> 'This inquiry reveals the oldest extant
> weights and measures linked by significant
> magnitude ratios to those current in historical
> times, and suggests that this ancient metrology
> was geodetic in origin.
I feel like quite the ass (and probably should) for saying anything like this in response to such an utterly commendable post about Berriman, but sadly this may be a part of Jim Alison's (or others') quite impressive and exemplary work that I cannot quite bring myself to agree with - would it quite make sense that geodesy should precede metrology?
The closest I seem to be able to comfortably get is that this ancient metrology was geodetic in application, even if it's still not perfectly clear if the ultimate application were geodetic measurement or geodetic modelling.
Perhaps there is no single ultimate application, but I notice I'm not the only one whose work seems to indicate geodetic modelling at ratios like 1 foot:1 mile, and that's still all I really know to do with a precisely 5280 mile even now is simply accept that ratio to the foot, rather than trying to make the mile relate to other units in a directly derivative way.
Like the foot itself perhaps, the 5280 foot mile may exist mainly to give meaning to other units. Reading some of these discussions, I've recently begun to wonder it that isn't where an ancient meter would also fit it - whether it wouldn't fit better into the scheme of things to simply accept its value in relation to other units, rather than trying to get the meter to relate to other units in a direct or derivative way.
Perhaps not on the other hand, I recently found a page from one of Munck's publications in a reference binder stating that a basic unit of conventional longitude at one of the Egyptian pyramid fields is 5277 feet. That may try to keep me up at night...
> So what you are doing without realising is
> repeating Berriman's calculations to support his
> argument without quite getting them to agree his.
Perhaps some of us independent minded types are more eager to participate in consensus when we don't realize that that's what we're doing? lol
I think I'm probably most likely to achieve some consensus with Jim Wakefield because he's not afraid of the Pi ratio, lol. I was quite amused and delighted to find an old post of yours with one of my Stonehenge numbers verbatim after you'd looked at some of his work. :-)
For myself, I think where Berriman undoubtedly shines is in recognizing relationships between units, as opposed to necessarily in recognizing the absolute nature of some of those units or their origins, just as I likewise think where Petrie shines is the securing of data as opposed to necessarily in the interpretation of it. I don't know if it's quite fair to expect any trailblazer get everything right, come to think of it.
(I think I will leave Petrie's struggles with the Royal Cubit to speak for themselves as to the possible perils of what has to be one of the most fundamental premises of "inductive metrology" since I've already made more detailed references to them recently enough).
> Berriman was an Oxford professor and had access to
> the Oxford library and his studies were his
> private work.
> The point i am trying to make here is that until
> we all realise whose analysis we are using or
> almost using correctly the same theories will
> appear with different calculations over and over
If so, I think it may happen rather easily because Berriman's relationships between units are quite effective, whichever particular numbers we are using.
> This was happening over 10 years ago on this very
> website, nothing has changed.
One would hope that if some of those debates were actually settled that some of this work wouldn't have so much a cyclical nature, but I can't quite think of much to offer for constructive suggestions except being careful of accidental cross-pollination between separate sets of numbers (Michell's long and short versions of units for example).
At least based on my own experience, that may sometime make for groups of numbers that are a bit "frayed" around the edges and may never quite fit together perfectly, which can be unfortunate if one is trying to get them to fit them together perfectly.
That said, I'm that much more impressed with how well the equations in your post fit together.
Perhaps you've managed to successfully isolate a particular functional group of numbers here. I imagine some congratulations are in order whatever the case, so may I say - Nice work!