Thursday, April 2, 2009

The Invariant Set

A direct link to the above video is at

Gevin Giorbran called it SOAPS - the "set of all possible states". For our universe, I called it "a point in the seventh dimension", and for the omniverse of all possible universes and information patterns, I called it the tenth dimension in its unobserved state of perfectly enfolded symmetry. Now, here's some excerpts from an article in the March 30 2009 issue of New Scientist Magazine that explores a concept from physicist Tim Palmer called "The Invariant Set". I would say we're all talking about the same thing: viewing the universe from a timeless perspective.

Can fractals make sense of the quantum world?
New Scientist Magazine, 30 March 2009
by Mark Buchanan

QUANTUM theory just seems too weird to believe. Particles can be in more than one place at a time. They don't exist until you measure them. Spookier still, they can even stay in touch when they are separated by great distances.

...what if there were a way of showing how quantum theory might emerge from a deeper level of non-weird physics?

If you listen to physicist Tim Palmer, it begins to sound plausible. What has been missing, he argues, are some key ideas from an area of science that most quantum physicists have ignored: the science of fractals, those intricate patterns found in everything from fractured surfaces to oceanic flows (see What is a fractal?).

...Palmer's ideas begin with gravity. The force that makes apples fall and holds planets in their orbit is also the only fundamental physical process capable of destroying information. It works like this: the hot gas and plasma making up a star contain an enormous amount of information locked in the atomic states of a huge number of particles. If the star collapses under its own gravity to form a black hole, most of the atoms are sucked in, resulting in almost all of that detailed information vanishing. Instead, the black hole can be described completely using just three quantities - its mass, angular momentum and electric charge.

Many physicists accept this view, but Palmer thinks they haven't pursued its implications far enough. As a system loses information, the number of states you need to describe it diminishes. Wait long enough and you will find that the system reaches a point where no more states can be lost. In mathematical terms, this special subset of states is known as an invariant set. Once a state lies in this subset, it stays in it forever.

A simple way of thinking about it is to imagine a swinging pendulum that slows down due to friction before eventually coming to a complete standstill. Here the invariant set is the one that describes the pendulum at rest.

Because black holes destroy information, Palmer suggests that the universe has an invariant set too, though it is far more complicated than the pendulum.

Complex systems are affected by chaos, which means that their behaviour can be influenced greatly by tiny changes. According to mathematics, the invariant set of a chaotic system is a fractal.

Fractal invariant sets have unusual geometric properties. If you plotted one on a map it would trace out the same intricate structure as a coastline. Zoom in on it and you would find more and more detail, with the patterns looking similar to the original unzoomed image.

Gravity and mathematics alone, Palmer suggests, imply that the invariant set of the universe should have a similarly intricate structure, and that the universe is trapped forever in this subset of all possible states. This might help to explain why the universe at the quantum level seems so bizarre.

...The key is the invariant set. According to Palmer's hypothesis, the invariant set contains all the physically realistic states of the universe. So any state that isn't part of the invariant set cannot physically exist.

...In a paper submitted to the journal Proceedings of the Royal Society A, he shows how the basic idea can account for quantum uncertainty, contextuality and other quantum puzzles (
I've talked before about fractals and recursion, and how those relate to this way of visualizing reality. While Dr. Palmer is not talking about extra dimensions with his theory, it's very easy to use his "Invariant Set" concept in the context of my project: in entries like The Fifth Dimension Isn't Magic, Our Non-Local Universe, and Aren't There Really 11 Dimensions? I've talked about what's possible and impossible within this way of viewing reality, and how the logical progression from one spatial dimension to the next that I'm portraying gives us a way to see how the universe, the multiverse, and the omniverse are related to each other: each is a subset of the next, and all make more sense when we learn to view them from the perspective where (as Einstein liked to say) "the distinction between past, present, and future is meaningless".

I mentioned that with my system, I would say our own universe's "invariant set" is locked in at the seventh dimension: this can also be connected to the string theory idea that our 3D universe is constrained by a seventh-dimensional brane. Now, here's a lovely video by artist Charles Gilchrist that shows a connection between the number seven, fractals, infinite recursion, timelessness, and the forms of sacred geometry.

A direct link to the above video is at

Enjoy the journey!

Rob Bryanton

Edit: Here's a link to a story on Tim Palmer's Invariant Set Postulate published August 17th 2009 at

Next: Illusions and Reality


Apocalypso Facto said...

Mindbending as usual Rob! Thanks for visiting my blog and for your comment, it was my pleasure, really.

luramos said...

Dear Sir

I just found your website today and the video "Imagining..." is really amazing. I have Portuguese as my first language and I know lots of people that can not access these ideas because of the language barrier. Is there any chance to have subtitles in Portuguese?
thanks a lot


Rob Bryanton said...

Hi luramos, that's a lovely idea. There have been quite a lot of translations created by fans of my original animation over the last few months: as I describe in the following blog, it's now available in Arabic, Chinese, Turkish, Greek, Polish, and Russian!

I think that's a great idea that it could be available in Portuguese some day as well - perhaps some fan will read your request and go ahead and create that version.

Best wishes,


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