The nature of existence is significantly different if there is a finite amount of matter or objects in the universe, as opposed to there being an infinite quantity in existence. Some proposals claim there may be an infinite number of universes in a multiverse and many cosmological models have spatial sections that are infinite, implying an infinite number of particles, stars, and galaxies. However, infinity is quite different from a very large number! Following David Hilbert, one can suggest these unverifiable proposals cannot be true: the word “infinity” denotes a quantity or number that can never be attained, and so will never occur in physical reality.38 He states:
Our principal result is that the infinite is nowhere to be found in reality. It neither exists in nature nor provides a legitimate basis for rational thought . . . The role that remains for the infinite to play is solely that of an idea . . . which transcends all experience and which completes the concrete as a totality . . .
This suggests “infinity” cannot be arrived at, or realized, in a concrete physical setting; on the contrary, the concept itself implies its inability to be realized!
Thesis I2: The often claimed physical existence of infinities is questionable.The claimed existence of physically realized infinities in cosmology or multiverses raises problematic issues. One can suggest they are unphysical; in any case such claims are certainly unverifiable.
This applies in principle to both small and large scales in any single universe:
The existence of a physically existing spacetime continuum represented by a real (number) manifold at the micro-level contrasts with quantum gravity claims of a discrete spacetime structure at the Planck scale, which one might suppose was a generic aspect of fully non-linear quantum gravity theories. In terms of physical reality, this promises to get rid of the uncountable infinities the real line continuum engenders in all physical variables and fields40. There is no experiment that can prove there is a physical continuum in time or space; all we can do is test space-time structure on smaller and smaller scales, but we cannot approach the Planck scale.
Infinitely large space-sections at the macro-level raise problems as indicated by Hilbert, and leads to the infinite duplication of life and all events. We may assume space extends forever in Euclidean geometry and in many cosmological models, but we can never prove that any realised 3-space in the real universe continues in this way—it is an untestable concept, and the real spatial geometry of the universe is almost certainly not Euclidean. Thus Euclidean space is an abstraction that is probably not physically real. The infinities supposed in chaotic inflationary models derive from the presumption of pre-existing infinite Euclidean space sections, and there is no reason why those should necessarily exist. In the physical universe spatial infinities can be avoided by compact spatial sections, resulting either from positive spatial curvature, or from a choice of compact topologies in universes that have zero or negative spatial curvature. Machian considerations to do with the boundary conditions for physics suggest this is highly preferable; and if one invokes string theory as a fundamental basis for physics, the “dimensional democracy” suggests the three large spatial dimensions should also be compact, since the small (“compactified”) dimensions are all taken to be so. The best current data from CBR and other observations indeed suggest k = +1, implying closed space sections for the best-fit FL model.
The existence of an eternal universe implies that an infinite time actually exists, which has its own problems: if an event happens at any time t0, one needs an explanation as to why it did not occur before that time (as there was an infinite previous time available for it to occur); and Poincaré eternal return will be possible if the universe is truly cyclic. In any case it is not possible to prove that the universe as a whole, or even the part of the universe in which we live, is past infinite; observations cannot do so, and the physics required to guarantee this would happen (if initial conditions were right) is untestable. Even attempting to prove it is future infinite is problematic (we cannot for example guarantee the properties of the vacuum into the infinite future—it might decay into a state corresponding to a negative effective cosmological constant).
It applies to the possible nature of a multiverse. Specifying the geometry of a generic universe requires an infinite amount of information because the quantities necessary to do so are fields on spacetime, in general requiring specification at each point (or equivalently, an infinite number of Fourier coefficients): they will almost always not be algorithmically compressible. All possible values of all these components in all possible combinations will have to occur in a multiverse in which “all that can happen, does happen”. There are also an infinite number of topological possibilities. This greatly aggravates all the problems regarding infinity and the ensemble. Only in highly symmetric cases, like the FL solutions, does this data reduce to a finite number of parameters, each of which would have to occur in all possible values (which themselves are usually taken to span an infinite set, namely the entire real line). Many universes in the ensemble may themselves have infinite spatial extent and contain an infinite amount of matter, with all the problems that entails. To conceive of physical creation of an infinite set of universes (most requiring an infinite amount of information for their prescription, and many of which will themselves be spatially infinite) is at least an order of magnitude more difficult than specifying an existent infinitude of finitely specifiable objects.
One should note here particularly that problems arise in the multiverse context from the continuum of values assigned by classical theories to physical quantities. Suppose for example that we identify corresponding times in the models in an ensemble and then assume that all values of the density parameter and the cosmological constant occur at each spatial point at that time. Because these values lie in the real number continuum, this is a doubly uncountably infinite set of models. Assuming genuine physical existence of such an uncountable infinitude of universes is the antithesis of Occam’s razor. But on the other hand, if the set of realised models is either finite or countably infinite, then almost all possible models are not realised. And in any case this assumption is absurdly unprovable. We can’t observationally demonstrate a single other universe exists, let alone an infinitude. The concept of infinity is used with gay abandon in some multiverse discussions, without any concern either for the philosophical problems associated with this statement, or for its completely unverifiable character. It is an extravagant claim that should be treated with extreme caution.
38An intriguing further issue is the dual question: Does the quantity zero occur in physical reality? This is related to the idea of physical existence of nothingness, as contrasted with a vacuum. A vacuum is not nothing!
40To avoid infinities entirely would require that nothing whatever is a continuum in physical reality (since any continuum interval contains an infinite number of points). Doing without that, conceptually, would mean a complete rewrite of many things. Considering how to do so in a way compatible with observation is in my view a worthwhile project.
So, given this discussion of infinities, the answer to the doubly hypothetical question, “Can God make a rock so big he can’t pick it up?” is likely a “Yes”! – D.O.
The Great Courses offers a number of excellent courses on DVD (also streaming and audio only). Here are my favorite episodes. (Note: This is a work in progress and more entries will be added in the future.)
Course No. 153 Einstein’s Relativity and the Quantum Revolution: Modern Physics for Non-Scientists, 2nd Edition – Richard Wolfson Lecture 8 – Uncommon Sense—Stretching Time “Why does the simple statement of relativity—that the laws of physics are the same for all observers in uniform motion—lead directly to absurd-seeming situations that violate our commonsense notions of space and time?” Lecture 9 – Muons and Time-Traveling Twins “As a dramatic example of what relativity implies, you will consider a thought experiment involving a pair of twins, one of whom goes on a journey to the stars and returns to Earth younger than her sister!” Lecture 12 – What about E=mc2 and is Everything Relative? “Shortly after publishing his 1905 paper on special relativity, Einstein realized that his theory required a fundamental equivalence between mass and energy, which he expressed in the equation E=mc2. Among other things, this famous formula means that the energy contained in a single raisin could power a large city for an entire day.” Lecture 16 – Into the Heart of Matter “With this lecture, you turn from relativity to explore the universe at the smallest scales. By the early 1900s, Ernest Rutherford and colleagues showed that atoms consist of a positively charged nucleus surrounded by negatively charged electrons whirling around it. But Rutherford’s model could not explain all the observed phenomena.” Lecture 19 – Quantum Uncertainty—Farewell to Determinism “Quantization places severe limits on our ability to observe nature at the atomic scale because it implies that the act of observation disturbs that which is being observed. The result is Werner Heisenberg’s famous Uncertainty Principle. What exactly does this principle say, and what are the philosophical implications?” Lecture 21 – Quantum Weirdness and Schrödinger’s Cat “Wave-particle duality gives rise to strange phenomena, some of which are explored in Schrödinger’s famous ‘cat in the box’ example. Philosophical debate on Schrödinger’s cat still rages.”
Course No. 158 My Favorite Universe – Neil deGrasse Tyson Lecture 8 – In Defense of the Big Bang “We now know without doubt how the universe began, how it evolved, and how it will end. This lecture explains and defends a “theory” far too often misunderstood.”
Course No. 415 The Will to Power: The Philosophy of Friedrich Nietzsche Robert C. Solomon & Kathleen M. Higgins Lecture 7 – Nietzsche and Schopenhauer on Pessimism “Schopenhauer, the severe pessimist, is a looming presence in Nietzsche’s thought. Nietzsche felt the weight of Schopenhauer’s pessimism, and struggled to counter it by embracing “cheerfulness,” creative passion, and an aesthetic viewpoint.” Lecture 19 – The Ranking of Values – Morality and Modernity “Why did Nietzsche refuse to think of values as being either objective or subjective? Why did he hold that values are earthly and culture- and species-specific? Why did he argue that, in the final analysis, there are only healthy and unhealthy values, and that modern values are unhealthy?” Lecture 22 – Resentment, Revenge, and Justice “We continue our discussion of Nietzsche’s idea of resentment, adding to it his ideas about revenge and justice. We revisit his condemnation of asceticism, the self-denial that is often a part of extreme religious practice, in light of these new ideas.”
Course No. 443 Power over People: Classical and Modern Political Theory – Dennis Dalton Lecture 10 – Marx’s Critique of Capitalism and the Solution of Communism “Karl Marx’s communism provided what is probably the best known ideal society. He blamed not only private property, but the entire institution of capitalism for the inequality and injustice in society. His program has never been implemented, certainly not in the Soviet Union. Marx never advocated totalitarian or despotic rule. Although his historical determinism has been discredited, his social criticism remains relevant. The democratic dilemma boils down to this: the more liberty, the less equality; and the more equality, the less liberty.” Special Note: I will eventually be adding more of the episodes from this excellent course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 700 How to Listen to and Understand Great Music, 3rd Edition – Robert Greenberg Lecture 23 – Classical-era Form—Sonata Form, Part 1 “In Lectures 23 and 24 we examine sonata-allegro form, but first, we observe the life and personality of the extraordinary Wolfgang Mozart. We discuss the many meanings and uses of the word “sonata.” The fourth movement of Mozart’s Symphony in G Minor, K. 550, is analyzed and discussed in depth as an example.” Special Note: I will eventually be adding more of the episodes from this excellent course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 730 Symphonies of Beethoven – Robert Greenberg Lecture 11 – Symphony No. 3—The “New Path”—Heroism and Self-Expression, III “Lectures 9 through 12 focus on Symphony No. 3, the Eroica Symphony. This key work in Beethoven’s compositional revolution resulted from his crisis of going deaf. Beethoven’s struggle with his disability raised him to a new level of creativity. Symphony No. 3 parallels his heroic battle with and ultimate triumph over adversity. The symphony’s debt to Napoleon is discussed before an analysis.” Lecture 13 – Symphony No. 4—Consolidation of the New Aesthetic, I “Lectures 13 through 16 examine Symphony No. 4 in historical context and in its relationship to opera buffa. Symphony No. 4 is the most infrequently heard of his symphonies. We see how it represents a return to a Classical structure. Its framework is filled with iconoclastic rhythms, harmonies, and characteristic motivic developments that mark it as a product of Beethoven’s post-Eroica period.” Lecture 23 – Symphony No. 7—The Symphony as Dance, I Lecture 24 – Symphony No. 7—The Symphony as Dance, II “Lectures 23 and 24 discuss Beethoven’s Symphony No. 7 with references to the historical and personal events surrounding its composition. The essence of the symphony is seen to be the power of rhythm, and originality is seen to be an important artistic goal for Beethoven.” Lecture 31 – Symphony No. 9—The Symphony as the World, IV “The last five lectures are devoted to Symphony No. 9, the most influential Western musical composition of the 19th century and the most influential symphony ever written. We see how this work obliterated distinctions between the instrumental symphony and dramatic vocal works such as opera. Also discussed are Beethoven’s fall from public favor in 1815, his disastrous relationship with his nephew Karl, his artistic rebirth around 1820, his late compositions, and his death in 1827.”
Course No. 753 Great Masters: Tchaikovsky-His Life and Music – Robert Greenberg Lecture 1 – Introduction and Early Life “Tchaikovsky was an extremely sensitive child, obsessive about music and his mother. His private life was reflected to a rare degree in his music. His mother’s death when he was 14 years old was a shattering experience for him—one that found poignant expression in his music.” Lecture 6 – “My Great Friend“ “With the generous financial support of Nadezhda von Meck, Tchaikovsky lived abroad, and in 1878 resigned from the Moscow Conservatory to compose full time. His Fourth Symphony was premiered in Moscow and was quickly followed by the brilliant Violin Concerto in D Major, which became a pillar of the repertoire within a few years.”
Course No. 754 Great Masters: Stravinsky-His Life and Music – Robert Greenberg Lecture 2 – From Student to Professional “Rimsky-Korsakov was so impressed with Stravinsky’s Piano Sonata in F♯ minor (1904) he agreed to take Stravinsky as a private student. In 1909, Stravinsky met the impresario Serge Diaghilev, who commissioned Stravinsky to write a ballet on the folk tale The Firebird, which was followed by the ballet Petrushka, a great success. Stravinsky’s next score, The Rite of Spring, would become arguably the most influential work of its time.”
Course No. 756 Great Masters: Mahler-His Life and Music – Robert Greenberg Lecture 7 – Symphony No. 6, and Das Lied von der Erde “Three events shattered the Mahlers’ lives in 1907: his resignation from the Royal Vienna Opera, the death of their elder daughter, and the diagnosis of his heart disease. In 1908, Mahler threw himself into composing Das Lied von der Erde as an attempt to find solace from the grief of his daughter’s death. The work is a symphonic song cycle about loss, grief, memory, disintegration, and transfiguration.”
Course No. 758 Great Masters: Liszt-His Life and Music – Robert Greenberg Lecture 2 – A Born Pianist “Liszt was surrounded by music from infancy and began to reveal his musical gifts at about age five. He stunned his teachers and, at his first performance at age 11, astonished reviewers and his audience. When Liszt was 15, his father died, sending Franz into depression and apathy for three years. He was finally blasted out of his lethargy by the July Revolution of 1830.” Lecture 7 – Rome “By the 1850s, Liszt became the focal point of a debate concerning program music versus absolute music and expression versus structure. Twenty years before, Liszt and his fellow young Romantic musicians had a common goal: to create a new music based on individual expression. As they grew older, many became conservative, but Liszt never lost his revolutionary spirit. But brokenhearted by the death of his daughter, he turned to the Catholic Church to find solace.”
Course No. 759 Great Masters: Robert and Clara Schumann-Their Lives and Music – Robert Greenberg Lecture 8 – Madness “In Düsseldorf, Robert was inspired to write the Symphony No. 3 in E-flat Major, along with trios, sonatas, orchestral works, and pieces for chorus and voice and piano. Robert and Clara also met Johannes Brahms there; he became a lifelong friend and source of strength for Clara. In 1854, Robert attempted to drown himself in the Rhine and was taken to an asylum. He died there two years later. Clara managed to sustain the family through her concerts but was dealt even more pain by the early deaths of several of her children.”
Course No. 1012 Chemistry, 2nd Edition – Frank Cardulla Lecture 5 – The SI (Metric) System of Measurement “Next, we continue to lay a strong foundation for our understanding of chemistry by learning about one of the key tools we’ll be using: the International System of Units (SI), or the metric system. This lecture explains why this system is so useful to scientists and lays out the prefixes and units of measurement that make up the metric system.” Lecture 10 – The Mole “One of the most important concepts to master in an introductory chemistry course is the concept of the mole, which provides chemists with a way to ‘count’ atoms and molecules. Learn how scientists use the mole and explore the quantitative definition of this basic unit.” Lecture 28 – The Self-Ionization of Water “After examining how different substances may behave when dissolved in water, we learn about the self-ionization of water and use this knowledge to solve problems. The lecture ends with a brief introduction to the pH of solutions.” Lecture 29 – Strong Acids and Bases – General Properties “We return to the topic of pH and learn about how pH relates to two kinds of compounds: acids and bases. Through an introductory problem, we explore the relationship of various ions within these compounds.”
Course No. 1257 Mysteries of Modern Physics: Time – Sean Carroll Lecture 10 – Playing with Entropy “Sharpen your understanding of entropy by examining different macroscopic systems and asking, which has higher entropy and which has lower entropy? Also evaluate James Clerk Maxwell’s famous thought experiment about a demon who seemingly defies the principle that entropy always increases.” Lecture 15 – The Perception of Time “Turn to the way humans perceive time, which can vary greatly from clock time. In particular, focus on experiments that shed light on our time sense. For example, tests show that even though we think we perceive the present moment, we actually live 80 milliseconds in the past.” Lecture 16 – Memory and Consciousness “Remembering the past and projecting into the future are crucial for human consciousness, as shown by cases where these faculties are impaired. Investigate what happens in the brain when we remember, exploring different kinds of memory and the phenomena of false memories and false forgetting.” Lecture 20 – Black Hole Entropy “Stephen Hawking showed that black holes emit radiation and therefore have entropy. Since the entropy in the universe today is overwhelmingly in the form of black holes and there were no black holes in the early universe, entropy must have been much lower in the deep past.” Lecture 21 – Evolution of the Universe “Follow the history of the universe from just after the big bang to the far future, when the universe will consist of virtually empty space at maximum entropy. Learn what is well founded and what is less certain about this picture of a universe winding down.”
Course No. 1280 Physics and Our Universe: How It All Works – Richard Wolfson Lecture 1 – The Fundamental Science “Take a quick trip from the subatomic to the galactic realm as an introduction to physics, the science that explains physical reality at all scales. Professor Wolfson shows how physics is the fundamental science that underlies all the natural sciences. He also describes phenomena that are still beyond its explanatory power.” Lecture 24 – The Ideal Gas “Delve into the deep link between thermodynamics, which looks at heat on the macroscopic scale, and statistical mechanics, which views it on the molecular level. Your starting point is the ideal gas law, which approximates the behavior of many gases, showing how temperature, pressure, and volume are connected by a simple formula.” Lecture 44 – Cracks in the Classical Picture “Embark on the final section of the course, which covers the revolutionary theories that superseded classical physics. Why did classical physics need to be replaced? Discover that by the late 19th century, inexplicable cracks were beginning to appear in its explanatory power.” Special Note: This entire series is outstanding! I will eventually be adding many of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 1360 Introduction to Astrophysics – Joshua Winn Lecture 5 – Newton’s Hardest Problem “Continue your exploration of motion by discovering the law of gravity just as Newton might have—by analyzing Kepler’s laws with the aid of calculus (which Newton invented for the purpose). Look at a graphical method for understanding orbits, and consider the conservation laws of angular momentum and energy in light of Emmy Noether’s theory that links conservation laws and symmetry.” Lecture 10 – Optical Telescopes “Consider the problem of gleaning information from the severely limited number of optical photons originating from astronomical sources. Our eyes can only do it so well, and telescopes have several major advantages: increased light-gathering power, greater sensitivity of telescopic cameras and sensors such as charge-coupled devices (CCDs), and enhanced angular and spectral resolution.” Lecture 11 – Radio and X-Ray Telescopes “Non-visible wavelengths compose by far the largest part of the electromagnetic spectrum. Even so, many astronomers assumed there was nothing to see in these bands. The invention of radio and X-ray telescopes proved them spectacularly wrong. Examine the challenges of detecting and focusing radio and X-ray light, and the dazzling astronomical phenomena that radiate in these wavelengths.” Lecture 12 – The Message in a Spectrum “Starting with the spectrum of sunlight, notice that thin dark lines are present at certain wavelengths. These absorption lines reveal the composition and temperature of the Sun’s outer atmosphere, and similar lines characterize other stars. More diffuse phenomena such as nebulae produce bright emission lines against a dark spectrum. Probe the quantum and thermodynamic events implied by these clues.” Lecture 13 – The Properties of Stars “Take stock of the wide range of stellar luminosities, temperatures, masses, and radii using spectra and other data. In the process, construct the celebrated Hertzsprung–Russell diagram, with its main sequence of stars in the prime of life, including the Sun. Note that two out of three stars have companions. Investigate the orbital dynamics of these binary systems.” Lecture 15 – Why Stars Shine “Get a crash course in nuclear physics as you explore what makes stars shine. Zero in on the Sun, working out the mass it has consumed through nuclear fusion during its 4.5-billion-year history. While it’s natural to picture the Sun as a giant furnace of nuclear bombs going off non-stop, calculations show it’s more like a collection of toasters; the Sun is luminous simply because it’s so big.” Lecture 16 – Simple Stellar Models “Learn how stars work by delving into stellar structure, using the Sun as a model. Relying on several physical principles and sticking to order-of-magnitude calculations, determine the pressure and temperature at the center of the Sun, and the time it takes for energy generated in the interior to reach the surface, which amounts to thousands of years. Apply your conclusions to other stars.” Lecture 17 – White Dwarfs “Discover the fate of solar mass stars after they exhaust their nuclear fuel. The galaxies are teeming with these dim “white dwarfs” that pack the mass of the Sun into a sphere roughly the size of Earth. Venture into quantum theory to understand what keeps these exotic stars from collapsing into black holes, and learn about the Chandrasekhar limit, which determines a white dwarf’s maximum mass.” Lecture 18 – When Stars Grow Old “Trace stellar evolution from two points of view. First, dive into a protostar and witness events unfold as the star begins to contract and fuse hydrogen. Exhausting that, it fuses heavier elements and eventually collapses into a white dwarf—or something even denser. Next, view this story from the outside, seeing how stellar evolution looks to observers studying stars with telescopes.” Lecture 19 – Supernovas and Neutron Stars “Look inside a star that weighs several solar masses to chart its demise after fusing all possible nuclear fuel. Such stars end in a gigantic explosion called a supernova, blowing off outer material and producing a super-compact neutron star, a billion times denser than a white dwarf. Study the rapid spin of neutron stars and the energy they send beaming across the cosmos.” Lecture 20 – Gravitational Waves “Investigate the physics of gravitational waves, a phenomenon predicted by Einstein and long thought to be undetectable. It took one of the most violent events in the universe—colliding black holes—to generate gravitational waves that could be picked up by an experiment called LIGO on Earth, a billion light years away. This remarkable achievement won LIGO scientists the 2017 Nobel Prize in Physics.”
Course No. 1434 The Queen of the Sciences: A History of Mathematics – David M. Bressoud Lecture 2 – Babylonian and Egyptian Mathematics “Egyptian and Mesopotamian mathematics were well developed by the time of the earliest records from the 2nd millennium B.C. Both knew how to find areas and volumes. The Babylonians solved quadratic equations using geometric methods and knew the Pythagorean theorem.” Lecture 5 – Astronomy and the Origins of Trigonometry “The origins of trigonometry lie in astronomy, especially in finding the length of the chord that connects the endpoints of an arc of a circle. Hipparchus discovered a solution to this problem, that was later refined by Ptolemy who authored the great astronomical work the Almagest.” Lecture 6 – Indian Mathematics – Trigonometry Blossoms “We journey through the Gupta Empire and the great period of Indian mathematics that lasted from A.D. 320 to 1200. Along the way, we explore the significant advances that occurred in trigonometry and other mathematical fields.” Lecture 14 – Leibniz and the Emergence of Calculus “Independently of Newton, Gottfried Wilhelm Leibniz discovered the techniques of calculus in the 1670s, developing the notational system still used today.” Lecture 15 – Euler – Calculus Proves Its Promise “Leonhard Euler dominated 18th-century mathematics so thoroughly that his contemporaries believed he had solved all important problems.” Lecture 19 – Modern Analysis – Fourier to Carleson “By 1800, calculus was well established as a powerful tool for solving practical problems, but its logical underpinnings were shaky. We explore the creative mathematics that addressed this problem in work from Joseph Fourier in the 19th century to Lennart Carleson in the 20th.” Lecture 21 – Sylvester and Ramanujan – Different Worlds “This lecture explores the contrasting careers of James Joseph Sylvester, who was instrumental in developing an American mathematical tradition, and Srinivasa Ramanujan, a poor college dropout from India who produced a rich range of new mathematics during his short life.” Lecture 22 – Fermat’s Last Theorem – The Final Triumph “Pierre de Fermat’s enigmatic note regarding a proof that he didn’t have space to write down sparked the most celebrated search in mathematics, lasting more than 350 years. This lecture follows the route to a proof, finally achieved in the 1990s.” Lecture 23 – Mathematics – The Ultimate Physical Reality “Mathematics is the key to realms outside our intuition. We begin with Maxwell’s equations and continue through general relativity, quantum mechanics, and string theory to see how mathematics enables us to work with physical realities for which our experience fails us.” Lecture 24 – Problems and Prospects for the 21st Century “This last lecture introduces some of the most promising and important questions in the field and examines mathematical challenges from other disciplines, especially genetics.”
Course No. 1456 Discrete Mathematics – Arthur T. Benjamin Lecture 8 – Linear Recurrences and Fibonacci Numbers “Investigate some interesting properties of Fibonacci numbers, which are defined using the concept of linear recurrence. In the 13th century, the Italian mathematician Leonardo of Pisa, called Fibonacci, used this sequence to solve a problem of idealized reproduction in rabbits.” Lecture 15 – Open Secrets—Public Key Cryptography “The idea behind public key cryptography sounds impossible: The key for encoding a secret message is publicized for all to know, yet only the recipient can reverse the procedure. Learn how this approach, widely used over the Internet, relies on Euler’s theorem in number theory.” Lecture 16 – The Birth of Graph Theory “This lecture introduces the last major section of the course, graph theory, covering the basic definitions, notations, and theorems. The first theorem of graph theory is yet another contribution by Euler, and you see how it applies to the popular puzzle of drawing a given shape without lifting the pencil or retracing any edge.” Lecture 18 – Social Networks and Stable Marriages “Apply graph theory to social networks, investigating such issues as the handshake theorem, Ramsey’s theorem, and the stable marriage theorem, which proves that in any equal collection of eligible men and women, at least one pairing exists for each person so that no extramarital affairs will take place.” Lecture 20 – Weighted Graphs and Minimum Spanning Trees “When you call someone on a cell phone, you can think of yourself as a leaf on a giant ‘tree’—a connected graph with no cycles. Trees have a very simple yet powerful structure that make them useful for organizing all sorts of information.” Lecture 22 – Coloring Graphs and Maps “According to the four-color theorem, any map can be colored in such a way that no adjacent regions are assigned the same color and, at most, four colors suffice. Learn how this problem went unsolved for centuries and has only been proved recently with computer assistance.”
Course No. 1471 Great Thinkers, Great Theorems – William Dunham Lecture 5 – Number Theory in Euclid “In addition to being a geometer, Euclid was a pioneering number theorist, a subject he took up in books VII, VIII, and IX of the Elements. Focus on his proof that there are infinitely many prime numbers, which Professor Dunham considers one of the greatest proofs in all of mathematics.” Lecture 6 – The Life and Work of Archimedes “Even more distinguished than Euclid was Archimedes, whose brilliant ideas took centuries to fully absorb. Probe the life and famous death of this absent-minded thinker, who once ran unclothed through the streets, shouting ‘Eureka!’ (‘I have found it!’) on solving a problem in his bath.” Lecture 7 – Archimedes’ Determination of Circular Area “See Archimedes in action by following his solution to the problem of determining circular area—a question that seems trivial today but only because he solved it so simply and decisively. His unusual strategy relied on a pair of indirect proofs.” Lecture 8 – Heron’s Formula for Triangular Area “Heron of Alexandria (also called Hero) is known as the inventor of a proto-steam engine many centuries before the Industrial Revolution. Discover that he was also a great mathematician who devised a curious method for determining the area of a triangle from the lengths of its three sides.” Lecture 9 – Al-Khwarizmi and Islamic Mathematics “With the decline of classical civilization in the West, the focus of mathematical activity shifted to the Islamic world. Investigate the proofs of the mathematician whose name gives us our term ‘algorithm’: al-Khwarizmi. His great book on equation solving also led to the term ‘algebra.'” Lecture 10 – A Horatio Algebra Story “Visit the ruthless world of 16th-century Italian universities, where mathematicians kept their discoveries to themselves so they could win public competitions against their rivals. Meet one of the most colorful of these figures: Gerolamo Cardano, who solved several key problems. In secret, of course.” Lecture 11 – To the Cubic and Beyond “Trace Cardano’s path to his greatest triumph: the solution to the cubic equation, widely considered impossible at the time. His protégé, Ludovico Ferrari, then solved the quartic equation. Norwegian mathematician Niels Abel later showed that no general solutions are possible for fifth- or higher-degree equations.” Lecture 12 – The Heroic Century “The 17th century saw the pace of mathematical innovations accelerate, not least in the introduction of more streamlined notation. Survey the revolutionary thinkers of this period, including John Napier, Henry Briggs, René Descartes, Blaise Pascal, and Pierre de Fermat, whose famous ‘last theorem’ would not be proved until 1995.” Lecture 13 – The Legacy of Newton “Explore the eventful life of Isaac Newton, one of the greatest geniuses of all time. Obsessive in his search for answers to questions from optics to alchemy to theology, he made his biggest mark in mathematics and science, inventing calculus and discovering the law of universal gravitation.” Lecture 14 – Newton’s Infinite Series “Start with the binomial expansion, then turn to Newton’s innovation of using fractional and negative exponents to calculate roots—an example of his creative use of infinite series. Also see how infinite series allowed Newton to approximate sine values with extraordinary accuracy.” Lecture 16 – The Legacy of Leibniz “Probe the career of Newton’s great rival, Gottfried Wilhelm Leibniz, who came relatively late to mathematics, plunging in during a diplomatic assignment to Paris. In short order, he discovered the ‘Leibniz series’ to represent π, and within a few years he invented calculus independently of Newton.” Lecture 17 – The Bernoullis and the Calculus Wars “Follow the bitter dispute between Newton and Leibniz over priority in the development of calculus. Also encounter the Swiss brothers Jakob and Johann Bernoulli, enthusiastic supporters of Leibniz. Their fierce sibling rivalry extended to their competition to outdo each other in mathematical discoveries.” Lecture 18 – Euler, the Master “Meet history’s most prolific mathematician, Leonhard Euler, who went blind in his sixties but kept turning out brilliant papers. A sampling of his achievements: the number e, crucial in calculus; Euler’s identity, responsible for the most beautiful theorem ever; Euler’s polyhedral formula; and Euler’s path.” Lecture 19 – Euler‘s Extraordinary Sum “Euler won his spurs as a great mathematician by finding the value of a converging infinite series that had stumped the Bernoulli brothers and everyone else who tried it. Pursue Euler’s analysis through the twists and turns that led to a brilliantly simple answer.” Lecture 20 – Euler and the Partitioning of Numbers “Investigate Euler’s contribution to number theory by first warming up with the concept of amicable numbers—a truly rare breed of integers until Euler vastly increased the supply. Then move on to Euler’s daring proof of a partitioning property of whole numbers.” Lecture 21 – Gauss – the Prince of Mathematicians “Dubbed the Prince of Mathematicians by the end of his career, Carl Friedrich Gauss was already making major contributions by his teen years. Survey his many achievements in mathematics and other fields, focusing on his proof that a regular 17-sided polygon can be constructed with compass and straightedge alone.” Lecture 22 – The 19th Century – Rigor and Liberation “Delve into some of the important trends of 19th-century mathematics: a quest for rigor in securing the foundations of calculus; the liberation from the physical sciences, embodied by non-Euclidean geometry; and the first significant steps toward opening the field to women.” Lecture 23 – Cantor and the Infinite “Another turning point of 19th-century mathematics was an increasing level of abstraction, notably in the approach to the infinite taken by Georg Cantor. Explore the paradoxes of the ‘completed’ infinite, and how Cantor resolved this mystery with transfinite numbers, exemplified by the transfinite cardinal aleph-naught.” Lecture 24 – Beyond the Infinite “See how it’s possible to build an infinite set that’s bigger than the set of all whole numbers, which is itself infinite. Conclude the course with Cantor’s theorem that the transcendental numbers greatly outnumber the seemingly more abundant algebraic numbers—a final example of the elegance, economy, and surprise of a mathematical masterpiece.”
Course No. 1495 Introduction to Number Theory – Edward B. Burger Lecture 12 – The RSA Encryption Scheme “We continue our consideration of cryptography and examine how Fermat’s 350-year-old theorem about primes applies to the modern technological world, as seen in modern banking and credit card encryption.” Lecture 22 – Writing Real Numbers as Continued Fractions “Real numbers are often expressed as endless decimals. Here we study an algorithm for writing real numbers as an intriguing repeated fraction-within-a-fraction expansion. Along the way, we encounter new insights about the hidden structure within the real numbers.” Lecture 24 – A Journey’s End and the Journey Ahead “In this final lecture, we take a step back to view the entire panorama of number theory and celebrate some of the synergistic moments when seemingly unrelated ideas came together to tell a unified story of number.”
Course No. 1802 The Search for Exoplanets: What Astronomers Know– Joshua Winn Lecture 4 – Pioneers of Planet Searching “Chart the history of exoplanet hunting – from a famous false signal in the 1960s, through ambiguous discoveries in the 1980s, to the big breakthrough in the 1990s, when dozens of exoplanets turned up. Astronomers were stunned to find planets unlike anything in the solar system.” Special Note: This entire series is outstanding! I will eventually be adding most of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 1816 The Inexplicable Universe: Unsolved Mysteries– Neil deGrasse Tyson Lecture 4 – Inexplicable Physics “Among the many topics you’ll learn about in this lecture are the discovery of more elements on the periodic table; muon neutrinos, tao particles, and the three regimes of matter; the secrets of string theory (which offers the hope of unifying all the particles and forces of physics); and even the hypothetical experience of traveling through a black hole.” Special Note: This entire series is outstanding! I will eventually be adding most of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 1830 Cosmology: The History and Nature of Our Universe – Mark Whittle Lecture 3 – Overall Cosmic Properties “The universe is lumpy at the scale of galaxies and galaxy clusters. But at larger scales it seems to be smooth and similar in all directions. This property of homogeneity and isotropy is called the cosmological principle.” Lecture 4 – The Stuff of the Universe “The most familiar constituents of the universe are atomic matter and light. Neutrinos make up another component. But by far the bulk of the universe—96%—is dark energy and dark matter. The relative amounts of these constituents have changed as the universe has expanded.” Lecture 6 – Measuring Distances “Astronomers use a ‘distance ladder’ of overlapping techniques to determine distances in the universe. Triangulation works for nearby stars. For progressively farther objects, observers use pulsating stars, the rotation of galaxies, and a special class of supernova explosions.” Lecture 8 – Distances, Appearances, and Horizons “Defining distances in cosmology is tricky, since an object’s distance continually increases with cosmic expansion. There are three important distances to consider: the emission distance, when the light set out; the current distance, when the light arrives; and the distance the light has traveled.” Lecture 10 – Cosmic Geometry – Triangles in the Sky “Einstein’s theory of gravity suggests that space could be positively or negatively curved, so that giant billion-light-year triangles might have angles that don’t add up to 180°. This lecture discusses the success at measuring the curvature of the universe in 1998.” Lecture 11 – Cosmic Expansion – Keeping Track of Energy “Has the universe’s rate of expansion always been the same? You answer this question by applying Newton’s law of gravity to an expanding sphere of matter, finding that the expansion was faster in the past and slows down over time.” Lecture 12 – Cosmic Acceleration – Falling Outward “You investigate why the three great eras of cosmic history—radiation, matter, and dark energy—have three characteristic kinds of expansion. These are rapid deceleration, modest deceleration, and exponential acceleration. The last is propelled by dark energy, which makes the universe fall outward.” Lecture 13 – The Cosmic Microwave Background “By looking sufficiently far away, and hence back in time, we can witness the ‘flash’ from the big bang itself. This arrives from all directions as a feeble glow of microwave radiation called the cosmic microwave background (CMB), discovered by chance in 1964.” Lecture 22 – The Galaxy Web – A Relic of Primordial Sound “A simulated intergalactic trip shows you the three-dimensional distribution of galaxies in our region of the universe. On the largest scale, galaxies form a weblike pattern that matches the peaks and troughs of the primordial sound in the early universe.” Lecture 24 – Understanding Element Abundances “The theory of atom genesis in the interiors of stars is confirmed by the proportions of each element throughout the cosmos. The relative abundances hardly vary from place to place, so that gold isn’t rare just on earth, it’s rare everywhere.” Lecture 27 – Physics at Ultrahigh Temperatures “This lecture begins your investigation of the universe during its first second, which is an immense tract of time in nature. To understand what happened, you need to know how nature behaves at ultrahigh energy and density. Fortunately, the physics is much simpler than you might think.” Lecture 29 – Back to the GUT – Matter and Forces Emerge “You venture into the bizarre world of the opening nanosecond. There are two primary themes: the birth of matter and the birth of forces. Near one nanosecond, the universe was filled with a dense broth of the most elementary particles. As temperatures dropped, particles began to form.” Lecture 30 – Puzzling Problems Remain “Although the standard big bang theory was amazingly successful, it couldn’t explain several fundamental properties of the universe: Its geometry is Euclidean, it’s smooth on the largest scales, and it was born slightly lumpy on smaller scales. The theory of cosmic inflation offers a comprehensive solution.” Lecture 31 – Inflation Provides the Solution “This lecture shows how the early universe might enter a brief phase of exponentially accelerating expansion, or inflation, providing a mechanism to launch the standard hot big bang universe. This picture also solves the flatness, horizon, and monopole problems that plagued the standard big-bang theory.” Lecture 33 – Inflation’s Stunning Creativity “All the matter and energy in stars and galaxies is exactly balanced by all the negative energy stored in the gravitational fields between the galaxies. Inflation is the mechanism that takes nothing and makes a universe—not just our universe, but potentially many.” Lecture 34 – Fine Tuning and Anthropic Arguments “Why does the universe have the properties it does and not some different set of laws? One approach is to see the laws as inevitable if life ever evolves to ask such questions. This position is called the anthropic argument, and its validity is hotly debated.”
Course No. 1866 The Remarkable Science of Ancient Astronomy – Bradley E. Schaefer Lecture 10 – Origins of Western Constellations “The human propensity for pattern recognition and storytelling has led every culture to invent constellations. Trace the birth of the star groups known in the West, many of which originated in ancient Mesopotamia. At least one constellation is almost certainly more than 14,000 years old and may be humanity’s oldest surviving creative work.”
Course No. 1878 Radio Astronomy: Observing the Invisible Universe – Felix J. Lockman Lecture 5 – Radio Telescopes and How They Work “Radio telescopes are so large because radio waves contain such a small amount of energy. For example, the signal from a standard cell phone measured one kilometer away is five million billion times stronger than the radio signals received from a bright quasar. Learn how each of these fascinating instruments is designed to meet a specific scientific goal—accounting for their wide variation in form and size.” Lecture 7 – Tour of the Green Bank Observatory “The Green Bank Observatory is located within the 13,000-acre National Radio Quiet Zone straddling the border of Virginia and West Virginia. Come tour this fascinating facility where astronomers discovered radiation belts around Jupiter, the black hole at the center of our galaxy, and the first known interstellar organic molecule, and began the search for extra-terrestrial life.” Lecture 8 – Tour of the Green Bank Telescope “At 17 million pounds, and with more than 2,000 surface panels that can be repositioned in real time, this telescope is one of the largest moveable, land-based objects ever built. The dish could contain two side-by-side football fields, but when its panels are brought into focus, the surface has errors no larger than the thickness of a business card. Welcome to this rare insider’s view.” Lecture 9 – Hydrogen and the Structure of Galaxies “Using the laws of physics and electromagnetic radiation, astronomers can ‘weigh’ a galaxy by studying the distribution of its rotating hydrogen. But when they do this, it soon becomes clear something is very wrong: A huge proportion of the galaxy’s mass has simply gone missing. Welcome to the topsy-turvy world of dark matter, which we now believe accounts for a whopping 90 percent of our own Milky Way.” Lecture 10 – Pulsars: Clocks in Space “In the mid-1960s, astronomers discovered signals with predictable periodicity but no known source. In case these signals indicated extraterrestrial life, they were initially labeled LGM, Little Green Men. But research revealed the source of the pulsing radiation to be neutron stars. Learn how a star with a diameter of only a few kilometers and a mass similar to that of our Sun can spin around hundreds of times per second.” Lecture 11 – Pulsars and Gravity “A pulsar’s spin begins with its birth in a supernova and can be altered by transfer of mass from a companion star. Learn how pulsars, these precise interstellar clocks, are used to confirm Einstein’s prediction of gravitational waves by observations of a double-neutron-star system, and how we pull the pulsar signal out of the noise.” Lecture 12 – Pulsars and the 300-Foot Telescope “Humans constantly use radio transmission these days, for everything from military communications to garage-door openers. How can scientists determine which signals come from Earth and which come from space? Learn how the 300-foot telescope, located in two radio quiet zones, was built quickly and cheaply. It ended up studying pulsars and hydrogen in distant galaxies, and made the case for dark matter.” Lecture 16 – Radio Stars and Early Interferometers “When radio astronomers discovered a sky full of small radio sources of unknown origin, they built telescopes using multiple antennas to try to understand them. Learn how and why interferometers were developed and how they have helped astronomers study quasars—those massively bright, star-like objects that scientists now know only occur in galaxies whose gas is falling into a supermassive black hole.” Lecture 18 – Active Galactic Nuclei and the VLA “The need for a new generation of radio interferometers to untangle extragalactic radio sources led to the development of the Very Large Array (VLA) in New Mexico. With its twenty-seven radio antennas in a Y-shaped configuration, it gives both high sensitivity and high angular resolution. The VLA provided a deeper and clearer look at galaxies than ever before, and the results were astonishing.” Lecture 19 – A Telescope as Big as the Earth “Learn how astronomers use very-long-baseline interferometry (VLBI) with telescopes thousands of miles apart to essentially create a radio telescope as big as the Earth. With VLBI, scientists not only look deep into galactic centers, study cosmic radio sources, and weigh black holes, but also more accurately tell time, study plate tectonics, and more—right here on planet Earth.” Lecture 20 – Galaxies and Their Gas “In visible light, scientists had described galaxies as ‘island universes’. But since the advent of radio astronomy, we’ve seen galaxies connected by streams of neutral hydrogen, interacting with and ripping the gases from each other. Now astronomers have come to understand that these strong environmental interactions are not a secondary feature—they are key to a galaxy’s basic structure and appearance.” Lecture 21 – Interstellar Molecular Clouds “In the late 1960s, interstellar ammonia and water vapor were detected. Soon came formaldehyde, carbon monoxide, and the discovery of giant molecular clouds where we now know stars and planets are formed. With improvements in radio astronomy technology, today’s scientists can watch the process of star formation in other systems. The initial results are stunning.” Lecture 22 – Star Formation and ALMA “With an array of 66 radio antennas located in the high Chilean desert above much of the earth’s atmosphere, the Atacama Large Millimeter/submillimeter Array (ALMA) is a radio telescope tuned to the higher frequencies of radio waves. Designed to examine some of the most distant and ancient galaxies ever seen, ALMA has not only revealed new stars in the making, but planetary systems as well.” Lecture 23 – Interstellar Chemistry and Life “Interstellar clouds favor formation of carbon-based molecules over any other kind—not at all what statistical models predicted. In fact, interstellar clouds contain a profusion of chemicals similar to those that occur naturally on Earth. If planets are formed in this rich soup of organic molecules, is it possible life does not have to start from scratch on each planet?” Lecture 24 – The Future of Radio Astronomy “Learn about the newest radio telescopes and the exhilarating questions they plan to address: Did life begin in space? What is dark matter? And a new question that has just arisen in the past few years: What are fast radio bursts? No matter how powerful these new telescopes are, radio astronomers will continue pushing the limits to tell us more and more about the universe that is our home.”
Course No. 1884 Experiencing Hubble: Understanding the Greatest Images of the Universe – David M. Meyer Lecture 5 – The Cat’s Eye Nebula – A Stellar Demise “Turning from star birth to star death, get a preview of the sun’s distant future by examining the Cat’s Eye Nebula. Such planetary nebulae (which have nothing to do with planets) are the exposed debris of dying stars and are among the most beautiful objects in the Hubble gallery.” Lecture 7 – The Sombrero Galaxy – An Island Universe “In the 1920s, astronomer Edwin Hubble discovered the true nature of galaxies as ‘island universes’. Some 80 years later, the telescope named in his honor has made thousands of breathtaking pictures of galaxies. Focus on one in particular—an edge-on view of the striking Sombrero galaxy.” Lecture 8 – Hubble’s View of Galaxies Near and Far “Hubble’s image of the nearby galaxy NGC 3370 includes many faint galaxies in the background, exemplifying the telescope’s mission to establish an accurate distance scale to galaxies near and far—along with the related expansion rate of the universe. Discover how Hubble’s success has led to the concept of dark energy.” Lecture 10 – Abell 2218 – A Massive Gravitational Lens “One of the consequences of Einstein’s general theory of relativity is evident in Hubble’s picture of the galaxy cluster Abell 2218. Investigate the physics of this phenomenon, called gravitational lensing, and discover how Hubble has used it to study extremely distant galaxies as well as dark matter.”
Course No. 3130 Origin of Civilization – Scott MacEachern Lecture 36 – Great Zimbabwe and Its Successors “Few archaeological sites have been subjected to the degree of abuse and misrepresentation sustained by Great Zimbabwe in southeastern Africa. Nevertheless, this lecture unpacks the intriguing history of this urban center and the insights it can provide into the development of the elite.”
Course No. 3900 Ancient Civilizations of North America – Edwin Barnhart Lecture 12 – The Wider Mississippian World “After the fall of Cahokia, witness how Mississippian civilization flourished across eastern North America with tens of thousands of pyramid-building communities and a population in the millions. Look at the ways they were connected through their commonly held belief in a three-tiered world, as reflected in their artwork. Major sites like Spiro, Moundville, and Etowah all faded out just around 100 years before European contact, obscuring our understanding.” Lecture 13 – De Soto Versus the Mississippians “In 1539, Hernando de Soto of Spain landed seven ships with 600 men and hundreds of animals in present-day Florida. Follow his fruitless search for another Inca or Aztec Empire, as he instead encounters hundreds of Mississippian cities through which he led a three-year reign of terror across the land-looting, raping, disfiguring, murdering, and enslaving native peoples by the thousands.” Lecture 19 – The Chaco Phenomenon “Chaco Canyon contains the most sophisticated architecture ever built in ancient North America—14 Great Houses, four Great Kivas, hundreds of smaller settlements, an extensive road system, and a massive trade network. But who led these great building projects? And why do we find so little evidence of human habitation in what seems to be a major center of culture? Answer these questions and more.” Lecture 24 – The Iroquois and Algonquians before Contact “At the time of European contact, two main groups existed in the northeast—the hunter-gatherer Algonquian and the agrarian Iroquois. Delve into how the Iroquois created the first North American democracy as a solution to their increasing internal conflicts. Today, we know much of the U.S. Constitution is modeled on the Iroquois’ “Great League of Peace” and its 117 articles of confederation, as formally acknowledged by the U.S. in 1988.”
Course No. 4215 An Introduction to Formal Logic – Steven Gimbel Lecture 8 – Induction in Polls and Science “Probe two activities that could not exist without induction: polling and scientific reasoning. Neither provides absolute proof in its field of analysis, but if faults such as those in Lecture 7 are avoided, the conclusions can be impressively reliable.”
Course No. 7210 The Symphony – Robert Greenberg Lecture 24 – Dmitri Shostakovich and His Tenth Symphony “Dmitri Shostakovich was used and abused by the Soviet powers during much of his life. Somehow, he survived—even as his Tenth Symphony made dangerously implicit criticisms of the Soviet government.”
Course No. 7261 Understanding the Fundamentals of Music – Robert Greenberg Lecture 9 – Intervals and Tunings “Resuming our focus on pitch, we will turn once more to Pythagoras, and his investigation into what is now known as the overtone series. This paves the way for an examination of intervals, the evolution of tuning systems, and an introduction to the major pitch collections.”
Course No. 7270 The Concerto – Robert Greenberg Lecture 13 – Tchaikovsky “Excoriated by colleagues and critics alike, Tchaikovsky’s concerti ultimately triumphed to become cornerstones of the repertoire. This lecture explores his Piano Concerto no. 1 in B flat Minor, op. 23; Piano Concerto no. 2 in G Major, op. 44; and Violin Concerto in D Major, op. 35, arguably his single greatest work and one of the greatest concerti of the 19th century.” Lecture 14 – Brahms and the Symphonic Concerto “Johannes Brahms’s compositional style is a synthesis of the clear and concise musical forms and genres of the Classical and Baroque eras, and the melodic, harmonic, and expressive palette of the Romantic era in which he lived. This lecture examines in depth his monumental Piano Concerto no. 2 in B flat Major, op. 83.”
Course No. 8122 Albert Einstein: Physicist, Philosopher, Humanitarian – Don Howard Lecture 1 – The Precocious Young Einstein “The aim of these lectures is to explore Einstein the whole person and the whole thinker. You begin with an overview of the course. Then you look at important events in Einstein’s life up to the beginning of his university studies in 1896.” Special Note: This entire series is outstanding! I will eventually be adding many of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 8535 America in the Gilded Age and Progressive Era – Edward T. O’Donnell Lecture 23 – Over There: A World Safe for Democracy “As the Progressive Era ends, follow the complex events that led the United States into World War I. Learn how an initial federal policy of neutrality changed to one of “preparedness” and then intervention, amid conflicting public sentiments and government pro-war propaganda. Also trace the after-effects of the war on U.S. foreign policy.” Special Note: This entire series is outstanding! I will eventually be adding many of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 8580 Turning Points in American History – Edward T. O’Donnell Lecture 23 – 1868 Equal Protection—The 14th Amendment “Many legal scholars and historians have argued that the 14th Amendment, which promises equal protection under the laws, is the most important addition to the Constitution after the Bill of Rights. Here, Professor O’Donnell retells the fascinating story of how this amendment was ratified in 1868—and its turbulent history in the 20th and 21st centuries.” Special Note: This entire series is outstanding! I will eventually be adding many of the episodes of this course as I rewatch them. (I watched this series before I began keeping track of “best” episodes.)
Course No. 30110 England, the 1960s, and the Triumph of the Beatles – Michael Shelden Lecture 8 – The Englishness of A Hard Day’s Night “In summer 1964, the cinematic Beatles vehicle A Hard Day’s Night broke almost every rule in Hollywood at the time. Professor Shelden reveals what lies underneath the film’s surface charm and musical numbers: an overall attitude of irreverence and defiance in the face of authority, and a challenge for audiences to think for themselves.” Lecture 12 – Hello, Goodbye: The End of the 1960s “In their last years together, all four of the Beatles seemed headed in new directions as they grew up—and apart. Nevertheless, witness how these final years brought a range of sounds, including protest songs, mystic melodies, anthems of friendship, and an iconic double album called simply, The Beatles, but better known as the ‘White Album.'”
Course No. 60000 The Great Questions of Philosophy and Physics – Steven Gimbel Lecture 3 – Can Physics Explain Reality? “If the point of physics is to explain reality, then what counts as an explanation? Starting here, Professor Gimbel goes deeper to probe what makes some explanations scientific and whether physics actually explains anything. Along the way, he explores Bertrand Russell’s rejection of the notion of cause, Carl Hempel’s account of explanation, and Nancy Cartwright’s skepticism about scientific truth.” Lecture 4 – The Reality of Einstein’s Space “What’s left when you take all the matter and energy out of space? Either something or nothing. Newton believed the former; his rival, Leibniz, believed the latter. Assess arguments for both views, and then see how Einstein was influenced by Leibniz’s relational picture of space to invent his special theory of relativity. Einstein’s further work on relativity led him to a startlingly new conception of space.” Lecture 5 – The Nature of Einstein’s Time “Consider the weirdness of time: The laws of physics are time reversable, but we never see time running backwards. Theorists have proposed that the direction of time is connected to the order of the early universe and even that time is an illusion. See how Einstein deepened the mystery with his theory of relativity, which predicts time dilation and the surprising possibility of time travel.” Lecture 8 – Quantum States: Neither True nor False? “Enter the quantum world, where traditional philosophical logic breaks down. First, explore the roots of quantum theory and how scientists gradually uncovered its surpassing strangeness. Clear up the meaning of the Heisenberg uncertainty principle, which is a metaphysical claim, not an epistemological one. Finally, delve into John von Neumann’s revolutionary quantum logic, working out an example.” Lecture 10 – Wanted Dead and Alive: Schrödinger’s Cat “The most famous paradox of quantum theory is the thought experiment showing that a cat under certain experimental conditions must be both dead and alive. Explore four proposed solutions to this conundrum, known as the measurement problem: the hidden-variable view, the Copenhagen interpretation, the idea that the human mind “collapses” a quantum state, and the many-worlds interpretation.” Lecture 11 – The Dream of Grand Unification “After the dust settled from the quantum revolution, physics was left with two fundamental theories: the standard model of particle physics for quantum phenomena and general relativity for gravitational interactions. Follow the quest for a grand unified theory that incorporates both. Armed with Karl Popper’s demarcation criteria, see how unifying ideas such as string theory fall short.” Lecture 12 – The Physics of God “The laws of physics have been invoked on both sides of the debate over the existence of God. Professor Gimbel closes the course by tracing the history of this dispute, from Newton’s belief in a Creator to today’s discussion of the “fine-tuning” of nature’s constants and whether God is responsible. Such big questions in physics inevitably bring us back to the roots of physics: philosophy.”
Course No. 80060 Music Theory: The Foundation of Great Music – Sean Atkinson Lecture 5 – The Circle of Fifths “Begin by defining the key of a piece of music, which is simply the musical scale that is used the most in the piece. Also discover key signatures in written music, symbols at the beginning of the musical score that indicate the key of the piece. Then grasp how the major keys all relate to each other in an orderly way, when arranged schematically according to the interval of a fifth.” Lecture 16 – Hypermeter and Larger Musical Structures “In listening to music, we sometimes hear the meter differently than the way it’s written on the page. Learn how the concept of hypermeter helps explain this, by showing that when measures of music are grouped into phrases, we often hear a pulse for each measure in the phrase, rather than the pulses within the measure. Explore examples of hypermeter, and how we perceive music as listeners.”
I attended the 234th meeting of the American Astronomical Society (AAS), held in St. Louis, Missouri, June 9-13, 2019. Here are some highlights from that meeting.
Day 1 – Monday, June 10, 2019
Research Notes of the AAS is a non-peer-reviewed, indexed and secure record of works in progress, comments and clarifications, null results, or timely reports of observations in astronomy and astrophysics. RNAAS.
The Bulletin of the American Astronomical Society is the publication for science meeting abstracts, obituaries, commentary articles about the discipline, and white papers of broad interest to our community. BAAS.
We still have many unanswered questions about galaxy formation. The rate of star formation in galaxies and central black hole accretion activity was highest between 10 and 11 billion years ago. This corresponds to redshift z around 2 to 3, referred to as “cosmic high noon”. This is the ideal epoch for us to answer our questions about galaxy formation. Near-infrared spectroscopy is important to the study of galaxies during this epoch, and we are quite limited in what we can do from terrestrial observatories. Space based telescopes are needed, and the James Webb Space Telescope (JWST) will be key.
Galaxies are not closed boxes. We need to understand how inflows and outflows affect their evolution (“galactic metabolism”).
There are five international space treaties, with the Outer Space Treaty of 1967 being the first and most important. The United States has signed four of the five treaties. The Moon Agreement of 1979 which states that no entity can own any part of the Moon does not include the United States as one of the signatories.
U.S. Code 51303, adopted in 2015, identifies asteroid resource and space resource rights, and states that “A United States citizen engaged in commercial recovery of an asteroid resource or a space resource under this chapter shall be entitled to any asteroid resource or space resource obtained, including to possess, own, transport, use, and sell the asteroid resource or space resource obtained in accordance with applicable law, including the international obligations of the United States.”
So, unfortunately, U.S. law does allow a commercial entity to own an asteroid, but you have to get there first before you can claim it. The large metallic asteroid 16 Psyche is highly valuable and will probably be owned by some corporation in the not-too-distant future.
Space law often relies upon maritime law as a model.
Astronomer Vayu Gokhale from Truman State University gave an interesting iPoster Plus presentation on how he and his students are operating three automated and continuous zenithal sky brightness measurement stations using narrow-field Sky Quality Meters (SQMs) from Unihedron. Even measurements when it is cloudy are of value, as clouds reflect light pollution back towards the ground. Adding cloud type and height would allow us to make better use of cloudy-night sky brightness measurements. In a light-polluted area, the darkest place is the zenith, and clouds make the sky brighter. In an un-light-polluted area, the darkest place is the horizon, and clouds make the sky darker.
A number of precision radial velocity instruments for exoplanet discovery and characterization will begin operations soon or are already in operation: NEID, HARPS, ESPRESSO, EXPRES, and iLocater, to name a few.
Dark matter: clumps together under gravity, does not emit, reflect, or absorb electromagnetic radiation, and does not interact with normal matter in any way that causes the normal matter to emit, reflect, or absorb electromagnetic radiation. The ratio between dark matter and normal (baryonic matter) in our universe is 5.36 ± 0.05 (Planck 2018).
What is dark matter? It could be a new particle. If so, can we detect its non-gravitational interactions? It could be macroscopic objects, perhaps primordial black holes. Or, it could be a mixture of both. Another possibility is that a modification to the laws of gravitation will be needed to mimic the effects of dark matter.
How “dark” is dark matter? Does it interact at all (besides gravitationally)? Can dark matter annihilate or decay? Even if dark matter started hot, it cools down rapidly as the universe expands.
Primordial black holes could have masses ranging anywhere between 10-16 and 1010 solar masses. LIGO is possibility sensitive to colliding primordial black holes with masses in the range of a few to a few hundred solar masses. Primordial black holes are a fascinating dark matter candidate, with broad phenomenology.
The Cosmic Microwave Background (CMB) is a nearly perfect blackbody with distortions < 1 part in 10,000. What this tells us is that nothing dramatically heated or cooled photons after 2 months after the Big Bang. Anisotropies are variances in the CMB temperature, and the angular power spectrum is variance of CMB temperature as a function of angular scale. CMB anisotropies are very sensitive to the ionization history of the universe. How the universe recombined plays a key role in CMB anisotropies.
Hydrogen: not such a simple atom.
The CMB is polarized. The polarization is caused by Mie scattering of photons.
At the NASA Town Hall, we learned about current and future missions: TESS, SPHEREx, HabEx, LUVOIR, Lynx, Origins Space Telescope (OST).
The highest image rate of standard CCD and CMOS video cameras for asteroid occultation work is 30 frames (60 fields) per second, providing time resolution of 0.017 seconds per field. Adaptive optics and autoguider imaging devices often have a higher sampling rate, and such a camera could perhaps be easily modified to be used for occultation work. A time-inserter would need to be added to the camera (either on-board or GPS-based), and improvements in quantum efficiency (because of the shorter exposures) would benefit from newer imaging technologies such as a Geiger-mode avalanche photodiode (APD); or the Single-photon avalanche detector (SPAD), which are frequently used in chemistry.
Gregory Simonian, graduate student at Ohio State, presented “Double Trouble: Biases Caused by Binaries in Large Stellar Rotation datasets”. The Kepler data yielded 34,030 rotation periods through starspot variability. However, the rapid rotators are mostly binaries. In the Kepler dataset, many rapid rotators have a spin period of the stars equal to the orbital period of the binary. These eclipsing binaries, also known as photometric binaries because they are detected through changes in brightness during eclipses and transits, need to be treated separately in stellar rotation datasets.
Granulation was discovered by William Herschel in 1801 and are vertical flows in the solar photosphere on the order of 1000 m/s, and 1000 km horizontal scale. Supergranulation (Hart 1954, Leighton et al. 1962) are horizontal motions in the photosphere of 300 to 500 m/s with a horizontal scale on the order of 30,000 km.
The amplitude of oscillations in red giants increase dramatically with age.
We’ve never observed the helium flash event in a red giant star, though models predict that it must occur. It is very brief and would be difficult to detect observationally.
Brad Schaefer, Professor Emeritus at Louisiana State University, gave a talk on “Predictions for Upcoming Recurrent Nova Eruptions”. Typically, recurrent novae have about a 30% variation in eruptive timescales, so predicting the next eruption is not trivial. Due to the solar gap (when the object is too close to the Sun to observe on or near the Earth), we are obviously missing some eruptions. However, orbital period changes (O-C curve) can tell us about an eruption we missed. U Sco and T CrB are well-known examples of recurrent novae. Better monitoring of recurrent novae is needed during the pre-eruption plateau. Monitoring in the blue band is important for prediction.
I had the good fortune to talk with Brad on several occasions during the conference, and found him to be enthusiastic, knowledgeable, and engaging. Perhaps you have seen The Remarkable Science of Ancient Astronomy (The Great Courses), and he is just as articulate and energetic in real life. Among other things, we discussed how the internet is filled with misinformation, and even after an idea has been convincingly debunked, the misinformation continues to survive and multiply in cyberspace. This is a huge problem in the field of archaeoastronomy and, indeed, all fields of study. People tend to believe what they want to believe, never mind the facts.
Astrobites is a daily astrophysical-literature blog written by graduate students in astronomy around the world. The goal of Astrobites is to present one interesting paper from astro-ph per day in a brief format accessible to its target audience: undergraduate students in the physical sciences who are interested in active research.
Helioseismology can be done both from space (all) and the ground (some). Active regions on the far side of the Sun can be detected with helioseismology.
All HMI (Helioseismic and Magnetic Imager) data from the Solar Dynamics Observatory is available online.
A good approach to studying solar data is to subtract the average differential rotation at each point/region on the Sun and look at the residuals.
The Wilcox Solar Observatory has been making sun-as-a-star mean magnetic field measurements since 1975.
It is possible to infer electric currents on the Sun, but this is much more difficult than measuring magnetic fields.
Future directions in solar studies: moving from zonal averages to localized regions in our modeling, and the ability through future space missions to continuously monitor the entire surface of the Sun at every moment.
Systematic errors are nearly always larger than statistical uncertainty.
Day 2 – Tuesday, June 11, 2019
It is probably not hyperbole to state that every star in our galaxy has planets. About 1/5 of G-type stars have terrestrial planets within the habitable zone. Life is widespread throughout the universe.
Gas-grain interaction is at the core of interstellar chemistry. Interstellar ices, charged ices, surface chemistry – there is more time for interactions to occur on a dust grain than in a gas. Grain collisions are important, too.
Hot cores are transient regions surrounding massive protostars very early in their evolution. Similar regions are identified around low-mass protostars and are called corinos.
Methanol (CH3OH) is key to making simple organic molecules (SOM). Evaporating ice molecules drive rich chemistry. Dust plays a key role in the chemistry and in transporting material from the interstellar medium (ISM) to planetary systems.
The Rosetta mission detected amino acids on comet 67P/Churyumov–Gerasimenko.
JUICE (JUpiter ICy moons Explorer) is an ESA mission scheduled to launch in 2022, will enter orbit around Jupiter in October 2029 and Ganymede in 2032. It will study Europa, Ganymede, and Callisto in great detail.
The gravitational wave event GW170817 (two infalling and colliding neutron stars) was also detected as a gamma-ray burst (GRB) by the Fermi gamma-ray space telescope, which has a gamma-ray burst detector that at all times monitors the 60% of the sky that is not blocked by the Earth.
The time interval between the GW and GRB can range between tens of milliseconds up to 10 seconds.
The Milky Way galaxy circumnuclear disk is best seen at infrared wavelengths around 50 microns. Linear polarization tells us the direction of rotation. The star cluster near the MW center energizes and illuminates gas structures. Gravity dominates in this region. The role of magnetic fields in this region has been a mystery.
Pitch angle – how tightly wound the spiral arms are in a spiral galaxy.
Are spiral arms transient or long lived? They are probably long lived. There may be different mechanisms of spiral arm formation in grand design spirals compared with other types of spiral galaxies.
In studying spiral galaxies, we often deproject to face-on orientation.
The co-rotation radius is the distance from the center of a spiral galaxy beyond which the stars orbit slower than the spiral arms. Inside this radius, the stars move faster than the spiral arms.
The Sun is located near the corotation circle of the Milky Way.
The origins of supermassive black holes (SMBH) at the centers of galaxies are unclear. Were they seeded from large gas clouds, or were they built up from smaller black holes?
The black holes at the centers of spiral galaxies tend to be more massive when the spiral arm winding is tight, and less massive when the spiral arm winding is loose.
Spiral Graph is in review as a Zooniverse project and has not yet launched. Citizen scientists will trace the spiral arms of 6,000 deprojected spiral galaxies, and 15 traces will be needed for each galaxy. Spiral arm tracings will provide astronomers with intermediate mass black hole candidate galaxies.
Barred spiral galaxies are very common. 66% to 75% of spiral galaxies show evidence of a bar at near-infrared wavelengths.
Magnetic fields in the inner regions of spiral galaxies are scrambling radio emissions to some extent, but radio astronomers have ways to deal with this.
For me, the plenary lecture given by Suvrath Mahadevan, Pennsylvania State University, was the first truly outstanding presentation. His topic was “The Tools of Precision Measurement in Exoplanet Discovery: Peeking Under the Hood of the Instruments”. His discussion of the advance in radial velocity instrumentation was revelatory to me, as his starting point was Roger F. Griffin’s radial velocity spectrometer we used at Iowa State University in the 1970s and 1980s, giving us a precision of about 1 km/s. My, we have come a long way since then!
To discover our Earth from another star system in the ecliptic plane would require detecting an 8.9 cm/s velocity shift in the Sun’s motion over the course of a year.
Precision radial velocity measurement requires we look at the displacement of thousands of spectral lines using high resolution spectroscopy.
The two main techniques are 1) Simultaneous reference and 2) Self reference (iodine cell). Also, externally dispersed interferometry and heterodyne spectroscopy can be used.
Griffin 1967 ~ km/s → CORAVEL 1979 ~300 m/s → CORALIE/ELODIE 1990 ~ 5-10 m/s → HARPS 2000 ~ 1 m/s → ESPRESSO/VLT, EXPRES/DCT, NEID/KPNO, HPF/HET.
We cannot build instruments that are stable over time at 10 cm/s resolution or less.
You can track the relative change in velocity much better than absolute velocity because of the “noise” generated by stellar internal motions.
Measuring the radial velocity at red or infrared wavelengths is best for M dwarfs, and cooler stars.
High radial velocity precision will require long-term observations, and a better understanding of and mitigation for stellar activity. Many things need to be considered: telescope, atmosphere, barycentric correction (chromatic effects can lead to 1/2 m/s error), fibers, modal noise, instrument decoupled from the telescope, calibrators, optics, stability, pipeline, etc. Interdisciplinary expertise is required.
NEID will measure wavelengths of 380 – 930 nm, and have a spectral resolution of R ~ 90,000.
Pushing towards 10 cm/s requires sub-milli-Kelvin instrument stability high-quality vacuum chambers, octagonal fibers, scrambling, and excellent guiding of the stellar image on the fiber to better than 0.05 arcseconds.
Precision radial velocity instruments such as NEID and HPF weigh two tons, so at present they can only be used with ground-based telescopes.
Charge Transfer Efficiency (CTE): need CCDs with CTE > 0.999999. Other CCD issues that don’t flat field out accurately: CCD stitch boundaries, cross hatching in NIR detectors, crystalline defects, sub-pixel quantum efficiency differences. Even the act of reading out the detector introduces a noise source.
10 cm/s is within reach from a purely instrumental perspective, but almost everything has to be just right. But we need to understand stellar activity better: granulation, supergranulation, flares, oscillations, etc. We may not be able to isolate these components of stellar activity, but we will certainly learn a lot in the process.
1s time resolution is required to properly apply barycentric corrections.
Gene Byrd, University of Alabama, gave an interesting short presentation, “Two Astronomy Demos”. The first was “Stars Like Grains of Sugar”, reminiscent of Archimedes’ The Sand Reckoner. And “Phases with the Sun, Moon, and Ball”. He uses a push pin in a golf ball (the golf ball even has craters!). Morning works best for this activity. The Sun lights the golf ball and the Moon and they have the same phase—nice! Touching as well as seeing the golf ball helps students understand the phases of the Moon. Here’s a link to his paper on these two activities.
Daniel Kennefick, University of Arkansas, gave a short presentation on the 1919 eclipse expedition that provided experimental evidence (besides the correct magnitude of the perihelion precession of Mercury) that validated Einstein’s General Relativity. Stephen Hawking in his famous book A Brief History of Time mis-remembered that the 1979 re-analysis of the Eddington’s 1919 eclipse data showed that he may “fudged” the results to prove General Relativity to be correct. He did not! See Daniel Kennefick’s new book on the subject, No Shadow of a Doubt: The 1919 Eclipse That Confirmed Einstein’s Theory of Relativity.
Brad Schaefer, Louisiana State University, gave another engaging talk, presenting evidence that the Australian aborigines may have discovered the variability of the star Betelgeuse, much earlier than the oft-stated discovery by John Herschel in 1836. Betelgeuse varies in brightness between magnitude 0.0 and +1.3 quasi-periodically over a period of about 423 days. It has been shown that laypeople can detect differences in brightness as small as 0.3 magnitude with the unaided eye, and with good comparison stars (like Capella, Rigel, Procyon, Pollux, Adhara, and Bellatrix—not all of which are visible from Australia—for Betelgeuse). It is plausible that the variability of Betelgeuse may have been discovered by many peoples at many different times. The Australian aborigines passed an oral tradition through many generations that described the variability of Betelgeuse. https://ui.adsabs.harvard.edu/abs/2019AAS…23422407S/abstract.
As a longtime astronomical observer myself, I have actually never noticed the variability of Betelgeuse, but Brad has. After his presentation, I mentioned to Brad that it would be interesting to speculate what would lead early peoples to look for variability in stars in the first place, which seems to me to be a prerequisite for anyone discovering the variability of Betelgeuse. His response pointed out that all it would take is one observant individual in any society who would notice/record the variability and then point it out to others.
If you haven’t looked at the NASA/IPAC Extragalactic Database (NED) lately, you will find new content and functionality. It has been expanded a great deal, and now includes many stellar objects, because we don’t always know what is really a star and what is not. There is now a single input field where you can enter names, coordinates with search radius, etc. NED is “Google for Galaxies”.
I noticed during the 10-minute iPoster Plus sessions that there is a countdown timer displayed unobtrusively in the upper right hand corner that helps the presenter know how much time they have remaining. I think this would be a great device for anyone giving a short presentation in any venue.
Galactic archaeology is the study of the oldest stars and other structures in our galaxy to better understand how our galaxy evolved.
Day 2 ended with an evening presentation of “Cielo”, a documentary film by Alison McAlpine. Highly recommended!
I noted that “Cielo” was presented on the Documentary Channel in Canada. Too bad we do not have a channel like that here in the U.S.!
Day 3 – Wednesday, June 12, 2019
Day 3 began with what for me was the finest presentation of the entire conference: Joshua Winn, Princeton University, speaking on “Transiting Exoplanets: Past, Present, and Future”. I first became familiar with Josh Winn through watching his outstanding video course, The Search for Exoplanets: What Astronomers Know, from The Great Courses. I am currently watching his second course, Introduction to Astrophysics, also from The Great Courses. Josh is an excellent teacher, public speaker, and presenter, and it was a great pleasure to meet him at this conference.
Transits provide the richest source of information we have about exoplanets. For example, we can measure the obliquity of the star’s equator relative to the planet’s orbital plane by measuring the apparent Doppler shift of the star’s light throughout transit.
Who was the first to observe a planetary transit? Pierre Gassendi (1592-1655) was the first to observe a transit of Mercury across the Sun in November 1631. Jeremiah Horrocks (1618-1641) was the first to observe a transit of Venus across the Sun in November 1639. Christoph Scheiner (1573-1650) claimed in January 1612 that spots seen moving across the Sun were planets inside Mercury’s orbit transiting the Sun, but we know know of course that sunspots are magnetically cooled regions in the Sun’s photosphere and not orbiting objects at all. Though Scheiner was wrong about the nature of sunspots, his careful observations of them led him to become the first to measure the Sun’s equatorial rotation rate, the first to notice that the Sun rotated more slowly at higher latitudes, and the first to notice that the Sun’s equator is tilted with respect to the ecliptic, and to measure its inclination.
An exoplanet can be seen to transit its host star if the exoplanet’s orbit lies within the transit cone, an angle of 2R*/a centered on our line of sight to the star. R* is the star’s radius, and a is the semi-major axis of the planet’s orbit around the star.
Because of the geometry, we are only able to see transits of 1 out of every 215 Earth-Sun analogs.
Space is by far the best place to study transiting exoplanets.
If an exoplanet crosses a starspot, or a bright spot, on the star, you will see a “blip” in the transit light curve that looks like this:
Are solar systems like our own rare? Not at all! There are powerful selection effects at work in exoplanet transit statistics. We have discovered a lot of “hot Jupiters” because large, close-in planets are much easier to detect with their short orbital periods and larger transit cones. In actuality, only 1 out of every 200 sun-like stars have hot Jupiters.
Planet statistical properties was the main goal of the Kepler mission. Here are some noteworthy discoveries:
Kepler 89 – two planets transiting at the same time (only known example)
Kepler 36 – chaotic three-body system
Kepler 16 – first known transiting exoplanet in a circumbinary orbit
Transiting Exoplanet Survey Satellite (TESS) – Unlike Kepler, which is in an Earth-trailing heliocentric orbit, TESS is in a highly-elliptical orbit around the Earth with an apogee approximately at the distance of the Moon and a perigee of 108,000 km. TESS orbits the Earth twice during the time the Moon orbits once, a 2:1 orbital resonance with the Moon.
TESS has four 10.5 cm (4-inch) telescopes, each with a 24˚ field of view. Each TESS telescope is constantly monitoring 2300 square degrees of sky.
TESS is fundamentally about short period planets. Data is posted publicly as soon as it is calibrated. TESS has already discovered 700 planet candidates. About 1/2 to 2/3 will be true exoplanets. On average, TESS is observing stars that are about 4 magnitudes brighter than stars observed by Kepler.
The TESS Follow-Up Observing Program (TFOP) is a large working group of astronomical observers brought together to provide follow-up observations to support the TESS Mission’s primary goal of measuring the masses for 50 planets smaller than 4 Earth radii, in addition to organizing and carrying out follow-up of TESS Objects of Interest (TOIs).
HD 21749 – we already had radial velocity data going back several years for this star that hosts an exoplanet that TESS discovered
Gliese 357 – the second closest transiting exoplanet around an M dwarf, after HD 219134
TESS will tell us more about planetary systems around early-type stars.
TESS will discover other transient events, such as supernovae, novae, variable stars, etc. TESS will also make asteroseismology measurements and make photometric measurements of asteroids.
The James Webb Space Telescope (JWST) will be able to do follow-up spectroscopy of planetary atmospheres.
Upcoming exoplanet space missions: CHEOPS, PLATO, and WFIRST.
Hot Jupiter orbits should often be decaying, so this is an important area of study.
Sonification is the process of turning data into sound. For example, you could “listen” to a light curve (with harmonics, e.g. helioseismology and asteroseismology) of a year’s worth a data in just a minute or so.
Solar cycles have different lengths (11-ish years…).
Some predictions: 2019 will be the warmest year on record, 2020 will be less hot. Solar cycle 24 terminate in April 2020. Solar cycle 25 will be weaker than cycle 24. Cycle 25 will start in 2020 and will be the weakest in 300 years, the maximum (such as it is) occurring in 2025. Another informed opinion was that Cycle 25 will be comparable to Cycle 24.
Maunder minimum: 1645 – 1715
Dalton minimum: 1790 – 1820
We are currently in the midst of a modern Gleissberg minimum. It remains to be seen if it will be like the Dalton minimum or a longer “grand minimum” like the Maunder minimum.
Citizen scientists scanning Spitzer Space Telescope images in the Zooniverse Milky Way Project, have discovered over 6,000 “yellow balls”. The round features are not actually yellow, they just appear that way in the infrared Spitzer image color mapping.
Yellow balls (YBs) are sites of 8 solar mass or more star formation, surrounded by ionized hydrogen (H II) gas. YBs thus reveal massive young stars and their birth clouds.
Antlia 2 is a low-surface-brightness (“dark”) dwarf galaxy that crashed into our Milky Way galaxy. Evidence for this collision comes from “galactoseismology” which is the study of ripples in the Milky Way’s disk.
The Large Magellanic Cloud (LMC), Small Magellanic Cloud (SMC), and the Sagittarius Dwarf Galaxy have all affected our Milky Way Galaxy, but galactoseismology has shown that there must be another perturber that has affected the Milky Way. Antlia 2, discovered in November 2018 from data collected by the Gaia spacecraft, appears to be that perturber.
Gaia Data Release 2 (DR2) indicates that the Antlia 2 dwarf galaxy is about 420,000 ly distant, and it is similar in extent to the LMC. It is an ultra-diffuse “giant” dwarf galaxy whose stars average two magnitudes fainter than the LMC. Antlia 2 is located 11˚ from the galactic plane and has a mass around 1010 solar masses.
A question that is outstanding is what is the density of dark matter in Antlia 2? In the future, Antlia 2 may well be an excellent place to probe the nature of dark matter.
Gravity drives the formation of cosmic structure, dark energy slows it down.
Stars are “noise” for observational cosmologists.
“Precision” cosmology needs accuracy also.
The Vera Rubin telescope (Large Synoptic Survey Telescope) in Chile will begin full operations in 2022, collecting 20 TB of data each night!
We have a “galaxy bias” – we need to learn much more about the relation between galaxy populations and matter distribution.
Might there be an irregular asymmetric cycle underlying the regular 22-year sunspot cycle? The dominant period associated with this asymmetry is around 35 to 50 years.
The relationship between differential rotation and constant effective temperature of the Sun: the Sun has strong differential rotation along radial lines, and there is little variation of solar intensity with latitude.
Solar filaments (solar prominences) lie between positive and negative magnetic polarity regions.
Alfvén’s theorem: in a fluid with infinite electric conductivity, the magnetic field is frozen into the fluid and has to move along with it.
Some additional solar terms and concepts to look up and study: field line helicity, filament channels, kinetic energy equation, Lorentz force, magnetic energy equation, magnetic flux, magnetic helicity, magnetohydrodynamics (MHD), meridional flow, polarity inversion lines, relative helicity, sheared arcade, solar dynamo.
We would like to be able to predict solar eruptions before they happen.
Magnetic helicity is injected by surface motions.
It accumulates at polarity inversion lines.
It is removed by coronal mass ejections.
Day 4 – Thursday, June 13, 2019
Cahokia (our name for it today) was the largest city north of Mexico 1,000 years ago. It was located at the confluence of the Mississippi, Missouri, and Illinois Rivers. At its height from 1050 – 1200 A.D., Cahokia city covered 6 square miles and had 10,000 to 20,000 people. Cahokia was a walled city. Some lived inside the walls, and others lived outside the walls.
Around 120 mounds were built at greater Cahokia; 70 are currently protected. Platform mounds had buildings on top, and some mounds were used for burial and other uses.
Monks mound is the largest prehistoric earthwork in the Americas. Mound 72 has an appalling history.
Woodhenge – controversial claim that it had an astronomical purpose. Look up Brad Schaefer’s discussion, “Case studies of three of the most famous claimed archaeoastronomical alignments in North America”.
Cahokia’s demise was probably caused by many factors, including depletion of resources and prolonged drought. We do not know who the descendents of the Cahokia people are. It is possible that they died out completely.
The Greeks borrowed many constellations from the Babylonians.
One Sky, Many Astronomies
The neutron skin of a lead nucleus (208Pb) is a useful miniature analog for a neutron star.
Infalling binary neutron stars, such as GW 170817, undergo tidal deformation.
Minisatellite: 100-180 kg
Microsatellite: 10-100 kg
Nanosatellite: 1-10 kg
Picosatellite: 0.01-1 kg
Femtosatellite: 0.001-0.01 kg
CubeSats are a class of nanosatellites that use a standard size and form factor. The standard CubeSat size uses a “one unit” or “1U” measuring 10 × 10 × 10 cm and is extendable to larger sizes, e.g. 1.5, 2, 3, 6, and even 12U.
The final plenary lecture and the final session of the conference was a truly outstanding presentation by James W. Head III, Brown University, “The Apollo Lunar Exploration Program: Scientific Impact and the Road Ahead”. Head is a geologist who trained the Apollo astronauts for their Moon missions between 1969 and 1972.
During the early years of the space program, the United States was behind the Soviet Union in space technology and accomplishments. The N1 rocket was even going to deliver one or two Soviet cosmonauts to lunar orbit so they could land on the Moon.
Early in his presidency, John F. Kennedy attempted to engage the Soviet Union in space cooperation.
Chris Kraft’s book, Flight: My Life in Mission Control is recommended.
The Apollo astronauts (test pilots) were highly motivated students.
The United States flew 21 robotic precursor missions to the Moon in the eight years before Apollo 11. Rangers 1-9 were the first attempts, but 1 through 6 were failures and we couldn’t even hit the Moon.
Head recommends the recent documentary, Apollo 11, but called First Man Hollywood fiction, saying, “That is not the Neil Armstrong I knew.”
The Apollo 11 lunar samples showed us that the lunar maria (Mare Tranquillitatis) has an age of 3.7 Gyr and has a high titanium abundance.
The Apollo 12 lunar excursion module (LEM) landed about 600 ft. from the Surveyor 3 probe in Oceanus Procellarum, and samples from that mission were used to determine the age of that lunar maria as 3.2 Gyr.
Scientists worked shoulder to shoulder with the engineers during the Apollo program, contributing greatly to its success.
Apollo 11 landed at lunar latitude 0.6˚N, Apollo 12 at 3.0˚S, Apollo 14 at 3.6˚S, and Apollo 15 at 26.1˚N. Higher latitude landings required a plane change and a more complex operation to return the LEM to the Command Module.
The lunar rover was first used on Apollo 15, and allowed the astronauts to travel up to 7 km from the LEM. Head said that Dave Scott did remarkable geological investigations on this mission. He discovered and returned green glass samples, and in 2011 it was determined that there is water inside those beads. Scott also told a little fib to Mission Control to buy him enough time to pick up a rock that turned out to be very important, the “seat belt basalt”.
In speaking about Apollo 16, Head called John Young “one of the smartest astronauts in the Apollo program”.
Harrison Schmitt, Apollo 17, was the only professional geologist to go to the Moon, and he discovered the famous “orange soil”. This is the mission where the astronauts repaired a damaged fender on the lunar rover using duct tape and geological maps to keep them from getting covered in dust while traveling in the rover.
When asked about the newly discovered large mass under the lunar surface, Head replied that it is probably uplifted mantle material rather than an impactor mass underneath the surface.
Radiometric dating of the Apollo lunar samples have errors of about ± 5%.
One of the reasons the Moon’s albedo is low is that space weather has darkened the surface.
The South Pole-Aitken basin is a key landing site for future exploration. In general, both polar regions are of great interest.
Smaller objects like the Moon and Mars cooled efficiently after their formation because of their high surface area to volume ratio.
We do not yet know if early Mars was warm and wet, or cold and icy with warming episodes. The latter is more likely if our solar system had a faint young sun.
Venus has been resurfaced in the past 0.5 Gyr, and there is no evidence of plate tectonics. The first ~80% of the history of Venus is unknown. Venus probably had an ocean and tectonic activity early on, perhaps even plate tectonics. Venus may have undergone a density inversion which exchanged massive amounts of material between the crust and mantle. 80% of the surface of Venus today is covered by lava flows.
A mention was made that a new journal of Planetary Science (in addition to Icarus, presumably) will be coming from the AAS soon.
I attend a lot of meetings and lectures (both for astronomy and SAS), and I find that I am one of the few people in attendance who write down any notes. Granted, a few are typing at their devices, but one never knows if they are multitasking instead. For those that don’t take any notes, I wonder, how do they really remember much of what they heard days or weeks later without having written down a few keywords and phrases and then reviewing them soon after? I did see a writer from Astronomy Magazine at one of the press conferences writing notes in a notebook as I do. I believe it was Jake Parks.
Anyone who knows me very well knows that I love traveling by train. To attend the AAS meeting, I took a Van Galder bus from Madison to Chicago, and then Amtrak from Chicago to St. Louis. Pretty convenient that the AAS meeting was held at the Union Station Hotel, just a few blocks from Amtrak’s Gateway Station. It is a fine hotel with a lot of history, and has an excellent on-site restaurant. I highly recommend this hotel as a place to stay and as a conference venue.
The bus and train ride to and fro afforded me a great opportunity to catch up on some reading. Here are a few things worth sharing.
astrometry.net – you can upload your astronomical image and get back an image with all the objects in the image astrometrically annotated. Wow!
16 Psyche, the most massive metal-rich asteroid, is the destination for a NASA orbiter mission that is scheduled to launch in 2022 and arrive at Psyche in 2026. See my note about 16 Psyche in the AAS notes above.
The lowest hourly meteor rate for the northern hemisphere occurs at the end of March right after the vernal equinox.
A tremendous, dynamic web-based lunar map is the Lunar Reconnaissance Orbiter Camera (LROC) Quickmap, quickmap.lroc.asu.edu.
I read with great interest Dr. Ken Wishaw’s article on pp. 34-38 in the July 2019 issue of Sky & Telescope, “Red Light Field Test”. Orange or amber light is probably better that red light for seeing well in the dark while preserving your night vision. You can read his full report here. Also, see my article “Yellow LED Astronomy Flashlights” here.
Jupiter and Saturn will have a spectacular conjunction next year. As evening twilight fades on Monday, December 21, 2020, the two planets will be just 1/10th of a degree apart, low in the southwestern sky.
The light curve of a stellar occultation by a minor planet (asteroid or TNO) resembles a square well if the object has no atmosphere (or one so thin that it cannot be detected, given the sampling rate and S/N), and the effects of Fresnel diffraction and the star’s angular diameter are negligible.
Astronomer Margaret Burbidge, who turns 100 on August 12, 2019, refused the AAS Annie Jump Cannon Award in 1972, stating in her rejection letter that “it is high time that discrimination in favor of, as well as against, women in professional life be removed, and a prize restricted to women is in this category.” In 1976, Margaret Burbidge became the first woman president of the AAS, and in 1978 she announced that the AAS would no longer hold meetings in the states that had not ratified the Equal Rights Amendment (ERA).
During the days following the conference when I was writing this report, I received the happy news from both the AAS and Sky & Telescope that AAS was the winning bidder of S&T during a bankruptcy auction of its parent company, F+W Media. I believe that this partnership between the AAS and Sky & Telescope will benefit both AAS members and S&T readers immensely. Peter Tyson, Editor in Chief of Sky & Telescope, stated in the mutual press release, “It feels like S&T is finally landing where it belongs.” I couldn’t agree more!
9.2 Issue H: The possible existence of multiverses If there is a large enough ensemble of numerous universes with varying properties, it may be claimed that it becomes virtually certain that some of them will just happen to get things right, so that life can exist; and this can help explain the fine-tuned nature of many parameters whose values are otherwise unconstrained by physics. As discussed in the previous section, there are a number of ways in which, theoretically, multiverses could be realized. They provide a way of applying probability to the universe (because they deny the uniqueness of the universe). However, there are a number of problems with this concept. Besides, this proposal is observationally and experimentally untestable; thus its scientific status is debatable.
My 100-year-old uncle—a lifelong teacher and voracious reader who is still intellectually active—recently sent me Max Tegmark’s book Our Mathematical Universe: My Quest for the Ultimate Nature of Reality, published by Vintage Books in 2014. I could not have had a more engaging introduction to the concept of the Multiverse. Tegmark presents four levels of multiverses that might exist. They are
Level I Multiverse: Distant regions of space with the same laws of physics that are currently but not necessarily forever unobservable.
Level II Multiverse: Distant regions of space that may have different laws of physics and are forever unobservable.
Level III Multiverse: Quantum events at any location in space and in time cause reality to split and diverge along parallel storylines.
Level IV Multiverse: Space, time, and the Level I, II, and III multiverses all exist within mathematical structures that describe all physical existence at the most fundamental level.
There seems little question that our universe is very much larger than the part that we can observe. The vast majority of our universe is so far away that light has not yet had time to reach us from those regions. Whether we choose to call the totality of these regions the universe or a Level I multiverse is a matter of semantics.
Is our universe or the Level I multiverse infinite? Most likely not. That infinity is a useful mathematical construct is indisputable. That infinite space or infinite time exists is doubtful. Both Ellis and Tegmark agree on this and present cogent arguments as to why infinity cannot be associated with physical reality. Very, very large, or very, very small, yes, but not infinitely large or infinitely small.
Does a Level II, III, and IV multiverse exist? Tegmark thinks so, but Ellis raises several objections, noted above and elsewhere. The multiverse idea remains quite controversial, but as Tegmark writes,
Even those of my colleagues who dislike the multiverse idea now tend to grudgingly acknowledge that the basic arguments for it are reasonable. The main critique has shifted from “This makes no sense and I hate it” to “I hate it.”
I will not delve into the details of the Level II, III, and IV multiverses here. Read Tegmark’s book as he adroitly takes you through the details of eternal inflation, quantum mechanics and wave functions and the genius and tragic story of Hugh Everett III, the touching tribute to John Archibald Wheeler, and more, leading into a description of each multiverse level in detail.
I’d like to end this article with a quote from Max Tegmark from Mathematical Universe. It’s about when you think you’re the first person ever to discover something, only to find that someone else has made that discovery or had that idea before.
Gradually, I’ve come to totally change my feelings about getting scooped. First of all, the main reason I’m doing science is that I delight in discovering things, and it’s every bit as exciting to rediscover something as it is to be the first to discover it—because at the time of the discovery, you don’t know which is the case. Second, since I believe that there are other more advanced civilizations out there—in parallel universes if not our own—everything we come up with here on our particular planet is a rediscovery, and that fact clearly doesn’t spoil the fun. Third, when you discover something yourself, you probably understand it more deeply and you certainly appreciate it more. From studying history, I’ve also come to realize that a large fraction of all breakthroughs in science were repeatedly rediscovered—when the right questions are floating around and the tools to tackle them are available, many people will naturally find the same answers independently.
References Ellis, G.F.R., Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285. [http://arxiv.org/abs/astro-ph/0602280]
Tegmark, Max. Our mathematical universe : my quest for the ultimate nature of reality. New York: Alfred A. Knopf, 2014.
“You passed your exam in many parallel universes—but not in this one.”
9.1.6 The metaphysical options …there appear to be basically six approaches to the issue of ultimate causation: namely Random Chance, Necessity, High Probability, Universality, Cosmological Natural Selection, and Design. We briefly consider these in turn. Option 1: Random Chance, signifying nothing. The initial conditions in the Universe just happened, and led to things being the way they are now, by pure chance. Probability does not apply. There is no further level of explanation that applies; searching for ‘ultimate causes’ has no meaning. This is certainly logically possible, but not satisfying as an explanation, as we obtain no unification of ideas or predictive power from this approach. Nevertheless some implicitly or explicitly hold this view. Option 2: Necessity. Things have to be the way they are; there is no other option. The features we see and the laws underlying them are demanded by the unity of the Universe: coherence and consistency require that things must be the way they are; the apparent alternatives are illusory. Only one kind of physics is self-consistent: all logically possible universes must obey the same physics. To really prove this would be a very powerful argument, potentially leading to a self-consistent and complete scientific view. But we can imagine alternative universes! —why are they excluded? Furthermore we run here into the problem that we have not succeeded in devising a fully self-consistent view of physics: neither the foundations of quantum physics nor of mathematics are on a really solid consistent basis. Until these issues are resolved, this line cannot be pursued to a successful conclusion. Option 3: High probability. Although the structure of the Universe appears very improbable, for physical reasons it is in fact highly probable. These arguments are only partially successful, even in their own terms. They run into problems if we consider the full set of possibilities: discussions proposing this kind of view actually implicitly or explicitly restrict the considered possibilities a priori, for otherwise it is not very likely the Universe will be as we see it. Besides, we do not have a proper measure to apply to the set of initial conditions, enabling us to assess these probabilities. Furthermore, application of probability arguments to the Universe itself is dubious, because the Universe is unique. Despite these problems, this approach has considerable support in the scientific community, for example it underlies the chaotic inflationary proposal. It attains its greatest power in the context of the assumption of universality: Option 4: Universality. This is the stand that “All that is possible, happens”: an ensemble of universes or of disjoint expanding universe domains is realized in reality, in which all possibilities occur. In its full version, the anthropic principle is realized in both its strong form (if all that is possible happens, then life must happen) and its weak form (life will only occur in some of the possibilities that are realized; these are picked out from the others by the WAP, viewed as a selection principle). There are four ways this has been pursued. 1: Spatial variation. The variety of expanding universe domains is realised in space through random initial conditions, as in chaotic inflation. While this provides a legitimate framework for application of probability, from the viewpoint of ultimate explanation it does not really succeed, for there is still then one unique Universe whose (random) initial conditions need explanation. Initial conditions might be globally statistically homogeneous, but also there could be global gradients in some physical quantities so that the Universe is not statistically homogeneous; and these conditions might be restricted to some domain that does not allow life. It is a partial implementation of the ensemble idea; insofar as it works, it is really a variant of the “high probability” idea mentioned above. If it was the more or less unique outcome of proven physics, then that would provide a good justification; but the physics underlying such proposals is not even uniquely defined, much less tested. Simply claiming a particular scalar field with some specific stated potential exists does not prove that it exists! 2: Time variation. The variety of expanding universe domains could be realised across time, in a universe that has many expansion phases (a Phoenix universe), whether this occurs globally or locally. Much the same comments apply as in the previous case. 3: Quantum Mechanical. It could occur through the existence of the Everett-Wheeler “many worlds” of quantum cosmology, where all possibilities occur through quantum branching. This is one of the few genuine alternatives proposed to the Copenhagen interpretation of quantum mechanics, which leads to the necessity of an observer, and so potentially to the Strong Anthropic interpretation considered above. The many-worlds proposal is controversial: it occurs in a variety of competing formulations, none of which has attained universal acceptance. The proposal does not provide a causal explanation for the particular events that actually occur: if we hold to it, we then have to still explain the properties of the particular history we observe (for example, why does our macroscopic universe have high symmetries when almost all the branchings will not?). And above all it is apparently untestable: there is no way to experimentally prove the existence of all those other branching universes, precisely because the theory gives the same observable predictions as the standard theory. 4: Completely disconnected. They could occur as completely disconnected universes: there really is an ensemble of universes in which all possibilities occur, without any connection with each other. A problem that arises then is, What determines what is possible? For example, what about the laws of logic themselves? Are they inviolable in considering all possibilities? We cannot answer, for we have no access to this multitude of postulated worlds. We explore this further below. In all these cases, major problems arise in relating this view to testability and so we have to query the meaningfulness of the proposals as scientific explanations. They all contradict Ockham’s razor: we “solve” one issue at the expense of envisaging an enormously more complex existential reality. Furthermore, they do not solve the ultimate question: Why does this ensemble of universes exist? One might suggest that ultimate explanation of such a reality is even more problematic than in the case of single universe. Nevertheless this approach has an internal logic of its own which some find compelling. Option 5: Cosmological Natural Selection. If a process of re-expansion after collapse to a black hole were properly established, it opens the way to the concept not merely of evolution of the Universe in the sense that its structure and contents develop in time, but in the sense that the Darwinian selection of expanding universe regions could take place, as proposed by Smolin. The idea is that there could be collapse to black holes followed by re-expansion, but with an alteration of the constants of physics through each transition, so that each time there is an expansion phase, the action of physics is a bit different. The crucial point then is that some values of the constants will lead to production of more black holes, while some will result in less. This allows for evolutionary selection favouring the expanding universe regions that produce more black holes (because of the favourable values of physical constants operative in those regions), for they will have more “daughter” expanding universe regions. Thus one can envisage natural selection favouring those physical constants that produce the maximum number of black holes. The problem here is twofold. First, the supposed ‘bounce’ mechanism has never been fully explicated. Second, it is not clear—assuming this proposed process can be explicated in detail—that the physics which maximizes black hole production is necessarily also the physics that favours the existence of life. If this argument could be made water-tight, this would become probably the most powerful of the multiverse proposals. Option 6: Purpose or Design. The symmetries and delicate balances we observe require an extraordinary coherence of conditions and cooperation of causes and effects, suggesting that in some sense they have been purposefully designed. That is, they give evidence of intention, both in the setting of the laws of physics and in the choice of boundary conditions for the Universe. This is the sort of view that underlies Judaeo-Christian theology. Unlike all the others, it introduces an element of meaning, of signifying something. In all the other options, life exists by accident; as a chance by-product of processes blindly at work. The prime disadvantage of this view, from the scientific viewpoint, is its lack of testable scientific consequences (“Because God exists, I predict that the density of matter in the Universe should be x and the fine structure constant should be y”). This is one of the reasons scientists generally try to avoid this approach. There will be some who will reject this possibility out of hand, as meaningless or as unworthy of consideration. However it is certainly logically possible. The modern version, consistent with all the scientific discussion preceding, would see some kind of purpose underlying the existence and specific nature of the laws of physics and the boundary conditions for the Universe, in such a way that life (and eventually humanity) would then come into existence through the operation of those laws, then leading to the development of specific classes of animals through the process of evolution as evidenced in the historical record. Given an acceptance of evolutionary development, it is precisely in the choice and implementation of particular physical laws and initial conditions, allowing such development, that the profound creative activity takes place; and this is where one might conceive of design taking place. [This is not the same as the view proposed by the ‘Intelligent Design’ movement. It does not propose that God tweaks the outcome of evolutionary processes.] However from the viewpoint of the physical sciences per se, there is no reason to accept this argument. Indeed from this viewpoint there is really no difference between design and chance, for they have not been shown to lead to different physical predictions.
A few comments.
1: Random chance. At first, this strikes one as intellectual laziness, but perhaps it is more a reflection of our own intellectual weakness. More on that in a moment.
2: Necessity. Our intellectual journey of discovery and greater understanding must continue, and it may eventually lead us to this conclusion. But not now.
3: High probability. How can we talk about probability when n = 1?
4: Universality. We can hypothesize the existence of other universes, yes, but if we have no way to observe or interact with them, how can we call this endeavor science? Furthermore, explaining the existence of multiple universes seems even more problematic that explaining the existence of a single universe—ours.
5: Cosmological Natural Selection. We do not know that black holes can create other universes, or that universes that contain life are more likely to have laws of physics that allow an abundance of black holes
6. Purpose of Design. The presupposition of design is not evidence of design. It is possible that scientific evidence of a creator or designer might be found in nature—such as an encoded message evincing purposeful intelligence in DNA or the cosmic microwave background—but to date no such evidence has been found. Even if evidence of a creator is forthcoming, how do we explain the existence of the creator?
I would now like to suggest a seventh option (possibly a variant of Ellis’s Option 1 Random Chance or Option 2 Necessity).
7. Indeterminate Due to Insufficient Intelligence. It is at least possible that there are aspects of reality and our origins that may be beyond what humans are currently capable of understanding. For some understanding of how this might be possible, we need look no further than the primates we are most closely related to, and other mammals. Is a chimpanzee self-aware? Can non-humans experience puzzlement? Are animals aware of their own mortality? Even if the answer to all these questions is “yes”1, there are clearly many things humans can do that no other animal is capable of. Why stop at humans? Isn’t it reasonable to assume that there is much that humans are cognitively incapable of?
Why do we humans develop remarkable technologies and yet fail dismally to eradicate poverty, war, and other violence? Why does the world have so many religions if they are not all imperfect and very human attempts to imbue our lives with meaning?
What is consciousness? Will we ever understand it? Can we extrapolate from our current intellectual capabilities to a complete understanding of our origins and the origins of the universe, or is something more needed that we currently cannot even envision?
“Sometimes attaining the deepest familiarity with a question is our best substitute for actually having the answer.” —Brian Greene, The Elegant Universe
“To ask what happens before the Big Bang is a bit like asking what happens on the surface of the earth one mile north of the North Pole. It’s a meaningless question.” —Stephen Hawking, Interview with Timothy Ferris, Pasadena, 1985
1 For more on the topic of the emotional and cognitive similarities between animals and humans, see “Mama’s Last Hug: Animal Emotions and What They Tell Us about Ourselves” by primatologist Frans de Waal, W. W. Norton & Company (2019). https://www.amazon.com/dp/B07DP6MM92 .
References G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285. [http://arxiv.org/abs/astro-ph/0602280]
The first requirement is the existence of laws of physics that guarantee the kind of regularities that can underlie the existence of life. These laws as we know them are based on variational and symmetry principles; we do not know if other kinds of laws could produce complexity. If the laws are in broad terms what we presently take them to be, the following inter alia need to be right, for life of the general kind we know to exist:
The neutron-proton mass differential must be highly constrained. If the neutron mass were just a little less than it is, proton decay could have taken place so that by now no atoms would be left at all.
Electron-proton charge equality is required to prevent massive electrostatic forces overwhelming the weaker electromagnetic forces that govern chemistry.
The strong nuclear force must be strong enough that stable nuclei exist; indeed complex matter exists only if the properties of the nuclear strong force lies in a tightly constrained domain relative to the electromagnetic force.
The chemistry on which the human body depends involves intricate folding and bonding patterns that would be destroyed if the fine structure constant (which controls the nature of chemical bonding) were a little bit different.
The number D of large spatial dimensions must be just 3 for complexity to exist.
It should not be too surprising that we find ourselves in a universe whose laws of physics are conducive to the existence of semi-intelligent life. After all, we are here. What we do not know—and will probably never know: Is this the only universe that exists? This is an important question, because if there are many universes with different laws of physics, our existence in one of them may be inevitable. If, on the other hand, this is the only universe, then the fantastic claims of the theists, or at least the deists, become more plausible.
You may wonder why I call the human race semi-intelligent. Rest assured, I am not being sarcastic or sardonic. I say “semi-intelligent” to call attention to humanity’s remarkable technological and scientific achievements while also noting our incredible ineptness at eradicating war, violence, greed, and poverty from the world. What is wrong with us?
References G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285. [http://arxiv.org/abs/astro-ph/0602280]
Mark Whittle, Professor of Astronomy at the University of Virginia, has put together the most comprehensive and comprehensible treatment on the subject of cosmology that I have ever encountered. Cosmology: The History and Nature of Our Universe, a series of 36 thirty-minute video lectures for The Great Courses (Course No. 1830), is a truly remarkable achievement.
Even though this course was released ten years ago in 2008, all of the material is still completely relevant. This is the course on cosmology that I’ve always wanted but never had. Enjoy!
Cosmology has come a long ways since I was a physics and astronomy student at Iowa State University from 1975-1980, and again in 1981, 1984, and 2000-2005. I’m glad to see a course specifically about cosmology is now offered at a number of universities. When I was an undergraduate student at ISU, it was unheard of. The University of Wisconsin at Madison Department of Astronomy currently offers both an undergraduate and a graduate course in cosmology: Astronomy 335 – Cosmology, and Astronomy 735 – Observational Cosmology. And the Department of Physics & Astronomy at Iowa State University now offers an undergraduate/graduate dual-listed cosmology course: Astro 405/505 – Astrophysical Cosmology.
When I retire in a few years, I would love to be a “fly on the wall” at the UW-Madison astronomy department. Wonder if they could use an expert SAS programmer to help analyze the massive quantities of data they surely must have? (Though the last time I interviewed for an astronomy job, at the McDonald Observatory in Texas, the interviewers had never heard of SAS but asked if I knew Python, which of course is what nearly everyone is looking for and using these days. Tomorrow, it will be something else…). In retirement, at the very least I would love to immerse myself in a few astronomy courses at UW-Madison. Something to look forward to!
9.1 Issue G: The anthropic question: Fine tuning for life
One of the most profound fundamental issues in cosmology is the Anthropic question: why does the Universe have the very special nature required in order that life can exist? The point is that a great deal of “fine tuning” is required in order that life be possible. There are many relationships embedded in physical laws that are not explained by physics, but are required for life to be possible; in particular various fundamental constants are highly constrained in their values if life as we know it is to exist:
Ellis goes on to quote Martin Rees.
A universe hospitable to life—what we might call a biophilic universe—has to be special in many ways … Many recipes would lead to stillborn universes with no atoms, no chemistry, and no planets; or to universes too short lived or too empty to evolve beyond sterile uniformity.
Also, why do we live in a universe with three spatial dimensions and one time dimension? Others are possible—even universes with two or more time dimensions.
But it appears that only three spatial dimensions and one time dimension is conducive to life (at least life as we know it), as shown in the diagram above (Whittle 2008).
In fact, altering almost any of the parameters would lead to a sterile universe and we could not exist. Is the universe fine-tuned for our existence?
Let’s assume for the moment it is. Where does that lead us?
As our understanding of physics advances, we will eventually understand why these parameters must have the values that they do. -or-
We will eventually learn that some of these parameters could have been different, and still support the existence of life. -or-
God created the universe in such a way that life could exist -or-
We’re overthinking the problem. We live in a life-supporting universe, so of course we find the parameters are specially tuned to allow life. -or-
There exist many universes with different parameters and we just happen to find ourselves in one that is conducive to life. (The multiverse idea.)
#4 is the anthropic explanation, but a deeper scientific understanding will occur if we find either #1, #2, or #5 to be true. #3 is problematic for a couple of reasons. First of all, how was God created? Also, deism has a long history of explaining phenomena we don’t understand (“God of the gaps”), but in time we are able to understand each phenomenon in turn as science progresses.
The anthropic explanation itself is not controversial. What is controversial is deciding to what degree fine tuning has occurred and how to explain it.
In recent years, the multiverse idea has become more popular because, for example, if there were a billion big bangs and therefore a billion different universes created, then it should not be at all surprising that we find ourselves in one with just the right set of parameters to allow our existence. However, there is one big problem with the multiverse idea. Not only do we have no physical evidence that a multiverse exists, but we may never be able to obtain evidence that a multiverse exists, due to the cosmological horizon problem1. If physical evidence of a multiverse is not forthcoming, then in that sense it is not any better than the deistic explanation.
To decide whether or not there is only one combination of parameters that can lead to life we need to rule out all the other combinations, and that is a tall order. Recent work in this field suggests that there is more than one combination of parameters that could create a universe that is hospitable to life (Hossenfelder 2018).
Thinking now about why our universe is here at all, it seems there are just two possibilities:
(1) Our universe has a supernatural origin.
(2) Our universe has a natural origin.
If our universe has a supernatural origin, then what is the origin of the supernatural entity (e.g. God)? If, on the other hand, our universe had a natural origin (e.g. something was created out of nothing), didn’t something have to exist (laws of physics or whatever) before the universe came into existence? If so, what created those pre-conditions?
In either case, we are facing an infinite regression. However, we could avoid the infinite regression by stating that something has to exist outside of time, that is to say, it has no beginning and no ending. But isn’t this just replacing one infinity with another?
Perhaps there’s another possibility. Just as a chimpanzee cannot possibly understand quantum mechanics, could it be that human intellect is also fundamentally limited? Are the questions in the previous two paragraphs meaningless or nonsensical in the context of some higher intelligence?
1We appear to live in a universe that is finite but very much larger than the region that is visible to us now, or ever.
G.F.R. Ellis, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
Sabine Hossenfelder, Lost in Math: How Beauty Leads Physics Astray (Basic Books, 2018).
M. J. Rees, Our Cosmic Habitat (Princeton and Oxford, 2003).
We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.
8.3 Limits of Representation and Knowledge of Reality
It follows…that there are limits to what the scientific method can achieve in explanatory terms. We need to respect these limits and acknowledge clearly when arguments and conclusions are based on some philosophical stance rather than purely on testable scientific argument. If we acknowledge this and make that stance explicit, then the bases for different viewpoints are clear and alternatives can be argued about rationally.
We human beings want so badly to be able to explain our existence and existence itself that we tend to “fill in the blanks” and treat speculation (no matter how well reasoned) as if it were something akin to fact. This is true for both science and religion. A more reasonable approach, it seems to me, is to reject absolute certainty—especially where physical evidence is sparse or nonexistent—while always striving to deepen our understanding. That is the scientist’s stock-in-trade—or should be. Each of us needs to become more aware of the limitations of our understanding!
Thesis F6: Reality is not fully reflected in either observations or theoretical models.
Problems arise from confusion of epistemology (the theory of knowledge) with ontology (the nature of existence): existence is not always manifest clearly in the available evidence. The theories and models of reality we use as our basis for understanding are necessarily partial and incomplete reflections of the true nature of reality, helpful in many ways but also inevitably misleading in others. They should not be confused with reality itself!
We humans create our own “realities”, but under the very best of circumstances (science, for example), our “reality” is only an imperfect model of what actually exists.
The confusion of epistemology with ontology occurs all the time, underlying for example the errors of both logical positivism and extreme relativism. In particular, it is erroneous to assume that lack of evidence for the existence of some entity is proof of its non-existence. In cosmology it is clear for example that regions may exist from which we can obtain no evidence (because of the existence of horizons); so we can sometimes reasonably deduce the existence of unseen matter or regions from a sound extrapolation of available evidence (no one believes matter ends at or just beyond the visual horizon). However one must be cautious about the other extreme, assuming existence can always be assumed because some theory says so, regardless of whether there is any evidence of existence or not. This happens in present day cosmology, for example in presentations of the case for multiverses, even though the underlying physics has not been experimentally confirmed. It may be suggested that arguments ignoring the need for experimental/observational verification of theories ultimately arise because these theories are being confused with reality, or at least are being taken as completely reliable total representations of reality.
Absence of evidence is not evidence of absence. But, without evidence, all we have is conjecture, no matter how well informed. As Carl Sagan once said, “Extraordinary claims require extraordinary evidence.”
No model (literary, intuitive, or scientific) can give a perfect reflection of reality. Such models are always selective in what they represent and partial in the completeness with which they do so. The only model that would reflect reality fully is a perfect fully detailed replica of reality itself! This understanding of the limits of models and theories does not diminish the utility of these models; rather it helps us use them in the proper way. This is particularly relevant when we consider how laws of nature may relate to the origins of the universe itself, and to the existence and nature of life in the expanding universe. The tendency to rely completely on our theories, even when untested, seems sometimes to arise because we believe they are the same as reality—when at most they are descriptions of reality.
Ellis makes a pretty good case here against dogma. Though he does not specifically mention religion (and why should he, as the subject at hand is cosmology), I do think these ideas apply to religion as well.
Always a journey, never a destination.
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
We continue our series of excerpts (and discussion) from the outstanding survey paper by George F. R. Ellis, Issues in the Philosophy of Cosmology.
The physical explanatory power of inflation in terms of structure formation, supported by the observational data on the fluctuation spectra, is spectacular. For most physicists, this trumps the lack of identification and experimental verification of the underlying physics. Inflation provides a causal model that brings a wider range of phenomena into what can be explained by cosmology, rather than just assuming the initial data had a specific restricted form. Explaining flatness (Ω0 ≅ 1 as predicted by inflation) and homogeneity reinforces the case, even though these are philosophical rather than physical problems (they do not contradict any physical law; things could just have been that way). However claims on the basis of this model as to what happens very far outside the visual horizon (as in the chaotic inflationary theory) results from prioritizing theory over the possibility of observational and experimental testing. It will never be possible to prove these claims are correct.
Inflation is one compelling approach to explaining the structure we see in the universe today. It is not necessarily the only one, but it currently has the most support. Basically, a tiny fraction of a second after the Big Bang, the universe expanded dramatically. Around 10-36 seconds after the Big Bang the universe had a diameter on the order of 1.2 × 10-27 meters. To put that size in perspective, the diameter of a proton is between 0.84-0.87 × 10−15 meters. So, when inflation began, the entire universe had a diameter almost a trillion times smaller than a single proton! 10-34 seconds later when the inflationary period was coming to an end, the size of the universe was a little over half the distance to Alpha Centauri!
The basic underlying cosmological questions are:
(1) Why do the laws of physics have the form they do? Issues arise such as what makes particular laws work? For example, what guarantees the behaviour of a proton, the pull of gravity? What makes one set of physical laws ‘fly’ rather than another? If for example one bases a theory of cosmology on string theory, then who or what decided that quantum gravity would have a nature well described by string theory? If one considers all possibilities, considering string theory alone amounts to a considerable restriction.
(2) Why do boundary conditions have the form they do? The key point here is, how are specific contingent choices made between the various possibilities, for example whether there was an origin to the universe or not.
(3) Why do any laws of physics at all exist? This relates to unsolved issues concerning the nature of the laws of physics: are they descriptive or prescriptive? Is the nature of matter really mathematically based in some sense, or does it just happen that its behaviour can be described in a mathematical way?
(4) Why does anything exist? This profound existential question is a mystery whatever approach we take.
The answer to such questions may be beyond the limits of experimental science, or even beyond the limits of our intellect. Maybe, even, these questions are as meaningless as “What lies north of the north pole?1” because of our limited intellect. Many would claim that because there appears to be limits to what science or human intellect can presently explain, that this constitutes evidence for the existence of God. It does not. Let’s just leave it as we don’t know.
Finally, the adventurous also include in these questions the more profound forms of the contentious Anthropic question:
(5) Why does the universe allow the existence of intelligent life?
This is of somewhat different character than the others and largely rests on them but is important enough to generate considerable debate in its own right.
Well, a seemingly flippant answer to this question is we wouldn’t be here if it didn’t, but that begs the question. Perhaps intelligent life is the mechanism by which the universe becomes self-aware, or is this just wishful thinking? In the end, I am willing to admit that there may be some higher power in the universe—in the scientific pantheist and humanist sense—but I will stop short of calling that “God” in any usual sense of the term.
The status of all these questions is philosophical rather than scientific, for they cannot be resolved purely scientifically. How many of them—if any—should we consider in our construction of and assessments of cosmological theories?
Perhaps the limitations of science (and, therefore, cosmology) is more a manifestation of the limitations of our human intellect than any constraint on the universe itself.
One option is to decide to treat cosmology in a strictly scientific way, excluding all the above questions, because they cannot be solved scientifically. One ends up with a solid technical subject that by definition excludes such philosophical issues. This is a consistent and logically viable option. This logically unassailable position however has little explanatory power; thus most tend to reject it.
Let’s call this physical cosmology.
The second option is to decide that these questions are of such interest and importance that one will tackle some or all of them, even if that leads one outside the strictly scientific arena. If we try to explain the origin of the universe itself, these philosophical choices become dominant precisely because the experimental and observational limits on the theory are weak; this can be seen by viewing the variety of such proposals that are at present on the market.
And let’s call this metaphysical cosmology.
1Attributed to Stephen Hawking
Ellis, G. F. R. 2006, Issues in the Philosophy of Cosmology, Philosophy of Physics (Handbook of the Philosophy of Science), Ed. J. Butterfield and J. Earman (Elsevier, 2006), 1183-1285.
Ryden, Barbara. 2003. Introduction to Cosmology. San Francisco: Addison Wesley.