How can quantity and quality best be distinguished? How can we get a feeling as to what the difference really is?

Definition -> Behavior : anything that changes over time has behavior.

Definition -> Model of behavior : a description of the behavior. This can be 1 dimensional ( speech ) , 2 dimensional ( drawing, text ) , 3 dimensional ( 2 Dimensions plus time : movie ), or 4 dimensional ( 3 dimensions plus time )

Quantifying is the process of measuring the implementation of the model.
Qualifying is the process of measuring the difference between the the model and its implementation.

A quality factor of 1.0 means the implementation is exactly that what has been modeled and it will not vary over time.
A quality factor of 0.0 means the implementation is orthogonal to the model, i.e. it behaves like a system that is the exact opposite of the model and this too will not vary over time.
A quality factor of 0.5 means the implementation behaves like the model 50% of the time. The other 50% of the time its behavior is orthogonal to the model. This too will not vary over time.

Furthermore : Anything you MEASURE and is a NUMBER is a quantity. Anything you DERIVE from the measurements and is NOT A NUMBER is a quality.

Example

A model :
A square.

The Implementation:
( Drawing of a square )

Quantifying the implementation :
– Measure all sides of the square
– Counting the number of sides in the square. This number should be equal to 4

Qualifying the implementation :
– All sides are equal in length
– The angle between any two joining sides is equal to 90 degrees ( or PI/2 radians )

Note : due to Heisenberg’s uncertainty principle, you can never make assertions as to the equality of the length of the sides of the square. This means you can’t accurately measure the relative distance in space or time with enough accuracy to validate the model.

Difference between verification and validation :
Verification is the process of quantifying the implementation
Validation is the process of qualifying the implementation

Quality of the model :
By repeatedly asking ‘why?’ questions and phrasing the answers as a more abstract model( the ‘what’ ), the model can be abstracted into a more condensed state. When you reach a state where no more answer can be given to the ‘why?’ questions , you reached the most abstract description of the model. This top level abstraction has the highest model quality.