Museum in Oxford the following morning, when he met Dr Michael Vickers of the Department of Antiquities. Vivian told Dr Vickers about the forthcoming book, "All Done with Mirrors" by his friend John Neal, of which he had seen a draft. He urged each of them to get in touch with the other. The outcome was a letter dated 19 April to Vivian from John Neal, saying: "I had given up any thoughts that Michael Vickers had a continuing interest in my work and, but for your encouragement to do so, would not have contacted him of my own accord. We struck up a correspondence whereby I sent him a series of essays that comprise my web page [john-neal@secretacademy.com]; he found them "persuasive" and requested a copy of the book.
He had recently been asked to write a commen-tary on the works of two respected scholars that were being reviewed in the prestigious science magazine 'Nature'. He noticed similarities between their findings and my work on linear measure; therefore he wanted to get my work reviewed in the same organ. "Well, Vivian! Had I been asked to write my own review I could not have done better. Be-cause he had a prior grasp of the subject, he im-mediately recognised the correctness of my rea-soning and, within the space available, he has been remarkably informative of the general the-ory. Thank you so much for pointing me in the right direction." Because of the importance of this review in 'Nature' (page 1030) in relation to the pre-historic origins of our customary measures - following on the great interest aroused by Robin Heath's article in our issue No. 14 - we are re-producing it here.
"Thanks to John Neal's remarkable new book, ancient metrology - once the playground of Newton but now largely ignored even by archaeologists - should cease to be a pariah subject and regain its place at the centre of the study of antiquity. In the past, the widely attested variations in ancient reported linear measure-ments have been put down to sloppiness on the part of our ancestors. But Neal is able to show that such variations belong to a logical, elegant and cohesive system partially based on divisions of the Earth's surface at different points on the longitudinal meridian. The Earth is not a true sphere, but is subject to polar flattening, which means that the longitudinal meridian, or the great circle through the poles, is essentially el-liptical. The distortion is minute, but it creates a measurable variation from degree to degree. Degrees nearer the poles are longer than those at the Equator. Thus, a widely accepted value for the Greek foot of 1.0114612ft proves to be 1/360,000th part of the longitudinal meridian degree at just under 38° latitude - the same latitude as that of the Aegean. Elaborating a scheme first noted by the philoso-pher and historian John Michell*, Neal observes that feet (or cubits) stand in a ratio of 175:176 to larger units in a series.
This at once explains the Roman architect Vitruvius' account of an odometer - an instrument for measuring the distance traveled by a wheeled vehicle - that contained a mechanism designed audibly to release a stone into a box every mile; in his case, 400 revolutions of the 12½ft perimeter to the 5,000ft mile. If Vitruvius' 4ft radius 12½ft pe-rimeter, or 3.125 pi ratio, was strictly adhered to, there would have been a discrepancy of more than 28ft in every mile. But if the shorter Roman foot of 0.967680ft was used for the diameter of the carriage wheel, and the longer Roman foot of 0.9732109ft used for the perimeter, the calculation of the mile is accurate in terms of the longer measure. The difference between 22/7 and 25/8 can be expressed as 3.142857 = 176, while 3.125 = 175 (both values of pi were used in the ancient world)…..There was thus a practical purpose underlying variational fractions between the ancient standards (and this is but one of many) and they can no longer be put down to carelessness or error. Although the system is complex, it is blindingly obvious once it is tabulated. Roman, Greek, Egyptian and Babylonian measures are seen to be inter-related. Life is breathed again into Alexander Thom's 'megalithic yard', a unit of measurement Thom found to have been consistently used at many prehistoric megalithic sites. As Neal points out, "not only is the megalithic system largely ignored by archaeologists, it is opposed - even by the numerate among their ranks." This position is now untenable, as it can be shown that the megalithic yard shared an origin with the Sumerian cubit. And the foot-measure used in England - equivalent to a Greek foot - proves to have played a pivotal role in the whole metrological system.
It is ironic that just as it is being thrown on the scrap heap of history, its historical importance is beginning to be recognized." [our emphasis] The review concludes: "…this is a sober and thoughtful analysis with far-reaching conse-quences for the study of the past. More than that, it is a major contribution to the history of science."

*John Michell is a close associate of John Neal, and likewise a supporter of BWMA. John Neal's book, 'All Done with Mirrors' (ISBN 0-9539000-0-2) is available directly from the author (johnneal@secretacademy.com), price £25.00. An excerpt from it appears in the BWMA handbook, 'A Guide to Customary Weights and Measures'.

The Spectator on 9 June published a review of John Neal's book by (guess who!) John Michell, of which this is worth quoting: "the old measures…express the dimensions of the earth and moon within a rational code of number. And from this same code are derived also the measures and ratios of music, geometry, astronomy, chronology and physics. John Neal's discoveries give firm ground to the Pythagorean world-view that 'all is number.' There have been many systems of measure throughout the world, but all of them, including the units extrapolated from Mexican monuments, are related to the others by simple fractions, and together make up a single universal system. At the root of all, the basic unit of reference is the ancient foot that we are now in the process of discarding. The best arguments against that process are in the find-ings of this book." John Neal has very generously undertaken to insert into every copy of his book an A5 'flyer' headed "Do you care about preserving our traditional systems of weights and measures?" followed by a paragraph beginning "If so, why not become a member of the British Weights and Measures Association?" and continuing with details of membership, our web-sites, etc.