Why I Believe Human Civilization is Unraveling

These illustrations are copies of photographs that I made into plastic dinner plates (see http://www.makit.com/images/PageGraphics/1234/Instructions/Make_A_Plate.pdf)
These illustrations are copies of photographs that I made into plastic dinner plates (see http://www.makit.com/images/PageGraphics/1234/Instructions/Make_A_Plate.pdf)

If you get the sense that problems are developing faster than we can solve them, you are not alone. Recently, Naomi Klein in This Changes Everything and Elizabeth Kolbert in The Sixth Extinction have dramatically documented radical changes taking place in the environment, and Ted Koppel in Lights Out has shown how vulnerable we are to a cyber-attack on the power grid (I confess that I haven’t had the courage to read any of these except The Sixth Extinction, which is predictably depressing, although beautifully written). But I found one scientist who has put his finger on the ultimate cause of our many environmental problems.

William Rees is a professor in the School of Community and Regional Planning at the University of British Columbia. He is best known as the co-originator of “ecological footprint analysis,” a quantitative tool that estimates humanity’s ecological impact in terms of appropriated ecosystem area. He wrote an essay that you can find on the web at https://www.scribd.com/fullscreen/63679469?access_key=key-a96x5ce4d4gcxibjc86&allow_share=true&escape=false&view_mode=scroll

It is a beautiful essay written in clear English with transparent logic, It is also devastating. Here is his prescription for solving our (un)sustainability crisis:

To reduce the human eco-footprint, the fetishistic emphasis in free-market capitalist societies on individualism, competition, greed, and accumulation must be replaced by a reinforced sense of community, generosity, and a sense of sufficiency.

I cannot think of anything less likely to occur in a world of competitive consumers, especially in the U.S. where individualism is a national religion.

Rees’s argument is based on evolution:

Numerous experiments show that unless or until constrained by negative feedback (e.g., disease, starvation, self-pollution) the populations of all species:
Expand to occupy all accessible habitats.
Use all available resources….

Scup

What can our genes possibly have to do with whether we act sustainably or not? The connection is actually quite simple. There are certain behavioral adaptations that helped our distant ancestors survive—and thus those predilections were passed on to us. But those same (now ingrained) behaviors today are decidedly not helpful in solving our sustainability crisis—they have become maladaptive. Moreover, these natural predispositions are reinforced by modern humanity’s technological prowess and addiction to continuous material growth.

Through our unique ability to cooperate and the technology that cooperation makes possible, humans have been able to push back against the negative feedback that keeps other species in check. We have run amok across the globe’s surface. Rees quotes an outspoken and prize-winning Canadian journalist (Andrew Nikiforuk):

“Let’s face it: Homo economicus is one hell of an over-achiever. He has invaded more than three-quarters of the globe’s surface and monopolized nearly half of all plant life to help make dinner. He has netted most of the ocean’s fish and will soon eat his way through the world’s last great apes. For good measure, he has fouled most of the world’s rivers. And his gluttonous appetites have started a wave of extinctions that could trigger the demise of 25 percent of the world’s creatures within 50 years. The more godlike he becomes the less godly Homo economicus behaves.”

In 1855, 80 years before I was born, there were 1.1 to 1.4 billion people alive. When I was born there were about 2.2 billion people alive. 80 years later, in 2016, there are 7.2 billion and growing. I belong to that small  cohort of humans that have lived during a tripling of the population (after humans became widespread – very early generations may have seen drastic population changes).

An exploding population intent upon a higher standard of living requires more food and water, eats away at the stock of irreplaceable natural resources such as rain forests and crucial minerals, and pollutes the land, atmosphere and oceans. Global warming is a direct result of an exploding population.

Those like Thomas Malthus who have predicted that we will run out of some crucial resource have typically been dismissed because they cite a specific resource such as food or oil, only to have a technological fix of some kind overcome the supposed limit. But in the 1970’s when the “green revolution” was completed, supposedly ending our food worries, there were half as many people on earth as there are today. We cannot rely on historical precedent, because we have never faced a world with 7 billion people, let alone the 10 or more billion now projected.

Sea Horse

Also, each technological fix moves us farther out on a limb of dependency, and requires yet more technological fixes to repair the damage it causes – our dependence on fossil fuels is the best example. Shortages and pollution are accelerating, while the technological fixes take longer to accomplish and require social conditions that are highly unlikely to occur.

Nearly every economist from Paul Krugman to Milton Friedman says that the only way to maintain prosperity is through growth, yet we can’t keep making more stuff indefinitely. So what is Plan B? The really scary answer is that there is no Plan B. Or rather, Plan B is so drastic that the chances of its use are vanishingly small. Let me cite another quote from Rees, one by the esteemed neuroscientist Antonio Damasio:

“[For humanity to survive the sustainability crisis] we must rely on highly-evolved genetically-based biological mechanisms, as well as on supra-instinctual survival strategies that have developed in society, are transmitted by culture, and require for their application consciousness, reasoned deliberation and willpower.”

OK, we know this because of science. We can do science because we know how to reason. Damasio is saying that we need to reason our way out of the mess we are in and change our behavior. So can we use our conscious reasoning powers to change our behavior as a species?

Psychologists have been busy trying to answer this question, and the results are not encouraging. The evidence is rapidly accumulating that our behavior is almost completely driven by emotion and built-in cognitive and sensory machinery that bypasses reason. We use our reasoning abilities primarily to construct belief systems and social structures to justify our behavior, not to guide it.

But we have in the last 0.2% of human history come up with a belief system, science, that drastically improved the match between what was believed (by scientists and engineers) and what seems to be happening in nature. This has allowed these specialists to make more and more precise predictions about an increasing range of phenomena, and to use those predictions to rapidly escalate our ability to bend nature out of the way of our desires. And our desires are, like those of any animal of our type, to use all available resources and occupy all available habitats.

Yes, when given a choice, women will limit their reproduction rate, as reproduction is expensive. As infant mortality declines, women (given a choice) choose to have fewer children, stabilizing the population. However, there is a lag between the decline in mortality and the decline in growth rate, and it is this lag that has created our exploding population. In several African countries, the expected decline in fecundity has not occurred, so that current population projections show skyrocketing population, which simply can’t be accommodated.

Science has its limits. Human institutions are far too complicated to explicate at the same level of precision as for example the findings of physics (always the touchstone of scientific validity). But you don’t need precision to make predictions. For example, we likely will never understand evolution in precise detail, but we know generally how it works, and can make accurate predictions even in our ignorance. Newton was fully aware that his theory had a serious flaw, but decided to ignore it because the theory was so useful (and still is).

Spider Crab

So by looking back into our evolution, and observing at present how we use our knowledge, we can come up with a conclusion that is as valid as any in science: we cannot continue to maintain a consumption-based economy for much longer. But all the evidence I can muster makes it extremely unlikely that we can act on the imperative described by Damasio: changing our behavior globally, quickly and in a way that defies our innate and culturally learned ways of doing things.

We must somehow invent a society and economy that is not based on growth, one in which the number of “natural” molecules that we turn into “useful” molecules abruptly stops growing, in which all are provided with basic goods and services and our efforts are focused laser-like on saving what is left of the biodiversity on earth. To the politician and economist, lack of economic growth equals stagnation, deflation and misery. So we plow ahead into a future using an economic model that by definition cannot survive over the long run and has already begun to break down.

Saving civilization will require a reversal of our value system from the accumulation of resources to their redistribution. We will need to be satisfied with what we have (or in the case of “advanced” societies, give up a lot of what we have). We will have to abruptly stop population growth. We will have to abandon or drastically modify the contemporary religion of personal liberty in the service of working together to survive. I am as dependent on personal liberty as the next American, but our quest for liberty is leading us to destruction. The New Hampshire license plate motto, “Live free or die,” seems prophetic, not exhortatory.

Far from being robust, the global economy has become perilously fragile. Everything that we rely on for survival depends upon a supply of electricity (you can’t run a motor generator without fuel, and fuel requires electricity to pump it). If a terrorist were able to damage key machines in our power grids that take months or years to replace (generators and transformers), tens of millions (maybe hundreds of millions) would die in the meanwhile. We have put all our eggs into an electrical basket with big holes in it. And it is unnecessary to remind you that the glorious luxury made possible by oil and coal is changing the climate.

Lobster and Scallop

Similarly, global trade and travel have made us incredibly vulnerable to pandemics and the ravages of invasive species. And who knows when we will exterminate a combination of organisms that proves to be essential for human survival? We may already have done so.

Science fiction writers, journalists and cinematographers have varying ideas about how our bloated civilization will react to growth limits, and I am not immune from this pastime. Wars are likely over land and resources, and they are likely to involve nuclear weapons. Rich countries that are using many times their share of global resources will fight to the death to hold onto their advantages. There will be a breakdown of the stable institutions without which modern society cannot exist, a breakdown of law and order. With it will be a breakdown in the science and technology upon which we have become as dependent as infants on their mothers.

Ironically, all this is truly unbelievable, in the sense that our brains (including mine) cannot constantly be aware of impending doom. We are built to discount risk, imagine impossibly optimistic outcomes and tolerate or even celebrate obvious contradictions. I have gathered together a ton of evidence convincing me that human civilization is rapidly unraveling, but I don’t act on the basis of my beliefs. And neither will you.

I truly admire the many efforts small and large that environmentally savvy people are doing to counteract the effects of specific problems like deforestation, extinction, global warming, atmospheric pollution, disease prevention, poverty – a long list. But until we develop a global perspective that is based on reason and sharing, versus emotion and acquisitiveness, these efforts cannot prevent the breakdown of human civilization.

The weirdest perspective is the largest one. Something like humans, I believe, are an inevitable outcome of evolution. The constant pushing of organisms against environmental and biological limits, the force that drives evolution, sooner or later will come up with a game-changing organism, one that overcomes limit after limit until it reaches ultimate, global limits. I suspect this dynamic is built into evolution and therefore life itself.

I believe this is why we haven’t heard from anyone out there. Just at the point when a species is able to manipulate nature to the extent of sending signals vast distances, the evolutionary dynamics that made such a feat possible destroy that capability. To get a sense of perspective on our modern civilization, take a look at the video at the end of https://www.youtube.com/watch?v=yNLdblFQqsw, which traces 100,000 years of human evolution at 1,000 years per second. After 9o seconds of stasis, civilization appears. In the last second, we vault from the Dark Ages to the present. Space travel occurs in the last 1/20th of a second, as does the population explosion.

Another weirdness: I am intensely aware of and dismayed by the rapidly accelerating and inevitable extinction crisis. I care passionately about migratory birds, one of the miracles of nature. Yet the evolutionary force that made it possible to think about such things is the same force that is exterminating the birds.

Sculpin

Conversely, a human that lived in dynamic harmony with the rest of a bio-diverse nature would know nothing about it except what they learn during their short lives. Apes, elephants, cetaceans, birds, octopi and many other animals have an advanced form of consciousness and can perform remarkable mental feats. But none of them are able to accumulate knowledge. The inventions of each non-human genius dies with its death. What we call progress is impossible for organisms that cannot accumulate knowledge.

So just as we learn who we are, we stumble and undermine the institutions that made such learning possible. Whoever survives the crisis will live in a mutilated world without modern technology, amid the ruins of modern civilization. The myths that emerge will be extraordinary, tall tales about what used to be and about the function and symbolism of this or that mysterious object. Likely there will be pockets of knowledge left intact, rather like the Arabs and monks of the Middle Ages (but only about things that are physically present, like books, because everything electronic will vanish along with the technology that supports it).

But I’ll leave it to the science fiction writers to picture such a world, which they are busy doing in print and cinema. Meanwhile, following Ecclesiastes, we privileged few will keep doing what we are doing, enjoying our luxurious way of life, until it goes away. And then the survivors will adjust. That’s human nature.

Crab

Steam Locomotives Part 2: Engines, Motors and Turbines

I find it annoying that there isn’t a comprehensive discussion readily available to distinguish the various types of engines, motors and turbines. I think we need this for its own sake, and in order to home in on where steam locomotives fit into the scheme of things.

Engines, motors and turbines convert a source of energy into rotary or reciprocating (back and forth) motion. While the term “motor” is always used when referring to electrical motors, it also refers to engines of various kinds, particularly the internal combustion engines used to power vehicles.

Energy is quite difficult to define because it takes many forms, and we are most interested in its transformations from form to form. The sources of the energy we use on earth are nuclear fission within the earth and nuclear fusion within the sun. And of course, the ultimate source of everything, including energy, is the Big Bang.

A practical definition of energy is the ability to perform “work”. Work is typically defined from a human-centered perspective – it has to be “useful.” Energy typically passes through a cascade of transformations from its ultimate source to useful work. To take one example: nuclear fusion within the sun creates electromagnetic radiation that strikes the earth and heats bodies of water; the water evaporates to form clouds; rain condenses out of the clouds to fill reservoirs; the potential energy of the elevated water is converted into rotary mechanical energy in turbines; the turbines rotate generators that create electrical energy; the electrical energy is converted back into rotary kinetic energy by an electric motor; and this energy does useful work by moving a vehicle, spinning a saw blade, or performing any of the myriad tasks for which we use electric motors.

The example is typical of an energy cascade in having many steps where energy is changed in form. Another example would be solar energy transforming chlorophyll into sugar, which powers the growth of plants, which become food that we consume (either directly or via domestic animals) and transform into sugar, which powers our muscles to do useful work. At each transformation of the source energy, some is lost and dissipated into the environment as diffuse heat. Only a fraction of the original source energy ends up doing what we call useful work, although some processes are much more efficient than others.

Internal Combustion Engines

Four stroke internal combustion cylinder CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=182044 E exhaust port cam I intake port cam S spark plug V valves P piston R connecting rod C crankshaft W water cooling jacket
Four stroke internal combustion cylinder
CC BY-SA 3.0, https://commons.wikimedia.org/w/index.php?curid=182044
E exhaust port cam
I intake port cam
S spark plug
V valves
P piston
R connecting rod
C crankshaft
W water cooling jacket

Engines that operate by burning fuel come in two varieties: internal and external combustion. Both types can further be subdivided into reciprocating piston engines and gas turbines. In an internal combustion piston engine, air and fuel burn in one or more enclosed cylinders, creating heat that expands the air, pushing on pistons that turn a crankshaft to power autos, trucks, motor vessels, small aircraft and equipment.

In an internal combustion gas turbine, fuel and air are burned in an open-ended chamber to create a continuing flow of expanding gas that moves turbine blades attached to a rotating shaft. The turbine blades expend some of their work in compressing the air entering the turbine. In a commercial turbofan or turbojet engine, the maximum amount of energy is extracted by the turbine blades to drive a propeller, with the residual used to provide additional thrust.

Turbofan gas turbine engine
Turbofan gas turbine engine

In the illustration, the fan (really a big propeller in a housing) shown on the left is turned by the turbine blades shown at the right, in the area colored red. Much of the air from the fan escapes around the engine, shown by the dark blue pointed shapes, while the air in the center passes through the multistage compressor, which is also turned by the turbine blades. The compressed air is mixed with fuel in the combustion chamber, creating hot gas that turns the turbine. Residual hot gas exits as a jet exhaust.

The turbines blades in a military jet engine only extract the amount of energy needed to run the compressor blades; the rest of the expanding gas roars out the jet exhaust, its kinetic energy thrusting the aircraft forward. Rockets are yet another kind of internal combustion engine. Instead of using the oxygen in air to create combustion, they carry their own oxidizing material (such as liquid oxygen) and can operate in a vacuum.

Gas turbines are also used to generate power.

A diesel-electric locomotive uses a diesel internal combustion engine to turn a generator, which creates electricity to power motors that turn the wheels.

External Combustion Engines

As the name implies, the fuel powering an external combustion engine is burned outside the engine, transferring the energy of combustion into a “working fluid” that then does the mechanical work. Steam is the working fluid of choice in most cases because changing water into steam stores energy equivalent to raising its temperature 1,000 degrees F. Today nearly all external combustion engines are steam turbines, where steam drives turbine blades to create rotary kinetic energy.

Another form of external “combustion” is nuclear power, where nuclear fission heats either water or a working fluid that ultimately heats water, to create steam for use in a turbine. The turbine either drives a generator or rotates the screws in a nuclear-powered ship.

Turbines have the great advantage of having few moving part, but the turbine blades must be of a high-strength material carefully machined, and were not available until late in WWII, when working jet engines were finally developed. At the very end of the age of steam locomotives, both internal and external combustion turbines were used briefly by a few railroads. They were no match for the diesel-electric.

Finally, we get to the steam engine! The classic design, invented in the late 18th Century, uses steam created by external combustion to move a piston back and forth, creating a reciprocating motion that does work by cranking a shaft or turning a wheel. Such a device was possible in the 18th Century, using the iron-based technology of the time, and burning wood or coal.

We can now derive a technical description of a typical steam locomotive: It is a wheeled vehicle running on metal rails, carrying a boiler to create steam, towing it’s own fossil fuel and water supply, with one or two reciprocating steam engines on each side turning paired driving wheels that provides the traction needed to pull a train of cars.

Oakland Bird Cage

In 1956, my good friend and excellent sculptor Bill Underhill organized a team of architecture students to design and build an all-aluminum geodesic dome birdcage, which is still extant in Merritt Park in Oakland, CA. It was funded by the Kaiser [Aluminum] Foundation, and Don Richter of Kaiser was our engineer. The following writeup can be found on the localWiki https://localwiki.org/oakland/Geodesic_Bird_Dome

Oakland Dome Photo

The Geodesic Bird Dome is a part of the Lake Merritt Wildlife Refuge in Oakland, California. Built in [1956] with Kaiser Foundation supplied materials, it was used for years as an exhibit cage for a variety of wild birds, but in later years has been utilized as a cage for sick and injured birds. 1

The birds in here have long been considered unwell and poorly kept. It is not clear if the birds are actually being warehoused or if this is a sanctuary.

A plaque on it says “designed by Buckminster Fuller”, which is incorrect. Fuller did the math behind geodesic domes and did much to popularize them, but was not the inventor of them. This particular dome was designed by William Underhill, Gordon F. Tully, Dick Schubert, Dan Peterson, and Marshall K. Malik, who were architecture students at UC Berkeley.

As I worked out the geometry and saw the project through to the end, I thought it worthwhile to set down the details of how it was designed. I have drawn over the photograph of the dome to help explain its geometry. The meanings of the lines, dots and diamond shapes are explained in the text.

Oakland Dome

Geodesic domes are based on the icosahedron, a 20-sided figure that is one of the five “Platonic” solids, the only convex solids with equilateral faces. The other Platonic solids are the tetrahedron, with four triangular faces, the cube with six square faces, the octahedron with eight triangular faces and the dodecahedron with 12 pentagonal faces. Bucky Fuller’s riveting lectures on the relationships among the Platonic solids inspired the dome, and the geometry continues to fascinate both Bill and myself (see the Wikipedia entry on Platonic solids at https://en.wikipedia.org/wiki/Platonic_solid )

Five triangles meet at each of the 12 vertices of the icosahedron. By spotting these five-spoked intersections, you can figure out the geometry of any geodesic dome. In the diagram, these intersections are shown with large white dots. In a complete icosahedron, there are 30 edges connecting the 12 vertices. The diagram highlights ten of these edges with yellow lines; our dome has a total of 20 such edges.

The vertices of all Platonic solids lie on the surface of an imaginary circumscribing sphere. The icosahedron is chosen as the basis for geodesic domes because it has the most faces, and they are all structurally rigid triangles. However, an icosahedron creates a crude, pointy structure with long edges. Since the edges of the underlying icosahedron become the straight members that form the dome’s structure, the larger the dome, the longer the edges. So for both practical and aesthetic reasons, it becomes necessary to subdivide the edges of the icosahedron to create shorter members and additional vertices which, when brought out to the surface of the imaginary circumscribing sphere, make the dome more nearly spherical.

The number of times each edge of the underlying icosahedron is subdivided is the “frequency” of the dome. To create reasonably sized members and screen panels for the dome, we chose to make it a “third frequency” structure, with each icosahedral edge subdivided into three segments. You can see in the diagram that each yellow edge is broken into three segments that bend outward. A complete sphere subdivided in this way has 180 triangular faces, 90 edges and 80 vertices.

Even if you subdivide the edges of the icosahedron into three equal lengths, the triangles will not be equal in size (if they were, this would be a Platonic solid with 180 sides, which does not exist). The best you can do in a third frequency design is to have two edge lengths and two sizes of triangles.

As we conceived of the dome to be a flight cage, it made sense to maximize its volume. We did this by designing it as a bubble-shaped three-quarter sphere, incorporating 15 of the 20 icosahedral faces. Each face of the icosahedron is subdivided into nine triangles. If you do the math, you will find that our three-quarter sphere, third-frequency structure has 135 triangular faces, 75 edges and 65 vertices.

Tables were available later on to aid designers in calculating the lengths of the struts. Not having such tables, I did the the complex spherical geometry calculations on a Marchant electro-mechanical calculator owned by the Oakland Park Department, in whose office we did our design work. Marchant calculators were much faster and more sophisticated than any others on the market at the time. (Wikipedia records that the firm was bought by Smith Corona in 1958 and the new firm, unsuccessful in switching to electronics, was gone by 1980).

The ingenious aspect of the design was suggested by our engineer from Kaiser, Don Richter. His idea was to join pairs of triangles to form 65 diamond-shaped panels (plus five infill triangles at the base). The two triangles forming each diamond bend around the dome like the covers of an opened book, and so are not in the same plane. When the screen is stretched across the diamond, it naturally forms a doubly curved surface (a  “hyperbolic paraboloid” or “hypar”). The screen panels are cut so that one set of screen wires runs from end to end of the diamond, curving outward, while the perpendicular strands run across the diamond, curving inward. As opposed to a flat screen, which has to deform before it can take pressure, our screens are already bent and can resist pressure immediately from either side. The diagram below shows how it works – naturally the screening is closer woven than is shown in the diagram.

Screen Panel

The doubly-curved screening also contributes  to the strength of the dome. Richter had constructed such a structure for Kaiser Aluminum out of a 1/16th inch thick corrugated aluminum panel, reinforced at the edges by beams. It was about 20 feet corner to corner. They tested the structure, which supported 18″ of sand before one of the beams buckled (it buckled upward, showing that the failure was due to compression and not bending). You can make a crude model by folding a piece of aluminum foil into corrugations, then flattening and doubling over the corrugations on opposite edges to create the edge beams. The foil pops into a hypar shape – a neat party trick.

There are two sizes of diamond-shaped panels. 20 symmetrical panels cut across the middle of each icosahedral edge, shown in light yellow in the diagram. The other 45 panels form the corners of each icosahedral face, shown in light red. These panels are asymmetrical. The diamond panels meet in the center of each icosahedral face, forming six-pointed vertices.

Across the center of each diamond, we designed a tubular strut to complete the triangular structural grid. If the strut were straight (like the spine of the folded book), it would lie outside the screening. Amadee Sourdry, our supervisor at the Oakland Park Department, vetoed this configuration because the exposed struts would form a perfect jungle gym, which would be an attractive nuisance and therefore a liability to the city. We were forced to put the struts on the inside of the screening, bending them inward to stay inside the curved screening. Each end of the tubular strut was flattened and bent, then bolted to the inside flanges of the C-shaped frame members that form the edges of each diamond.

The screen is clamped between the outside flange of the C-shaped frame member and a neoprene gasket held in place by (as I recall) a 3/8″ x 1″ aluminum plate, all secured by closely-spaced bolts. The outside flanges of the diamond panel frame members is bent inward so that the flanges of two adjoining frame members lie in the same plane, allowing them to be bolted snugly together. At the points of the diamonds, the bottom flanges are likewise bolted together. The complex construction of the screen panels and struts made it necessary to hand-craft all the members and hand-assemble each screen  panel. If you built hundreds of these, you could use specialized machinery to do the job. This being a one-off project, we instead relied on a wonderful Polish metalworker. The cross section through a typical screen frame member shows all these parts.

Detail

After the foundation was poured, assembly of the dome took one long day, after which we celebrated with a spaghetti dinner. Unfortunately, Bill had been drafted into the army and could not be there. The dome was assembled from the top down, suspended from a crane that raised it up as diamond panels were added and bolted to adjacent panels. The weight was supported only at the top (I don’t recall whether they used a single cable or five separate ones, as the pictures of the dome under construction have disappeared).

As a result of the limited number of supports while the dome was being assembled, bolts began to pop as sections were added near the equator , causing considerable alarm. Luckily, enough survived until the dome was set on its foundation, where it was held up at a sufficient number of points that it became (more) structurally sound. I speculate that any dome which is more than a hemisphere is structurally suspect because it wants to bulge at its equator.

The bulbous configuration of the dome was a result of it being designed as a flight cage, with a small footprint and a large volume. Only well into design and construction, did we learn from Sourdry that it would house waterfowl instead of perching birds. It would have made more sense to widen the base somewhat by eliminating the bottom layer of triangles.

Five triangular infill panels were required at the bottom to complete the enclosure, one of which made a natural entry. The blue triangle in the diagram shows the nearest such panel – the actual entry is on the opposite side. To keep the birds from escaping, an entry lock was needed with a door at each end. Because the panel leans toward the ground, if the panel was used as a door, it would have to open inward and upward.

[The following paragraph was revised in February 2017] Instead, we built an awkward-looking but serviceable tunnel between two rectangular doors, transitioning to fit into the triangular sector as it passes through the dome. My memory here is somewhat fuzzy, but you can check out the actual solution by visiting the dome (which I haven’t done since it was built).

All this is still vividly imprinted on my memory 60 years after its construction in 1956. It was a most rewarding experience, one of the highlights of my career.

PS: I can’t resist inserting a reference to an extraordinary item I found on the web at https://bfi.org/about-fuller/resources/everything-i-know/session-11 , a verbatim transcript of one of Bucky Fuller’s long lectures. He gave several of these lectures while I was at Berkeley, and held his audience from 2 PM to 11 PM, with a break for dinner. In it there is a reference to Don Richter, which I insert below. I also found a patent filed by Richter in 1955 and granted in 1959 for the corrugated hypar roof that he had tested. at https://www.google.com/patents/US2891491

One of my boys at the Institute of Design in Chicago was Don Richter. Don was an extraordinary man and he stayed with me during all the early years of the developing of the geodesic dome, after he graduated from the Institute of Design. He had been a sailor in the Merchant Marine during the war. Please hold the pictures for a minute. Don’t do anymore with them for a second. And Don wanted to really go on. Many architectural students asked me what they ought to do, and I would say, what I think you ought to do is to get production engineering. And the only way you can do that, to really get it first class, would be in the aircraft industry. Don did work for a while with Kaiser Aluminum and he then got a job in Texas with the Republic Aircraft. They were building an enormous bomber and he began he did so well in general engineering that he did get into production engineering, and he lived with the Head of the Production Engineering and developed extraordinary capability.

Don, then, Kaiser Aluminum Company were looking for somebody with design capability and I recommended Don and he went to them, and Don had made his small geodesic dome of aluminum and had it on his desk. He made it at home, and brought it in one day and put it on his desk, and Henry Kaiser, old Henry Kaiser walked by the desk and he thought this was a Kaiser product and he simply said, “I’d like to have one of those built for Hawaii,” and he had just been building a big hotel out there, and so everybody just takes Henry’s orders and so they had to make deals with Don, and there was a great deal of negotiating from there on`. The Kaiser patent attorneys came in to get license from my patent attorney.