18 Functional Communication
In contrast to the use of functional to mean goal-oriented, here I want to approach function as in a type of formula applied to some input, in the mathematical sense of \(y = f(x)\). Here, functional communication is a tool comprised of two primary functions, which mirror two fundamental math functions:
- Transformation functions
- A change in state, a conversion. Communication is the act of translating from one scale onto another
- Aggregation Functions
- Synthesizing information, summarizing, compilation. Communication is the act of aggregating from many to one
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 |