How Everything That Exists Could Be Related By Sankofakanian Introduction

How Everything That Exists Could Be Related by sankofakanian Introduction Often times I have heard of the Universe being 'One'. Yet, it has been easier for me to imagine that things may influence each other than to grasps that all that is is united. In this text, I want to convince myself that it could be possible that 'All' is 'One'. I use some mathematics (http://en.wikipedia.org/wiki/Relation_(mathematics) ) in order to achieve this result. It should be noted that I do not formaly prove many of the assertions I make in this text and that the arguments are not meant to be rigorous. Rather they are there help me in seeing that such a 'NonDuality' is logically possible. Moreover, I am limited by my imcomplete knowledge of mathematics. What I want to clarify for myself is whether or not anything could exist in our universe that would be totally independent of anything else. I also want to understand if something could exist in our universe that may be totally independent of just one other thing. Can anything in our universe be totally independent of the rest of that universe? Let U be the set of all objects that exists in our universe at a time t. Let x and y be any two distinct objects belonging to U. Let assume that at that time t any object x in our Universe can be described to have a state sx. Let's denote by ^ the relation on the set U such that (x,y) is in ^ if , in a way or another, the state sx of x at time t can be shown to depend on the state sy of y at the same time t. We can see that if x^y and y^z then x^z. That is ^ is transitive. Example: If being at a meeting on time depends on me getting up early, and me getting up early depends on my alarm clock ringing, then me being at the meeting on time depends on my alarm clock ringing. What would it mean to say that « there exists an object a in U such that, for any x in U distinct from a, (a,x) is not in ^ » ? In plain english that would mean that in that universe U there's an object whose state does not depend, in any way, on any other object in that universe U. If ^ is not reflexive then such an object's state could not even be said to depend on the object itself. Such an object could not be described as having a state since itself could not be used as a reference to its state. We would be confronted whith an object that has no state. By definition such an object does not exist in universe U. Therefore, in our model, ^ would need to be reflexive. So far, in our simple model of the universe it is possible for some object to be totally independant from the rest of the universe.

Now, let's have our universe U obey the rule that any object in U must depend on, be influenced by, some other object in the universe U. In such an universe U, for any object x there would exist an object y such that x^y. Can something in our universe U be totally independent of just one object in that universe? I ask myself the question about «what would it mean in the same universe U to say that « for some b in U there may exist a y in U such that (b,y) is not in ^ » ? That would mean that in our redefined U there may be a specific object denoted by b, whose state is not influenced by some specific object y in that universe U. By definitions of the relation ^ and of the universe U, there must be an object z, distinct from b, such that b^z. And for such an object z there must be an object, say o distinct from z, such that z^o. This would mean that b^o. Following from the definitions of ^ and U, a grammatically correct1 expression E of the form b^z^o^p...^w could be written in which would figure a number of object-denoting symbols inferior or equal to the cardinality of U. Now, if ^ is antisymmetric, then no object-denoting symbol can appear more than once in such an expression E. It is so because we have said that in our universe U, ^ is transitive. That is, in any grammatically correct2 expression E of the form b^z^o^p...^w containing a substring e of the form b^z^..o^b, that substring could be rewritten as a substring e' of the form b^o^b. This will contradict the fact that ^ is antisymmetric. Therefore ^ is antisymmetric would mean that any grammatically expression E, representing interdependent objects in our universe U, must not contain an object-denoting symbol more than once. In that case, if the cardinality of U is a finite number, then the last element to appear in the expression will not be in relation with any other object. This is a contradiction of the fact for any object x in U there would exist an object y such that x^y. In the same way, if the number of elements in U is infinite, for any finite-length (counting objectdenoting symbols and '^' symbols) grammatically correct expression, no object-denoting symbol can appear more than once. Which violates our rule concerning the elements belonging to U. Hence, by the definitions of ^ (transitive,reflexive) and U (for all x in U there exist y such that x^y) , ^ must be symmetric. ^ would then become an equivalence relation and there could exist an object b of U such that Pb would be the set of elements of U that are related to b and Py would be the set of elements of U related to y, such that the intersection of Pb and Py would be empty. ^ would induce a partition P of U. It would then be acceptable to say « for some b in U there may exist a y in U such that (b,y) is not in ^ » 1 We mean that the relation-denoting '^' symbol always appears between two object-denoting symbols and an objectdenoting symbol may only be followed by the relation-denoting symbol '^' or nothing. 2 We mean that the relation-denoting '^' symbol always appears between two object-denoting symbols and an objectdenoting symbol may only be followed by the relation-denoting symbol '^' or nothing.

The exception would happen when the set of objects related to b is the same as U. We would not really have a partition of U and it would not be true that « for some b in U there may exist a y in U such that (b,y) is not in ^ » . In the case of a « proper » partition of U we would have an universe U partitionned in islets(parts) of interrelated objects.

Otherwise, we have a universe U where all objects are related directly or by transitivity.

Let's note that in the case of the partitionned universe U, an object belonging to one of the islets (parts) would have no way to interact with one in another islet. From the point of view of an object in one of the partitions its universe would be the islet(part). One can also note that all objects in a part must mutually depend on one another at any time t. The same thing applies to the non-partitionned version of universe U.

Conclusion If we live in a universe where: 1. the state of anything existing at any time t is dependent on the state of at least one other object; 2. x depends on y means y depends on x; 3. x depends on x then any object in that universe, that we know to react with some other object of the universe, would in fact influence the whole of the universe. The implication would be very interesting, to say the least. For example, since my mind feels real to me I will count it as an object in our universe. Moreover, my mind interacts with my body. I don't know exactely how, but I know that I can voluntarily perform some actions. Now according to our model of the universe, my mind would influence the whole of the universe. The reverse is also true. Everything else in the universe would influence my mind.