Through the Gates of the Silver Key: Chapter V, part 1: Higher Dimensions

 Yog-Sothoth by Chivohit (www.deviantart.com)

At the end of Chapter IV of “Through the Gates of the Silver Key,” written by H.P. Lovecraft and E. Hoffmann Price, Randolph Carter says to Yog-Sothoth that he is ready to peer beyond the Veil of reality. Suddenly, Carter’s mind is flooded with knowledge on the true nature of the cosmos. One concept that was discussed in some detail was how our perception of a “tri-dimensional world” or even a four-dimensional Space-Time does not represent the true nature and structure of the Universe / Multiverse. Additionally, Carter realizes that human senses can only perceive of a portion of reality; however, once he passed beyond the Ultimate Gate he saw “…in the brooding shadows of that which had been first a vortex of power and then an illimitable void, a sweep of creation that dizzed his senses.”

Yog-Sothoth continued to fill Carter’s mind with energy waves of information to obtain a better understanding of the Universe. Carter then understood that he was an infinitesimal part of a multiform entity; was this a realization and subsequent access to other beings in other Multiverses? Carter also understood that

“…every figure of space is but the result of the intersection by a plane of some corresponding figure of one more dimension – as a square is cut from a cube or a circle from a sphere. The cube and sphere, of three dimensions, are thus cut from corresponding forms of four dimensions that men know only through guesses and dreams; and these in turn are cut from forms of five dimensions, and so on up to the dizzy and reachless heights of archetypal infinity.”

                                                               Yog-Sothoth by Nightserpent

The net result of this higher multi-dimensional view of reality is that our 3-space and 1-time Universe is merely a shadow or illusion of the true nature of substance and reality. Thus, the way the shadow of a cube is 2-dimensional representation of a cube in a 2-dimensional world, the Tesseract is a 3-dimensional shadow representation of a hypercube in 3-dimensional space (see below). According to Lovecraft and Price, if we had the appropriate knowledge and senses, where the Veil of reality has been pulled aside, we would perceive the true, multi-dimensional nature of reality.

                                                             The shadow of a cube is a 2-dimensional representation of the cube

                                                     The Tesseract is a 3-dimensional shadow representation of a 4-dimensional hypercube.

In the late 19^th and early 20^th centuries mathematicians were investigating geometry beyond the three known spatial dimensions, as well as working on “non-Euclidean” geometry, which is essentially a description of curved space and shapes. A lot of misinformation and pseudoscience was developed in light of these investigations, essentially from people who knew very little about the science. However, to many mathematicians surprise, such investigations into curved fourth dimensional Space-Time had a practical application in Einstein’s work on gravity and how the amount of matter determines the type of geometry that exists in the surrounding space (https://web2.ph.utexas.edu/~coker2/index.files/4d.shtml). As Kip S. Thorn put it in his essay Spacetime Warps and the Quantum World in The Future of Spacetime (2002), “…Einstein concluded that space and time are warped by matter and energy and that this warpage is responsible for the gravity that holds us to the surface of the Earth.”

                                                                           Yog-Sothoth by John Coulhart (www.johncoulhart.com)

While higher dimensional mathematics continued through the 20^th century, incorporating high dimensional concepts into physics and the nature of reality went largely unsuccessful. However, with quantum physics, the need to include more dimensions seemed apparent but it was in the 1980’s with the development of String Theory that the need for higher dimensional math appeared necessary. In order to include gravity into a single equation with the other forces of nature (electromagnetic, weak nuclear and strong nuclear) String Theory needed 9 or 10 spatial dimensions and one dimension of time (https://web2.ph.utexas.edu/~coker2/index.files/4d.shtml). In turn, String Theory has led to M-Theory, where the strings are looped and/or tethered to surfaces or membranes, possibly stitching together the Multiverse.

Again, before there was a mathematical need for higher dimensions in many of the leading theories of physics, discussions on this subject were largely thought of purely the stuff of fiction. Not only that, but many were criticized for considering such concepts or ideas. In his article “H.P. Lovecraft and Pseudomathematics” in Darrell Schweitzer’s Discovering H.P. Lovecraft (1995), Robert Weinberg dismisses Lovecraft’s thoughts of higher dimensions discussed in many of his stories. Weinberg states, “The existence of higher dimensions should be of little concern to this world as any contact with such dimensions is impossible.” Based on the current state of both String Theory and M-Theory higher dimensions are absolutely essential working through the development of a Standard, Unifying Theory.

Weinberg also goes on in the article to state, “It is impossible (not unlikely or not yet possible, but impossible, actually shown to be never possible) to construct a higher dimension from a lower one.” That is a pretty definitive statement. While it may not be possible to construct a higher dimension, we can represent or model high dimensions (see above). Also, such higher dimensions may be useful in obtaining a better understanding of the Universe. Thus, I think casually discarding an idea or hypothesis and saying it’s just not possible or relevant can be dangerous in science. Who knows, maybe the next generation of physicists will come up with a new theory that completely does away with the need for String Theory and the consideration of higher dimensions. However, if working through String Theory and these ideas have led others into investigations that shine a little more light on the true nature of reality then that is a good thing. Science is very much built upon its history; Einstein’s General Relativity did not result in throwing out Newton’s Principles of Gravity, just like Quantum Mechanics did not result in throwing out General Relativity. It should also be emphasized that we always learn something even when our hypothesis is not proven correct.

Yog-Sothoth (www.lostsouls.org)

Getting back to “Through the Gates of the Silver Key,” three dimensional entities like us who exist in linear time, cannot perceive the higher dimensions that are “wrapped and curled up,” tucked away from our perception. However, other entities, from other Universes with slight modifications in their natural laws, may be able to perceive or even have access to higher dimensions, which may allow them to travel through time and space in very unconventional ways (e.g. The Dreams in the Witch-House).

Based on what we know about dimensionality and Space-Time, life can only exist in a Universe of three spatial dimensions and one temporal dimension. Based on Max Tegmark’s paper “On the Dimensionality of Spacetime” (Class. Quantum Gav. 14 (1997), L69-L75), other realities with more or less dimensions than ours would be “dead worlds.” Tegmark states in his abstract “In a space with more than three dimensions, there can be no traditional atoms and perhaps no stable structures.” This may be the case, however maybe many Lovecraftian entities can access the energy in these higher dimensions to conduct incredible feats thorough time and space. Thus, Yog-Sothoth maybe a unique and fluid form of life that both easily travels through and exists in all of these dimensions at the same time. If Tegmark’s idea does hold true, then any inhibited Universe, where atoms are stable enough to eventually rise to life, would be squeezed into that little box labeled “We Are Here” in the figure shown below.

Next time we will wrap up our discussion of Chapter V in “Through the Gates of the Silver Key” with a discussion of some of the exoplanets described by Randolph Carter. Thank you – Fred.

The Mathematics of the Witch House, Part 3 – Higher Dimensions

Symbols from the Necronomicon (from propnomicon.blogspot.com, by Vemisery)

In a previous article on hyperspace I mentioned that  Michio Kaku describes in his book Hyperspace: A Scientific Odyssey Through Parallel Universe, Time Warps, and the Tenth Dimension that the laws of nature become simpler and more elegant when expressed in higher dimensions.  Since Euclid and up to the mid-19th century, flat or planar geometry has been THE only geometry of western civilization, used in various practical applications including architecture.  However, more so than presenting the subject of geometry in a cohesive format, it was Euclid’s methods of using logic, deductive reasoning, evidence and proofs that is his larger contribution to mathematics and science.

While Euclid’s contributions were monumental, they also limited alternative thought and theory in geometry and mathematics in general.  In planar geometry one dimension is a straight line ( a point has no dimensions), two dimensions is plane shape (square, circle, triangle, etc.) and three dimensions can be represented as solids (cubes, spheres, cylinders, etc.).  Each higher dimension is created by adding another line at a 90 degree angle and once you get to three dimensions there is no additional “directions” for another line.  Thus, the conclusion was there is no 4th dimension.

Representation of one, two and three dimensions (www.merlot.org; Duane B. Karlin)

As I have previously mentioned many mathematicians and philosophers agreed with this.  For example, Ptolemy from Alexandria  stated that “proof that the fourth dimension is impossible.” – Michio Kaku, 1994.  This quote is very similar to some of the statements made in Robert Weinberg’s article H.P. Lovecraft and Pseudomathematics (Discovering H.P. Lovecraft by Darrell Schweitzer, 1995) such as “The existence of higher dimensions should be of little concern to this world as any contact with such dimensions is impossible.”, “There is no way that we can construct a four-dimensional object.”, and “It is impossible (not unlikely or not yet possible, but impossible, actually shown to be never possible) to construct a higher dimension from a lower one.”

I bring this quotes up not to criticize Mr. Weinberg but to make the point I get the impression that when he wrote this article in 1971 he was in the camp with many of the classical mathematicans that higher dimensions are impossible.

However, as a teenager of the 1980’s I got to watch the series and read the book Cosmos by Carl Sagan.  During one episode / chapter (The Edge of Forever) Sagan spoke about creatures living in flatland.  I strongly recommend you either rent the DVD of Cosmos, read the book or at least look up Sagan’s flatland discussion on YouTube.  The point I want to make here is that while we can’t “see” a 4th dimensional being with our three dimensional senses, just like a two dimensional being can not see a three dimensional being, experiments can be done to detect the presence of a higher dimension.

In Cosmos, Sagan made the point that a 3-dimenional “apple creature” passing through the 2-dimensional plan of Flatland (moving from above to under Flatland) would appear as a point, an expanding line, then a contracting line, then as another point and then disappear.  The square or triangle creature observing this may think they are insane and would not be able to understand what they just saw.  Could something similar happen if a 4th dimensional creature passed through our 3 dimensional world?  Is it possible that some individuals have actually experienced this, resulting in nervousness, phobia or even severe mental disorders such as schizophrenia?

Carl Sagan’s apple creature visiting Flatland

While we can’t see a 4th dimensional creature or object we may be able to see an interpretation or representation of it.  Again, from Carl Sagan’s Cosmos, you can make a representation of a 3-dimensional object (say a cube) on a 2-dimensional surface or plan (see below)

Point = 0D, Line = 1D, Square =2D, Cube =3D and Tesseract =4D

A three dimensional cube held by Carl Sagan

Every school child learns how to draw a representation of a cube on a 2 dimensional surface (piece of paper).   This same method can be done to draw a representation of a “hypercube” – a 4 dimensional cube.  Below is a “3-dimensional” representation of a hypercube, also known as a Tesseract.

A hypercube also known as a Tesseract

Again, this is just a representation of what a Tesseract looks like not a Tesseract itself, since we can’t look into the 4th dimension.  Thus, the strange shapes and images Walter Gilman sees and experiences he has as he travels through hyperspace – the prisms, labyrinths, limitless abysses of inexplicably coloured twilight, and bafflingly disordered sound; clusters of cubes and planes, groups of bubbles, octopi, centipedes, living Hindoo idols, and intricate arabesques roused into a kind of ophidian animation – may essentially be his 3-dimensional mind trying to perceive and comprehend higher dimensions.

To make one final point on Mr. Weinberg’s critical analysis of that story, I can’t actually see an electron but I can conceptually visualize what one looks like (a small particle, a traveling wave or hazy cloud) and more importantly I can see evidence of electrons (see below).  Now I understand that Mr. Weinberg’s article is dated (early 1970’s), Cosmos was in the 1980’s and most serious higher dimensional thought and research is less than 20 years old; this obviously has to be taken into account in this analysis.  So I can certainly understand stating that something is very unlikely but to say impossible may be a little too hasty (in my opinion).

Electron particle tracks (credit: Brookhaven National Laboratory / Science Photo Library).  Do these particle tracks somewhat resemble the curious symbols found in the Necronomicon?

Next time the discussion will concentrate on hyperspace travel in The Dreams in the Witch House and later articles will discuss Brown Jenkin and the appearance of Elder Things and the Black Man (Nyarlathotep).  Thank you.  Fred