High- and low-level
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A high-level description is one that describes "top-level" goals, overall systemic features, is more abstracted, and is typically more concerned with the system as a whole, and its goals.
A low-level description is one that describes individual components, detail rather than overview, rudimentary functions rather than complex overall ones, and is typically more concerned with individual components within the system and how they operate. Low and high level are relative; for example the graphics engine that drives a computer game and works at the level of entities in the game, is high level compared to the video subsystem DirectX that works on the level of renderable objects, which itself is high level compared to a vertex shader within that system.
Differences and similarities 
Due to the nature of complex systems, the high-level description will often be completely different from the low level one. For example, there are features to an ant colony that are not features of any individual ant; features of the human mind that are not known to be descriptive of individual neurons in the brain, features of oceans which are not features of any individual water molecule, and features to a human personality that are not features of any cell in a body. The descriptions of these differ depending at what level they are studied. Features which emerge only at a high level of description are known as epiphenomena.
- In computer science, a high-level programming language is one which has a relatively high level of abstraction, and manipulates conceptual structures in a semi-naturalistic manner. A low-level programming language is one like assembly language that contains rudimentary microprocessor commands.
- In formal methods, a high-level formal specification can be related to a low-level executable implementation (e.g., formally by mathematical proof using formal verification techniques).
- In sociology and social anthropology, high-level descriptions would be terms like economy and political structure, and low level descriptions would be individual peoples' motivations and work.
- In neuroscience, high-level and low-level would relate to the functioning of a cell (or part of a cell, or molecule) and high level to the overall function or activity of a neural system.
- In documentation, a high-level document contains the executive summary, the low-level documents the technical specifications.
- In business, corporate strategy is a high-level description, a list of who does what jobs is a low level description.
- Climate is a high-level description of the actions of the atmosphere and oceans. Physics of water and gas molecules is a low-level description of the same system.
- The instruction "write a creative poem on love" is a high-level instruction. The instruction "tighten the tendons in the dominant wrist to grip the pen" is a low-level description of an activity within that.
- "Wikipedia is an encyclopedia" is a high-level description compared to "Wikipedia is a collection of textual articles on many topics". The former reflects a higher level view of organization, purpose, concept and structure, but does not explain what Wikipedia physically is. The latter is more detailed as to what exactly Wikipedia contains and how it's made up, but doesn't explain what its overall purpose and goals are. These are typical features of high-level and low-level descriptions.