I don’t seem to be coming up with the stupendous post on the subject that I’d hoped for, but at least a little bit really should be said about a few things nonetheless.
I’m more impressed with the work of David Kenworthy and Bogna Krys (rodz) than ever, after having done some more detailed work with Mayan Calendars lately, particular with values related to actual surviving codices.
I may never be able to accept all of their work, but I haven’t hesitated to say that I think a lot of what they are doing is valid and important. Still, I’ve had a great struggle defining exactly what it is they’re working with.
I’ve seen for myself now the importance of some of their numbers like 346.6666666 with my recent work with Mayan Calendar numbers. I’ve seen how integral it is to some of these systems or subsystems. I may never agree that we should chop 346.6666666 in half and call it 100 Cubits, even with my predilection for associating metrological units with astronomical values, but I do think they are working with numbers that are “real” and important.
The fact that 346.6666666 does fit into simple whole numbered systems suggests once more – and particularly so – that what they and some other researchers are working with is largely the “common math”, if I must coin any phrase for “everyday” mathematics or “mathematics for the masses” as it were. Our 365 day, 52 week year would be an example of the very same – it isn’t exact, but it works fine for the average person for general purposes and we have corrections we can make when the simple approach begins to make a mess of it (for us, that’s the occasional leap year).
It’s an important point that the interactions between simple round numbers aren’t always themselves simple and round. Eventually we either have to start ignoring the output that isn’t simple and round, or forfeit the very idea of exactitude. No system of numbers that I know of is able to make all of astronomy into nice round numbers, and if things are going to inevitably get complicated, I’m quite content with my own complicated way of doing things which offers a great many advantages.
This is what ancient people aspired to do – something that there probably is no simple way to do, because as many fortuitous near-coincidences may happen with astronomical data (the heart and soul of complex calendar systems), the heavens apparently aren’t quite so perfectly synchronized for the math to describe them to be that simple.
I remain firm in the belief that our task is to never mind simplicity, even if fits some of our stereotypes about simple-minded ancients, and to go ahead and find the complex systems that are most useful and universal. It’s not a simple minded-business, period.
Thus DavidK and rodz and others may often be on the cutting edge of orthodox historical mathematics, to which their work may be a great boon, and it’s difficult to justify completely ignoring it. For me, these orthodox numbers or “common math” are at very least what my own math aspires to emulate (approximate), albeit in more useful and more fluid ways.
Of course, a lot of their work is supported by historical sources – there was undeniably a “common math” in use by some – even if this only represent the tip of the iceberg, whereas my own work is supported by various chains of logic and surviving architecture rather than surviving written records that we are able to recognize.
With any system of ancient math, the only we may have to recognize intent with the complex numbers and options that eventually set in, is to look at the numbers that are grouped together in close proximity particularly and why they are grouped together. I approach any ancient architecture with the premise that length / width will be meaningful, length x width should be meaningful also, and so forth.
What poses problems for imposing such stringent criteria isn’t that it does work, it’s been proven often enough – it’s that the ancients still seem to be 10 steps ahead of us when it comes to ancient calendar math so that half the time it’s still hard to tell if it is working until we catch up.
Even for being measured to the nearest centimeter, George Andrews’ data (or Flinders Petrie’s for that matter) isn’t accurate enough to settle many questions about individual measures. It’s still up to the groupings of numbers themselves, and their properties in combination (including exponential value).
How else would the ancients have ever hoped to clarify their intent when writing numbers in the physical medium of architecture?
I should also note that my work does achieve some welcome simplicity through the “recycleability” or multifunctionality of certain numbers. Figures like 1.622311470 and 1.177245771 belong to a number of different astronomical formulas. They are reusable, making for substantially fewer numbers to memorize or learn to recognize on sight.
At any rate, yes – there was a “common math” and the “common man” is still working to advance it even after the voluminous efforts of academicians, but ancient man had thousands of years to find out its shortcomings and be inspired in the direction of something more useful.
It’s critical for us to not confuse the “common math” with what is possible simply by applying a little accurate geometry to idealize and standardize metrological unit values (the Remen, Royal Cubit, etc etc).
With the realization that they are working with “real” Mayan numbers, I should also commend DavidK and rodz on having done so much to advance the premise of the Maya working with reciprocal numbers. The repeating decimals they are so fond of are often the sign of a whole number in reciprocal form, something else that’s been emphasized by my recent efforts to wrestle just a bit with actual codices.
It’s not just DavidK and rodz that deserve some free advertising, though. I maintain that my compatriots Mercurial, DUNE, molder, drew, Jim Alison, and others at GHMB are all doing some valid and meaningful – and often inspiring – work with ancient mathematics. It may attract its share of trolls, but it’s a very rewarding discussion forum, and I cannot help but admire Graham Hancock’s efforts to get it across to the general public that however you look at it, much of our history has gone missing, leaving only what we can manage to piece together.
–Luke Piwalker
Luke Piwalker 