Causal modeling determines probabilistic correlations through known arrangements and numerically applied sequences. This causal model has discovered a nonlinear visual sequence which is five-based and numerical. It is a fixed order embedded in the visible physical reality that is all around us. The sequence is geometric. The geometrical visual sequence illustrates non-contextuality. Contextuality in quantum physics means that there are no pre-existing values. The values one through five exist prior to observation and measurement. The value five is an innate value.
An absolute point a priori infers a visual sequence of a point, a line, a triangle, a square, and a right angle. If this sequence of geometrical objects is evenly arranged in an order from left to right, then the numerical sequence is represented and known. This visual sequence is deductive a priori from an absolute point that is threaded in physical space and time. It is necessary to fix it to a number line. The implication is measurement of the geometric design holding a five-based sequence.
A visual sequence has an innate separation and order, such as the spectrum of color (red, yellow, green, blue, violet) when viewing light through a prism. This color spectrum holds a rational sequence without numbers. The separate colors are visible and sequenced before they are given numerical assignments. However, when assigning numerical value, the spectrum of color becomes defined in nanometers, a measurement. However, like light, this geometric sequence has a nonlinear arrangement. Opposed to a numerical sequence that is linear. Therefore, physical geometry should not be separated from mathematical geometry or relegated to the status of visual aids. The claim of an accurate mathematical geometry without visualization is false.
Logical positivism favors the application of mathematical reasoning. Hempel (1942) provides an understanding of general laws or universal hypotheses. Hempel applies formal causation to historical explanation. Past events must be defined using objective criteria that order and measure. The order of an event is the place in a sequence that it occurs, whether it be the first or originating event or a later or concluding event. The measure of an event must employ some numerical assignment, like time or anything quantifiable. Using these defined events, general laws are stated to infer prior causes and their anticipated outcome. Other logical positivists take an insular approach in applying general laws and attempt to reduce everything into numerical language. Euclidean geometry founded on axioms and postulates are causal but not logically connected to mathematics and therefore are denied inclusion in its general laws. Although logically causal, without applied numerical assignment to physical reality, deductive assertions and their implications are not seemingly empirical enough.
Mathematical reasoning is perceived within physical space and time, such as the visualization of any quantity and its arrangement. An arrangement may or may not have a sequential order. A sequence of five requires fifteen arranged objects to assign notation. Any objects, such as sticks, arranged into distinct sets are visualized then given notation, such as 1 to 5. One set would have one stick, the second set two sticks, the third set three sticks, the fourth set four sticks, and the fifth set five sticks. The first set notated 1, the second set notated 2, the third set notated 3, the fourth set notated 4, and the fifth set notated 5, respectively. A distinct visualization of object reality must occur before numerical notation is assigned.
Although Euclidean geometry is that of ordinary experience, it is also wholly deductive in reason. Euclid's postulate that a straight line can be drawn from one point to any other point can reasonably and deductively infer a measure. A straight line of two points can locate a third point, and three points can construct a triangle. A fourth point can construct a quadrilateral of equal dimension, and a fifth point can verify its right angle. Therefore, a sequence of five can be inferred from a single point using non-notational geometry or Euclidean geometry. The priority of Euclidean geometry to math is not only asserted, but true. Moreover, Euclid's postulates require geometrical visualization, which can then be converted to mathematical geometry by assigning the numbers 1 to 5.
This visual sequence in space and time is illustrated with specific geometrical shapes. A point, a line, a triangle, a square, and right angle can be joined in a design. The shapes become isomorphic, a nonlinear arrangement, and can infer correlations. Three points of a right triangle represent physical points in a contained area. Three points determine known origin, direction, and distance. Therefore, three points give a known location in space and time. The five quantified and measurable shapes form together in an isomorphic design and provide conceptual representation of physical space.
