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The Mantissa in Ancient Reckoning of Time:
A Case Study of .890411

Charles William Johnson

Recently, Vigor Berg has sent me some of his computations of the Venus synodic cycle, whereby he proposes the figure 583.890411.  Professor Berg asked me if I thought that his figure was exact and reflective of the Venus synodic cycle.  My first impression was to express the idea that the synodic cycle is simply an average of the apparent cycle of Venus as viewed from Earth.  The synodic cycle in fact varies by full day-counts.  In ancient times it would appear that computations of the Venus cycle may be been based on variations from 580 to 585 days, if not even below or above that.  For example, the Maya may have employed the 576 day-count ---along with remainder math---, in order to reach the 584c and 585c counts.

In my mind, the significant point is that the Maya may have known the sidereal count of Venus, not only its apparent synodic cycle.  This point has been discussed treated in various essays published in the Earth/matriX series a few years ago.  The synodic cycle, in fact, does not actually exist as such in terms of planetary motions.  Let me explain. The sidereal cycle involves the motion of the Sun and the orbiting planet of Venus.  The synodic cycle involves the moving planet of Venus in relation to an observer on the planet Earth.  The sidereal cycle reflects an orbital time of 224.7 Earth days; possibly rounded off to 225c day by the Mesoamerican scientists.  The point-to-point precision of the Sun:Venus relationship makes sense and can be measured effectively.  The floating relationship of Earth Observer : Venus can only be expressed as an average figure; the average number in fact does not exist in terms of spacetime/motion. 

Yet, as a perception of a relationship, one can speak about this average time cycle and measure it precisely as an average of an accumulated number of apparent observations.  Hence, the idea that the 583.890411 is more precise as a perceived average, possibly employed by the Maya, is valid in this sense.  The generally cited average for the synodic period of Venus is that of 583.92 Earth days. Again, this number succumbs to the same observations stated above; it is simply an average and hence non-existent as such.  In other words, at no time, other than out of happenstance possibly, does the planet Venus actually orbit from the perspective of the Earth a time cycle of 583.92 days (or even that of 583.890411 days).    The analogy is that of a runner, who runs one mile in 4.01, 4.02, 4.05, 4.06 and 4.07 minutes. His average time was 4.042 minutes.  On none of those five occasions did the runner run the mile in 4.042 minutes; this was the average.  The same occurs with the concept of a synodic planetary time cycle.

So, even though, we may state that the synodic period of Venus, of 583.92 or 583.890411 does not actually exist, the fact remains that possibly the Maya may have employed these numbers in their computations for the average period.  Professor Berg has determined in his studies that the Maya employed the 583.890411 figure.  In his writing he is attempting to prove this computation in his own way, some of his work has been posted in the “Forum” of Earth/matriX, which we invite you to read.

A possible confirmation of the 583.890411 number may come from other computations.  Professor Berg has asked me to review the number and communicate my opinion in that regard.  One way to confirm the fractional expression of 583.890411 is to examine the mantissa of the figure (.890411).  It has been stated that the Maya avoided the fractions and remained with whole numbers.  I have always held that such a statement means that the Maya “knew” the fractions, the decimal places.  The issue is to know whether they simply discarded the fractions, as some scholars suggest, or whether they remained with the whole numbers, but computed the fractions, yet leaving them out of their results. 

A review of the mantissa of some of the ancient reckoning numbers may offer some insight into the computational math and remainder math in this respect.  Here, I will examine only a few computations based on the mantissa of .890411.  There are two ways to accomplish the computations of historically significant numbers.  One may employ only the whole numbers, or one may employ only the mantissa.  Either procedure leads to finding relationships among the historically significant numbers.  The third procedure would be to employ both the whole numbers and the mantissa of those terms.  For now, I will look only at the mantissa.

To view this entire 8-page essay go to: Mantissa_Ancient_Reckoning.pdf (complete version)

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Earth/matriX: Science in Ancient Artwork ISBN 1-58616-416-3

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