-Johann von Goethe Theory of Colors
The great mystery of the world is why reality is divided into knower and the known, where both are in a relationship but the knower knows itself more than the known. From this we can proceed no further.
Arithmetic comes to us via the perception of time, of a succession between moments. The inner experience of time is the most basic cognition, which is a one dimensional succession of experiences. The beating of our heart, the expansion of our lungs, the most vital involuntary bodily processes are the origin of our a priori sense of time. From time comes our knowledge of arithmetic, the rules governing numbers which succeed one another in an ordered fashion. Arithmetic follows the rules of discrete succession, whereas music, which seems to be the most immediate form of art, follows rules of relative succession, to our aesthetic senses.
The pleasing sound of our familiar parent's voices, and the sound of their beating hearts when they hold us, being so immediate could make music like arithmetic and time so primary. Our sense of sound is more developed than our sense of sight when born.
Geometry is known to us via spatial perception of several dimensions together. Outer experience of space requires several dimensions, experiences occurring in different successions. Memory brings this plurality of experience together. Beginning with the contraction and relaxation of muscles the effects of past experiences exist with current more intense sensations. Contraction is potential energy and relaxation is kinetic energy. The effects of the build up and release of energy remain in the body for some time and can lead to mechanical change, muscle memory. The notion of spatial extension comes from the possibility of continual experience, inferred from past experience (time). The notion of infinite space is the possibility of taking one step further. The knowledge of geometry comes from spatial perception, giving mutual relationships for different successions between points. Geometry is the static application of rules to successive dimensions. Physics, the most ancient of which seems to be astronomy, is the study of objects in motion in spatial dimensions.
Causality is a synthesis of both space and time, which is systematized into science, the body of knowledge. A preceded B in time in this space, and B succeeds A in this space at a different time, so A caused B.
That the a priori is an actual part of the world of experience, though a very selective part, is demonstrated by the fact that there are non-Euclidean geometries which does not assume space is flat and only three dimensional. The shortest distance between two points in curved space is a geodesic! A curve, not a straight line. Kant died before these discoveries, first made by the Russian Lobachevsky in the 19th century. In this geometry Euclid's synthetic fifth postulate, that between a line and a point not on the line there is one parallel line which does not intersect, is not a priori. The two parallel lines intersect in curved space.

The more we explore the interconnection between the a priori and the world, the more we see it as an an aspect of the world of perceptual experience. Phenomena is a part of the world just as objects, noumena, are. The a priori is part of the world of experience itself, it follows the same rules as objects.
Causality is a synthesis of both space and time, which is systematized into science, the body of knowledge. A preceded B in time in this space, and B succeeds A in this space at a different time, so A caused B.
That the a priori is an actual part of the world of experience, though a very selective part, is demonstrated by the fact that there are non-Euclidean geometries which does not assume space is flat and only three dimensional. The shortest distance between two points in curved space is a geodesic! A curve, not a straight line. Kant died before these discoveries, first made by the Russian Lobachevsky in the 19th century. In this geometry Euclid's synthetic fifth postulate, that between a line and a point not on the line there is one parallel line which does not intersect, is not a priori. The two parallel lines intersect in curved space.

The more we explore the interconnection between the a priori and the world, the more we see it as an an aspect of the world of perceptual experience. Phenomena is a part of the world just as objects, noumena, are. The a priori is part of the world of experience itself, it follows the same rules as objects.
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