To start with I have not yet formulated this geometry yet. However I do have a sense about where it will be going. Starting with a point as in Euclidian geometry we find it has no metrics because it is alone. If there is space there is no more space than can envelope that point. Space can not exist without more than one point for anything to be beyond or between as space. A second point could , COULD, in this theory form a line with the first point as in Euclidian Geometry except that probability is key. Two points can offer a variety of permutations between the two . I suppose there can be distance between the two points and if so than there is space or the points can be connected or they can rotate around each other or one can rotate around the other and if they form a line that line can rotate forming a circle or a sphere . Of course those possibilities require other dimensional attributes as variables that can include time and energy. The two points can grow closer together or further apart from each other they can work to create space between them though not necessarily beyond unless your line between the two is deemed to be infinite. Points are also interchangeable with themselves and with nothing.
A third point makes a hole new set of variables with considerable complexity and it again includes various types of interactive rotations, formations of line, planes spheres. In Euclidian geometry there are no basic rotation variables not until a circle is studied and that circle tends to have a circumference where as the ones formed between points no necessary circumference as if a line that is infinite rotates there can be a sphere that is infinite. The geometry then goes to four point which can be two separate lines, four lines or even just one line with all points on that same line. So maybe you get the sense about where this is going? If you do then we can map out probability using this new form of geometry
Probability Geometry is a new geometry based on probability being a basic dimension of reality.
Multi-variable conditional theory in physics leads to a new type of geometry. That is because Euclidian geometry and it's manifestations are about arbitrary human organization of our physical perspective and not about natural organization derived from happenstance and random uncontrolled relationships . We tend to think of reality as made of points and then particles and if not that we end up with harmony and string theory . If there is music in the universe it does seem to have a melody in far too many places for our conscious desires to understand things in a rational way to explain. Probability as a basic dimensions quickly explains everything because we know we can count on probability and we don't really understand why. Counting on probability is being able to predict or deduce either a future event that will occur or explain why it has occurred. So Therein lies the need for a geometry based on probability . I am surprised no one has figured it out before. The disjunction between our mathematics geometry and the every day reality of probability should lead to a logical format that allows probability to explain itself.
Probability Geometry is a new geometry based on probability being a basic dimension of reality.
Multi-variable conditional theory in physics leads to a new type of geometry. That is because Euclidian geometry and it's manifestations are about arbitrary human organization of our physical perspective and not about natural organization derived from happenstance and random uncontrolled relationships . We tend to think of reality as made of points and then particles and if not that we end up with harmony and string theory . If there is music in the universe it does seem to have a melody in far too many places for our conscious desires to understand things in a rational way to explain. Probability as a basic dimensions quickly explains everything because we know we can count on probability and we don't really understand why. Counting on probability is being able to predict or deduce either a future event that will occur or explain why it has occurred. So Therein lies the need for a geometry based on probability . I am surprised no one has figured it out before. The disjunction between our mathematics geometry and the every day reality of probability should lead to a logical format that allows probability to explain itself.
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