Dimensional Consistency Check¶
Check that quantities, units, and scale relationships are compatible before trusting equations, comparisons, or transfers.
The Diagnostic Story¶
Symptom: A calculation produces a plausible number but nobody can say what units the output has. Raw totals are compared across differently sized entities, percentages and percentage-point changes are used interchangeably, and one-time costs are compared with recurring costs without conversion. A model works in a pilot but fails after rollout, and a dashboard ranking changes dramatically after normalization with no explanation of why.
Pivot: Expose the quantity structure of the proposed expression, test compatibility across units, dimensions, denominators, time bases, and scale meanings, then correct or reject operations that are structurally invalid before they shape decisions.
Resolution: Invalid comparisons are caught before they become evidence. Metrics become more interpretable and auditable, model transfers become safer, and decision confidence is grounded in valid structure rather than the false precision that formal notation can project.
Reach for this when you hear…¶
[biomedical research] “You cannot add absolute risk reduction to relative risk reduction in the same summary table — they look like the same kind of number and they are not.”
[financial modeling] “The model divides an annual revenue figure by a monthly cost figure and calls it a ratio — nobody caught it because the output looked reasonable.”
[urban planning] “We compared transit ridership across cities by total boardings, which made the tiny city look terrible and the huge city look great — you have to normalize by population before the numbers mean anything.”
When This Archetype Applies¶
No catalog groundingNone of the structural conditions is currently represented by an accepted prime or domain-specific abstraction.
Diagnostic problem
A formal calculation, comparison, metric, or rule treats quantities as compatible even though their dimensions, denominators, time bases, scales, or semantic meanings are not aligned.
What this problem means
The structural problem is that formal operations are easier than meaningful operations. A spreadsheet can add columns whose units do not match. A dashboard can rank percentages, totals, and rates side by side. A model can accept inputs with hidden unit conventions. A policy memo can compare regions of very different size without exposing denominators. These artifacts produce numbers that look usable even when the underlying quantities are incompatible.
The dangerous feature is that the error is often invisible. The output may be precise, visually polished, or mathematically sophisticated. Without an explicit compatibility check, reviewers may focus on the conclusion rather than the structure of the quantities that produced it.
Show the applicability expression
Applicability expression2 distinct conditions
groundedpartly groundedopen
2 conditions, all required.
2Required in every casenumbered 1–2
These hold no matter which pattern applies.
Same-unit semantic mismatch · open
Values share a unit label but have different semantic meanings.
The source archetype describes the situation as follows: Values have the same unit label but different semantic meaning. The normalized requirement above isolates the load-bearing portion used in this condition set.
Invalid quantity alignment · open
The semantically different quantities are nevertheless combined or compared without a valid alignment, and a result relies on that operation.
This condition preserves a load-bearing part of the diagnostic problem that was not captured by a source-condition atom. It remains explicit because omitting it would weaken the sufficient condition set.
Other requirements and context (6)
Why these sit outside the expression
Supporting context — it may accompany or help interpret the situation, but it is not a load-bearing condition in a sufficient diagnostic set.
Supporting contextA formula or spreadsheet combines values from different sources.
It is less useful when the main problem is corrupt source data, missing evidence, representational aesthetics, or disagreement about values. In this archetype, the relevant contextual consideration is: A formula or spreadsheet combines values from different sources. It helps interpret the situation or strengthens the practical case for examining the archetype.
Supporting contextTeams compare totals, percentages, rates, indexed values, or normalized scores.
A dashboard can rank percentages, totals, and rates side by side. In this archetype, the relevant contextual consideration is: Teams compare totals, percentages, rates, indexed values, or normalized scores. It helps interpret the situation or strengthens the practical case for examining the archetype.
Supporting contextA metric or model is transferred from one scale, population, jurisdiction, or system to another.
A model, calculation, comparison, metric, or policy rule mixes quantities whose units, dimensions, denominators, time bases, or scale meanings may be incompatible. In this archetype, the relevant contextual consideration is: A metric or model is transferred from one scale, population, jurisdiction, or system to another. It helps interpret the situation or strengthens the practical case for examining the archetype.
Supporting contextA result looks precise, automated, or mathematically formal.
The output may be precise, visually polished, or mathematically sophisticated. In this archetype, the relevant contextual consideration is: A result looks precise, automated, or mathematically formal. It helps interpret the situation or strengthens the practical case for examining the archetype.
Supporting contextA decision depends on a ratio, rate, index, or coefficient.
Use this archetype when a decision depends on a formula, metric, dashboard, model output, benchmark, normalized score, rate, ratio, or cross-context transfer. In this archetype, the relevant contextual consideration is: A decision depends on a ratio, rate, index, or coefficient. It helps interpret the situation or strengthens the practical case for examining the archetype.
Supporting context groundings
A decision depends on a ratio, rate, index, or coefficient.
domainCross Elasticity of Demand— The unit-free ratio of the percentage change in one good's quantity demanded to the percentage change in another good's price — whose sign classifies goods as substitutes, complements, or independent and whose magnitude ranks how tightly they constrain each other's prices.
Coverage
0 of 2 conditions grounded · 2 open.
Mechanisms / Implementations¶
- Unit Check: The first-line check that every input, output, and intermediate expression carries a compatible unit label before a calculation is trusted.
- Dimensional Analysis Table: A worksheet that lists every quantity with its units and base dimensions and tracks how they cancel through a formula, so no scale-dependent term is ever combined blindly.
- Unit Conversion Workflow: Converts every quantity into one shared unit convention before combining them, keeping the conversion factors and assumptions attached to the result.
- Normalized Metric Design: Designs a metric on a comparable basis — indexed, standardized, or denominator-adjusted — so entities of different size or context can be set side by side honestly.
- Per-Capita or Per-Unit Conversion: Divides a total by a clearly chosen denominator — people, units, transactions — turning raw counts into rates so differently sized things can be compared.
- Dimensionless Ratio Construction: Combines quantities into a ratio whose units cancel — a pure number that carries meaning across scales, but only when its parts are chosen to mean something.
- Stock / Flow Separation Check: Separates accumulated stocks from the flows that fill or drain them — balances from rates, prevalence from incidence — so a level is never compared directly with a speed.
- Spreadsheet Unit Audit: Walks an actual spreadsheet cell by cell — columns, hidden intermediate cells, and formula chains — to surface the unlabeled unit and denominator slips that spreadsheets breed.
- Model Input / Output Contract: A written specification pinning the unit, dimension, scale basis, and valid range of every model input and output, so an upstream change cannot silently corrupt a downstream result.
- Cross-Scale Transfer Review: Rechecks whether a metric, rule, or equation that held at one scale still holds after it moves to another — and draws the boundary where its validity ends.
- Finance / Accounting Unit Check: Separates money-like quantities that share a currency symbol but are not interchangeable — nominal vs. real, one-time vs. recurring, cash vs. accrual — before they are added or compared.
- Engineering Equation Sanity Check: Checks a formula and its computed result for both dimensional coherence and physically plausible magnitude before the number is trusted.
Related Abstractions¶
Abstractions this archetype builds on — directly (a source ingredient) or as a related pattern. Links follow the typed catalog namespace.
Built directly on (3)
- Dimensional Analysis: Ensures consistency in units.
- Representation: Model complex ideas.
- Scale: Properties change with size.
Also references 6 related abstractions
- Correspondence Principle: New theories match old limits.
- Engineering Tolerances: Acceptable variation.
- Equivalence Principle: Gravity indistinguishable from acceleration.
- Gauge Invariance
- Scale Invariance: Behavior unchanged under scaling.
- Uncertainty: Incomplete knowledge.
Variants¶
Narrower or domain-specific specializations that share this archetype's core structure. Recognized variants are established; candidate variants are provisional.
Unit Consistency Check · mechanism family variant · recognized
A narrower variant focused on compatible unit labels and conversions across inputs, formulas, and outputs.
Scale Normalization Check · scale variant · recognized
A variant that verifies totals, rates, percentages, indexed values, and normalized metrics are being compared on a compatible basis.
Dimensionless Ratio Design · mechanism family variant · recognized
A variant focused on constructing ratios, coefficients, or indices that remove units or expose scale-invariant structure.
Semantic Quantity Alignment · other · candidate
A candidate variant that checks whether quantities with compatible units actually represent the same construct or decision-relevant meaning.
Cross-Scale Transfer Check · scale variant · recognized
A variant that verifies whether an equation, rule, metric, or comparison remains valid when moved across scale, population, scope, or context.
Stock / Flow Separation · subtype · recognized
A variant that prevents accumulated quantities from being confused with rates or flows over time.
Editorial Notes¶
Problem Classification¶
Classification: Correctness, Conformance & Formal Validity Failure → Quantitative, Dimensional & Transform Consistency
Problem kernel: quantities with incompatible units or bases are combined
Rationale: Dimensions, denominators, time bases, and scale meanings do not support the mathematical comparison being claimed.
Independent corroboration: The earliest necessary condition in the frozen evidence is: A model, calculation, comparison, metric, or policy rule mixes quantities whose units, dimensions, denominators, time bases, or scale meanings may be incompatible. That is a quantitative dimensional and transform consistency problem because Quantities or states are combined under invalid units, measure rules, linear assumptions, scale bases, monetary bases, or transform-linked precision requirements.
Review outcome: Independent reviewer agreement; high confidence.