In February 1951, Henrietta Lacks, a thirty-year-old mother of five, went for an examination at the John Hopkins hospital after noticing blood stains on her underwear. Doctors were quick to conclude that she had most likely contracted cervical cancer. To confirm their diagnosis they took a sample of her tissue and had it analyzed. The news was anything but encouraging: the tumor contaminating the cervix turned out to be malignant. In October, the same year, and only after a few months’ struggle with the disease Henrietta Lacks died.Sunday, 19 October 2008
The afterlife of Henrietta Lacks
In February 1951, Henrietta Lacks, a thirty-year-old mother of five, went for an examination at the John Hopkins hospital after noticing blood stains on her underwear. Doctors were quick to conclude that she had most likely contracted cervical cancer. To confirm their diagnosis they took a sample of her tissue and had it analyzed. The news was anything but encouraging: the tumor contaminating the cervix turned out to be malignant. In October, the same year, and only after a few months’ struggle with the disease Henrietta Lacks died.Saturday, 18 October 2008
A mathematical intrigue at the Swedish court
Monetary prizes for solving complex scientific and technical problems are not awarded as often as they used to be. Today, tenders where a committee of experts offers prizes for the best creations that are sent to its address by a certain date are a common way of finding solutions in the fields of architecture and other artistic/technical disciplines, but not so much in science. Every once in a while an organization or an individual still announces that a prize will be given to anyone who can solve some seemingly insoluble problem, but these awards are not really significant in terms of more extensive financing of scientific work. In the past, however, this used to be quite different.A little more than a hundred years ago, the Swedish mathematician Gösta Mittag-Leffler persuaded King Oscar the 2nd of Sweden to organize a mathematics competition in honor of his 60th birthday. As the king was a student of mathematics himself, he took to the idea quickly, especially because Mittag-Leffler had succeeded in convincing two highly distinguished European mathematicians to take part in the jury that would set the tasks and evaluate the solutions. The invitation was accepted by Karl Weierstrass of Berlin and Charles Hermite of Paris.
Is the solar system stable?
Four tasks were given, all relating to the essential problems that were also principal subjects of mathematical research of the time. Even though the king’s birthday was not until 1889, the preparations already started in 1884, so that scholars from across Europe would have enough time to examine the problems thoroughly and come up with their solutions. In the middle of 1885 Nature magazine printed an announcement inviting scientists to participate in a mathematical competition in honor of King Oscar the 2nd’s 60th birthday. The deadline for submitting the solutions to the Swedish court and the president of the jury Gösta Mittag-Leffler was June 1st 1888. Naturally, the essay in which its author would describe his solution was not allowed to be signed in order to enable unbiased evaluation of the work. That is why everyone was required to enclose his solution with a sealed envelope containing his name.
The first of the four questions which were given in formal mathematical language pertained to the problem of the movement of three bodies. In other words, the jury was interested in the question of the stability of our solar system. Today, more than a hundred years after the event took place, what happened a couple of months after the announcement of the winner is more interesting than the initial question and its answers. When the winning solution was already being prepared to be published the editor of the magazine noticed that the jury had rewarded a work which was not completely flawless. One of the mistakes actually turned out to be of key importance.
The winner was no surprise
The winner of the competition was none other than the eminent French mathematician Henri Poincaré who, despite his young age at the time, already enjoyed a very high reputation. In the period between the announcement of the competition and the deadline for submissions he was even elected a member of the French Academy of Sciences which was a great honor for a man of only 32.
The competition was not about winning the money. The awarded sum came nowhere close to that of today’s Nobel Prize. The winner received 2500 Swedish kronor which was approximately one third of a professor’s yearly salary. The award improved the young mathematician’s scientific career significantly and enabled him to secure a good position at one of the renowned universities, but it certainly did not make him rich. As we are about to find out, the prizewinning Poincaré actually lost more than he gained on account of the award.
With his 158 pages long solution to the first problem Poincaré enclosed a short accompanying letter which he signed, even though all of the submitted essays were supposed to be anonymous. It was during the evaluation process that the jury already knew exactly who the author of the solution, which was later unanimously voted to be the best, was. The winner was announced during the celebration of the king’s birthday on January 21st 1889. A part of the prize was also the publication of the solution in the prominent mathematical journal Acta Mathematica.
It was at this moment that the problem occurred. In July of 1889 when the editor of the journal was preparing Poincaré’s article for publication he noticed a few minor mistakes in the manuscript. He notified Mittag-Leffler who, in turn, wrote a letter to Poincaré on 16th July to inform him that all of the mistakes but one could be fixed immediately. The one mistake was neither a typing error nor a minor mathematical error. It turned out to be of a much greater importance. As it soon turned out, Poincaré overlooked something essential in his proof which was only discovered after the prize had already been awarded and the article was almost put into print.
How to avoid a scandal?
What to do? If it were to become known that the wrong solution had been rewarded, the reputation of both the king and all of the highly esteemed mathematicians that took part in the evaluation process would be destroyed. The disgrace would be especially devastating to Poincaré who had just begun to shine as the new star on the European scientific scene.
Poincaré went back to work in order to correct the mistake, but the more he examined the problem the more it seemed it was not merely a minor error that could be fixed easily. At first, he sent extensive comments to the text which were meant to clarify the issue, but it became increasingly obvious that explanations alone would not be enough to deal with the difficulty.
So what kind of an error was it? In his original solution Poincaré used a completely new method that made his work much easier and caused a minor revolution in the solving of similar mathematical problems. Instead of calculating the entire orbits of individual bodies or planets, Poincaré chose to focus only on specific moments when a planet or asteroid intersects with a chosen plane. In other words, this method would be best compared to taking an image of the solar system at the exact moment when the observed body circles the sun. In the case of Earth, this would happen once a year.
Poincaré only wanted to determine if a planet or an asteroid, after circling the sun, returns to the same spot, or to find out how the yearly positions change with time. In simpler words: if a chosen plane is always intersected at the same point, the orbit of the motion is obviously stable, but if the plane is crossed at a slightly different point each time, this change has to be described and examined to determine whether these deviations occur within a stable system.
The chaotic mechanics of the stars
Poincaré’s discovery which he had also argued for in his original essay was that the solar system was stable, at least in a simple model of the sun with one bigger planet and one small asteroid orbiting in the same plane. His first finding was that, in this case, the orbits of motion were stable. When he examined the problem again, it became evident that he had forgotten to take into account an entire range of solutions which were not stable, but would lead to chaos.
It turned out that Poincaré had forgotten to take into consideration a geometrical configuration which leads to completely different solutions than the ones he had described in his original essay. Today, we would describe these new solutions, which he overlooked at first, as chaotic. Even though they are precisely determined by clear equations and the paths of the bodies in question are such that their future motion is possible to predict, this kind of a prediction depends on the knowledge of the initial conditions. If there is only a slight difference in the position of the bodies at the beginning, they are bound to move in a completely different way. On the basis of this finding Poincaré could only conclude that not all forms of movement in a simplified system of three bodies were stable, which also meant that the solar system or any other similar system were not necessarily or absolutely stable.
In the couple of months when Poincaré was striving to correct the mistake he had made in his original article, he set the foundations for a new branch of mathematics which later developed to become the chaos theory. The 158 pages of the original essays were expanded to 270 pages. The problem, however, was that the original article had already been printed in Sweden. Fortunately for all those involved it was not yet distributed to the subscribers. To avoid a scandal Poincaré paid 3585 kronor for the reprint of the issue which was much more than the sum of the prize money he had received. They also made sure that most of the first prints of the journal were destroyed, but a couple of the original issues remained. In 1985, during his research visit to Sweden, the American mathematician Richard McGehee was looking through some archives and came upon a couple of copies of the 13th issue of Acta Mathematica in an unlabeled box containing Mittag-Leffler’s letters. When he was scanning through it he discovered that Poincaré’s article was different than the one he was familiar with from other copies of the same journal.
Even though Poincaré won the prize for the first, flawed version of the article, the edited article, with which he made a giant leap towards the science of chaos, is much more important from today’s point of view. It might seem contradictory, but the award was definitely given to the right person, although for the wrong solution and the wrong essay.
Tuesday, 14 October 2008
The priest who came up with the Big Bang

The Big Bang theory is believed to be one of the most popular scientific theories today. According to this theory, the universe began as an extremely hot and dense substance which expanded and cooled down with time until, 14 billion years later, it acquired the form that we can observe today whenever we look towards the sky on a clear night. The theory is well supported by experiments and represents a good example of the almost incredible capacity of modern science for taking a small number of data gathered on our small planet and reconstructing the history of the entire universe from the first moments on.
Despite the popularity of the Big Bang theory only a few people today are aware that the first to describe it was a Belgian priest called Georges Lemaître who, in addition to preaching, dedicated his time to science and was among other things a friend of Albert Einstein himself. Einstein accepted the primeval atom theory, as Lemaître called his idea about the development of the universe which was later given its much more resounding name, the Big Bang, with great interest which was not followed by the larger scientific community until the 1960s. That was when two American scientists accidentally discovered that microwave radiation, which can only be explained by the notion that the universe was once much hotter than today, was reaching us from all the directions of the universe.
The universe as a radioactive atom
Of course, Georges Lemaître was not merely an amateur scientist. Even though he was ordained a Catholic priest in the fall of 1923, he always remained true to science. After earning his doctoral thesis in mathematics the same year he was ordained, he started his postdoctoral studies at Cambridge where he furthered his knowledge under the tutelage of Arthur Eddington who was believed to be one of the most eminent astronomers of the time. It was with him that Lemaître became acquainted with the latest discoveries and the newest research methods in astronomy as well as cosmology which was already gradually becoming a branch of science within which experimentally verifiable theories could be formed.
After a year spent in England, he left for Harvard in the USA where he collaborated with Harlow Shapley, another great name of contemporary astronomy. In Boston, which is believed to be one of the most important academic centers of the world due to its elite universities, he also perfected his knowledge at the prestigious MIT, where he became even more drawn to cosmology and started to study models of the universe implied by Einstein’s completely new general theory of relativity. He obtained his doctoral degree at MIT before returning to Belgium and becoming a professor at the Catholic University of Leuven.
Soon after his return, he published the first drafts of his theory of the origin of the universe. Even though one might have expected that, as a Catholic priest, he would look to the biblical story of creation when forming his idea about the Big Bang, this was far from so. His inspiration came from neither astronomy nor the theory of relativity, but from at the time completely new quantum physics. More specifically, he became inspired to form his idea about the primeval atom when studying the phenomenon of radioactivity.
Is the creation of the universe a mere coincidence?
It is known that radioactive elements are not stable, but decay with time, releasing energy. Even though one can not predict exactly when a particular radioactive atom would disintegrate completely it is possible to predict with great precision when, for instance, one half of the radioactive atoms in a multitude of identical atoms would disintegrate. When getting acquainted with the principles of quantum physics, Lemaître asked himself whether it might be more than a mere coincidence that the half-life of some radioactive elements comes very close to the estimations of the age of the universe, based on the measurements of the expansion rate of the universe. Could it be that we are living in some worn out version of a radioactive universe?
According to Lemaître’s original idea the universe began as a kind of a “large radioactive atom” which is why we can determine its exact age. The analogy between the universe and radioactivity was also of key importance in terms of overcoming the famous problem of explaining the very beginning of the universe. If we wanted to give a causal explanation of the first moment, we would have to refer to an even older event, but we can not do so for the very reason that we want to explain the very first event. Many different thinkers throughout history have dealt with this problem at length, but its most well-known formulation probably came from Immanuel Kant who described it as the first antinomy of pure reason.
The essential thing that one should keep in mind when dealing with radioactive atoms is that their disintegration is completely coincidental. It is impossible to predict when exactly a particular atom would disintegrate which is also why there no exact cause for its decay can be determined. It is completely unpredictable, only the probability that the decay will take place within a certain period of time can be predicted. Lemaître expanded his idea about the coincidental decay of the radioactive atom to his idea about the universe as the primeval atom to which all the laws of quantum physics must apply as well. Even though it does not describe exactly the same type of event, the analogy that Lemaître tried to establish is quite obvious. Just as a particular decay has no cause, even though it is dictated by exact laws of quantum physics, the universe as a whole might lack a cause, which still does not mean that exact physical laws do not apply to it.
The universe began shortly before the beginning of time
In 1931 he described his idea in an article published in Nature magazine in which he wrote, among other things: “If the world began with a single quantum particle, the concepts of time and space had no particular meaning in the beginning; they only acquired meaning when the original quantum particle multiplied to a substantial number of quanta. If this idea is correct, the beginning of the world took place just before the beginning of space and time.”
At first glance, this way of thinking might be something that one would never expect from a Catholic priest, but anyone who is familiar at least some of the history of the Christian theological thought will quickly realize that the similarity with the famous doctrine of creation is evident. Just as God, according to the doctrine of creation, is absolutely free in his creation of the world and is not subjected to any kind of limitations, thoughts or higher purposes, Lemaître’s primeval atom is completely free in terms of the moment it “chooses” to disintegrate.
Although the analogy with the coincidental radioactive disintegration was of key importance at the beginning, it became less and less relevant while the theory was being perfected. Lemaître himself developed his theory in the years to follow, founding it on the general theory of relativity, but it was considered to be much too unusual at the time to be accepted within the wider scientific community as a serious description of the actual universe and not merely as one of many hypotheses. In science, a rule exists that the more a theory is unusual, the stronger arguments and experimental proofs it needs in order to be accepted by the scientific community. As we have already mentioned, cosmic microwave background radiation, which meant a great contribution to the acceptance of the Big Bang theory, was only discovered a couple of decades after the Second World War, and the idea about the primeval atom was long regarded as an exotic hypothesis rather than a description of the actual history of the universe. Lemaître died soon after he had received the news about the discovery of cosmic microwave radiation which confirmed his visionary idea about the origins of the universe.
In 1936 he was elected member of the Pontifical Academy of Sciences which advises the Pope on matters relating to science. In 1960 he even became its president and kept the post until his death in 1966. He always defended the belief that there is no ideological conflict between science and religion. He claimed this to be true as a high dignitary of the Church as well as one of the most esteemed scientists of his age.
He was not pleased when Pope Pius XII referred to science, including the cosmology of the Big Bang which had been his area of expertise all along, to try and prove that scientific and divine truths were actually one and the same. Even today, high Church dignitaries often declare that science has been coming to similar conclusions as those described in Church doctrines. According to them, The Big Bang theory is supposed to describe the development of the universe all the way back to the beginning of time with the exception of the first moment which is of course said to be the work of God
Lemaître strongly disagreed with such interpretations which have also been defended by later Popes: “In my opinion, the theory (of the primeval atom) remains beyond all metaphysical or religious questions. It allows the materialist to deny the existence of any transcendent Being. (…) At the same time it corresponds to the words of the prophet Isaiah who spoke of the ‘hidden’ God who was not even seen at the beginning of the universe …”
Cannibals, Insomnia and Mad Cows Disease
Not long after the Second World War, Australian colonial officials assigned to the remote planes of Papua New Guinea noticed an unusual disease among the members of a small tribe called Fore. The locals called it kuru which, in their language, means “to tremble”. That is because those affected by the disease were gradually unable to control their muscles so they started to shake and sometimes even laugh or cry uncontrollably. Once the first symptoms of the disease appeared the sufferer’s death would follow in a matter of months.