I enjoy writing, at least when the idea is to try to share what I’ve learned with others. I like to think I have some advice based on 20 years of experience working with the amazing numbers that I work with, and there seems to be something I’d like to say, but I’m still not sure how to say it.
I guess the essence of it, if I’m putting it correctly, is that certain nice round numbers can show limited exponential value, even when the heart and soul of data storage and retrieval through architectural proportions and metrological units, is exponential utility.
Exponential value and the relatedness of certain numbers through a recursive system means that by combining the right numbers, we can write a dozen important numbers, or even two and perhaps even three dozen, simply by writing two, just with a particularly well chosen length and width of a room or a building, if we don’t have some other important mathematical statement we prefer to make.
I suppose this goes back to the terrible Star Wars “joke” of how to “use the Fours”. Sometimes even the number eight, and sometimes even 8 / 2 = 4 are lacking enough in exponential utility that it’s preferable to “hot rod” them by multiplying them by the “king” of the fine ratios, 1.000723277.
This, even while the exponential value of the number 6, or even 12 or 360, can be astonishing.
This not only often leads to departures from the direction others are following, but even sometimes disagreements. Most people are going to look at something resembling the number 64 and think that’s what it is, and in certain frameworks they may be right.
Often someone will drag in the hekat or the Eye of Horus when making a pitch for 64 although that hardly guarantees exactly what was intended.
In a framework where data capacity is deliberately maximized, I’m going to most often see something resembling the number 64 as 64 x 1.000723277 = 64.04628973.
Anyone happen to recall that that is precisely ten times the perimeter / height ratio of the Mycerinus pyramid in the revised model I had to construct on account of Munck using IES Edwards as a data source for the Mycerinus? (The “data” from Edwards are in apparent conflict with some of the most trusted and respected sources of Egyptological metric data such as Petrie and Dash).
In the last post, I showed that in Munck’s model, the Great Pyramid’s volume / base area ratio is
((3018.110298 / 4)^2) x height 480.3471728) / 3) = volume 91155.78091 cubic feet
Volume 91155.78091 / (base area (3018.110298 / 4)^2) = 160.1157243
Of course we know that just as 64 / 16 = 4, 64.04628973 / 160.1157243 = 4.
In this case, there isn’t much incentive to “hot rod” the number 4 into 4 x 1.000723277, because it’s already directly linking a classic pair of “hot rods”, the souped-up versions of 16 and 64.
I know even then that “hot rodding” selected whole numbers like that may often still only afford them limited exponential utility, but if we have even only quadrupled our data storage and retrieval capacity that way, that’s still quite an achievement.
“Big Numbers” have also appeared in the subject of metrology lately. Pertaining to the relationship between the Egyptian Royal Foot and the Hashimi Cubit (rest assured the ancient Egyptians knew and used this unit well before its tenure as the “Hashimi Cubit” even if we cannot seem to produce a name they called it beyond assigning synonymy with the Egyptian Royal Foot).
One could be seen as a derivative of the other, and yet given their relationship, the Hashimi Cubit still manages to stand as in independent unit and Imperial value, just because it so often manages to make more sensible numbers out of particular measurement than does the Egyptian Royal Foot.
This pertains in part to the fact that the Imperial Version of the Egyptian Royal Foot, 1152/1000 Imperial feet, is a “big number”.
Such a situation may yet turn out to be present in the case other examples of related ancient metrological units. (This is still very much the subject of work that is recent, rather than “time-tested”, although much has become self-evident lately).
One of us working with these numbers – I think it was me – once said that 1.000723277 is the reason that Munck’s height for the Great Pyramid is 480 x 1.000723277 = (sqrt 240) x (Pi^3) = 480.374728 ft high rather than 480 ft – a literally brilliant example of a “hot rodded” number.
We can see some of the value of this in this in things like
480.374728 ft x 4 = 192.1388691, which would be ten times the proposed height of the King’s Chamber.
192.1388691 is another apparent ancient unit value that may be partly justified by the geometric relationships between units through squares and rectangles or the Vesica Piscis. Even though it can be seen as directly derivative of the Hashimi Cubit or Egyptian Royal Foot, this value may also have its own integrity.
Some of our ancient metrological units then may themselves have greater exponential value that do some “big numbers” no matter how interesting they may be. We should always be aware of that, because these unit values that were probably chosen with meticulous care often have exponential value.
That is when this work begins to transcend simple metrology, wherein only the use of a unit value to the first power, as in converting one unit to another, generally occur to us, in which case we may miss 4/5 of what was written and revealed by applying the Remen or Royal Cubit at the 2nd, 3rd, or even the 4th power.
We also look at the example of the Venus Orbital Period, which can be legitimately represented by 225. 225 is already a “big number” in its own way. It’s 15^2, whereupon 15^3 = 3375 is such a “big number” as to be pretty much almost unheard of in the countless equations examined by Munck, Morton, or myself.
Perhaps it speaks to the reciprocal relationship between the Hashimi Cubit and the unti of measure proposed by Petrie as occuring at Stonehenge of about 224.8 inches that in this case, we can “hot rod” 225 not by multiplying 225 by 1.000723277, but by “shaving” 225 by dividing 225 by it.
225 / 1.000723277 = 224.8373808
Given that consideration, perhaps it seems much less surprising that we are going to find little use indeed for the square of 225, we may often find 224.8373808 useful at up to the current record of the fifth power. Simply doing that can as much as quintuple the data strange and retrieval capacity related to the Venus Orbital Period value.
I will have to go back to my notes about it and double check to make sure, but it may be something else that is also new to announce, that the Hashimi Cubit value, whose exponential use is generally thought to be limited to the 2nd or 3rd power, may have been spotted functioning at a considerably higher exponential value.
The series may also point to a hitherto unknown approximation of the almighty Half Venus Cycle (Mayan Long Count) that is so new that it has yet to undergo investigation, the value being 18989.50038 approximating 18980. The series in question is thought to involve the reciprocal of the square of the indispensable 1.177245771, Munck’s might “Alternate Pi” and my nomination for the primary value of the Megalithic Foot, which is the exact value found in the relationship between the primary values for the Remen and Royal Cubit.
Again, the utility of the standard Hashimi Cubit value of 1.067438159 may be related to the fact that it is a “hod rodded” version of the valie in strict Imperial units, 1.0666666666 x 1.000723277 = 1.067438159.
One can remember a wealth of important numbers by remembering the “King of Fine Constants”, 1.000723277, as if it were an important phone number. The first time I saw it in print in Munck’s newsletter it was called a “gremlin” in the workings, but of course it’s hugely important in the scheme of things, including that it has the ability to transform certain numbers into more powerful data storage and retrieval tools.
Speaking of the Megalithic Foot, it’s probably time I put in another unsolicited plug for this
This is where the idea of the Megalithic Foot comes to us from, hence it is often called the Harris-Stockdale Megalithic Foot (HSMF). I tend to want to call it simply the Megalithic Foot to distinguish that I’m using the very slightly different figure of 1.177245771 which is not the HSMF precisely, but that would deprive Harris and Stockdale of the frequent mention they so richly deserve if I didn’t make it a point to remind people of just how highly I recommend this book.
It’s absolutely essential reading if one has even a passing interest in the idea ancient recording of numbers though architectural measurement. Not only is the most important Megalithic work since Professor Thom in my opinion, it will be essential to understanding the work of Professor Thom.
One of things I was talking about to people earlier today is that applying the concept of units of measure that provide that while the diameter of a circle is measured out in one unit, its circumference is measured out in another (the “diametral-circumferential” relationship espoused by GJ Bath), the standard Hashimi Cubit relates this way to a Megalithic Yard value that can be seen as derivative of the Megalithic Foot.
Seen that way, it may be fair to say that the Harris-Stockdale Megalithic Foot may be even more important than the Thom Megalithic Yard itself (not to mention that the two support the existence and legitimacy of one another as part of a much larger package of ancient metrological units that support each other’s validity and antiquity).
Be sure to check here https://northernearth.ecwid.com/Astronomy-&-Measurement-in-Megalithic-Architecture-p71162950 to make sure you’re getting this priceless work at a intended price.
One last thing I might mention under the subject heading of “Big Numbers” is volumetric calculations. I don’t have anyone’s work to point to and think I’ve proved it wrong, quite the contrary.
That’s just the thing about volumetric calculations is that when we multiply or divide a, b, and c in compound equations, the more components in the equation, the more sensitive the whole equation may become to even small changes in just one of the parameters.
This was something I learned back when working with Munck’s “geomathematical” method of “degrees x minutes x seconds”. With 3 parameters, the equations become sensitive to small changes in the seconds figure, so that a wealth of possibilities may be present over a surprisingly small stretch of terrain, and particularly so if there were a zero in the degrees or minutes column.
In fact, Munck’s would-be detractors have probably pointed out this problem on several occasions – it provides too much variance in a small range to be very certain of the outcome – and of course they seem to have had a good point.
Readers may have noticed that outside of calculations of volume, it’s exceedingly rare that I deal in compound equations. The more I can stick to simply y times or divided by z, the better. There is a reason for that, and it’s the sensitivity of compound equations to adjustment.
This very same problem may be present with architectural volume. It’s best to have the parameters of length, width, and height identified as certainly as possible before embarking on volumetric calculations, or the result may be a whole menagerie of possible volume figures that will want to be carefully evaluated one-by-one.
I would rarely if ever consider volume calculations to be reliable guides to the identity of an uncertain figure. It’s again why I tend to be excited about GJ Bath’s proposals for the Great Pyramid’s King Chamber – if we are very lucky, we may have something else there that might finally allow us the proper guidance to rest some certainty in a candidate for the length of the “King’s Coffer” which has eluded me for 20 years, even when some of its other proportions have been rather obvious for almost as long.
Cheers!
–Luke Piwalker
Luke Piwalker 