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INTEGRAL WORLD: EXPLORING THEORIES OF EVERYTHING
An independent forum for a critical discussion of the integral philosophy of Ken Wilber
Publication dates of essays (month/year) can be found under "Essays".
Since 1990 Gary Stogsdill has been a faculty member at Prescott College where he currently teaches courses in humanistic mathematics, science appreciation, and wisdom studies. He has a blog called "Pursuing Wisdom Now", which features articles on contemporary spirituality.
Intimations of Higher Dimensional Realities
This essay explores intimations of higher dimensions that could be the home of invisible spiritual realities.
Many of us are convinced that spiritual realities exist, whether in the context of spiritual/paranormal experiences, religious teachings, or philosophies like Plato's theory of Forms and Ken Wilber's integral theory. But where do spiritual realities reside? Where is the reality that gave rise to our universe? Where would something like astral planes or an afterlife actually be? If they exist, why are these spiritual realities undetectable to science and invisible to us?
An intimation is the merest whisper of suggestion; it's as far away from proof as we can get. However, if several intimations line up pointing in the same direction, then we may have something that warrants further consideration. This essay explores intimations of higher dimensions that could be the home of invisible spiritual realities. The basis for our journey is science and mathematics, venturing through infinity, light, relativity, quantum renormalization, string theory, and mathematical definitions of dimensions.
What are Dimensions?
The word dimension is popularly used in a variety of ways, but its meaning for this essay can best be captured mathematically. In math, no dimension is represented by a point, which has no length, width, or depth, just a hypothetical position in an imaginary realm. An infinite array of points is said to form a line, which shows the one dimension of length. An infinite array of lines would form a plane, which shows the two dimensions of length and width. Similarly, an infinite array of planes forms a three-dimensional space of length, width, and depth; 3‑D space is what we humans inhabit, it's our home.
Let's indulge in a bit of fantasy and make you an inhabitant of a mathematical point; you would likely have no concept, and certainly no experience, of any dimensions whatsoever because your world is a hypothetical point that exists “nowhere.” Now let's give you a little more breathing room and imagine you inhabiting a mathematical line; your experience would be entirely one-dimensional, and you would not be able to see anything beyond your cozy reality of a line. Similarly, if we expand your world to become a mathematical plane, even though your horizons have now increased beyond your wildest dreams, you are still confined to a two-dimensional reality, you would not be able to see anything beyond your 2‑D plane, and you would likely doubt the existence of anything “higher.”
Now let's bring you safely back into the next higher dimension, our familiar 3‑D space, and consider the following. An inhabitant of a lower dimension would not be able to see higher dimensions and would therefore be prone to doubt the existence of anything higher because higher dimensions themselves are invisible. This invisibility actually works in the reverse direction as well. An inhabitant of a line would not see points, an inhabitant of a plane would not see lines or points, and we lucky inhabitants of 3‑D space do not see planes, lines, or points. Those lower dimensions are still nested within our reality, but we don't see them because our reality has transcended the lower dimensions. Different dimensions are always invisible to each other.
How puzzling, then, that physicists and cosmologists tend to believe that extra dimensions should be accessible to our 3‑D perception of spatial reality. Here's from the Wikipedia article on dimension: “If extra dimensions exist, they must be hidden from us by some physical mechanism”. No, extra dimensions would not be hidden from us 3‑D-space-dwelling creatures by “some physical mechanism.” That's like saying a plane must be hidden from the reality of a line by some linear mechanism. No, a plane extends in a whole new direction that's not accessible to the reality of the line. Extra dimensions would be hidden from us by the simple mathematics of dimensions. This understanding shows why we need to work with intimations of higher dimensional realities instead of having solid evidence: because we don't perceive the higher dimensions themselves due to the fact that we're stuck in a 3‑D spatial reality.
What is Infinity?
While defining dimensions above, I made statements like “an infinite array of points is said to form a line, which shows the one dimension of length.” What does it mean for something to be infinite? In common parlance, infinite means endless, as in numbers are infinite because you can keep on counting endlessly. But defining infinity as endless does not work for our mathematical discussion of points, lines, planes, and 3‑D spaces because we can string together all the points we want without creating an actual line. Remember that points have zero dimensions and a line has one dimension. A whole lot of nothing does not make one, no matter how much nothing we have. Or put mathematically, zero multiplied by anything, no matter how big, is still equal to zero.
When dealing with dimensions, a better definition of infinity would be that which transcends our concept of quantity. This suggests that we define lines, planes, and 3‑D spaces in terms of an infinity of lower dimensions to indicate that each higher dimension completely transcends the lower dimension, even though the lower dimensions are still nested within the higher. Understanding infinity in terms of transcendence allows us to investigate where infinities show up in the equations of established physics and to wonder why these infinities are there.
Quantum theory (really a unified collection of theories) describes the subatomic particles and energies that comprise our universe. It captures the essence of fundamental reality and has been referred to as the most successful theory in the history of science because every experimental observation performed has corroborated the equations of quantum theory with exceptional precision. What we seldom hear about is the fact that almost all of the equations of quantum physics don't work until we perform a magic trick on them called quantum renormalization. Without this magic trick the equations produce infinities. Quantum renormalization is a way to cancel out the infinities so that the equations make sense for our 3‑D spatial reality. Here's Stephen Hawking:
Seemingly absurd infinities occur in the other quantum theories [besides Heisenberg's uncertainty principle]. However, in these other theories, the infinities can be canceled out by a process called renormalization. This involves adjusting the masses of the particles and the strengths of the forces in the theory by an infinite amount. Although this technique is rather dubious mathematically, it does seem to work in practice.” (The Theory of Everything, 2002, p. 150)
When Hawking calls renormalization “rather dubious mathematically,” what I believe he means, at least in part, is that there's no logical reason for doing it other than to get rid of the pesky infinities. Perhaps we should take these infinities seriously and consider them as a possible intimation that the fundamental principles governing our universe may belong to a higher dimensional reality that completely transcends our 3‑D space.
String theory is also a collection of theories that attempt to explain the fundamental reality of our universe. For more than 30 years many physicists and cosmologists have looked to string theories as possibly being the Holy Grail in the much coveted search for the theory of everything, which means an equation or set of equations that successfully mesh the forces of quantum theory with gravity as described in general relativity. Although string theories have yet to produce this Holy Grail, they remain at the forefront of research for many scientists. As with quantum theory, “string theories also lead to infinities” (Stephen Hawking, The Theory of Everything, p. 155), but our focus here is with extra dimensions themselves instead of the infinities.
String theories require an outrageous number of dimensions from a mildly staggering 10 to a jaw-dropping 26. If we subtract our 3‑D space and also time from the dimensions of string theories, we find that even the most modest theory requires six more dimensions than we are aware of in our day-to-day lives. Considering that just one extra dimension expands horizons in ways that inhabitants of the lower dimension will have difficulty even beginning to fathom, a minimum of six extra dimensionsand up to 22is more than mind blowing.
Most scientists have the interesting view that these extra dimensions of string theory are “curled up” so small that we can't detect them, somehow believing that inhabitants of a 3‑D space should be able to perceive extra dimensions that behave normally and don't curl up. And where do scientists think we will find these six to 22 higher dimensions all snug and cozily curled up? Somewhere out in deep space between clusters of galaxies? No, they're supposedly curled up everywhere throughout the universe but so tiny as to be invisible and undetectable.
Let's return for a moment to our mathematical definitions of dimensions. According to those definitions, it might make sense to speak of a one-dimensional line or even a two-dimensional plane being curled up inside of a 3‑D space, but it makes no sense to speak of a 3‑D space being curled up inside of a line or a plane. Lower dimensions inhabit higher dimensions, not the other way around. The notion of a whole bunch of higher dimensions curled up inside of our 3‑D space seems preposterous, but one aspect of this notion does make sense: they are everywhere but invisible.
Isn't that what we might expect of a higher dimensional reality: it would completely permeate and also transcend the lower dimensional reality such that it is invisible? Imagine a mathematical 2‑D plane cutting across the room you're in right now (this would be an invisible plane because you'll remember that different dimensions are always invisible to each other). The space of your 3‑D room would permeate that plane, but also be invisible to that plane and completely transcend it.
Relativity and Light
Einstein's general theory of relativity also requires extra dimensions including the idea that time behaves like an extra dimension of space, thus creating spacetime. The essence of general relativity is that the fabric of spacetime bends or warps to create the force of gravity. Imagine a trampoline with a large steel ball in the center. Now imagine rolling marbles around the outside of trampoline. Eventually they sink to the center and join the large steel ball, simply because the trampoline is sagging.
If you're rockclimbing and fall, you are like a marble that rolls straight to the center of the trampoline. If you're a planet in our solar system, you are like a marble with so much velocity and angular momentum that it constantly orbits around the center of the trampoline. Gravity, says Einstein's general relativity, is just how spacetime curves around objects with mass, and if that's correct then there has to be at least one higher dimension for spacetime to curve into. Picture again that mathematical 2‑D plane cutting across your room. Such a plane can only bend if there's a 3‑D space to bend into; otherwise it remains perfectly flat.
Ten years prior to general relativity, Einstein laid its foundation with his special theory of relativity, which suggests that the only absolute in our universe is the speed of light, meaning that the speed of light is the same for all observers regardless of the observer's motion compared to that of light and also regardless of the motion of the source of light. Because of this absolute nature of light, everything else that we can measureincluding spatial distance, mass, and even timebecomes relative depending on our frame of reference, which essentially means how fast we're moving in comparison to something else. If we share a frame of reference, as we earthlings do in our cosmic journey through space, then our measurements hold true for everyone.
However, if objects are moving considerably faster than our earthly frame of reference, three peculiar things happen from our perspective: they get heavier, they grow smaller, and time slows down for them. So if I launch you into space and accelerate your ship to a velocity of 90% the speed of light, those of us watching the live feed from earth will observe that you now weigh twice as much as before (technically, you'll be twice as massive since weight requires a gravitational force pulling on your mass), you are now half your normal size (along with the rest of your spaceship), and time for you has slowed to half the rate of our earthly time.
It gets even stranger with special relativity. For an object to reach the speed of light would require infinite energy, and the object itself would become infinitely massive, it would shrink to invisibility, and time would stop for that object. Because of these unusual circumstances, scientists are certain that nothing with mass can ever reach the speed of light. However, could this be an intimation that if an object were to reach the speed of light, it would have to enter a higher dimension? Hence the infinities, and hence the impossibility of anything from our current dimensional reality ever “going there.” For example, picture an imaginary inhabitant of a 2‑D plane trying to “jump off” into 3‑D space… it just doesn't happen because inhabitants of lower dimensions cannot access higher dimensions.
While nothing with mass can attain the speed of light, it should be obvious that light itself attains this speed. In fact, the natural state of light is to travel at this speed, and light is only slowed down when it passes through a medium like water (which is why your arm or leg looks crooked when you see it underwater with your head above water). Given that the natural condition of light is to travel at lightspeedthe one absolute in an otherwise relative universewhat would we observe if we could peer into the reality of light itself as it goes about its business at lightspeed, just as we previously observed you in your high-velocity spaceship?
First, we would see that time has stopped for light. When time becomes zero, distance also shrinks to zero by the simple equation “distance equals velocity multiplied by time.” (Remember that anything, no matter how big, multiplied by zero is equal to zero.) And here's the kicker: when there's no time or distance, there's also no motion or speed. This presents a bewildering paradox; if we could perceive the reality of light, we would observe that light traveling at lightspeedthe fastest motion possible and the one absolute of our universedoes not participate in the conditions that define our 3‑D spatial reality: time, distance, and motion. Apparently, light just is.
This all sounds suspiciously like what we might expect of our insufficient ability to understand a higher dimensional reality. It would transcend our dimension in ways that would be likely to place absolute limits on our reality, and it would present paradoxes to our perspective because we're not able to think in the ways that higher dimensions might require us to think. The logic of our rational minds is 3‑D logic. Again, imagine yourself inhabiting a 2‑D plane, and then try to wrap your 2‑D brain around how a 3‑D space would expand your thinking to a whole new level that completely transcends 2‑D logic and conceptualization. It would create paradoxes and conundrums to your 2‑D capabilities, as Edwin Abbot delightfully portrayed in his 1884 fantasy Flatland: A Romance of Many Dimensions.
Is all of this an intimation that light itself may be the product of a higher dimension? And no, this possibility doesn't contradict what we learned earlier about dimensions always being invisible to each other. The intimation here is that light may be a product of a higher dimension, not the higher dimension itself. Recall the imaginary 2‑D plane cutting across your room; our 3‑D space would permeate that plane while remaining invisible to it. Is light what happens from our perspective when a specific higher dimensional reality enters our 3‑D space?
What Does It Mean?
To those whose lives are confined within the boundaries of a rational-scientific worldview, these intimations of higher dimensional realities will likely mean nothing at all… just another example of meaningless random coincidences along with misguided thinking on my part. To those whose lives are dedicated to a specific religious or spiritual doctrine, something from this essay may support their beliefs, but it will surely be uninspiring compared to the bold teachings they've sworn allegiance to. For example, think of Deepak Chopra entering an auditorium and booming, “YOU ARE THE UNIVERSE!” What I've said in this essay cannot compete with the spiritual teachers who claim to know things that no one can actually know.
But between those two extremes of belief should exist at least a few folks who value both scientific and spiritual inquiry, without being radicalized into the worldview of either. For those who possess such an open mind, I will write future essays exploring possible meanings and explanations resulting from the intimations in this essay that seem to point toward higher dimensional realities.