Category: Science

Stephen Hawking Explains The Origin of the Universe

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The Origin of the Universe, a lecture, by Stephen Hawking

According to the Boshongo people of central Africa, in the beginning, there was only darkness, water, and the great god Bumba. One day Bumba, in pain from a stomach ache, vomited up the sun. The sun dried up some of the water, leaving land. Still in pain, Bumba vomited up the moon, the stars, and then some animals. The leopard, the crocodile, the turtle, and finally, man.

This creation myth, like many others, tries to answer the questions we all ask. Why are we here? Where did we come from? The answer generally given was that humans were of comparatively recent origin, because it must have been obvious, even at early times, that the human race was improving in knowledge and technology. So it can’t have been around that long, or it would have progressed even more. For example, according to Bishop Usher, the Book of Genesis placed the creation of the world at 9 in the morning on October the 27th, 4,004 BC. On the other hand, the physical surroundings, like mountains and rivers, change very little in a human lifetime. They were therefore thought to be a constant background, and either to have existed forever as an empty landscape, or to have been created at the same time as the humans. Not everyone, however, was happy with the idea that the universe had a beginning.

For example, Aristotle, the most famous of the Greek philosophers, believed the universe had existed forever. Something eternal is more perfect than something created. He suggested the reason we see progress was that floods, or other natural disasters, had repeatedly set civilization back to the beginning. The motivation for believing in an eternal universe was the desire to avoid invoking divine intervention to create the universe and set it going. Conversely, those who believed the universe had a beginning, used it as an argument for the existence of God as the first cause, or prime mover, of the universe.

If one believed that the universe had a beginning, the obvious question was what happened before the beginning? What was God doing before He made the world? Was He preparing Hell for people who asked such questions? The problem of whether or not the universe had a beginning was a great concern to the German philosopher, Immanuel Kant. He felt there were logical contradictions, or antimonies, either way. If the universe had a beginning, why did it wait an infinite time before it began? He called that the thesis. On the other hand, if the universe had existed for ever, why did it take an infinite time to reach the present stage? He called that the antithesis. Both the thesis and the antithesis depended on Kant’s assumption, along with almost everyone else, that time was Absolute. That is to say, it went from the infinite past to the infinite future, independently of any universe that might or might not exist in this background. This is still the picture in the mind of many scientists today.

However in 1915, Einstein introduced his revolutionary General Theory of Relativity. In this, space and time were no longer Absolute, no longer a fixed background to events. Instead, they were dynamical quantities that were shaped by the matter and energy in the universe. They were defined only within the universe, so it made no sense to talk of a time before the universe began. It would be like asking for a point south of the South Pole. It is not defined. If the universe was essentially unchanging in time, as was generally assumed before the 1920s, there would be no reason that time should not be defined arbitrarily far back. Any so-called beginning of the universe would be artificial, in the sense that one could extend the history back to earlier times. Thus it might be that the universe was created last year, but with all the memories and physical evidence, to look like it was much older. This raises deep philosophical questions about the meaning of existence. I shall deal with these by adopting what is called, the positivist approach. In this, the idea is that we interpret the input from our senses in terms of a model we make of the world. One can not ask whether the model represents reality, only whether it works. A model is a good model if first it interprets a wide range of observations, in terms of a simple and elegant model. And second, if the model makes definite predictions that can be tested and possibly falsified by observation.

In terms of the positivist approach, one can compare two models of the universe. One in which the universe was created last year and one in which the universe existed much longer. The Model in which the universe existed for longer than a year can explain things like identical twins that have a common cause more than a year ago. On the other hand, the model in which the universe was created last year cannot explain such events. So the first model is better. One can not ask whether the universe really existed before a year ago or just appeared to. In the positivist approach, they are the same. In an unchanging universe, there would be no natural starting point. The situation changed radically however, when Edwin Hubble began to make observations with the hundred inch telescope on Mount Wilson, in the 1920s.

Hubble found that stars are not uniformly distributed throughout space, but are gathered together in vast collections called galaxies. By measuring the light from galaxies, Hubble could determine their velocities. He was expecting that as many galaxies would be moving towards us as were moving away. This is what one would have in a universe that was unchanging with time. But to his surprise, Hubble found that nearly all the galaxies were moving away from us. Moreover, the further galaxies were from us, the faster they were moving away. The universe was not unchanging with time as everyone had thought previously. It was expanding. The distance between distant galaxies was increasing with time.

The expansion of the universe was one of the most important intellectual discoveries of the 20th century, or of any century. It transformed the debate about whether the universe had a beginning. If galaxies are moving apart now, they must have been closer together in the past. If their speed had been constant, they would all have been on top of one another about 15 billion years ago. Was this the beginning of the universe? Many scientists were still unhappy with the universe having a beginning because it seemed to imply that physics broke down. One would have to invoke an outside agency, which for convenience, one can call God, to determine how the universe began. They therefore advanced theories in which the universe was expanding at the present time, but didn’t have a beginning. One was the Steady State theory, proposed by Bondi, Gold, and Hoyle in 1948.

In the Steady State theory, as galaxies moved apart, the idea was that new galaxies would form from matter that was supposed to be continually being created throughout space. The universe would have existed for ever and would have looked the same at all times. This last property had the great virtue, from a positivist point of view, of being a definite prediction that could be tested by observation. The Cambridge radio astronomy group, under Martin Ryle, did a survey of weak radio sources in the early 1960s. These were distributed fairly uniformly across the sky, indicating that most of the sources lay outside our galaxy. The weaker sources would be further away, on average. The Steady State theory predicted the shape of the graph of the number of sources against source strength. But the observations showed more faint sources than predicted, indicating that the density sources were higher in the past. This was contrary to the basic assumption of the Steady State theory, that everything was constant in time. For this, and other reasons, the Steady State theory was abandoned.

Another attempt to avoid the universe having a beginning was the suggestion that there was a previous contracting phase, but because of rotation and local irregularities, the matter would not all fall to the same point. Instead, different parts of the matter would miss each other, and the universe would expand again with the density remaining finite. Two Russians, Lifshitz and Khalatnikov, actually claimed to have proved, that a general contraction without exact symmetry would always lead to a bounce with the density remaining finite. This result was very convenient for Marxist Leninist dialectical materialism, because it avoided awkward questions about the creation of the universe. It therefore became an article of faith for Soviet scientists.

When Lifshitz and Khalatnikov published their claim, I was a 21 year old research student looking for something to complete my PhD thesis. I didn’t believe their so-called proof, and set out with Roger Penrose to develop new mathematical techniques to study the question. We showed that the universe couldn’t bounce. If Einstein’s General Theory of Relativity is correct, there will be a singularity, a point of infinite density and spacetime curvature, where time has a beginning. Observational evidence to confirm the idea that the universe had a very dense beginning came in October 1965, a few months after my first singularity result, with the discovery of a faint background of microwaves throughout space. These microwaves are the same as those in your microwave oven, but very much less powerful. They would heat your pizza only to minus 271 point 3 degrees centigrade, not much good for defrosting the pizza, let alone cooking it. You can actually observe these microwaves yourself. Set your television to an empty channel. A few percent of the snow you see on the screen will be caused by this background of microwaves. The only reasonable interpretation of the background is that it is radiation left over from an early very hot and dense state. As the universe expanded, the radiation would have cooled until it is just the faint remnant we observe today.

Although the singularity theorems of Penrose and myself, predicted that the universe had a beginning, they didn’t say how it had begun. The equations of General Relativity would break down at the singularity. Thus Einstein’s theory cannot predict how the universe will begin, but only how it will evolve once it has begun. There are two attitudes one can take to the results of Penrose and myself. One is to that God chose how the universe began for reasons we could not understand. This was the view of Pope John Paul. At a conference on cosmology in the Vatican, the Pope told the delegates that it was OK to study the universe after it began, but they should not inquire into the beginning itself, because that was the moment of creation, and the work of God. I was glad he didn’t realize I had presented a paper at the conference suggesting how the universe began. I didn’t fancy the thought of being handed over to the Inquisition, like Galileo.

The other interpretation of our results, which is favored by most scientists, is that it indicates that the General Theory of Relativity breaks down in the very strong gravitational fields in the early universe. It has to be replaced by a more complete theory. One would expect this anyway, because General Relativity does not take account of the small scale structure of matter, which is governed by quantum theory. This does not matter normally, because the scale of the universe is enormous compared to the microscopic scales of quantum theory. But when the universe is the Planck size, a billion trillion trillionth of a centimeter, the two scales are the same, and quantum theory has to be taken into account.

In order to understand the Origin of the universe, we need to combine the General Theory of Relativity with quantum theory. The best way of doing so seems to be to use Feynman’s idea of a sum over histories. Richard Feynman was a colorful character, who played the bongo drums in a strip joint in Pasadena, and was a brilliant physicist at the California Institute of Technology. He proposed that a system got from a state A, to a state B, by every possible path or history. Each path or history has a certain amplitude or intensity, and the probability of the system going from A- to B, is given by adding up the amplitudes for each path. There will be a history in which the moon is made of blue cheese, but the amplitude is low, which is bad news for mice.

The probability for a state of the universe at the present time is given by adding up the amplitudes for all the histories that end with that state. But how did the histories start? This is the Origin question in another guise. Does it require a Creator to decree how the universe began? Or is the initial state of the universe, determined by a law of science? In fact, this question would arise even if the histories of the universe went back to the infinite past. But it is more immediate if the universe began only 15 billion years ago. The problem of what happens at the beginning of time is a bit like the question of what happened at the edge of the world, when people thought the world was flat. Is the world a flat plate with the sea pouring over the edge? I have tested this experimentally. I have been round the world, and I have not fallen off. As we all know, the problem of what happens at the edge of the world was solved when people realized that the world was not a flat plate, but a curved surface. Time however, seemed to be different. It appeared to be separate from space, and to be like a model railway track. If it had a beginning, there would have to be someone to set the trains going. Einstein’s General Theory of Relativity unified time and space as spacetime, but time was still different from space and was like a corridor, which either had a beginning and end, or went on forever. However, when one combines General Relativity with Quantum Theory, Jim Hartle and I realized that time can behave like another direction in space under extreme conditions. This means one can get rid of the problem of time having a beginning, in a similar way in which we got rid of the edge of the world. Suppose the beginning of the universe was like the South Pole of the earth, with degrees of latitude playing the role of time. The universe would start as a point at the South Pole. As one moves north, the circles of constant latitude, representing the size of the universe, would expand. To ask what happened before the beginning of the universe would become a meaningless question, because there is nothing south of the South Pole.

Time, as measured in degrees of latitude, would have a beginning at the South Pole, but the South Pole is much like any other point, at least so I have been told. I have been to Antarctica, but not to the South Pole. The same laws of Nature hold at the South Pole as in other places. This would remove the age-old objection to the universe having a beginning; that it would be a place where the normal laws broke down. The beginning of the universe would be governed by the laws of science. The picture Jim Hartle and I developed of the spontaneous quantum creation of the universe would be a bit like the formation of bubbles of steam in boiling water.

The idea is that the most probable histories of the universe would be like the surfaces of the bubbles. Many small bubbles would appear, and then disappear again. These would correspond to mini universes that would expand but would collapse again while still of microscopic size. They are possible alternative universes but they are not of much interest since they do not last long enough to develop galaxies and stars, let alone intelligent life. A few of the little bubbles, however, grow to a certain size at which they are safe from recollapse. They will continue to expand at an ever increasing rate, and will form the bubbles we see. They will correspond to universes that would start off expanding at an ever increasing rate. This is called inflation, like the way prices go up every year.

The world record for inflation was in Germany after the First World War. Prices rose by a factor of ten million in a period of 18 months. But that was nothing compared to inflation in the early universe. The universe expanded by a factor of million trillion trillion in a tiny fraction of a second. Unlike inflation in prices, inflation in the early universe was a very good thing. It produced a very large and uniform universe, just as we observe. However, it would not be completely uniform. In the sum over histories, histories that are very slightly irregular will have almost as high probabilities as the completely uniform and regular history. The theory therefore predicts that the early universe is likely to be slightly non-uniform. These irregularities would produce small variations in the intensity of the microwave background from different directions. The microwave background has been observed by the Map satellite, and was found to have exactly the kind of variations predicted. So we know we are on the right lines.

The irregularities in the early universe will mean that some regions will have slightly higher density than others. The gravitational attraction of the extra density will slow the expansion of the region, and can eventually cause the region to collapse to form galaxies and stars. So look well at the map of the microwave sky. It is the blue print for all the structure in the universe. We are the product of quantum fluctuations in the very early universe. God really does play dice.

Follow your curiosity to Nassim Taleb on the Notion of Alternative Histories.

Real vs. Simulated Memories

Blue Brain

Software memory is increasingly doing more and more for us. Yet it lacks one important element of human memory: emotion.

This thought-provoking excerpt comes from Mirror Worlds: or the Day Software Puts the Universe in a Shoebox…How It Will Happen and What It Will Mean, a book recommended by Marc Andreessen.

When an expert remembers a patient, he doesn’t remember a mere list of words. He remembers an experience, a whole galaxy of related perceptions. No doubt he remembers certain words—perhaps a name, a diagnosis, maybe some others. But he also remembers what the patient looked like, sounded like; how the encounter made him feel (confident, confused?) … Clearly these unrecorded perceptions have tremendous information content. People can revisit their experiences, examine their stored perceptions in retrospect. In reducing a “memory” to mere words, and a quick-march parade step of attribute, value, attribute, value at that, we are giving up a great deal. We are reducing a vast mountaintop panorama to a grainy little black-and-white photograph.

There is, too, a huge distance between simulated remembering—pulling cases out of the database—and the real thing. To a human being, an experience means a set of coherent sensations, which are wrapped up and sent back to the storeroom for later recollection. Remembering is the reverse: A set of coherent sensations is trundled out of storage and replayed—those archived sensations are re-experienced. The experience is less vivid on tape (so to speak) than it was in person, and portions of the original may be smudged or completely missing, but nonetheless—the Rememberer gets, in essence, another dose of the original experience. For human beings, in other words, remembering isn’t merely retrieving, it is re-experiencing.

And this fact is important because it obviously impinges (probably in a large way) on how people do their remembering. Why do you “choose” to recall something? Well for one thing, certain memories make you feel good. The original experience included a “feeling good” sensation, and so the tape has “feel good” recorded on it, and when you recall the memory—you feel good. And likewise, one reason you choose (or unconsciously decide) not to recall certain memories is that they have “feel bad” recorded on them, and so remembering them makes you feel bad. (If you don’t believe me check with Freud, who based the better part of a profoundly significant career on this observation, more or less.) It’s obvious that the emotions recorded in a memory have at least something to do with steering your solitary rambles through Memory Woods.

But obviously, the software version of remembering has no emotional compass. To some extent, that’s good: Software won’t suppress, repress or forget some illuminating case because (say) it made a complete fool of itself when the case was first presented. Objectivity is powerful.

On the other hand, we are brushing up here against a limitation that has a distinctly fundamental look. We want our Mirror Worlds to “remember” intelligently—to draw just the right precedent or two from a huge database. But human beings draw on reason and emotion when they perform all acts of remembering. An emotion can be a concise, nuanced shorthand for a whole tangle of facts and perceptions that you never bothered to sort out. How did you feel on your first day at work or school, your child’s second birthday, last year’s first snowfall? Later you might remember that scene; you might be reminded merely by the fact that you now feel the same as you did then. Why do you feel the same? If you think carefully, perhaps you can trace down the objective similarities between the two experiences. But their emotional resemblance was your original clue. And it’s quite plausible that “expertise” works this way also, at least occasionally: I’m reminded of a past case, not because of any objective similarity, but rather because I now feel the same as I did then.

What If? Serious Scientific Answers to Absurd Hypothetical Questions

xkcd-title

Randall Munroe, creator of xkcd, has written a book: What If?: Serious Scientific Answers to Absurd Hypothetical Questions

Here are a few questions, which I loved, that are sure to spark your curiosity and imagination.

What would happen if you tried to hit a baseball pitched at 90 percent the speed of light?

xkcd-baseball 1

The answer turns out to be “a lot of things ,” and they all happen very quickly, and it doesn’t end well for the batter (or the pitcher). I sat down with some physics books, a Nolan Ryan action figure, and a bunch of videotapes of nuclear tests and tried to sort it all out. What follows is my best guess at a nanosecond-by-nanosecond portrait.

The ball would be going so fast that everything else would be practically stationary. Even the molecules in the air would stand still. Air molecules would vibrate back and forth at a few hundred miles per hour, but the ball would be moving through them at 600 million miles per hour. This means that as far as the ball is concerned, they would just be hanging there, frozen.

The ideas of aerodynamics wouldn’t apply here. Normally, air would flow around anything moving through it. But the air molecules in front of this ball wouldn’t have time to be jostled out of the way. The ball would smack into them so hard that the atoms in the air molecules would actually fuse with the atoms in the ball’s surface. Each collision would release a burst of gamma rays and scattered particles.

xkcd-baseball 2

These gamma rays and debris would expand outward in a bubble centered on the pitcher’s mound. They would start to tear apart the molecules in the air, ripping the electrons from the nuclei and turning the air in the stadium into an expanding bubble of incandescent plasma. The wall of this bubble would approach the batter at about the speed of light— only slightly ahead of the ball itself.

The constant fusion at the front of the ball would push back on it, slowing it down, as if the ball were a rocket flying tail-first while firing its engines. Unfortunately, the ball would be going so fast that even the tremendous force from this ongoing thermonuclear explosion would barely slow it down at all. It would, however, start to eat away at the surface, blasting tiny fragments of the ball in all directions. These fragments would be going so fast that when they hit air molecules, they would trigger two or three more rounds of fusion.

After about 70 nanoseconds the ball would arrive at home plate. The batter wouldn’t even have seen the pitcher let go of the ball, since the light carrying that information would arrive at about the same time the ball would. Collisions with the air would have eaten the ball away almost completely, and it would now be a bullet-shaped cloud of expanding plasma (mainly carbon, oxygen, hydrogen, and nitrogen) ramming into the air and triggering more fusion as it went. The shell of x-rays would hit the batter first, and a handful of nanoseconds later the debris cloud would hit.

When it would reach home plate, the center of the cloud would still be moving at an appreciable fraction of the speed of light. It would hit the bat first, but then the batter, plate, and catcher would all be scooped up and carried backward through the backstop as they disintegrated. The shell of x-rays and superheated plasma would expand outward and upward, swallowing the backstop, both teams, the stands, and the surrounding neighborhood— all in the first microsecond.

Suppose you’re watching from a hilltop outside the city. The first thing you would see would be a blinding light, far outshining the sun. This would gradually fade over the course of a few seconds, and a growing fireball would rise into a mushroom cloud. Then, with a great roar, the blast wave would arrive, tearing up trees and shredding houses.

Everything within roughly a mile of the park would be leveled, and a firestorm would engulf the surrounding city. The baseball diamond, now a sizable crater, would be centered a few hundred feet behind the former location of the backstop.

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Major League Baseball Rule 6.08( b) suggests that in this situation, the batter would be considered “hit by pitch,” and would be eligible to advance to first base.

***

What would happen if everyone on Earth stood as close to each other as they could and jumped, everyone landing on the ground at the same instant?

This is one the most popular questions submitted through my website. It’s been examined before, including by ScienceBlogs and The Straight Dope. They cover the kinematics pretty well. However, they don’t tell the whole story.

Let’s take a closer look.

At the start of the scenario, the entire Earth’s population has been magically transported together into one place.

xkcd-prejump

This crowd takes up an area the size of Rhode Island. But there’s no reason to use the vague phrase “an area the size of Rhode Island.” This is our scenario; we can be specific. They’re actually in Rhode Island.

At the stroke of noon, everyone jumps.

xkcd-jumping

As discussed elsewhere, it doesn’t really affect the planet. Earth outweighs us by a factor of over ten trillion. On average, we humans can vertically jump maybe half a meter on a good day. Even if the Earth were rigid and responded instantly, it would be pushed down by less than an atom’s width.

Next, everyone falls back to the ground.

Technically, this delivers a lot of energy into the Earth, but it’s spread out over a large enough area that it doesn’t do much more than leave footprints in a lot of gardens. A slight pulse of pressure spreads through the North American continental crust and dissipates with little effect. The sound of all those feet hitting the ground creates a loud, drawn-out roar lasting many seconds.

Eventually, the air grows quiet.

Seconds pass. Everyone looks around. There are a lot of uncomfortable glances. Someone coughs.

A cell phone comes out of a pocket. Within seconds, the rest of the world’s five billion phones follow. All of them —even those compatible with the region’s towers— are displaying some version of “NO SIGNAL.” The cell networks have all collapsed under the unprecedented load. Outside Rhode Island, abandoned machinery begins grinding to a halt.

The T. F. Green Airport in Warwick, Rhode Island, handles a few thousand passengers a day. Assuming they got things organized (including sending out scouting missions to retrieve fuel), they could run at 500 percent capacity for years without making a dent in the crowd.

The addition of all the nearby airports doesn’t change the equation much. Nor does the region’s light rail system. Crowds climb on board container ships in the deep-water port of Providence, but stocking sufficient food and water for a long sea voyage proves a challenge.

Rhode Island’s half-million cars are commandeered. Moments later, I-95, I-195, and I-295 become the sites of the largest traffic jam in the history of the planet. Most of the cars are engulfed by the crowds, but a lucky few get out and begin wandering the abandoned road network.

Some make it past New York or Boston before running out of fuel. Since the electricity is probably not on at this point, rather than find a working gas pump, it’s easier to just abandon the car and steal a new one. Who can stop you? All the cops are in Rhode Island.

The edge of the crowd spreads outward into southern Massachusetts and Connecticut. Any two people who meet are unlikely to have a language in common, and almost nobody knows the area. The state becomes a chaotic patchwork of coalescing and collapsing social hierarchies. Violence is common. Everybody is hungry and thirsty. Grocery stores are emptied. Fresh water is hard to come by and there’s no efficient system for distributing it.

Within weeks, Rhode Island is a graveyard of billions.

The survivors spread out across the face of the world and struggle to build a new civilization atop the pristine ruins of the old. Our species staggers on, but our population has been greatly reduced. Earth’s orbit is completely unaffected— it spins along exactly as it did before our species-wide jump.

But at least now we know.

What If?: Serious Scientific Answers to Absurd Hypothetical Questions is sure to spark your imagination and reignite your creativity.

The Book of Trees: Visualizing Branches of Knowledge

“There certainly have been many new things
in the world of visualization; but unless
you know its history, everything might seem novel.”

— Michael Friendly

***

It’s tempting to consider information visualization a relatively new field that rose in response to the demands of the Internet generation. “But,” argues Manual Lima in The Book of Trees: Visualizing Branches of Knowledge, “as with any domain of knowledge, visualizing is built on a prolonged succession of efforts and events.”

This book is absolutely gorgeous. I stared at it for hours.

While it’s tempting to look at the recent work, it’s critical we understand the long history. Lima’s stunning book helps, covering the fascinating 800-year history of the seemingly simple tree diagram.

Trees are some of the oldest living things in the world. The sequoias in Northern California, for example, can reach a height of nearly 400 feet, with a trunk diameter of 26 feet and live to more than 3,500 years. “These grandiose, mesmerizing lifeforms are a remarkable example of longevity and stability and, ultimately, are the crowning embodiment of the powerful qualities humans have always associated with trees.”

Such an important part of natural life on earth, tree metaphors have become deeply embedded in the English language, as in the “root” of the problem or “branches” of knowledge. In the Renaissance, the philosophers Francis Bacon and Rene Descartes, for example, used tree diagrams to describe dense classification arrangements. As we shall see, trees really became popular as a method of communicating and changing minds with Charles Darwin.

The Kept

In the introduction Lima writes:

In a time when more than half of the world’s population live in cities, surrounded on a daily basis by asphalt, cement, iron, and glass, it’s hard to conceive of a time when trees were of immense and tangible significance to our existence. But for thousands and thousands of years, trees have provided us with not only shelter, protection, and food, but also seemingly limitless resources for medicine, fire, energy, weaponry, tool building, and construction. It’s only normal that human beings, observing their intricate branching schemas and the seasonal withering and revival of their foliage, would see trees as powerful images of growth, decay, and resurrection. In fact, trees have had such an immense significance to humans that there’s hardly any culture that hasn’t invested them with lofty symbolism and, in many cases, with celestial and religious power. The veneration of trees, known as dendrolatry, is tied to ideas of fertility, immortality, and rebirth and often is expressed by the axis mundi (world axis), world tree, or arbor vitae (tree of life). These motifs, common in mythology and folklore from around the globe, have held cultural and religious significance for social groups throughout history — and indeed still do.

[…]

The omnipresence of these symbols reveals an inherently human connection and fascination with trees that traverse time and space and go well beyond religious devotion. This fascination has seized philosophers, scientists, and artists, who were drawn equally by the tree’s inscrutabilities and its raw, forthright, and resilient beauty. Trees have a remarkably evocative and expressive quality that makes them conducive to all types of depiction. They are easily drawn by children and beginning painters, but they also have been the main subjects of renowned artists throughout the ages.

bookoftrees18-compressed

Our relationship with trees is symbiotic and this helps explain why it permeates our language and thought.

As our knowledge of trees has grown through this and many other scientific breakthroughs, we have realized that they have a much greater responsibility than merely providing direct subsistence for the sheltered ecosystems they support. Trees perform a critical role in moderating ground temperature and preventing soil erosion. Most important, they are known as the lungs of our planet, taking in carbon dioxide from the atmosphere and releasing oxygen. As a consequence, trees and humans are inexorably intertwined on our shared blue planet.

Our primordial, symbiotic relationship with the tree can elucidate why its branched schema has provided not only an important iconographic motif for art and religion, but also an important metaphor for knowledge-classification systems. Throughout human history the tree structure has been used to explain almost every facet of life: from consanguinity ties to cardinal virtues, systems of laws to domains of science, biological associations to database systems. It has been such a successful model for graphically displaying relationships because it pragmatically expresses the materialization of multiplicity (represented by its succession of boughs, branches, twigs, and leaves) out of unity (its central foundational trunk, which is in turn connected to a common root, source, or origin.)

While we can’t go back in time it certainly appears like Charles Darwin changed the trajectory of the tree diagram forever when he used it to change minds about one of our most fundamental beliefs.

Darwin’s contribution to biology—and humanity—is of incalculable value. His ideas on evolution and natural selection still bear great significance in genetics, molecular biology, and many other disparate fields. However, his legacy of information mapping has not been highlighted frequently. During the twenty years that led to the 1859 publication of On the Origin of Species by Means of Natural Selection, Darwin considered various notions of how the tree could represent evolutionary relationships among specifics that share a common ancestor. He produced a series of drawings expanding on arboreal themes; the most famous was a rough sketch drawn in the midst of a few jotted notes in 1837. Years later, his idea would eventually materialize in the crucial diagram that he called the “tree of life” (below) and featured in the Origin of Species.

Darwin was cognizant of the significance of the tree figure as a central element in representing his theory. He took eight pages of the chapter “Natural Selection,” where the diagram is featured, to expand in considerable detail on the workings of the tree and its value in understanding the concept of common descent.

1872_Origin_F391_figdiagram

A few months before the publication of his book, Darwin wrote his publisher, John Murray: “Enclosed is the Diagram which I wish engraved on Copper on folding out Plate to face latter part of volume. — It is an odd looking affair, but is indispensable to show the nature of the very complex affinities of past & present animals. …”

The illustration was clearly a “crucial manifestation of his thinking,” and of central importance to Darwin’s argument.

As it turned out it was the tree diagram, accompanied by Darwin’s detailed explanations, that truly persuaded a rather reluctant and skeptical audience to accept his groundbreaking ideas.

Coming back to the metaphor, before we go on to explain and show some of the different types of tree diagrams, Lima argues that given the long-lasting nature of the tree and its penetration into our lives as a way to organize, describe, and understand we can use the tree as a prism to better understand our world.

As one of the most ubiquitous and long-lasting visual metaphors, the tree is an extraordinary prism through which we can observe the evolution of human consciousness, ideology, culture, and society. From its entrenched roots in religious exegesis to its contemporary secular digital expressions, the multiplicity of mapped subjects cover almost every significant aspect of life throughout the centuries. But this dominant symbol is not just a remarkable example of human ingenuity in mapping information; it is also the result of a strong human desire for order, balance, hierarchy, structure, and unity. When we look at an early twenty-first-century sunburst diagram, it appears to be a species entirely distinct from a fifteenth-century figurative tree illustration. However, if we trace its lineage back through numerous tweaks, shifts, experiments, failures, and successes, we will soon realize there’s a defined line of descent constantly punctuated by examples of human skill and inventiveness.

Types of Tree Diagrams

Figurative Trees
Figurative Trees

Trees have been not only important religious symbols for numerous cultures through the ages, but also significant metaphors for describing and organizing human knowledge. As one of the most ubiquitous visual classification systems, the tree diagram has through time embraced the most realistic and organic traits of its real, biological counterpart, using trunks, branches, and offshoots to represent connections among different entities, normally represented by leaves, fruits, or small shrubberies.

Even though tree diagrams have lost some of their lifelike features over the years, becoming ever more stylized and nonfigurative, many of their associated labels, such as roots, branches, and leaves, are still widely used. From family ties to systems of law, biological species to online discussions, their range of subjects is as expansive as their time span.

 

Tree-Eagle Joachim of Fiore

tree of consanguinity-compressed

the common law-compressed

Vertical Trees

vertical trees

The transition from realistic trees to more stylized, abstract constructs was a natural progression in the development of hierarchical representations, and a vertical scheme splitting from top or bottom was an obvious structural choice. … Of all visualization models, vertical trees are the ones that retain the strongest resemblance to figurative trees, due to their vertical layout and forking arrangement from a central trunk. In most cases they are inverted trees, with the root at the top, emphasizing the notion of descent and representing a more natural writing pattern from top to bottom. Although today they are largely constrained to small digital screens and displays, vertical trees in the past were often designed in larger formats such as long parchment scrolls and folding charts that could provide a great level of detail.

La Chronique Universelle-compressed

Horizontal Trees
horizonatal tree

With the adoption of a more schematic and abstract construct, deprived of realistic arboreal features, a tree diagram could sometimes be rotated along its axis and depicted horizontally, with its ranks arranged most frequently from left to right.

Horizontal trees probably emerged as an alternative to vertical trees to address spatial constraints and layout requirements, but they also provide unique advantages. The nesting arrangement of horizontal trees resembles the grammatical construct of a sentence, echoing a natural reading pattern that anyone can relate to. This alternative scheme was often deployed on facing pages of a manuscript, with the root of the tree at the very center, creating a type of mirroring effect that is still found in many digital and interactive executions. Horizontal trees have proved highly efficient for archetypal models such as classification trees, flow charts, mind maps, dendrograms, and, notably, in the display of files on several software applications and operating systems.

Jurisprudence-compressed

Web trigrams-compressed

The Book of Trees: Visualizing Branches of Knowledge goes on to explore multi-directional, radial, hyperbolic, rectangular, Voronoi, and circular tree maps as well as sunbursts and icicle trees.

The Uses Of Being Wrong

Confessions of wrongness are the exception not the rule.

Daniel Drezner, a professor of international politics at the Fletcher School of Law and Diplomacy at Tufts University, pointing to the difference between being wrong in a prediction and making an error, writes:

Error, even if committed unknowingly, suggests sloppiness. That carries a more serious stigma than making a prediction that fails to come true.

Social sciences, unlike physical and natural sciences, finds a shortage of high-quality data on which to make predictions.

How does Science Advance?

A theory may be scientific even if there is not a shred of evidence in its favour, and it may be pseudoscientific even if all the available evidence is in its favour. That is, the scientific or non-scientific character of a theory can be determined independently of the facts. A theory is ‘scientific’ if one is prepared to specify in advance a crucial experiment (or observation) which can falsify it, and it is pseudoscientific if one refuses to specify such a ‘potential falsifier’. But if so, we do not demarcate scientific theories from pseudoscientific ones, but rather scientific methods from non-scientific method.

Karl Popper viewed the progression of science as falsification — that is science progresses by elimination of what doesn’t work and hold. Popper’s falsifiability criterion ignores the tenacity of scientific theories, even in the face of disconfirming evidence. Scientists, like many of us, do not abandon a theory because the evidence may contradict it.

The wake of science is littered with discussions on anomalies and not refutations.

Another theory on scientific advancement, proposed by Thomas Kuhn, a distinguished American philosopher of science, argues that science proceeds with a series of revolutions with an almost religious conversion.

Imre Lakatos, a Hungarian philosopher of mathematics and science, wrote:

(The) history of science, of course, is full of accounts of how crucial experiments allegedly killed theories. But all such accounts are fabricated long after the theory has been abandoned.

Lakatos bridged the gap between Popper and Khun by addressing what they failed to solve.

The hallmark of empirical progress is not trivial verifications: Popper is right that there are millions of them. It is no success for Newtonian theory that stones, when dropped, fall towards the earth, no matter how often this is repeated. But, so-called ‘refutations’ are not the hallmark of empirical failure, as Popper has preached, since all programmes grow in a permanent ocean of anomalies. What really counts are dramatic, unexpected, stunning predictions: a few of them are enough to tilt the balance; where theory lags behind the facts, we are dealing with miserable degenerating research programmes.

Now, how do scientific revolutions come about? If we have two rival research programmes, and one is progressing while the other is degenerating, scientists tend to join the progressive programme. This is the rationale of scientific revolutions. But while it is a matter of intellectual honesty to keep the record public, it is not dishonest to stick to a degenerating programme and try to turn it into a progressive one.

As opposed to Popper the methodology of scientific research programmes does not offer instant rationality. One must treat budding programmes leniently: programmes may take decades before they get off the ground and become empirically progressive. Criticism is not a Popperian quick kill, by refutation. Important criticism is always constructive: there is no refutation without a better theory. Kuhn is wrong in thinking that scientific revolutions are sudden, irrational changes in vision. [The history of science refutes both Popper and Kuhn: ] On close inspection both Popperian crucial experiments and Kuhnian revolutions turn out to be myths: what normally happens is that progressive research programmes replace degenerating ones.

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A lot of the falsification effort is devoted to proving others wrong and not ourselves. “It’s rare for academics, Drezner writes, to publicly disavow their own theories and hypotheses.”

Indeed, a common lament in the social sciences is that negative findings—i.e., empirical tests that fail to support an author’s initial hypothesis—are never published.

Why is it so hard for us to see when we are wrong?

It is not necessarily concern for one’s reputation. Even predictions that turn out to be wrong can be intellectually profitable—all social scientists love a good straw-man argument to pummel in a literature review. Bold theories get cited a lot, regardless of whether they are right.

Part of the reason is simple psychology; we all like being right much more than being wrong.

As Kathryn Schulz observes in Being Wrong, “the thrill of being right is undeniable, universal, and (perhaps most oddly) almost entirely undiscriminating … . It’s more important to bet on the right foreign policy than the right racehorse, but we are perfectly capable of gloating over either one.”

As we create arguments and gather supporting evidence (while discarding evidence that does not fit) we increasingly persuade ourselves that we are right. We gain confidence and try to sway the opinions of others.

There are benefits to being wrong.

Schulz argues in Being Wrong that “the capacity to err is crucial to human cognition. Far from being a moral flaw, it is inextricable from some of our most humane and honorable qualities: empathy, optimism, imagination, conviction, and courage. And far from being a mark of indifference or intolerance, wrongness is a vital part of how we learn and change.”

Drezner argues that some of the tools of the information age give us hope that we might become increasingly likely to admit being wrong.

Blogging and tweeting encourages the airing of contingent and tentative arguments as events play out in real time. As a result, far less stigma attaches to admitting that one got it wrong in a blog post than in peer-reviewed research. Indeed, there appears to be almost no professional penalty for being wrong in the realm of political punditry. Regardless of how often pundits make mistakes in their predictions, they are invited back again to pontificate more.

As someone who has blogged for more than a decade, I’ve been wrong an awful lot, and I’ve grown somewhat more comfortable with the feeling. I don’t want to make mistakes, of course. But if I tweet or blog my half-formed supposition, and it then turns out to be wrong, I get more intrigued about why I was wrong. That kind of empirical and theoretical investigation seems more interesting than doubling down on my initial opinion. Younger scholars, weaned on the Internet, more comfortable with the push and pull of debate on social media, may well feel similarly.

Still curious? Daniel W. Drezner is the author of The System Worked: How the World Stopped Another Great Depression.

The Simple Problem Einstein Couldn’t Solve … At First

Albert Einstein and Max Wertheimer were close friends. Both found themselves in exile in the United States after fleeing the Nazis in the early 1930s, Einstein at Princeton and Wertheimer in New York.

They communicated by exchanging letters in which Wertheimer would entertain Einstein with thought problems.

In 1934 Wertheimer sent the following problem in a letter.

An old clattery auto is to drive a stretch of 2 miles, up and down a hill, /\. Because it is so old, it cannot drive the first mile— the ascent —faster than with an average speed of 15 miles per hour. Question: How fast does it have to drive the second mile— on going down, it can, of course, go faster—in order to obtain an average speed (for the whole distance) of 30 miles an hour?

Einstein fell for this teaser
Einstein fell for this teaser

Wertheimer’s thought problem suggests the answer might be 45 or even 60 miles an hour. But that is not the case. Even if the car broke the sound barrier on the way down, it would not achieve an average speed of 30 miles an hour. Don’t be worried if you were fooled, Einstein was at first too. Replying “Not until calculating did I notice that there is no time left for the way down!”

Gerd Gigerenzer explains the answer in his book Risk Savvy: How to Make Good Decisions:

Gestalt psychologists’ way to solve problems is to reformulate the question until the answer becomes clear. Here’s how it works. How long does it take the old car to reach the top of the hill? The road up is one mile long. The car travels fifteen miles per hour, so it takes four minutes (one hour divided by fifteen) to reach the top. How long does it take the car to drive up and down the hill, with an average speed of thirty miles per hour? The road up and down is two miles long. Thirty miles per hour translates into two miles per four minutes. Thus, the car needs four minutes to drive the entire distance. But these four minutes were already used up by the time the car reached the top.