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For the past 13 years -- ever since an unmanned NASA
Viking spacecraft successfully photographed the surface of the
planet Mars in 1976 -- a mystery has loomed . . . a mile-long,
1500-ft high humanoid "face" discovered in a northern Martian desert
called "Cydonia." In its immediate vicinity have been
identified other "anthropomorphic objects": most notable,
several "pyramids" (see
Fig. 1).
Various investigators [Owen, 1976 -- see Hoagland
(1987); DiPietro and Molenaar (1980); Hoagland
(1986); Pozos (1986); Hoagland (1987); and Carlotto
(1988)] have examined this collection of objects over the past 13
years, and have reached widely varying conclusions.
The essence of
the controversy -- its potential importance or non-importance as a
"scientific" problem -- is perhaps summed up best by Hoagland
(1987):
"Either these
features on Mars are natural and this investigation is a complete
waste of time, or they are artificial and this is one of the most
important discoveries of our entire existence on Earth.
If they are
artificial it is imperative that we figure them out, because they
'do not belong there.' There presence may be trying very hard to
tell us something extraordinary."
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The initial purpose of this study was an examination of the "Cydonia
mathematics," which at first glance emphasize the importance
of two "dimensionless constants": "e" (the base of
natural logarithms = 2.718282);and "pi" [the ratio of
the circumference of a circle (or sphere) to its diameter =
3.14159]. These two constants appear, both separately (as "e" and
"pi"), and apparently together (as "e/pi"), redundantly encoded in
the fundamental geometry of the layout of the "anomalous
features" at Cydonia.
Following Hoagland's proposal (op cit) that a mathematical
"relationship model" would be the key to validating the basic
reality of Cydonia as an architectural construction,
and that
"e/pi" might be one significant relationship related to the
Complex, Torun (1988) made key mathematical discoveries
within a major geometric "Rosetta Stone" located at
Cydonia
-- a unique, five-sided, symmetrical "pyramid": the so-called "D&M".
He elegantly "decoded" a series of internal angles found within the
pyramid, and discovered the two mathematical constants, "e" and
"pi," encoded several times and in several different ways (via
angle-ratios, trigonometric functions, and radian measure) -- to
three significant-figure accuracy (see
Fig. 2).
Hoagland (1988), in re-measuring the "complex" he initially
proposed, promptly verified the existence of identical constants,
encoded via identical "dimensionless ratios," in geometry linking
*all* the previously identified key objects at Cydonia
-- and to at least the same measurement accuracy as Torun (see
Fig. 3a, "Cydonia Geometric Relationship Model").
Subsequently, using geodetic data from "The 1982 Control Network of
Mars" (Davies and Katayama, 1983), up-dated by
Davies
for Cydonia (1988), Hoagland discovered (op cit) that the
critical object Torun had "decoded" -- the Pyramid
-- lies precisely astride the key geodetic Martian latitude expressive
of the ArcTangent equivalent of "e/pi": 40.87 degrees = ArcTan
0.865!
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Verification of a highly-specific and redundant communication of
"circumscribed tetrahedral geometry" -- including its obviously
*deliberate* extension to the sitting of the Cydonia Complex
on the planet -- would be deemed a phenomenal discovery. If this is
indeed "the message of Cydonia," crafted by what Mars'
hostile environment strongly implies was a visiting interstellar
culture (Hoagland, 1987), then what could have been its purpose?
Apparently: To communicate the "importance" of tetrahedral geometry
itself!
If this is the successful "decoding of the Message" -- its
existence (if not the sheer effort expended in its communication)
must in turn raise obvious questions regarding "hitherto
unrecognized properties" of circumscribed tetrahedra.
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Since the latitude of the entire Cydonia Complex seems
to have been carefully chosen to reflect the ArcTANGENT of this
circumscribed tetrahedral "message, it occurred to the authors that
"something important might lie at the LATITUDE represented by the
vertices of a circumscribed tetrahedron -- placed 'inside a
planet'." This would represent the most elegant expression of
the ArcTANGENT trigonometric function emphasized repeatedly within
the Complex -- especially the choice (out of more than 18,000
possible other choices, to equal numerical precision) of the
specific Martian latitude:
40.87 N.
In working out the several possible implications of such geometry,
Torun promptly discovered the following: if a circumscribed
tetrahedron is placed inside a globe representing a gridded
planetary surface, with one vertex located either on the
geographical "North" or "South" polar axis, the resulting latitude
TANGENT to the other three vertices will lie at 19.5degrees N. or S.
-- 120 degrees of longitude apart.
Torun (1989) immediately noted on Earth the existence of
several significant Meso-American ceremonial complexes
at this specific northern latitude -- raising intriguing cultural and
scientific possibilities for lost or forgotten "ancient knowledge
of the significance of circumscribed tetrahedral geometry" (Becker
and Hagen, 1987). Unfortunately, these implications are too
extensive for inclusion here.
Hoagland noted something more physically significant: the
largest shield volcanic complex on Earth -- the Hawaiian
Caldera
-- is located very close to 19.5 North! He then realized
that a similar latitude marks the location of the largest shield
volcano currently known in the entire solar system: Olympus
Mons, at 19 N. -- on Mars. (more info about
Number 19)
Subsequent survey of solar system geodetic maps -- made from
spacecraft photography of the past thirty years, encompassing
planetary surfaces from Lunar Orbiter images of the
Farside of the Moon, to Voyager 2 close-ups of Uranus,
its satellites, and now (at this writing) the planet Neptune
-- revealed a remarkable (and currently inexplicable)
geophysical phenomenon (see
Table 1)
The majority of "active centers" on these objects -- from the greatest
shield volcanoes on the "terrestrial planets" (including equivalent
features on their most anomalously active satellites!), to the
enormous atmospheric disturbances seen on some "gas giants" ("The
Great Red Spots" of Jupiter and, now, of Neptune) seem preferentially to occur very close to
19.5 degrees N. or S., irrespective of other planetary
factors -- mass, rotation rate, obliquity to their respective
orbits, etc. (see
Fig. 6)!
There was some indication, however, that the polarity of the dipole
magnetic field, offset from the spin-axis, determined in *which
hemisphere* the phenomenon appeared; Jupiter's GRS, at approximately
20 degrees S., is consistent (in this model) with its opposite (from
terrestrial convention) dipole field polarity. [This raises the
interesting possibility of a "magnetic field prediction" vis a vis
Neptune, before the up-coming Voyager Encounter (Aug 25, 1989) --
based on observation that its "Great Red Spot" is at the same
latitude, and in the same hemisphere, as Jupiter's . . .]
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Following this striking, system-wide geophysical confirmation of a
predictive (if baffling) "embedded tetrahedral model," the authors
made another significant geometrical discovery at Cydonia
itself:
The critical 19.5-degree tangential latitude of the "embedded
tetrahedron" is specifically associated with a massive, *tetrahedral
pyramid* located TANGENTIALLY, on the circular rim,
of a 2-mile impact crater; in turn, this "pyramid" is connected
TANGENTIALLY (via a line denoting the exact North/South meridian) to
a circular (planet-like?) feature termed "the Tholus";
which, in turn, is connected to a third, linear feature ("the
Cliff") positioned TANGENTIAL to the same crater (see
Fig. 3b).
This highly-specific geometric "statement" -- a 19.5-degree angle
offset to the local meridian, connecting three objects (one of them
a tetrahedron!) in a way that reinforces the TANGENTIAL importance
of that relationship -- seems to explicitly establish a "geometric
connection" between "a tetrahedron" (the pyramid), a
circular, "planet-like" construction (the Tholus), and
the linear "Cliff' (the 19.5-degree offset reference),
a relationship also known to be coded elsewhere in the Complex,
in terms of derived mathematical constants: specifically, "e'/pi."
This explicit geometric statement also uniquely establishes an
*identical* 19.5-degree angle offset between the D&M
(at the other end of the Complex) and the resulting "map grid" --
further underscoring the significance of the D&M's
unique latitude relationships (see
Fig. 5).
Conclusion:
These interlocking, extremely meaningful, and highly predictive
relationships -- coded now in both the mathematical and blatant
geometric aspects of the Complex -- can only be
interpretated with extraordinary effort as anything other than the
result of a deliberate and systematic plan -- designed to underscore
the importance of "tetrahedral geometry."
That the anomalies predicted by this "geometry" encompass a range of
demonstrable solar system phenomena -- from deeply-buried planetary
mantle "hot spots," to associated shield volcanoes, to atmospheric
thermal "upwellings," etc. -- is also now readily apparent-- Even if
the reason for their specific "latitude-dependence" is not!
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Lest there be any confusion, the authors are NOT claiming there is "a
tetrahedron buried inside each planet!" Rather, it is suggested that
the "tetrahedral geometry" explicitly designated by "Cydonia"
is revealing an equivalent higher-order mathematical topology: i.e.,
a vorticular "two-torus" energy flow and internal fluid dynamics,
equivalent to tetrahedral mathematics.
That such an internal
"vorticular pattern" could be explicitly modeled by an "embedded
tetrahedral topology" is mathematically well-known (Porteous,
I. R., 1981). That such a "geometric short-hand" -- directing us
specifically to some underlying physical manifestation of
tetrahedral mathematics -- was left specifically for us at
Cydonia, seems now almost inescapable . . . if not
inescapably significant.
A quantitative treatment of the physics underlying this phenomenon
would appear likely to advance our understanding of energy transfer
inside planets considerably -- a not unexpected outcome, if this
indeed is "Mankind's first successfully-decoded extraterrestrial
message." Additional observations suggest, however, that the
significance of these predictions could extend far beyond "the
simple sitting of active volcanic centers on the surfaces of near-by
worlds . . ."
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We have already alluded to the surprising conformance of the planet
Neptune to this mysterious "embedded tetrahedral model".
Its newly-discovered "Great Red Spot" (as imaged by the
Voyager 2 spacecraft) now strikingly coincides with the
"19.5-degree latitude predictions" (more info about
Number 19) communicated by
Cydonia. It is the growing suspicion of the authors,
however, that the imminent
Voyager studies of Neptune, coupled with a
re-analysis of those studies it conducted of Uranus,
may provide vital evidence that the "Cydonia equations"
are trying to tell us about more than just energy transfer . . .
Based on the evidence detailed below, it is our suggestion that these
observations may relate to actual energy generation.
For many years there have been observed "energy excesses"
in the overall energy balances exhibited by the four major planets
of the outer solar system: Jupiter, Saturn,
Uranus and Neptune. These planets, inexplicably,
all radiate significantly more energy into space than they receive
from the Sun at their respective distances (Hubbard,
1980).
Jupiter's positive energy balance (1.67 -- compared to
solar input) apparently derives mainly from primordial heat retained
during it's "collapse phase" from the original solar nebula, 4.5
billion years ago. A secondary contribution is calculated as created
by the internal separation of helium from hydrogen ("helium drip"),
with the resulting release of additional gravitational potential
energy (Smoluchowski, 1967; Graboske et
al., 1975).
Saturn, far less massive than Jupiter, is considered too
small to have retained significant primordial heat. Thus, it's
observed "excess" (1.78 solar input) is wholly ascribed to the
gravitational separation of helium from hydrogen, tentatively
verified by the 1980 and 1981 Voyager infrared observations of
Saturn (Hanel, et al., 1983).
Ground-based data prior to Voyager's 1986 Uranus Encounter indicated
that Uranus and Neptune, similar
telescopically from Earth, differ dramatically in their observed
"energy excesses" (Pollack, et al., 1986). Uranus from
ground-based studies seemed to possess only a marginal (if any) heat
source, compared to Jupiter and Saturn; Voyager's January, 1986
fly-by enabled investigators to lower even this minimal estimate (Pearl,
et al., 1989). The new upper-limit on the ratio of internal Uranian
heat to solar input is 1.14 -- almost non-existent compared to
Jupiter and Saturn, and dramatically lower (by comparison) than
current ground-based measurements of Neptune's radiated excess (2.7)
over solar input.
Conventional sources for explaining Uranus' internal
energy, as slight as it is, encounter difficulties. Based on
Voyager data interpreted as evidence of a non-depleted
helium/hydrogen ratio in the Uranian atmosphere, the "helium drip"
model (so successful for Saturn) is not thought applicable (Conrath,
et al., 1987). And, for assumed early solar system nebula
compositions, resulting in a "rocky core" for Uranus equal to
between one and three earth masses, only 15-50% of the formal excess
can be accounted for in terms of "radiogenic heating" (decay of
radioactive elements -- Williams and von Herzen,
1974).
This leaves "exotic elemental compositions" (more than 6
earth masses of "rocky materials") and novel energy transport
mechanisms ("suppressed deep-atmosphere convection") as remaining
"conventional" possibilities (Stevenson, 1987). These
difficulties in accounting for the source of Uranus' internal heat
are only made more difficult when the planet is compared to
Neptune -- it's supposed "twin" in terms of size and
(presumably) composition.
Because of these potential compositional problems, and the great
disparity in internal energy-generation between these two otherwise
so-similar planets, the authors are led to propose another
possibility:
That the "Cydonia equations" may really be attempting to
describe, not merely internal energy transport, but internal energy
generation -- most evident (because of sheer distance from the Sun)
in the overall energy balances of Uranus and Neptune.
Further, the authors believe study of the detailed Voyager
infrared Uranus observations support this possibility:
Uranus, because of its
extreme obliquity (98 degrees) relative to its orbit, alternates
each pole toward and away from the Sun for a quarter of its 84-year
revolution. Despite this unique geometric shadowing effect (the
Uranian south pole not having "seen" sunlight for over 20 years, at
the time of the Voyager Encounter)-- THERE WAS NO GLOBAL
TEMPERATURE DIFFERENCE OBSERVED
BETWEEN THE DAY AND
NIGHTSIDE POLES.
Because of the problems
cited above with any internal Uranian heat source, and the distinct
possibility that (within the error's of Voyager's measurements)
Uranus actually possesses zero internal energy, discussion in
the literature has attempted to explain this global temperature
uniformity as "redistribution of intercepted solar input," via
"shallow atmospheric advection" (Friedson and Ingersoll,
1987); if the solar energy is being transported around to the
nightside of the planet by a shallow, upper atmospheric mechanism,
this would radically decrease (because of the non-necessity for
warming the entire nightside atmosphere) the amount of heat (energy)
required for transport to the nightside -- otherwise needed to
account for Voyager's global-temperature distribution
measurements.
A major problem for this model, however, was the Voyager
observation that the winds (clocked by observing several discrete
clouds) blow in the same direction as the rotation of the planet (Smith,
et al., 1986); pre-Encounter theoretical predictions had firmly
anticipated a four-day retrograde rotation of the upper atmosphere,
driven by external solar radiation. [The planet Venus,
where such opposite winds (to the rotation of the planet) are
observed, has its atmosphere dynamically-determined by intense
external solar radiation.]
Further, the fact that the observed Uranian clouds were seen circling the pole in a series of concentric
circles (parallel to decreasing latitude) as Voyager approached,
leads to difficulties in modeling heat transport to the nightside,
pole to pole -- across the latitudinal windflow.
These observations make it at least plausible to the authors that
internal energy, not "shallow advection of absorbed solar radiation"
constitute the primary driver for the Uranian atmosphere; a final,
detailed Voyager infrared observation, would seem to
add significant support to this hypothesis.
In scanning both hemispheres -- the dayside South pole and the
nightside North -- the Voyager IR instrument detected
a small but significant 1-2 K temperature drop in both hemispheres
-- at approx. 20 degrees N. and S. latitude (Pearl, et al, op cit).
Interpretated as the spacecraft viewing small-scale emissive and
reflected temperature profiles of colder, higher clouds (consistent
with similar observations made at Jupiter and Saturn
-- including measured temperatures of Jupiter's Great Red Spot,
which is also colder because it is higher than the surrounding
Jovian atmosphere), the Uranus' observations could be interpreted as
"some kind of massive 'upwelling' within the Uranian atmosphere,"
creating condensation products -- clouds -- as the atmosphere rises
to higher altitudes--
Narrowly straddling the "plus and minus 19.5-degree latitude"
where the "embedded tetrahedral model" of the Cydonia
equations
would predict -- for an internal, energy-driven "upwelling" on the
planet!
The difficulties involved in modeling a process, driven by external
solar radiation, which could create such upwellings and then "know"
where to create them -- at the "magic 19.5-degree latitude"
(more info about
Number 19)
predicted by Cydonia
-- are formidable. In the opinion of the authors, it is much easier
to ascribe these symmetrical upwellings to an internal energy source
-- released according to the now-familiar Cydonia pattern
observed elsewhere in the solar system of "internally-driven energy
emission."
The fact that these upwellings appear symmetrically in Voyager
IR scans of both hemispheres presents, however, an
interesting contradiction to other "planetary upwellings" -- which
seem to be restricted to one hemisphere, and to one localized
latitude region. Those on Uranus (if the model is
applicable) are not.
The apparent enigma is resolved, we think, by the fact that the
Uranian magnetic field is radically different from any other planet:
aligned at approximately 55 degrees to the inertial spin axis (Ness,
et al., 1986). It is at least interesting to propose that somehow
this almost right-angles magnetic orientation with respect to the
geographic poles "allows" the internal energy processes predicted by
the "embedded tetrahedral model" to manifest symmetrically in both
hemispheres. If true, this in turn allows some insight into the role
of planetary magnetic fields in the "Cydonia phenomenon":
in some geometries, that of selective hemispheric suppression of an
internal energy-transport mechanism.
Based on all of the above, it is the considered opinion of the authors
that at Uranus, the Cydonia "embedded
tetrahedral model" reveals itself as not only a mechanism for
energy transport within planets -- but, quite likely, as a process
of internal energy generation as well. The implications of verifying
this hypothesis -- for all planets where these phenomenon are
observed to follow the "Cydonia predictions," including Earth -- the
authors think are obvious . . . if not highly significant in terms
of other astro-physical environments, where involving a potential
"new source" of energy might lead to wholly different fundamental
models.
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Heartened by the apparent success of this "embedded tetrahedral
model" in empirically predicting surface manifestations of
internal planetary dynamics, the authors decided to extend the model
to the Sun. This is the result.
With no solid lithosphere, the solar plasma "photospheric surface" is
of course far more like the banded, turbulent atmospheres of the
giant outer planets (though much hotter!), than the dense, solid
crusts of the "terrestrial" planets. And like the atmospheres of the
giant planets, there is a recurring "surface phenomenon" which is
measurable -- in terms of a coordinate system referenced with
relation to the rotational axis: sunspots.
Though appearing dark against the surrounding photospheric background,
sunspots are still measured at approximately 3500 K, and radiate
enormous energy per unit area. More significant for our discussion
here, though convection within the spot "umbra" (the darkest,
central part) is suppressed by intense, local magnetic field
strengths (Hale, 1913), there is evidence of enhanced energy
emission around the spot itself -- perhaps as much as one or two
percent over the normal photospheric background.
When flare activity is considered (which occurs in the intense,
tangled magnetic fields between sunspot groups), spots -- as opposed
to being "regions of lower solar output" -- are in fact localized
areas of "enhanced energy emission" (Brandt, 1966)
The recurring 22-year solar sunspot cycle is made up on average of two
back-to-back 11-year components. Sunspots at the beginning of each
cycle usually appear in pairs, with opposite magnetic polarity -- N.
and S. (though, entire localized "sunspot regions" -- see above --
can also form), at high solar latitudes (-- 40 degrees). The
appearance of new additional "spot pairs" (and the dying of "old"
ones), as the cycle progresses, subsequently drift North and South
(depending on the hemisphere) -- eventually converging late in the
cycle in the solar equatorial regions. 11 years later, on average, a
new cycle begins, with sunspot pairs of now opposite polarity
(compared to the initial cycle) "breaking out" once again at high
solar latitudes -- with subsequent spots appearing at decreasing
latitudes as the new cycle moves toward its 11-year completion.
To our amazement, when the mean latitude of the majority of sunspot
and associated flare activity was examined, the mean in both
hemispheres -- from beginning to end of each cycle -- was found to
be remarkably close to 20 degrees (Fig.
7)!
The apparent appearance in the Sun of the same phenomenon so
successfully predicted by Cydonia for planets --
including the possibility that the effect is somehow related to a
new source of energy generation and not "merely" energy transport --
opens up extraordinary possibilities.
These must include consideration that solar luminosity could be a
mixture of two energy sources: the "traditional" fusion of
hydrogen within the solar core; and another, still inexplicable
process, somehow modulated by the general wax and wane of solar
magnetic activity!
[R. C. Wilson, after many years of careful
observations at Mt. Wilson, has demonstrated direct variation of the
solar constant in synchronization with the solar sunspot cycle (Wilson,
et al., 1980). Newer Solar Max satellite data from above the
atmosphere confirm the findings.]
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