Exclusion

Especially if anyone is “just tuning in”, they may wonder what on Earth I’m doing with whole numbers. I still struggle to find the correct way to explain it, but for purposes of illustration, for the whole numbers 0 through 99, the numbers in this chart in green are the ones I work with, and the ones in red are ignored.

To some degree, it can be explained that I work with whole numbers that are factors of the number 360 – whole numbers that can create the number 360 through multiplication or division, but at best that might be confusing, and at worst perhaps not exactly true.

If we looked at 360 / 64 = 5.625, we might not guess that this is keeping with a such a rule.

From https://www.calculatorsoup.com/calculators/math/factors.php

Alternately we might say we use the whole numbers that can be created from 2 through 9 excepting 7 and hope that that remains true in the bigger picture.

Adding more zeroes to 360 finds more valid whole numbers used in this work, yet it still can’t pick up the valid whole number series 27 x 2 = 54; 54 x 2 = 108; 108 x 2 = 216; 216 x 2 = 432, etc. (216 x 1000 = 60^3)

At any rate, I’ve elected to put up the chart so that people can have a quick reference to the lower whole numbers that I do and do not work with.

I’ve also put it up to help make a point.

Notice what is happening here – 100 possible whole numbers have been thinned down to only 30.

I should admit that sometimes I struggle to embrace the work of others who work with ancient mathematics. These rules have become so ingrained that watching other use numbers like 7 or 11 or 13 is like watching them set fire to their cat – such things simply aren’t done and I feel a bit as if as being a responsible citizen, I should perhaps summon the authorities.

The point to be made is that even by reducing the pool of available whole numbers from 0-99 by a whopping 70%, we have still not prevented the often confusing metrological overlap that happens just because ancient cultures for some reason demonstrably used multiple units of measure.

If you think what I’ve shown in the last few posts or more looks like a mathematical traffic jam, imagine what a mess it might be if 70% of the available whole numbers had not been excluded from the proceedings.

In the last post especially we tried to capture some of that metrological overlap and harness it to good use, but we still ended up with 4 different Palestinian Cubits to go with 4 different Megalithic Yards in order to do it.

Another way of illustrating metrological overlap might be that in spite of the case that has been made for the two numbers from “Another Tale of Two Numbers” and what we have discovered about the relationships to the Palestinian Cubit, we still get figures that run contrary to this such as

2 Hashimi Cubits / 1.5 = (2 x 1.067438159) / 1.5 = 1.423250879, which is neither of the two number from the “Tale”, 1.423799344 or 1.424280286.

Even with such a simplified pool of whole numbers, it’s still that easy to generate from a whole number and a metrological unit a number that so closely resembles others that also arise from very simple numbers of metrological units – and we’re not using that many metrological units either, especially after having reduced the relatively few that we have looked at to a smaller number of unit families.

Please don’t get me wrong, people can and do make functional schemes using the numbers that are banished here, and someone probably did the same in ancient times. On the other hand, probably everyone I have seen go that route may end up adjusting their Pi ratio and/or Royal Cubit value until the proverbial cows come home – and by way of equivalency, some other unit values related to the Royal Cubit along with it. If a Royal Cubit x 64 = 100 Indus Feet, changing the Royal Cubit value may mean the same as changing the Indus Foot value, creating an equal number of different speculative Indus Foot values, or else specialized rules like only changing the Indus Foot along with the Royal Cubit sometimes, and so on.

So while I often make a case in point out of having excluded 7 and 22 preventing clashes with the Pi ratio (22/7 = 3.142857143, Pi = 3.141592653), there is more to it than simply that.

The bottom line is that all sorts of great expectations from numbers that numbers may or may not be capable of living up to generate something of such complexity that we are best advised to take our simplicity where we can get it, and that is exactly what this exclusion of many whole numbers is providing, believe it or not, is simplification.

That’s not to say that with such a gesture we are necessarily accepting limitations. Quite the contrary, the invalid status assigned many of these numbers means that when we do encounter them in architecture, say a temple with 22 columns or a stone circle with 37 stones, that they may function is “wildcards” so that they are substituted for not by single values, but by a variety of different approximations that may make a wider variety of mathematical expressions true.

I’ve never really gone down the list and suggested substitutions; rather I rest somewhat assured that the correct substitution should be what a particular situation requires or benefits most from – sometimes even multiple substitutions.

For example the inverse of 1.423799344 that we have been talking about the last few posts, 1 / 1.423799344 = 7.023461587 might be considered a substitution for 7; other times 7 might be substituted for by 19.46773746 x 360 = 7.008385550 x 10^n, or even 6.981317008 (1 / (Radian 57.29577951 / 4)), and etc.

This is really nothing new because of course even though we divide a 365 day year into 52 weeks of 7 days, 365 does not really divide by 52 or 7 evenly

365 / 52 = 7.019230769 — see where I find justification for suggesting that of all things, 7.023461587 might substitute for 7? I don’t have to look far — and 365 / 7 = 52.14285714.

Of course, we can easily see that 52 x 7 isn’t 365, it’s 364!

I’m not the only one with some strange math, it seems.

At Stonehenge 260 / 10 seems to be substituted for by 259.7575758 / 10 (to name one); the number 56 suggested by the 56 holes of the Aubrey Circle may see multiple substitutions depending on both the cycles of the planets that are being expressed (56 or thereabouts seems to be important to a number of astronomy equations) and the parts we have been given at Stonehenge to construct things out of.

(By the way, I’m not sure if this is a new discovery, but decimal point placement aside, the Stonehenge inner sarcen circle circumference squared times 24 = the Aubrey Number that I’ve long thought may belong to scheme of the Stonehenge Aubrey Circle’s measurements)

305.7985077^2 x 24 = 224.4305456 x 10 — what a remarkable “coincidence”, yet another for Stonehenge.

11 and its multiples are of course well covered by the Indus Foot values I work with (1.1008744628 ft and 1.100078966 ft substituting for the “1.100000000” ft Indus Foot); 73 is substituted for by 6 Remens = 6 x 1.216733603 = 73.00401618, and etc.

At any rate, there is more again of why I work with numbers the particular way that I do – it’s the way that it makes sense to me for ancient peoples to have used them in order to have made their very grand and complex calendar schemes work best, even if has managed to elude the historical record.

–Luke Piwalker