The Archimedean Solids & Their Dual Catalan Solids

The Archimedean solids and their duals the Catalan solids are less well known than the Platonic solids.  Whereas the Platonic solids are composed of one shape, these forms that Archimedes wrote about are made of at least two different shapes, all forming identical vertices.  They are 13 polyhedra of this type.  And since each solid has a ‘dual’ there are also 13 Catalan solids.  There are 26 in total.  If  our two-dimensional letters of the alpha-bet were three dimensional forms, these solids would be a great representation of our language. Share85Pin34TweetShare119 SharesSubscribe to Blog via Email Enter your email address to subscribe to this blog and receive notifications of new posts by email. Join 689 other subscribers Email Address Subscribe

Continue reading

The Divine Proportion: Golden (Phi)nomena of Nature

golden number phi calipers

There is one proportion that is divine.  A ratio of two numbers, the simplest of which being one.  Paired with unity, there is only one number that is capable of fractal expansion and contraction.  By using the four operations of mathematics: addition, subtraction, multiplication, and division, this golden number (1.6180339..) is the key to understanding fractality, holograms, life, and the nature of reality.  This is the number (or ratio) the universe uses to become more aware of itself. The divine proportion is the only mathematical ratio that the Universe needs to intelligently design all life.  Phi, aka the Golden Ratio,  is a truly divine number.  It’s quite a phinomenon.  Along with unity this number creates the perfect proportion.  Let’s demystiphi some of the more esoteric geometric concepts attributed to this golden proportion.   Phi is found everywhere and yet nobody talks about it.  It’s missing from the calculator.  Its…

Continue reading

Vitruvian Man Handled

Vitruvian Man Square the Circle

Leonardo da Vinci’s famous depiction of Vitruvius encodes geometrical gnosis that’s hidden deep beneath the collective unconscious. Let’s man handle these esoteric concepts and bring light to where there is darkness Leonardo was familiar with the golden ratio and modeled Vitruvian’s square and circle off it. It turns out that this Phi ratio is almost exactly smack dab in the middle of the two solutions of ‘squaring the circle’, that is drawing a square that is commensurate to a circle, either by having equal areas, or equal perimeters ( or lengths). Share468Pin96TweetShare564 SharesSubscribe to Blog via Email Enter your email address to subscribe to this blog and receive notifications of new posts by email. Join 689 other subscribers Email Address Subscribe

Continue reading

The Dodecad

Dodecahedron Flower of Life

The numbers 1 through 12 are what’s called the Dodecad.  Do means 2.  Decad means 10. These are not just numbers, but qualities of reality and the numerical armature that nature uses to build herself.  There’s twelve hours on the clock, twelve inches in a foot, and twelve signs of the Zodiac.  Have these measures any correlation? Is it all just a big coincidence? “There are too many coincidences for it to be all just coincidence” – unknown This is 99.99% accurate according to NASA in 2014.  Now, NASA has been known to lie… Perhaps they are just playing a trick on us? Who knows! Some days I think they might knock on my door and congratulate me on recognizing their cosmo canonical number prank. The dodecahedron is the most mysterious of the Platonic solids.  Even mentioning this archetypal form outside the walls of Plato’s academy…

Continue reading

Reciprocal Gnosis

49 Octave of Light

Therein lies esoteric gnosis of the inner-workings of reality through analyzing the first principle of the Quadrivium, Number.  The reciprocals of the natural numbers reveal patterns that are visible only when we put on our goggles of decimal expansion and peer deep into the realms of numeric possibilities. The reciprocal of a number is simply one divided by that number. The reciprocal of 5 is .2 because 1/5 = .2  Conversely, the reciprocal of 2 is 5, because 1/5 = .2 This resembles patterns that arise is what is known as vortex based math.  The reciprocals of certain numbers reveal patterns that are easily recognizable at first, but then disintegrate into the apparent randomness. But it’s not random. There exists intelligence in the way nature operates.  With this reciprocal gnosis we can analyze the quality of Number itself and reveal order from ostensible chaos. The reciprocal of 49 (1/49) reveals binary numbers,…

Continue reading

Cosmic Proportions

Earth Moon and Phi

The physical sizes of Earth and Moon are encoded into the proportions and measurements we commonly use in our daily lives.  From Renaissance artists to 21st century school teachers, we all use these cosmic proportions.  Very few are cognizant of their underlying meaning. If our Moon sat directly tangent to Earth, these are the proportions that arise.  The circumference of the circle is equal to the perimeter of the square to 99.97% accuracy according to NASA’s own data. The Great Pyramid’s dimensions can be broken down to 7 high, and 11 across.  The perimeter of the base equals the circumference of a circle whose radius is equal to the height of the pyramid. The Moon and Earth can be summed up amazingly well using the numbers 3 and 11.  Maybe that punk rock band understood these sacred geometrical concepts and hid it in their name. Share173Pin3TweetShare176 SharesSubscribe…

Continue reading

Flower Power

FLower orange geometry joe dubs

The power in the flowers is generated by geometry, the second discipline in the study of the Quadrivium (Number, Geometry, Music, Cosmology). Before that is Number.  Can you define a triangle without the certain ‘threeness’ that is embedded in its creation?  This trinity develops the first shape in our reality.  Maybe this is why the Pythagoreans thought that numbers began at three instead of unity. Four is the first number that models three dimensions.  Think of a tetrahedron with its four points and four sides. Nature always uses the simplest and most efficient numbers and geometries when organizing itself.  Geometry exists everywhere.  Some of the most beautiful displays of nature’s intelligent design are encoded in the makeup of a flower. “In ancient Greece the advanced students of the philosopher Pythagoras who were engaged in deep studies of natural science and self-understanding were called “mathematekoi” “those who studied all.” ‘ The…

Continue reading