Bradford Hansen-Smith: What is a Circle? How would you define a Circle?

This is an introduction to the fascinating work of Bradford Hansen-Smith – an author, consultant, geometer and sculptor – who notes the following on his blog,  Wholemovement ?:

I am intrigued that we have used the circle as a static symbol for both everything and nothing. Today we agree on mostly nothing, zero, yet desiring everything. We really don’t understand either. Together they suggest total integration in evolutionary understanding and in revelation through movement. A circle is a complete, inclusive, and self-referenced concentricity indicating there is no inner or outer boundary, only the perception of an infinite change in scale. The origin for the circle is the sphere, the only dimensional form that can be called Whole, demonstrating unity, and that looks the same whether moving or not. Going to origin reveals more about the nature of something and purpose, than only looking at the function or the thing itself. Only in origin will we find the necessity and understanding for change.

Compressing the sphere changes its form in a single direction of symmetry perpendicular to the expanding circle plane; similar to how galaxies are formed. Three circles are revealed in transforming spherical unity to a triunity. There is no separation only differentiation of surface and redistribution of volume. Nothing is added or taken away, the circle/sphere is Whole. Between the two circle planes is a circle ring, the dynamic agent of differentiation. Triunity of the circle is structural pattern revealed through precessional movement and is principle for all subsequent realization of potential formation; thus is the prologue for another creation story:

Wholeness through movement causes division becoming duality intriangulation with each part consistent to the movement and totallyinner-dependent to the Whole. The individual nature of part to Whole regulates the interactions between all formed and unformed parts on all scale, in all time, with purpose.

Excellent work.  Here is a video introduction to his DVD,


Henry Lincoln: The man behind the Da Vinci Code

“Rejected by academics and derided by ‘experts'”.  That’s probably why he’s one of my heros.  Enjoy:

Mandelbrot to Mandelbulb – 3D Infinity

This is visually spectacular and well worth a look. 🙂

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The ADOMAH Periodic Table

This is a profound and powerful way to visualize the periodic table of the elements –  due to the fact that it mirrors 3-D physical reality:

Geometry of the Periodic Table.

It can be observed that four blocks of ADOMAH Periodic Table, that is built strictly in accordance with the quantum numbers n, l, ml and ms, follow quite curious rule: perimeters of all blocks are equal to 18 units (if elements are placed in rectangular boxes so that any given pair of elements fits in one unit square, see“Description” page): Unit Square or 

s-block is 1 unit high and 8 units long (or wide) (1+8 = 9, is half of the perimeter);

p-block is 3 units high and 6 units long (3+6 = 9);

d-block is 5 units high and 4 units long (5+4 = 9);

f-block is 7 units high and 2 units long (7 +2 = 9);

Therefore, perimeter of each block: P=2×9=18 units.

Those are only four possible rectangles that could have perimeter of 18, if only natural numbers are used. What can it possibly mean? Can it be a coincidence?

Apparently not, this is not a coincidence. In 3D world there is one geometric shape that, if sliced in a certain way, would produce rectangles with the same proportions, orientation, alignment and order as spdf blocks of ADOMAH Periodic Table. This shape is Regular Tetrahedron!

If a regular tetrahedron with edge E is intersected by a plane that is parallel to two opposite edges, cross section will always be a rectangle or a square with perimeter P=2E.

Proportions of fdps blocks of ADOMAH PT, as well as their sequence, alignment and orientation, suggest only one possible conclusion: all four blocks of the Periodic Table are consecutive slices of Regular Tetrahedron, with edges equal to 9 units, produced by the planes spaced 2 units apart, as measured along the edges.

There is another indication that the Periodic System has something to do with regular tetrahedron: Atomic Number of every other alkaline earth element (Be, Ca, Ba, Ubn…) corresponds to every second Tetrahedral Number: 1, 4, 10, 20, 3556, 84120… Remaining alkaline earth elements (Mg, Sr and Ra) have atomic numbers that are equidistant between the Tetrahedral Numbers shown above in bold: 12=(4+20)/2, 38=(20+56)/2, 88=(56+120)/2. See more on this topic below.

Generally, a Periodic System of any size can be described in terms of a regular tetrahedron with edge E:

1) number of the periods NOP=E-1;

2) number of values of the quantum number ‘n’n max=E-1

3) number of blocks representing subshells (number of values of ‘l’): NOS=ceil(0.5(E-1)), where ceil stands for “ceiling function”, that means “rounded to a higher integer if the result has fractional part” (in case of even ‘E’).

4) maximum value of quantum number ‘l’l max=ceil(0.5(E-3))

5) dimensions of the subshell blocks corresponding to l =0,1…, l max:

as measured along the periods a=4l +2 elements; as measured along the groups b=E-(2l +1).

6) number of elements in each block corresponding to quantum number l =0,1…, l max:


7) length of the periods: LP=2(l’ +1)2 ( here, l’ is the maximum value of l for each period).

8) number of the elements (NOE) in the periodic system that corresponds to the tetrahedron with edge ‘E’:

, where lmax=ceil(0.5(E-3)) as defined above.

The Pentachoron

In geometry, the pentachoron is a four-dimensional object bounded by 5 tetrahedral cells. It is also known as the 5-cellpentatope, or hyperpyramid. It is a 4-simplex, the simplest possible convex regular 4-polytope (four-dimensional analogue of a polyhedron), and is analogous to the tetrahedron in three dimensions and the triangle in two dimensions.

The regular pentachoron is bounded by regular tetrahedra, and is one of the six regular convex polychora, represented by Schläfli symbol {3,3,3}.