Modern History as the development of geometric awareness


In the first section of Buckminster Fuller’s wonderful book Synergetics he condenses into a few pages an explanation of some of the dynamics of modern history. He begins with the discovery of use of the all important zero to mathematics, and concurrently the (re)discovery of the spherical nature of the Earth. He shows how the belief in scarcity of resources lead to competition and war, and he shows that the constant advance in human technology whereby we learn to achieve more using less and less matter and energy is the complete solution to this illusory physical problem. All that remains is to solve the metaphysical problem of humanities fearful beliefs.

I hope you get as much of a blast out of the simplicity of his analysis as I did. I wish I had read this decades ago!


Humans in Universe
000.101 The combined land areas of Africa, Europe, and Asia embrace within
their perimeters the Mediterranean, Black, Caspian, Aral, China, Arabian, Red,
Baltic, and North seas: altogether their area was historically thought of only as a flat
Universe sandwiched between heaven above and hell below and seemingly
stretching away to infinity in all lateral directions. Yet the total land area of this flat
world constitutes less than 17 percent of the subsequently-discovered-to-bespherical
Planet Earth’s surface. All the great empires of written history before A.D.
1500 lay well within that “known” flat world: it was and as yet remains the
spontaneous theater of popular historical conceptioning.

000.102 How did this pervading historical concept become outdated? What
changed the terrestrial conceptionings adopted by the leaders of the world’s power

000.103 When the archaeologists’ artifact-proven history of mathematics opens
4,000 years ago in Babylon and Mesopotamia, it is already a very sophisticated
science. Mathematics may well have had its beginnings much earlier in India or
Indochina, as it is an art and science that has traveled consistently westward. Over
3,000 years ago the Greeks made further magnificent contributions to geometry,
algebra, and calculation. Then about 2,000 years ago the Roman Empire all but
obliterated mathematics. A little more than 1,000 years ago Arabs and Hindus
traveling through North Africa began to restore some of the ancient mathematics to
the westward-evolving culture. When al-Khwarizmi’s original A.D. 800 treatise on
algebra was republished in Latin in Carthage in 1200, it required a further 200 years
for his elucidation of the function of zero-the cipher-to be diffused into the
university systems of Europe .

history-of-zero-mathematics-9-638000.104 The cipher made possible the positioning of numbers, which in turn
facilitated division and multiplication. Imagine trying to multiply or divide with
Roman numerals . . . impossible! The Renaissance began with the new calculating
facility introduced by the cipher. The cipher was not only an essential tool in the
work of Copernicus, Kepler, Galileo, and Newton, but it also brought about
Columbus’ revised concepts of terrestrial navigation. It went on to instrument the
mechanical and leverage calculation capabilities of Leonardo; and in the art of ship
design the cipher gave birth to structural and mechanical engineering, which made
possible the intertensioning and compressioning calculations of the ribbed structural
strength of a sailing vessel as well as that of its vast wind-energy-driven complex of
compression and tension spars, sails, and rigging-replacing the trial-and-error
guesswork that had previously been used in naval and land architecture. This
capability in mathematical multiplication and division opened up a whole new field
of safely anticipated structural engineering and navigation.

000.105 This new anticipatory science made large engineering projects possible,
but it became known to, and then was employed by, only the world’s richest
schemers, monarchs, nations, and pirate enterprisers. No others could afford to buy
great ships. With more powerfully engineered ships, humans emerged westward
through Gibraltar to explore the Atlantic, to sail around Africa, to reach the Orient
and the Pacific by water, and to circumnavigate the globe. Thus it became public
knowledge that the old open-edged, infinite world system had closed back on itself
in all circumferential directions to become a finite system: a closed sphere. The
monarchs and merchants realized that, within that closed system, whoever
commanded the line of most efficient high seas supply would become the masters
of world wealth. Ships could carry cargoes that overland caravans could not.

000.106 In 1600 the East India Company was founded as a private enterprise by
Queen Elizabeth and a small group of her intimates. The limited legal liability of
their enterprise was granted by royal decree, and its projects were thereafter
militarily sustained and protected by Great Britain’s Royal Navy and colonial
troops. In England the East India Company College was established to train the
officers of the enterprise for their world-wide deployment; that college and its
handsome campus are still in operation as of 1979. The British Empire became the
first in history of which it could be said that the Sun never set.

000.107 As professor of economics at the East India Company College in 1810
Thomas Malthus became the first economic authority ever to receive in toto the
vital statistics of a world-embracing spherical empire. At the very end of the 18th
century Malthus published his documented thesis that humanity was multiplying its
numbers at a geometric (exponential) rate of gain while increasing life-support
production at only an arithmetic (linear) rate of gain. And since the Earth is a finite,
closed-system sphere, it apparently became scientifically manifest that there is a
fundamental inadequacy of life support on our planet. Until then all opinions on
such matters had been pure guesses.

scarcity-vs-abundance000.108 A third of a century after Malthus, Darwin attributed biological evolution
to survival of only the fittest species (and individuals within species). Though he
denied there was any economic significance in his theory of evolution, the
economists insisted that superior physical fitness obviously governed economic
survival as well. Karl Marx accepted the scientific viewpoints of both Malthus and
Darwin when he declared in effect that the working class is the fittest to .survive:
they know how to use the tools and to cultivate the fields-the wealthy are parasites.
This inaugurated the supranational concept of two world-wide political classes and
two competing theories of political organization.

000.109 As a consequence of the discoveries of Malthus and Darwin all the great
political ideologies have since adopted a prime philosophy that says: “You may not
like our political system, but we are convinced that we have the fairest, most
logical, and ingenious method of coping with the inherent inadequacy of terrestrial
life support, but since there are others who disagree diametrically about the best
method of coping, it can be determined only by force of arms which system is the
fittest to survive.” Thus survival of the physically fittest became the basis for
national departments of defense with their priority of access to the most advanced
science and technology. The military took command of all the highest performance
materials, brains, instruments, and tools of production.

000.110 Mutually assumed survival-only-of-the-fittest is the reason why the
United States and the USSR have for the past 30 years appropriated 200 billion
dollars annually to buy ever more effective weapons of potential destruction. The
great political and industrial power structures have all become supranational
comprehensivists, while the people have been passport-chained to their respective
150 national preserves-the people have become educationally divided into
“specialists” for exploitation by the supranational powers who divide to conquer
and divide to keep conquered.

000.111 Up until the 20th century reality consisted of everything that humans
could see, smell, touch, and hear. Then at the entry into the 20th century the
electron was discovered. A century after the time of Malthus much of science
became invisible with the introduction of an era of electronics, electromagnetics,
and atomics. These invisible micro- and macro-exploring cosmic instruments
provided for rearrangements of atomic interpositioning whose metallic alloying and
chemical structuring produces ever more powerful and incisive performances per
pound of physical matter employed.

000.112 Structures are complexes of visible or invisible physical events
interacting to produce stable patterns. A structural system divides Universe into all
Universe outside the structural system (macrocosm) and all Universe inside the
structural system (microcosm). Newton’s discovery of mass interattraction showed
that the interattraction force of atoms, planets, stars, or galaxies increases
exponentially as the interdistances decrease arithmetically, and vice versa: halve the
interdistance and make fourfold the interattractive integrity of the remotely bodied
structural system. That is the law of gravity. Symmetrical, noncontacting,
concentric interpositioning of already-symmetrical arrays of atoms produces
exponentially increased interatomic coherence of “materials.”

000.113 Gravity is the inwardly cohering force acting integratively on all systems.
Radiation is the outwardly disintegrating force acting divisively upon all systems.
000.114 All structural systems are comprised of tension and compression
components. Stone masonry has a high compression-resisting strength of 50,000
pounds per square inch ultimate. But masonry has low tensional coherence; it can
withstand only 50 pounds per square inch tensing. Stone-Age-derived masonry is a
thousand times more effective in its resistance to compression than to tension.

tensegrity000.115 Throughout the three million known years of the Stone Age humans
relied on gravity to hold their vertical stone walls together until (as often happened)
they were shaken apart by earthquakes against which they had almost no tensionally
cohering resistance. Gravity pushed humanity’s stone structures inward toward the
Earth’s center. Humans had to build their structures on bedrock “shoes” to prevent
them from sinking vertically into Earth’s center. Stone buildings could not float on
water. But nature had invented low-weight wood of high self-cohering tensile
strength (averaging approximately 10,000 p.s.i.) and of relatively low compression
resistive capability (also approximately 10,000 p.s.i.). Wood floated on water and
could move useful loads horizontally; wood made good rafts for transporting
humans but not for floating heavy cargoes. Thus the high tensile strength of wood,
combined with the human discovery of the intertrussing principles of structuring
and the low overall displacement weights involved, made possible for humans to
design and fabricate air-enclosing wooden vessels whose structure and space
enclosure combined to produce highly successful wooden vessels of the sea that
could carry great cargoes.

000.116 In the 1850s humans arrived at the mass production of steel, an alloy of
iron, carbon, and manganese having a tensile strength of 50,000 p.s.i. as well as a
compression-resisting capability of 50.000 p.s.i. Steel has the same compression
resistance capability as masonry, but it also has a thousand times greater tensile
capability than masonry and five times the tensile or compressive strength of wood.
Steel brought mankind a structural-tension capability to match stone’s previous
millions of years of exclusive compressional supremacy. With far higher tensile
strength per weight than wood, steel made possible even more powerful watertight,
air-containing vessels than did wood, even though steel by itself does not float.

000.117 The technology of metallurgy began developing metal alloys of ever
higher strength-to-weight ratios. Out of this came aluminum production by the
opening of the 20th century-and aluminum alloys and stainless steel by the 1930s.
These new materials made it possible to design and build engine-powered all-metal
airplanes (structural vessels), which could pull themselves angularly above the
horizontal and ever more steeply aloft. With the advent of successively higher
strength-to-weight ratios of metal alloys and glass-reinforced plastic materials, ever
more heavily laden airplanes were designed, which could climb ever more steeply
and faster. Finally humans developed so much strength per weight of materials
capability that they accomplished “vertol” jet plane flight and vertical space-vehicle
blastoffs. Since then human scientists developing ever greater strength per weight
of material have gone on to carry ever greater useful loads in vertical takeoff
vehicles at ever more accelerated rates of ascent.

000.118 As of the 1970s the human mind has developed a practical tensile
structuring capability of 600,000 p.s.i. The means of accomplishing this new and
overwhelming structural strength has become entirely invisible. Fully 99 percent of
humanity has as yet no idea that this increase in tensile capability has come about or
how it came about or why it works. While humans cannot see the ever-lessening
interatomic proximity of atoms and electrons of electromagnetic events, they can
witness the ever more vertical takeoff-angle capabilities manifesting human
comprehension of the fundamental structuring principles and their military
developments and profitable commercial uses. But only vast money investments or
vast governments can afford to exploit the increased technical advantages.

000.119 Before the airplane humans said, “You cannot lift yourself by your
bootstraps.” Today we are lifting ever lighter and stronger structural vessel “selves”
by ever less effort of our scientific know-how bootstraps. No economist knows this.
It is the most highly classified of military and private enterprise secrets. Industry
now converts the ever-increasing work capacity per pound of materials invested
primarily to yield monetary profits for the government-subsidized private-enterprise
producers of weapons.

000.120 Now in the 1970s we can state an indisputable proposition of abundance
of which the world power structures do not yet have dawning awareness. We can
state that as a consequence of the myriad of more-with-less, invisible, technological
advances of the 20th century, and employing only well-proven technologies and
already mined and ever more copiously recirculating materials, it is now technically
feasible to retool and redirect world industry in such a manner that within 10 years
we can have all of humanity enjoying a sustainably higher standard of living-with
vastly increased degrees of freedom than has ever been enjoyed by anyone in all

000.121 During this 10-year period we can also phase out all further use of fossil
fuels and atomic energy, since the retooled world industry and individual energy
needs will have become completely supplied by our combined harvests of
electromagnetic, photosynthetic, chemical, and biological products of the daily
energy income initially produced by Sun and gravity. Industry, retooled from
weapons production to livingry production, will rehouse the deployed phases of
world-humans by single-family, air-deliverable, energy harvesting, only-rentable
dwelling machines. When humans are convergent, they will dwell in domed-over
moon-crater cities that will be energy-harvesting and -exporting centers rather than
energy sinkholes.

000.122 All of the foregoing makes it possible to say that since we now know that
there is a sustainable abundance of life support and accommodation for all, it
follows that all politics and warring are obsolete and invalid. We no longer need to
rationalize selfishness. No one need ever again “earn a living.” Further living for all
humanity is all cosmically prepaid.

000.123 Why don’t we exercise our epochal option? Governments are financed
through taxation and would have no way of putting meters between the people and
their directly received individual cosmic incomes. So too, private enterprise should
no more meter the energy than it meters the air. But all of Earthians’ present power
structures-political, religious, or capitalist-would find their interests disastrously
threatened by total human success. They are founded upon assumption of scarcity;
they are organized for and sustained by the problems imposed by the assumption of
fundamental inadequacies of life support.

000.124 Why does not the public itself demand realization of its option for a
revolution by design science? Less than one percent of humanity now knows that
the option exists; 99 percent of humanity cannot understand the mathematical
language of science. The people who make up that 99 percent do not know that all
that science has ever found out is that the Universe consists of the most reliable
technology. They think of technology as something new; they regard it as
threatening both in terms of modern weaponry and as job-eliminating competition
for their life-sustaining opportunities to “earn a living.” Ergo, humanity thinks it is
against technology and thinks itself averse to exercising its option.

000.125 The fact that 99 percent of humanity does not understand nature is the
prime reason for humanity’s failure to exercise its option to attain universally
sustainable physical success on this planet. The prime barrier to humanity’s
discovery and comprehension of nature is the obscurity of the mathematical
language of science. Fortunately, however, nature is not using the strictly
imaginary, awkward, and unrealistic coordinate system adopted by and taught by
present-day academic science.

000.126 Nature’s continuous self-regeneration is 100 percent efficient, neither
gaining nor losing any energy. Nature is not employing the three dimensional,
omniinterperpendicular, parallel frame of the XYZ axial coordinates of academic
science, nor is nature employing science’s subsequently adopted
gram/centimeter/second weight/area/time exponents. Nature does not operate in
parallel. She operates in radiational divergence and gravitational convergence. She
grows outwardly by omniintertriangulated structuring from nuclei.


He continues with in depth discussion of the equilateral triangles all important role in universal dynamics, but we will leave him here to contemplate the insights he gained from his geometric understandings ~


2 User Comments: Share your thoughts

  1. Leave a comment – join the forum – dont be a ghost hehehe ~

  2. Finally had a moment to read this through. What a monumental genius of the century was Bucky. Astonishing tour de force of history and political philosophy that makes complete sense in the simplest terms. Thanks so much for leading me to look further into Bucky’s brilliance.

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