Horizon (1964) Episode Scripts

N/A - The World of Buckminster Fuller

Archive programmes chosen by experts.
For this collection, Prof Alice Roberts has selected a range of programmes to celebrate Horizon's 50th anniversary.
More Horizon programmes and other BBC Four Collections are available on BBC iPlayer.
WIND HOWLS These are what we call geodesic radomes, and they are designed to protect brave, powerful, important apparatus from the great storms of nature.
We think of structures as being something very powerful, but these are very delicate.
We think of eggshells as being very delicate structures.
An eggshell is only 1/100 the diameter of the eggshell itself.
These domes are one half of that thickness.
They are only 1/200 their own diameter.
Yet they've been through about ten years of the most formidable conditions in the Arctic that any structures have ever had to stand.
But I'm not a dome salesman, I'm an explorer in structures.
I'm interested in the fundamental principles by which nature holds her shapes together.
NARRATOR: Buckminster Fuller has a worldwide patent on his own way of holding shapes together.
He is famous for his domes.
They have made him a million dollars, but at one time or another in the last 40 years he has made front-page news as an architect, aviator, engineer, a sailor, a scientist and a philosopher.
But he is none of these by profession.
He cannot be classified.
He spans both the arts and the sciences in a way that few other men have done.
Horizon aims to present science as an essential part of our 20th-century culture, a continuing growth of thought that cannot be subdivided.
So, tonight, in this, our first monthly programme, we explore this undivided, all-embracing world of Buckminster Fuller.
A Cambridge scientist who knows him well is Dr Aaron Klug.
Dr Klug has been working on the molecular structure of viruses for the last ten years and first saw the relevance of Fuller's structures to his own work some five years ago.
KLUG: Well, er since that time, I have followed Fuller's work much more closely.
And I have found a lot about his early experiments.
He is a kind of experimental mathematician.
He has found a lot of things for himself.
I think this is his great strength, because he has made domes and other kinds of things.
I mean, he has made cars and houses of various kinds, houses that hang rather than stand on the ground.
He has done all these things, I think, because he has never been content with the an ideal description of things.
He has always set himself the rather strange problems.
"How would I do this, given these materials?" And so on.
Um He hasn't started from the limitations of mathematics or algebra or conceived notions.
And he has also rethought all these things in a rather unique way.
NARRATOR: Fuller's rethinking is certainly unique.
As an experimental mathematician, he has had the satisfaction of seeing his experiments proved right.
He explains some of the structural ideas that have been fundamental to his success to a group of students at the Architectural Association School in London.
I'm here in England .
visiting some scientists I've just come from Africa and I'm on my way immediately afterwards to India and around the world.
I've come to see these scientists, which should really be of fundamental interest to you as architects, because the structural exploration I've been engaged in over a great many years .
has now become of interest to the scientists themselves.
And I'm going to talk for a moment about structure.
We are very familiar with the rectilinear form.
And children just making their first picture of a house are very liable to use this cube.
But the cube will notdoes not really have structural integrity.
I have There are some diagonals in each of the faces of the cube here.
And they are really responsible for its holding the shape that it is holding.
I am going to take away the .
disconnect the I'm going to take this away and we will find that our cube has no structural integrity whatsoever.
LAUGHTER So But this has not lost its shape.
This is what was giving the cube its shape.
It is our friend, the tetrahedron.
And A lot of people say, "Why do you use the word 'tetrahedron'?" Simply because it means a system that has four faces.
The Greeks had one word where we need to say "four faces", "a figure with four faces".
So they were more efficient than we are, so we might as well use their nice, efficient word.
Now, if we try to make a whole new shape, something we might say about shapes Here are some energy actions in the universe.
There are enormous number of energy actions in the universe.
One of the things I've learned is that two actions can't go through the same point at the same time.
It's like knitting needles.
It's very important to recognise that.
I've found that the scientists I am visiting here in England are now very excited by the realisation that that new axiom, that two lines of action can't go through the same point at the same time is really beginning to prove very worthwhile.
Because every architect and every engineer has assumed that you can put a point on the paper and you run a great number of lines through that same point.
In fact, all the geometries, Euclidean geometry, or the non-Euclidean geometries, assume planes with points and lines going through the same points.
But I have given myself .
a discipline which I Whatever I use in the way of tools must be experimentally derived.
And when the mathematician says to me, "I'm a very pure mathematician, "and I have a line that hasn't any dimension," I ask him why he uses the word "line"? Because the word "line" is something that is an experience.
It is a word derived from experience.
And I say, "Why, if you're so pure, can't you invent a new word "that is so pure that means whatever you mean?" Something that has no dimension or experience.
He hadn't thought about that, but anyway When we then become empirical, we say then that we find that two lines can't go through the same point.
And on the cover of this month's Scientific American you see a picture of the cloud chamber .
used by the nuclear physicists in bombarding the nucleus.
And you read very recently about the discovery of omega-minus.
And the work they do in the cloud chamber, the bubble chamber, is to send in a very high-speed neutron or some other particle and it suddenly collides with some other component and then there is a parting of company, some angular resultants.
And they are able to identify all the different nuclear components by the different kinds of angles that they take.
Now, if two lines could go through the same point at the same time, then there would be no such interferences, and there would be no such Each one would just go through the other one and there would be no breaking up in angles.
So, when we go down to the bubble chamber, we were going down the very finest lines that nature has ever made.
And actually it is not a continuous straight line, it is a series of bubbles.
And it demonstrates really clearly that two actions can't go through a point at the same time.
So that is why we have interferences and why we have reflection and refraction.
At any rate, let's get two actions that get very close to each other.
They get what we call a critical proximity, the way the Earth is attracted to the moon.
So we get a mass attraction.
So once these two are attracted to each other that way, then we find that they could They'd be like a pair of scissors.
They hinge together.
Now we have an angle that is really an unstable kind of an angle.
And what I would like to do is to have a stable angle, so that I will be able to have a persistent shape.
That's what I mean by a structure.
So I find that I take a hold of this side of the angle.
The other side, these are levers.
The further I go away from that fulcrum, the less effort it takes to stabilise that angle.
So, having come to the very ends, we can take another action and let it cross here as a push-pull member.
So with minimum effort it stabilises the opposite angle.
So I find that triangles are a very extraordinary kind of device in that each side stabilises the opposite angle with minimum effort.
In other words, minimum effort is essential to the physicist because he's found that nature is always doing things with minimum effort.
Now, we find then there are no other polygons that will do this.
If I take out this, use the square, we find it is completely unstable.
Make more sides, this gets more and moreless and less stable.
So that Then the triangle is the only stable pattern.
And now I am going to want to do something, which is I like to develop, then, a local system that returns upon itself, that subdivides the total universe into withinness and withoutness.
And that is what I will then call a structural system.
And in order to be able to have a withinness and withoutness If I have two triangles hinged together like this, they simply become congruent.
There is no inside and outside.
They are too thin.
So I find that the minimum subdivision of space is to have Say I have now two triangles.
Again, it's like the hinge.
I had a fulcrum before and now I have a hinge.
So, again, with minimum effort here, taking the end of the levers I can stabilise that as opposite.
That becomes our friend, the tetrahedron.
Now, unique, then, to the tetrahedron, to the system, of omnitriangulated, symmetrical system, is the fact that the minimum is with three triangles around each vertex.
I can get four triangles around each vertex.
And we call this the octahedron.
We just count by counting on the faces.
Eight equilateral triangles.
It's always four.
I can get a five equilateral triangles around each vertex.
And we call that the icosahedron.
I can't get I can get six equilateral triangles around a common .
But they add up to 360 degrees.
Therefore it becomes a plane and it goes to infinity and won't return upon itself, so it won't subdivide the universe locally into withinness and withoutness.
So there are only three possible cases of omnitriangulated, omnisymmetrical, minimum-effort shape stability.
That's tetrahedron, octahedron and icosahedron.
NARRATOR: The shapes that fascinate Fuller - the tetrahedron, octahedron and icosahedron - are three of the five regular Platonic solids.
There can only be five solids with their faces, edges and angles all absolutely alike.
And this fact has always fascinated philosophers.
Plato thought that the four elements, earth, air, fire and water, had atoms of these shapes, and that the fifth represented the vaults of the heavens.
To the astronomer Johannes Kepler, all five regular solids represented the heavens by tracing, he believed, the orbits of the planets.
The solution seemed so neat.
"The intense pleasure I have received from this discovery "can never be told in words.
" But the discovery was just too neat to be right.
To a practical man like Alexander Graham Bell, the inventor of the telephone, these shapes were interesting, not as solids, but a structural skeletons.
In 1889 he addressed the International Academy of Science in Washington.
"I have come to the clear realisation "of the fundamental importance of the skeleton of a tetrahedra "as an element of the structure of a kite or flying machine.
" Fuller wasn't interested in ideal Greek solids and knew nothing of Bell's tetrahedral kites.
His interest stemmed not from flying, but from a childhood love of ships.
"Ships," said Fuller, "do not survive "unless designed to use winds, tides, tension and compression "to human advantage.
" In 1928, Fuller used these tension principles to design a ten-deck apartment house using lightweight alloys and hanging the decks from a huge central mast.
Delivery would be by airship.
On approaching the building site it drops its anchor and then dropsa bomb.
The ten-deck tower house is lowered into the crater like planting a tree.
It's made fast with temporary stays until the concrete poured round its base is set.
The airship then goes off to make a few more deliveries.
One practical use Fuller saw for these tower blocks was as stopping off-points on the great circle air routes over the globe.
The towers could be carried to the most remote parts of the world.
Using traditional building techniques was, to Fuller, quite absurd.
But lightweight, mass-produced buildings were of no interest to the New York architects of the time.
In 1930, Fuller was asked to speak in New York at a dinner given in honour of some of the famous American architects responsible for the new skyscrapers.
When I went to that dinner then, I knew that these other architects were famous.
Everybody understood those big buildings.
But what I was working on was quite invisible in 1930.
When I stood up, I said, "I'm working on the potential industrialisation "of the shelter industry "at a time when the kind of industry that now goes into shipbuilding "and aircraft building might be applied "to the production of buildings for men "which could be even light enough to fly.
" And I said, "Buildings What buildings weigh "is not thought of today.
"Everything in industry is done on performance per pound.
"It's not so in the world of architecture and building.
"Just to prove that, we are very fortunate "to have these famous architects here.
" So I said to Ralph Walker, "Can you tell me "what the Telephone Company Building weighs?" And he said, "No.
" "Could you tell me just roughly within 100,000 tons?" "No.
" "Can you tell me within one million tons?" He said, "Architects don't bother with things like that.
" Then I tried each one of these famous architects - Ray Hood, about his Daily News Building and what the Rockefeller Center was going to weigh, what the Empire State and the Chrysler Building None of them could answer.
So it was very clear that architects were not dealing in what buildings weigh, therefore they were not ratioing performance to the pounds, which is what you do do in the development of ships for the sea and ships for the sky.
And because of the high performance requirements of ships of the sea and ships of the sky, men are continually bringing in better alloys.
The most advanced technology is brought to bear in weaponry development in order to do more with less, to get the greatest hitting power, the greatest distance, the shortest time, the least effort.
I saw that over in that world of the advanced performance per pound, there might come a time when we could take the world's resources, which are serving only a very small percentage of humanity By upping the performance per pound we might be able to design a way of applying it to the whole world where they are not considering performance per pound.
And if we ever did, we might be able to make the world's resources serve 100% of humanity at very high standards of living.
When I sat down, Frank Lloyd Wright got up.
He said, "My young friend Buckminster is as good a designer "as he is as bad a speaker.
" And he felt this was very irrelevant to the other talking.
But he made me his friend.
From that time on he always treated me as a friend and an expert on science.
Frank Wright, in introducing me to his fellows at hisTaliesin said, "I am an architect interested in science.
"And Buckminster is a scientist interested in architecture.
" NARRATOR: The explorers in architecture, like Frank Lloyd Wright, and the explorers in science, like Einstein, have always intrigued Fuller.
In the early 1930s I had written my first book.
And some publishers became interested and took the manuscript.
And they wrote me a letter after a few months saying thatthey that three chapters I had written about Einstein made them feel that the book would have to be returned to me because they said they'd looked looked up the list of all the men that understood Einstein.
Nine people at that time were supposed to understand him.
They said, "You're not on the list.
" "In fact," they said, "you're not on any list.
" And I have to tell you what my three chapters were.
My first one explained Einstein's philosophy and how this motivated his going into his mathematics.
And I explained his mathematics and how it made translated this into his famous equation.
Then I said, "The individual scientist leads science.
"Science paces technology.
Technology paces industry.
"Industry paces economics.
"So that in the end what the advanced scientist does, "if it's really important, "affects all world societies, quite a long lag in it.
"Therefore," I said, "if Einstein's equations prove to be correct" - because in the early '30s they had not been proven to be correct "So if his equations prove to be correct, "then they will affect all world societies.
" My third chapter was called E = MC2 = Mrs Murphy's Horsepower.
I examined what would be the consequence in everyday society if we accepted relativity and Einstein.
The publishers Having read this letter saying that I wasn't qualified to speak, I just thought quickly and I wrote a letter saying, "Why don't you send this, my manuscript to Einstein?" And Einstein had just come to America in those days from Europe.
He was at Princeton University.
I forgot all about the incident.
I expected Princeton, my publisher, to send my manuscript back, when one day a doctor called me up in New York and said, "My friend, Dr Albert Einstein, "is coming in from Princeton this weekend "and he has your typescript, and he would like to talk it over with you.
" So I went to meet with the old man.
And it was an extraordinary, moving meeting for a young man who thought so much of another man.
And he said, "I'm going to write to your publishers and tell them "I approve of your explanation of my philosophy and my mathematics.
" He said, "This third chapter" He said, "Young man, you amaze me.
"I cannot conceive anything I've ever done "having the slightest practical application.
" NARRATOR: Fuller has always been practical.
35 years ago he saw the need for what he called an auto-airplane, a jet-powered car that would fly.
It was to have a triangular frame .
rear-wheel steering like a boat, and inflatable wings.
It had to be aerodynamic if it was to fly, unlike the 1930s motorcar, which appeared to be no great advance on the horse and carriage.
The final design was intended to be a ground-taxiing model for an auto-airplane.
A friend gave him some money and he rented a factory.
Fuller and a yacht designer, Starling Burgess, set to work to build a three-wheeled, ten-passenger vehicle, powered with a standard V8 engine which was capable of 120mph.
They built three prototypes, but the motor industry refused to back it.
It was even refused space in the New York Motor Show of 1934.
So Fuller parked it outside and caused a sensation.
Ten years later he got involved with industry again.
This time it was a circular house of aluminium and steel designed for mass production by an aircraft company.
The house could be packed into a cylinder 22 feet high.
It was suspended from a central mast held by steel cables.
Each part was carried and fixed by one man.
It took a few hours to build and cost no more than a Cadillac.
But again industry dropped the idea.
These setbacks never deterred his exploration into structural geometry, which he carried on alone or with groups of students.
It was with students rather than with any big industrial organisation that Fuller developed his geodesic domes.
The basic dome structure was achieved by subdividing the 20 triangular faces of an icosahedron.
And keeping these vertexes always at the same distance from the common centre, you begin to get, then, spherical triangles.
But you can see, even with your eye, this is an isosceles triangle - that angle is wider, these two are the same.
There is an isosceles here, an isosceles here.
And this is a symmetrical or equilateral.
Now, that has a quality of a propeller blade, that is The centre is symmetrical.
The terminals, there are three terminals, in perfect balance with each other, and they are, even though they are asymmetrical, they become a dynamic balance like the propeller blade going round, each blade being the same.
Now, we can go on to make further subdivisions, which we do here.
Here will be the same icosahedron triangle.
Now it has three I had two subdivisions on the edge of the icosahedron triangle.
Now it has three.
And you can see The moreare these subdivisions on the edge of the icosahedron, the more spherical it becomes, and the smaller each triangle becomes.
And it develops an extraordinary structural kind of a capability because if I push in on one of these vertices .
the worst thing I can do is get a dimple.
If it's very high frequency, it becomes a very tiny little dimple.
NARRATOR: In theory, the domes are strong and economic in material.
Industry began to catch up with Fuller.
They wanted to put his domes into mass production.
This time Fuller had hit the jackpot.
The basic unit of this dome is an aluminium strut three feet long, weighing five ounces, 19,680 of them spanning 93 feet, and all designed to celebrate the 50th anniversary of the Ford Motor Company.
Like a spider's web 250 feet in diameter, another dome rises - this time for the American Society of Metals in Ohio.
The domes went into mass production and began to spring up all over the world.
An aluminium dome 145 feet in diameter was put up in Hawaii in 22 hours and recorded by time-lapse camera.
In 1956, Fuller found himself involved with the United States government and the Cold War.
In 1956, the United States Department of Commerce was notified by the State Department that the British had had found that in Kabul, Afghanistan, that the Russians and the Chinese and the Czechs and the East Germans were spending a very large amount of money getting ready for a big exhibition at the Jeshyn fair of Afghanistan, which is a great annual festival.
And remembering that Afghanistan is bordered by Russia and China and India and Pakistan and so forth.
It is a very extraordinary state.
And the West was in there but it was slipping out very fast.
The Russians were obviously courting them.
We had no competitive exhibit.
And the Department of Commerce was caught off balance.
They didn't have any budget money for an exhibit.
And no time.
Just 30 days were left.
They came to me and asked if I could produce a geodesic dome within the 30 days, get it to Afghanistan in 30 days.
They could only give me a very small amount of money to produce it, and we could only have one DC-4 to deliver it to Afghanistan and they would send one engineer with it.
That is all the weight that would be permitted.
The engineer arrived in Afghanistan and he showed the Kabulians that were assigned to put it up "You put the blue to the blue and the red to the red "and the green to the green.
" The Kabulians didn't know what they were putting together.
It could have been a cube or any kind of a building.
But suddenly they found they'd build a sphere.
And society tends to think of the people who put a structure up - the bricklayer or the carpenter - as being really responsible for that kind of structure, that the architect can ask him to vary it in various ways but he is responsible for the structure.
So the Kabulians looking at their own Kabulians putting up a dome structure said, "You're very good dome builders, aren't you?" So the Kabulians said, "Yeah, we're all right.
" They suddenly decided this was Afghan architecture because it had been put up by Afghans.
It was simply a very large, new, modern dome of aluminium and plastic.
And, as a consequence, they fell in love with the dome.
The exhibit inside was inconsequential.
It was bouncing ball bearings and a talking cow and things.
People didn't pay any attention to that.
But more than a quartermore than a totalinhabitants of Kabul showed up for the exhibit.
And it became by far the most popular item in the fair and way outperformed the Russians and the Chinese.
NARRATOR: The Kabul dome has been flown to Warsaw, Casablanca, Istanbul, Tunis, New Delhi, Bangkok and Tokyo, and is now on its way round the world for the second time.
There are now over 4,000 of his domes dotting the Earth's surface, made of every material from metal to cardboard.
But for Fuller, the success of his domes is merely one proof of his theories.
What interests him now is the fact that his ideas have stimulated the thinking of many scientists.
One of them is Dr Aaron Klug.
KLUG: In fact, the parallel between this and your dome is very close.
I mean, it's fantastically close.
They are based upon the same structure, although they are realised in different ways.
You have struts and tripods.
We have rubber tubes and chemical bonds.
Yes, yes.
But there's parallels even closer than that.
Because this is, so to speak, a distribution of matter.
This doesn't represent the real thing.
After all, these bits of rubber tubing must be molecules, which come together with chemical bonds.
And these bonds aren't rigid things.
They are more like a ball joint, although the angle is at a certain preferred angle.
And to represent And moreover, when they come together it must be automatically.
- You know my tensegrity structure? - Yes.
And that the three basics that come together - They have that same - Oh, yes.
The same No, what I wanted to say was this is another point.
I did notice that your domes In your book you make a point that the dome in Kabul was put up by unskilled labour.
Oh, yes, that's right.
So, because the Afghans putting up the dome don't, can't follow the complicated rules, you paint the ends.
Well, we did a similar thing.
I mean, almost.
It was rather different.
We have a different rule, which we call among ourselves Crick's rule - that's Francis Crick, who did some work on biostructures some years ago.
And he always said it's a joke - the way we know with a virus is a child will be able to build it.
This model here, it's rather difficult to see.
You will recognise it's your own d-sticks we've used.
FULLER: Yes, yes.
KLUG: Remember, Don Caspar - you remember, in Boston - he realised that you could use your d-sticks models for building this kind of tensegrity model.
And now the rule you give to the child, or the or theunskilled person, is you join red to red.
- And green to green.
- Yes.
If I join red to red I get that dimer.
If I join three of them, I get a trimer, three of them.
FULLER: Yes, yes.
KLUG: If I join the greens I get a hexamer or pentamer, whichever way you like.
And then you start building out.
You build this extended net.
I think this is one of nets, actually one of the nets you've used.
FULLER: It is.
I suppose if you make it by this rule, it must come out like this.
Yes, yes.
Well, of course, we have a complication here.
I mean, you If you have an engineering structure you can put in the angles.
But to make this more realistic we have to have bonds of more than one level.
Alternatively, we have to fix the angles slightly, - so the thing tapers round.
- Right.
When you put the angles right, it will fold up into this.
FULLER: The The elasticity of your model makes up the spherical trig KLUG: Yes, yes.
You don't do any calculations.
That's the marvellous thing about it.
I mean, this is the People often ask me, "Can you do spherical trig?" The answer is, "Yes, but I don't use it.
" Not for this.
What nature does She puts it together in the simplest way.
Then she tries to get more comfortable, so she stretches into the spherical trig in due course.
Because there's just enough Just slight differences.
Look, look, there's one of these bonds has come undone.
- It's got broken.
- Yes, yes.
But the amazing thing is the thing hangs together quite well.
We find in all the geodesics you keep breaking, or open locally, and just to have a local break of that sort doesn't It doesn't matter.
The rest of the system isn't bothered.
It's an equilibrium, yes.
One of the things that I think we've tried to teach electron microscopists is that shape, so to speak, is incidental.
The thing comes out to be whatever shape it turns out.
We don't worry about getting the shape.
People It's amazing, people who are not used to these things Of course, I discovered them for myself.
I, you know, it took me some time to realise that a thing could turn out to have the shape of an icosahedron, actually look like an icosahedron, but in fact there are many rounded versions in which the triangles are spherical triangles.
And this is I really think this is a more incidental property.
I don't know what you think.
I think it's interesting, something you just said because I've given myself the problem of giving man some advantage of enclosures with a minimum of investment.
KLUG: Yes, yes.
And I always say I pay absolutely no attention to what they are going to look like.
KLUG: Yes.
Oh, yes.
When I've finished they tend People tend to think of them as good looking.
- They say that.
- Oh, yes.
But that is purely incidental.
KLUG: Yes, well, I agree with you absolutely.
Because this is the - There's a function to be served.
- Yes, because this is an object.
Mathematicians like this object but, I mean, one of the things I've learnt from, well, from the way you make your things is that you abandon the traditional classical mathematics when you are discussing making real objects.
That's right.
And although this is a sort of useful starting point, you've got to - Well, you learn to forget.
- Yes.
And that, in fact, in my own work was the hardest Well, it's the hardest step because I am a physicist by training and I Although I wasn't brought up in polyhedra because it was unfashionable.
I went right through school without knowing anything about these and I had to learn for myself.
I read the mathematical books.
I always thought of an icosahedron as this perfect You know, in the Greek sense, a perfect object.
I did never think of it as made of Well, of course, when you You see on the edge You actually see it as made up of real rods and struts and things.
This took some forgetting, I can tell you, because, in fact, one of the stumbling blocks that we had when we were trying to think of structures for spherical bio We made exactly this mistake.
We always wanted to make the Greek ideal and never, you know, never the real thing.
Nature doesn't care less about ideals.
I mean It was in that way, for instance, I discovered that two lines couldn't go through the same point at the same time.
- Oh, yes.
- If that was so, then how is it Well, exactly.
It's quite clear things won't be leading up to Oh, yes.
And that really is the very essence of the skewing.
Things will not go through the same point at the same time.
Well, I must say, when I read your note, when I did see your notes and I read one of your theorems, that two lines can't intersect, you know, it seems a bit odd.
You want, in the first instance, to laugh at it.
Because this is not what one learns at school.
But when you think of the real world, the world of objects, you realise this is absolutely bound by this.
And I have learned that.
I think we were showing that in the cloud chamber NARRATOR: Dr Krug and his American colleague, Dr Caspar, have studied Fuller's work in great detail.
Recently, Fuller met for the first time an electron microscopist working on the structure of certain biological enzymes - Robert Horne.
Structure of some basic proteins in the electron microscope.
They are much smaller than virus particles.
In fact, the size of the protein is equivalent to some of the small units that people have been seeing - on the surface of viruses.
- Mm-hm.
This particular protein is what we call an enzyme.
It's a type of catalyst.
It, you know, it has properties of breaking down chemical components in biological systems.
And this particular enzyme is an extremely small one.
And it is known as glutamic dehydrogenase, a rather long Will you say that once more for me, sir? Glutamic dehydrogenase.
It's a protein with a molecular weight of about a million.
And in the electron microscope in some of the preparations, we see these roughly triangular-shaped particles, and in some cases we see a number of sort of V-shaped or U-shaped units.
Well, you can see the sort of problem.
We are right down now to molecular levels and we have a pretty strong suspicion that the tetrahedral symmetry - is coming up again.
- Yes.
And we've found it We found the icosahedral symmetry, as you well know, in the viruses.
And, um, going down even further, we are pushing the microscope more or less to its limit here as to what we can see directly, and I think it's I find it very fascinating anyway that this type of arrangement is coming up over and over again.
At the Massachusetts Institute of Technology, the .
a crystalline professor of crystallography, confronted the computer with .
the question about the coordinate system.
You know about this? Dr Loeb.
And he And the computer came back, said that nature in crystallography was really using 60-degree coordination instead of 90-degree coordination.
It seems to be quite exciting because it brings us back to our tetrahedron.
- It's come back again.
- Yes.
I think there are a number of instances where we have this threefold symmetrical plan.
But the thing I wanted to perhaps ask you, as a matter of interest, of creating order out of disorder like this, is what are the possible configurations? Could you build it perhaps with three or on multiples of three? Or are there other arrangements in the tetrahedron? You could, of course, do it with six - - the six edges of the tetrahedron.
- Yes.
But I find that you can do it very beautifully with three.
- With three? - Yes.
HORNE: Now, this is putting two units rather than three together.
FULLER: Two units, which are - FULLER: You see the form? - HORNE: Yes.
FULLER: I call this an event.
I call the central line here, this is an action.
This is a reaction, this is a resultant.
FULLER: They are necessary to all actions that there be reactions and resultants.
And they do not occur in 180-degree planes or lines.
There is always a precession effect, so that, as I call it, a negative event and then there's a positive event.
Those come together and give you a tetrahedron.
HORNE: Another tetrahedron.
So we could in fact have a protein, which is folded in this way, the angles being reasonably constant throughout.
Yes, yes.
But it would have a positive and a negative Yes, yes.
NARRATOR: For many of the scientists who have met Fuller, the experience has been rewarding.
He does not set out to copy nature, but he is pleased, though not surprised, that scientists are finding that major solutions to her own structural problems coincide with his.
FULLER: This Ping-Pong ball is quite translucent.
You look at the light, you see the light coming through it.
The only reason light can come through it, it's full of holes.
Some of the holes are smaller than the human eye can see.
So, in as much as it's full of holes, it turns out to be all triangulated and it is a geodesic structure.
In the same way, then, we know that smaller and smaller things get to beare also full of holes, and are taking the most comfortable geodesic positions, therefore it becomes very interesting.
Down, for instance, to the cornea of the human eye.
Dr von Hochstetter has succeeded in staining the membrane of the human eye, cornea, and we find that it, too, is, very clearly, a geodesic structure.
A tensegrity geodesic structure.
Then we get down much smaller still, down to the size of the little animals in the water, called radiolaria.
And we find, again, these structures are geodesic structures.
They are also usually on the icosahedron and sometimes the octahedron and sometimes on the tetrahedron.
Then we get The same level as those little animals, we have some little plants called the diatoms or the algae.
And this picture was taken in the with an electron microscope in the Max Planck Institute by Dr Helmcke.
And you'll see it, too, is a geodesic structure.
NARRATOR: A microorganism has the same basic structure as his two-mile-diameter dome project over Manhattan.
The same principles work on any scale.
At the age of 68, Buckminster Fuller is still exploring.
Behind all his varied explorations stands the promise he made to himself in 1927 - to discover the principles operative in the universe and share them with his fellow men.
He has never pursued novel structures for their own sake.
He is determined to do the most with the least, not as an intellectual exercise, but because he firmly believes that of the possibility of a good life for any man depends on the possibility of realising it for all men.