
Post by krusader74 on Jan 4, 2015 6:35:49 GMT 6
The Dreams in the Witch HouseH. P. Lovecraft completed the manuscript to The Dreams in the Witch House on February 28, 1932. It was published in the July 1933 issue of Weird Tales on pages 86111. This is my favorite Lovecraft story. I originally read it sometime in the 80s. Recently, I reread it on my Kindle, as part of the Free Complete Works of H.P. Lovecraft for Nook (ePub) and Kindle (mobi) and PDF compilation by CthulhuChick. 1. Plot SummaryI. ExpositionWalter Gilman studies nonEuclidean calculus and quantum physics. He connects the higherdimensional math and physics he's learning to the case of the disappearance of an accused witch, Keziah Mason, from Salem gaol in 1692, never to be seen again, leaving behind in her cell "curves and angles smeared on the grey stone walls with some red, sticky fluid" that were inexplicable even to Cotton Mather. Gilman suspects Keziah had developed "an insight into mathematical depths perhaps beyond the utmost modern delvings of Planck, Heisenberg, Einstein, and De Sitter." Following this hunch, in January 1928 Walter Gilman enrolls as a grad student at Miskatonic University in Arkham, Massachusetts. He rents a room from Mr. and Mrs. Dombrowski in a house once used by Keziah Mason. The dimensions of Gilman's room are unusual, and seem to conform to a kind of unearthly geometry. Gilman also consults Miskatonic's collection of rare books, including the Necronomicon, the Book of Eibon and Unaussprechlichen Kulten. II. Rising actionSoon Gilman begins having strange dreams: He floats through a 4Dspace inhabited by sentient polyhedrons made of unknown colors that rapidly shift surface angles. He also dreams of Keziah Mason and her ratbodied/humanfaced familiar, Brown Jenkin. In one such dream, Keziah and Brown Jenkin take Gilman to a city of "Elder Things." In these dreams, Keziah tells Gilman that "He must meet the Black Man and go with them all to the throne of Azathoth at the centre of ultimate chaos... He must sign the book of Azathoth in his own blood and take a new secret name now that his independent delvings had gone so far." He awakes with evidence that he actually went therea miniature statue of a starheaded Elder Thing, made of an unearthly alloy. III. ClimaxSoon after, Gilman dreams that Keziah, Brown Jenkin, and the "Black Man" force him to be an accomplice in the kidnapping of an infant. He awakes to find mud on his feet and news of the kidnapping in the newspaper. On May 1, 1928 (Walpurgis Night), Gilman dreams that Keziah and Brown Jenkin are about to sacrifice the kidnapped child. Gilman stops Keziah by strangling her, but Brown Jenkin bites through the child's wrist to complete the ritual and then escapes through a portal. IV. Falling actionGilman awakes to a deafening sound. He confesses what's happened to Frank Elwood, a fellow student and another boarder in the Witch House. Then Gilman starts screaming loudly. The landlord and other tenants in the building rush to Gilman's room to see what's going on. They witness Brown Jenkin burst out of Gilman's chest and scurry away into a rat hole!!! By the end of the week, the landlord and other tenants have all abandoned the building. V. DénouementIt's March, 1931. A gale destroys the roof of Arkham's now longdeserted Witch House. Workmen sent to raze the building find Keziah's skeleton and books of black magic. In a space between the walls, they find children's bones, a sacrificial knife, a bowl made of an unearthly metal alloy, and the miniature statue of a starheaded Elder Thing. They contact the police who give the items to Miskatonic University, where they continue to mystify scholars. Most baffling of all these items are the skeletal remains of a huge deformed rat with hints of human or primate anatomy! 2. InspirationThe story was inspired by the lecture, The Size of the Universe, by Willem De Sitter, which Lovecraft attended three months prior to writing the story. Lovecraft even mentions De Sitter in the story. You can read this lecture online here or download the PDF here. I will have a lot more to say about this lecture in a later post. But the two main ideas to take away from it are: (1) The cosmos is really, really big. And (2) the cosmos is getting even bigger. These key ideas must have reinforced Lovecraft's philosophy of cosmicism, which simply states that humans are insignificant in the scheme of things. De Sitter's speech doesn't really delve into any math or nonEuclidean geometry. Lovecraft seems to have gotten those influences from A. S. Eddington's The Nature of the Physical World. Keziah's house seems to have been inspired by the Salem Witch House: 3. CriticismThis is my favorite Lovecraft story. It's very cerebral. I love the references to De Sitter and nonEuclidean geometry. But the story hasn't gotten much love from the critics. Here's a sampling:  August Derleth: "a poor story."  Lin Carter: "a minor effort" that "remains singularly onedimensional, curiously unsatisfying."  Peter Cannon: ranks with "the poorest of Lovecraft's later tales."  S. T. Joshi: "one of [Lovecraft's] poorest later efforts."  Steven J. Mariconda: "Lovecraft's Magnificent Failure... its uneven execution is not equal to its breathtaking conceptions, which are some of the most original in imaginative literature." 4. Adaptations and derivative works: Films, TV, music and RPGs.1947. Underground film maker Kenneth Anger writes a screen treatment for The Dreams in the Witch House. 1963. Fritz Leiber writes an essay entitled "Through Hyperspace with Brown Jenkin: Lovecraft's Contribution to Speculative Fiction," in which he states: This essay is available in several Leiber compilations. 1968. The first film adaptation was Curse of the Crimson Altar, starring Barbara Steele, Christopher Lee, Boris Karloff, and Michael Gough. You can watch the trailer here on YouTube. The whole film is available on archive.org. I have watched this movie. It's a very loose adaptation. Names and places have been changed. But major plot points are still recognizable. I may give a critique in a later post. I will not spoil it here. If you like B Horror films, female nudity and British accents, then you might enjoy this flick! Here is a still image from the movie: 1990. Chaosium released a supplement for the Call of Cthulhu RPG called Arkham Unveiled with a lot of background information, including  history and floor plans of the Witch House  stats for Gilman, Keziah, and Brown Jenkin This is a great supplement. However, it only provides background, not a runnable adventure. Here is the floorplan of Keziah Mason's house excerpted from this supplement: 1992. The Call of Cthulhu/Delta Green RPG scenario Devil's Children by David Conyers and Godley Witteveen. It features the witch Keziah Mason. Originally a tournament scenario played at Conquest 1992 (Melbourne, Australia); and later published by Pagan Publishing in 1993 as the first part of the Witch Cycle. Available for free from YogSothoth dot com but requires registration. This is an updated 2004 version issued as a 60 page PDF. Looks very well done! 1999. The novel Prey by Graham Masterton. The flap text on the dust cover says: I have not read it, but I gather from the Amazon reviews that the roof of the house is built with impossible angles, a bunch of children went missing there, and Keziah Mason's rat/human familiar Brown Jenkin lives in the walls! 2002. Wizards of the Coast releases Jenkin Lives: A Web Enhancement for the Call of Cthulhu d20 Roleplaying Game. This was actually the first d20 adventure I DM'd (prior to that, I had only DM'd Moldvay Basic and AD&D). It was a short, enjoyable, free scenario. There's a plausible explanation as to how Keziah and her familiar are still at large, even though their bodies were discovered in the wreckage of the Witch House. A child has been kidnapped. You play an investigator. The goal is to find the child. Along the way, you need to survive attacks by rats, including Brown Jenkin. Unfortunately, d20 CoC is discontinued. But you can still find archived copies of this scenario online:  d20 Call of Cthulhu (main page, archived)  Jenkin Lives: A Web Enhancement for the Call of Cthulhu d20 Roleplaying Game (description page, archived)  Zipped PDF (archived)  PDF (archived, from another site)2005. Showtime's "Masters of Horror" series made a 1hour film version called H. P. Lovecraft's Dreams in the WitchHouse that's much closer to Lovecraft's original story than Crimson Altar. You can watch the trailer here on YouTube. There are some changes: Gilman studies string theory. He believes Keziah takes advantage of places where two branes intersect in order to traverse large spacetime intervals. Frank Ellwood is now a woman, Frances, who has a baby boy. I would have liked to have seen...  projections of 4D objects into 3D space  the City of Elder Things  the "Black Man," i.e., the satanic avatar of Nyarlathotep Instead, we get standard B Horror fare, including full frontal female nudity and bloody gore. 2011. Morgan Scorpion reads an audiobook version of the story. Listen on YouTube:  Part 1  Part 2The H. P. Lovecraft Literary Podcast does two episodes on WitchHouse with guest host Ken Hite:  Part 1  Part 2 2012. Brett Piper makes another loose film adaptation entitled The Dark Sleep. There is a trailer on YouTube. 2013. A rock opera based on the story. I'm not familiar with it, but it looks interesting. You can watch a musical number entitled No Turning Back (feat. Alaine Kashian) on YouTube. 2014. The H. P. Lovecraft historical society makes an audio drama, Dark Adventure Radio Theatre: The Dreams in the Witch House. I don't have this yet, but I have several of their audio dramas and like those a lot. There's some promotional items for it available online:  Teaser trailer on YouTube  Script (pdf)  Liner Notes (pdf)Adaptations I'd like to see in the future: (1) A proper movie adaptation, not another B Horror film! (2) A new RPG adventure, perhaps one set in Salem 1692 or sometime in the far future. Most of all (3) a comic bookthe weird, nonEuclidean milieu and City of Elder Things would be awesome to see illustrated! 5. Coming Soon.I've already written up some more notes related to this story, including an indepth summary and analysis of De Sitter's influential speech, The Size of the Universe. I also have some thoughts on Gilman's role as a "Mad Scientist" and speculate about Keziah's motivations in recruiting Gilman to help her sacrifice children. If you've read the story and have opinions you'd like to share or questions you'd like to raise, please join the discussion!



Post by The SemiRetired Gamer on Jan 4, 2015 13:55:20 GMT 6
I just watched this on Netflix. It's listed as The Crimson Cult on there. Not bad at all. Reminds me of the horror movies they used to play late on Saturday night around here back in the '80s; called it Creature Feature. I haven't read the original story but the movie was decent in a B or Hammer sort of way. BTW, that isn't a bad place to be for a horror film.



Post by krusader74 on Jan 4, 2015 22:34:48 GMT 6
Found two references to The Dreams in the Witch House in the Rhode Island archival and manuscripts collection online: 1. In a letter to H. P. Lovecraft, Clark Ashton Smith says "eager to see The Dreams in the Witch House." 2. In a letter dated November 7, 1947 from August Derleth to Donald Wandrei: "[Kenneth] Anger has created a screen treatment for 'Dreams in the WitchHouse.'" Wandrei was another scifi/fantasy writer. H. P. Lovecraft helped to launch his career. Quoting Wikipedia: Kenneth Anger is an underground experimental filmmaker. His films are known for their occult themes and homoeroticism. Anger is a Thelemite. Anyway, it's a shame this film never got made. It would have been fascinating to see Anger's take on the story. I wonder if the screen treatment itself still exists?



Post by stevemitchell on Jan 5, 2015 0:45:27 GMT 6
The 2012 film THE DARK SLEEP is another (loose) adaptation of "The Dreams in the WitchHouse." A lady novelist moves into a house out in the countryside, and finds a strange mural on the basement wall that seems to be a map of Lovecraft's multiverse. Later she starts having weird dreams about traveling to other dimensions. Her sister tells her to consult Water Gillman, a college professor with a background in the occult. Brown Jenkin appears, and something else that might be an avatar of Nyarlathotep.
A lowbudget, smallcast effort, with creature effects handled in stopanimation. Not great, but far from being the worst HPL film adaptation, either. You can find more details on IMDB.



Post by Finarvyn on Jan 5, 2015 5:18:20 GMT 6
That's some awesome research! I don't think I've ever read that story, but now that it's on my radar I'll give it a go. I have a few Lovecraft books and I'm hoping it's in one of them...



Post by krusader74 on Jan 6, 2015 18:45:59 GMT 6
The 2012 film THE DARK SLEEP is another (loose) adaptation of "The Dreams in the WitchHouse." A lady novelist moves into a house out in the countryside, and finds a strange mural on the basement wall that seems to be a map of Lovecraft's multiverse. Later she starts having weird dreams about traveling to other dimensions. Her sister tells her to consult Water Gillman, a college professor with a background in the occult. Brown Jenkin appears, and something else that might be an avatar of Nyarlathotep. A lowbudget, smallcast effort, with creature effects handled in stopanimation. Not great, but far from being the worst HPL film adaptation, either. You can find more details on IMDB. Thanks very much for mentioning this adaptation! I hadn't heard of it. I watched the trailer on YouTube. Unlike the other adaptations, at least this director attempts to put Lovecraft's fantastic vision of nonEuclidean geometry and higherdimensional space into the film, and deserves a lot of credit for that. I will add this to the chronology of adaptations in the OP. I tried to contact Kenneth Anger about his 1947 screen treatment of WitchHouse, but GoDaddy's spam filter keeps bouncing my emails! Anger began film making in 1937. He's still at it. His last film, about Elliot Smith's suicide, released in 2013. His films are always short, with no dialogue, and accompanied by powerful soundtracks. There's a sampling on YouTube. His style is very well suited to the fantastic elements in WitchHouse. I also found some additional info: In 1963, Fritz Leiber wrote an essay, "Through Hyperspace with Brown Jenkin: Lovecraft's Contribution to Speculative Fiction." It's included in several Leiber compilations. After criticizing WitchHouse, he writes: Then Leiber goes on to spellout what he means in detail. In September 2011, the H. P. Lovecraft Literary Podcast did two episodes on WitchHouse with guest host Ken Hite:  Episode 90 – The Dreams in the Witch House – Part 1  Part 2There was a series of articles on WitchHouse on this blog. The first page of the story's original publication in Weird Tales is reproduced there: The illustration for the story is by Erik York. The logline reads:



Post by krusader74 on Jan 24, 2015 17:29:33 GMT 6
Found two more derivative works of "The Dreams in the Witch House". Will add these to the OP: 1992. The Call of Cthulhu/Delta Green RPG scenario Devil's Children by David Conyers and Godley Witteveen. It features the witch Keziah Mason. Originally a tournament scenario played at Conquest 1992 (Melbourne, Australia); and later published by Pagan Publishing in 1993 as the first part of the Witch Cycle. Available for free from YogSothoth dot com but requires registration. This is an updated 2004 version issued as a 60 page PDF. Looks very well done! 1999. The novel Prey by Graham Masterton. The flap text on the dust cover says: I have not read it, but I gather from the Amazon reviews that the roof of the house is built with impossible angles, a bunch of children went missing there, and Keziah Mason's rat/human familiar Brown Jenkin lives in the walls!



Post by krusader74 on Jan 25, 2015 0:51:18 GMT 6
The Size of the UniverseAs promised, here are a few comments and elaborations on Willem De Sitter's speech, The Size of the Universe. Lovecraft went to see this speech at the end of 1931 and it helped inspire him to write "The Dreams in the Witch House" in early 1932. Unless stated otherwise, the remaining quotations come from the text of De Sitter's speech. I'm not 100% sure if De Sitter is using the term "dark matter" the same way we mean it today. Today's "dark matter" is the proposed solution to the galaxy rotation problem. Jan Oort is generally credited with the discovery of dark matter in 1932. But Lovecraft heard this lecture in Q4 1931. Furthermore, De Sitter explicitly says this dark matter was discovered 1015 years prior. I'm wondering if "dark matter" in the sense De Sitter is using it here refers to some proposed solution to Olber's paradox? Today, the Big Bang Theory provides the solution to that paradox. Shortly we will prove De Sitter's assertion that General Relativity isn't so difficult by reproducing De Sitter's own exact analytical solution to GR with no more than high school algebra, trigonometry and calculus. Keeping with the theme of De Sitter's lecture, this solution will provide information about The Size of the Universe. Expanding on De Sitter's remark: The principle of relativity simply says that laws of nature look the same to all observers in inertial frames of reference. "Inertial frame" means the observer is traveling in a straight line at a constant velocity. This implies that the laws of nature must be second order differential equations, i.e., they're about acceleration. Galileo formulated a transformation to go from one frame to another. Newton formulated the two most basic laws of motion: F=ma and the law of gravitation F=GMm/r^2 which says the gravitational force of attraction between two masses M and m is directly proportional to the product of their masses and inversely proportional to the square of the distance r between them. G is the constant of proportionality. The "principle of the invariance of the speed of light" says all observers measure the speed of light in a vacuum as the same constant c. This principle comes from Maxwell's equations and was confirmed by the Michelson Moreley experiment. It requires a modification to the Galilean transformations. The modifications were made by Hendrick Lorentz in the late 1800s and are called the Lorentz transformations. But there's a big problem with Newton's Law of gravitation: It says "two masses attract each other etc." What about light? Light is massless. But photons of light still fall in a gravity field! Einstein's special relativity corrects this mistake in Newtonian mechanics: It equates energy (E) with momentum (p) and mass (m). In a paper he published in 1907, we find the equation E² = (pc)² + (mc²)² (You could call this the "Pythagorean Theorem" for matterenergy.) Later, Einstein's general theory of relativity (1915) further equates gravitygeometry with matterenergy. In symbols, G=T. Reading the equation lefttoright it says: "Gravity tells matterenergy how to move." Reading the equation righttoleft: "Matterenergy tells spacetime how to curve." More precisely, Einstein's Field Equations (EFE) are written like so: Gμν + gμν Λ = 8πG/c⁴ Tμν where Gμν is called the Einstein tensor, 8πG/c⁴ is a constant, Tμν is called the energymomentum tensor, Λ is the "cosmological constant," gμν is a metric for measuring spacetime intervals, and the indices μ and ν run over the 4 spacetime coordinates. This yields a system of 4x4=16 partial differential equations. But the two tensors are symmetric matrices, meaning the 6 terms above the diagonal are the same as the 6 below, reducing the system to 10 equations. Furthermore, 4 equations turn out to be tautologies (the Bianchi identities), reducing the system to just 6 equations. The Einstein tensor is further decomposed into the sum of the Ricci tensor and the product of the Ricci constant and the metric. But we can skip that level of detail here. At first, Einstein didn't think the EFE could be solved. Then Karl Schwarzchild provided an exact analytical solution in 1916. His solution is a massive nonrotating sphere that warps the space around it. From this model, one can derive effects such as time dilation (clocks on earth run slower than clocks in orbit) and gravitational redshifts. The model is used to study black holes. But it is not a complete picture of the cosmos, since it only has one object in it. Einstein and De Sitter independently proposed exact analytical solutions in 1917. By "A" De Sitter means Einstein's "cylinder world" solution, and by "B" De Sitter means his own solution. We're going to discuss these in detail later. First, let's take a look at some subsequent solutions. In 1919, Theodor Kaluza sent Einstein an exact analytical solution that unifies gravity and electromagnetism. But it imagines the world has 4 spatial dimensions. Electromagnetism is modeled as motion in the 4th dimension. GR doesn't say how many dimensions the universe has. It works for any number of dimensions. But Einstein worried about Kaluza's solution: Why don't we see the 4th dimension? What makes the 4th dimension special with respect to electromagnetism? As a result, Einstein held back publication of Kaluza's paper for several years until 1921. Then in 1926, Oskar Klein reworked Kaluza's model to incorporate quantum mechanics. He also showed that the 4th spatial dimension could be rolled up into a microscopic cylinder, explaining why we can't see it. The result is the KaluzaKlein theory. String theory builds on this approach of unifying the forces at high energies and explaining why gravity is so weak (16 orders of magnitude) compared with the other forces (the socalled "hierarchy problem") by adding extra dimensions. For the most part these extra dimensions are microscopic, but there are some modern theories of Large Extra Dimensions. A good example is the Randall–Sundrum (RS1) model, a socalled "braneworld" model in which there are two infinite branes: The Planckbrane, where gravity is strong; and the Tevbrane, where we live. (A "brane" in this case is an infinite 3dimensional space. But multiple branes are "layered" together in an extra dimensional space called the "bulk".) Ordinary particles like protons and electrons are vibrations in open strings with each end attached to the Tevbrane. Gravitons are vibrations in closed (loop) strings that are not attached to a brane but are free to move about the bulk. The probability wave function for a graviton makes it much more probable to find in the Planckbrane; this probability decreases exponentially as one moves away from the Planckbrane through the bulk; therefore, the small distance separating the Planckbrane from the Tevbrane is enough to weaken gravity by 16 orders of magnitude. The Planckbrane has high positive energy whereas the Tevbrane has high negative energy. These high energies severely warp spacetime (remember G=T) but only along the fifth dimension. If you could move from the Tevbrane to the Planckbrane, your weight and size would change by 16 orders of magnitude; but such movement is not possible except for gravitions. You can find out more about this theory here:  Lisa Randall promoting her 2005 book Warped Passages on CSpan, Book TV (video)  A Large Mass Hierarchy from a Small Extra Dimension (PDF)Lovecraft's plot in "The Dreams in the Witch House" depends on the existence of a 4th spatial dimension. For example, Lovecraft writes: KaluzaKlein theory is the only hyperdimensional solution to GR Lovecraft could have known about, and so while it is never mentioned by name in "The Dreams in the Witch House", it is difficult to imagine Lovecraft didn't know about it and didn't have it in mind as he plotted the story. The 2014 DART radio dramatization of "The Dreams in the Witch House" explicitly mentions KaluzaKlein theory. Furthermore, Stuart Gordon's "The Dreams in the Witch House" makes Walter Gilman a string theorist studying braneworld models; he theorizes branes intersect allowing travel between branes. The Soviet mathematician Alexander Friedmann produced another exact solution in 1922. Einstein refereed Friedmann's journal article and acknowledged its correctness, but failed to appreciate its significance. It remained largely unnoticed. As a result, it was later rediscovered by Belgian priest Georges Lemaître in 1927, and again by US and UK mathematicians Howard P. Robertson and Arthur Geoffrey Walker in 1935. For this reason it's called the Friedmann–Lemaître–Robertson–Walker model. It's worth mentioning one more solution even though it wouldn't have been known to Lovecraft: The mathematician Kurt Gödel enjoyed pointing out inconsistencies in other peoples' theories. He discovered that Russell and Whitehead's formalistic approach to mathematics was either incomplete or inconsistent. He discovered an inconsistency in the US Constitution that would allow the US to become a dictatorship, which he explained to the judge at his citizenship exam. In 1949, he developed his "rotating universes" modelan exact analytical solution to GR that allows time travel and violates Mach's principle. Einstein originally developed GR in an attempt to formalize Mach's principle. Gödel presented his solution to Einstein for his 70th birthday, causing Einstein to have doubts about his own theory. We could imagine Lovecraft seizing on the "rotating universes" model to explain how the Great Race of Yith migrate across time into new bodies and new civilizations. At this point, we'll return to Einstein's "cylinder world" and "De Sitter Space." Here is a sidebyside comparison of what they look like excerpted from Jonathan Bain's lecture notes on the Philosophy of Relativity in this paper. These spaces are illustrated with with 1 time dimension and only 1 space dimension. The time axis runs vertically. A snapshot of space at a point in time is a circle in the horizontal plane. Such a circle is a 1sphere. Note that the 2D surface of a globe is a 2sphere. Our space is a 3sphere. So you need to think of each of the circles in this diagram as substitutes for 3spheres. The problem is that you can't think about a 3sphere unless you can visualize 4dimensions. But you can get an intuitive idea for it as follows: On a 1sphere (a circle), no matter which of the two directions you go in, you'll loop around and arrive back at your starting point. Similarly, on a 2sphere, if you start at any point and travel in a straight (geodesic) line, you eventually get back to your starting point. Locally, a 3sphere looks like a hunk of flat 3D of space. But no matter which direction you go, as long as you go in a straight line, you will eventually get back to your starting point. It's been known the universe is expanding since about 1912. Einstein's "cylinder world" is staticit stays the same size forever. It was never infinitely small (as the Big Bang Theory presupposes) nor does it ever get any larger. So it can't be the actual solution to the Einstein Field Equations, merely a possible solution. De Sitter's model of the universe starts out infinitely big an infinite amount of time ago. It shrinks to a finite size exponentially, then it starts to grow exponentially again. This expansion continues forever. De Sitter's model has no Big Bang (a finite point in time when the universe is infinitesimally small)this doesn't necessarily disqualify it (you can make his universe arbitrarily small). And De Sitter's model expands exponentially forever, agreeing with current observations. Note that it doesn't get infinitely big in a finite amount of time (the socalled Big Rip). Most astonishingly, De Sitter's model assumes the density of ordinary matter and energy is zero. Let's hold off judgement on that and first see how De Sitter derived his solution. We're interested in the size of the universe and how that changes over time. We're going to imagine that the galaxies are particles of dust. Instead of imagining these particles as being embedded in a grid, we're going to imagine a stretchable grid embedded in the space containing these particles. The grid can grow or shrink over time. The length of an edge in this grid at time t is called the "scale factor" and is denoted a(t). Often we'll drop the time parameter and just call it "a." It's first derivative with respect to time is denoted ȧ (read: adot). We usually let t=0 mean "now", a(0)=aₒ, and ȧ(0)=ȧₒ. We're going to use EFEs to describe a and ȧ. Here is the timetime (or 00) component of Einstein's Field Equations: (ȧ² + κ²)/a² = 8πG/3 ρ + Λc²/3 A few more symbols to define before we begin: ρ : the density of matterenergy ȧ/a : the relative rate of expansion of the universe, AKA the Hubble parameter H κ/a² : the spatial curvature in any timeslice of the universe κ=0 if the shape of the universe is flat κ=1 if the shape of the universe is a closed 3sphere, a is the radius of curvature of the universe κ=1 if space is 3D hyperboloid We're going to make two simplifications here: First, we're going to use natural units, so set c=1. Second, after setting c=1, the rightmost term is Λ/3. But there's no point writing Λ/3 over and over... A constant divided by a constant is still just a constant. We're going to abbreviate it as Λ. Just remember to mentally substitute Λ/3 for Λ where ever you see it below. De Sitter Space. Assume ρ=0, Λ>0, κ=0,±1 There are three cases (κ=0,±1). Actually, all three of these cases are the same after a change of coordinates. That's why they are all called "De Sitter Space". So we will only do the first case in detail: Case 1: ρ=0, Λ>0, κ=0 (flat space) Under these assumptions, the timetime component of the EFEs becomes (ȧ/a)² = Λ. Take the square root of each side to get: ȧ/a = √Λ. Multiply by a to get: ȧ = √Λ a. Rewrite the derivative ȧ to get: da/dt = √Λ a. This differential equation has the solution: a = aₒ e^(√Λ t). We can check this solution by differentiating as follows: ȧ = d(aₒ e^(√Λ t))/dt = aₒ d(e^(√Λ t))/dt = aₒ e^(√Λ t) d(√Λ t)/dt = aₒ e^(√Λ t) √Λ = a √Λ. That checks OK. Note that H = ȧ/a = √Λ a / a = √Λ = the constant Hₒ. So a(t) = aₒ e^(Hₒ t). Case 2: ρ=0, Λ>0, κ=1 (space is 3D sphere). The solution is a(t) = 1/√Λ cosh √Λ t = 1/(2 √Λ) (e^(√Λ t) + e^(√Λ t)). Case 3: ρ=0, Λ>0, κ=1 (space is 3D hyperboloid). The solution is a(t) = 1/√Λ sinh √Λ t = 1/(2 √Λ) (e^(√Λ t)  e^(√Λ t)). If you'd like to see these derivations done in more detail with more background info, I highly recommend the following two playlists on YouTube:  Cosmology by DrPhysicsA (10 videos)  Cosmology by Leonard Susskind (10 videos)Anyway, Einstein was highly dissatisfied with these solutions and wrote to De Sitter, complaining: In other words, Einstein was insistent that ρ>0. So what was De Sitter's intuition behind his assumption that ρ=0? The density of matter is ρ ∝ 1/a³. If Λ>0, then space is expanding, i.e., a→∞ as t→∞, and therefore ρ→0 as a→∞. So at some point, ρ will become so small that we should be able to ignore it. Additionally, Einstein believed the cosmological constant was a big blunder and that Λ=0. So what happens if we assume ρ>0, Λ=0 and κ=0 (flat space)? Friedmann solved this case in 1922. In a matterdominated universe where ρ ∝ 1/a³, a(t) = aₒ t^(2/3) This space expands forever, but slowlyit asymptotically approaches a finite size (in contrast to De Sitter space which expands to an infinite size in an infinite amount of time). Einstein's concerns led Einstein and De Sitter to adopt this as the "standard" solution for the EFE. This was the standard cosmological model until 1998, when it was discovered that the universe is expanding at an exponential rate, in accordance with De Sitter's original solution!



Post by krusader74 on Jan 25, 2015 1:43:40 GMT 6
Looking at the map of the Witch House reproduced above from Chaosium's Arkham Unveiled (1990) supplement, we see an "unnamed tenant" living across the hall from Walter Gilman. If I were running an RPG scenario based on that map, here's the NPC I'd put in that room... René Emile Belloq, a protoNazi occultist, lives in the room across from Gilman. He's one of Gilman's classmates at Miskatonic University. He's a student of linguistics and archaeology. But he's also trying to unlock the secrets of traveling through the 4th dimension using math and the occult. Belloq is a member of Jörg Lanz von Liebenfels's Ordo Novi Templi and possesses all current issues of Ostara magazine (which you can view/print as props from archive.org). Belloq is a rabid antisemite and suspects Gilman is a Jew. He may be poisoning Gilman with psychedelic drugs ( ergot of rye?) in order to embarrass him or simply knock out the competition at school. Therefore, the "dreams" Gilman is having may just be a symptom of ergotism!Note that TSR included Belloq in a collection of unpainted metal miniatures in 1984 as shown here (excerpted from Dan Curto's Cool Toy Review):



Post by krusader74 on Feb 6, 2015 23:08:17 GMT 6



Post by krusader74 on Feb 6, 2015 23:14:27 GMT 6
MultiversityHow can the 4D universe inhabited by Lovecraftian horrors coexist with the 3D universe we inhabit? And what lies at the interface of our two universes? To answer this question, I want to discuss Max Tegmark's four levels of the Multiverse. Level I: Beyond our cosmological horizonThe farthest objects we can see emitted their light 13.8B years ago. But the universe is expanding at an exponential rate. In the 13.8B light years since they emitted their light, these farthest objects moved even farther away from us. We can calculate that they are now 46B light years away. These furthest objects are in regions of space moving away from us faster than the speed of light! While it's impossible for a massive body to travel faster than light, it is possible for the space containing a massive body to move faster than light. Hubble's law says v = Hₒ D, i.e., we're going to measure a distant object's velocity v as the result of cosmic expansion as equal to the Hubble parameter Hₒ times its distance D from us. The "cosmic horizon" is the distance D at which v = c, the speed of light. So let's restrict ourselves to the cosmic horizon  the region of space around us expanding slower than the speed of light. That space is called the Hubble Volume. It's value is (c/Hₒ)^3 = 10^10^1.5 cubic light years. The ergodic hypothesis says that all states of a system are equiprobable over a long enough period of time. The consequence for our infinitely expanding universe is that it must contain Hubble volumes realizing all initial conditions. Given infinite space, there are an infinite number of Hubble volumes identical to ours in the Universe. Our Hubble volume is not special or unique. There is another Hubble volume exactly like ours 10^10^10^2.06 meters away! Furthermore, given infinite time, our own Hubble volume will repeat itself endlessly. This follows directly from the Poincaré recurrence theorem. Simplifying a bit: the observable universe has something like 10^10^1.96 quanta, and therefore a finite number of quantum states, and therefore it can be expected to recur every 10^10^10^10^10^1.1 Planck times. This is called the "Poincaré recurrence time." After that span of time, I will be sitting here again, typing this exact post, oblivious to that fact that I typed it before, an infinite number of times. This is Nietzsche's eternal recurrence. I find this possibility more alienating and horrifying than anything Lovecraft wrote. All of humanity's atrocities committed over and over again endlessly...with no way to escape! Level II: Universes with different physical constantsIn chaotic inflation theory, the multiverse as a whole is stretching and will continue doing so forever, but some regions of space stop stretching and form distinct bubbles, like gas pockets in a loaf of rising bread. Symmetrybreaking leads to universes with different physical constants (the finestructure constant, universal gravitational constant, speed of light, the Planck constant etc.) It also breeds universes with different numbers of dimensions from ours. The number of such universes is about 10^10^10^7. Level III: Manyworlds interpretation of quantum mechanicsA d6 is thrown and the numeric result of the throw corresponds to a quantum mechanical observable. All six possible ways the die can fall correspond to six different universes. Such quantum splits (as well as symmetrybreaking) lead to other universes that live on other quantum branches in infinitedimensional Hilbert space. Level IV: Mathematical UniversesEvery conceivable mathematical structure corresponds to a real universe. Since the set/class/category of all such structures is itself a mathematical structure, it too corresponds to a real universe. The computer scientist Jürgen Schmidhuber says the "set of mathematical structures" isn't welldefined. Therefore only universes describable by constructive mathematics (computer programs) correspond to real universes. I lean the opposite way: Even structures defined by paraconsistent logics and inconsistent mathematics correspond to real universes. And we may inhabit one of them! ReferencesIf you like these ideas, you can watch an actual physicist (Dr. Tony Padilla) discuss it on the Sixty Symbols channel on YouTube: Four Types of Multiverse  Sixty SymbolsIf you want to read Max Tegmark's original papers on the 4 levels of multiverse, you can find them on arXiv.org: Is the "theory of everything" merely the ultimate ensemble theory? by Max Tegmark The Mathematical Universe by Max Tegmark And for more on Poincaré recurrences, see the talk on the Numberphile channel on YouTube The LONGEST timeOr read the paper Information Loss in Black Holes and/or Conscious Beings by Don Page



Post by krusader74 on Feb 6, 2015 23:32:04 GMT 6
Zenith: Phase One = Superheroes vs 4D Lovecraftian horrors and NazisToday I read the graphic novel Zenith: Phase One by Grant Morrison and Steve Yeowell. This is relevant to H. P. Lovecraft's "The Dreams in the Witch House." In this story, the Lovecraftian horror, Yog Sothoth, lives in a 4D bubble of space adjacent to our 3D universe. He sees all the delicious souls here, and desires nothing more than to cross over and devour them. The problem is that to do this, he must bind himself to mortal flesh. But mortals are too weak and fragile to hold this 4D monstrosity. So he makes a deal with the Nazis. He gives them advanced technology, so they can create a superpowered race of human beings: Übermenschen. Only these supermen will be able to hold his essence. Then he can incarnate and indulge his appetite for souls. But some Nazi scientists defect and use this alien technology to create superheroes in Great Britain. And that's the setup for the story. It was a great premise with great art. I love Lovecraftian horror. And I also enjoy watching superheroes beat up Nazis! It was a treat to get both in one book. Highly recommended!!! This blog post has more detailed info about Zenith including some artwork samples. Here is one excerpt that takes place inside the bowels of Yog Sothoth in 4D space:



Post by krusader74 on Feb 6, 2015 23:37:22 GMT 6
Miegakure: A 4D puzzle platform game (coming to the PS4)Soon you can experience Walter Gilman's travels through the fourth dimension in the safety of your own home! Miegakure is a puzzle platformer with a unique premise: You can solve puzzles by rotating your character through the fourth dimension in order to walk through walls and accomplish otherwise impossible feats...just like Keziah Mason! You can watch a walkthrough of the game here on YouTube. The author is Marc ten Bosch. There's more about him and his games on his website. Here is a comic strip about the game from xkcd



Post by krusader74 on Feb 6, 2015 23:55:03 GMT 6
A reallife Keziah Mason?Mary Perkins Bradbury (baptized September 3, 1615 – December 20, 1700) was tried, convicted and sentenced to hang as a witch in Salem, Massachusetts in 1692. But somehow, she escaped from her jail cell before she was executed. By some accounts she was allowed to escape. Others claim she bribed her jailer. Another account claims that her husband bribed the jailer and took her away to Maine in a horse and cart. Perhaps she used witchcraft or escaped by rotating herself through the fourth dimension, allowing her to walk through the wall of the prison? Mary Bradbury's descendants include:
 Ralph Waldo Emerson  a fourth greatgrandson of Mary Bradbury, descendant through her daughter Judith.
 Ray Bradbury, the American fantasy, sciencefiction, horror and mystery writer.



Post by krusader74 on Feb 7, 2015 0:08:14 GMT 6
It happened on Walpurgis!
The climax of "The Dreams in the Witch House" occurs on Walpurgis (May 1st). Walpurgis Eve is the evening of April 30th.
I began to compile a list of historical events that happened on Walpurgis, to use in case I run a Call of Cthulhu RPG adventure based on "Witch House":
1776 Establishment of the Illuminati in Bavaria by Adam Weishaupt. 1786 Premiere of Mozart's opera The Marriage of Figaro in Vienna. 1846 Mormons formally dedicate the Temple in Nauvoo, Illinois. It is abandoned in less than 3 months. 1866 The Memphis Race Riots: proConfederacy Irish rape, rob and murder 46 blacks. 1871 (April 30): The Camp Grant massacre: American and Mexican civilians massacre 144 Apache women, elderly and infirm. (The Apache men were out hunting.) They also sell 29 captured Apache children into slavery in Mexico. 1894 May Day Riots in Cleveland Ohio. 1919 May Day Riots in Cleveland Ohio. 1930 The planet Pluto is officially named. 1931 The Empire State Building is dedicated in New York City. 1945 Hitler's suicide happened on the night of April 30/May 1. In the TV documentary Hitler and the Occult, Dusty Sklar comments "With Hitler gone, it was as if a spell had been broken." 2011, May 1, 20:00 UTC: Osama bin Laden killed.



Post by stevemitchell on Feb 7, 2015 17:03:37 GMT 6
"A d6 is thrown and the numeric result of the throw corresponds to. . ." the SAN loss I take every time I visit this topic!



Post by krusader74 on Jun 26, 2015 6:34:41 GMT 6
Quoted from The Dreams in the Witch House by H. P. Lovecraft How could your knowledge of the fourth dimension astonish your math professor and floor your class? Isn't ℝ⁴ a pretty boring space? Not quite. Quoted from Exotic spheres, or why 4dimensional space is a crazy place by Richard Elwes. The exact mathematical formulation of this idea comes from the paper Gauge theory on asymptotically periodic 4manifolds (1987) by Clifford Henry Taubes in the Journal of Differential Geometry 25: pp. 363430: Informally, there are a bunch of "fake" ℝ⁴s that "look like" ℝ⁴ topologically, but aren't really ℝ⁴. In fact, there's so many, we can't count them or even put them into a onetoone correspondence with the natural numbers ℕ = {0, 1, 2, 3, ...}. OK, so this is a weird result about ℝ⁴ that wouldn't be known for 60 years after Gilman's story. So it would be surprising if Gilman knew about it. But is there anything about ℝ⁴ that Gilman might have learned through direct experience that we still don't know by now? Formally, the Poincaré conjecture states: "Every simply connected, closed 3manifold is homeomorphic to the 3sphere." Informally, it says: If it looks like a sphere, it's a sphere. You might have heard that the reclusive Russian mathematician Grigori Perelman solved this problem in 20023. His solution was confirmed in 2006. The Clay Mathematics Institute awarded Perelman the $1,000,000 Millennium Prize for solving this problem in 2010, but Perelman actually turned it down! What does the Poincaré conjecture, a hypothesis about 3spheres, have to do with ℝ⁴? I'll get to that in a moment, but first I want to recount a humorous episode I saw in the video The Geometry of 3Manifolds (at approximately 54 minutes, 15 seconds): There's a generalization of the Poincaré hypothesis for nspheres. It's difficult to formulate, because there are 3 different views as to how to define an nsphere: 1. Purely topological 2. Piecewiselinear 3. Differentiable These views aren't reconcilable. They were first described by John Milnor in the following sequence of 3 lectures on differential topology given at Princeton University, Fall term 1958, filmed by the Mathematical Association of America (MAA). These differences give rise to 3 versions of the generalized Poincaré hypothesis: 1. Purely topological: The topological Poincaré hypothesis is true in all dimensions. The case for n>4 was proved by Newman (1966) and Connell (1967). The case for n=4 was proved by Freedman. The case for n=3 was proved by Perelman (20023). 2. Piecewiselinear: The piecewiselinear Poincaré hypothesis is true for ndimensional manifolds except possibly when n=4. 3. Differentiable: The differentiable Poincaré hypothesis is true in some dimensions (such as n=1,2,3,5,6,12), false generally for n>=7, and totally mysterious in dimension n=4. These results are summarized in the paper Differential Topology Fortysix Years Later (2011) by John Milnor. WRT the n=7 counterexample to the "smooth Poincaré hypothesis"... In 1956, Milnor was investigating 7dimensional manifolds. He found a strange shape. It had no holes. He could morph it into a sphere, but he could not do so smoothly. In math jargon: the shape was homeomorphic to a sphere, but it was not diffeomorphic to a sphere. In fact, he eventually found that in 7 dimensions, there are 27 different exotic spheres in addition to the 28th mundane sphere! The inaugural paper on this subject is On Manifolds Homeomorphic to the 7Sphere (1956) by John Milnor in the Annals of Mathematics Vol. 64, No. 2: pp. 399405. So n=7 is a weird case. But at least we know how many exotic spheres exist there. But look at the n=4 case. No one knows how many exotic 4spheres exist there. Could be 0, 1, ..., or uncountably many! So, perhaps Gilman knew the answer. Maybe he even knew that the answer unraveled mathematics itself, showing it to be inconsistent, driving him mad! Quoted from Exotic spheres, or why 4dimensional space is a crazy place by Richard Elwes The main takeaway is that if you want to set your horror story (or horror RPG adventure) in a very strange place that we still don't know much about, then ℝ⁴ isn't a bad choice after all. Did HP Lovecraft know that when he wrote "Witch House," or was it a lucky guess?



Post by krusader74 on Jun 27, 2015 5:44:31 GMT 6
Literary inspirations for "The Dreams in the Witch House"So far, I spent most of this thread discussing the scientific and mathematical inspirations for Lovecraft's "The Dreams in the Witch House." Now I want to explore his literary inspirations. I. The Witchcult in Western Europe (1921) by Margaret Alice MurrayThis book is freely available on Project Gutenberg at www.gutenberg.org/ebooks/20411This is perhaps the most important source used by Lovecraft. Even though it is never mentioned by name in this story, we know it is possessed and quoted by characters in 3 other Lovecraft stories:  The Call of Cthulhu  The Horror in Red Hook  The Whisperer in Darkness "The Dreams in the Witch House" borrows several major details from The Witchcult in Western Europe, including: initiation, child sacrifice, familiars, and spell books. These elements form the backbone of the plot of the story. A. Initiation.According to Murray, initiates to the witch cult must 1. Sign a contract with the devil in their own blood. It may be permanent or temporary. The initiate gets new powers in exchange. 2. Be baptized and take a new name. The baptism may be in one's own blood. The devil may claw a chunk out of your shoulder, suck blood out and sprinkle it over your head or spit it on you. This blood may be used to sign the compact. 3. Let the devil make a mark (devil's mark or witch's mark) on your body (throat/shoulder/abdomen/thigh/buttock). It may be same as wound he made for your baptism. We see all three initiation elements in "The Dreams in the Witch House": 1. "She [Keziah] had spoken also of the Black Man, of her oath, and of her new secret name of Nahab." 2. "He [Gilman] must meet the Black Man and go with them all to the throne of Azathoth at the centre of ultimate chaos. That was what she said. He must sign the book of Azathoth in his own blood and take a new secret name now that his independent delvings had gone so far." 3. "Then there were those dark, livid marks on his [Gilman's] throat, as if he had tried to strangle himself. He put his hands up to them, but found that they did not even approximately fit." Why would Gilman make a deal with the devil? What "new powers" is he tempted with? Clearly, knowledge of the fourth dimension. Why does Keziah need to initiate Gilman? According to Murray, the coven seems to work optimally with about 13 members, some of whom are male priests. It seems Keziah is simply rebuilding her coven, and she's looking for talented mathematicians and physicists like Gilman, because they are better equipped to understand the bizarre landscape of the fourth dimensional world she now calls home. B. Child sacrifice.Murray explains 4 different kinds of sacrifice:  initiate  animal  child (witch's own or unbaptized kidnapped child)  witchgod A child sacrifice plays a pivotal role in "The Dreams in the Witch House." Keziah, Brown Jenkin, and the "Black Man" force Gilman to be an accomplice in the kidnapping of an infant they plan to sacrifice. According to Murray, human fat, especially of nonbaptized children, was used to make an unguent that enabled the witches to fly. So perhaps Keziah needs this ingredient to travel through the 4th dimension? Beyond Murray's book, the "Wicked Witch" trope routinely involves witches killing and eating children (or at least using their fat):  Such an ointment is also referred to in "Young Goodman Brown" by Nathaniel Hawthorne in a conversation between Goody Cloyse and the dark stranger.  The witch in Hansel and Gretel eats kids: "The old woman had only pretended to be so kind; she was in reality a wicked witch, who lay in wait for children, and had only built the little house of bread in order to entice them there. When a child fell into her power, she killed it, cooked and ate it, and that was a feast day with her."  The Lamia of Greek mythology  Baba Yaga of Slavic folklore  Cronos/Saturn, lord of magic, known for devouring his own children! In traditional medicine in Europe, human fat was believed to have a healing magic significance until the 19th century. Many executioners recovered the fat called "Armsünderfett" or "Armsünderschmalz" (German for "sinners fat") from the bodies of their victims and sold it. The human fat was used to make ointments for treatment of various diseases such as bone pain, toothache and gout. It was also regarded as a cure for diseases like tuberculosis. Also as an analgesic for rheumatoid arthritis. Additionally, in the years just before Lovecraft wrote "Witch House", there were several infamous cases of child murder and cannibalism: 19209 Albert Fish in Brooklyn, NY: This cannibal killed and ate 15 children! 1931 New York Times reporter William Seabrook obtained a hunk of human flesh from a hospital and ate it. He said it tasted like veal. 1930s reports of Appalachian Mountain residents practicing ritualistic cannibalism However, Stuart Gordon's "The Dreams in the Witch House" makes it clear Keziah wants to collect Gilman's soul, not the infant's. The infant's is useless, because it hasn't reached the age of reason. She gets Gilman's soul if he participates in the child sacrifice. Mazurewicz warned him about this. Similarly, in the "Crimson Altar", Levinia wants vengeance on descendants of her accusers. She gets them condemned by persuading them to commit human sacrifice. C. Familiars.Murray explains there are 4 ways to obtain a familiar: Get it from the devil, from another witch, as an inheritance or from a magical ceremony. Author Ken Hite speculates that Brown Jenkin may be a 4th dimensional being and that he might be the offspring of Keziah and the Black Man/Nyarlathothep. D. Spell Books.Keziah Mason and Brown Jenkin do their work "in a crude, windowless little space" which contains among other things "low cases full of books of every degree of antiquity and disintegration." After the gale destroys the witch house, Keziah's spell books are discovered in the rubble; they're taken back to Miskatonic University for further study. Murray's book discusses a spell book known as the The Red Book of Appin. In reality, it may have at one time been a Scottish book on veterinary medicine. But folklore claims the book was stolen from the devil as a trick by a young shepherd. In his History of Witchcraft and Demonology, Montague Summers says it "contained a large number of magic runes and incantations for the cure of cattle diseases, the increase of flocks and the fertility of fields" and possessing it gave the owner certain powers. Further References to Murray's influence on LovecraftThere is more information on the connection between Lovecraft's stories and Murray book in the article "Dr. Margaret Murray and H.P. Lovecraft: The WitchCult in New England" by Robert H. Waugh in Lovecraft Studies 31 (Fall [October] 1994). Robert M. Price also talks about this connection in The Nyarlathotep Cycle (2006). He says Murray's thesis is that witchcraft came from a preChristian fertility religion. Christianity misunderstood it as diabolical and persecuted it. Lovecraft reinterprets the preChristian witch cult as worshipers of cosmic horrors like Azathoth and Nyarlathotep. Price says: II. Septimius Felton, or The Elixir of Life (1872) by Nathaniel HawthorneThis book is freely available from a number of sources:  PSU at www2.hn.psu.edu/faculty/jmanis/hawthorn/septimiusfelton.pdf  Project Gutenberg at www.gutenberg.org/ebooks/7372  Amazon Kindle (free) at www.amazon.com/SeptimiusFeltonElixirNathanielHawthorneebook/dp/B0084AW8X0Unfortunately, I haven't had a chance to study this source. But skimming it, I saw many parallel themes: New England localism, an Aunt Keziah, witchcraft, and dreams. III. Wonderful Wizard of Oz (1900) by Frank BaumRobert M. Price says this book was a big influence on Lovecraft's "Dream Quest of Unknown Kadath." But I see a clear influence on "Witch House" too:  Both are stories of long, dangerous journeys.  Wicked Witch of the West = Keziah Mason  Winged Monkeys = Brown Jenkin  Emerald City = City of Elder Things  Wizard of Oz = Azathoth  Dorothy = Gilman  In both, the hero decides to return home rather than stay.  In both, the hero kills the witch. Availability.Wikisource at en.wikisource.org/wiki/The_Wonderful_Wizard_of_OzProject Gutenberg at www.gutenberg.org/ebooks/55There is also a 1910 silent film version at archive.org/details/The_Wonderful_Wizard_of_OzIV. Book of Job.A. Justification.Lovecraft is known as an atheist, so saying a book of the Bible was a major inspiration requires justification before I begin to detail the parallels. 1. In January of 1920, Lovecraft published a short guide titled "Literary Composition" for United Amateur Press Association, in which he advises, 2. Former Baptist minister, theologian and Lovecraft scholar Robert M. Price wrote an article called "Biblical Bits in Lovecraft" appearing in the book Lovecraft and Influence: His Predecessors and Successors (2013). Price says Lovecraft read the King James Version of the Bible, a copy he inherited. For a time he aligned with the Universalist Church, but he was never, as far as we know, a Christian believer. However, the Bible provides a "lingering background" for Lovecraft's stories. Price provides many specific examples of Bliblical background appearing in Lovecraft's stories:  Shaddow over Innsmoth: This references the Philistine deity Dagon, mentioned in Judges and Samuel.  Enoch of Gen 4 & 5 is mentioned in both "The Haunter of the Dark" and "The Case of Charles Dexter Ward"  The Colour out of Space: Price says this refers to Genesis 19, the destruction of Sodom & Gomorrah in a rain of sulfuric fire from the heavens.  The Call of Cthulhu talks about the Millerites.  The Other Gods: Price compares this to the story in the Babylonian Talmud, tractate Hagigah, of The Four Who Entered Pardes  The Dunwich Horror: Price says it is the reverse of the gospel. Wilbur Whately is an antiChrist figure, and Yog Sothoth is the Father. B. ParallelsI contend Job provides a lot of background for "Witch House": 1. The name Keziah 2. Job/Gilman are tempted by Satan/the Black Man 3. Giants (Orion/Azathoth) in sky, the music of the spheres, and the infinite extent of heavens Let's go through these points one by one, starting with the name Keziah. It is the name of the second of three daughters in Job's second batch of daughters (the first batch was killed by Satan): Quoted from King James Bible, Job 42:1415 The Hebrew name Keziah (קְצִיעָה) is pronounced ketseeaw'. The name refers to sweet smelling cinnamon powder. It is related to the Greek name Cassia. Here is a painting of Job and his three daughters by William Blake: Lovecraft's Keziah is the opposite of Job's. Job's daughter is the fairest in the land, while Lovecraft's is an "evil old woman"... So how do we get from fair to foul? There is a logical connection. In alchemical texts, there seems to be a parallel between Job's three daughters and the three Fates ( Moirai) of Greek mythology. From there to the Roman Parcae. Then to the Norse Norns. And from the three Norns to the three witches in Shakespeare's Macbeththe weyward Sisters or Three Weird Sisters: Even Keziah Mason's secret name "Nahab" has a Biblical source: Nahbi (נַחְבִּי) comes from the root word chabah (חָבָה) which means "to hide" or "secret." It is used in Numbers 13:14 as the name of one of the spies Israel sends to Canaan, who bring back an "evil report": "Of the tribe of Naphtali, Nahbi the son of Vophsi." The Talmud (Sotah 34b) elucidates: "R. Johanan said: We can also explain [the name] Nahbi the son of Vophsi. [He was named] Nahbi because he hid [hikbi] the words of the Holy One, blessed be He." In Job 1:612, God lets Satan tempt Job. Throughout "Witch House," The Black Man tempts Gilman. Orion was a giant huntsman, the son of Poseidon. He tried to hunt Mother Earth. So she sent a scorpion to sting him. For his foolish rebellion, Zeus chains him up in the sky. This is referred to directly in Job 38:31. In Lovecraft, we have Azathoth, also a giant and an idiot, located in the stars at a point somewhere between the constellations Hydra and Argo Navis. Job 38:7 talks about the music of the spheres: "When the morning stars sang together, and all the sons of God shouted for joy?" While in Lovecraft we read about "the throne of Chaos where the thin flutes pipe mindlessly" and "the endless, Cyclopean city almost two thousand feet below. As he listened he thought a rhythmic confusion of faint musical pipings covering a wide tonal range welled up." In Job 38:18, we're asked "Have you comprehended the Size of The Universe?" While in Lovecraft, Gilman sees "an infinity of specific points in the cosmic pattern" and "an infinitely distant curving horizon of low mountains. Behind him tiers of higher terraces towered aloft as far as he could see. The city below stretched away to the limits of vision, and he hoped that no sound would well up from it."



Post by Finarvyn on Aug 4, 2015 17:25:50 GMT 6
That's some awesome research! I don't think I've ever read that story, but now that it's on my radar I'll give it a go. I have a few Lovecraft books and I'm hoping it's in one of them... Here I go, quoting myself. As a little update, I finally got around to reading this story. Loved it. I'm having a tough time convincing my wife to read any Lovecraft fiction, but the combination of witches and mathematics might be just the ticket! (She is a mathematician and likes witch stories. Perfect fit.)



Post by krusader74 on Dec 12, 2015 8:13:43 GMT 6
100 Years of General RelativityI already spent a lot of time discussing de Sitter, since Lovecraft actually went to see him lecture, and drew the inspiration for "Witch House" from de Sitter's speech on the "Size of the Universe." But I want to talk about one of the other 3 thinkers mentioned by Lovecraft in this excerpt. Now is an opportune moment to discuss Einstein... This year (2015) was the 100th anniversary of Einstein's General Theory of Relativity and the 150th anniversary of Maxwell's equations. Here are two sources about the commemorations held: There's a close connection between the two theories. You can take Maxwell's 4 equations apart and put them back together as one wave equation ∂ ^{2}u/∂t ^{2} = c ^{2} ∇ ^{2}u where c ^{2} = 1/(μ _{0}ε _{0}) is the square of the speed of light, and μ _{0} is the vacuum permeability (or magnetic constant), and ε _{0} is the vacuum permittivity (or electric constant). What this says is that the speed of light is constant no matter who's observing it. Two observers in relative motion measure the same constant speed of light. The Galilean transforms don't apply to light. Maxwell thought this was a mistake. But Michelson and Morley proved it experimentally. And Einstein explained how it was possible, and how it must give rise to time dilation and length contractionthe Lorentz transforms. There have been a few recent YouTube videos celebrating the centennial of GR:  100 Years of General Relativity: An hour long lecture given about a month ago by Robbert Dijkgraaf at the institute for Advanced Studies at Princeton, where Einstein worked.
 100 Years of Einstein's Relativity (And How it Underlies Our Modern Understanding of the Universe): An hour long lecture given about 6 months by Dr. Jeffrey Bennett.
 Nearly 100 years after General Relativity: Was Einstein right?: An hour long lecture given about a year ago by Michael Kramer from the MaxPlanckInstitut für Radioastronomie in Bonn.
The first video listed above begins with a joke about another thinker mentioned by Lovecraft, namely Heisenberg. It was a funny physics joke, so I'll repeat it here: In addition to the "centennial" celebrations, there was an episode of the "Sixty Symbols" YouTube channel 3 weeks ago on Einstein's Famous Blunder, a 20 minute long video on the cosmological constant and the expanding universe. The PBS "Crash Course Astronomy" YouTube channel is currently doing a series of 1015 minute shows on cosmology that relate to stuff we've been discussing about GR: There are also plenty of recent human interest stories about Einstein, like 5 Things You Didn't Know About Einstein on the "How Stuff Works" YouTube channel:  Einstein took up speaking late as a child, and didn't really converse with others until he was about 7 YO. It's thought maybe he had Asperger syndrome.
 After WWI, he and Max Born negotiated a hostage crisis at the University of Berlin.
 He and Leó Szilárd coinvented a refrigerator with no moving parts.
 In 1952, he was offered the presidency of Israel.
 Einstein's brain and eyeballs were stolen by Dr. Thomas Harvey in 1955.
This kind of stuff makes great background material for a historical "Call of Cthulhu RPG" campaign setting! While I find the math in GR interesting, I'm not convinced it's the right theory of spacetime. It may not even be a theory at all. Here's two recent alternative theories to GR:  Entropic gravity: Erik Verlinde's theory says that gravity doesn't exist. What we observe as gravity is really just entropy. Verlinde was able to derive Einstein's Field Equations from the laws of thermodynamics.
 What Is Spacetime, Really?: Steven Wolfram's idea that spacetime is really just a graph dynamical system. Wolfram (the creator of Mathematica) was also able to derive the EFE from his alternate postulate.
Is GR really a scientific theory? One early philosophical attack on GR is described in the recent article, Albert Einstein's SciFi Stories: Eberty's scifi developed a thought experiment based on the finite speed of light. Einstein continued this though experiment, culminating in SR and GR. For Bergson, GR was not science, just science fiction, like Eberty's short stories. For me, a more robust philosophical attack on GR than Bergon's starts by noting that GR has so many "knobs and dials" you can adjust to make it fit any empirical evidence. This means it isn't falsifiable. Therefore, it isn't really a theory. Examples of these knobs and dials are the values of the cosmological constant, the curvature of space, and the density of matter. I already showed that Einstein originally believed the universe was static (nonexpanding) and chose values for these constants in 1917 that achieved this resultthe socalled cylindrical model. When Hubble discovered the universe was expanding in 1929, Einstein and de Sitter came up with new values to fit Hubble's observationsthe socalled standard model. When it was discovered the universe was expanding exponentially in the late 1990s, physicists went back to de Sitters original model... So, it doesn't matter what we actually observe, it won't disconfirm GR, because we can always adjust the knobs and dials to make GR fit the data! Is such an unfalsifiable belief a theory or a religion? There is a similar debate raging right now between philosophers and string theorists... Physicists (String Theorists) and Philosophers Debate the Scientific Method: So, as we wait for LIGO to detect the gravity waves predicted by the EFE, it's unsettling not just that we don't know if we have the right theory of spacetime yet, but more so that we apparently don't even know what a theory is!!! I'll conclude this post with some fitting "Oldskool" style ASCII art: _________________________________ / God does not play dice with the \ \ universe. /  \ \ / ( ( ( ( ( ( ( ( ( ( ( (_ _/ `. `. `. `. `. `. `. `. `. `. `. `. `._ / ) ) ) ) ) ) ) ) ) ) ) ) ) ) _ / .' .' .' .' .' .' .' .' .' .' .' .' .' .' .' _  ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( ( _ . `. `. `. `. `. `. `__`__`__`__`. `. `. `. `. `. `_ ) ) ) ) )__)__)/ _)__) ) ) ) ) )_ .' .' .' .'/ .' .' .' .' .' .'_  ( ( ( / ( ( ( ( ( ( `. `. `.  `. `. `. `. `. `.  ) ) ) ) ) ) ) ) ) .' .' .'  ' .' .' .' .' .'   ( ( ( ______ _____ ( ( ( ( ( ( `. `. `.  /______) (_____  `. `. `. `. `.   ) ) )// \_ ) ) ) ) / ' .' .'  _____ _____ '__' .' .' ./ ( ( ( ( [O] ) ( [O] ) / ( ( ((  `. `.  ___/ ___/ `. `. ` _ ) ) , /  ) ) .' .  . / .' .' .' _ (  ( ) _/ ( ( ( ( ) `. ___/ . `. `. `. `__/ __  ) ) ) __/  _______ ' .' .__/  _/////\\____ _/.____/_____  ///////\\\\ / .,%,%,%\_______ ///////\\\\ _/ .%,%,%,%,%,%,____ __________/ / /. %,%,%,%,%,%,%,% __ / /. /%,%,%,%,%,%,%,%, _/%,_ __/ /. /%,%,%,%,%,%,%,%,% _________/%,%,%_ ___/ _/. /,%,%,%,%,%,%,%,%, _/%,%,%,%,%,%/XX_______/ _/. ./,%,%,%,%,%,%,%,%,% __/,%,%,%,%,%,%/XXXXX_ __/. ./%,%,%,%,%,%,%,%,%,% /%,%,%,%,%,%,%/XXXXXXXX /. . ./%,%,%,%,%,%,%,%,%,%,



Post by krusader74 on Dec 12, 2015 8:24:17 GMT 6
The Appendix N PodcastThe Appendix N Podcast describes itself as follows: The most recent episode, The Appendix N Podcast  Episode 24  Selected Works by H. P. Lovecraft, Part 4, contains a review of "The Dreams in the Witch House." The show program with approximate start/stop times is  Show intro (0:001:10)
 Noble Knight, the sponsor (1:101:30)
 Guest panel introductions (1:302:00)
 "The Whisperer in Darkness" (2:0022:25)
 "The Shadow over Innsmouth" (22:2552:00)
 "The Dreams in the Witch House" (52:001:11:49)
 Concluding comments (1:11:491:20:56)
Here is the direct link to this episode: MP3 audio. Size: 92.6 MB. Length: 1 hour 21 minutes. I found the discussion of "The Shadow over Innsmouth" interesting. They talk about:  Amphibian humanoid races in D&D inspired by Deep Ones (starting around 38:00)
 The Useries modules ("U" for "underwater")
 Zadok Allen, the "exposition NPC" trope
During the discussion of "Witch House," they raise a few interesting questions:  Are the math equations Walter Gilman studies like spells that let you fold spacetime without the need for a machine?
 Does the interdimensional travel happen only in Gilman's dreams?
 Did Gilman actually kill Keziah Mason? Or was she dead (in the walls) the whole time?
Overall, these reviewers did not like "Witch House." Here are a sampling of their comments on it: Pieces you could use in your game: Description of the city of Elder Things, the Witch Cult. (1:10:53)



Post by krusader74 on Feb 13, 2016 8:52:46 GMT 6
Gravity wavesGravity waves made big news last Thursday morning. Since we were discussing Einstein's theory of General Relativity, I wanted to talk about them. Before we get there, I first wanted to talk about what a wave is, mathematically. We'll start with the classic example of a wave: A sinusoid has the following wave function in 1+1 dimensions Ψ(x, t) = A sin(k x ± ω t + ϕ) + D where ± = rightmoving wave if minus (), leftmoving if plus (+) A = amplitude f = ordinary frequency, i.e., oscillations per second ω = 2 π f is the angular frequency ϕ = the phase: A sinusoid with a phase of ϕ differs from a sinusoid with a phase of 0 by a time shift of ϕ/ω seconds. D = nonzero center amplitude v = linear speed λ = wavelength λ = v / f k = the wave number, i.e., spatial frequency of a wave in cycles per unit distance k = ω / v = 2 π f / v = 2 π / λ This function has an interesting property: the second partial derivatives with respect to space and time are the same up to a constant of proportionality. Second partial derivative of Ψ with respect to time: ∂²Ψ/∂t² =  A ω² sin(k x + ω t + ϕ) Second partial derivative of Ψ WRT space: ∂²Ψ/∂x² =  A k² sin(k x + ω t + ϕ) Therefore, ∂²Ψ/∂x² = (1/v)² ∂²Ψ/∂t². This says that rate of rate of change of the wave function Ψ in space is proprtional to its rate of rate of change in time. This relationship is called the wave equation. When you have three dimensions, instead of using the partial differential operator ∂²/∂x², you use the Laplace operator (or "Laplacian") ∇². Also, the wave equation is often written using c for velocity instead of v, and multiplied through by c² like this ∂²Ψ/∂t² = c² ∇²Ψ (The Wave Equation)In physics literature, you might see the wave equation written with the d'Alembert operator (or "d'Alembertian") □ = 1/c² ∂²/∂t²  ∇², so that the wave equation may be written simply as □Ψ = 0 This equation describes any wave, not just sine waves. (Aside: The Schrödinger equation is actually a Heat Equation, not a Wave Equation. These exhibit oscillatory behaviour too, but I still wouldn't call it a wave equation. But the Klein–Gordon equation, a relativistic version of the Schrödinger equation, is a wave equation.) The general solution to this equation was discovered by Jean le Rond d'Alembert in 1747, and PierreSimon Laplace was one of his students. The general solution is u(x, t) = F(x  ct) + G(x + ct) where F and G are any differentiable functions of a single real variable. In words, the general solution of the 1+1D wave equation is the sum of a rightmoving function F and a leftmoving function G, where "moving" means that the shape of these individual arbitrary functions with respect to x stays constant, however the functions are translated right and left with time at the speed c. Example: Let ξ = x  c t. Then, in the case of the rightmoving sinusoid, the solutions to the wave equation are F(ξ) = A sin(k ξ + ϕ) + D and G = 0. Here's how the wave equation applies to gravity waves. Start with the Einstein Field Equations (EFE) G _{μν} + Λ g _{μν} = 8 π G / c⁴ T _{μν}We talked about these equations before in detail. You solve this equation by specifying a metric g _{μν}. (I'm going to drop the indices μν for now.) We're going assume a solution that looks like this g = η + h η ("eta") denotes the Minkowski metric. This metric describes the spacetime you study in Special Relativity. This metric describes "flat" 3+1D spacetime. No gravity. Space itself is flat. Spacetime is hyperbolic. The Minkowski metric is already one solution to the EFE, it is just not an exciting solution because there's no matter, no energy, no gravity, no curvature. h is a small perturbation. By small, I mean it is negligible compared to η. The determinant η = 1, so h << 1. These assumptions are are called linearized gravity. The metric g must be symmetric. This means g _{ab} g ^{bc} = δ _{a}^{c}, the Kronecker delta. This symmetry and the assumption h is small make it possible to solve the EFE. The solution involves an awful lot of tensor algebra. You need to expand g into Christoffel symbols and Riemannian tensors and then reduce. Best to do all this tedious math with specialized software like Cadabra. Eventually, under our assumptions, you can reduce the EFE to this: ∇²h _{bd} = 16 π G / c⁴ (T _{bd}  T _{ac} η ^{ac} η _{bd} / 2) ∂²h _{bd}/∂t² But this is just a wave equation! Putting this in even simpler terms, h _{bd} is the wave function, and □h _{bd} = 0. What's "waving"? The curvature of spacetime. SimplificationChapter 16 " Gravity Waves" of the draft of the book Exploring Black Holes: Introduction to General Relativity (2e) (2015) by Edmund Bertschinger & Edwin F. Taylor provides a simple way to think about this topic. Imagine a Cartesian coordinate frame. You're at the origin. A gravity wave moves along the zaxis. We already talked about the differential displacement formula, how it was the most important formula in physics, and how it's really nothing but a generalization of the Pythagorean Theorem. Here's what it looks like in this scenario: ds ^{2} = (1 + h) dx ^{2} + (1  h) dy ^{2} + dz ^{2}  dt ^{2}If you take a look at Bertschinger and Taylor, they talk about "proper time" τ, whereas I'm using "proper distance" s. "Proper" just means it's an invarianteveryone measures the same distance between two events. Proper time and proper distance are basically interchangeable, since we're assuming natural units c=1, so that space=time. You could use dimensional analysis to put back the c in this equation if you really wanted: ds ^{2} = (1 + h) dx ^{2} + (1  h) dy ^{2} + dz ^{2}  c ^{2} dt ^{2}Now compare this formula to the Pythagorean version: ds ^{2} = dx ^{2} + dy ^{2} + dz ^{2}There's two main differences:  There's no time component dt^{2} in the Pythagorean version. That's because it assumes absolute time rather than relative time.
 x and y distances are stretched (and shrunk) by a factor of (1 ±h). Remember h<<1. A fractional deviation in length is called a strain. In this case, h is called a gravitational wave strain.
So what's happening is that space is literally shrinking and expanding in the x and y directions, by a teeny tiny amount. Note that the coefficients of the differential displacement formula are the metric g. You can see this by rewriting the formula as a matrix equation. The metric is the matrix sandwiched in the middle: With this metric and the assumption that h<<1, the Einstein Field Equations reduce to the following wave equation: ^{}The most general (d'Alembert) solution to this wave equation is h = h _{+z}(z  t) + h _{z}(z + t) where h _{+z} is a wave moving in the positive zdirection and h _{z} is a wave moving in the negative zdirection. In practice, you're only going to see a wave moving in one of these directions, and the other will be identically zero. Remember that h can be any function of (z ±t) whatsoever, as long as we can differentiate it twice and get a continuous function as a result. Addendum: The vacuum solutionI don't want to copout on a mathematical proof of gravity waves. We can do a trivial proof in 1+1D if the Riemannian tensor is zero. In plain English, it means there's no curvature. Physicists call this a vacuum solution: The Einstein tensor G vanishes. Therefore, the stressenergy tensor T also vanishes, which implies there's no matter or energy. Why make such an unrealistic assumption? Because it makes the math really, really easy(er). Specifically, we don't need to do any tensor algebra, just a little calculus. Definitions: The Minkowski metric η is just the constant matrix 1 0 0 0 0 1 0 1 0 0 1 0 0 0 0 1 By g⁻¹, I just mean the contravariant components (upper indices) of the covariant metric g (lower indices). The negative one superscript just indicates that it is the multiplicative inverse of g. Assuming g = η + h (lower indices) implies g⁻¹ = η  h (upper indices). A Christoffel symbol is Γ = 1/2 g⁻¹ ∂g/∂x. Christoffel symbols have indices like tensors (we dropped them here), but they are not tensors. The Riemannian tensor is R = ∂Γ/∂x + Γ Γ. This is a tensor, not a scalar, but we dropped the indices. The physical dimensions of R are [R] = 1 / length². Assumptions:  g = η + h
 h is small
 R = 0
Proof: ∂η/∂x = 0 because η is a constant Γ = 1/2 g⁻¹ ∂g/∂x = 1/2 g⁻¹ ∂(η + h)/∂x = 1/2 g⁻¹ (∂η/∂x + ∂h/∂x) = 1/2 g⁻¹ (0 + ∂h/∂x) = 1/2 g⁻¹ ∂h/∂x R = ∂Γ/∂x + Γ Γ = 1/2 (g⁻¹ ∂²h/∂x²  (∂h/∂x)²) + (1/2 g⁻¹ ∂h/∂x)² (∂h/∂x)² = 0 because h is small Therefore, R = 1/2 g⁻¹ ∂²h/∂x². But we assumed R = 0, so 1/2 g⁻¹ ∂²h/∂x² = 0. Multiply both sides by 2 g to get ∂²h/∂x² = 0 But this is just a wave equation. QED.



Post by krusader74 on Mar 12, 2016 6:10:48 GMT 6
Black Hole TechStephen Wolfram, creator of Mathematica, recently wrote a blog post entitled Black Hole Tech?. It got me thinking, what if R'lyeh were "powered" by black holes, engineered  As a source of energy
 As a means of space propulsion
 To provide defensive shields
 To timetravel to the future
Wolfram discusses all this in his article. The black hole tech would also explain the city's nonEuclidean geometry! In the Call of Cthulhu RPG, if your investigators find R'lyeh and get too close to the engine room, and the black holes therein, maybe only minutes or hours seem to elapse for them, but when they finally return to the outside world, thousands or millions of years might have passed! In fact, Cthulhu may only seem to be deadorsleeping for millennia to his followers on the outside. To Cthulhu, it may only be a short nap. The reason is the time dilation caused by all the black hole tech in the city. Time DilationLet's use the General Relativity we've learned so far to do a practical time dilation calculation! Astronaut Scott Kelly just returned from 342 days aboard the International Space Station (ISS). The press and blogosphere carried many stories about how Scott aged at a different rate on the ISS than his twin brother Mark on earth. Here's an excerpt from one such article: Quoted from the article " The Real Twin Paradox: Astronaut Scott Kelly will return from a year in space both older and younger than his twin brother" by Gideon Lichfield, March 27, 2015. (Emphasis mine.) I've looked at a number of these articles, and they're all missing something: The formulas used to compute these numbers and an explanation of where they came from. With the information I've already told you about General Relativity, it's possible to derive these formulas ourselves and do the calculations. As I've repeated often: The differential displacement formula ds ^{2} = g _{μν} dx ^{μ} dx ^{ν} is the most important formula in physics. All solutions to General Relativity have this form. Furthermore, there is nothing complicated about this formulait is simply a generalized version of the Pythagorean Theorem. The solution to General Relativity (GR) we're going to use here is called the Schwarzschild metric. It was the first exact solution to GR. It assumes a universe with one object of mass M that generates a gravity field. We explore this universe using infinitesimally small test masses we can put anywhere in the gravity field. I mentioned this metric before, but I didn't show the metric or derive it. For now, I'll just show you what it looks like. We can derive it later if we talk more about black holes. Here is its differential displacement formula in Cartesian coordinates: dτ ^{2} = (1  (2 G M)/(R c ^{2})) dt ^{2}  1/c ^{2} (1  (2 G M)/(R c ^{2})) ^{1} (dx ^{2} + dy ^{2} + dz ^{2}) where
 τ is the proper time. It's the time associated with a test mass sufficiently far away from the mass M that gravity has no measurable effect on it.
 t is coordinate timethe time associated with the test mass we're interested in.
 (x, y, z) are the usual Cartesian coordinates associated with the test mass we're interested in.
 The expression (2 G M)/c^{2} is repeated in a couple of places. It's called the Schwarzschild radius and denoted R_{s}. It's the radius an object of mass M would need in order to become a black hole. It's also a measure of the gravitational potential energy of the object.
The factor (dx ^{2} + dy ^{2} + dz ^{2}) is just the usual Pythagorean differential displacement. Remember that velocity v = √(dx ^{2} + dy ^{2} + dz ^{2})/dt. Now divide both sides of the differential displacement formula by dt ^{2} and take square roots to get: F(R, v) = dτ/dt = √((1  R _{s}/R)  (1  R _{s}/R) ^{1} (v/c) ^{2}) This function F of radial distance R and velocity v tells us the instantaneous rate of change of proper time with respect to coordinate time. This is the main thing we need to know. It's going to tell us everything! (In relativity theory, it's common to abbreviate β= v/c. In words, beta is velocity as a fraction of the speed of light. I'm not going to use that here. I'm just telling you in case you see it elsewhere.) The actual orbit of the ISS is complicated and looks like this from the ground: \ The exact coordinates of the ISS are all functions of coordinate time t. If I knew these functions, I could compute v and R exactly as functions of time. But I don't know what these functions are! So I am going to do an approximation by assuming that the ISS is orbiting directly above the equator. In standard international (SI) units, the universal gravitational constant is G = 6.67408 ×10 ^{11} m ^{3} kg ^{1} s ^{1}, and the speed of light is c = 299,792,458 m s ^{1}. The mass of the earth is M = 5.9742 ×10 ^{24} kg. The earth is egg shaped. Its radius at the poles are smaller than its radius at the equator. At the equator, its radius is R _{eq} = 6,378,137 m. The height of the ISS above the equator varies between 404 and 406 km. But we're going to assume it's a constant h = 405,000 m. The excerpt above tells us the velocity of the ISS. But if we didn't know it, we could calculate it from the orbital speed equation v _{ISS} = √((G M)/(R _{eq} + h)). In addition to the velocity of the ISS, you also need to know that a point on the equator moves with velocity v _{eq} = 465 m s ^{1}. Or you could calculate it from v _{eq} = 2 π R _{eq} / p. One day on earth is p = 86162.4 s. Here are the steps we need to compute the daily time dilation (gain if positive, or loss if negative) in microseconds of the ISS according to GR:  Calculate F_{ISS} = F(R_{eq} + h, v_{ISS}), which tells us how fast proper time changes with respect to a clock on the ISS.
 Calculate F_{eq} = F(R_{eq}, v_{eq}), which tells us how fast proper time changes wrt a clock on earth.
 Divide the two derivatives above to get the quotient q = F_{ISS} / F_{eq}, which tells us how a clock on the ISS changes wrt a clock on earth.
 To get the daily time dilation (gain if positive, or loss if negative) in microseconds of ISS according to GR, compute Δt = 10^{6} ∫^{p}_{0} (q  1) dt, where p is the number of seconds in a day on earth. (We multiply by a million to convert seconds to microseconds.) Our assumption that radial distance and velocity remain constant wrt time simplifies this stepinstead of integrating wrt time over an earth day, we just multiply by the length of an earth day: Δt = 10^{6} p (q  1)
That's it. Now we have everything we need to crunch the numbers. I wrote a short program in Python to crunch the numbers. Python is free, portable across platforms, and easy to use. The result is Δt = 24.494490 microseconds, very close to the last paragraph of the excerpt, which says, "So Scott will become 25 microseconds a day younger" per earth day. Multiplying this by 342 earth days yields 8,377 microseconds. Notice the article excerpt breaks the 25 microseconds per day into two parts:
 part due to velocity only: 28 microseconds per day
 part due to gravity only: +3 microseconds per day
How do you get this? Simple: in the original differential displacement formula, set M=0. That tells you the part due to velocity only, since there's no more gravity. When you do this, you get the Minkowski metric η for flat spacetime: dτ ^{2} = dt ^{2}  1/c ^{2} (dx ^{2} + dy ^{2} + dz ^{2}) Divide both sides by dt ^{2} and take square roots to get dτ/dt = √(1  (v/c) ^{2}) In Special Relativity (SR), this quantity is called alpha, α(v). It is the reciprocal of gamma, γ(v), AKA the Lorentz contraction factor. This derivation shows the consistency between SR and GR. The Python script performs the calculation for time dilation using these values to get 28.176500 microseconds per day, due to velocity only. This implies the time dilation due to gravity only is 24.494490  (28.176500) = 3.682010 microseconds per day. Another thing that the Python code does is to figure out the distance from earth at which time dilation due to gravity cancels time dilation due to velocity. The answer is 1.497409 earth equatorial radii. Finally, the Python program plots a graph of time dilation versus earth equatorial radii, and gets a graph that matches the one on Wikipedia's page for Time Dilation:



Post by stevemitchell on Apr 6, 2016 3:07:21 GMT 6
I checked in at the Arkham Bazaar today, and found a listing for a special edition of THE DREAMS IN THE WITCH HOUSE. Here are the details:
"This special limited edition, handmade book is available only from Arkham Bazaar, and has an offset print hand binding, foilstamped cover, cloth bookmark, and each is numbered (only 200 printed). The book contains the full text of H.P. Lovecraft's "Dreams in the Witch House," plus an introduction by game designer and scholar Kenneth Hite, an article on the science of "Dreams in The Witch House" by scientist Dr. Fred Lubnow, HPLFF Director Brian Callahan on film adaptations (intentional and not), and Mike Dalager on adapting the story to a Rock Opera. Features cover art in foil stamp by Liv RaineySmith, interior illustrations by Nick Gucker and Liv RaineySmith, and back cover artwork and design elements by Brian Callahan.
"BONUS: includes the full length CD  Dreams In the Witch House: A Lovecraftian Rock Opera.
"See and hear Lovecraft as you never have before in this handbound limited edition keepsake book."
How could I resist? I've ordered this, and hope to see it in a few days.



Post by krusader74 on Apr 7, 2016 12:52:12 GMT 6
I checked in at the Arkham Bazaar today, and found a listing for a special edition of THE DREAMS IN THE WITCH HOUSE. Here are the details: "This special limited edition, handmade book is available only from Arkham Bazaar, and has an offset print hand binding, foilstamped cover, cloth bookmark, and each is numbered (only 200 printed). The book contains the full text of H.P. Lovecraft's "Dreams in the Witch House," plus an introduction by game designer and scholar Kenneth Hite, an article on the science of "Dreams in The Witch House" by scientist Dr. Fred Lubnow, HPLFF Director Brian Callahan on film adaptations (intentional and not), and Mike Dalager on adapting the story to a Rock Opera. Features cover art in foil stamp by Liv RaineySmith, interior illustrations by Nick Gucker and Liv RaineySmith, and back cover artwork and design elements by Brian Callahan. "BONUS: includes the full length CD  Dreams In the Witch House: A Lovecraftian Rock Opera. "See and hear Lovecraft as you never have before in this handbound limited edition keepsake book." How could I resist? I've ordered this, and hope to see it in a few days. Wow! That's an incredible find!!! I definitely want one of these. This is the link to the product page: Dreams In The Witch House Arkham Bazaar edition.



Post by stevemitchell on Apr 8, 2016 20:56:27 GMT 6
My copy of the Arkham Bazaar Dreams in the Witch House arrived today. Physically, a very nice package, although I was expecting more depth in the accompanying articles. I can't speak to the rock opera yetmy music system is in need of repair, so it will be a while till I can play the CD.



Post by krusader74 on Apr 29, 2016 0:26:19 GMT 6
The Simulation HypothesisLast week, I watched the 2016 Isaac Asimov Memorial Debate  Is the Universe a Simulation? on YouTube. It was about 2 hours long. Neil Tyson deGrasse hosted. The panel consisted of
 Zohreh Davoudi  Theoretical Physicist, MIT
 Max Tegmark  Cosmologist, MIT
 James "Morpheus" Gates  Theoretical Physicist, U. Maryland (you just need to see it to get the "Morpheus" reference)
 Lisa Randall  Theoretical Physicist, Harvard
 David Chalmers  Philosopher, NYU
The purpose was to discuss Nick Bostrom's Simulation hypothesis. The basic idea is that the universe is computable, based on what we know. But there are reasons to believe that it is not merely computable, but that it's being computed in a giant simulation, in the next universe up. Like in the Matrix. Most of the panelists were physicists, so here are some of the reasons they put forward to believe we're living in a simulated universe:
 Computer simulations only have a finite amount of disk space, memory and CPU to render the simulation. If you run the simulation too fast, or drill down too far into the miniature, then the simulation gets pixelated  it looks grainy, quantized. In the physical world, space, time and energy are similarly quantized. Why should this be?
 Leonard Susskind discovered that the amount of quantum information in a black hole is proportional to the surface area of the event horizon, not its volume as expected. This applies generally to all volumes, not just black holes. It's called the Holographic principle. This makes sense if the universe is a hologram.
 James Gates recently discovered error correcting codes in the rules governing quarks. These error correcting codes resemble the kind you find in video graphics software! Why the heck would a real universe need error correcting codes in its fundamental building blocks?
Max Tegmark's argument against the hypothesis said: If it's probable that we're living in a simulation, then it's just as likely that the beings running the simulation in the "next universe up" are likewise living in a simulated universe. So we're actually living in a simulation inside a simulation. But if that's true, then this argument can be continued ad infinitum, leading to an infinite regress, which isn't allowed. (Aristotle uses similar reasoning to "prove" God: Everything has a cause, yada, yada, so there must be First Cause, otherwise we get stuck with an infinite regress, which isn't allowed.) I don't find Tegmark's counterargument convincing. All it shows is Tegmark's dislike for actual infinities and infinite regresses. As a mathematician, I have no disdain for the Infinite. If Wittgenstein came up to me muttering: "...6295141.3, there, I've recited all the digits of Pi," then I'd think he was crazy, but if Zeus came down from Mount Olympus muttering the same thing, I'd believe it, because it seems likely that Zeus could do a countably infinite number of things in a finite amount of time. If there are paradoxes with the infinite, it's probably some ambiguity in how we're stating the problem. Someone else pointed out that the quantization of the universe may result from mathematical incompleteness, rather than from it being a computer simulation. Maybe. But Godel's Incompleteness theorems are overused and poorly understood. The full title of Godel's paper is "On formally undecidable propositions of Principia Mathematica and related systems." The process of Godelization and the construction of the (unprovable but true) Godel formula depends 100% on the choice of language. Godel chose to work with L _{ωω}, the language underpinning Russell and Whitehead's Principia Mathematica. The first ω means that we allow sentences to have only a finite number of conjuncts. The second ω means we allow sentences to have only a finite number of quantifiers. There are infinitary logical languages where Godel's Incompleteness Theorem is not true. The smallest example is L _{ω1 ω}, which allows sentences to have an infinite number of conjuncts. Here godelization does not work and you can't construct the Godel formula. Moreover, you can actually prove that theories in L _{ω1 ω} are complete! There is one problem though, L _{ω1 ω} only admits countably infinite models. This means you can have arithmetic on the Rationals, but not the Reals. Not a big deal. You can, in fact, create what are called "algebraic extensions" of the Rationals, that include π, √2, √3, ... and all the other computable irrational numbers too  all you'll practically ever need. If the universe were infinitary in this sense, then I wouldn't expect any graininess or quantization. So there's no good reason to expect a finite, incomplete or inconsistent universe  unless it's a computer program. A simulated universe has a secular "god" of sorts  a creator  but one who doesn't necessarily have wisdom or benevolence. I have a 2YO niece and nephew. We sit and build blocks. Then what do they do? Smash them to the ground and laugh. Older kids play the Sims and Minecraft and Second Life. They build buildings, cities, worlds. And then they rain down fire and brimstone on them, or march Godzilla through them razing them to the ground. This jives with my impression of the "real" world: bad things happen to good people, good things happen to bad people, things are going great one moment and then disaster strikes at random. It seems the "real" world could just be a video game being played by a kid with a mean streak. About 3 months ago, I read a Philip K. Dick short story in a magazine from the 1950s. In it, the current fad is a device like a snow globe. Inside, you actually create a "big bang" and watch a universe develop. There's a view screen that allows you to zoomin to planets with promising life forms. There are knobs and buttons on the device that allow you to slightly alter conditions to help promote intelligent life. Every year, there is a competition, and an award is given out to the person whose globe has produced the most advanced civilization. But then the sore losers smash their globes in frustration. The main character lobbies to get a law passed to make it illegal to smash these globes, since there is sentient life inside. The lawmakers debate whether these life forms are really real or just simulated. At the same time, intergalactic spacecrafts arrive back from the edge of the universe to report that they themselves are inside a such an artificial globe! Then cataclysm strikes  rifts and fissures start to open up all over "reality"  as people realize that the artificial globe they are in has just been smashed. This short story was written quite some time before Nick Bostrom's argument, but it immediately evoked the Simulation Hypothesis for me. What does any of this have to do with "Witch House"? What if H. P. Lovecraft's universe were a computer simulation being run by a group of malicious kids? It would help explain a lot. Sometimes, these brats would put on their Oculus rift gear, and "incarnate" in avatars like "The Black Man" to screw with our minds. They almost surely would put "backdoors" and "shortcuts" through spacetime for themselves to use. Perhaps Keziah Mason found them. She's like "Neo" or "Morpheus" in the Matrix. To someone with a background in math and physics, like Walter Gilman, these shortcuts would just seem like exotic topological features or 4D space. I think if I ran "Witch House" as an RPG scenario now, I might use this "Simulationist" reinterpretation of Lovecraft's Cosmicism.



Post by stevemitchell on Apr 29, 2016 13:03:12 GMT 6
Or, as the Mad Seer of Providence once wrote:
Then, crushing what he chanced to mould in play, The idiot Chaos blew Earth’s dust away.



Post by krusader74 on Dec 1, 2016 19:10:10 GMT 6
Fred S. Lubnow Ph.D.I saw this short (15 min 52 sec) lecture on YouTube. It's about Lovecraft and science, not specifically DWH, but it covers a lot of the same topics as this thread: The Lovecraftian Cosmos by Fred S. Lubnow  YouTubeBriefly, the topics covered in this video are
 The Big Bang Theory & Azathoth
 String Theory & MiGo (Whisperer in Darkness)
 The Bulk, Branes, Hawking's 10^500 universes & The Dreamlands
 From Beyond: Lovecraftian horrors are powerful beings from other branes (or the bulk) that are trying to squeeze into our universe.
 Biology of Lovecraftian horrors
 Evolution, Darwin & Lovecraft's racist views
 AI, downloading consciousness into artificial devices, beaming consciousness through space using light, deep intersteller travel & the Great Race of Yith (Shadow Out of Time)
There's more in depth treatments of these topics on Lubnow's blog and in his ebook: The Black ManRegarding Lovecraft's racist views, a topic brought up in Lubnow's YouTube lecture, I wanted to point out that the narrator in DWH explicitly states that The Black Man has Caucasoid features: However, other eyewitnesses, describe him differently: A pair of drunks report seeing "a huge robed negro." This is also how he's described by the police on a raid on "revellers in a ravine beyond Meadow Hill just before dawn" in search of the missing child (kidnapped by Keziah, Gilman, the Black Man and Brown Jenkin). In New England, there is a tradition that dates back to the Puritans and the Salem witch trials linking the Devil to a large darkskinned man. This is the main thing Lovecraft seems to be alluding to in DWH: And this: Lovecraft also links The Black Man to Nyarlathotep in DWH: There's a great illustration of The Black Man by Jens Heimdahl:



Post by stevemitchell on Dec 1, 2016 19:51:53 GMT 6
Thanks for the tip on the Journal of Lovecraftian Science!

