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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