Resonance

Frequently in my writing, I use the term “resonance”, referring to “mathematical resonance” or “resonant” numbers, but I’m not still not sure if I’ve ever given any adequate explanation for the term.

In acoustics,

noun

1. the quality in a sound of being deep, full, and reverberating.”the resonance of his voice”.
2. (physics) the reinforcement or prolongation of sound by reflection from a surface or by the synchronous vibration of a neighboring object

I’m not certain who first applied the term to our work, but I suspect that if I could find the documentation, it would be Michael L Morton who deserves credit for first having used it, and not someone like me who tends to come up with rather unimaginative names for things.

It really is a very apt term for what it attempts to describe in mathematics, particularly the part about resonating with neighboring objects (or in our case, neighboring numbers).

In practice, I use to “resonance” to mean when a number has strong connections to notable number of other important numbers, or when a number has a notable quantity of aliases – aliases simply meaning different names or formulas that we can use to refer to a particular numerical value.

((sqrt 3.75) x Pi) / 5 = 1.216733603 is one aliase for the 1.216733603 ft Remen, sqrt (.15 x (Pi^2)) = 1.216733603 is another, and so on – and yes, the Remen value has so many meaningful aliases that we can consider it one of the more resonant numbers in our vocabulary.

Although each ancient monument represents a data repository unto itself, Munck and his students tend to see each monument as also belonging to a larger network, or web – or as Munck called it, a “matrix” – of numbers larger than itself that also incorporates and “speaks to” a larger number of ancient monuments.

One analogy is plucking a single strand of a spider’s web – the whole web will shake, or reverberate, or resonate.

The most resonant numbers being those with the strongest or largest number of meaningful connection to other important numbers, or those that have the largest numbers of impressive aliases, should also mean that these numbers will appear in many places because they can be constructed so many different ways, so that they can be found to be fairly widespread in their occurrence even though radical difference in proportion or measure or shape may be seen between any two constructs that can generate the same number.

The Great Pyramid and Stonehenge, which have little in common in terms of shape or structural design, manage to both incorporate a surprising collection of the same important numbers.

When I talk about using a “strength of the numbers” approach to architectural interpretation, or starting out our interpretive experiences with “good numbers”, I’m referring to “resonant” numbers. It’s this resonance that makes them “strong” numbers, or “good” numbers, or numbers with “strong connections”.

From there you can probably guess that I’d say that the two most “resonant” numbers I know are the two that I keep referring to as “the two most powerful mathematical probes ever discovered” – these numbers “reverberate” or “resonate” throughout the network to sometimes remarkably high exponential values (current record is still sqrt 60 or (1 / sqrt 60)) resonating throughout the system to as high as the 33rd power or possibly even higher.

Resonance is, at least for me, what helps define Munck’s system of numbers as having outstanding qualifications as an ancient system for data storage and retrieval, and that is again what so many of us mathematical and metrological researchers are attempting to do, is to mine ancient architecture for data that we suspected to be stored within them.

This phenomenon of mathematical resonance also creates resonance between seemingly unrelated monuments. I often mention cases of this; I will be talking about Egyptian pyramids and suddenly bring up data from a Mexican pyramid or stone circles, which some may accidentally read a little too much into.

I have no way of really knowing if the designers of Stonehenge were actually thinking of the Great Pyramid, or vice versa, but I do know that because of the mathematics resonance between the two, either one is a great place to go to learn more about how the other works.

I could add a reinforcement that resonance isn’t always measured in terms of exponential utility. The Hashimi Cubit value of 1.067438159 (ft) has rather poor exponential value to be honest, yet what makes this number particularly resonant is the number of places it can actually fit in with exact precision. Many equations point to it, and it is not only predicted that it will be found in a great many places because of this, but such predictions have largely already come true.

We can also say that because of some serendipitous coincidences which helped to make the impossible task of working out an ancient all-inclusive calendar system into an actual reality (the Mayan Calendar is an actual if somewhat crude example of exactly this), that the planets themselves express some surprising “resonance” with one another – they are “singing” in deep “resonant” voices that reverberate throughout their system.

–Luke Piwalker