16  Functional Communication

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Communication is a tool comprised of two primary functions, which mirror the two fundamental math functions

Communication is translating from one scaling onto another, i.e. state conversion, a transformation function.

Communication is aggregating from many to one, i.e. synthesizing information, an aggregation function.

Beginning as mathematical functions …

Metrics	Transformation Functions	Aggregation Functions
Diagram	<image placeholder>	<image placeholder>
Input	A set of values	A set of values
Function is Applied to	Every value individually	The entire set of values as a whole
Literal Output	A set of values as large as the input	A single value, typically.
Figurative Output	Information in a new functional state	Information in a representative metric
Simplified Understanding	“Change of state”, “State conversion”, “Rescaling”	“Creation of new metrics”, “Less is more”, “Combined metrics”
Potentially Detrimental Consequences	Information loss due to unintuitive relationship of new values to intuitive original values (i.e. lost in transformation)	Non-representative metric due to known or unknown systematic error (i.e. various forms of systematic bias)
Pitfalls	Inappropriate transformations invalidates downstream work (?)	Uninformative metric Inappropriate function for the set of values (e.g. mean of a set of values with a skewed distribution)
Desired Beneficial Consequences	Information in a new state that is easier to understand or allows for new downstream methods.	Reduce complexity to an easily understood and manageable representative metric that minimizes information loss
Math Examples	Log transformations, Square/cubed root, exponents Z-scores, standardization	Measures of location and spread
Conceptual cousins in data science	Feature engineering transforms input from it’s native state into a state necessary for downstream algorithms.	PCA reduces the number of features by synthesising component axes. Clustering reduces the number of observations by collecting similar profiles into clusters
Colloquial examples	Sales tax, BMI (Body-Mass Index), temperature conversions (also weight, volume, distance, etc.)	GDP (Gross Domestic Product), GPA (Grade Point Average), IQ Score, medical diagnoses of complex diseases, stockmarket analytics

… superimposed onto communication:

	Communication as Translation	Communication as Synthesis
Diagram	<image placeholder>	<image placeholder>
Input	A set of information	A set of information
Function is Applied to	Every piece of information individually	The entire set of information as a whole
Literal Output	A set of information	A single piece of information
Figurative Output	Information in a new functional state	Information compression
Simplified Understanding	“Change of state”	“Reduction of information”
Potentially Detrimental Consequences	Information loss due to inaccurate and imprecise encoding that enables faulty decoding (i.e. lost in transformation)	Non-representative metric due to known or unknown systematic error (i.e. various forms of systematic bias)
Pitfalls	Inappropriate transformations invalidates downstream work (?)	Uninformative metric Inappropriate function for the set of values (e.g. mean of a set of values with a skewed distribution)
Desired Beneficial Consequences	Information in a new state that is easier to understand or allows for new downstream methods. Target audience decodes transition state to return to a state as close as possible to the original state	Reduce complexity to an easily understood and manageable representative metric that minimizes information loss
STEM Examples	Scientific Writing, Oral presentations, teaching, Data Visualization	Measures of location and spread
Critical STEM examples	Standard operating procedures (SOPs), material safety data sheet (MSDS), Software documentation, Prescription drug inserts
Conceptual Cousins in science	Water changing states DNA -> mRNA -> Protein	Macro & macro molecules comprising a cell
Colloquial examples
Beyond STEM	Creative arts including physical, experimental, visual, written, audible, etc.
Conceptual Cousins in Society	Design