Monday, January 5, 2015
Interstellar and Pendulum Clocks
This Christmas our family had an unusual set of occurrences that started the night of December 20th, 2014. On top of the stereo stand in our living room we have an old mantle clock which once belonged to my wife's grandparents. This clock worked faithfully for us for many years, but then at least ten years ago it stopped. Still, we've left it where it was because we like the look of it.
That night we were having a big family supper in the living room when out of nowhere the clock started chiming the hour! We went over to look and sure enough it had started ticking. It went for almost an hour, then stopped.
As a bit of background, we've lived in this house for thirty years. The previous owners converted the double garage to become the living room we were in. Because this room used to be the garage, its floor sits on a concrete pad and is very solid feeling - there is no visible springiness or give to this floor. If there were to be vibrations somehow transmitted to this broken clock that were strong enough to push the pendulum back and forth, one would think that all of the action movies we've watched through a sound system which includes a hefty subwoofer only a few feet away from the clock would have had ample opportunity to activate it, but that has never happened, and there was no activity in the room that night that was any different from many many previous family get-togethers in that same space.
The following night a group of us were just sitting in the room having a chat when the clock started up again, bonged nine times on the hour and again on the half, then stopped once again. But that night my wife had trouble sleeping, was up and down through the night and heard the clock bonging the hours a number of times through the night. When she told me this the next morning I went and looked, and the clock had once again stopped.
The night of the 22nd I decided I'd tell this story to my friends on Facebook, so I went and stood in front of the clock to take the picture you're seeing here. As soon as I took it the clock once again started ticking. As I walked out of the room to tell my wife the clock bonged once, and once again it continued to run for a few hours that evening.
The night of the 23rd, we were again chatting in the room when the clock started up for what proved to be its final performance. On Christmas Eve we had another big family supper and gift opening with our grand-daughters in that room, and this time there was not a peep from the clock, nor has there been any further mysterious activity from it since. It looks like our spooky clock story has come to its conclusion!
Thinking about Professor Thorne's idea of pushing on the "world tube" of a space-time object from the fifth dimension, doesn't a clock's pendulum sound like it would be substantially easier than a book to influence with gravitational force from an extra dimension? I can imagine pendulum clocks all over the world starting and stopping at unexplained times, using this particular effect.
There's so many different kinds of spin we can put on this story. Is there a non-spiritual explanation? No doubt one can be surmised. For me, I'm no expert on pendulum clocks, but my experience with them is they don't start by themselves: you have to give the pendulum a push to get it going. So I have to ask: were we visited by some long-lost family member, happy to see the whole family together? My wife's cousin, a good friend of hers since they were children, spent the Christmas holidays with us for the first time ever. Our sons, their wives, and our granddaughters were all here in town for the big suppers on the 20th and again on the 24th. Who might have been responsible? Perhaps I'll learn the answer when I die. One friend even suggested I should be extra careful in 2015, because perhaps it was my future self come back to warn me about the possibility of an upcoming fatal accident? Wouldn't that make an interesting movie!
The idea that gravity is the only force that exerts itself across the extra dimensions is an important idea I first explored in my book, and again in dozens of videos and blog entries published since. Here's a few:
Your Sixth-Dimensional Self
Living in the Fifth Dimension
Hypercubes and Plato's Cave
Dark Matter, Dark Energy, Dark Information
Strength of Gravity, Speed of Light
Love and Gravity
Enjoy the journey!
Rob Bryanton
Update: Readers of my facebook feed will know that the clock did start up for a few hours the following year, on Dec 22nd 2015, and once again it was my wife's cousin staying with us. The following year he did not stay with us, and for Christmas 2016 there was not a peep from a clock. But on December 24th, 2017, it once again started up by itself while my son Mark and his wife Lana were staying with us: this year it ran for about a half hour, chimed once, and went silent once again. Mysterious!
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Tuesday, December 30, 2014
The Science of Interstellar
Last month Christopher Nolan's Interstellar was released, and in this blog we looked at Interstellar and the Fifth Dimension. I've been particularly excited about this film because world-renowned physicist Kip Thorne was a consultant throughout its creation, tasked with making sure that the science represented in the show was not, in fact, pseudo-science. As Professor Thorne says in the book's introduction:
…in the end I have no qualms about defending what Chris did with the science. On the contrary, I'm enthusiastic! He turned into reality… my dream of a blockbuster movie with foundations of real science, and with real science woven throughout its fabric.
There are lots of interesting discussions in this book about the science of black holes, wormholes, relativistic time dilation, and so on. But here's the question that has attracted so many new visitors to the Imagining the Tenth Dimension project: is representing the fifth dimension as I have with my project able to be aligned with the scientific approach supported by Kip Thorne in this movie? Here's some of his thoughts on the subject from his book:
How can space "bend down"? Inside what does it bend? It bends inside a higher-dimensional hyperspace, called "the bulk", that is not part of our universe!This is important! Professor Thorne is saying (as I have often said) that you can't talk about the fifth dimension without implicitly acknowledging that it is part of a multi-dimensional system. The fifth dimension can't exist in isolation, any more than it's possible in the third dimension to have an object with only a length, with no width or depth. And for those nitpickers who claim "there is no fifth dimension, there are only five dimensions", Professor Thorne is yet another expert comfortable - as I am - with using the phrases interchangeably.
...In Interstellar, the characters often refer to five dimensions. Three are the space dimensions of our own universe or brane (east-west, north-south, up-down). The fourth is time, and the fifth is the bulk's extra space dimension.
Does the bulk really exist? Is there truly a fifth dimension, and maybe even more, that humans have never experienced? Very likely yes.
(Spoiler Alert, stop reading here if you don't want to know about the climax of the movie)
The other idea which I have talked about extensively, and which figures prominently in the plot of Interstellar, is that gravity is the only force which exerts itself across the extra dimensions. But there is one plot point that I wish had been made clearer: this movie's logic collapses into contradiction if the fifth dimension does not include the many potential probabilistic outcomes which exist for our universe, as described in Everett's Many Worlds Interpretation of Quantum Mechanics. Is Everett wrong? Is there really only one single and inevitable world line for our universe? Then free will is an illusion, and all of Cooper's efforts in the movie to use extra-dimensional gravity to communicate with his daughter are pointless, because he has already achieved his goals before he began. But if free will and multiple outcomes do really exist, then what Cooper is looking at from his fifth dimensional vantage point is a branching set of possibilities, and his goal is to navigate towards the versions where his efforts become effective and the desired outcome is achieved.
This is the contradiction we keep coming back to: if Everett is correct, then the timeless underlying quantum fabric already includes a version of the universe where what any of us are about to do has already happened! And yet we can still make other choices and get to "other versions" where some other choice has been made. When we get to the end of the movie, or when we get to the end of our lives, we see that only one set of choices was made, but I remain convinced that this inevitability is an illusion.
Professor Thorne describes the climactic scene in which Cooper sees his daughter in a kaleidoscopic vision of cascading rooms:
...the various bedrooms are out of time synch with each other. ...Cooper can move far faster than the flow of time in the bedroom extrusions, so he can easily travel through the tesseract complex to most any bedroom time that he wishes!
A few pages later he talks about a concept I called "the long undulating snake" in the book and animation that got this project rolling, a way of representing the space-time object (or "spime") of a person from their conception to their death. Professor Thorne shows us a diagram of a book as viewed from this same outside-of-space-time vantage point, and refers to the book as having a "world tube": same concept.
In the movie, Cooper uses extra-dimensional gravity to maneuver his daughter's "Many Worlds" to the version where a book mysteriously falls from the bookshelf:
...Cooper slams his fist on the book's world tube over and over again, creating a gravitational force, which travels backward in time ... the book's tube responds by moving. The tube's motion appears to Cooper as an instantaneous response to his pushes. And the motion becomes a wave traveling leftward down the tube (Figure 30.2). When the motion gets strong enough, the book falls out of the bookcase.If you, like me, have fond memories of the way the pieces of the puzzle fit together in one of Christopher Nolan's earliest movies, Memento, then you may have felt similarly satisfied as the mysteries presented in the first two thirds of Interstellar are gradually solved by the "reverse causality" Professor Thorne found a way to explain with modern scientific theories. For me, though, I feel it's important to remember that there must still be many other versions of the universe depicted in the movie where Cooper hadn't yet formed his plan, or wasn't able to execute his plan successfully, and so on, causing the disastrous future for our planet depicted in the movie's opening act to continue unabated.
Ultimately, the statistical unlikelihood of any of us being right here and right now must surely represent a miniscule subset of the Many Worlds universes where none of us exist. One of my favorite blog entries from a few years ago where we explored this idea was called Beer and Miracles, check it out.
Enjoy the journey!
Rob Bryanton
Biographical note from the back cover of The Science of Interstellar:
Kip Thorne is the Feynman Professor of Theoretical Physics, Emeritus, at the California Institute of Technology, scientific advisor and executive producer of Interstellar, and the author of four books, including the best-selling Black Holes & Time Warps.
Coming up next: Interstellar and Pendulum Clocks
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Monday, December 8, 2014
The Zero Theorem
Last entry we talked about psychobiologist and author David Jay Brown, who gave my approach to visualizing the dimensions a very positive mention in his recent textbook The New Science of Psychedelics. This time we're going to talk about a film released this year by Terry Gilliam, who regular readers of the blog will know I'm a huge fan of, and who I had the chance to work with when one of his stranger films, Tideland, was shot here in Saskatchewan in 2006*. Terry's new film, The Zero Theorem, is rooted in a mystery I've talked about many times with this project. Here's one of my videos about this concept: Imagining the 'Zeroth' Dimension.
In The Zero Theorem, Christoph Waltz puts in an electric performance as Qohen Leth, a worker for the mega-corporation Mancom, charged by Management with the dreaded task of proving the Zero Theorem. Here's some dialogue from the film, in which "Bob" (the precocious teenage son of Management) explains to Qohen one version of the solution to the Theorem:
this one-time-only big bang glitch.
if you really think about it.
just as it was at the beginning.
Mr. Leth. Nothing is for nothing.
A harsh conclusion? You bet, and this takes us back to another point I mentioned last time: there is a certain mindset which teaches that anyone who believes in free will is being tricked by the chemistry of their body into believing they have control, when in reality every outcome is inevitable. Looking back at our lives, do we see any evidence of multiple outcomes, of cats that are both alive and dead? No, there is only one reality, one possible version set in motion at the beginning of the universe and continuing inexorably to the end.
The counterpoint to that idea, for me, has always been contained within the fifth dimension - the dimension at "right angles" to our 4D space-time, where the multiple outcomes of Everett's Many Worlds Interpretation of Quantum Mechanics have room to co-exist. As I mentioned a couple of entries ago, the fact that Christopher Nolan's new film Interstellar also embraces the idea of a fifth spatial dimension (with the approval and support of a mainstream physicist!) is very exciting.
What's tricky, then, is trying to show that both points of view -- free will vs. the inevitable universe -- are really two ways of viewing the same outcome, the same "enfolded everything" or "ultimate ensemble" that must underlie our reality or any other. Early on in this project I mentioned the fable of the six blind men and the elephant: each touches a different part of the elephant and comes away with a very different impression. The blind men in that story, though, have no pre-conceived notion, they are only reporting their findings. The difference in what we're discussing here is that mindset is the key - if you expect to see free will, that's what you see. If you expect to see an inevitable chain of causality and nothing more, then that's the conclusion you will draw. Both are ways of describing exactly the same thing, even though the two camps are unlikely to acknowledge such a heresy.
I believe that Terry Gilliam's film does a masterful job of showing these two viewpoints, and how accepting that there is something unchanging and everlasting from which our universe or any other is derived does allow us a certain peace, regardless of which viewpoint you subscribe to. Please watch The Zero Theorem and see if you agree.
Next entry we'll do a quick review of The Science of Interstellar, the new book written by Kip Thorne, the famed physicist who acted as a technical advisor to Christopher Nolan's challenging film throughout its creation.
Enjoy the journey!
Rob Bryanton
*As I've mentioned before, my son Todd and I co-wrote a song that one of the on-screen characters sang in Tideland. My company, Talking Dog Studios, also was in charge of dubbing all of the daily location recordings from Dolby SR to a digital format.
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Thursday, November 27, 2014
The New Science of Psychedelics
What happens when a pattern becomes aware of its own existence?
Here's the question we are asking: what is the source, the background pattern, the underlying process, from which our observed universe emerges? Some theorists ascribe meaning to that pattern, while others call it chaos, or "just a bunch of stuff that happened" (a useful phrase from Homer Simpson). But however we think about them, those underlying patterns exist, and modern research in a wide variety of disciplines inches us ever closer to understanding their nature.
If all I am, if all you are, is a space-time pattern, a spime if you prefer, then that pattern exists within the realm Einstein liked to talk about, where the distinction between past, present, and future is an illusion. I began this entry asking this: what happens when a pattern recognizes itself?
Life Happens
Life recognizes life. Awareness is drawn to awareness. Patterns of similar nature congregate together because of their structural similarities, and order really does sometimes arise from chaos. With Imagining the Tenth Dimension, the 400+ YouTube videos, 26 songs, animations and of course the book have all provided people from around the world with a new way of thinking about how their reality is created. But it's more than that: it's because so many people see patterns within my approach which easily tie to their own observations. Case in point: psychobiologist and science writer David Jay Brown said this about my project in his recent book The New Science of Psychedelics:
Physicist Michio Kaku's book Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the Tenth Dimension and Rob Bryanton's Imagining the Tenth Dimension both seem to provide uncanny maps of the territory that one encounters after smoking salvia or DMT. Like the two-dimensional character in Edwin Abbott's book Flatland, we seem just as limited in our three-dimensional perspective.
Patterns happen
Do psychedelics provide a way of "lifting the veil", so to speak, to allow us to see the hidden connections that we all share across the extra dimensions? Since I have no personal experience with psychedelics, I'm not the best person to answer that question, but here's what I believe: researchers are finding commonalities across cultures, across widely separated geography, and across the ages, that indicate there is something more than just random misfiring of neurons embedded within aspects of the psychedelic experience, and other meditative or trance-based states of the mind. Here's how David finishes the above-quoted paragraph:
From a three-dimensional point of view it seems like there aren't any other directions to go besides backward and forward, right and left, up and down. But there is another direction that we can move into, another dimension that contains this one within it, and the way to get there is by going directly into the center of our own minds.My approach to visualizing the dimensions helps us to see those patterns as existing within the timeless background that lies beyond the observed limits of our constantly evolving 4D space-time bubble. And David Jay Brown, who has written for Wired, Discover, and Scientific American on the subject of modern psychedelics research, and who has published a number of books exploring the interesting outer fringes of science, has given his enthusiastic support to my project. For that I am very grateful. Unfortunately, though, these zen-like concepts of "everything and nothingness" also happen to have been a popular line of questioning for mystics and the enlightened (of whatever definition you care to associate with that term) throughout the ages, a fact that makes those intent upon an atheistic, free-will-is-an-illusion point of view likely to dismiss these discussions outright. Be that as it may, I stand firm in my belief that there are things about this approach that speak directly to the underlying truth of where our reality comes from, so I will continue to fight the good fight for these ideas.
Now that we're holding within our minds the idea of there being a version of 4D space-time where everything happens at once, let's go back and look at one of my most popular videos: Imagining the Fourth Dimension.
A direct link to the above video is at https://www.youtube.com/watch?v=MN4KC_zlW4g
Enjoy the journey,
Rob
P.S. - Ultimately, finding a way to imagine what the big beautiful zero our reality comes from could be like brings with it a certain peace, as Terry Gilliam reminds us in his current film, The Zero Theorem. We'll talk about that film next.
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Monday, November 17, 2014
Interstellar - the Fifth Dimension
Sometimes science fiction movies deliver crazy ideas that have no connection to real science, and we are asked as an audience to simply suspend our disbelief and enjoy the ride. Interstellar has a much more interesting pedigree though, since world-renowned physicist Kip Thorne was heavily involved with the film: Thorne is the Feynman Professor of Theoretical Physics Emeritus at Caltech, and he acted as an executive producer for Interstellar. As an author, his books include the bestselling Black Holes and Time Warps. Here's what Thorne has to say about the fifth dimension in a Mashable interview published a few days ago:
That tesseract is not inside the black hole — it’s a four-dimensional cube, with four space dimensions and time — it lives in the Fifth Dimension. One of the faces is in our universe. Cooper is scooped up in the face of that tesseract and carried into the bulk.
In the Fifth Dimension, the distance between Gargantua and Earth is quite short; about the same as the Earth and the sun … whereas in our universe it’s 10 billion light years. So [the tesseract] can take him into our universe and docks beside the bedroom.”
This is really all based on some beautiful ideas; what I talk about is a ‘complexified tesseract. It fits with our understanding of what a tesseract is … [it] fits with ‘brane worlds’ of science … [or] what I call the Fifth Dimension. There is so much science that is in there that people have puzzled about, and I don’t know any way for people to get un-puzzled other than to read the book.

This is not the first time the fifth dimension has been portrayed in films as our "probability space", as I like to call it. For instance, Men in Black 3, released in 2012, featured an alien who had the special ability of being able to see into the fifth dimension, seeing the different possible timelines (or "world lines" as some physicists prefer) that surrounded him. I've talked previously about Watchmen, the 2009 film featuring a character who develops the ability to see past, present, and future simultaneously, and in my book and this blog I've paid tribute to Kurt Vonnegut, who invented an alien race with similar abilities, the "Trafalmadorians", in such novels as his 1969 classic Slaughterhouse-Five. But with the Trafalmadorians we are definitely only thinking of the fourth dimension as an unchanging block, where the one possible outcome for our universe, set into inevitable motion by the big bang, means that free will is an illusion and there is therefore no need to bring a fifth dimension into the discussion.
A surprisingly good film that doesn't explicitly say "fifth dimension" but is obviously talking about the same "probability space" concept came out earlier this year: Edge of Tomorrow. Here's the key: just as the first dimension can only contain a line, but that could be any line, the fourth dimension only has room for one version of space-time. In order to consider two 1D lines, you need to move to the second dimension. To see more than one version of space-time, a power attributed to the aliens in Edge of Tomorrow, those fictional creatures must logically be navigating within the fifth dimension.
In my 2011 video below, Imagining the Fifth Dimension, I talk about the evidence I've collected for thinking of the fifth dimension as our probability space, and how that so easily connects to well-known theories such as Everett's Many Worlds Interpretation of quantum mechanics. At the end of the video I mention some very kind conversations I've had with Oxford University's Professor of Physics David Deutsch. Why do I say "very kind"? I've always made it clear that I'm not a physicist and I'm not pretending to be one: I'm simply a creative person who came up with a methodology for visualizing ten spatial dimensions, and as a hobby I've published over 400 videos about the ramifications of that concept on my youtube channel which has just surpassed the 12 million views mark (!). I'm sure Professor Deutsch is a very busy man, and even though ultimately his response was to say he didn't accept my interpretation of the fifth dimension, I'm still very grateful that he was generous enough to respond. Imagine how exciting it is for me now to see Professor Thorne gently moving mainstream consciousness towards considering an idea which I've pursued so passionately for almost a decade.
A direct link to the above video is at https://www.youtube.com/watch?v=eN24Sv0qS1w
Curious? You might enjoy some of the other videos/blogs in this series:
Imagining the Tenth Dimension, 2012 version
Imagining the "Zeroth" Dimension
Imagining the First Dimension
Imagining the Second Dimension
Imagining the Third Dimension
Imagining the Fourth Dimension
Imagining the Fifth Dimension
Imagining the Sixth Dimension
Imagining the Seventh Dimension
Imagining the Eighth Dimension
Imagining the Ninth Dimension
Wrapping It Up in the Tenth Dimension
Next entry, I'm going to look at a recent book published by Psychobiologist and author David Jay Brown (you may have seen his articles in magazines like Wired, Discover, and Scientific American), in which he mentions my approach to visualizing the dimensions as having a direct connection to his own research. Thanks for your support, David!
Enjoy the journey,
Rob Bryanton
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Tuesday, June 18, 2013
What's Beyond "Everything"?
I've always argued that by the time we get to the tenth dimension
there's no need to keep counting past that, because "there's no place
left to go": but the fact is that many people embrace M-Theory's idea that there are eleven dimensions, one of which is "time". So here we are, visualizing ten spatial dimensions, plus an eleventh dimension as the point of
indeterminate size that we start from, the point that moves within those other dimensions to create
change from state to state, and that is what we can equate to the moving point that we know of as the "arrow of time".
No Place Left to Go
Here's the question though: if we've described, through logical application of simple principles, a way to get to "everything", then what created the everything?
I prefer to think that there is something within this everything, a universal creative force that is an emergent property within the information that becomes reality. Whether we call this force (which is the spark that drives all living things, from a primitive bacterium to you and I, to want to continue) "God" or some other word makes no difference: this organizing pattern exists, there is a specific pattern that causes our unique universe to exist, there are specific patterns elsewhere within the multiverse that cause other completely different universes to exist. Call those patterns whatever you like, changing names doesn't change their existence. The idea that the multiverse allows for the existence of what some have argued is a highly unlikely combination of factors to create the universe we find ourselves to be in has always been central to my way of thinking about the dimensions.
Likewise, consciousness can be looked upon as an emergent property, but I disagree with those who say only humans have consciousness: I think all living things have their own degree of consciousness. In the same way I think some human beings are more conscious: more immersed and engaged in their reality, more aware of the other possibilities that exist outside the moving "point" of their tiny space-time window... than others.
Are There Really Fourteen Dimensions?
Earlier this month there were news stories about a new "theory of everything" that encompasses fourteen dimensions: here's a brief article which includes links to other more in-depth reporting. How's this for an interesting thought: with this project I've always argued that "time" is a way of thinking about change from state to state within any dimension, and that's why it works to acknowledge there are ten spatial dimensions plus time. But it's also useful to think that for our unique situation, living in a universe with physical atoms and molecules that are embedded within a 3D membrane, there is definitely something about our own experience of time which makes it appear to only be a function of 4D space-time. Would my dimensional analysis make any more sense if we accept that we have our own unique viewpoint of that concept of "time"? Perhaps it's better if we acknowledge the fact that from our perspective time and space are most definitely intimately intertwined.
Where does that lead us? Suddenly we find ourselves with a way of thinking about ten spatial dimensions plus the moving 4D point we call the arrow of time. Is this a way to accomodate fourteen dimensions? Perhaps. By counting our 4D Minkowski "Block Universe" space separately (since that is what our unique experience within the multiverse reveals itself to be, as its own self-contained structure), the whole discussion of temporal vs spatial dimensions might be less confusing for some: in doing so, the ten spatial dimensions all become nothing more than patterns of information that are orthogonal to one another, and our movement is just that: movement through those patterns of information. Moving through a map doesn't change the map, but moving through a map does provide different experiences as we move from position to position.
Everything
Still, no matter how you slice and dice it, the concept of "everything" remains as our goal line. So to the question of "what's beyond everything?" I would say the answer is this: nothing. For more about how that connects to the underlying symmetry from which our universe or any other springs, here's one of my favorite videos from this project: Imagining the Zeroth Dimension.
Enjoy the journey!
Rob Bryanton
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Sunday, June 2, 2013
Just what IS a dimension?
A direct link to the above video can be found at http://www.youtube.com/watch?v=RmQqDJwnmAw
The above video is about a meme that has risen in popularity this year: "it's incorrect to talk about imagining the fourth dimension, one should instead talk about 'imagining four dimensions' because these dimensions are all intertwined". My response is that's at best a semantics discussion, and at worse leads to the faulty conclusion that there is no difference between the degrees of freedom available to a 1D line versus a 2D plane and so on. Would I be saying different things if my project were called Imagining Ten Dimensions instead of Imagining the Tenth Dimension? No. Both are different ways of talking about the same idea.
So, while it's all well and good to say "let's imagine ten dimensions", perhaps there's an even more basic question to ask before we begin:
Let's take a look.
Very generally, if you wanted to describe all the possible states for a certain quality of something, that would be a dimension. We could create a database of temperature for a given location, and all possible temperatures for that location would be a dimension. But we would need to add a dimension if we also wanted to plot windspeed. And so, if this is the approach we are using to define the word "dimension", then there is no reason to assume there are only ten: couldn't there potentially be an infinite number of ways to describe something, and therefore an infinite number of dimensions?
Theorists have said our reality comes from ten spatial (or "space-like") dimensions. How can we imagine them? Well, the point-line-plane postulate is the accepted way to visualize any number of spatial dimensions. Please note, though, those two important words: "any number". This means that we can easily say that this postulate results in an infinite number of spatial dimensions, because there's no reason to stop at any particular number.
But with this project, I do indeed say that we can stop at a number, and that there are really only ten dimensions... or eleven if you count the "zeroth" dimension, the point that we start from. Wow, isn't that quite a jump, from the mind-boggling realm of infinity down to a measly ten dimensions? And yet with this project, I insist that because we are assigning meaning to each of these dimensions rather than just abstractly adding one upon another, we really have reached an infinite "everything" by the time we get to ten.
As I've said elsewhere, the point-line-plane postulate and the line/branch/fold visualization that Imagining the Tenth Dimension uses are very related concepts, two different ways of describing the same idea. Both say there is a repeating logical structure we can use to extend from our intuitive knowledge of the first three spatial dimensions into the extra spatial dimensions that lie beyond.
One of the words used to describe spatial dimensions is that each is orthogonal to the next. "Orthogonal", as defined in the Mirriam-Webster Online Dictionary, means "intersecting or lying at right angles". "Perpendicular" has much the same definition, and the two words are often used interchangeably.
Let's go back to our windspeed/temperature example for one way to think about dimensions. What if we were to add an additional dimension which plotted the elevation above sea level? Now we have three dimensions for our given location, two of which are constantly changing, one which stays the same. In this way we can see how with multiple dimensions, some can be "pinned in place" so to speak, while others change. With my approach to visualizing the dimensions, I suggest that our universe is "pinned in place" at a position within the seventh dimension and above, with the sixth dimension and below allowing for the phase space of all possible states for a unique universe such as ours to be expressed. (String theorists have said our universe is embedded within a seven-dimensional "brane", or membrane, which could be another way of expressing the same idea).
Are windspeed and temperature "orthogonal" to one another? Only in one sense of the word. If you read through the entire Mirriam-Webster definition for orthogonal, the last interpretation listed is "statistically independent". Does temperature have to go up when windspeed goes down, or do both have to go up and down in lockstep? No. In other words, they are statistically independent. One could even say that windspeed, temperature, and elevation above sea level are at right angles to each other, in that you could plot these values on a three dimensional graph, with each axis at right angles to the others.
But how can we visualize a four-dimensional, a five-dimensional graph (and so on), where each axis is at right angles to the others? This is very hard for our monkey brains to envision, and that's the beauty of the point-line-postulate: it gives us a way to keep building the idea of spatial dimensions one upon another in our minds.
So, we've established what dimensions are, but have we established what spatial dimensions are yet? Here's how I would define the difference between elevation/wind speed/temperature as a set of three dimensions, as opposed to three spatial dimensions such as length, width, and height:
1. wind speed does not require temperature to exist, or vice versa: so those are not spatial dimensions. The third dimension that you and I are within, on the other hand, can't exist without the first and second, because they are all spatial dimensions.
2. The third dimension, like any of the spatial dimensions, is really a set of dimensions that are intertwined. Because of this interdependence, it doesn't matter what label you put on the third dimension: so while height or depth are different ways of thinking about what gets added by the third dimension, any term you use is dependent upon your reference frame. As I've often said, changing labels doesn't change what we're talking about, and "a rose is still a rose by any other name". On the other hand, you can't take your values for wind speed and say they are now temperature: the labels are not interchangeable, so those are not spatial dimensions.
That's it in a nutshell. There are many dimensional systems which can lay claim to an unlimited number, and that includes spatial dimensions if you're speaking in abstract terms. But with this project, we discuss the quality that gets added with each spatial dimension, and that's how we end up with the bold statement that there are really only ten spatial dimensions.
Enjoy the journey!
Rob Bryanton
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Rob Bryanton
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