High Tide and Low Tide
No tension member is innocent of compression, and
no compression member
is innocent of tension. That is, when we are tensing
a rope visibly and axially, its girth
contracts as it goes untwistingly into compression,
precessionally, compressing in planes
at 90 degrees to the axis of our purposeful tensing.
We learn experimentally that tension
and compression always and only coexist and operate
precessionally at right angles to one
another, covarying in such a way that one is ebbing
toward low tide while the other is
flowing toward high tide, or vice versa, in respect
to relative human apprehendability, as
they fluctuate between visibly obvious and human subvisibility.
Tension and compression are inseparable and coordinate
structural systems, but one may be at its "high tide"
aspect, i.e., most prominent phase,
while the other is at low tide, or least prominent aspect.
The visibly tensioned rope is
compressively contracted in almost invisible increments
of its girth dimensions everywhere
along its length. This low-tide aspect of compression
occurs in planes perpendicular to its
tensed axis. Columns visibly loaded by weights applied
only to their top ends are easily
seen to have their vertical axes in compression, but
invisibly the horizontal girths of these
columns are also in tension as the result of a cigar-shaped,
swelling pattern of forces
acting in the column at right angles to its loaded axis,
which tends, invisibly, to transform
toward the shape of a squash or a banana. As a result
of the visible, or high-tide, vertical
compressioning aspect of such axial loading of the column's
system, this swelling force
imperceptibly stretches, or tenses, the column's girth
as a low-tide reciprocal function of
the overall structural-integrity reciprocity.
Functions are never independent of one another. There
is a plurality of
coexistent behaviors in nature; these are the complementary
behaviors. Functions occur
only as inherently cooperative and accommodatively varying
subaspects of synergetically
transforming wholes. Functions are covariants. Wave
magnitude and frequency are
experimentally interlocked as covarying cofunctions,
and both are experimentally gear-
locked with energy quanta. The meaning of a function
is that it is part of a complementary
pattern. No function exists by itself: X only in respect
to Y. Tension and compression are
always and only interfunctioning covariables whose seeming
relative importance is a
consequence of local pattern inspection. Multiplication
is accomplished only by division.
Universe expands through progressively differentiating
out or multiplying discrete
Tetrahedral Models of Functions
Covarying functions are tetrahedrally modelable. A
series of covarying
tetrahedral models is presented in Secs.
Tension and Compression: Summary
|Compression is IN.
|| Tension is OUT.
|Compression is dispersive both laterally and circumferentially,
inherently electrostatic because differentiative, divisive, temporary,
||Tension is omniradially conversive
and is both electromagnetically
eternally and integrally
|Compression tends to local dichotomy and multiplication
||Tension is unit: universally cohering
and comprehensively finite.
|Compression is locally expressive in
discrete tones and frequencies internal to the octave.
||Tension is both internal and external
to the octave and is harmonic with
either the unit octave or octave pluralities.
|Compression accumulates potential.
As demonstrated in the arch, compression is limited to absolute, local,
and within-law relationships of one
||Tension is comprehensive, attractive, and gravitational.
Tension is inherently integral and eternally, invisibly, infinitely
comprehensive. Tension is comprehensively without law.
|Compression tends toward arcs of
||Tension tends toward arcs of increasing radius.
|Compressions are plural.|| Tension is singular.
|Compression is time.|| Tension is eternity.
|Compression is specifically directional.
||Tension is both omni- and supra- directional.
|Compression is inherently partial.|| Tension is inherently
Limitless Ratios of Tension
I adopted as a working hypothesis that there is a
limit to slenderness ratio of
the girth diameter of a compression member in respect
to its longitudinal axis and that
there is no limit to the slenderness ratio of structures
dominated by tensional components.
Astronomical magnitudes of structural-system coherence
are accomplished by tensionally
dominated structural functions of zero slenderness ratio,
i.e., by gravitational functioning.
Compressionally dominated structural components tend
toward contour transformation in
which the radius of curvature steadily decreases under
axial loading, that is, the cigar-
shaped column forces tend toward squash- or bananalike
bending of their contours. This
tending of compressionally loaded systems toward arcs
of lessening radius is in direct
contrast to the contour transformation tending of tensionally
components, which always tend toward arcs of ever-increasing
radius of axial profile. For
instance, the coil of rope tends toward straightening
out when terminally tensed, but it
never attains absolute straightness; instead, it progresses
toward ever-greater radius of
locally spiraling but overall orbital arcing, which
must eventually cycle back upon itself.
Tensionally dominated patterning is inevitably self-closing
Compressionally dominated functions of structural
systems are inherently
self-diminutive in overall aspect. Tensionally dominated
functions of structural systems are
inherently self-enlarging in overall involvement. The
sum of all the interactive-force
relationships of Universe must continually accelerate
their intertransforming in such a
manner as to result in ever more remotely and locally
multiplied, islanded, compressional
functions__comprehensively cohered by ever-enlarging
finite patternings of the tensional
functions. Universe must be a comprehensively finite
integrity, permitting only a locally
islanded infinitude of observer-considered and regenerated-differentialing
have herein discovered a workable man-awareness of a
complete reversal of presently
accepted cosmology and of general a priori conceptioning
regarding the general patterning
scheme of Universe, which has heretofore always conceived
only of locally finite
experiences as omnidirectionally surrounded by seemingly
The ratio of length to section in tension appears
to be limitless. I once
wondered whether it was a nonsensical question that
we might be trending toward bridges
that have infinite length with no section dimension
at all. As a sailor, I looked
spontaneously into the sky for indicated clues. I observed
that the solar system, which is
the most reliable structure that we know of, is so constituted
that Earth does not roll
around Mars as would ball bearings, which is to say
that the compressional components of
celestial structures are astro-islands, spatially remote
from one another, each shaped in the
most ideal conformation for highest compressional-structure
effectiveness, which is the
approximately spherical shape. All other spheroidal
shapes (cigar, turnip, egg, potato,
spider) have only one most neutral axis. This is why
spherical ball bearings are the ideal
compressional-system structures of man's devising, as
they continually shift their loads
while distributing the energetic effects to the most
parts in equal, ergo relatively
minuscule, shares in the shortest time. I saw that the
astro-islands of compression of the
solar system are continuously controlled in their progressive
repositioning in respect to
one another by comprehensive tension of the system.
This is what Newton called gravity.
The effective coherence between island-components varies
in respect to their relative
proximities and masses, in ratio gains and losses of
the second power in respect to the
dimensional distance as stated in terms of the radius
of one of the component bodies
Throughout the Universe, we find that tension and
energetically and complementarily interactive. A steel
wire of ever stronger metallic alloys
can span ever greater distances. In this kind of patterning,
we find that the
nonsimultaneous structural integrities of Universe are
arranged by the tensional
coherences. As thinner and thinner wire can span ever
greater and greater distances,
visible cross section of the tension members trends
toward ever lesser and lesser
Finally, because there is no limit ratio in tension,
may we not get to where
we have very great lengths and no section at all? We
find this is just the way Universe is
playing the game. This is demonstrated astronomically
because it is just the way the Earth
and the Moon are invisibly cohered . . . remotely cohered
and coordinated, noncontiguous,
nontangent, physical entities with their respective
coherence decreasing at a second-power
rate of their relative remoteness multiplied by their
combined masses. It is the way the
solar system coheres.
The gravitational, mass-attractive cohering is noncontiguous,
and so there is
no cross-sectional diameter or identifiable local entity.
This is why tension and coherence
are able to approach larger and larger magnitudes while
working toward no cross section
at all: for there never was any cross section in the
adjacent atoms. You have enormous
tension with no section at all. This is also true in
the atoms: true in the macrocosm and
true in the microcosm. The same relative distance intervenes
as between the Earth and the
Moon in respect to their relative masses. The only surprise
here is that man has been so
superficially misled into ever having thought that there
could be solids or continuous
compressional or tensional structural members. Only
man's mentality has been wrong in
trying to organize the idea of structure.
The trends are to increasing amplification of tension
to infinite length with
no section. Every use of gravity is a use of such sectionless
tensioning. The electric
tension first employed by man to pull energy through
the nonferrous conductors and later
to close the wireless circuit was none other than such
universally available sectionless
tension. In the phenomenon tension, man is in principle
given access to unlimited
performance. It seems fantastic, but there it is!
Tension is shown experientially to be nondimensional,
accountable, continuous, comprehensive, ergo timeless,
ergo eternal. Comprehensive
Universe is amorphous and only locally finite as it
transformingly differentiates into serially
conceptual pattern integrities, some much larger than
humanly apprehendable, some much
smaller than humanly apprehendable, ever occurring in
nonsimultaneous sets of human
observings, most of whose time-canceling, harmonically
integrative synchronizations are
supra- or subhuman sensibility and longevity experienceability
and whose periodicities are
therefore so preponderantly unexpected as to induce
human reaction of overwhelming
disorder, so that . . . suddenly, around comes the comet
again, for the first known time in
humanly recorded experience, periodically closing the
gap and periodically pulsing through
eternally normal zero.
In our old ways of thinking, infinity was expressible
numerically as N + 1.
We tried to get a static picture of a sphere, but we
could not understand one more layer
beyond it and what was beyond that__in order for it to
In the nonsimultaneous experiencing of Universe, there
is no simultaneous
"one frame." We are not faced with that at all. We get
to the finite physical world of the
physicist and then to the local compressionals and we
find that the local is continually
subdivisible. We started with a whole that was finite
and then began to subdivide it. So
there is, in a sense, an infinity of subdivisions locally.
This is very much the way the
intellectual pattern goes, so that the only thing you
might call infinity here is the further
subdivision of finity. So it is really never infinite
because you are not looking at one part.
It is never just Plus One. It is always plus the rest
of Universe when you separate that One
out. You can separate unity up further and further.
You can multiply the subdivisions of
Copyright © 1997 Estate of R. Buckminster Fuller