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Applications in Nature, Science and Life

Most of the great thinkers from antiquity have incisively penetrated polyhedra and their symmetric properties. Since many early number systems were inferior by today’s standards, the ancients concentrated on shapes, proportions and spatial relationships. On the other hand, today we have robust numerical paradigms, but they are primarily wedded to cubic symmetry, so we have unwittingly become a cube-centric culture of thinkers. The ubiquity of the term ‘3D’ belies the point. Consequently, our mental skills regarding proportions and spatial relationships are atrophied, and the ancients were undeniably superior to us in this regard. They appreciated better the basic power of geometry in forming an intellectual view of the universe, and they regarded it a sublime pursuit.

There are many academic reasons to become intimately familiar with perfect solids. Crystals use spatial symmetry for their growth, so polyhedra are important in crystallography, which has many technical applications. Also, scientists on the cutting-edge in unexpectedly diverse fields are discovering new, important applications for spatial symmetry. Investigations of natural phenomena, running the gamut from quantum effects to the formation of soap bubbles, rosebuds and spiral galaxies, are finding use for Plato and his five perfect solids. Plato has even weaseled his way back into life sciences after two millennia of relative neglect. The self-assembly of viral particles and body structures of microscopic organisms owe their existence to regular solids. Proteins and nucleotides are riddled with platonic forms as well.

Erwin Schrödinger, an Austrian physicist who won a Noble prize for helping formulate quantum theory, noted the quantum connections between inorganic crystals and life when he described life as an aperiodic crystal. Code World can help us understand how to make use of Schrödinger’s fabulous observation. I say this because while developing Code World I discovered something very strange about the basic information structure of the genetic code: it is perfectly symmetrical within a dodecahedron (4 nucleotides permuted in sets of 3 to assign 20 objects). I have therefore decorated Code World so that its star icons can stand for nucleotides, and the space inside triangles can stand for nucleotide triplets that permute into amino acid sequences of proteins. This spatially informative treatment embodies and expands the standard Watson-Crick codon spreadsheet. It is a more robust mapping of information.

A little personal background is perhaps helpful at this point. Friends like to tease me about where in my twisted mind I found Code World. Was it a nightmare or a flying saucer that delivered it? Perhaps both. I trained as a geologist, a computer programmer, and a physician, so I have some small familiarity with information theory, crystals, and life sciences. However, I honestly had no way to anticipate that they would all combine in Code World. I invented the device merely in response to a math question brought home from school by my son, Logan, who was a fifth-grader at the time. After months of prototyping movement of the device, I then needed a special language to allow a dodecahedron to talk to a tetrahedron. Information must pass from one form to another – the shapes must communicate - and so I came up with polyhedrish, which I view as a universal language of primitives. A search for the ‘best’ system within a virtually infinite set of possible polyhedrish systems revealed that the structure of Code World and the structure of the genetic code were numerically one and the same.

DNA, it turns out, is a sequence of dodecahedrons, and protein is a sequence of tetrahedrons. So now the magically curious and undeniably powerful patterns of these biopolymers begin to make sense, to me at least. Life adheres to the concept of ideal forms first put forth by Plato. After all, life cannot accurately be seen as the sterile square grid of a spreadsheet, as is our modern vogue. The ideal form of a DNA molecule is a double helix, and the ideal form of this double helix is a dodecahedron. What then is the ideal form of the code that translates DNA into protein?

Again, the correct answer is a dodecahedron. Just as DNA must take a real shape based on an ideal form within the real universe, there must be a shape to the logic that processes the genetic information stored in DNA. Remarkably, the question of what this shape might be never really got asked, let alone answered. Therefore, we must begin to seriously question the ‘truth’ that is being dogmatically passed down from the ivory tower today regarding a formless genetic code. It is precisely by missing the point on this, the most basic of questions about genetic information, that we are presently unable to find the proper context for interpreting genetic translation.

Life on our planet, and perhaps the entire universe, is based on the ideal form of a dodecahedron. It is the starting reference for all further understanding of these curious ‘aperiodic crystals’. Code World demonstrates the informative utility and logic of dodecahedral spatial relationships, and we can easily recognize life’s penchant for five-fold symmetry. This curiosity tends to set it apart from other natural processes preferring six-fold symmetry, such as snowflakes. Life favors the unique five-ness of fingers, toes and starfish at the very marrow of its bauplan. We will soon accept this, and we will also recognize that far more information passes from DNA to protein than suspected. We have been laboring under a misperception about genetic information that finds its roots in a 1950s computer metaphor of the genetic code. Like in the movie Contact, the actual solution is not linear or flat but lies in spatial dimensions.

Most genetic information travels in space and time through molecular form, order and proportion – as it must in all molecular assemblies. Spatial symmetry is the starting point of all such processes. The ideal form of salt is a cube, but it translates little information since its symmetry is generally unbroken. In the system that life has put together, information is indeed based on symmetry; however, only through the complexity of matching relative symmetries, and the leverage of basic rules of symmetry breaking can genetic information emerge and eventually come alive.

All language or communication must relate one thing to another, and a code is merely a set of rules to do this, but both things must share a common key. Spatial symmetry is the key available to all molecules, including the molecules of life. Interestingly, the process of communicating a minimum amount of information for traveling the surface of Code World is the same as the rudimentary amount of crystal information required at a protein construction site. How much spatial information then is at work in this translation? I suspect there is quite a bit, but the dogma of today says that there is none. I sense that the official tune will soon change though, because the old paradigm has now convincingly failed. The linear paradigm is now a husk of its glory days, and a new one will be needed ASAP. Code Warriors will have the advantage in providing it. (Clue #2: look at the tRNA).

This absurd, basic and serendipitous discovery was anticipated centuries ago by Leonardo Da Vinci in the following quote: “Man has been called by the ancients a lesser world, and indeed the term is rightly applied, seeing that man is compounded of earth, water, air, and fire, this body of earth is the same.” Da Vinci is specifically referring to the names that Plato gave to the perfect solids. He is saying that man can be constructed from perfect symmetry. He should know; he was the master. Yo, Leo, you da man!

As far as life is concerned, Plato was right - genetic information is the cosmos; it embroiders the organic heavens. It now seems that the fundamental rules for a comprehensive genetic code should defer to Plato and his five perfect solids. It is a molecular information system where DNA is the hard drive, and the ideal forms in Code World symbolize the CPU.


Unfortunately, the academic graybeards have oft repeated the little white lie that the genetic code has already been broken, while in reality it is only partially understood. In fact, the genetic code is an Enigma, literally, and so proteins remain chaste with their most intimate secrets of formation. Code World is a useful intellectual tool to eventually break this biological riddle, and it is surely a puzzle worth solving. Campers, have at it!

Code World’s behavior is a model for other cryptic properties of the universe as well. In addition to symmetry and information theory, it models basic forms of complexity, chaos, and non-linear functions. These are properties of the molecules of life, and they can provide useful insights in helping one manage the chaos and challenges that life brings with it. Despite the apparent simplicity of its parts, Code World demonstrates complex dynamic behavior. Solutions to Code World puzzles are diverse, so strategies of non-linear, creative puzzle solving and visualization are needed. These skills are hallmarks of effective behavior in school, business and family. In this way, Code World is a polyhedral mandala for exploring complex problems and strategies to solve them. It grows the brain and the spirit, like cerebral weight lifting or neural aerobics. A few good ideas are bound to bubble up to your consciousness in the process.

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