Beans, Beans, the Mystical Fruit

The use of beans as a tool for the exploration of number leads to the discovery of triangular numbers. When arranging groups of spheres, the patterns they fall into are dictated by their shape. Three spheres of equal size are going to assume the shape of a triangle.

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Four spheres brought together in the shape of a square form an unstable structure.

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The spheres naturally maintain a sixty degree relationship with one another. The power of attraction pulls the square into a diamond shape.

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Hence it follows that triangles are an inherent feature of numerical structure while squares are less so. The ratios found in the New Testament are built from the first three triangular numbers.

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But once again, the value of these numbers stems from the manner by which like quantities of spheres can be stacked one upon the other.

Consider the one verse within the Gospels which contains the word PSEPHIZO:

For which of you, intending to build a tower, sitteth not down first, and counteth (PSEPHIZO) the cost, whether he have sufficient to finish it?
Luke 14:28

Notice what is being built, a tower, which is perfectly in keeping with the shape of the structure formed from the spheres.

Such clues provide us with a window into an alternative system of numerical understanding, one not based on axioms, but one built around experience. Axioms are 'self-evident' beliefs, while experience supplies one with knowledge.

Consider the classic Platonic dimensional progression. A zero dimensional point moves in a straight line generating a one-dimensional object. A line moving perpendicular to itself in a plane generates a square, the basic object of the second dimension. Move a square perpendicular to itself and you form a cube, a three-dimensional object.

Where are the axioms above? Observe the various imaginary objects. The illusionary zero dimensional point, the one dimensional line, and the two dimensional square. All are abstractions, without basis in reality and yet somehow, from them one arrives at a real object, a cube.

A progression built up from physical experience begins not with an idealized concept of an imaginary point but with a single sphere.