A direct link to the above video is at http://www.youtube.com/watch?v=amcTK7Mnu70
Image from wikipedia: "Borromean Rings".
With my approach to visualizing the ten spatial dimensions, I group three dimensions together, call that a "triad", and condense it into a single entity so that it becomes a point in the next dimension up. By the time I've done that three times, I arrive at ten, the same number which Pythagoras also defined as the ultimate number encompassing all possible expressions of our reality. Let's look at some of the ways that ancient wisdom ties into all this, starting first with this mystical insight from the current Grand Archdruid of the Ancient Order of Druids in America:
In a binary, though, every action is balanced by an opposite reaction, so thinking in binaries is very problematic if you want to foster change. If you’re a mage, you respond to dysfunctions of this sort by shifting numbers. The traditional rule here is that numbers always change in a specific order: one becomes two, two becomes three, and three becomes one and shifts to another level. (The reasons for this rule, again, are too complex to go into here.)
When I came across the above text I was struck by how strongly it seemed to relate to the triads from my approach. Here's another quote, this one from a site dedicated to Chinese martial arts:
Then the link between the qi of the earth and the qi of the sky can be formed, causing the practitioner to shape the unity of heaven, earth and person; three becomes one.
In Strength of Gravity, Speed of Light, I summed up the dynamics of creation like this: "One thing pushes against another, and out pops a third thing". Is this a schoolboy description of sex? Sure, why not! Long before sex came along, there's been single-celled fission, mitosis, a dividing apart: that's one kind of creation, binary and asexual. The other is sexual reproduction, a more robust form of creation because it takes elements from two sources and combines them to create something new. Hegel's dialectic is often summed up in a similar way: thesis, antithesis, synthesis.
Monad, Dyad, Triad
Pythagoras taught that odd numbers are masculine and divine, and even numbers are earthly and feminine. While such a conclusion might seem misogynistic, it's worth noting that Pythagoras welcomed females into his discipline, and his wife and daughters were accomplished mathematicians. In chapter four of my book, "The Binary Viewpoint", I suggested that the desire to catalog things into yes/no, right/wrong (and so on) tends to be a more masculine approach, while the holistic "yin/yang/both together" tends to be a more feminine one. Does this mean I would disagree with Pythagoras and say that odd numbers are more feminine, because they're less dualistic, less binary? It's an interesting thought.
"One state/an opposing state/both simultaneous" is also, of course, the basis of quantum mechanics, science's most-proven description of the foundation of our reality, and something which I've insisted will eventually be shown to be just as connected to our macro reality as it is to the quantum: it's all part of the same continuum. The June issue of Scientific American has just published an article about the first demonstration of quantum superposition on an object large enough to be seen by the naked eye! This demonstration is a major leap forward: while scientists have previously demonstrated superposition with atoms and molecules, this new experiment shows quantum superposition in an object made out of roughly ten trillion atoms. Suddenly, Schrödinger's cat, usually portrayed as nothing more than a fanciful thought experiment, moves a little closer to being something connected to our actual physical reality.
The Law of Threes
So. Two is a dynamic push and pull, while three is more stable, more balanced. In jokes and in fairy tales, it seems more satisfying when something happens three times. Lots of superstitions gravitate to this number: good luck, bad luck, celebrities dying, and so on are seen to come in threes. Father, Son, and Holy Ghost - entire belief systems are built on threes. To be sure, the phrase "Law of Threes" means a number of things depending upon who you consult, but here's the most popular answer as provided by "Galeanda" at Answerbag.com:
The Law of Threes states "every whole phenomenon is composed of three separate sources, which are Active, Passive and Reconciling or Neutral. This law applies to everything in the universe and humanity, as well as all the structures and processes".
It's interesting to relate this to Popperian cosmology. Philosopher Karl Popper made a similar proposal that there are three worlds: the physical, the mind which observes, and mental patterns of information. And imagine my surprise to be told that there are branches of Kabbalah which also teach that we can divide our reality into three triads, which can be summed up as the material, the moral, and the intellectual.
Here's an interesting version of my approach to visualizing the dimensions, using ideas connected to the point-line-plane postulate: which, as we've said before, can be used to visualize any number of spatial dimensions.
Start with a point. Choose a second point. Join those two points with a line, you're in the first dimension.
How far away are those two points from each other? Now find an additional point that is the exact same distance away from those first two points but not on the line. What have you created? An equilateral triangle, and you're in the second dimension. The fact that such a triangle can be created with nothing more than a compass and a straight edge is well known to students of sacred geometry and the vessica piscis, concepts we've looked at before in this blog.
Now find an additional point that, again, is the same distance away as those first three points are from each other. What have you created now? This four-sided pyramid is called a tetrahedron. As you can see, it's made from four equilateral triangles, and now you're in the third dimension.
An article published last week in New Scientist magazine suggests that the tetrahedron is the most efficient shape for packing a large number of items into a 3D space. When we're thinking about how three becomes one, imagine collapsing this tetrahedron's outlying points towards any single point. This gives us a useful mental image for seeing how the underlying structures of our 3D space could be connecting to the fourth dimension, as we enfold all of our 3D universe in its current state -- its current "now" -- into a planck-length-sized frame which then becomes a "point" on our 4D line of time.
In Our Universe as a Dodecahedron, we looked at what happens when you rotate five superimposed tetrahedrons so that all their points are equidistant from each other, which took us to the discussion of the now-proven Poincaré Conjecture, and the proposal that the slight curve of our spacetime gives rise to the fifth-dimensional Poincaré Dodecahedral Space that our universe resides within. But once again, if you look at these beautiful symmetrical shapes, can you imagine how all of those points could easily be converged to a single central point?
In that same entry we talked about fascinating fellows like Dan Winter and Nassim Haramein who are showing us ways of visualizing how everything is connected through points or point-like structures. With "Three Becomes One", what we're trying to head towards is a way of imagining an underlying symmetry, and how that symmetry can be enfolded to eventually arrive at the unobserved whole, the big beautiful zero that our universe is moving towards and springing from within timelessness. Pull those points apart symmetrically and you get beautiful shapes like the vessica piscis, the triangle, the tetrahedron, and the dodecahedron. Allow the points to converge and you end up back where we started, at a point of indeterminate size.
Since gravity is the only force that exerts itself across the extra dimensions, that pushes or pulls, it must factor in here at a fundamental level. Let's continue to explore this idea more in our next two entries, Gravity and Free Will, and Gravity and Entrainment.
Enjoy the journey!
Pictured at left: diagram showing congruence of null lines from Twistor Theory.
Pictured at right: diagram of Marko Rodin's Rodin Coil.
According to the June issue of Scientific American, there's new excitement about
Twistor Theory and String Theory being united by the highly respected theoretical physicist Ed Witten. A number of people have asked me to talk about the work of Marko Rodin, I wonder what he would have to say about this latest development?