Spring 2009 Semester

It has been a wile since a new post. But, I have been attentive to school; and since the break is over once again, back to school again.

During this break I did not get much work completed. I played Tetris for hours, which, may be considered work, but not constructive work. On my arrival to Erie, I continued to play Tetris on my Dreamcast; and then would spend 20 min to 1 hour a day working. This is not enough time and focus to get much work done. But I again read sections from a discrete and combinatorical mathematics handbook; this strenghted my views on the topic. And, thus far, I have developed the following.

* The continued basis containing the axioms
* A translation from predicate statements to the propositional logic
* The generation of combinatorial space oracles in deterministic bounded time
* And, the relationship between the $\forall x \in L P(x) \rightarrow \bigwedge_{x\in L}^n \exists P(x)$. This allows for the predicate $\forall$ to be removed from the basis and replaced with the existential predicate as a propositional form. The notation $P(x)$ can be removed, and is done with the operation of independent negation from the previous axiom definitions. This is omitted for clarity.

The final bullet can be applied as the combinatorial space itself, or more likely a subset of the combinatorical space as a constraint on the system.

Much still needs to be done in the formalization of this system but must be set aside for the sake of the current semester.

The existential predicate and the acquisition of information.

You are reading this; or you may be looking outside, listening to your music, or doing any other activity as we can go on for hours and days... But, you are processing the events of the moment. This is the simple activity that we are interested in on today's post.

As we learn new information from our various senses, information is never forgotten (perhaps misplaced), that information is stored in a non-volatile memory location in our CNS. This process, continues throughout the span of our lives. It is not the memory that we are concerned with however, rather we must be interested in what it is that our CNS does with the information gathered.

Consider each synaptic moment to be a write and read cycle, thought will not differentiate itself, for if thought were to then no new thoughts would ever exist, and we would be limited to a distinct potential set by only our input. Thought does, on the contrary, allow us to consider implications of situations or possibility's that would be absurd in the known realm of the universe that we operate. Hence, there is no bound on the imagination.

Although this may be precisely that same story that our mind told us that can be true. It is not, and the following will help convince you that it may not be.

Suppose that each synaptic moment we gather a well defined set of information, this may be restricted to our senses for a human, but beyond that we can think of other sensor's which may capture events in a situation. This array of information must be immediately stored in acted upon with those other past information that was collected. To do this, we must apply combinatorics so that every possibility of the situation may be represented. Note: this is purely a conservative case supplying the ideal situation, in a mind one may need to ponder an idea to generate the same effect.

Thus, with this operation acting on every object of our input array, we build a stronger complete view of that same input data set. And, from this we can then see the possibilitilities for a given situation (SAT).

We will continue, and I will continue to unleash this journey. Although, at the moment this is much of the writing that I get done. I am using the majority of my time to focus on school work and cannot diverge far from the topics...

The truth of the matter.

I moved back to school this past Wednesday and have been relaxing before courses start for the fall semester.

In the mean time I am continuing to work through Gödel's work on the incompleteness theorem, along with the ZF axiom system.

Truth is the main premise to this thesis, and how this truth can be interpreted through a machine; as for you and almost any being (perhaps there are some that do not perceive the world as I do) realize our surrounding as what we perceive it to be. Where if it is not the case and we rather perceive some false premise, this is also fine, as you have first have perceived those fallacies as truths, but have then (from more sensory input, or cognitive consideration) realized the inconsistency of the situation and have adapted your reality accordingly.

Given a statement of logic, we would like to see what variable combinations give truth to this statement. This is first done by accepting all variables and possible negations as truths, contrary to the Boolean algebraic approach of neg(1)=0, and assigning a specific mapping to these variables (to integers, letters, symbols, etc...) such that each variable along with any necessary negations of variables of the same class to be defined independently. It is now that we can define the statement of logic in a variable independent sense, allowing us to understand completly under the basis of truth.

Next, on to bounded combinatorical spaces and the existential prediacte axioms!