Key 5: NUMBER and dimension as a crystallizer agent for form Borchers understands mathematics as the only discipline capable of making possible the relationship between ideas and the real world, as something inevitable in the step from thought to built work, as the crystallizer agent of the real form. However, neither as a calculation nor as an application, as all the mathematical systems previously used by architects. Not as something post-imposed onto form, but as its origin and internal genesis. He devotes much time to this issue in order to build a mathematical system linking the sensory phenomenon with the abstract harmonic structure that requires the coordination of measurements in the dimensional control of the work. Is book Meta-architecture contains his thoughts and the system he created to solve this problem: the Cubic Series, which relates real extension with perception and the ability of the senses to discriminate. He also distinguishes - among the different operations and meanings of this discipline – from the symbolic capacity of the “pure number” to the complex logistic operations of geometric and algebraic systems in their relation with the various arts. He discriminates between the acts of measuring and sizing. The first, measuring, originates from a specific extension to which a measuring unit is applied, which is then repeated until reaching the full extension and obtaining a number from this operation. The second operates conversely; from a number a specific magnitude is obtained. Then, if the work does not exist before its creation and therefore there is no magnitude to measure, it must be defined in advance, but which shall the unit be? How can we determine it? To Borchers, this unit must comply with several requirements: Incorporate the dimensions of the human body. Embrace the full “mesocosm”, i.e., the full concrete extension, as defined by the sensory capacity of man. Include the ability of senses to discriminate, i.e., the limits of differentiation between two magnitudes. Be able to transform from its condition of discrete magnitude to a continuous magnitude, i.e., into a geometric shape. Be able to operate on all scales simultaneously from the faraway distance to the immediate proximity without losing the condition of continuity. The homologation of the different planes and horizons in which human existence unfolds, i.e., contain a plastic unit standard. Be capable of combination. Allow the calculation of lines, areas and volumes, have logistic capacity.
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