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LADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity.THE RINDLER HORIZON
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
ANATOMY OF A HATCHET JOB O f all the reviews of Incandescence rendered irrelevant by hostility or carelessness, one stands out from the rest. In fact, I believe this particular review is probably the first genuine hatchet job I’ve ever received. There is no precise, generally accepted definition of the term hatchet job, so I’m going to feel free to specify my own.The distinguishing quality, I’d contend, is not GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity.THE RINDLER HORIZON
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
ANATOMY OF A HATCHET JOB O f all the reviews of Incandescence rendered irrelevant by hostility or carelessness, one stands out from the rest. In fact, I believe this particular review is probably the first genuine hatchet job I’ve ever received. There is no precise, generally accepted definition of the term hatchet job, so I’m going to feel free to specify my own.The distinguishing quality, I’d contend, is notWORKS ONLINE
Online at Tor.com, August 2017. The Best Science Fiction of the Year: Volume Three, edited by Neil Clarke; Night Shade Books, New York, 2018. “Bit Players”. Online at Subterranean Online, Winter 2014 issue, guest edited by Jonathan Strahan.SCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | Catacaustics 1: SPECIAL RELATIVITY The notation “(x,y)” beside the point P is a reminder that points can be referred to by their x– and y-coordinates, written as an ordered pair.The arrow drawn from O to P is a reminder that every point can be thought of as defining a vector from the origin to the point. The advantage of dealing with vectors, rather than just points in space, is that the same geometry can then be applied DISTRESS — GREG EGAN Illustrations for Distress by Greg Egan. Synopsis “All right. He’s dead. Go ahead and talk to him.” The bioethicist was a laconic young asex with blond dreadlocks and a T-shirt which flashed up the slogan SAY NO TO TOE! in between the paid advertising. RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian and ZENDEGI — GREG EGAN Fifteen years later, Martin is living in Iran with his wife and young son, while Nasim is in charge of the virtual world known as Zendegi, which is used by millions of people for entertainment and business. When Zendegi comes under threat from powerful competitors, Nasim draws on her old skills, and data from the now-completed Human Connectome HYPERCUBE (TECHNICAL NOTES) Euler characteristic. We can use our formula for the number of parts of an n-cube to find the Euler characteristic of a sphere of any dimension. The Euler characteristic of a space is the alternating sum of the number of objects of each dimension — the number of vertices, minus the number of edges, plus the number of faces, etc. — in a division of the space into polygons, polyhedra, orDICHRONAUTS
Seth is a surveyor, along with his friend Theo, a leech-like creature running through his skull who tells Seth what lies to his left and right. Theo, in turn, relies on Seth for mobility, and for ordinary vision looking forwards and backwards. Like everyone else in their world, they are symbionts, depending on each other to survive. ANATOMY OF A HATCHET JOB O f all the reviews of Incandescence rendered irrelevant by hostility or carelessness, one stands out from the rest. In fact, I believe this particular review is probably the first genuine hatchet job I’ve ever received. There is no precise, generally accepted definition of the term hatchet job, so I’m going to feel free to specify my own.The distinguishing quality, I’d contend, is notIN THE RUINS
In the Ruins. “Y ou’ll never get tenure. You don’t have the abs.”. Emma waited for Jacob’s mask of bemusement to give way to the hint of wounded pride that she’d been aiming for. They both knew that she was speaking the truth. GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity. RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian andTHE RINDLER HORIZON
GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity. RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian andTHE RINDLER HORIZON
SCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | CatacausticsWORKS ONLINE
Online at Tor.com, August 2017. The Best Science Fiction of the Year: Volume Three, edited by Neil Clarke; Night Shade Books, New York, 2018. “Bit Players”. Online at Subterranean Online, Winter 2014 issue, guest edited by Jonathan Strahan. DISTRESS — GREG EGAN Illustrations for Distress by Greg Egan. Synopsis “All right. He’s dead. Go ahead and talk to him.” The bioethicist was a laconic young asex with blond dreadlocks and a T-shirt which flashed up the slogan SAY NO TO TOE! in between the paid advertising. 2: FROM SPECIAL TO GENERAL 2: From Special to General. T he first article in this series described some of the ways in which the geometry of spacetime affects travellers moving (relative to their destinations, or each other) at a substantial fraction of the speed of light. By generalising from the Euclidean metric, which captures such familiar aspects of geometry as RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian and HYPERCUBE (TECHNICAL NOTES) Euler characteristic. We can use our formula for the number of parts of an n-cube to find the Euler characteristic of a sphere of any dimension. The Euler characteristic of a space is the alternating sum of the number of objects of each dimension — the number of vertices, minus the number of edges, plus the number of faces, etc. — in a division of the space into polygons, polyhedra, or KLEIN’S QUARTIC EQUATION Topology. The first thing to note is that Klein’s quartic equation (KQE) is a homogeneous equation in three complex variables, u, v and w.If any triple of complex numbers, (u,v,w) solves the equation, then any multiple of that triple, (zu,zv,zw) for any complex number z, will also solve the equation.What this means is that the solution space we’re really interested in is not C 3, theTHE TELL-TALE BOARD
The applet below implements an ingenious puzzle. (I did not invent this puzzle myself. But I won’t link to any other source from this page because I don’t want to give spoilers.)IN THE RUINS
In the Ruins. “Y ou’ll never get tenure. You don’t have the abs.”. Emma waited for Jacob’s mask of bemusement to give way to the hint of wounded pride that she’d been aiming for. They both knew that she was speaking the truth. ORPHANOGENESIS (EXCERPT) T he conceptory placed the new orphan seed in the middle of the womb’s memory, a single strand of information suspended in a vacuum of zeros. The seed meant nothing to itself; alone, it might as well have been the last stream of Morse, fleeing through the void past a distant star. But the womb was a virtual machine designed to execute the seed’s instructions, and a dozen more layers of GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity. RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian andTHE RINDLER HORIZON
GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for theSUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity. RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian andTHE RINDLER HORIZON
SCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | CatacausticsWORKS ONLINE
Online at Tor.com, August 2017. The Best Science Fiction of the Year: Volume Three, edited by Neil Clarke; Night Shade Books, New York, 2018. “Bit Players”. Online at Subterranean Online, Winter 2014 issue, guest edited by Jonathan Strahan. DISTRESS — GREG EGAN Illustrations for Distress by Greg Egan. Synopsis “All right. He’s dead. Go ahead and talk to him.” The bioethicist was a laconic young asex with blond dreadlocks and a T-shirt which flashed up the slogan SAY NO TO TOE! in between the paid advertising. 2: FROM SPECIAL TO GENERAL 2: From Special to General. T he first article in this series described some of the ways in which the geometry of spacetime affects travellers moving (relative to their destinations, or each other) at a substantial fraction of the speed of light. By generalising from the Euclidean metric, which captures such familiar aspects of geometry as RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian and HYPERCUBE (TECHNICAL NOTES) Euler characteristic. We can use our formula for the number of parts of an n-cube to find the Euler characteristic of a sphere of any dimension. The Euler characteristic of a space is the alternating sum of the number of objects of each dimension — the number of vertices, minus the number of edges, plus the number of faces, etc. — in a division of the space into polygons, polyhedra, orTHE TELL-TALE BOARD
The applet below implements an ingenious puzzle. (I did not invent this puzzle myself. But I won’t link to any other source from this page because I don’t want to give spoilers.) KLEIN’S QUARTIC EQUATION Topology. The first thing to note is that Klein’s quartic equation (KQE) is a homogeneous equation in three complex variables, u, v and w.If any triple of complex numbers, (u,v,w) solves the equation, then any multiple of that triple, (zu,zv,zw) for any complex number z, will also solve the equation.What this means is that the solution space we’re really interested in is not C 3, theIN THE RUINS
In the Ruins. “Y ou’ll never get tenure. You don’t have the abs.”. Emma waited for Jacob’s mask of bemusement to give way to the hint of wounded pride that she’d been aiming for. They both knew that she was speaking the truth. ORPHANOGENESIS (EXCERPT) T he conceptory placed the new orphan seed in the middle of the womb’s memory, a single strand of information suspended in a vacuum of zeros. The seed meant nothing to itself; alone, it might as well have been the last stream of Morse, fleeing through the void past a distant star. But the womb was a virtual machine designed to execute the seed’s instructions, and a dozen more layers of GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
SCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | Catacaustics PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for the RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity.SUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian and GREG EGAN’S HOME PAGETHE PLANCK DIVEFOUNDATIONSSCHILD'SLADDERSCIENCE NOTES
Greg Egan’s. Home Page. www.gregegan.net. Last revision: Monday, 10 May 2021. RSS feed for updates. Twitter: @gregeganSF. I am a science fiction writer and computer programmer. This site contains: information, illustrations and applets to supplement some of my work; EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
SCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | Catacaustics PROBABILITIES OF RUNS There are many scenes in Quarantine where probabilistic events yield a long run of identical outcomes: a silver atom crossing a magnetic field swerves up rather than down, over and over again, or a pair of dice repeatedly fall as “snake eyes”. How can we calculate the odds of this happening when the normal rules of probability apply? If we toss a fair coin N times, there are 2 N different DIASPORA — GREG EGANSEE MORE ON GREGEGAN.NET GENERAL RELATIVITY IN 2+1 DIMENSIONS Basic concepts. In 2+1 dimensions, Einstein’s equation in a vacuum requires that spacetime is completely flat. This is in stark contrast to the situation in 3+1 dimensions, where the vacuum solutions are only required to be “Ricci flat”, that is, the Ricci curvature tensor must be zero, but the complete, Riemann curvature tensor need not be, allowing for gravitational waves, and for the RIEMANNIAN GENERAL RELATIVITY Yes, We Have No Black Holes. How different is the behaviour of gravity in the Riemannian universe from the way it works in our own? Here’s one possible change: since there is neither a fixed speed of light nor any speed limit on material objects, it would seem that there can beno black holes.
RELATIVISTIC ELASTICITY X (τ,λ) = λ + A Z (τ,λ) and then discard terms that are higher than first order in A, the result is: ∂ t,tZ = 2 K2 ∂ λ,λZ. This is just the linear wave equation, with a speed of sound equal to K√2. So for infinitesimal deformations, there is no difference between relativistic and classical elasticity.SUPERPERMUTATIONS
RIEMANNIAN GENERAL RELATIVITY The first term represents centrifugal acceleration, a roughly inverse-cube repulsion for a given amount of angular momentum L.In the Lorentzian version the numerator here is r–3M, so the term changes sign at r=3M, which is why there can be no orbits around a black hole closer than that.But here, centrifugal force stays centrifugal everywhere, and is always stronger than the Lorentzian andSCIENCE NOTES
If you link to this page, please use this URL: https://www.gregegan.net/SCIENCE/Science.html; Ball Bearings in a Hypersphere | Born Rigid Motion | Catacaustics EBOOKS — GREG EGAN This page lists eBooks that I have published myself. They are all currently priced at US$2.99-US$3.99, and they are DRM-free (that is, the eBook’s use is not restricted by Digital Rights Management). For Diaspora, as well as the standard eBook there is an Enhanced Multimedia Edition, for iPads and for Apple computers running Mac OS10.9 or later.
ORBITS AND TIDAL ACCELERATIONS What is the role of the station’s spin in all this? The acceleration found from looking at these test particle orbits is greater than the usual tidal stretching by an amount which can be attributed, equally well, either to a difference in orbital centrifugal force at different radii, or to centrifugal force associated with the spin of the stationaround its axis.
THE RINDLER HORIZON
Now, consider a family of hyperbolas of the form: x2 – t2 – s2 = x x – s2 = 0, or. ( t ( q ), x ( q )) = ( s sinh ( q ), s cosh ( q )) These will intersect all of the straight lines of constant q orthogonally. So, in the region to the right of the Rindler horizon, we can use q and s as coordinates: Along the x -axis, s agrees with xTHE PLANCK DIVE
Synopsis. Gisela wanted to understand the universe at its deepest level, to touch the beauty and simplicity that lay beneath it all. That was why she was taking the Planck Dive. The polis of Cartan has been in orbit around the black hole Chandrasekhar for almost three centuries. Now, a group of polis citizens are preparing to encodeclones of
DICHRONAUTS
Seth is a surveyor, along with his friend Theo, a leech-like creature running through his skull who tells Seth what lies to his left and right. Theo, in turn, relies on Seth for mobility, and for ordinary vision looking forwards and backwards. Like everyone else in their world, they are symbionts, depending on each other to survive.THE TELL-TALE BOARD
The applet below implements an ingenious puzzle. (I did not invent this puzzle myself. But I won’t link to any other source from this page because I don’t want to give spoilers.)IN THE RUINS
In the Ruins. “Y ou’ll never get tenure. You don’t have the abs.”. Emma waited for Jacob’s mask of bemusement to give way to the hint of wounded pride that she’d been aiming for. They both knew that she was speaking the truth. ORPHANOGENESIS (EXCERPT) T he conceptory placed the new orphan seed in the middle of the womb’s memory, a single strand of information suspended in a vacuum of zeros. The seed meant nothing to itself; alone, it might as well have been the last stream of Morse, fleeing through the void past a distant star. But the womb was a virtual machine designed to execute the seed’s instructions, and a dozen more layers of GOOGLE, THE STUPIDITY AMPLIFIER 25 August 2012. Update: The photo of professor of engineering Gregory K Egan is once again appearing in Google’s mash-up, merged with biographical details of the SF writer Greg Egan. And this time the fault is 100% Google’s, since they’re taking the photo straight from the Monash University engineering department, rather than fromsome SF
LATEST BOOKS:
INSTANTIATION, eBook, Greg Egan, 2020. Amazon Kindle (USA) , Amazon Kindle (UK) , Amazon Kindle (Australia) , Smashwords, iTunes
, Barnes
and Noble Nook
,
Kobo
* “The Discrete Charm of the Turing Machine” * “Zero For Conduct” * “Uncanny Valley” * “Seventh Sight”* “The Nearest”
* “Shadow Flock”* “Bit Players”
* “Break My Fall”* “3-adica”
* “The Slipway”
* “Instantiation” THE BEST OF GREG EGAN , Subterranean Press,2019.
* “Learning to Be Me”* “Axiomatic”
* “Appropriate Love” * “Into Darkness” * “Unstable Orbits in the Space of Lies”* “Closer”
* “Chaff”
* “Luminous”
* “Silver Fire”
* “Reasons to be Cheerful”* “Oceanic”
* “Oracle”
* “Singleton”
* “Dark Integers” * “Crystal Nights” * “Zero For Conduct”* “Bit Players”
* “Uncanny Valley”* “3-adica”
* “Instantiation”RECENT BOOKS:
• DICHRONAUTS
Night Shade Books ,
2017 (print editions worldwide, eBook for North America). Paperbackedition: June 2018.
OUTSIDE NORTH AMERICA, the eBook is available from Amazon UK, Amazon Australia
, iTunes UK
, iTunes Australia
, Kobo UK
, Kobo Australia
and Smashwords
.
Read an excerpt .
Greg Egan’s
Home Page
www.gregegan.net
Last revision: Saturday, 21 March 2020 RSS feed for updates Twitter: @gregeganSF I am a science fiction writer and computer programmer. This sitecontains:
* information, illustrations and applets to supplement some of mywork;
* a bibliography ;
* links to works online (including TWENTY-THREE FREE STORIES); * the Foundations series of introductoryscience articles;
* some more technical science notes ; * an applets gallery ; * side-bar and full-screen sitemaps.
* CONTACT DETAILS: My email address can be formed from parts of the URL of this web site. Please don’t send messages to my agents or to other third parties to pass on to me, and please don’t ask me tosign books.
* THERE ARE NO PHOTOS OF ME ON THE WEB. The world contains many people besides me who are named Greg Egan, and thanks to the idiots at Google and the trashy click-bait sites they rely on it’s possible to find images online of half a dozen different people that are labelled as “Australian SF writer Greg Egan,” but none are what they claim tobe.
LATEST SHORT:
• “Zeitgeber”
Free to read online at Tor.com, September 2019. (Also available as a DRM-free eBook from all the usual outlets, for about US$1, from 9October.)
• “The Slipway” _Analog_, Jul/Aug 2019. • “This is Not the Way Home” _Mission: Critical_, edited by Jonathan Strahan, Solaris, 2019. • “Perihelion Summer” Paperback/eBook novella from Tor.com books, April 2019. • “Instantiation” _Asimov’s Science Fiction_, Mar/Apr 2019.• “3-adica”
_Asimov’s Science Fiction_, Sep/Oct 2018.• “Phoresis”
Hardback novella from Subterranean Press , April 2018; also availableas an eBook .
“Border Guards”
DIASPORA
DICHRONAUTS
DISTRESS
INCANDESCENCE
“Oceanic”
ORTHOGONAL
PERMUTATION CITY
“The Planck Dive”QUARANTINE
SCHILD’S LADDER
TERANESIA
ZENDEGI
------------------------- Greg Egan’s Home Page / created Saturday, 25 October 1997 / revised Saturday, 10 December 2016 IF YOU LINK TO THIS PAGE, PLEASE USE THIS URL: https://www.gregegan.net _Copyright © Greg Egan , 1997-2016. All rightsreserved._
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