We talk about the third dimension a lot, but most humans don’t live in it. Abbot’s Flatland was not so much a metaphor as an operational description of the sensory world most people inhabit: a continuous, unbroken plane that, despite surface variations and wrinkles, remains a flat stage for our two dimensional lives. This is inevitable, since humans cannot hover or fly without technology assistance, and few of us can jump higher than three feet off the ground.

And let’s be serious, here—what is a dimension? Have ever even proved they existed? Sure, you can draw a Cartesian XYZ grid on paper, but you can also draw a unicorn vomiting angels. I’ve digging through the concept of time for a month, and it’s a concept nobody can really define, despite the fact we all experience it. I’ve come to realize there’s very little humans can say for sure about space, either. The more we learn, the less we know. Everything you were taught in school is currently falling apart—so let’s take a look at a theory that will likely be replacing all this Big Bang horseshit: the Universe is fractal and infinite at every level of scale.

Rethinking Occam’s Razor

“Each time we formulate a hypothesis, we take the simplest one possible. But what obligates the Universe to be simple?”

--James Peebles

I seriously question the assumption that the simplest explanation is usually the best. I find it truly bizarre that after the past century of scientific discovery, which has shown every single aspect of our Universe to be stranger and more complex than we ever thought possible, people still discuss the concept of Occam’s Razor with a straight face. Of course, most people having that discussion don’t even know Occam’s Razor, since the literal translation goes like this:

“...entities should not be multiplied beyond necessity.”

Before I dismiss the concept, I want to bring up one of the more interesting cognitive biases that humans are afflicted with: The Conjunction Fallacy. As puts it in his excellent paper, “Cognitive Biases Affecting Assessment of Global Risk”:

According to probability theory, adding additional detail onto a story must render the story less probable. Yet human psychology seems to follow the rule that adding an additional detail can make the story more plausible.

Of course, once you really dig into the field of cognitive bias, you’re left with the disturbing realization that our brain is just a hall of mirrors run by a monkey. It can be hard to get work done under those circumstances, so the less said about it, the better.

“Entities Should Not Be Multiplied...”

“There is a coherent plan in the universe, though I don’t know what it’s a plan for.”

--Fred Hoyle

In the Brainsturbator Fractal Toolkit, I covered a very wide range of applications for fractals, including modeling the reality we exist within. Fractal processes describe the growth of plants (L-Systems), the bifurcation of human lungs (23 levels of bifurcation), standing acoustic waves, and even the expression of human genes.

Is it reasonable to assume that this model, which has been so successful in accurately representing reality here on Earth, would somehow not apply at other levels of scale? Perhaps it is. After all, that’s exactly what’s implied by Quantum Theory—that once you reach a certain level of scale, the laws which previous governed motion and probability no longer apply. This kind of schizophrenia is also taken for granted in political science, where once imaginary lines get crossed, the laws of one nation no longer apply because you’re Officially Somewhere Else.

It’s hard for humans to really grasp how small we are. Even 26 million years from now, we will still be a part of the milky way galaxy. Even 2.6 billion years from now, the milky way galaxy will still be just a small part of the Virgo Supercluster. Mainstream cosmology insists that the Universe is ultimately homogenous—equally distributed. Observation of reality increasingly contradicts this. Not only is the Universe, even at the vastest levels of scale we can contemplate, not homogenous, it also turns out to exhibit geometric patterns. Take a look at the octahedron of superclusters we inhabit:

“...Beyond Nescessity.”

Here’s the other side of the razor—is it nescessary to propose a Fractal Model? It would appear so—the existing model has been falling apart for awhile. It is often noted that Euclidian space and Newtonian physics, while limited, are also good enough to get humans to the moon and back. However, it’s been 50 years since Sputnik, and we can begin to see the margin of error today, as satellites and “space junk” comes crashing down from on high. As PhysOrg recently reported, space is a more dangerous place:

The report said China’s test “created 1500 pieces of trackable debris in heavily used orbits - one of the worst manmade debris-creating events in history - but debris caused by routine space operations is also a problem.”

“Even a small piece of metal, traveling at 7.5 kilometers per second, can destroy a spacecraft worth billions of dollars,” said William Marshall of the NASA Ames Research Center, an advisor to the space index.

“The number of objects in Earth orbit have increased steadily; today there are an estimated 35 million pieces of space debris,” said the report, noting that 90 percent of 13,000 orbiting objects large enough to damage or destroy a spacecraft are space debris.

As Earth becomes increasingly surrounded by a cocoon of scrap metal and space waste, though, the strongest arguments for a Fractal Universe come from the VLA radio telescope in New Mexico, which recently identified an enormous gaping hole in the fabric of the cosmos:

Radio astronomers have found the biggest hole ever seen in the universe. The void, which is nearly a billion light years across, is empty of both normal matter and dark matter. The finding challenges theories of large-scale structure formation in the universe.

Journalists tend towards understatement, and “challenges” is a very polite euphemism for what this finding does to mainstream cosmology theory. (I would have leaned towards “sodomizes” or “annihilates,” myself.) For a general rundown of the holes in Big Bang theory, start here, I won’t diverge into that territory now. Although science does in fact progress, it does so under great protest, often dragging the heels of Consensus for over a century. Despite the fact reality continuously validates his work, Luciano Pietronero has been waiting a long time for cosmology to catch up with him.

A good, quick intro to Peitronero’s work is the New Scientist article, “Is the Universe a Fractal?”

The fact that the fractal patterning extends to far bigger scales than anyone had expected means that there must be far bigger structures than anyone expected - structures that are even bigger than superclusters. The fractal team argues that the standard model cannot explain the existence of these galactic giants. “If you look at the galaxy data, you can see enormous objects hundreds of millions of light years across, stuff that’s really huge,” says Pietronero. “This is a huge problem. You’re going to have to change the story very radically.”

Not Simple, but Beautiful

“The more closely a phenomenon is observed, the more complex it is seen to be.”

--Heinrich Weisskopf

Does this mean that a phenomenon observed for an infinite amount of time would be seen to be infinitely complex? The interesting thing about history is that details get filled in based on the details that already existed, simply because it’s easier to look for connections in existing research than it is to do original work.

Obviously, I don’t propose the Fractal Universe model as a Solution—even if this model gets adopted as the Official Reality, it too will eventually fall apart and be replaced by something more accurate. One likely candidate is Constructal Theory, developed by former MIT professor Adrian Bejan. It’s a remarkable theory: it makes sense immediately, it changes how you look at things, and it’s backed up by decades of proven predictions. For some reason, people are more excited about string theory...humans are weird...but meanwhile, we can learn a lot from Prof. Bejan.

Constructal theory says that a system not in equilibrium will, over time, generate paths that allow currents to flow with easiest access and least resistance. Essentially, systems evolve so they experience the least friction and maximize efficiency. In terms of locomotion, this means animals move in a way that minimizes energy spent.

Bejan boasted that his theory can explain patterns found in nature that are often deemed random or chaotic; he believes constructal theory shows that randomness is not a factor in natural patterns.

“This is the end of the story. The end of the argument. A law of physics that says it all, and it takes less space in a future physics book than all this debate that currently has led to things such as chaos and chance and fluctuations and turbulence and other buzz words that mean ‘I don’t know.’”

---from Seed Magazine

Magic or Geometry?

The controversy between the followers of the physics of Descartes and of Newton was at its height at the end of the seventeenth century. Descartes, with his vortices, his hooked atoms, and the like, explained everything and calculated nothing. Newton, with the inverse square law of gravitation, calculated everything and explained nothing. History has endorsed Newton and relegated the Cartesian construction to the domain of curious speculation. The Newtonian point of view has certainly fully justified itself from the point of view of its efficiency and its ability to predict, and therefore to act on phenomena.

In the same spirit, it is interesting to reread the introduction to Dirac’s Principles of Quantum Mechanics, wherein the author rejects as unimportant the impossibility of giving an intuitive context for the basic concepts of quantum methods. But I am certain that the human mind would not be fully satisfied with a universe in which all phenomena were governed by a mathematical process that was coherent but totally abstract. Are we not then in wonderland? In the situation where man is deprived of all possibility of intellectualization, that is, of interpreting geometrically a given process, either he will seek to create, despite everything, through suitable interpretations, an intuitive justification of the process, or he will sink into resigned incomprehension which habit will change to indifference.

In the case of gravitation there is no doubt that the second attitude has prevailed, for we have not, in 1975, less reason to be astonished at the fall of the apple than had Newton. The dilemma posed all scientific explanation is this: magic or geometry?

--Rene Thom, Structural Stability and Morphogenesis

Further Reading for Curious Primates

Is the Universe a Fractal?—New Scientist article, a great, readable intro to the concept and the work of Prof. Pietronero.

Certainly the universe does not look smooth. Some regions contain clusters of matter; others are virtually empty. Hundreds of billions of stars group together to form galaxies, and galaxies congregate in clusters. Clusters assemble into colossal structures called superclusters that can stretch out for 100 million light years and look uncannily like fractal patterns.

Even superclusters string together in long filaments and sheets that stretch like ghostly cobwebs across an otherwise empty sky. The Sloan Great Wall, for example, which was discovered in 2003, spans more than a billion light years. These filaments and sheets seem to encircle huge voids of empty space. The voids range from 100 to 400 million light years in diameter, making the whole assemblage appear as an immense, glowing lattice punctuated by wells of darkness.

Constructal Dot Org—the single best clearing house for information on Constructal Theory, which is really worth looking into—it’s simple, it’s smart, it works. Hard to beat that trifecta, you know?

The Fractal Structure of the Galaxy Universe—a long, detailed chapter about the development of the fractal cosmology theory, and the personalities involved.