Too little
Losing the particulars
“It was a large-looking track.”
The description leaves readers unable to tell whether “large” belongs to the object or the drawing.
Exactitude
Keep the particulars that change what a finding means.
Dispositional fidelity to the particulars and limits of what one observes or represents.
Exactitude preserves the relevant detail, degree and limits of an observation. In science, a number, drawing or description should let a reader understand what was actually found. Faithfulness includes uncertainty: extra decimal places cannot create information the observation did not supply.
Exactitude gives a faithful scale for the finding
The footprint in your sketch fills half a page. The real track fits beside the end of a small ruler. Without a scale, your field notes appear to document a bird of alarming proportions. You add the measurement and its limits. The drawing keeps its detail; the imaginary giant departs.
Finding the balance in Exactitude
An enlarged drawing of a tiny track needs information about its actual size.
A fitting response
Faithful detail
“Here is the scale, and this edge was indistinct.”
Size and uncertainty remain visible together.
Pursued too far
Invented precision
“I will give five decimal places so the record looks exact.”
The pursuit of precision produces digits unsupported by the observation.
Accuracy includes saying how well something is known. A carefully bounded approximation can be more exact than a long number.
What Exactitude makes possible
Exactitude lets people compare records made at different times or by different observers. Units, scale, conditions and uncertainty give a finding its usable shape. You can preserve a delicate distinction without making the prose difficult: the important detail is the one that changes how the result should be understood.
Exactitude in ordinary life
A graph axis
Keep units and axis limits visible when moving a graph into a presentation.
A quoted result
Carry the qualification with the claim when summarizing a source; a precise sentence can become misleading when shortened carelessly.
Nearby virtues, different work
Honesty
Honesty aims at truthful representation. Exactitude gives attention to the particulars through which that representation remains faithful.
Diligence
Diligence sustains careful checking; Exactitude determines which distinctions and limits must survive it.
Exactitude and its counterfeits
Counterfeit Exactitude: the immaculate redraw
Replacing an uncertain trace with a clean sharp edge can make the drawing look more exact while removing information. Preserve the blur or state its uncertainty where it affects interpretation.
How to cultivate Exactitude
Record units and scale alongside values or drawings.
Distinguish a measured value from an estimate.
Preserve a qualification if removing it changes the claim.
Try it today
Inspect one graph, sketch or measurement in your own work. Add a missing unit, scale or uncertainty that would help someone interpret it correctly.
Questions worth returning to
- Which detail would change a reader’s interpretation?
- Does my presentation look more certain than my observation?
Quotations and further reading
Seven selections to return to through the week. Follow a source link to read the surrounding passage.
In reasoning upon our observations, the existence and possible amount of quantitative error is always to be allowed for; and the extent to which theories may be affected by it is never to be lost sight of.
John F. W. Herschel · Preliminary Discourse on the Study of Natural Philosophy · § 124
Herschel carries measurement error into the interpretation of a theory. Exactitude keeps the uncertainty beside the number instead of dropping it at the conclusion.
This should be repeated frequently; and after some practice, he should note how many times in a hundred his reading differs from his friend's, and also how many divisions they usually differ.
Charles Babbage · Reflections on the Decline of Science in England · Chapter V, Section 2
Babbage proposes comparing independent readings of an instrument. Counting both the frequency and size of disagreements reveals more than presenting one reading with an immaculate appearance.
In my judgment, there is no mode of exercising the faculty of observation and the faculty of accurate reproduction of that which is observed, no discipline which so readily tests error in these matters, as drawing properly taught.
Huxley values drawing because the representation can be compared with what was seen. A scale on the footprint sketch is part of making that comparison possible.
All the world believes it firmly, because the mathematicians imagine that it is a fact of observation, and the observers that it is a theorem of mathematics.
Poincaré reports an unnamed physicist’s joke about the law of errors. The joke asks each reader to locate the actual basis of a precise-looking rule.
If one sees a star at one instant, and records it, the record of another, of the same thing, is not the same.
Maria Mitchell · Maria Mitchell: Life, Letters, and Journals · Chapter IX
Mitchell introduces differences in observers’ timing, historically called the personal equation. The recording process itself belongs among the particulars of the observation.
In all cases which admit of numeration or measurement, it is of the utmost consequence to obtain precise numerical statements, whether in the measure of time, space, or quantity of any kind.
John F. W. Herschel · Preliminary Discourse on the Study of Natural Philosophy · § 115
Herschel contrasts measurement with misleading impressions of size and distance. The claim is useful here because the enlarged track drawing needs a numerical scale.
… consequently a very small error in observation occasions an enormous error in the determination of quantities at that distance.
Mary Somerville · On the Connexion of the Physical Sciences · Section XXXVI.
Somerville is discussing remote stellar systems. A small observational uncertainty can matter greatly to the inferred quantity; its importance depends on the relation being measured.
Continue through the catalog
Practice this collection
Choose this approved collection as an optional workbook program, or select individual virtues in My Virtues.