The Man Who Counted Infinity

“There is a concept which shatters all others and leaves them in disarray. I am not talking about evil which is only limited to ethics, but about infinity.” Even though one might expect these words to have been written down by a mathematician or a scientist, this is not so. Their author is an Argentine writer, Jorge Luis Borges, who succeeded in revealing the very essence of the problem that has intrigued many thinkers before him. Infinity is a concept that has appeared time after time in all kinds of different philosophical, mathematical and physical discussions, but has always been clouded by difficulties and contradictions. People simply can not grasp infinity directly as we are used to do with other concepts, but we have to imagine infinity in an indirect way. Usually, we describe infinity as an endless or limitless sequence, but we quickly come upon problems, as we are entering a dimension where our intuitions can not be completely trusted.

There is no single infinity

Throughout the history, a great number of scholars have thought about the concept of infinity and they have come to many interesting and important conclusions, but the greatest development in the process of understanding this difficult concept had only occurred in the second half of the 19^th century when a mathematician called Georg Cantor (1845-1918) approached the subject of infinity from a completely new angle.

With a couple of simple definitions Cantor succeeded in setting the boundaries of this complicated area of thought, so that he could examine the concept of infinity thoroughly and systematically. To the great amazement of the scientific and philosophical community he soon found out that there is no single infinity, but, in fact, an infinite number of different infinities. He came to this conclusion after careful and accurate consideration and was also able to formally prove all the phases that lead to his findings, so that his ideas have become incorporated into the very core of modern mathematics.

One of the first challenges he had to overcome was defining what infinity actually was. Of course, the simplest way to define infinity was to describe it as having no limits: infinity is what is larger than anything finite. This is were Cantor made an important step forward as he defined something to be infinite, if some of its parts are as big as the whole. This might sound contradictory as we are all intuitively used to finite dimensions whose parts are always smaller than the whole, but as we have already mentioned, when it comes to questions of infinity, intuition does not offer the best answers.

How to compare infinities?

Cantor did not only invent new ways to deal with infinity, he also came up with the well known set theory that children have now been learning in elementary school for decades. When thinking about his new theory, he soon had to face the question of how to compare the size of two sets. He proceeded from the completely intuitive supposition that two sets were of the same size if each element from the first set could be matched-up with exactly one element from the second set. Two groups of children are of the same size if a child from one group can hold hands and pair up with a child from the other group.

Cantor generalized the method of comparison by “holding hands” to infinite sets. Two infinite sets are of equal size if we can match-up each element from one set with an element from the other set. According to this definition, the set of even numbers is just as big as the set of all natural numbers as we can pair up each natural number with an even number simply by multiplying it by two. One holds hands with two, two holds hands with four, three holds hands with six and so on all the way to infinity. As we have matched-up each element from the first set with an element from the second set, both of the sets, in accordance with our definition, are of the same size, even though we could also say that the entire list of natural numbers is twice as large as the list of all even numbers, because natural numbers are made up of both even and odd numbers.

It was with the help of this strange notion that two sets were of the same size even though one is twice as large as the other that Cantor defined the infinite set. An infinite set contains a subset of the same size, when size is defined according to the principle of holding hands. Natural, even and odd numbers thus represent infinite sets.

How to count points on a line?

The question that immediately arises is whether all infinite sets are of the same size. For example, is a set of all points on a line as big as the set of natural numbers? In other words: is it possible to count all the dots on a line? One of Cantor’s important achievements is the proof that it is impossible to count all the dots on a line. Let us have a look at his proof, also called the diagonal argument.

Suppose we are counting points on a line which is one unit long. Each point is matched-up with a number between zero and one. As points fill out all the line because there can be no space between them, otherwise we would not have a line, but a sequence of dots, all of the points on a line can only be matched up with numbers if we use numbers with an infinite decimal representation, called real numbers. Every point on a line which is one unite long can be matched up with a real number between zero and one.

Now imagine we wrote down all of the real numbers one under the other in an endlessly long list on which every line contains one real number and the lines are marked with natural numbers. Cantor proved that we can always find at least one real number missing from every such list of numbers. How come? We simply take away the first decimal from the first real number on the list and change it, then take the second decimal from the second number and change it … If we continued to do so until we came to the end of the list, we would create a new real number different from any number already written on the list.

Coming back to our analogy with the two groups of children that we have compared in size by matching the children up in pairs, we have now proven that pairing up natural numbers with points on a line or real numbers never works. We can always find one real number or point on the line left that has no pair.

Infinities come in infinite numbers

The diagonal argument can also be used to prove that the set of all subsets of a given set is always larger than the set itself. It is the easiest to do so with natural numbers. We write down the subsets of natural numbers as lists of on and off numbers in the set of natural numbers. Odd numbers, for example, are written as {1,0,1,0,1,0 …}, and prime numbers as {1,1,1,0,1,0,1 …}. Now, we arrange these sets into a long list and apply the same argument as before to show that we can always construct another subset of natural numbers that has not been on the list before, simply by taking one element from each subset and changing its value. The set of all subsets of an infinite set is larger than the set itself. Infinite sets come in infinite numbers.

However, a problem already occurs with the smallest infinite sets. We know that natural numbers are the smallest infinite set. It still remains unclear though which is the next bigger infinite set. Is it the set of real numbers or points on a line? Or is there another infinity in between, bigger than natural numbers and smaller than real numbers? Cantor presumed that such a set does not exist, but he was unable to prove it. Many years later, mathematicians solved this question not by finding the answer, but by showing that the question had no answer at all.

Many books about Cantor’s efforts to solve problems concerning infinity also mention his illness which caused him to spend the last years of his life in a mental hospital. Today, he would have been diagnosed with bipolar disorder or manic depression, but at the time most of the patients suffering from this illness were simply labeled insane. Many writers have implied it was actually his work on infinity that drove Cantor over the edge of sanity. This might sound interesting, but his illness and his research are most probably not in a direct causal relationship.

Erythropoietin – the story about 2550 liters of powdered urine

Nobody has probably ever heard of Eugene Goldwasser, a retired professor from the University of Chicago. This is not strange as he is neither a Nobel laureate nor an eminent figure in his field of science. However, his name definitely sounds more familiar if we mention that he dedicated several decades of his scientific career to finding the molecule of erythropoietin, commonly known as EPO.

Erythropoietin is a hormone that promotes the formation of red blood cells within an organism or, in simpler terms, provides cells with a better supply of oxygen. This, in turn, improves the endurance of athletes, making the hormone a popular prohibited stimulant which has recently also caused problems for the cycling champion Lance Armstrong.

In search of a cure against the effects of radioactivity

The story about Eugene Goldwasser, recently popularized by Merrill Goozner in his resounding book The $800 Million Pill – The Truth Behind the Costs of New Drugs (University of California Press, 2004), is interesting from several points of view.

On the one hand, it tells the story of a typical scientist who was so much drawn to his research that he persisted in continuing his work despite decades of failed attempts and dead ends until all the long years of hard labor finally led him to an important scientific discovery. In the late 1970s, after decades of experimenting with sheep blood and after collecting and dehydrating 2550 liters of urine, he succeeded in producing 8 milligrams of pure natural human erythropoietin.

On the other hand, it also tells the story about one of the first great commercial breakthroughs resulting from the biotechnological revolution in the field of drug production. Today, pharmaceutical companies produce synthetic EPO in large quantities and sell it for similarly large amounts of money. The biotechnology company Amgen, one of the main producers of EPO, creates more than a half of its multibillion dollar yearly profit on this hormone alone.

Unfortunately, Goldwasser does not receive his share of this enormous heap of money, founded on the production of “his” molecule, even though with more than twenty years of enduring work he made the largest contribution to isolating this molecule from the mass of others, found in the human body. As he failed to patent his discovery at the time (he wrote to state financiers, asking them to take care of his patents, but received no response), he has to be content with the thirty thousand dollars graciously deposited to the account of his laboratory at the University of Chicago by Amgen each year.

The story about the discovery of erythropoietin, not unlike many other stories of science in the 20^th century, begins during the Cold War, an era extremely generous to scientific research. Soon after the Second World War, young Goldwasser was invited to join a research group commissioned by the state to discover ways of defending against the consequences of a nuclear war. The government was interested in finding an antidote to the deadly effects of nuclear radiation on the human body. It was in the beginning of the 20^th century when scientists had already come to understand that blood has to contain a substance which instructs the bone marrow to produce red blood cells that carry oxygen around the body. Scientists named this molecule erythropoietin after the term for the process of red blood cell formation called “erythropoiesis”, even though they knew nothing about the molecule itself at the time.

Looking for a needle in the haystack

In 1955 Goldwasser was entrusted with a research mission to find the erythropoietin molecule and discover a way to produce it in large quantities, so it could be used to cure radiation sickness. The search took longer than they expected, it extended over more than two decades. However, if one takes a closer look at how demanding the job Goldwasser and his colleagues had taken on, the time spent to complete the task does not seem to be quite as long anymore. A healthy person produces two to three million red blood cells each second which adds up to nearly half a ton of blood in a lifetime, yet in the same period barely enough erythropoietin to make a tiny pill goes through the human body. The search for a molecule they knew almost nothing about was therefore far from simple and could be compared to, for instance, looking for a lost coin on a long sandy beach.

During the first years of his research, Goldwasser wanted to find out which part of the body actually created EPO. His assistants carefully removed organs from lab rats until they were certain that it was the kidneys that were responsible for the bad blood. In the next phase they injected sheep, waiting to be slaughtered, with a chemical that destroyed all the red blood cells in the test animals. They were convinced that the destruction of the red blood cells would result in a mass production of EPO which could in turn be detected in the blood serum of these “sacrificial lambs”. They then injected the serum into the anemic sheep and looked for an increase in the number of blood cells in their blood streams. Unfortunately, there were no visible results, even though the experiments had already been going on for more than a decade. It was obvious that they had reached a dead end. When they were already on the edge of despair another research group fortunately published its discovery, revealing that the excess EPO was not to be found in blood, but in urine. After fifteen years of hard work it must have been quite depressing to find out that you have been looking in the wrong place all along. Nonetheless, they at least had a new goal.

A stroke of good fortune from the Far East

The lucky side of this misfortune was that a Japanese researcher Takaji Mijake offered Goldwasser his help in collecting urine samples from anemic patients in his neighborhood who supposedly produced excess EPO naturally due to their illness. In just a few years, he collected and dehydrated 2550 litres of urine. In 1975, when the two scientists first met in the lobby of a Chicago hotel, Mijake bowed solemnly to Goldwasser and handed him a large package wrapped in Japanese silk. Inside the neatly wrapped container was a priceless treasure, at least for the two scientists: a great amount of dehydrated, powdered urine. After a complex process of purification, Goldwasser and his colleagues managed to isolate 8 milligrams of pure human EPO from the collected urine. In August 1977 they revealed their discovery in scientific literature. Goldwasser and his team were overwhelmed with joy.

The goose that laid golden eggs

The story does not end here, though. In order to use EPO as a medicine it was necessary to find a way to produce it in large amounts outside the human body. Goldwasser was confident in the potential of his discovery, but at first no one took him seriously. He went from company to company, from one investor to the other, but did not succeed in getting anyone’s attention. Fortunately, his search coincided with the beginning of the biotechnological revolution. It was at that time when they started to produce synthetic insulin with the help of bacteria cultures to cure diabetes patients. The more far-sighted entrepreneurs gradually came to understand that investing in biotechnology would earn them good money. Some of them are already enjoying their profits today.

After many difficulties, that over the years began to spread increasingly from the fields of science to the courts of law, EPO became one of the first biotechnological geese that steadily laid golden eggs. Unfortunately, all these heaps of money do not always lead to heaps of new scientific discoveries, but mostly to thinking up new ways to increase the already substantial amounts of cash. Amgen, after EPO’s enormous commercial breakthrough in the 90s, was once said to have been quickly transformed from a powerful research group into an outstanding law firm that just happens to hide, somewhere deep in its cellars, a department for medical research.

The Hermit of the Pyrenees

In August of 1991, Alexander Grothendieck, who is thought by many to be one of the most important mathematicians of the 20^th century and whose influence is often compared to that of the likes of Albert Einstein, suddenly left his home in the south of France and headed for the Pyrenees. Since then, he has been living as a hermit high in the mountains somewhere between France and Spain, completely cut off from civilization. In the mid-nineties, a few mathematicians still managed to reach his wilderness dwelling, but for the last couple of years he has remained unseen. His mail is still piling up at the University of Montpellier, but he explicitly prohibited even the handful of his friends who, at the beginning, knew where in the mountains he lived, to bring it to him. Today, even his closest relatives are not completely certain if he is still alive.

Even before his departure into the deep wilderness, Grothendieck lived a very secluded, ascetic life in an old house with no electricity in a village near Montpellier in France. After a successful mathematical career in the fifties and sixties, when he was also one of the principal members of the infamous Bourbaki group (see article The Genius Who Wasn’t), he became increasingly interested in ecological and anti-war political movements in the seventies. He became so involved with the struggle for social justice that he traveled to Vietnam in protest, participated in numerous demonstrations and even went so far with his ideals as to refuse a national research scholarship in order to avoid tactically supporting the national politics which he strongly opposed.

To be able to at least come near understanding Grothendieck’s utter and complete devotion to first mathematics and then politics and ecology, one must look back to his childhood. His father Sasha was a convinced anarchist and had already taken part in several rebellions in the imperial Russia at the beginning of the 20^th century. In 1921, he moved from Russia to Berlin where he moved in radical circles and met Hanka who came from a wealthy bourgeois family, but associated with members of avant-garde movements. They had little Alexander on the 28^th of March 1928. At the time, the young family also supported Hanka’s daughter Maidi from her first marriage.

In 1933, when Nazis came to power, Alexander’s father Sasha fled Berlin for Paris and was soon followed by Alexander’s mother, but she did not take her son and daughter with her. She placed Alexander into foster care with a family that lived near Hamburg, and left her daughter in an institution for handicapped children, even though she was a perfectly healthy child. Alexander lived with his foster family from his fifth to his eleventh year. He rarely received letters from his mother and never even heard from his father nor from his other relatives who lived in the nearby Hamburg. Naturally, this period of separation from his parents left a deep mark on young Alexander.

In 1939, the political pressure became too great and the foster family could no longer take care of all the children. The trouble with Alexander was that he looked distinctly Jewish which could be dangerous for him as well as for the rest of the family. So they found Hanka with the help of the French consulate, sat little Alexander on a train and sent him from Hamburg to Paris. Both of his parents spent some of the years away from their son in Spain where they fought against Franco. On his return to France his father was arrested as a “dangerous foreigner” by the French authorities of the time and sent to an internment camp. He died a few years later in Auschwitz.

Hanka in Alexander spent the war in different internment camps, but as soon as the war was over Alexander enrolled at a University and started studying mathematics. He was not impressed with his teachers, so he mostly studied on his own. Before his twentieth birthday, and much like young Einstein, he independently came upon several important mathematical findings for which he did not know that they had already been published before by other mathematicians.

When he moved to Paris he started to spend time with the most prominent French mathematicians of the time and joined the Bourbaki circle of which he quickly became a driving force. He was becoming more and more famous for his highly abstract approach to solving mathematical problems. His friends later claimed that he was unable to think about concrete things, because his mind only functioned on a universal level.

After a long and productive collaboration with the Bourbaki, he left the group in protest, because most of the members refused to accept his suggestion to use the more general category theory, which he had also helped create, as the foundation for the formalization of mathematics instead of the set theory. The set theory was limited by several paradoxes and so it became too narrowly oriented to be appropriate for describing the entire diversity of modern mathematics. The mathematician Pierre Cartier, one of the more important members of the Bourbaki group summed up the essence of the problem: “The set theory is to constraining; an element can either be a member of a set or not, there is no intermediate possibility.”

The decision of the Bourbaki to refuse Grothendieck’s suggestion to move away from the set theory to the category theory was, as it soon turned out, a big mistake. It was the category theory that became a very important area in mathematics in the years to follow, and Grothendieck received many awards for his achievements, among others the Fields Medal, also known as the “Nobel Prize of Mathematics”.

When a new, unknown disease breaks out

On February 28^th, 2003, the local office of the World Health Organization in Hanoi, Vietnam, received a call from a small private hospital with a capacity of no more than 60 beds. Two days before, its staff admitted a patient showing symptoms of atypical flu. To rule out a potential case of “bird flu” they requested the help of WHO’s experts to try and determine what the disease was.

Their call was answered by Dr Carlo Urbani, an Italian-born contagious disease specialist and Doctors Without Borders veteran who was, as the president of the Italian section of this important medical society, in the very delegation which received the Nobel Peace Prize in 1999.

“We do not know what kind of disease it is, but it is not flu.”

When Urbani, as the official representative of WHO, examined the patient named Johnny Chen, an American-Chinese businessman, it quickly became clear that the situation was very serious. He suspected the unfortunate businessman to have contracted a completely unknown disease that doctors have never heard of before and were therefore unable to tell how dangerous and contagious it was. Dr Urbani and the hospital’s medical staff spent the following days collecting different samples and other pieces of information they could gather from the patient, and organized them before sending them to those responsible at the WHO in order to determine the cause of the illness as quickly as possible.

Urbani also made sure that a special secured, quarantined department was set up within the hospital which soon turned out to be an important decision as one of the first conclusions made by the doctors was that they were dealing with an extremely contagious disease. It was later found out that of the first 60 patients half were members of the medical staff. When the first doctors started showing symptoms of the disease they had to face the difficult decision to isolate themselves as well or risk infecting their nearest and spreading the disease across the city. So they stayed in the hospital for the entire duration of the research. In one of his reports to a colleague, Urbani said: “I am in a hospital full of crying nurses. People are running around, yelling, and are completely frightened. We do not know what kind of disease it is, but it is not flu.”

None of the precautions taken by the hospital’s medical staff turned out to be excessive. It soon became obvious that this was a case of a new viral disease which was not only highly contagious, but also very dangerous. They were unaware of this during the first weeks, but statistics later showed that one patient out of ten died. On the 9^th of March WHO had already gathered enough information to meet with the highest representatives of Vietnamese authorities and warn them about the gravity of the situation. The hospital had also started receiving professional help from the international community. These experts brought with them all the equipment otherwise used for research of the most deadly and contagious diseases like the Ebola virus. The private hospital was shut down and its patients were transferred to a special department of the Bach Mai public hospital where local doctors teamed up with members of Doctors Without Borders who were already used to dealing with similar situations.

When all the key precautions for fighting epidemics were taken care of, the death rate stabilized and the eruption of the disease in Vietnam became a good example of how to act when such a disease is suspected to have occurred. If Dr Urbani had not been as convincing in warning the authorities to react as quickly and transparently as they did, we could have witnessed a catastrophe of epic proportions.

On September 11^th, soon after the situation in Hanoi was at least partially under control, Dr Urbani flew to Bangkok to take part in a science conference. While still on the plane, he felt ill and already started showing typical symptoms of the newly discovered disease. A colleague was waiting for him at the airport, but he did not let him come near as it was obvious that the virus had attacked him as well. For over an hour, Urbani and his colleague sat quietly each on his side of the waiting room, waiting for the ambulance to bring all the equipment necessary for doctors to protect themselves from dangerous infections.

Dr Urbani was taken straight from the airport to a local hospital quarantine where he spent the next 18 days fighting for his life. He could only talk to his wife and three children over the phone as the infection was so dangerous that no one without adequate protection was allowed to come in direct contact with him. Despite his extensive knowledge of infectious diseases and the help of his doctor colleagues who flew in from Germany and Australia and brought with them several new antiviral drugs, he finally lost his battle with this new and deadly disease. On the 28^th of March 2003, a month after his expert advice was requested by the hospital in Hanoi, his lungs were flooded. He left his diseased lung tissue to science.

The great Hong Kong virus carrier

However, Johnny Chen who brought the disease to Vietnam was not the first to have been affected by the virus. WHO started receiving information about this new, highly infectious form of flu that quickly became known as SARS from other parts of the world as well. In no more than a few weeks the disease had spread to three continents and it seemed that humankind was threatened by a pandemic of unforeseeable proportions. That is why on March 15^th the WHO Director-General issued an alarming warning in which he urged that strictest precautions be taken in order to stop the pandemic.

Researchers later found out that the first case of SARS had probably already occurred in November 2002 in a Chinese boy from Foshan. On the 16^th of November 2002 he was admitted into the local public hospital for atypical respiratory disease. How he had contracted the disease remains unknown, but we do know that he recovered after infecting several others who quickly spread the disease first across China and Hong Kong, then across the globe.

In China, the first “great disease carrier”, as epidemiologists call individuals who, due to their lifestyle or workplace, are likely to infect a large number of people, was a fish merchant called Zhau Zuofeng who caught the virus in January 2003 in Guangzhou. He did not only transmit the disease to the staff of three hospitals (at the end of the epidemic it was found out that 20% of all the infected were medical staff), but also to a nephrology professor who had just left for Hong Kong where he stayed in the ninth floor of the Metropole Hotel, room 911. After only ten days, the elderly man succumbed to the disease after infecting several other guests of the hotel who also stayed on the ninth floor. In turn, they carried the disease to Toronto, Singapore and Vietnam. And it was during his business trip from Shanghai to Hanoi that Johnny Chen, the man who carried the disease to Vietnam, made a stop in Hong Kong and spent the night on the ninth floor of the Metropole Hotel.

On March 15^th when WHO issued a warning urging all travelers to be extremely cautious, no one knew much about the disease, except that it was a highly contagious form of atypical pneumonia. At first, experts suspected it was a modified flu virus, which was also implied by the symptoms of the disease, but the tests that followed did not confirm this hypothesis. Because the lungs of the deceased were extremely damaged, suspicions arose that it might even be a case of the lung plague, but as antibiotic treatment had no effect, this hypothesis was rejected as well. Soon, scientists agreed that SARS was the first serious new illness discovered in the 21^st century.

A record-breaking discovery of the cause

On March 17^th WHO assembled a team of the best microbiologists, virologists, epidemiologists, and clinicians in the world to battle against the new disease. With conferences being held daily and all the information transmitted via the Internet it was in the beginning of April when it was already found out that the disease was caused by a new virus of the coronavirus family that has never before been noticed in humans or in animals. Coronaviruses are relatively harmless and cause common colds while SARS, as it seemed, was no typical coronavirus. On April 12^th, the scientists were already familiar with the entire genome of the virus and on the 1^st of May an article giving a detailed description of the virus was published.

In the middle of May, when the epidemic reached its peak and each day was filled with reports of several hundred newly diseased, scientists were still without any medication or vaccine that could prevent the pandemic, so the authorities had to resort to usual measures that have been practiced by humankind for thousands of years. All those contaminated were immediately isolated in order to prevent any further spreading of the disease. In Singapore, the quarantine of the potentially ill was controlled with webcams, installed in their homes. Penalties for breaching the quarantine were very severe. In Hong Kong, the building where the highest number of the diseased lived was evacuated and its residents were moved to a special camp for ten days.

In China, it took longer for the authorities to realize the gravity of the situation. In the end, this was the reason why one fourth of all the diseased in the entire world were from Beijing. Of course, it could have been even worse if, at a certain point in time, the Chinese authorities had not reacted so firmly. They shut down all the schools, theatres and cinemas, and prohibited all public events. In the end of April they decided to build a new hospital in the suburbs of Beijing, specializing in SARS treatment. Seven thousand construction workers set a record by building the hospital in no more than eight days for 170 million dollars.

As suddenly and mysteriously as the disease had appeared, it started to disappear in the summer of 2003. Considering the fact that during the epidemic 774 people died of SARS, it was a stroke of good luck that only 8096 people were infected.

Lucy, more precious than diamonds

It was just another morning in Africa. The paleoanthropologist Donald C. Johanson was sipping his morning coffee with his young colleague Tom Gray, trying to decide where to go fossil hunting for the day. He was drawn to the remote parts of Ethiopia by his desire to find the skeletal remains of our distant ancestors or at least their close relatives. He studied the evolution of man and other hominids and was now searching for fossils from the period when our ancestors had just started to stand on two feet.

His young friend Tom, who was at the time a postdoctoral researcher, had a different mission. With the aid of fossil remains of plants and animals he was to reconstruct as accurately as possible the natural environment which prevailed several million years ago when our ancestors roamed these lands. It is known that Africa used to be much more forested, even in areas where today only desert remains. The characteristics of an environment which existed in a certain area in a certain period could most easily be reconstructed from fossil finds.

Fossil hunting

That day, Donald did not intend to leave the base camp where scientists were lodged as he had to catch up on a lot of unfinished administrative work. Only a day before, Richard and Mary Leakey, two famous and successful human fossil hunters who lived in nearby Kenya, had concluded their visit of the camp. During their stay Donald did not spend much time on cataloguing the discovered specimens, so he decided to make up for the lost work. But, as he later remembered, something drove him to the field that day, even though he was aware that it would be wiser to stay in the tent and arrange his papers. Even so, he wrote in his journal: “November 24^th 1974. I’m spending this morning on location 162 with Gray. Feeling good.”

Looking for fossils is time-consuming work requiring a fair amount of luck. Many renowned paleoanthropologists spent their entire lives wandering through potential sites without succeeding in finding a single relevant specimen. This was Donald’s third expedition to the Ethiopian region Hadar and he had already gotten quite lucky with some of his finds, but he certainly never expected that it would be that very day that he would come upon the trail leading him to the fossils that remain one of the most important paleoanthropological discoveries to this day.

After they have had their coffee, Donald and Gray got into one of the four Land Rovers and drove to site No. 162. Their destination was actually only a few kilometers away from the scientific expedition’s base camp, but they needed half an hour to reach it because of the difficult terrain. When they arrived, the African sun was already scorching hot and all the morning freshness had gone from the air.

The Hadar region in Ethiopia is well known for having fossils scattered all across the surface of its ground. Hadar is the center of the Afar Desert where there once was a lake in which all different kinds of sediments accumulated. When the lake dried out they surfaced, bearing witness to the events that took place in this area several million years ago.

When searching for fossils, the most important thing to have is an eye for distinguishing a potential fossil from a common rock. Then, only a careful and systematic analysis of the area remains to be performed until someone gets lucky. While searching through site No. 162 that morning, all that Tom and Donald found were a couple of teeth belonging to an extinct species of horse, a part of an extinct pig’s skull, and a piece of a monkey’s jaw. Noon was approaching and the temperatures had risen to more than 40 degrees Celsius.

A three-million-year-old skeleton

After an entire morning of searching for fossils, Tom and Donald decided to head back to their vehicle and drive off for lunch. When they were already on their way back, Donald decided to scan the area again, even though others had already examined it at least twice without finding anything. His eyes stopped on a small bone penetrating the surface of the ground. Donald suddenly cried: “It’s a part of a hominid’s arm!” But Tom did not believe him: “It can’t be. It’s too small. It probably belongs to a monkey.”

However, when they came across a piece of a skull lying nearby even Tom was completely convinced that it was not a monkey, but a hominid. After a more thorough examination of the surroundings, they also discovered some vertebrae and a part of a pelvis. They immediately realized that this was almost certainly one of the greatest discoveries in the history of paleoanthropology. Never before had a scientist succeeded in finding so many preserved parts belonging to an individual hominid of this age. When they found the remains of ribs, they started to jump for joy, in spite of the temperature which was now well over forty degrees.

They carefully marked the site, gathered some more remains of the jaw and set off for the camp to get some help. On the way back they picked up two geologist colleagues who were carrying samples of rocks. Tom was so excited that he started to sound the horn before they even reached the camp and started shouting that they had discovered something truly important.

Soon, all of the members of the expedition were on site 162 by the remains of the skeleton that had been discovered by Donald and Tom only a couple of hours earlier. During the three weeks that followed they diligently dug through every part of the area looking for as many remains they could include in the reconstruction of the skeleton as possible. In the end, they gathered several hundred pieces of bones which represented approximately forty percent of the skeleton belonging to a single individual.

But who was this being they had excavated? At first, the only thing they could be certain about was that nobody had ever discovered anything like it. The first night after the discovery had been made nobody went to bed, because the excitement was too overwhelming. They discussed the find into the late hours of the night, drinking beer and going over all the possible implications of this important discovery. A portable radio was loudly playing a tape on which the song Lucy in the Sky with Diamonds was repeated several times. Sometime during the night the fossil happened to get stuck with the name Lucy and we have known it as Lucy ever since, even though the finds official name is AL 288-1.

Such a small brain, and already walking upright

Lucy was only a meter high and weighed a bit less than thirty kilos. She was classified as a new species of hominids for which the technical term on the site was Australopithecus Afarensis. When the world found out about this important discovery made by the researchers in Ethiopia, Lucy became a true sensation. From the form of her pelvis the scientists concluded and affirmed that she had walked on two feet. With 3.2 million years of age she was the oldest preserved specimen of a man’s ancestor who already walked upright.

Only four years later in a place called Leatoli in the nearby Tanzania, another group of scientists led by Mark Leakey came across a series of footprints that had been preserved in volcanic ash which, mixed with rain, had solidified into a substance similar to cement. When a nearby volcano erupted 3.7 million years ago, there was, among other creatures, a being like Lucy walking on two feet across the wet ashes.

Before Lucy was discovered, scientists were convinced that our ancestors decided to walk on two feet because they had gradually become more intelligent and realized that freeing up the hands might be a good idea. With their hands they could do useful things while walking, unlike monkeys. Lucy refuted this theory as she obviously walked on two feet, yet her head was not much bigger than that of a chimpanzee. All evidence implies that our ancestors had begun to walk upright long before they developed a brain big enough to allow them to figure out that it might be a good idea.

The latest research comparing the consumption of energy used for walking in chimpanzees and humans shows that humans with their upright walk use four times less energy than chimpanzees. This means that it was definitely an important development which, among other things, enabled the brain to start consuming more energy. As we all know, people use great amounts of energy even when we sit still and do nothing but think. About one fifth of all energy produced in our bodies is spent to fuel the brain, which is a lot in comparison to what other animal species use.

To supply our brain with energy, people need appropriate food, preferably cooked so we can digest it more easily and absorb more nutritious substances than we would if we consumed it raw. To obtain meat and other food, rich in calories, we need tools, weapons and knowledge for which free hands and a brain of an appropriate size are essential.

The African Lucy is now on a six-year tour of the U.S. As a part of the promotion, scientists in cooperation with the Ethiopian authorities decided to include the fossil remains of our distant ancestor in the exposition Lucy’s Legacy: The Hidden Treasures of Ethiopia which began its worldwide tour in Texas (Houston Museum of Natural Science) and is currently on display in Seattle (Pacific Science Center).

How to release the energy of atoms?

Leo Szilard was sitting in the lobby of his hotel in London reading the Times. It was Tuesday, September 12^th 1933. In that issue, the newspaper featured an in-depth report on a scientific conference where the renowned physicist Ernest Rutherford lectured on the use of energy which was supposedly stored in atoms. Journalists carefully put down every word of Rutherford’s lecture which seemed to annoy Szilard immensely. Rutherford claimed that all the talk about atomic energy was no more than a senseless daydream, and most of the scientists of the time believed him. But Szilard thought otherwise.

Rutherford’s statements on the impossibility of the use of nuclear energy made him so angry that he decided to dedicate himself to solving this problem and prove that the famous physicist was wrong. He left the hotel and took a walk through the city to clear his mind. When he was already strolling down one of the nearby streets an idea flashed through his mind. He had thought of a way to release the energy of an atom. This is how he later remembered that moment: “I stopped at the crossing on Southampton Row because the traffic light was red.” In a few moments cars started to slow down and stop and pedestrians were able to cross the road. It was at this very moment that Szilard came to realize how it would be possible to release the enormous amounts of energy, stored in every atom. He would have to create a chain reaction using neutrons.

“Eureka” at the pedestrian crossing

“I was waiting for the traffic light to change and when the green light turned on and I started crossing the road I suddenly realized. If I could find an element which, when colliding with neutrons, would split up or emit two neutrons after absorbing another, a sufficient amount of this element could maintain the chain reaction. At the time, it was not yet clear to me how we could find such an element or what kind of experiments would have to be conducted to do so, but the idea stuck in my mind. In certain circumstances it would be possible to establish a chain reaction, to produce large quantities of energy and build a nuclear bomb. The fact that something like that was really possible became my obsession.”

During the winter, Szilard put his ideas down on paper. The neutron was then a completely new particle, discovered only one year earlier. Of course, the crucial discovery was that neutrons, unlike protons with which they constitute the nucleus of an atom, are not influenced by the repulsive force, so they could penetrate the nucleus and reshape it in such a way that it would become unstable and split into two parts.

Naturally, finding an element which would emit energy and free neutrons after being split up was essential. According to Szilard, this method of nuclear fission was supposed to result in the release of energy, stored in an atomic nucleus, because the combined energy of the newly created nuclei would be smaller than that of the original nucleus, which meant that excess energy would be released in the form of heat. If a couple of additional neutrons that could cause fission of the neighboring nuclei were to be released during this process, a chain reaction would take place.

The most important challenge in achieving this was to find an element which would, during fission, release energy as well as free neutrons. At first, Szilard surmised that the appropriate elements were beryllium and iridium, but this supposition turned out to be wrong. Only later did it become evident that the most suitable element for exploiting nuclear energy was uranium.

A writer’s prediction of the future more accurate than a scientist’s

To finance his research he first turned to a factory-owner. It is interesting that he did not enclose scientific articles with his letter of request, but a passage from the novel by H. G. Wells, The World Set Free. In the novel, a scientist called Holsten invents a way to release the energy stored in atoms. “Of course, all of this is no more than a fantasy,” Szilard wrote in his letter to the factory-owner, intentionally citing Rutherford’s own words, “but I have good reasons to believe that, when it comes to industrial applications of today’s discoveries in the field of physics, it could soon turn out that the predictions of writers are more accurate than the predictions of scientists.” It was also none other than H. G. Wells that invented the term “atom bomb”.

Soon after this, Szilard had to face an important decision. Should he reveal his findings on nuclear energy to the public by publishing them and risk his idea going into the wrong hands, or should he keep it a carefully protected secret? Holsten, the scientist from H. G. Wells’s novel, decided that he was no more than an insignificant instrument in the grand machinery of progress and change. Even if he burned all his papers, someone else would come to the same conclusions in a few years. But Szilard decided otherwise. Rather than describe his idea in a scientific article and publish it in some renowned science magazine, he decided to keep it secret.

He first thoroughly described the details of his discovery of the possibilities of exploiting the energy of atoms. Then, he patented his idea about critical mass and chain reaction, produced with the aid of neutrons. In 1935, he transferred the rights to the patent for the realization of these important ideas to the British Army on condition that everything remains an absolute secret. During the following years, before the Second World War, everyone who new about the idea made an effort to prevent any information revealing the discovery of the exploitation of nuclear energy from reaching Hitler’s scientists. It was only in 1939 that Szilard confirmed his theory by experiment. In February that year, an experiment was carried out in the laboratories of Columbia University in New York which later lead to the realization of the first controlled chain reaction, starting the era of the exploitation of nuclear energy. Szilard built the nuclear reactor on Manhattan with Enrico Fermi, an expert on bombarding atomic nuclei with neutrons. Several years earlier in Rome, Fermi had already discovered that decelerated neutrons fuse better with atomic nuclei than faster neutrons, so it was important to find an appropriate substance that could slow down neutrons. It turned out that one suitable option was heavy water, but it was difficult to obtain it in sufficient quantities. To execute the experiments, a more accessible medium that could perform the task had to be found.

How to beat the Nazis?

As Szilard feared, German scientists were also thinking of ways to build a nuclear reactor. However, they also had difficulties in obtaining sufficient amounts of heavy water, so they were searching for alternative solutions as well. Both were testing graphite, but fortunately the Germans gave it up quickly after they had concluded that graphite absorbed neutrons too well. Szilard, on the other hand, discovered that the problem lied in the addition of boron to the industrial manufactured graphite and not in the graphite itself. It turned out that pure graphite was a very suitable medium for slowing down neutrons in a nuclear reactor. Szilard was much more aware of the gravity of the moment than Fermi. In the summer of 1939, Fermi left for the University of Michigan to study cosmic radiation, so Szilard decided to turn to his old colleague Albert Einstein who, at the time, lived on Long Island some hundred kilometers from New York. He presented his idea which was actually based on the famous equation E=mc². Einstein replied that he had never thought of anything like that when he was contemplating the possible applications of his infamous equation relating mass to energy.

On his second visit to Einstein, Szilard brought with him a letter he had written to President Roosevelt warning him of the danger that Hitler’s Germany might be researching the use of nuclear fission to create an atomic weapon, and suggesting that the U.S should seriously consider studying the possibility itself. It is reported that Einstein read and signed the letter which later turned out to be extremely important wearing only his dressing gown. The letter began with the words “The recent discoveries of E. Fermi and L. Szilard …” and was dated August 2^nd 1939.

Of course, Szilard did not simply send the letter to the President by mail as it might have come into the wrong hands, but asked an acquaintance who was on of the President’s economic advisers to bring it directly into the White House. When Roosevelt finally read the letter he realized that something absolutely had to be done to “prevent the Nazis from blowing us all into the air”. He founded the Uranium Committee, of which Szilard was made member and which set in motion the research that ultimately lead to the creation of the atom bomb, but also nuclear reactors which we use to produce great amounts of electrical energy today, and are, according to many environmentalists, one of the most acceptable energy sources in terms of the effects of global climate change.