Topics 2 Worlds

Not a literal world, rather it refers to an opaque process or mechanism that is: - Embedded within a larger system or exist alone. - Produces an output or moves into a state that is of interest.

“No matter if it is a white cat, or a black cat; as long as it can catch mice, it is a good cat.”

— Deng Xiaoping（鄧小平）

The ‘world’, more precisely the world’s output or state is the subject of a model. The quality of this model rest completely on its ability to replicate and explain the outputs or states of interest.

Achieving Its Goal - A model’s goal can be achieved by directly mapping and reflecting or approximating the elements of the real world.

A model’s goal can be achieved by totally abstracting the elements of the real world.

Its Implementation

Model is implemented as part Data Structure and Part Process (Composition of Algorithms).
Has a verbose description (Story) as to how it operates to give rise to the data it produces.
Can query itself to answer questions about it own structure.
Together it explains the real world phenomenon which it is intended to reflect.
Runs on a cycle where the model hences it’s outputs are updated as new evidence flows into the model.

The value of storytelling

The data story has value, even if you quickly abandon it and never use it to build a model or simulate new observations. Indeed, it is important to eventually discard the story, because many stories always correspond to the same model. As a result, showing that a model does a good job does not in turn uniquely support our data story. Still, the story has value because in trying to outline the story, often one realizes that additional questions must be answered. Most data stories are much more specific than are the verbal hypotheses that inspire data collection. Hypotheses can be vague, such as “it’s more likely to rain on warm days.” When you are forced to consider sampling and measurement and make a precise statement of how temperature predicts rain, many stories and resulting models will be consistent with the same vague hypothesis. Resolving that ambiguity often leads to important realizations and model revisions, before any model is fit to data.

— Statistical Rethinking (McElreath 2016)

2.1 Small Close Worlds

Closed world models are actual what the name suggest, that are absence any of noise and messiness of the real world.

All the possibilities are nominated, no pure surprises, all the unknowns are known.
Having the unknowns identified allow us to reason about them.
The models’ logic can be verified under given assumptions.

Reasoning in the small world is based on negation by failure, ie: Not finding a condition or object is adequate to conclude it does not exist.

2.2 Large Open Worlds

Open world or open universe, aka real-life is vastly more complex and dynamic than the small worlds we build in our heads. Entities in the real world adaptive based on their own set of innate heuristics. These development shortcut gives rise to the following:

Entity Uncertainty, where an object may exist in the real world which is unknown or unobservable.
Magnitude Uncertainty, where the impact of a known or unknown object is not nominated.

Hence, to conclude a subject does not exist in the open world, requires proofing that the existence of subject is not possible. Not being able to do so simply mean it state or value is unknown.

2.3 Moving Between Worlds

Small world models need to graduate to the open world before they can deliver any value.
No guarantees that a logically consistency small world model, will scale or perform well in a large world setting.
Yet a logically inconsistent small world model, will certainly not perform well in a large world setting.
A models’ performance in the open universe needs to be demonstrated as it can not logically deduce.