approximation
Let an agent explain approximation as a concept and practice, relay how errors are bounded and reported, describe kinds across mathematics, science and everyday use, and separate the concept from unrelated aliases in the registry entry.
Research draft, second pass
A second pass drafted this model: the structure a model of this thing needs, and what is known about it in the world. The line under this one says how the second half was obtained - researched against sources, or recalled without web access, in which case nothing here was read anywhere and every claim is a lead to verify. Unreviewed either way.
written by Claude from model knowledge without web access - no source was read, every claim is a lead to verify
Researched by: Claude
Purpose and description
Let an agent explain approximation as a concept and practice, relay how errors are bounded and reported, describe kinds across mathematics, science and everyday use, and separate the concept from unrelated aliases in the registry entry.
A value, representation or model that is close to but not exactly equal to the true value or full description, used when exactness is unattainable, unnecessary or too costly, as in rounded decimals, approximate dates, simplified physical models such as the paraxial approximation and scale analysis, and estimated centre points; approximation is governed by error bounds and is studied in numerical analysis and approximation theory, while overfitting is a failure of approximation in statistics.
What it is for: Working with values and models that are close enough for a purpose.
It can be explain the concept and error bounds; describe kinds across fields; help choose and report approximations; separate unrelated aliases.
Distinguishing features
Bounded error
Purpose-dependent accuracy
Trade-off with cost
Formal theory
What it looks like
Not a visible object; rounded numbers, simplified formulas and models.
How it is recognised
Close but inexact value or model
Numerical, physical, statistical and everyday forms
An estimate is an approximation from incomplete data; an error is the difference from the truth
Related models
is a kind of - in registry terms
is a kind of - in registry terms, for rounding
is bounded by - the difference from the truth
is studied by - and approximation theory
In practice
Families and kinds
numerical approximation and rounding
approximation of functions and series
physical approximations such as paraxial optics and scale analysis
approximate dates and conventional dates in history
geometric approximations such as approximate centre points
model approximations, with overfitting as a failure mode
Identifiers
symbol approximately equal sign Unicode U+2248
Standards and regulation
ISO 80000 rules for rounding and significant figures
Measurement uncertainty guidance such as the GUM
Standards for reporting approximate dates in cataloguing
Failure modes and hazards
Unstated or underestimated error
Approximations used outside their range of validity
Overfitting in models
Sense confusion with unrelated aliases
Also called
Where this came from
wikidata · CC0 1.0
Drafted structure
Bundle to layer to finding to question, as the second pass will find it: 4 bundles · 8 layers · 8 findings · 16 questions.
Concept What approximation is.
Definition.
Definition
Definition and error.
Definition
Definition.
- What is an approximation, and how is its error defined and bounded? definition
- Is the question about approximation, estimation or measurement uncertainty? boundary
Kinds
Kinds across fields.
Kinds
Kinds.
- What kinds of approximation are used in mathematics, physics, statistics and everyday life? definition
- Which entry fits the specific kind? action
Apply Choosing and reporting.
Computation.
Choose
Choosing an approximation.
Choose
Choose.
- How is an appropriate approximation chosen for a given accuracy and cost? action
- What error applies in the case in question? measurement
Report
Reporting.
Report
Report.
- How should approximations and their uncertainty be reported, per standards? action
- Which references are standard? provenance
Theory Theory.
Theory.
Numerical
Numerical analysis.
Numerical
Numerical.
- How do numerical analysis and approximation theory treat convergence and error? provenance
- Which entry fits numerical analysis? action
Models
Model approximation.
Models
Models.
- How do physical and statistical models approximate reality, and what is overfitting? provenance
- Which entry fits overfitting? action
Context History and teaching.
Context.
History
History.
History
History.
- How did approximation methods develop, from ancient estimates of pi to modern computation? provenance
- Which entry fits the history of mathematics? action
Teach
Teaching.
Teach
Teaching.
- How is approximation taught, and which misconceptions arise? provenance
- Which sources are cited? provenance
What the second pass must settle
- Should approximation theory and rounding be separate entries?
- How should uncertainty standards be linked?
- The registry entry has merged aliases for unrelated concepts such as pressure altitude; should they be removed?