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Enigma Issue 9: Natural Sizes

by Ray Tomes | 9th May 1995

On the northern coast of the Whangaparaoa peninsula north of Auckland there are some very interesting rock formations which have been exposed by the sea undermining a nicely stratified cliff.

At the base of a vertical cliff are flat rocks which look as if they have been layed by a careful stonecutter in regular almost square and rectangular stone slabs. There are a variety of different sized features but each exhibits very accurately repeated distances between the cracks between the "tiles".

There are also narrow but deep rivulets cut by flowing water which are extremely evenly spaced and run parallel for long distances. Near the surface these are straight but as they cut deeper they produce sinusoidal waves of consistent wavelengths.

Some of the flat rocks have little indentations which contain tiny pools. Again these are arranged with very many at almost exactly the same distances from each other. At different parts of the beach the distances may be different but there are a small number of different sizes which are found repeatedly at different locations.

When I visited the beach yesterday I didn't have a tape measure, so used my shoes as a measure by counting the repeated patterns and seeing how many shoe lengths fitted. For example if 6 regular widths of the "tiles" was just under 10 shoe lengths (say 9.9) then each tile was 1.65 shoe lengths. It turned out that most of the tiles were either 1.1, 1.65 or 2.2 shoe lengths for their basic unit. These values are 0.55 shoe lengths times 2, 3 and 4 respectively. I might as well tell you that my shoes were later measured as being 27.8 cm long.

My friend, Shuji, and I estimated the larger rivulets as being in two sizes of 60 and 90 centimetres apart. The little pools were exactly one handspan (extended fingers) between centres and he said that his hand span was 22 centimetres. It is hard to convey the consistency of the spacings by words. We took some photos and I put my foot in each one (no wisecracks please) so as to get an accurate reference. The photos will allow accurate measurements as well as for others to see these interesting patterns.

Rachel, another member of our little group, also took back a small rock with tiny circular indentations at regular intervals. I should also mention that the square tiles often had little dents in them so that they looked like dice with either 4's or 9's on each face.

Once we returned to my friend's house we were able to measure my shoe and do some calculations to make up a table of all the sizes we found. It turned out that the three different types of structures had common sizes in many cases and that all the measurements related to each other. Better measurements will be able to be made from the photos and perhaps I will return with a tape measure.

As an aside, last year in Russia I was told that some researchers there have found a tendency for natural things to occur in certain sizes and had established these sizes over the range from about a millimetre to a thousand kilometres. I am expecting to receive information on this at some time and it will be interesting to compare their results to these ones.

The sizes may be summarised as follows:

Rivulets ~90 cm, ~60 cm and other smaller sizes yet to be measured from photos.
Tiles mainly 61 cm, 45.8 cm, 30.5 cm but some of 22-23 cm and a half and a quarter of that.
Indentations mainly 22 cm but some 15 cm.
Tiny indentations in small rock had many spaced at 1.27 cm.

All of the sizes fit the following sizes in cm:

      91.6  45.8  22.9  11.4   5.7
61.0  30.5  15.3   7.6  (3.8)
                  (2.54) 1.27

Note that there are ratios of 2 horizontally and 3 vertically. The values in brackets were not observed but show how the 1.27 cm figure fits the larger ones by ratios of 2 and 3 also.

Suddenly it hit me that the figures were much nicer in the old inches and feet units where they become (to high precision):

      36"  18"   9"           of course 36" = 1 yard
24"   12"   6"   3"           and 12" = 1 foot
                 1"   1/2"

I remembered that when the change to metric units occurred in New Zealand there were many people who said that they shouldn't change as the old units were "natural sizes" and the new ones quite arbitrary. At the time I put this down to them being so used to cutting bits of 4x2 and suchlike that they thought that trees grew that way. However I now think that I made a mistake in that assessment.

If rocks naturally divide up into units of yards and feet then it is hardly surprising that they were used as sizes when building stone houses. The pyramid and megalithic units although related to human body parts may be more importantly related to natural sizes for stones to divide up into.

Actually the units of inches, feet and yards are not the only ones used in old times. According to my Handbook of Chemistry and Physics the following units are defined:

Group 1

Fathom   Yard    Cubit  Span       --    Nail
 (72")   (36")   (18")  (9")    (4.5")  (2.25")
         Foot     --    Palm       --
         (12")   (6")   (3")
         Hand     --    Inch       --
         (4")    (2")   (1")
                        Barleycorn  Em   Line
                        (1/3")    (1/6") (1/12")
                                          --   Point

Again, the ratios are 2 horizontally and 3 vertically.

So the old english units have a pattern very similar to those found in nature. The pattern even continues to smaller units.

Other groups of larger units that I found in the above book:

Group 2

Cablelength Skein
 (720')     (360')
            Bolt                             Ell
            (120') (60') (30') (15') (7.5') (3.75')
                    Rope              Pace
                    (20')             (2.5')
Group 3
Chain     --    Perch
(22 yards)      (5.5 yards)
(1/100 chain)
Group 4
(3 miles)
Mile    --     --     Furlong
(1 mile)              (1/8 mile)

Note that group 1 is related to group 2 by a factor of 5 and to group 3 by a factor of 11. Group 4 is also related to group 3 by a factor of 5 and to group 2 by a factor of 11. So we can show all of this by the relationships:

group-4 group-3
group-2 group-1

with a ratio of 5 horizontally and 11 vertically.

The pattern of many ratios of 2 and 3 is the same as that found by Edward Dewey in the periods of cycles from many different disciplines. The single ratio of 5 to larger units was also found in the cycle periods by me and extended Dewey's table. The ratio of 11 is a new one. Why should all these patterns exist in units of length?

According to the harmonics theory, there are patterns of waves in the universe with the most powerful ones being related mainly by multiples of 2 and 3 but also by the larger primes less often. The whole pattern of these waves has been predicted based on some very simple assumptions. The pattern applies to both time and space because it is due to standing waves which divide up both dimensions. The observed relationships between the old units and my observations of stones suggests that the old units are all based on "natural sizes" and for what follows I will assume that this is indeed true.

If the regular patterns in the rocks are due to some sort of standing wave patterns then there will be a relationship between the sizes of the waves and their periods. The velocity of wave propagation will be important in this relationship. Generally I assume that the relationships are electromagnetic and that the speed of light is the correct conversion factor between distance quanta and cycle periods, but it is also possible that the speed of sound in the rocks or even the sea is the correct factor.

At present I have managed to establish linkages between all commonly reported cycle periods from about 600 million years down to about a week. There are some well established cycle periods in the range of minutes but these have not been linked with any certainty to the longer cycles. There are also many well established periods in the atomic realm which also stand as an "island of linkages" unconnected to the main continent. The above establishes another island of cycles.

Using the speed of light as a conversion factor turns an inch into about a one nanosecond period and a mile into 5.4 microseconds. Ideally larger and smaller sized structures are needed to establish the linkages between these various islands and continents.

Accurate determinations of the "natural sizes" need to be made. My rough values agree with the english units within 1% but in historical times there were slight variations between countries. The more information that is gathered, the better the results will be. Therefore I would be interested in receiving any other reports of measurements of repeated structures in nature.

I am hopeful that this year there will be enough material on the various scales to link them all together. There is a need for information relating to sizes from 1 to a million kilometres or a millisecond to a second. At such time it should also be possible to state accurately what the size of the universe is and how long it takes to go through one complete cycle. This will be based on comparing the observed pattern of ratios between cycles and distance units and the pattern predicted by the harmonics theory. Only at one value for "the size of the number one cycle" should all the data agree with the theory.

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