Search Results

This post is about C. N. Yang, one of the greatest physicists of the 20th century, who passed away last week at the age of 103. Yang received the Nobel prize in 1957 and made towering contributions to several areas in physics, as detailed below. Quick academic bio : Yang was born and educated in China until the masters level; he obtained his thesis in theoretical physics from the University of Chicago under Edward Teller (sometimes known as the father of the Hydrogen bomb). Subsequently, he worked for a year as an assistant to Enrico Fermi . Then he was at the Institute of Advanced Study at Princeton for a decade and a half, after which he moved to Stony Brook. He retired from Stony Brook in 1999, and moved to a position at the Tsing Hua University in Beijing. Contributions : Yang had wide interests in theoretical physics. Some of his major contributions: Parity violation : This is the work for which he and T. D. Lee were awarded the Nobel in '57. They predicted that the laws of nature were not mirror symmetric: some experiments and their mirror reflections gave different outcomes. This was experimentally confirmed by C. S. Wu by looking at the radioactive decay of Cobalt-60 nuclei. It turns out that the weak nuclear force (responsible for radioactivity) does not respect mirror symmetry (i.e. parity). A very accessible description of the physics can be found here . The violation of parity is directly related to the fact that in our universe neutrinos are always left-handed and anti-neutrinos are always right-handed. Yang-Mills theory: Arguably his biggest contribution to physics. This theory generalizes Maxwell's theory of electromagnetism and provides our current understanding of fundamental particles and their interactions. In other words, it underlies the Standard Model of physics, providing a unified framework for understanding electromagnetism and the weak and strong nuclear forces. The only force it does not apply to is the gravitational force. Solutions to problems related to Yang-Mills theory are worth a million dollars. Lee-Yang theory: This is his contribution to the study of phase transitions (e.g. when liquid turns to gas). Yang-Baxter relations : These relations are very important in the systems where many particles scatter of off each other. Lee-Huang-Yang correction: This formula applies to the study of Bose gases and has recently been used to create a new form of liquid matter, quantum droplets . Byers-Yang theorem: This result describes the connection between the behavior of magnetic fields passing through loops of superconducting material (as in devices like SQUID s) and the current in the superconductor. The C. N. Yang Institute for Theoretical Physics : At Stony Brook university; Yang was the founding director. One of the dominant themes in Yang's work was the role of symmetry in physics. His talk here reflects (pun intended) that interest. Afterword Anecdote: When C. N. Yang and T. D. Lee took a graduate course in astronomy at the University of Chicago in the late 1940s, they found they were the only two students enrolled. Their professor S. Chandrasekhar drove about 80 miles each way to come from Yerkes Observatory to teach them. In the end it was worth the effort, as the entire class won the Nobel prize (Chandrasekhar was awarded in 1983). There are some biographical notes available on Yang's life; of course the original papers and books; and many videos on YouTube. Nonetheless, when the dust settles from the fall of this colossus, a full-fledged biography, if not several, would definitely be in order.

This is a review of the book This Amazingly Symmetrical World by L. Tarasov. Published in 1982, it is nonetheless an all-time Russian science popularization gem issued from Mir Publishers in the last century. It is very well-written and gorgeously illustrated, with arresting pictures on almost every page. The discussions are accessible, yet quite profound and revealing. Symmetry plays an incredibly fundamental role in physics. Nature seems to use symmetry as a way of imposing order and harmony on otherwise random phenomena. The branch of mathematics which quantitatively deals with symmetry is called group theory . This is a quite abstract, though powerful, branch of knowledge. So it is very nice to see the basic ideas spelt out for a popular audience (the book demands no more mathematical knowledge than freshman algebra and geometry). The book is divided into two parts. Symmetry in the physical universe : The first part describes the symmetries we can observe visually in nature. The book takes off with the accessible notion of mirror symmetry and the accompanying idea of enantiomorphs (mirror images which are not superimposable, like our hands). Translational and rotational symmetry and their combination are then considered in two dimensions. There is a gorgeous chapter on repeating two-dimensional symmetric patterns, with examples from Egyptian art and Escher . Moving to three dimensions brings us to a revealing discussion of the five platonic solids (cube, tetrahedron, octahedron, icosahedron, dodecahedron), including Kepler's unsuccessful attempt to model the planets using these regular (faces are the same size) polyhedra, as well as speculations about alien dice (they can't have any other shape if the probability of each face showing up has to be the same). More three dimensional examples are made of crystal gems and snowflakes, plants (apparently most flowers have five-fold rotation symmetry) and animals (which, including us, have bilateral symmetry). An entire chapter is devoted to the role of symmetry in assemblies of atoms and molecules, with examples such as water, methane and benzene. We also learn about the phenomenon of polymorphism , which allows the same atoms to assume different symmetries, resulting in entirely different materials (e.g. graphite and diamond). This part of the book concludes with a fascinating discussion of spirals, steroisomerism and DNA (which is a right helix). Symmetry of physical laws : This is a more technical part of the book, one which refers to considerations of symmetry in phrasing the mathematical laws of nature. The idea is introduced using special relativity, which follows from the symmetry principle that the laws of physics are the same in any frame which is not accelerating. Further, it is discussed how translation in space or time, and rotation do not change the laws of physics (and how this leads to conservation of linear momentum, energy and angular momentum, respectively). However, mirror reflection sometimes does change the laws of physics. More abstract physical concepts, such as charge, spin and 'anti-particle-ness' are shown to be conserved due to more abstract symmetries. The last chapter in the book discusses the effects of symmetry in particle physics in some detail. This material could be specialized for many readers (it was for me). In the epilog, the author points out how symmetry considerations are useful in making predictions in physics (Mendeleev predicted elements that were not yet known, Maxwell predicted the displacement current , Gell-Mann predicted fundamental particles). He also points out how the method of analogy is based on the principles of symmetry. Afterword : The book explains how symmetry underlies all of (especially physical and biological) existence. The book suggests also how to think of asymmetry, and how it gives character to individual structures and organisms. One of the things I enjoyed: It assembles in one text (but distributed throughout the chapters) many famous and relevant quotes on symmetry by physicists (Einstein, Dirac, Wigner, Feynman), writers (Lewis Carroll), poets (Blake, Paul Valery), mathematicians (Weyl and Hardy), popular science writers (Martin Gardener) and architects (Le Corbusier). An omission I found strange: there is no mention of Noether's theorem , which is a fundamental theorem linking continuous symmetries to conservation laws.

A colleague from economics recently said he was interested in how physicists think, and more specifically, how they come up with research ideas. I thought it would be a good idea to try to set up a list, based on my reading and experiences, of the various techniques, voluntary or involuntary, that I have seen physicists use: Yielding to inspiration : These ideas come from the subconscious. First one has to fill the brain with a lot of information, then a lot of thinking has to be done to activate the neuronal circuits. Then without predictability, an idea, inspiration or flash of insight comes. I have discussed this previously, in reference to the books on creativity and flow by Hadamard and Ciskszentmihalyi respectively. Identifying necessity : The mother of invention. A pressing need or question well-posed (by the community or by nature) often forces the answer. The idea is to work on, or identify, such questions. Criticizing : Weaknesses or shortcomings pointed out by others often provide strong impetus for creative research. I once got a paper out of something somebody said was trivial and pointless (turned out it was neither). Likewise, the critiques (when sincere) by anonymous referees can lead to major improvements in a scientific paper. Discussing : Even meandering discussions with colleagues and apparently irrelevant remarks can stick in the mind and stimulate advances. This is why - even the most isolated - physicists love talking shop. This category includes collaborations. Analogizing : The form of certain mathematical statements or experimental arrangements can be very suggestive. I have written about this in some detail earlier. Tinkering : Just playing, with equations or equipment, can lead to discoveries. This requires the willingness to sometimes do things that are discouraged or forbidden (my PhD work was in this category) or mathematically ill-defined. Admitting accidents : When tinkering goes out of control. Nonetheless, this can lead to scenarios that can expose us to things we had no idea existed. Thus, accidents must be tolerated, in physics as much as in chemistry. Being perceptive : The ability to notice things subtly out of the ordinary, or an overall structure from a few patterns. The corresponding discoveries are usually accompanied by the words, "That's funny...". Translating : Talking to experts from other disciplines is often very stimulating, as one is forced to frame or reframe one's own knowledge in new ways, and come into contact with analogous or related structures. Teaching : This is related to the previous category. Teaching is a wonderful way to keep in touch with the roots of the subject and questions from students can force us to think about the subject in new ways, find easier solutions, or go down unexplored paths. It gives us reasons to constantly reexamine the fundamentals of our knowledge. Debating : As distinguished from discussing. I use this very little myself, but some very distinguished people (including Nobel laureates) have admitted they get their best ideas during heated arguments with others. I have also seen less distinguished people debate but get nothing out of it -:). Persisting : When Newton was asked how he solved so many hard problems, he replied, "By thinking unto them." Even if one leaves the subject for a while, to come back afresh, a new attack often yields dividends. Believing in luck : An irrational confidence in being able to find the solution can play a role in solving a problem. Please note that I am talking about luck in point no. 13 -:). Thinking independently : The willingness to think differently from the established dogma. Probably there is no greater example of this than Einstein. Leveraging failure: The ability to paint a target where your arrow lands. Creative scientists typically manage to find something interesting about their project, though it may not be faithful - may even be opposed - to their original aim. A good example is Hawking's discovery of black hole radiation; he had originally set out to prove it does not happen. Undoubtedly there are more 'techniques' for making research advances in physics; I would love to hear about them from the readers.

This post is a review of What is Inside a Black Hole? by Stephen Hawking. It is a 67-page reissue of two of his essays from his longer book Brief Answers to the Big Questions . Apart from the title essay, it includes the essay Is Time Travel Possible ? Inside a black hole : The essay recalls the early black hole thoughts of John Mitchell, the grand impetus provided by Einstein's general theory of relativity, the quantitative work of Karl Schwarzschild, the pioneering contributions of John Wheeler, the papers of Oppenheimer, and the results of Chandrasekhar and Landau. The picture that emerged from these advances: stars above a certain mass (the 'Chandrasekhar limit') eventually collapse into a black hole; the simplest black hole is spherical; its radius (the 'event horizon') is where gravity becomes strong enough to trap light; at the center of the sphere is a singularity. The laws of physics break down at the singularity - space and time cease to exist there. In response to this catastrophic scenario, Roger Penrose proposed the Cosmic Censorship Principle: nature does not allow naked singularities: they are always hidden behind event horizons, so physics is well behaved outside of black holes (which is where all live observers are located). The Principle has yet to be proved. At this point Hawking describes a discovery, which stemmed from his trying to bring quantum mechanics to the study of black holes. He found that a black hole not only allows something to escape, it in fact radiates stuff continuously. A typical process involves particle-antiparticle pairs popping out of the vacuum just outside the black hole. One of the particles is swallowed by the black hole; the other escapes and appears to an observer as radiation coming from the black hole. The smaller the black hole, the faster it radiates. Hawking speculates about trapping one in orbit around Earth to power civilization. He also rues no one has found one yet, or he would have surely received a Nobel prize for his prediction. The biggest worry he states is the implication that when something falls into it, the black hole swallows up all of its information (the emission seems to be random and does not contain any information). This information loss could mean we cannot be certain about the past or the future of the universe as black holes can appear and cycle information into nonsense. This apparent loss of determinism is still one of the open problems in physics. Is time travel possible? Hawking starts this essay by pointing out that, as per special relativity, time slows down for moving observers. But the fastest one can move is the speed of light. At that velocity time comes to a stop. But that is not good enough - to travel into the past time needs to go backwards. While special relativity does not seem to allow for time travel, Hawking points out that general relativity does. This follows from Einstein's discovery that spacetime can be curved by massive objects (special relativity assumes a flat spacetime). In this context, Godel's universe and string theory offer (presently impractical) possibilities for time travel. Hawking discusses the use of wormholes for time travel. This would require warping spacetime using negative energy (from the vacuum via the Casimir effect), not very practicable currently. He concludes by discussing conceptual issues associated with time travel - Why haven't we been visited by people from the future? How does time travel jive with free will? Are there other universe which we can visit going back in time? He suggests the Chronology Protection Conjecture: the laws of physics prevent time travel so we can keep history straight (and historians employable). Summary Both essays are lucid and thoughtful; one can hear the master think. A highly recommended read.

This post is a review of The World Treasury of Physics, Astronomy and Mathematics (859 pages) . The book came out a while ago, in 1991. Since science moves on, one might expect that the material is quite dated (the classic advice is to read the latest in science and the oldest in literature). But I think the volume, which is a collection of essays and popular writing (all reprints) on the topics mentioned above, has merits which keep it relevant and valuable even today. For me, the book appealed on several fronts. The giants explain themselves : One of the attractions of the book is the large number of articles penned by the giants themselves who made the discoveries: we have Einstein writing on relativity, Planck writing on thermodynamics, Feynman writing on quantum mechanics, Pierre Curie writing on radioactivity, Dirac writing on electrons, Penrose and Hawking writing on black holes, Weinberg and Lemaitre and Hubble writing on cosmology, von Neumann and Turing writing on computers...and many more. While of course, the scientific material is contained in their published papers, it is revealing to see in these simplified and largely nontechnical accounts how these pioneers thought about the problems they were tackling, how they regarded the advances they themselves had made. This is the stuff that gets weeded out of the formal papers, but is of interest to anyone who wishes to attain a deeper understanding of the intellectual process and circumstances involved. The giants talk about the work of other giants : It is also curious to see what distinguished scientists thought of an area in which they are not the leaders, or even active workers (Bertrand Russell commenting on relativity; a panoramic perspective by Freeman Dyson on everything from superstrings to butterflies) ; or their philosophical stances towards their own domain of knowledge (Wigner with his famous essay on the unreasonable effectiveness of mathematics in physics, or Hardy with an extract from his classic book on what it means to do mathematics). I should mention that there are articles by lesser known scientists which are also very penetrating and useful. An example is the outstanding article on the nature of mathematics by J. D. Barrow. It has the best treatment I have seen of the question: do mathematicians make inventions or discoveries? I also enjoyed Alfred Adler's pungent essay on the culture of mathematics ("One good definition is worth three theorems") originally written for the New Yorker in 1972; and a prescient essay about AI by the medical doctor Lewis Thomas. The giants talk about the lives of other giants: There are some classics here, such as Einstein's obituary for Planck and Schwinger's eulogy for Tomonaga. Also some well known writers (but not scientific giants) writing about great scientists (C.P. Snow's sensitive obituary of Rutherford, Jagdish Mehra's anecdote about Dirac, Halmos writing on von Neumann, Lee Dembert on Erdos, Nigel Calder on Abdus Salam). The giants talk poetry and philosophy: The penultimate section in the book contains poems about physics, astronomy and mathematics. I encountered familiar gems by James Clerk Maxwell (writing on molecular dynamics), John Updike (neutrinos) but also discovered for the first time pieces by Goethe (physics), Wallace Stevens (chaos) and Rilke (machines). The last section in the book includes pieces that address the role of philosophy, creativity and belief in physics, mathematics and astronomy. Asimov has an entry, as do Thomas Kuhn, Karl Popper and Jacob Bronowski; Heisenberg and Einstein also pitch in, among others. Summary Overall a great collection. Good as entertainment, as reference, and as a gateway to further reading. A complaint: I thought there were too few articles by and about women (though Vivian Gornick's penetrating article on Alma Norovsky is wonderfully revealing, and it's reassuring to see a poem by the great Emily Dickinson in the collection). It would have been great to hear Marie Curie's voice, read something Emmy Noether wrote, or C. S. Wu's view of her motivations for doing her pioneering experiments.

This post is about the award of the Nobel prize in physics 2025 to John Clarke, Michel Devoret and John Martinis. From the announcement , it seems that the prize was given most directly for their observation of macroscopic quantum tunnelling in 1985, when Clarke was a professor at Berkeley, Devoret was a postdoc in his group, and Martinis was a senior graduate student. The announcement also referred to the impact this discovery had on the subsequent development of superconducting circuits and quantum computing, a field in which Devoret and Martinis are world leaders. Apart from their academic affiliations (to Yale and Santa Barbara, respectively) they are associated with Google, which is interested in quantum computing. Background The story goes back quite a bit, but we may pick it up in the early days of quantum mechanics. This was when it was realized that particles can quantum tunnel through barriers which would be too high for them to climb over if the particles were behaving classically. An early and famous example of the identification of quantum tunneling was in the process of alpha decay , a type of radioactivity. A more sophisticated type of quantum tunneling was proposed by Brian Josephson after the discovery of superconductivity. Superconductors allow flow of current without resistance, basically because electrons pair up in a coordinated fashion. Josephson predicted that if a thin slice of insulating material was placed between two superconductors, pairs of electrons would pass through the barrier, in a form of quantum tunneling. This effect was eventually observed and the effect was named after Josephson (who is still alive, though no longer a practicing physicist), who received the Nobel for his discovery in 1973. Following suggestions by Tony Leggett , Clarke's group investigated macroscopic (large) Josephson junctions at various temperatures and demonstrated quantum tunneling as well as quantization of energy in the device. This pioneering experiment led, over decades of development, to the Josephson (phase, flux and charge) qubits realized using electrical circuits (the Josephson junction can be electrically thought of as a nonlinear inductor). Today, based on these qubits, superconducting circuits pose themselves as one of the two leading platforms for the implementation of a quantum computer. The other candidate consists of trapped ions, which has been acknowledged with a couple of Nobels ( Paul , Dehmelt , Wineland ). This year's prize may be understood as an acknowledgement of the large community of superconducting circuits researchers who are using these cool devices to investigate fundamental physics as well as life-changing applications. From a broad perspective, the Josephson qubits are sometimes thought of as artificial atoms whose properties can be engineered via nanofabrication, as opposed to real atoms, whose properties are determined by nature. Afterword One of the cool experiments I heard Devoret give a talk on some years ago was how To catch and reverse a quantum jump mid-flight , eventually published in Nature. Transitions in quantum systems were thought to be fundamentally random and unpredictable, but using his superconducting system Devoret showed (it was actually his graduate student's idea) that such jumps could be predicted and indeed reversed deterministically. Of course, this is a nontrivial insight into the fundamental nature of quantum mechanics. But one can also apply it to practical problems such as error correction in a quantum computer.

In 2022, I became a minor celebrity among my friends for a week for correctly predicting that Alain Aspect would win the physics Nobel prize. In this post I list some contenders for the prize this year, which will be announced next week, Tuesday, October 7. Topological physics : Topological physics studies the fundamental properties of matter and systems that are protected by virtue of their underlying geometric shape and symmetry, rather than by local forces. A name that has been in consideration for a long while is Michael Berry , whose eponymous phase plays a fundamental role in explaining the quantum Hall effect and topological insulators. Another major player in the field is Alexei Kitaev , whose work also connects to quantum computing. Quantum cryptography : Although a quantum computer seems some distance away from being built, quantum cryptography systems went commercial quite some time ago. The pioneers in this area were people like Peter Shor , Charles Bennett , and Giles Brassard . Shor, through his demonstration that quantum computers can break the RSA cryptosystem , pioneered post-quantum cryptography. Bennett and Brassard developed the BB84 protocol for cryptography. Metamaterials : This is an area yet to be recognized by a Nobel, though quite deserving. Metamaterials are substances designed by human beings which have properties not naturally found in nature, such as negative refractive index. One of the high profile aspects of the subject is invisibility research. The pioneers of the field were Victor Veselago , and John Pendry . Graphene redux : Some of the prominent journals in physics have alphabets associated with them: the Physical Review A (atomic and molecular physics), B (condensed matter physics), C (nuclear physics), D (particle physics and cosmology) , E (statistical physics, networks). There was a time when graphene as a research topic was so popular a colleague joked they would have to start a journal entirely devoted graphene: Physical Review G. While that excitement has somewhat subsided, bilayer graphene is now a hot topic, important for energy storage and electronics as well as showing unconventional superconductivity. The pioneers in this area are Pablo Jarillo-Herrero (experiment) and Allan H. MacDonald (theory). Orbital angular momentum of light : One might think that everything about light became known after Maxwell set down his classical theory and later, quantum mechanics clarified the photon nature of electromagnetic radiation. It therefore came as a surprise in 1992 when it was pointed out that photons can carry much more than the one unit of spin angular momentum (in their polarization) recognized thus far. They can carry practically an infinite amount of orbital angular momentum in their wavefronts. This discovery has revolutionized many fields, such as quantum communication, imaging and nanotechnology. Les Allen was one of the pioneers, but sadly he passed away in 2016. Other major contributors to the field are Johannes Woerdmann and Miles Padgett . Afterword This is not a comprehensive list. I apologize to anyone whose field has not been represented - astronomy for example. For other forecasts, see: physiology or medicine , literature , chemistry . I did not find any good links for economics or peace.

It has been said that the death and taxes are the two inevitable facts of life. To this list I am inclined to add reviews. It seems no matter who you are - an academic trying to get research money, a company trying to land a government contract, a magnate trying to take over the entire steel industry of a whole country - you have to write some sort of document which is going to be reviewed by someone. In this post I will compare and contrast two types of review structures that I have been personally exposed to: scientific and literary. Of course, many other types of reviews exist, for cinematic and musical performances, for yearly performances at jobs and contracts, for restaurants, etc. But I will stick to the ones I have experience with. Scientific review : For brevity I will consider only the submission and review of papers. Most scientific journals are open to accepting papers that have already been posted on the arxiv. This is an informal bulletin board which is heavily in use for posting the latest results, without peer review, long before they appear in a peer-reviewed scientific journal. It helps share the latest news, and also establish priority (a big deal in academia). All journals I know of accept only electronic submissions. Submissions are open around the year. Each publishing house (the American Physical Society, the Institute of Physics publisher, Springer, etc.) has its own submission portal. Typically, a paper must be submitted to a single scientific journal at a time, and can be submitted to a second journal only if it has been rejected by the previous journal. The paper usually comes back with comments from technical experts on the subject; it is rare not to hear back at all from the journal, though in some cases the editor in charge might need prodding to get the article reviewed in a timely fashion. The authors are usually allowed a second round to satisfy the objections of the referees. The rejection/acceptance letter usually arrives from an editor in the form of an email. There is a mechanism for appealing a rejection at most journals. I have seen very few appeals being successful. Usually, a correct scientific paper can be published in some journal. Meaning it can find a home somewhere, though the journal might not be of as high impact factor, relatively speaking, compared to where it was first sent. For example, in my field, I might send a paper to Nature; it might eventually be published Optics Express. It's rare for a bonafide scientific result, no matter its importance, not to be published somewhere. Literary review: For brevity I will consider the submission and review of fiction and nonfiction articles. Almost no literary magazine will accept writing that has appeared in public in any form elsewhere - even in a blog. There are exceptions for reprints and anthologies. Many magazines accept hard copy submissions, in addition to electronic, and provide a street mailing address on their website. Most magazines are only open for submissions between well defined dates, typically a few months of the year. Then they close for their reading period(s). A large number of literary magazines accept electronic submissions through the Submittable portal. Most literary magazines allow multiple submissions, meaning a story might be submitted to many magazines simultaneously. The proviso is that, if the article is accepted somewhere, the author should perform the courtesy of withdrawing it from the remaining magazines immediately. Most submissions never receive a reply indicating a rejection. The reason is that magazines are overwhelmed by submissions, and are shortstaffed. E.g. in 2021 the New Yorker received about 1500 fiction submissions, i.e. about 10 a week. So if you don't hear back, it's probably safe to assume you got rejected. In my experience, most acceptances occur within 2-4 weeks of submission; the editor/reviewer read it, thought it was good and fit the mission of the journal, and accepted it. I have seen some exceptions, though; I once got accepted after 4 months. Some magazines will send a stock rejection letter/email around 6-8 months after submission. Acceptance is usually in the form of an email, though once I did receive a call from the editor informing me of the news. Very few journals provide feedback on a piece; none, to my knowledge allow a second round for 'fixing mistakes'. It is entirely possible, and in fact the fate of most stories, that they are never published in any literary magazine. Afterword It is interesting to compare the two fields. Although science is suppose to be more objective than the arts, I find the reviewing process in the literary magazines to be far fairer. Scientific papers are reviewed by our peers, a fact that immediately presents a conflict of interest since they are competing with the authors for resources such as recognition, grant money and career advancement. In my experience it is always a surprise to receive an unbiased review. Editors also operate under a conflict of interest as they try to focus on securing publication for results from established groups - these are what raise the impact factors of their journals. Literary magazines, in my experience, suffer from fewer of these problems. Editors/reviewers usually have no sharp conflicts of interest with the authors. Generally the operating principle is that if they find the piece suits their purpose, i.e. it is the style of story they believe in, they don't care where it comes from, and act quickly and decisively. Hence a lot of authors get picked from the `slush pile'. Of course, the resume of the author can play a role, but many magazines advertise the fraction of unpublished authors they accept in each issue. It's usually quite substantial. And the reviews I have received have been honest - even when I disagree with them - and to the point. Maybe the review is more clear cut because unlike in science there is no accounting for literary truth (which boils down to someone's personal taste) and hence less room for argument. In any case, there seems to be no way around the review process.

This post is about the recently reported experimental confirmation of a theoretical prediction of Stephen Hawking about black holes. First a bit about the theorem, and then the experiment: Hawking's area law : A black hole is a region in space where matter has been compressed to such a small volume that nothing, not even light, can escape its gravitational pull. Black holes are interesting since the effects of gravity - which are typically weak elsewhere in the universe - are extreme in their case. Therefore, their study can tell us about the nature of the gravity (and possibly its relation to quantum mechanics), the dynamics of galaxies, the character of spacetime, etc, etc. A black hole is not a point-like object; it has a boundary at a nonzero radius. If anything approaches closer than this boundary, it cannot escape the black hole. This boundary is called the event horizon of the black hole. We can think of the event horizon as a sphere surrounding the black hole, out at some radius. Now, the second law of thermodynamics says that disorder (more technically entropy) cannot decrease in the universe. But we could throw a disordered system (like my clothes closet) into a black hole and then the total entropy of the universe would decrease. This would violate the second law of thermodynamics. The second law could be saved, realized Jacob Bekenstein , if the black hole carried its own entropy and it registered an increase larger than the entropy of the object being thrown into it. This would result in a net increase of the entropy of the universe and thus save the second law. Now Bekenstein knew of Stephen Hawking's theorem, derived from classical general relativity in 1971, that the surface area of a black hole event horizon never decreases. He put two and two together in 1972 and argued that a black hole's entropy should be proportional to the surface area of its event horizon. Hawking himself opposed Bekenstein's idea initially. He argued that black holes cannot have entropy as they do not have temperature and do not emit radiation. But he realized that this was only true if he took the laws of classical physics into account. When he included quantum mechanics in his calculation, he found that black holes indeed have temperature, emit (Hawking) radiation and possess entropy. The formula for the temperature of a black hole is now engraved on Hawing's gravestone at Westminster Abbey. A simple demonstration of Hawking's area law: throw a black hole into another black hole. The result? A third black hole, of course. The area law says that the event horizon area of the resulting black hole is larger than the sum of the areas of the two original black holes. And this is exactly what the experiment observed. The experiment at LIGO : As its name says, the Light Interferometer Gravitational Wave Observatory can detect gravitational waves (the work I am referring to is a collaboration with VIRGO and KAGRA ). Interestingly, the collision - coalescence - of two black holes releases gravitational waves as a way of shedding energy and angular momentum. The pre- and post-merger gravitational wave signals - which contain information about the frequencies and damping rates of the black hole oscillation modes - can be used to infer the mass and spin of each black hole. And mass and spin are the only two parameters we need to know to characterize these black holes - in this sense black holes are astonishingly simple objects. In fact, Equation 1 in the LIGO paper quotes the beautifully compact formula for the event horizon area in terms of the black hole mass and spin. Plugging their data into this formula, the experimentalists confirmed Hawking's area theorem. Afterword As you may expect, Hawking radiation causes a black hole to radiate - shrink its event horizon area - and eventually evaporate into nothing. So Hawking's area theorem should perhaps be stated in a more refined manner: any process that increases the mass of a black hole cannot decrease its entropy and hence its event horizon area. For more nuances, read the paper.

The Nobel prize for physics will be announced on Tuesday October 7, 2025. As a warm up exercise in preparing for this event, I will dedicate this post to some scientists who missed out on a Nobel. Nikola Tesla : His greatest and most enduring discovery was the alternating current (AC) motor and its use for electrification of modern societies. He made many other discoveries, including some of the first wirelessly controlled machines and electrical charging at a distance. Although he won a large number of prizes and medals, he was never awarded the Nobel. Theories ascribe this to his idiosyncratic and critical personality and his opposition to quantum physics and relativity. Arnold Sommerfeld : Sommerfield's contributions lay in significantly extending the Bohr model of the atom using ideas from classical mechanics, before Schrodinger and Heisenberg ushered in the new quantum mechanics. The lack of a Nobel is ascribed to the absence of a single pathbreaking achievement on his part. Consolation can perhaps be found from i) the Google claim that Sommerfeld holds the record for being nominated the most times (84) for the physics Nobel and ii) four of his students - Heisenberg, Pauli, Debye and Bethe - won Nobels. S. N. Bose : He was responsible for developing Bose-Einstein statistics (particles obeying these statistics are called bosons in his honor) and gave his name to the Bose-Einstein condensate. Apparently his nomination was examined and found wanting by the physicist Oscar Klein, the expert appointed by the Nobel committee. Some blame for the non-award is also given to Bose's complete indifference to honors and the consequent lack of advocacy and political support for his candidature. Lise Meitner : Meitner (along with her nephew Otto Frisch) identified (and named) nuclear fission from the experimental data of Hahn and Strassmann. Apart from being a fundamental phenomenon in physics, this of course forms now the basis of military, commercial and scientific technologies: it was a monumental discovery. She was nominated for the Physics (30 times) as well as Chemistry (19 times) Nobels. That she was not awarded could well be ascribed to sexism as well as antisemitism. Georges Lemaitre : He was the first person to relate astronomical observations to the expansion of the universe, and hence was the progenitor of what is now called the Big Bang theory. Guesses as to why he was not awarded the physics Nobel range from astronomy being not so well recognized at the time to lack of experimental evidence for the Big Bang in those early days. C. S. Wu : She performed the first experiments showing parity violation in nature - the fact that the laws of physics were not always mirror-symmetric. This fundamental discovery won the theorists C. N. Yang and T. D. Lee, who had predicted it, a Nobel. Wu was excluded, a fact some put down to pure sexism, but the real issue was likely more complicated . Edwin Hubble : Indisputably a giant in astronomy, he experimentally established that there were galaxies beyond our own (the Milky Way) and that they were receding, since the universe is expanding. His exclusion is also ascribed to the fact that astronomy was not recognized as a field by the Nobel committee (apparently the first Nobel prize to target astronomy directly was awarded in 1974, see below). E.C.G. Sudarshan : Sudarshan's Nobel-worthy contribution involved an explanation of the weak nuclear force. This historically preceded, but was overshadowed by, a paper on the same subject by Feynman and Gell-Mann. No one was awarded a Nobel for this exact work, but several Nobels were given out for advances in understanding of the weak force. Jocelyn Bell Burnell : She was the graduate student who identified the first pulsar . Burnell did not make the list of Nobel awardees (Martin Ryle and Antony Hewish, her PhD advisor) in 1974 for the discovery, both for reasons of sexism as well as academic low rank (professors, not graduate students, were supposed to get Nobel prizes). Happy to report that both ceilings were later broken by Donna Strickland . Vera Rubin : She found evidence for dark matter . She was the first to show that galaxies must contain large quantities of invisible matter - or else the gravitational pull keeping their stars in orbit cannot be accounted for. Reasons proposed for why she was not awarded the Nobel range from sexism to lack of definitive experimental evidence for dark matter. Afterword Soon: predictions for the 2025 Physics Nobel!

This is a review of David Nasaw 's biography of Andrew Carnegie, the Scottish-born American industrialist and philanthropist. At 880 pages, the book is extensive and detailed. I will summarize my report along what I perceived to be the main themes of the book. Life and Family : The book moves chronologically, with Carnegie's early years in Dumfermline (Scotland), in a weaver's family; followed by his family immigrating to Pittsburgh, America (led by his mother) to escape poverty; his careers first in telegraphy and then in the railroad industry; his certified rise to riches by the approximate age of 30; his late marriage; fatherhood at 60; and his death at 83 years of age leaving behind his wife and daughter. In the book, Carnegie comes across as upbeat and energetic, charming and loquacious. These qualities are shown to be crucial to his rise to wealth and his success as an industrialist; and hindrances to his efforts at influencing politics and commandeering social situations: our best qualities can be our worst enemies. Of course, there is no doubt that he certainly had an immense influence on America and even Europe, if not on the rest of the world. I thought the book does a very good job of describing Carnegie's personal life. Relationship to wealth and labor : It emerges from the book that Carnegie was proud of his working class roots. He claimed that being born poor was the best start to becoming rich. He did not think hard work was necessary for acquiring riches, as he had not spent many hours per day working after he had turned 30, though he had kept long hours as a younger man. Buying and trading in stocks was not Carnegie's thing; he was a manufacturer. He needed to get a product out. He was a philanthropist from age 30: he believed a man who died rich was a failure. Upon his death he left $26 million to be distributed among various entities. He opposed imperialism and war, as being inimical to big business; the book suggests he died from the shock of World War I starting. The book shines in its detailed depiction and analysis of Carnegie's business thinking and maneuvers, his ideas about society and its advancement, and especially his thought and actions about industrial labor, with the crescendo occurring at the infamous and violent confrontation with labor unions at his steel plant in Homestead, PA in 1892. Relationship to knowledge and education : One of the running themes in the book that caught my attention was Carnegie's concern about his own education. Someone (can't remember who, and I am paraphrasing) said Carnegie collected intellectuals like other millionaires collect art. Especially close were his relations to philosopher Herbert Spencer; poet and critic Matthew Arnold; novelist Mark Twain; and politicians Teddy Roosevelt and William Gladstone. With his wealth Carnegie funded libraries, observatories, music halls and natural history museums (to my knowledge he is the only millionaire with a dinosaur named after him - the Diplodocus Carnegii ). He toured Europe whenever he could, catching up on its history and geography. He was a great reader, constantly quoting full acts from Shakespeare and lines from Burns, and always ready with interesting and funny stories. He was an ambitious writer as well. His books include The Gospel of Wealth, Success and How to Attain it, The ABC of Money, as well as his autobiography. Carnegie was a staunch abolitionist and promoted the educator Booker T. Washington. Summary Given the current political situation in the US and the involvement of millionaires in it, some people might find the book interesting from that perspective. There is also an entire chapter on tariffs. I would have liked to see more about Carnegie's interactions (maybe there weren't many) with the other millionaires who were his contemporaries: Rockefeller, J.P. Morgan, and Vanderbilt. All in all an amazingly substantial and well-written book.

Millionaires (this includes billionaires) who dropped out of high school or college are often invited to universities to speak to students, sometimes to give commencement addresses. A famous (and entertaining) example is that of Bill Gates speaking at Harvard . Recently, Adani spoke at one of the prestigious Indian Institutes of Technology. More recently, a relative of mine told me that an alum (who had flunked the 11th grade) of his daughter's school had been invited back to speak at her school. A lot of people, including my relative, ask me - what is the point of education if one can become a millionaire without even clearing 11th grade? This post is aimed at discussing this question. For the sake of argument, I will break the discussion up into smaller pieces. Is it easy to become a millionaire ? I would not say it is easy, but it is not as hard as one might think. Of course, a lot depends on variables such as the person's background - if they are born in extreme poverty then they may find it difficult to become very rich; if they are born in a millionaire's family, wealth is likely almost automatic. But let's look at the numbers - Google says there are 58 million dollar-millionaires in the world today. This is about 1.5% of the global adult population. The chances of becoming a millionaire are therefore small, but not astronomically so. On the other hand, there are only about 3000 billionaires in the world today. That's about one ten-millionth of the world population. So a real measure of extreme financial success might be the achievement of billionaire, rather than millionaire status. Still, flunking 11th grade and becoming a millionaire seems to present a dramatic counterexample to the necessity for education. Can everyone failing 11th grade become a millionaire ? This question can be settled by making a list of all 11th grade dropouts and counting the number of millionaires in that pool. I invite the reader to confirm that the answer is no. The fact is that achievement of millionaire status depends on many factors, including some luck, and is not exclusively inversely correlated with education (otherwise we should just shut the high schools down after 11th grade; or force our children to fail). In fact, Google says: "Approximately 88% of millionaires have a college degree, according to a comprehensive study by Ramsey Solutions . This is significantly higher than the general population, where only about 38% of people have a college degree. The study also found that 52% of millionaires hold a master's or doctoral degree, compared to just 13% of the general population." It also says that about 70% of billionaires hold at least a college degree. These facts imply that although a significant number of currently wealthy folks dropped out of or never attended college, they are still in a minority. Going purely by the numbers, the probability is much higher that you will become a millionaire if you have an advanced degree. Millionaires and billionaires are, on average, actually better educated than the rest of the population. We get to hear more about dropouts like Jobs, Gates, and Zuckerberg because they provide dramatic examples. For every such example, if the numbers are correct, we can find multiple counter-examples: Jeff Bezos graduated Princeton for college, Warren Buffet has a masters degree, Elon Musk has two bachelors degrees (though Buffet and Musk both argue against the need for higher education), Larry Page has a masters, Sergey Brin has a masters (although Page and Brin both dropped out of the PhD program at Stanford). Does dropping out of school indicate the end of education ? Typically, those who dropped out of high school, college or PhD programs and became millionaires climbed a learning curve as steep or even steeper than they would have in conventional education. Musk spent enormous amounts of time learning about coding; Adani worked first as a diamond sorter then as a manager of a plastics factory (he believes he would have benefited from more formal education); Gates still reads one book per week and watches lectures constantly. I will end this part with a quote from the late Charlie Munger , Buffet's partner at Berkshire Hathaway: " In my whole life, I have known no wise people (over a broad subject matter area) who didn’t read all the time—none. Zero. You’d be amazed at how much Warren reads—and how much I read. My children laugh at me. They think I’m a book with a couple of legs sticking out. " Conclusion Formal education provides knowledge, practical experience brings wisdom. Being educated is helpful, because then you know (much) better what you are doing. In either case, you cannot afford to stop learning. Even if you are a (m,b)illionaire. Afterword I am currently reading David Nasaw's biography of Andrew Carnegie , the Scottish born American billionaire (his legacy includes Carnegie Hall, Carnegie-Mellon University, the Carnegie Endowment for International Peace, etc.), who in the early 1900s was perhaps the richest person in the world. What I find remarkable about him, in addition to his tremendous business drive, was his great worry and obsession about being educated. He read the great authors extensively; wrote complaint letters to the Pittsburgh municipality about underfunded public libraries when he was still poor; took off to visit museums, galleries and monuments in Europe the first thing after becoming financially independent. I hope to review the book, in the near future, on this site.