Science

By Brandon C. Look 

While all previous philosophers were, in (above) Immanuel Kant’s mind, guilty of various errors, Gottfried Wilhelm Leibniz occupied a special position in his conception of the history of philosophy and the history of reason’s pretensions.

If the eighteenth century is to be seen as the “Age of Reason,” then one of the crucial stories to be told is of the trajectory of philosophy from one of the most ardent proponents of the powers of human reason, Gottfried Wilhelm Leibniz (1646–1716), to the philosopher who subjected the claims of reason to their most serious critique, Immanuel Kant (1724–1804). Not only is the story of Kant’s Auseinandersetzung with Leibniz important historically, it is also important philosophically, for it has implications about the nature and possibility of metaphysics, that branch of philosophy concerned with fundamental questions such as what there is, why there is anything at all, how existing things are causally connected, and how the mind latches onto the world. Like many philosophical debates, however, it is also prone to a kind of “eternal recurrence” to those who are ignorant of it. 

Leibniz was a “rationalist” philosopher; that is, he was committed to two theses: (i) he believed that the mind has certain innate ideas—it is not, as John Locke and his fellow empiricists say, a tabula rasa or blank slate; and (ii) he believed in—and, in fact, made explicit—the “principle of sufficient reason,” according to which “there is nothing for which there is not a reason why it is so and not otherwise.” This principle had enormous metaphysical consequences for Leibniz, for it allowed him to argue that the world, as a series of contingent things, could not have the reason for its existence within it; rather there must be an extramundane reason—God. Further, as a response to the mind-body problem, Leibniz advanced the theory of “pre-established harmony,” according to which there is no interaction at all between substances; the mind proceeds and “unfolds” according to its own laws, and the body moves according to its own laws, but they do so in perfect harmony, as is fitting for something designed and created by God. Strictly speaking, however, Leibniz was not a dualist; he did not believe that there were minds and bodies—at least not in the same sense and at the most fundamental level of reality. Rather, in his mature metaphysical view, there are only simple substances, or monads, mind-like beings endowed with forces that ground all phenomena. Finally, according to Leibniz, since these simple substances are ontologically primary and ground the phenomena of matter and motion, space and time are merely the ordered relations derivative of the corporeal phenomena. Leibniz contrasted his view with that of Isaac Newton, according to whom there is a sense in which space and time can be considered absolute and space can be considered something substantial.

By Chang S. Chan, Suzanne Christen, and Asad Naqvi 

This plot of genetic data from an individual with autism shows a deletion in the gene NCAM2, one of four genes that researchers in the Simons Center for Systems Biology found to be associated with autism.

Autism is a common child­hood neurodevelop­mental disorder affecting one in 180 children. It is characterized by impaired social interaction and communication, and by restric­ted interests and rep­etitive behav­ior. Autism is a complex disease exhibiting strong genetic liability with a twenty-five-fold increas­ed risk for individuals having affected first-degree relatives. Moreover, the concordance for developing autism is over 90 percent in identical twins, but only 5–10 percent for fraternal twins. Recent advances in genetics show that autism is associated with many diverse genes, with each gene accounting only for a few percent of cases, as well as complicated multigenic effects.

Researchers at the Simons Center for Systems Biology have been studying autism for the past two years. We have identified novel genes associated with autism. Our approach is to use single nucleotide polymorphism (SNP) genotyping chips that measure differences between individuals and can uncover candidate genes or regulatory elements (which control gene activity) associated with the disease.

Most individuals differ very little from one another across the human genome. SNPs are the largest class of DNA sequence variation among individuals. A SNP occurs when one base out of the four bases used in DNA is exchanged for another base at the same locus, such that the minor allele frequency is at least 1 percent in a given population. SNPs are found at the rate of roughly one out of every 1,000 base pairs of the human genome. These SNPs provide the best chance of detecting genetic variation, both normal and otherwise, between people.

By Cécile DeWitt-Morette 

Cécile DeWitt-Morette with (from left to right) Isadore Singer, Freeman Dyson, and Raoul Bott at the Institute in the 1950s

In Brief 

It all began with a cable from Oppenheimer that I received on March 10, 1948, in Trondheim, Norway: ON THE RECOMMENDATION OF BOHR AND HEITLER I AM GLAD TO OFFER YOU MEMBERSHIP SCHOOL OF MATHEMATICS FOR THE ACADEMIC YEAR 1948 – 1949 WITH STIPEND OF $3500. ROBERT OPPENHEIMER.

I did not know that this was a great offer. I did not even know where Princeton was, but as a general rule, I would rather say “yes” than “no.” I was then on leave from the French Centre National de la Recherche Scientifique (CNRS), having been awarded a Rask-Oersted Fellowship for the academic year 1947–48 at the Nordiska Institutet för Teoretisk Fysik in Copenhagen.

In retrospect, I think that in the days of the Marshall plan, Oppie was looking for a couple of European young postdocs who would benefit from a year at the Institute. Did I benefit? More than I could ever have imagined.
During my two-year stay, 1948–50, Bryce DeWitt, a postdoc at the Institute, 1949–50, asked me to marry him, and I conceived the Les Houches Summer School as my self-imposed condition for marrying a “foreigner.” Thanks to Freeman Dyson and Richard Feynman, I learned about functional integration and am still fascinated by it. 

By Jeremy Bernstein 

Debates at the fifth Solvay Conference in Brussels in 1927 helped shape the modern interpretation of quantum mechanics. Participants included Niels Bohr (second row, far right) and Albert Einstein (first row, fifth from left).

In the two years I spent at the Institute, 1957–59, I had the opportunity of meeting two of the founders of the quantum theory—Niels Bohr and Paul Dirac. In the case of Bohr, perhaps “meeting” overstates the case. He was a Mem­ber in the spring of 1958 and Oppenheimer, who had known him since the 1920s and who had a feeling of adulation for him, decided that a fitting thing to do was to have a sort of seminar in which the physicists would trot out their wares with Bohr looking on and possibly commenting. As it happened, I had had a brief collaboration with T. D. Lee and C. N. Yang, who had won the Nobel Prize that fall. They had better things to tell Bohr than our modest work, so I was the designated spokesman. I was given ten minutes and took about three. After which Bohr commented, “Very interesting,” which meant he did not think so. If he had had any real interest, he would have engaged in a Socratic dialogue, which would have proceeded until he was satisfied. There is a famous story concerning Erwin Schrödinger—with whom I later spent an afternoon in Vienna—arriving in Copenhagen after having created his version of the quantum theory. Bohr disagreed with some of what Schrödinger was saying and pursued him into his bedroom where the now sick Schrödinger had taken refuge.

On a visit to the Institute ten years earlier, Bohr had written his wonderful account of his discussions with Einstein about the theory. Bohr found writing incredibly difficult and always had an amanuensis who acted as a sounding board. In this case, it was Abraham Pais who told the following story. Einstein had given Bohr his office for the visit and was in the adjoining smaller office of his assistant. Where the assistant had gone is not recorded. Bohr was facing away from the door and saying, “Einstein, Einstein” several times. As if summoned by a genie, Einstein stealthy came into the office. Before Bohr could turn around, Einstein helped himself to some of Bohr’s pipe tobacco. When Bohr did turn around, Einstein explained that his doctor had ordered him not to “buy” any more tobacco, but there was no injunction against his “stealing” some.

Robbert Dijkgraaf will become the ninth Director of the Institute, as of July 1, 2012.

On November 14, the Institute for Advanced Study announced the appointment of Robbert Dijkgraaf as its ninth Director, succeeding, as of July 1, 2012, Peter Goddard, who has served as Director since January 2004.

Below, Dijkgraaf speaks about his enthusiasm for the Institute and for using knowledge, creativity, and collaboration to further our understanding of a world of diverse facts, structures, ideas, and cultures.

––––––––

I am delighted to come to the Institute for Advanced Study, one of the intellectual centers of the world. The position of Director is highly distinguished, and the list of former Directors is quite intimidating. But I am particularly looking forward to combining at the highest level three elements that have been important in my professional life: the opportunity to collaborate with the very best scientists and scholars; to organize a stimulating environment for great talent from around the world; and to play an active role in science education, advocacy, and diplomacy to engage future generations.

Taking up my appointment as Director of the Institute will feel a bit like coming home. My family and I have only the best recollections of our stays in Princeton. I also expect that in many ways my life will become more focused. My present position as President of the Royal Netherlands Academy of Arts and Sciences requires giving attention to many different areas, from elementary school programs to industrial affairs, from government policy to international relations. The Institute is remarkably effective as a place for concentration and inspiration.

By Scott Tremaine 

Scott Tremaine explores the stability of our solar system, one of the oldest problems in theoretical physics, dating back to Isaac Newton.

The stability of the solar system is one of the oldest problems in theoretical physics, dating back to Isaac Newton. After Newton discovered his famous laws of motion and gravity, he used these to determine the motion of a single planet around the Sun and showed that the planet followed an ellipse with the Sun at one focus. However, the actual solar system contains eight planets, six of which were known to Newton, and each planet exerts small, periodically varying, gravitational forces on all the others.

The puzzle posed by Newton is whether the net effect of these periodic forces on the planetary orbits averages to zero over long times, so that the planets continue to follow orbits similar to the ones they have today, or whether these small mutual interactions gradually degrade the regular arrangement of the orbits in the solar system, leading eventual ly to a collision between two planets, the ejection of a planet to interstellar space, or perhaps the incineration of a planet by the Sun. The interplanetary gravitational interactions are very small—the force on Earth from Jupiter, the largest planet, is only about ten parts per million of the force from the Sun—but the time available for their effects to accumulate is even longer: over four billion years since the solar system was formed, and almost eight billion years until the death of the Sun.

By Juan Maldacena 

Albert Einstein, pictured at left with J. Robert Oppenheimer at the Institute, tried to disprove the notion of black holes that his theory of general relativity and gravity seemed to predict. Oppenheimer used Einstein's theory to show how black holes could form.

The ancients thought that space and time were preexisting entities on which motion happens. Of course, this is also our naive intuition. According to Einstein’s theory of general relativity, we know that this is not true. Space and time are dynamical objects whose shape is modified by the bodies that move in it. The ordinary force of gravity is due to this deformation of spacetime. Spacetime is a physical entity that affects the motion of particles and, in turn, is affected by the motion of the same particles. For example, the Earth deforms spacetime in such a way that clocks at different altitudes run at different rates. For the Earth, this is a very small (but measurable) effect. For a very massive and very compact object the deformation (or warping) of spacetime can have a big effect. For example, on the surface of a neutron star a clock runs slower, at 70 percent of the speed of a clock far away.

In fact, you can have an object that is so massive that time comes to a complete standstill. These are black holes. General relativity predicts that an object that is very massive and sufficiently compact will collapse into a black hole. A black hole is such a surprising prediction of general relativity that it took many years to be properly recognized as a prediction. Einstein himself thought it was not a true prediction, but a mathematical oversimplification. We now know that they are clear predictions of the theory. Furthermore, there are some objects in the sky that are probably black holes.  

Black holes are big holes in spacetime. They have a surface that is called a “horizon.” It is a surface that marks a point of no return. A person who crosses it will never be able to come back out. However, he will not feel anything special when he crosses the horizon. Only a while later will he feel very uncomfortable when he is crushed into a “singularity,” a region with very high gravitational fields. The horizon is what makes black holes “black”; nothing can escape from the horizon, not even light. Fortunately, if you stay outside the horizon, nothing bad happens to you. The singularity remains hidden behind the horizon.

By Edward Witten 

Edward Witten explains how mathematicians compare knots that differ by how a missing piece is filled in (as indicated by the question mark above).

In everyday life, a string—such as a shoelace—is usually used to secure something or hold it in place. When we tie a knot, the purpose is to help the string do its job. All too often, we run into a complicated and tangled mess of string, but ordinarily this happens by mistake.

The term “knot” as it is used by mathematicians is abstracted from this experience just a little bit. A knot in the mathematical sense is a possibly tangled loop, freely floating in ordinary space. Thus, mathematicians study the tangle itself. A typical knot in the mathematical sense is shown in Figure 1. Hopefully, this picture reminds us of something we know from everyday life. It can be quite hard to make sense of a tangled piece of string—to decide whether it can be untangled and if so how. It is equally hard to decide if two tangles are equivalent.

Such questions might not sound like mathematics, if one is accustomed to thinking that mathematics is about adding, subtracting, multiplying, and dividing. But actually, in the twentieth century, mathematicians developed a rather deep theory of knots, with surprising ways to answer questions like whether a given tangle can be untangled.

But why—apart from the fact that the topic is fun—am I writing about this as a physicist? Even though knots are things that can exist in ordinary three-dimensional space, as a physicist I am only interested in them because of something surprising that was discovered in the last three decades.