Here are some strong statements - Information equals reality - Algorithm equals Information - Observation equals information - Consciousness equals information - Consciousness equals reality - Algorithm equals number - Imagination equals potentiality.
How real is a real for somebody. Is it real for anybody, anywhere and whenever. What is real to me today is not that tomorrow in all aspects, be course i do not remember all happened today. We have personal view for reality. I cal this posterior reality, be course there is something observed and measured in my view to reality.
I tell difference in reality that is not in my knowledge and may be new unknown for anybody and exist in some unobserved region of reality. I make now a speculation, It is my a priory reality that I can integrate over the likelihood of observable I can find. This is a Bayesian method.
Observable are like arguments. Posterior opinions are B-statements and a priory statements are A-statements. There may be B = Rel(A). My B is related to A. This sound possible. But what is the relation like.
B is sometime in my mind and concluded some way from A in some context, for instance in my mind. Your opinion is different although you B and my B may be the same. The conclusion is different and done in different branes,
In mathematics A information is non-contradictory and common to all. The path B=P|A is not unique. The path is network a network of all equivalent proves. The truth will not change.
Now Information equals reality is A statement and B statement. Formally
B|Information equals reality is B = Rel(A|Information equals reality is A). Where the relation integrate over all free conclusions leading to the related conclusion.
Now in meta level wee can forget the morfisms from A-statements to B statements and speak about reality with two flowers posterior-reality and a priory reality.
My interest is to ask how simple is A-statement. What we know about it by inverse relation from B-statements to A-statements and what we need in between. My conclusion is Bayesian like. We need likelihood and a measure that is convertible.
If this inversion is possible, then we can conclude that the reality has a priory model. This statement is the same as our observation proof that there is a priority model for reality.
What is the model? It must be Independent of you and me. I have good candidates for Haar measure. My favorite measure is in integers, be course they do not depend our opinions or observations. The second favorite to me is number PI in digital form.
Every stories of the universe is coded in it. Believe or not. It is the truth. PI is a priory to Universe.
Addendum 25.11.2014
In my blog https://everythingintheory.wordpress.com/author/zuristo/ I have described some general operational eqvivalensies in context of Points, Paths and Connectomes. In this modelling frame there are structures and there states with sespec to operations.
In this context I mension two imporatant eqvivalensies that ara very basic one
- Hamiltonian equals energy, H|S> = E|S>
- History equals information, H|S> = I|S>
- Hypernetworks are Path Structures H=P+P|P+P|P|P+.....
This can be sayed that Paths define history, energy and information. This way Paths define everything. This means Paths Equals reality iff everything equals hypernetworks.