3 Prevailing Conditions in the Arts
1When very young in school I often felt that I could make jokes about the axioms from which we proceeded to formulate. Since we knew about the relatively vast spatial relationships of atoms and electrons, I thought that solids were impossible. I remember just before World War I, I began to say that I didnt think nature had separate departments of Physics, Chemistry, Biology, and Mathematics requiring meetings of department heads in order to decide how to make bubbles and roses! I had a suspicion that nature had just one department! The exploration capabilities of the scientists of my youth were meager compared to todaywhat the biologist was able to see with his very low-powered microscope looked very different from what the chemists seemed to be dealing withthe chemist couldnt see what he was dealing with anyway! He just simply found that things associated or dissassociated in unique manner and he had ways of measuring the rates and quantities. The physicist didnt know what he was looking at eitherhe seemed to feel that what he was dealing with was very different from what the biologist saw, so they felt they had to have different departments. They all made unique measurements. If the information was to be turned to practical account, some kind of coordination of the data, from the different departments several methods of quantation, had to be developed. In matters of spatial arrangements the x-y-z coordinate system was used. Men seemed to think that breadth, height, and width were all very logical.
2 Everybody in this room, as I speak today 60 years later, has lived through the days when man began to talk about other dimensions, such as time. He began thinking vaguely about time as a fourth dimension. Science advanced and changed rapidly without any adequate way for the nonscientist population to bridge the great break between the sciences and the humanities. C. P. Snow became well-known around the world for his two worldsthe concept of the great dichotomy between the sciences and humanities. Snow attributed it to an antipathy at the beginning of the Industrial Revolution on the part of the literary men for the smells of the laboratories and the noisiness of the industry which ensued. Snow also attributed the initial dichotomy not only to carelessness on the part of the scientist toward the antipathy of the literary man, but also to the scientists snob enjoyment of being mysteriously obscure. Snow said that the chasm widened until it could never be spanned again.
3 A year ago I talked with C. P. Snow in London; I said that I agreed with him about the existence of the chasm. I felt that anybody who had ever been a science writer would feel that way. In 1938 to 1940 I was the technical advisor to the editors of Fortune magazine. Whenever I attempted to report the scientific content of industrial enterprises to Fortune readers in words, the scientists within those industries said I would be unable to do so. They said that science is entirely mathematical and unless the Fortune readers read the mathematics, there would be no way to explain their scientific formulations. I felt them to be wrong. I battled hard to find ways of spanning this chasm. However, I didnt make my start to find the answer in 19381940. I had been looking for it a long time. It went back beyond 1917 when I said I didnt think science and nature had different departments. It went back to kindergarten and to my earliest schoolboy skepticism about the very axioms of geometry and arithmetic. Id been exploring seriously since 1917, at first spasmodicallygradually more intensivelyto discover whether we might not be able to find the coordinate system employed by nature. I felt that if and when we did find it, that it would be characterized by arithmetic and geometry which would be extremely simple. Chemistry showed us that nature was associating and disassociating in terms of simple, whole, rational numbers such as H2O, not as H pi O which would prevent nature from ever making anything because pi may never be resolved. Pi is irrational. There were no irrational numbers in chemical combinings of atoms and molecules.
4 What I was able to say to C. P. Snow was that I thought that the break was not due to
antipathy on the part of the literary man, but due to a fundamental event that occurred in the
world of science in the mid-19th century. I explained that it occurred after Faraday discovered
electrical behaviors, and the work of Maxwell and Hertz indicated the existence of invisible
electromagnetic waveswaves going through the walls and through each other without interference
with one another. In this new electromagnetic world, man found himself dealing with
discrete apparatus such as a specific number of copper wire coils wound around a
magnet. Each additional coil had a discretely measurable effect all statable in neat
algebraic equations. Ohms law was typical of this development. The scientists, though
dealing with invisible energy phenomena, were able to get beautifully neat answers to
experimentally posed questions regarding various arrangements. They found themselves
getting on very well without seeing what was going on. It was during some of these
early experiments on energy behaviors that a fourth-power relationship was manifest.
The equation contained a fourth power x 4. You can make a model of x 3, e. g., as a
cube, and you can make a model of x 2 (x to the second power), and call it a square,
and a model of x 1 and call it a line; but you could not make a geometric model of x
to the fourth power. The consequences of this unmodelable fourth-power event are
tied up with other events. At the same historical period literary men were trying to
explain the new invisible electrical energy, which could do yesterdays tasks with new and
miraculous ease, to their scholarly readers and the public in general. They began to use
visually familiar analogies to explain the invisible behaviors. The concept of a current of
water running through a pipe as analogous to electricity running through a wire was
employed by the nonscientific writers. The scientists didnt like that at all, because
electricity really did not behave as does water. Electricity ran uphill just as well as
downhill (but did not really run). The scientists felt that analogies were misleading and
they disliked them. When the experiments that showed a fourth-power relationship
occurred, the scientists said Well, up to this time we have felt that visual models were
legitimate (though not always easy to formulate), but now, inasmuch as we cant make a
fourth-power energy-relationship model, the validity of the heretofore accepted generalized
law of models is broken. From now on physically conceptual models are all suspect.
Were going to work now entirely in the terms of abstract, empty-set, mathematical
expressions.
Their invisible procedures thenceforth to this day have a counterpart in modern air transport
and night fighter flyingwhich is conductable and is usually conducted entirely on instruments
Figure 13. When you qualify for instrument flight you are able to fly in fog and night without
seeing any terrain. You get on very well, and arrive where you want on instruments. Scientists
went onto instruments about 1875almost entirely. By the time I went to school at the turn of the
century we were taught about instruments and equations and how to conduct experiments
Figure 14. We were told that the fourth dimension was just ha-ha,you could never
do anything about it. Frustrated by the withdrawal of models to describe, literary
men invented the myth that the fourth dimension was time and therefore logically
invisiblewhile the other three dimensions were as yet visible. Though it was incorrect, few
scientists contradicted this explanation of time; for the scientists no longer thought of, or
discussed, models. The cliché of the fourth dimension is time became a knowing-ones
mystique.
5 So I told C. P. Snow of my own investigation of natures coordinating system. In thinking about natures coordinate system, I assumed it must embrace some kind of omnirational geometry and arithmetic, because of chemical structuring rationality. Figure 15 I also found myself well-impressed with something we call vectors. Vectors had first been developed to important extent in electrical engineering (though Galileo used them tentatively and erroneously in developing his parallelogram of forces). Figure 16 According to Galileo we could make a vectorial pattern of a ship A of such and such a weight, going in such and such a direction at such and such a velocity. You multiplied the velocity times the weight and that gave you a vector: x. You then made a vectorial line AC on your diagram that was x units long, that was shown going in the compass direction that the ship was goinglet us say due east. Ship A collided with another ship B at point C. Ship B weighed such and such an amount. You multiplied ship Bs weight by its speed (velocity) and it gave you the length, y, of a vector line BC. BC had a compass direction, toolet us say northeast, reading from B to C. Galileo then constructed a parallelogram ACBD with BD parallel to AC running west from B to D, then DA constructed parallel to BC, running northeast from D to A. Galileo then drew a vectorial line diagonally from D to C, the point of collision of ships A and B, and then Galileo extended the line DC outward of the parallelogram to E with CE = DC, and with the angle DCE = 180ř, i.e., a straight line. Galileo called CE the resultant of forcesthe vector of the combined forces x, y. Galileos resultant of forces was wrong because two colliding ships do not waltz gayly east-northeast 12 miles together. Usually one of the ships goes downinto the seatoward the center of earthwhich multidirection vector was not in Galileos plane geometry scheme. Nevertheless I found his vectoral diagram exciting Figure 17. It suggested a comprehensive geometry consisting entirely of vectors. A vectorial line was a very nice kind of a line because it had a discrete lengthit didnt go on absurdly forever to the nowhere of two infinitiesin both directions as potential extensibilities of lines. It didnt have the time to do so. It had a discrete amount of time, which time was a component factor of the vectors velocity. I wondered if nature might have a set of omnidirectionally operative vectors that represented all of our experiences. It is experiences that we are dealing with in nature. Nature and universe are alike the aggregate of all experience. Couldnt I then find vectors that represented any and every unique experience? Vectors are like spears. I could massage any object into a spear shape, point and thrust-throw it in a discrete direction. I intuitively liked those directional vector spears. I felt that they tended at least to embody all the energetic qualities of represented experiences. That thinking-feeling, however, was only an intuition and not an accomplished, mathematically coordinate, generalized-experience system. That intuition was followed by another pure intuition. I had liked Avogadro, just as soon as I had heard about him. Avogadro came into the world of chemistry at a time when chemists were excited about gases. The gases came into recognition as chemical elements through Lavoisiers explanation of Priestleys experiment with the isolation of fire. All the chemical elements up to the Priestley-Lavoisier event were metalseasy to recognize by their weights and colors. Lavoisier explained Priestleys experiment of fire under a bell jar which had resulted in water vapor and ash whose combined weight was more than the weight of the item which had burned. Lavoisier said, Well something that was in this space under the bell jar must have been there all the time which combinedwith the visible item which burnedduring the process of burning whatever that might be. He said that the nothingness under the jar (something men had called both nothingness and air) must indeed be something which, though invisible, is physically real which combined to make the water vapor as well as the ashes.
6 I think Lavoisiers intuitive conceptioning was possibly the most intellectually daring of all
history. For a man to dare to think that the nothingness could be something fundamental, so
fundamental as to be identified as a chemical element, and not only that, but that the
nothingness could be divided into a plurality of fundamental chemical elements was an enormous
jump from the conditioned reflex concept of chemical elements only as metals. And so he called
one of the invisibles oxygen and he had it combine with the carbohydrate item releasing the
carbon and combining with the hydrogen to form the water vapor. I have oversimplified to get on
with my story. Other humans were involved, etc. But it is close enough not to be
misleading. From that point on scientists came swiftly to understand what fire was.
It was fast oxidation. Therefore, they also knew what steam was for they now also
knew what H2O was, and how it combined. And they knew what iron rust was. It
was iron and oxygen, as was iron ore. The metallurgical, chemical, thermodynamic
bases of the invention of the steam engine were implicit in the chemical conceptioning
of Lavoisier. As an indirect recognition of his general integrity, he was guillotined.
With the steam engine came the ability to drive ships without wind. With that came vast
acceleration of world commerce and with it enormous amounts of wealth. Realizing for the first
time in history that great wealth accrued to scientific discovery the rich masters of
commerceprivately I call them the great piratesput up large amounts of their wealth for further
scientific discovery. This brought great scientific competition to determine who would run the
world with the new steamships. In the scientific endeavor which ensued the next five chemical
elements to be isolated were all gases found by Cavendish in England. Whoever understood
energy and gases was apparently going to run the world. At this time the laws of
thermodynamics evolved.
Avogadro entered the scientific era at the time of its preoccupation with gases. He
began to study the total pattern of what men had found out about the gaseswhat
characteristics they had found so far? He saw something which seemed significant
and intuitively hypothesized a theoretical statement. He next devised experiments
which could prove or disprove his theory. Experiments proved his hypothesis to be
correct, to wit that all gases under identical conditions of heat and pressure always
disclose the same number of molecules per given volume. Gases are individual elements;
therefore, fundamentally different from one another. That individually fundamental
elements, such, precisely because they were different, should show the same number of
molecules in a given volume under identical energy conditions of both heat and pressure
persuaded me that Avogadro had found at least a corner of the Grand Central Station of
natures fundamental coordinate system. Here were common conditions of chemistry,
physics, arithmetic, and geometrya wedding of number and volume. I then said we
know that Avogadro did what he did when gases were thought to be a special class of
elements. Since that time we have learned that all the chemical elements including
the metals can be liquefied and incandescently plasmacized or gasified, and, in the
other direction, that gases can be liquefied. Apparently we can run any of the elements
back and forth through this transformation hierarchy depending on how much energy
is present in the form of heat or pressure. So I intuited that it might be possible to
generalize Avogadro by hypothesizing that all elements under identical conditions of
energy may disclose the same number of something per given volume. So I said: If
this becomes experimentally provable we may be getting somewhere in our search
for natures comprehensive coordinating system; if the answer lies in this direction
the coordination will be expressible in neatly coordinate arithmetical, geometrical
terms. There are and have been a great number of scientists looking for comprehensive
coordinate systems. What has been lacking in all, other than Avogadros limited coordinate
system of a plurality of individual elemental atomic gases, has been the failure to
coordinate the arithmetic and geometry. We have number values galore in respect to
invisible energy relationships. We have hypothetical chemical constructs but no true
geometry which is reliably conceptual. Avogadros volume requires a geometric container
quantum.
7
So I said, all right; if all the conditions of energy were the same, what would such a
condition look like in vectors? (And that brings me back to where I detoured from
Galileo to Avogadro.) Well, it would mean that all vectors would have to be the same
length. All of them would have to be running into each other at the same angles. So I
said, can we make realistic, multidimensional, visible, tangible models of equilength
vectors all running into each other at the same angles? Such a vectorial system in
local universe would be inherently finite. It would not imply additional vectors. It
wouldnt have to go on forever, because vectors, unlike Greek lines, dont have to go on
forever.
8 I found I could make just such a model. It came out as what we call the tetrahedron-octahedron complex; some scientists call it the isotropic vector matrix. Aston, in 1929, made the discovery for the physicists of what he called closest packing of spheres. The fruit dealer selling oranges and the cannoneers stacking equiradius cannonballs learned about this closest packing of spheres earlier, but the scientists never noticed it Figure 18. Two spheres may become tangent Figure 19. We may then rest a third ball in the valley between them with the third ball tangent to both of the first two. The three balls, each one tangent to both of the others, now form an equiangular triangle group with a valley at their center. A fourth ball may be rested in that triangular valley. The fourth one touches each of the other three, and vice versa. The four closest packed spheres make a closest-packing array. This closest packing of spheres may go on triangulating in all directions. Because the spheres are all the same size, equilength vectors may connect each and every adjacent sphere, with the vectors running from the centers of the spheres through the points of tangency to the adjacent spheres centers Figure 20. Remove the spheres and leave the vectors and youve got the tetrahedron-octahedron complex. The isotropic vector matrix is a structure that I discovered quite independently in kindergarten in 1899.
9 I related to Lord Snow how I experimented with this kind of geometry, and how I found that the vector-edged octahedron with the same length edge as the vector-edged tetrahedron had a volume of four times the tetrahedron Figure 21.
10
A symmetrical cube has six faces, and a tetrahedron has six symmetrically-oriented edges.
If you put a continuity of six diagonals in each of these six faces of the cube, a tetrahedron is
formed Figure 22. If you make a model of a cube with rubber joints, it collapses; it is completely
unstable. If theres a tetrahedron secreted in the six diagonals of the cubes six faces, it
will not fold up. A triangle is the only structurally stable polygon. A tetrahedron is
the minimum omnitriangulated, omnistructural system. A tetrahedron is the most
fundamental of all structures. There are only three basically stable omnitriangulated,
omnisymmetrical structuresthe octahedron, the tetrahedron, and the icosahedron Figure 23.
Each is a basic system because each stably and symmetrically subdivides the universe
into two parts: all of the universe inside and all of the universe outside its system
Figure 24. When I then began to explore the volume relationships of the simplest basic,
symmetrical structures and gave the simplestthe tetrahedrona volume value of 1, I found
that an octahedron had a volume of exactly 4 and a cube had a volume of exactly 3
Figure 25. Thats very interesting because if you try to account in cubes for natures
energy associabllitiesas structural systemsyou use up three times as much space as you
do if you count space volumes in tetrahedron units. The physicists have found that
nature is always most economical; therefore, she could not use cubes to quantitate her
structurings. The cubes, you know, represented our x-y-z coordinate system Figure
26.
If you use tetrahedra as your coordinating system, something very economical and fundamental
happens. The cube angles are each 90ř. When you want to make a bigger cube out of littler
cubeswant to double the size of the cubeyou then put eight little cubes together and get eight
cubes symmetrically closest-stacked, the big cube, around one point Figure 27. The edges of the
big cube are each 2 units of cube-edge long. The cube edges are 2. The face areas are
each 4. The volume of the 2 linear-module-edged cube is 8, 8 being the third power of
2.
11
When we deal in tetrahedra, were dealing in 60ř-angle systems because in a regular tetrahedron,
all the angles are 60ř; theyre equilateralor equiangulartriangles.
12 You remember that what I told Lord Snow was that when the scientists found an energy relationship in the fourth-power value, they couldnt make a visual model of it because they couldnt find a fourth perpendicular to a cube which was not in a plane parallel to one of the planes of the cube. But the scientists did not need a model to calculate fourth-power problems. They were able to handle it very easily algebraically. They did it by using what they called an imaginary number, e. g., by using the square root of 11. If that sounds complex, dont let it bother you. What they were doing was simply saying they had a cubical clock. In effect, their cubical day consisted of eight little cubes around the center of the big cube Figure 28. The first dimension used up one cube, the second dimension used up four cubes, and the third dimension used up all eight cubes. Their days entire clock capacity would only take care of three dimensions. So what they did was to borrow cubes from tomorrowor from yesterday. They then carried out their problem algebraically without reference to any conceptual models. After they got finished, theyd paid back the borrowed time and once again had a visual three-dimensional-model quantity. When you use 60ř for your coordination, you dont need imaginary or complex numbers to carry out fourth-power calculations because there is a volume of 20 tetrahedra around one point instead of 8. Two to the fourth power is 16, and Ive got 20 tetrahedra around a point. There is an additional 2 to the second power in the model which comes in very usefully when this vectorial grouping around a common nucleus is employed to account for nuclear-energy behaviors. When the nuclear group of vectors has a radial or edge molecule of 2 (as do the 8 cubes in closest packing), then the vectorial system has a volume around its center of 160, which is 5 x 25 It is perfectly possible today, then, for a child to make fourth- and fifth-power models with tetrahedronal and octahedronal building blocks. Einstein was working on fifth-power problems in his last days, trying to reconcile gravity and electromagnetics.
13 I was able to say to Lord Snow, who was then Sir Charles, that I had found an arithmetical-geometrical energy-coordinating system which apparently coincided rationally and comprehensively with natures behaviors which you could make models of and which could handle the fourth- and fifth-power problems which three-dimensional cubes could not, which latter fact had accounted for the discard of models and the preoccupation of science with a completely abstract treatment of nature.
14 Linus Pauling received his first Nobel prize for his contributions to the general knowledge of chemical structures. He gave me his Nobel laureate paper to read and it was the best and most concise history of chemical structures. The first part of his paper is about organic chemistry.
15 It was in the years around 1800 that the organic chemists, in making experiments, discovered that associating/disassociating of organic chemistry seemed to be always in number increments of 1, 2, 3, 4. Those were the only numbers you had to have to account for your experiments. In about 1810, a man named Frankland was the first to make any written notation of that. Then two men, Kékulé and Cooper, added a little more of the same. In 1835 a Russian, Butlerov, was the first to use the expression chemical structure. And he was the first to say that 1, 2, 3, 4 seemed to have something to do with bonding together. He called the bonding valence. Then there is a gap in further fundamental discovery up to 1885 when a man named vant Hoff said he thought the oneness, twoness, threeness, and fourness were the tetrahedrons four vertexes. Vant Hoff was looked at askance by the other chemists. He was called an outright charlatan. He was called a faker of every kind. Otherwise the chemical scientists paid no attention to him. He was greatly stunned, but went on with his experiments and lived to make optical proof of the tetrahedronal cube configuration of carbon, the combining master of organic chemistry. Vant Hoff was the first chemist ever to receive the Nobel prize. From this point on, chemistry recognized that organic chemistry was tetrahedronally coordinate. Two tetrahedra linked together by one vertex of each is a single bondingvery flexible, like a universal jointlike gas Figure 29. Many tetrahedra so linked could be stretched to fill much more space than if linked mutually by two or three vertexes. Two bonds form a hingeas yet flexible but quite compact as a systemlike water. Triple bonding is rigid, like crystals. You can get four vertexes of tetrahedra together, which means they are congruent and most densely compacted, possibly like diamonds.
16 In vant Hoffs day, the majority of the chemists were metallurgists and they found no vertexial
bondings. That was probably one reason the chemists in general had been so against vant Hoff.
Even though he was finally successful, his contemporary metallurgists said, We dont find any
tetrahedra in our metals! Even though there seem to be visible crystals in nature such as
octahedra, rhombic dodecahedra, etc., we cant find any way to account for their atomic
structuring.
Linus Pauling, in 1932, approximately a half century after vant Hoff, was the first to use X-ray
diffraction machines to probe metal structures. X-ray diffraction machines operate very much as
does radar. X-ray diffraction sends X-rays right into the atoms and they bounce back and give
pattern information, but not regular photographs. But you could make a photograph. The
photograph was of X-rays bounced in against something and bounced out angularly so that what
was really at the center was outward in the photograph and vice versa. Its really quite difficult to
reconstruct the X-ray diffraction photographs into pictures of the shape of the explored
patterns. Expertness is involved. Linus Pauling, applying X-ray diffraction to metals,
discovered that all the metals which he analyzed were tetrahedronally coordinate, but
instead of being linked vertex to vertex, they were linked midedge to midedge often
with common centers of gravity Figure 30. We can make a red edged tetrahedrons six
edges by making a set of six contiguously-ended red diagonals in each of the six faces
of a cube. Each red diagonal will occupy only one of the two diagonal paths across
each of the six faces of the cube. We may therefore make a second blue tetrahedron
occupying the six alternate diagonal paths of the cubes six faces. The blue tetrahedron and
the red tetrahedron have a common center of gravity. Thats one way metallic atoms
combine.
17 While Linus Pauling has not to my knowledge said as yet that all metals are tetrahedronally
coordinated, so far no exceptions have come to my attention. Paulings Nobel laureate
discourse twenty years after commencing his X-ray diffraction explorations discussed no
exceptions.
I will now say to you that organic chemistry has for 80 years recognized tetrahedronal
coordination. Twenty years of X-ray diffraction has found the metals tetrahedronally coordinate.
I came to this subject in an entirely different way from that of the chemists and have found the
tetrahedron to be the coordinating unit in experimental mathematics, which is what the
scientists call my work. Therefore, I will say to you what I said to C. P. Snow: All of natures
formulating is tetrahedronally coordinate. Snow, a scientist, said, From what you have related to
me, I am inclined to agree with you; in fact, this information happens to come at a very strategic
moment in my life. In the 1965 New Year statements harvested by the press from world leaders,
Lord Snow had quite a long piece saying that he now was retracting his two forever unjoinable
worlds statements. He felt he was wrong and it looked as though the chasm between the two was
closing.
18 I was in Ghana in January, and I received a telephone call from the British Broadcasting Corporation, asking me to come to London. When I reached London, I learned something which to me seemed extraordinary. This, too, is a long story but pertinent. Six years ago I had begun to get letters and photographs from two nuclear physicists who were leading virologistsDr. Aron Klug, of Birkbeck College at London University, and Dr. Donald Casper, director of cancer research at the Boston Childrens Hospital, now at the Cavendish Laboratories at Cambridge University. These men, using X-ray diffraction also, were finding the shape of the protein shells of the virus to be similar in appearance to my geodesic domes.
19 Very quickly I want to point out the general significance of virology. In the range of magnitudes between macro- and microcosmic limits of exploratory knowledge, there seem to be octave-like levels of unique pattern-phase relationships. The microdomain of the virus is that in which the tobacco-mosaic experiments first showed that the domain of the virus is apparently the threshold between what we have known in the past as the inanimate and the animate. The virus follows all the behavioral laws of an inanimate crystal, but also follows all the laws of animate biology. It is both animate and inanimatein fact, because it follows both requirements, you have to say there is no difference between animate and inanimate phenomena. As a threshold, the virus overlaps both. It does not divide them. It calls for a very different concept of what we are, physically; it asks just how physical is life and what is unique to the individual? Within the virus, we have the now famous DNA and RNA, the nucleic acids consisting of four chemical compounds whose interpatterning sequences in helixes control all patterning of all the designs of all lifeall the biological forms design-scheduled by DNA and RNA. Investments by world society for the search in the virus domain are great. This is the most probable area in which to find the clues to the possible control of cancer, for here in the virus is the control of the design of life. DNA-RNA may also control the design of antilife.
20 A virologist is a very interesting kind of man. He was rarely trained to be a virologist; he was trained as a specialistas a nuclear physicist, a mathematician, a chemist, a biologist, or a geneticist. But as virologists, they become one: an unusually comprehensive thinkeran integrator of widely held findings of science.
21 Just preceding and during World War II, scientists began to find their microscopes getting far more powerful. As a result, their field of observation began to overlap. My original hunch about nature having only one department became increasingly valid. The scientists found themselves forced to adopt hyphens to describe their workbio-chemistry, etc. The virological teams find themselves inherently comprehensivethey deal with the whole show. And so the men who are good in virology are really extraordinary men, and tremendously articulate. Any good virologist sitting in with us today would find no trouble in participation in your subject. In fact he would probably be able to lead you in formulating a grand strategy of attacking your special problem. Virologists deal exclusively in fundamentals of structural design and how best to communicate our findings and intuitive formulations.
22 The virologist discovered the proliferation of my geodesic structures, which had emerged from structuring aspects of my energetic geometry studies which pursued natures most economical stratagems. In 1957 Klug asked if I could identify the geodesiclike protein shell of the polio virus. I was able to give him the mathematical explanation of the structuring Figure 31. Gradually, I heard from more virologists. I was told by a Johns Hopkins scientist the other day that she had read over twenty papers by scientists identifying my mathematical worksuch as Ive been giving you todaywith the findings of their own investigation areas.
23 I was told by BBC (February 1964) that they were about to open up a broadcasting on a new channel 2, using colored TV, Telstar, and other electronic advances, and that they were about to reach audiences many times larger than their old channel 1 viewers. New receiving sets would be necessary for tuning in channel 2. To warrant their old audiences purchase of new TV sets BBC felt that they must present programs of higher standards than ever before. They said, Lets see if we cant take our experience and step up the quality of our program. For their step-up in content quality they took the most popular hour, which is 9:30 Saturday night, and set about to produce a science program once a month which they hoped could be so well done that it would displace lower-caliber amusements through spontaneous popularity. BBC got together its directors who had done science programs and chose the director who had done the Cavendish Laboratory documentary of Drs. Watson, Wilkins, and Crickthe DNA-RNA team which won the 1963 Nobel prize. This BBC directorRamsey Shortwent out to the Cavendish Laboratories at Cambridge University and asked their scientists what they recommended as the subject of the first channel 2 science program. The Cavendish scientists said, Buckminster Fuller would be appropriate because TV must employ visible phenomena and Fuller has found the bridge of structural conceptuality to pure science exploration.
24 In the 19th century the literary man had the models taken away from him. He had no model to explain science to the people. Popularization of science employed superficial romance. True science was shunned as too difficultor as dry, obscure, blackboard equations.
25 Since conceptuality is returning, it was felt that the first television program should deal with a fundamental bridge.
26 So the program started with giant geodesic radomes in North Riding, Yorkshire, and was done
partly in the Cavendish Laboratories and partly with architectural students of Londons
Architectural Association. When it was finished, the BBC art directors were delighted with
itthey said it was a good art show. This alarmed the BBC executives who said if it was very good
art, it couldnt be very good science!
The program was broadcast in April 64. Those of you who are familiar with England know that
the English critics are both plentiful and articulate. The science critics acclaimed it, so that it
was successful scientifically. So also did the art critics. (I havent seen the program myself, but
thats the way life goes!) However, Im confident that we have, in reality, closed the
science-humanities gap with kindergarten conceptuality.
27 At start of todays meeting, when we were talking with the representative from the U.S. Science Foundation about what science is, science remained obscure in its advanced mathematics wrappings. I asserted (before presenting the integrated information I am now reciting) that man is coming into an extraordinary new era on earth, in which we are going to be able to deal conceptually with advanced science. Inasmuch as conceptual communication is art, art will become intimate with science; and philosophy will be able to comprehend the significance of developments; and thought may enter upon new speculation and altogether new comprehension.
28 One more itemhave any of you read a book by Professor Benjamin Bloom of Chicago University? He is Professor of Education and head of the universitys curricula committee. He has written a book, Stability and Change in Human CharacteristicsWiley, publishersin which he has listed a number of experiments and case histories of lives from birth through university age which correlates progressively taken IQ tests with environment and the effects of events upon immature life at various age levels. The conclusions are astonishing! If you can give Dr. Bloom an adequate report of environmental factors governing a given young life from birth to seventeen years of agesuch as description of the homeprivate bathroom or nodrunken parentsplay only in streetsetc., he can give you the IQ of that life within 1 %. There are built-in alarm clocks, according to the neurophysiologists, which go off at unique moments, which put capabilities progressively in operation in the new life. If the new capability is frustrated at outset it is frequently relegated to disuse. At the age of four, 50 % of the capacity to improve his IQ capabilities either have been expended or protected. Teaching doesnt add capability. Teaching can either gratify or frustrate capabilities. Usually they get badly damaged. The IQ is most directly affected by what happens in the first four years. Between four and eight, the next 30 % of capability to self-improve IQ is brought into operation and either frustrated or gratified. Between eight and thirteen years, 12 % more of potential capability is actuated totaling 92 %, and at seventeen 100 %. After seventeen, the most any human being can do to actuate more IQ is 0 %. About $ 3 billion a year is appropriated jointly by the United States and the local governments for higher education, where the most possible self-improvement of IQ capability is 0 %. Where 50 % activatability of IQ occursthat is from zero to four yearsno appropriation is made. The only area where important chance of conserving and improving capacity occurs gets the small money going into kindergarten, elementary, and junior high school. The greatest schooling opportunity birth to four is operative through the TV only. The right TV programs for both child and parents could up the national IQ by a large percentage.
29 Dr. Bloom shows that from birth to four years old there are three clearly defined factors which govern the inauguration of capability to improve IQ (at any later date) or what part of that first 50 % is to be lost. Factor number one is trust. Human young stay helpless longer than any other living species. If the new life, for any reason, has its utter trust in its parents violated, it is pretty sure to be a dropout. The next two factors after trust which govern the one to four years are autonomy and initiative. You dont know how to tell the extraordinary new life how to stand upit just stands up by itself when ready. The initiative is innate. The parents have to be sure the child has room of its own and expendables for the new lifes checkout of: tensioncohesion, etc., by trying to tear things, etc. From four to eight, there are several clearly defined factors governing favorable or unfavorable inauguration of 30 % of total capability to ever improve IQ. The new five-to-eight-year-old factors are ones to do primarily with the leadership of the parents. If the parents speak their native language properly, effectively, and with joy in a constantly improving vocabulary, it will have a very favorable effect on the child. Blasphemy or slang, a mark of an inferiority complex that is afraid to speak out clearly and constructively, will block off the six-year-olds brain capabilities.
30 Availability of good books on the shelves is an important environment plus. While the child cannot read the grownups books, its intuition detects a drive or lack of drive for self-improvement in its parents. It seems important to our meeting on clues for detecting the gifted schoolchild through art teachers that Dr. Blooms findings be known. When we know that ages zero to four are the biggest school opportunity and when we discover that entirely new mathematical simplicities are at hand, we must realize that educational theory is in for a complete revolution. There is no question about itan educational revolution is upon us.
31 Labor opposes automation only because everybody is scared about their jobs. Its perfectly logical for them to be scared about their jobs. But were beginning to do something about it which goes back to the post-World War II GI Bill.
32 We have said we will take all the people who are unemployed because their machines have become automated, and teach them a new skill relating to another machine. But soon the advancing state of automation will be such that by the time they have learned to operate a new machine, that one will have been automated too! They will simply stay in school studying how to operate obsolete tools. What we are going to do about all this is the following. First we must reorient our eons-long nervous-reflex conditioning. It is not strange that we are so negative-minded regarding mans potential behavior on earth. He has had, up to this century, a 1 in 100 chance of economic success. It is logical that we think of unemployment as a negative, rather than realizing that it is signaling that society now has the ability to free people from the necessity of demonstrating their right to live by gaining and holding employment.
33 The kind of wealth were actually dealing withthe industrial wealthhas nothing to do with the old monetary gold, whose retention in balance-of-trade accounting is a mark of innocence of society and an economic-expansion cancer. Our present real wealth is, exclusively, the tool-organized capability to take energies of the universe, which are transforming their patternings in various ways as yet uncontrolled by man, and shunt them through channels onto the ends of circularly arranged levers which man invents so that the energy turns wheels and shafts to do all the work. In doing the foregoing were taking nothing from the energy capital of the universe. The physicists make it very clear that energy can neither be created nor destroyed. You cant exhaust that kind of wealth. It is not physically exhaustible. And in fact, our relationship to the energy wealth is an intellectual one. It says that every time we make an experiment with physical-energy wealth we learn more. Even when we only learn that something we thought might work wont work, thats learning more! Every time we make an experiment we learn more, we cant learn less. Because universal energy is inexhaustible, and our intellectual advantage only gains, our wealth is continually gaining. Were continually upping the relative metabolic advantage of man in the universe.
34 One of the reasons I can talk to you the way I do is because I am a comprehensivist in an era of almost total specialization. By fortune I go many places and get experience in many directionsI keep in touch with many. I can tell you that at the present regenerative state of intellectual experience and mass science and mass technology that there is the probability that for every 100,000 we educate through to a bachelors degree, there will be a science-technology realization by one of the 100,000 so world-advancing that it will pay for all the other 100,000 peoples education and livelihood without their direct contribution to the technoscientific breakthrough. That capability is now in operation so that in order to progressively elevate human dignity, were going to be able to afford to give everyone student fellowships in any subjects they electfly-fishing studies are O.K.everyones going to go back to school! Man no longer has significance as a muscle-and-brain-reflexing machine. The Marxian worker-slave is going into extinction. He is not needed. Man is essential to the success of the industrial equation as a consumer. The more consumers there are, and the more frequently they consume, the more successful and swiftly increasing is the industrial wealth capability. We can only justify the vast investments in world-around industrial networks of structures and machinery by the numbers of spontaneous consumers that are served. Because the initial tool-up undertakings take months and years, as well as vast billions of dollars, the more active consumers there are to divide up costs, the lower the costs and the quicker the total amortization and inauguration of improved tools and efficiency. Therefore, man becomes a regenerative consumer. The more he consumes, the more he learns, and the factor that increases the wealth is the know-more factor. We can afford to send everybody back to school. There are a great many people intent on learning and finding out something which increases the common wealth. Those who go fishing may inadvertently make a great contribution through just taking it easy and doing some good retrospective thinking. And this inexorably is the way history is going to unfold. We will not undertake this new education and wealth-regenerating spontaneously within our country. We wont agree and coordinate that fast. But the competition from Russia, China, and others will force us to this logical measure. Economic competition is the catalytic factor. Because the Chinese now have the most potential consumers they can eventually produce at the lowest prices! To underprice all that competition, in a very short time were going to be forced to go into total automation only to find ourselves amazedly successfulautomated wealth!
35 Ill give you one more picture to vivify what is happening to us. This picture is of the now visibly developing new world man. We had him in the news a few years ago, a man who talked about being a world citizen, you may remember, an American in Paris. Society not only laughed at him as a dopey renegade, but now, unexpectedly to all, everybody is beginning to experience more and more travel. World citizenry is coming about by itself.
36 There is something going on with respect to the U.S.A. we havent paid much attention to. Figures were published in last months Exchange magazine, published by the New York Stock Exchange, regarding foreign investments. There are two kinds of foreign investmentone is called indirect investment, which means purchase of shares in foreign enterprise. The other kind is called direct investment, where you buy land, put up a factory, and start producing something. Thats called direct enterprise, or direct investment. U.S.A.s citizens and corporations investments in foreign countries started up at the turn of the 19th into the 20th century Figure 32. There was a jog down in the historically rising curve during the 19291942 Depression, and now its going up again, ZOOM! Its resumption of the original acceleration rate indicates that it was trying to happen all the time and that the depression dent was abnormal. Its now up to better than $ 70 billion and the direct earnings from it each year now exceed $ 4 12 billion. Every major corporation is in this outward-bound move. The hundred largest corporations in the U.S.A. are now spending four out of every five new-plant-and-machinery dollars in countries outside the U.S.A. General Motors last year, though its total foreign investment is only 10 % of its whole, made one-third of its total profits from its foreign operations. General Motors total net profits after taxes were $ 1 12 billion.
37 Arthur Watson, of IBM International, says that the old foreign-trade language such as speaking of Germany trading with Russia or England with France, or any country trading with any other country, is now as obsolete as speaking of New York City trading with the city of Chicago. Industry is inherently world-around and is inherently world businesswe have no other characteristic but world.
38 This world-identity-only trending of big business promises a surprise which is that world
citizenship will not occur as a political initiative. The economics of this exploding
industrial-world activity soon will require world citizenship for its personnel.
I want to precipitate your awareness of the reality of the points I have been making by asking
you, If everybody who teaches school because its the simplest way of making a living were
given a well-funded fellowship to lifelong research would they accept? If humanity
receives universal fellowshipsall expenses paid plus a comfortable bonus, would humanity
not stop asking itself, How can I earn a living, and start asking, What is it that Im
interested in, and what could I do to help make the world work more satisfactorily, more
interestingly? This used to be a stupidly altruistic question. It suddenly becomes a very logical
one.
39 I feel that the high capability of the young who do not happen to have been trained in science goes into their intuitive formulations. Artists are now extraordinarily important to human society. Many who have been called artists are healthy human beings who have kept their innate endowment of capabilities intact. The greatest of all their faculties is the ability of the imagination to formulate conceptually. I feel that it is the artists who have kept the integrity of childhood alive until we reached the bridge between the arts and sciences. Suddenly we realize how important that conceptual capability is. Professor Kepes of M.I.T. took uniform-size black-and-white photographs of nonrepresentational paintings by many artists. He mixed them all together with the same size of black-and-white photographs taken by scientists of all kinds of phenomena through microscopes and telescopes. He and students classified the mixed pictures by pattern types. They put round-white-glob types togetherwavy-gray-line-diagonals, little circle types, etc., together. When so classified and hung one could not distinguish between the artists works and scientific photographs taken through instruments. What was most interesting was that if you looked on the backs of the pictures you could get the dates and the identities. Frequently the artist had conceived of the patterns or arrangements before the scientists had found their counterparts in infra- or ultravisible realms. The conceptual capability of the artists intuitive formulation of the evolving new by subconscious coordinations are tremendously important. Much of the essence of what I have been saying to you may or may not be news, but I would not be surprised if tomorrows biggest news is that the artists who best appreciate and conserve our natal capabilities have ascended by acclaim to the premiership of this new era of man on earth.