(Keynote lecture ICOEV 2018)
Linear to a 3D topology of integrating events: For a hundred year, the foundation of information theory is based on the fundamental principle that every single event happening in nature could be explained as a sequence of simplest event, switching between “yes” and “no”. This was a very strong principle because it rejects all other forms of geometry that could connect events. We propose to connect events using a topology, a geometric shape whose corner points are events. There would be multiple ways to generate closed loops between points. We also consider a corner point holding unique geometric shape inside. The only way to self-assemble different events and creating a new one is that a topology of events start behaving as a single point and connect with different events to build a new one. In this existing philosophy of information integration, when we connect dots representing events, we do not have any problem about the gap between the events or dots. However, now it is a big problem. Because we need to find by ourselves the gap between events or dots. Connecting the dots along a line could be done blindly, what all we need to think is if the sequence is right. However, for topological integration of events we need to find exact distance between events, or phase gap. Imagine you are given 8 points and you have to make a cube, so the information you need is the distance between the points, what is equal for all points. However, the situation changes dramatically if the distances are not equal. We say that the problem occurs when distances between the points are different. We define a distance as phase.
Say, we are given a number of events as discrete points, and we are asked to build a topology using these events as a set of points. Can we do it following a rule or any trick? If we can, then if an unknown set of events happen around us, we can integrate them. If information of relative phase differences are not known we cannot build anything, because using a given number of events a large number of structures could be created. Without getting nervous, we calculate the possibilities how can we integrate, being as wild as possible. We use simple mathematics to find maximum randomness in topology for a given set of events.
The birth of a system point: Topology is rich because if a linear set of events are connected in a close loop it is an example of the existing Turing philosophy itself. The topology would not only encompass a volume but also have the ability to give birth to a system point. How? every event is a single point, it has a topology inside. When all system points in the internal topology synchronize, effectively it becomes a single system point for the higher topology and could move along the higher topological structure, i.e. available above. This is how a system point is born at the event point.
Counting the randomness of a given number of events: For us, integration of phase is the way a set of events integrate to generate a new event. Why? Because we imagine a topology or a cube, how do you move from one point to another? Addition of phase takes place when we take the product of vectors, as indices of exponential term. So, we find how many ways phase integration is possible, this is done by finding the number of ways we can make the composition, for 12, it is 3 (we get a topology triangle), the number of ways one could make combinations of those triangles & lines etc for 12, we can have quadrilateral of triangles (4×3=4×3=12). So, for every single integer in the number system, we can have a composition of typologies, as if one is given infinite sets of balls, now arrange them in the number of ways you can, only one restriction, make it productive integration, so that sum of phase is taken always as supreme. Because we follow the philosophy of topological integration, that is information is written in the topology of silence.
You give me a set of integers, I give you a movie: So, if one gives us only an integer, we can find a large amount of information. Only a set of numbers could represent a whole movie, with a past, present and future. How much this is reality we do not know, whether universe actually follows this or not is an open question, but, it is always interesting to see how much could we stretch information from geometric alzebra.
Thank you for this interesting work. Dirk K.F. Meijer