WORK IN PROGRESS (WIP) Revision 0.3 September 17th, 2020
In classical systems
Axioms
Summary
Information is Relative
No information function is omniscient
No information function is omnipotent
Necessary information increases certainty
Information cannot be reduced below what is necessary
Complexity cannot be reduced below what is necessary
Equivalent functions cannot be reduced below necessary information
Equivalent functions cannot be reduced below necessary complexity
Information is (in)sufficient
Information is (un)clear
Information is (in)accurate
Necessary information is sufficient, clear, accurate
Summarization reduces information
Summarization reduces certainty

Figure 1. Information is Relative, Uncertain, and Distributed in Space
A1. Information is Relative
Information resources are distributed in space
Movement of information resources has a finite speed
Movement of information resources takes time
Information is relative to where an information function is in space
Different observers, separated in space, will disagree on when an event occurred and the sequence of events.
A2. No information function is omniscient
Information is relative to were an information function is in space
No information function has instantaneous access to all information
No information function is omniscient (all knowing)
A3. No information function is omnipotent
Information resources are distributed in space
No information function has access to all resources at any given point of time
No information function is omnipotent (all powerful / infinite resources)
A4. NECESSARY Information increases certainty
A + B = C
If A and B are known, the value of C is certain
A and B increase certainty
If A and Z are known, but B is not known, then C is also not known.
A and Z do not increase certainty.
Necessary information increases certainty.
A5. Information cannot be reduced below what is necessary
A + B = C
The value of C is not certain unless A and B are known
A and B is the necessary information to be certain of the value of C
For a given function, equation, etc information cannot be reduced below what is necessary
A6. Complexity cannot be reduced below what is necessary
A + B = C
The value of C is not certain unless A is added to B
Adding A and B is necessary complexity
For a given function, equation, etc complexity cannot be reduced below what is necessary
A7. Equivalent functions cannot be reduced below necessary information
A + B = C
G + H = C
A=2, H=2
Therefore, G = B
Superficially the equations look different
Substantively the equations are the same, differing only by how information was labelled
Equivalent functions cannot be reduced below necessary information
A8. Equivalent functions cannot be reduced below necessary complexity
A + B = C
G + H = C
A=2, H=2
G=2, B=2
Superficially the equations look different
Substantively the equations are the same, differing only by how information was labelled
Both equations add two numbers to derive a third (C)
Equivalent functions cannot be reduced below necessary complexity
A9. Information is (in)sufficient
A + B = C
The value of C is not certain unless information is sufficient (A,B)
At the moment the equation ‘A + B = C’ is computed, the available information is either sufficient (A,B) or insufficient (A or B but not both)
A10. Information is (un)clear
A + B = C
The value of C is not certain unless information is clear (A,B)
At the moment the equation ‘A + B = C’ is computed, the available information is either clear (A,B) , impacted by noise (A,Z), or impacted by redundancy (A,A,A,B,B,B)
Information is clear or unclear
A11. Information is (in)accurate
A (2) + B (2) = C (4)
The value of C is not accurate unless information is accurate (2,2)
Information is either accurate or inaccurate
A12. Necessary information is sufficient, clear, accurate
A bowl as two apples and three oranges in it
The quantity of fruit is computed by the function A + O = F
Information available for equation (2,3)
Information available is sufficient (both A & O)
Information available is clear (not having noise or redundancy)
Information available is accurate (the correct quantities for A & O)
Quantity of fruit is computed as 2+3=5
Quantity of fruit is accurate
Necessary information is sufficient, clear, and accurate
A13. Summarization reduces information
{2,2,2,2,2,2,2,2,2,52}
Average = 7
The information that most values were 2 was lost
Summarization reduces information
A14. Summarization reduces certainty
Information increases certainty
Summarization reduces information
Summarization reduces certainty
Appendix A - Definitions of Information
The unit of information is a bit
A bit has one value only, either zero or one
Information storage, processing, and propagation obey the laws of physics
The maximum speed of information is the speed of light
The minimum propagation delay of information is ( distance / speed of light )
Appendix B - Equations and Values
The speed of light is a vacuum is, 299,792,458 meters per second
The number of links in a complete graph is equal to: n (n-1) / 2
Time = distance / velocity
Appendix C - Time
Time is how long it takes light to travel a measured distance
Measured time changes, if measured distance changes, relative to observation
Time and sequence of events is relative to the frame of reference
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