Learning objectives
- Critique a figure for encoding, uncertainty, accessibility, and claim scope.
- Explain scales, colormaps, uncertainty displays, annotations, and captions with the formal object.
- Separate evidence, transformation, inference, and limitation.
Terms Developed in Context
These terms form the lecture's reasoning chain from observable through model to a bounded physical conclusion.
- Visual encoding
The mapping of data variables to position, length, color, shape, or other graphical channels. In this lecture it supports the evidence-to-model chain for scales, colormaps, uncertainty displays, annotations, and captions.
Use and relationship: Read it together with Scientific caption and Color map. The governing relation \(information density=encoded variables/visual channels\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.
Boundary: A plot must disclose transformations, units, limits, and uncertainty encodings. This caveat prevents the term from being treated as a unique explanation or a context-free number.
- Color map
An ordered mapping from numerical values or categories to colors. In this lecture it supports the evidence-to-model chain for scales, colormaps, uncertainty displays, annotations, and captions.
Use and relationship: Read it together with Visual encoding and Uncertainty display. The governing relation \(information density=encoded variables/visual channels\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.
Boundary: A plot must disclose transformations, units, limits, and uncertainty encodings. This caveat prevents the term from being treated as a unique explanation or a context-free number.
- Uncertainty display
A graphical representation of measurement spread, interval estimates, covariance, or model variation. In this lecture it supports the evidence-to-model chain for scales, colormaps, uncertainty displays, annotations, and captions.
Use and relationship: Read it together with Color map and Axis transform. The governing relation \(information density=encoded variables/visual channels\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.
Boundary: A plot must disclose transformations, units, limits, and uncertainty encodings. This caveat prevents the term from being treated as a unique explanation or a context-free number.
- Axis transform
A declared mapping such as logarithmic scaling applied between values and plotted coordinates. In this lecture it supports the evidence-to-model chain for scales, colormaps, uncertainty displays, annotations, and captions.
Use and relationship: Read it together with Uncertainty display and Scientific caption. The governing relation \(information density=encoded variables/visual channels\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.
Boundary: A plot must disclose transformations, units, limits, and uncertainty encodings. This caveat prevents the term from being treated as a unique explanation or a context-free number.
- Scientific caption
Text that identifies data, transformation, uncertainty, and the claim supported by a figure. In this lecture it supports the evidence-to-model chain for scales, colormaps, uncertainty displays, annotations, and captions.
Use and relationship: Read it together with Axis transform and Visual encoding. The governing relation \(information density=encoded variables/visual channels\) shows where the concept enters quantitatively; the student should state whether its value is measured, calibrated, adopted, or inferred.
Boundary: A plot must disclose transformations, units, limits, and uncertainty encodings. This caveat prevents the term from being treated as a unique explanation or a context-free number.
Method in context
A figure is an argument with visual premises: the caption must say what is measured, transformed, and model-dependent. Ask what a second researcher needs to reproduce the claim: raw input, processing state, software or database version, and inferential step.
Derivation and assumptions
Define every symbol and explain the failure mode. A method becomes scientific when assumptions are visible enough to be tested.
Worked example
A log-log slope is d log(y)/d log(x); changing axes changes visual sensitivity, not the data.
A plot must disclose transformations, units, limits, and uncertainty encodings. Require an independent recomputation and one perturbation.
Misconceptions and study guidance
Do not confuse a data service with a measurement, a catalog identifier with physical identity, a formal error with total uncertainty, or a polished figure with a validated inference. Reconstruct the evidence chain before interpreting.
Verified reading
Matplotlib Choosing Colormaps; Astropy Visualization documentation.
Use the exact documentation anchor in the reference log and record any access mismatch.