The history of psychophysics explains how researchers made the relationship between physical stimulation and perceptual experience experimentally tractable. They varied measurable stimuli, asked people to detect, compare or judge them, and examined the patterns in the responses. The achievement was not a machine that could read another person’s sensations directly. It was a set of methods and arguments that made particular claims about perception open to quantitative investigation.
This guide follows selected developments through Fechner’s 1860 work, nineteenth-century debates about discrimination, Thurstone’s comparative judgement and later questions about scaling and response decisions. Original worked examples explain why a threshold needs a procedure, why a ratio matters, and why the same response can have more than one explanation. All numerical cases are fictional teaching examples. They are not historical datasets, clinical assessments or recommended sensory exposure experiments.
For present-day methods, begin with The Gold Standard of Psychophysics. The Gold Standard master locates the wider collection, while The Gold Standard of Education connects explanation with learning that transfers. The How X Works hub provides routes into the physical and biological systems involved. This is a methodological history with a defined selection of sources, not a complete chronology of every sensory research tradition.
Choose your psychophysics history route
Chapters 1–3: Stimuli, Fechner and relative change
Chapters 4–6: Logarithms, thresholds and procedures
Chapters 7–9: Debates, comparisons and scaling
Chapters 10–12: Decisions, instruments and transfer
Chapter index
Stimuli, Fechner and relative change · Chapters 1–3
1. The historical problem: a stimulus is public, an experience is not
2. Fechner’s 1860 project: measurement as a programme of inquiry
3. Weber’s relation: the increment must be compared with its starting point
Logarithms, thresholds and procedures · Chapters 4–6
4. The logarithmic argument: why equal ratios suggest equal steps
5. A threshold is an operational result, not a single magical boundary
Debates, comparisons and scaling · Chapters 7–9
7. James in 1890: discrimination belonged to a wider psychological debate
8. Thurstone in 1927: variability becomes part of comparative judgement
9. Competing scaling forms: logarithms and powers ask different questions
Decisions, instruments and transfer · Chapters 10–12
10. Detection and decision: a response is not a transparent window
11. Instruments, adaptation and the reproducibility of an experience
12. Changed-context exercise: when improved performance has several explanations
Learning projects and source routes · Chapters 13–14
CHAPTER 1 OF 14 · Stimuli, Fechner and relative change
1. The historical problem: a stimulus is public, an experience is not
Two people can inspect the same measuring instrument and agree about its reading. They cannot exchange experiences in the same way. One person’s report that a light looks bright does not place that brightness on a shared physical scale. Psychophysics begins with this asymmetry and develops procedures for studying it without pretending it has disappeared.
Separate four things from the start: the physical stimulus, the conditions of presentation, the perceptual process and the response. A patch on a screen has a measurable luminance, but its appearance also depends on its surroundings and the observer’s state. A spoken answer adds another layer: the observer has to understand the instruction and choose how to describe or classify the experience.
A simple comparison with three possible questions
Imagine two printed grey patches. Asking which one is lighter is a discrimination question. Asking whether a faint patch is present is a detection question. Asking how much lighter one appears is a scaling question. These questions can use similar materials while requiring different evidence and different interpretations of the answers.
An archive that preserves only “correct responses” may hide this distinction. Correct according to what task? Were there two alternatives, several alternatives or a yes–no report? Was the observer comparing simultaneous patches or remembering an earlier one? A historical measurement becomes intelligible only after those procedural details have been recovered.
The first useful habit is therefore to reconstruct the observation before praising or criticising the conclusion. Identify what the investigator changed, what the observer could perceive and what response was recorded. Then ask which inference joins them. This habit will recur throughout the guide because it is the practical link between reading old experiments and understanding modern ones.
The companion How Vision Works follows the visual system from light to perception. It helps explain why a physical input and a perceptual outcome are connected through a biological system rather than being interchangeable descriptions of the same quantity.
CHAPTER 2 OF 14 · Stimuli, Fechner and relative change
2. Fechner’s 1860 project: measurement as a programme of inquiry
Gustav Theodor Fechner’s Elements of Psychophysics appeared in 1860. The selected sections available in Herbert Sidney Langfeld’s 1912 translation discuss both the measurement of sensation and the relation between a fundamental formula and a measurement formula. The edition matters: an English passage in this collection is a later translation of selected sections, not the complete original German work.
Fechner’s text is more qualified than a slogan about a universal law might suggest. It recognises limits to Weber’s law and argues that measurement methods remain useful where a particular simple relation fails. That distinction is central to the history. A scientific programme can survive the failure of one proposed formula if its methods still allow alternatives to be tested.
Read the argument in layers
The first layer concerns observations: how changes in stimulation relate to discriminable changes. The next concerns assumptions about how those differences can be represented. A further layer connects the resulting expression with a scale of sensation. Each step deserves examination. A successful calculation at the last step cannot retroactively turn every earlier assumption into an observation.
Consider a fictional researcher who finds that the increment needed for a chosen discrimination performance grows with the starting intensity. That finding could motivate a relative-change model. It would not immediately demonstrate that each discriminable step is an equal unit of subjective magnitude. The second claim adds an interpretation of the units.
This is why the history is useful beyond remembering a publication date. It teaches the reader to locate where an empirical regularity becomes part of a measurement theory. When reading a modern graph, ask the same question: which quantities were directly recorded, which were estimated, and which were defined through the model? The distinction does not make models useless. It makes their results inspectable and their limitations discussable.
Fechner’s work is an important starting point for this route, but “starting point for this guide” should not be confused with “first human attempt to compare sensations.” Historical scope is a choice that should remain visible.
CHAPTER 3 OF 14 · Stimuli, Fechner and relative change
3. Weber’s relation: the increment must be compared with its starting point
In the selected Fechner text, Weber’s law provides a major point of departure. A common working expression for a difference threshold is ΔI/I = k: the required increment ΔI is proportional to the baseline intensity I within a range where the approximation is useful. The constant k is a ratio for the specified task and conditions, not a universal number shared by every sense and observer.
Worked calculation: constant fraction, changing increment
Assume a fictional discrimination task has a Weber fraction of 0.04 over the range being studied. At a baseline of 50 arbitrary physical units, the predicted increment is 0.04 × 50 = 2 units. At a baseline of 200 units, it is 0.04 × 200 = 8 units. The absolute increments differ, while the relative increments are the same: 2/50 = 8/200 = 0.04.
Now suppose an investigator compares an increment of 4 units at both baselines. That increment is 8% of 50 but only 2% of 200. Under the stated model, the two comparisons should not be expected to produce the same discrimination performance. “The change was the same” is true in absolute units and misleading in relative terms.
This example is a mathematical illustration, not a measured constant for weight, brightness or sound. An actual experiment would have to define the response criterion used to estimate the difference threshold, calibrate the physical stimulus and examine the range over which the ratio remained approximately stable.
Diagnostic and repair
When a historical report appears to violate a simple proportion, first check whether the baseline, units, task or conditions changed. If those checks do not explain the discrepancy, retain the discrepancy. Do not redefine the observation merely to preserve the law. Fechner’s own discussion of limits makes room for asking where a relation works and where another description is needed.
The transferable lesson is to inspect denominators. A difference can be small in raw units and large relative to a baseline, or the reverse. This is a general mathematical habit, but here it arose within a specific problem about discriminating stimulation.
CHAPTER 4 OF 14 · Logarithms, thresholds and procedures
4. The logarithmic argument: why equal ratios suggest equal steps
Fechner’s selected mathematical discussion connects small relative stimulus increments with sensation increments and then considers the corresponding logarithmic relation. In modern notation, the proposed form can be written S = K ln(I/I₀), where I₀ is a reference threshold and K sets the scale. This notation is used here to explain the structure of the argument, not to claim that the formula is an unrestricted law of every sensory experience.
The logarithm has a useful property: multiplying its input by a fixed factor adds a fixed amount to its output. That is why it can represent equal relative changes as equal steps. The calculation is exact mathematics. Whether the representation describes particular perceptual data remains an empirical and interpretive question.
Worked calculation with an explicit reference
Let I₀ = 10 and K = 1 in fictional units. At I = 10, S = ln(1) = 0. At I = 20, S = ln(2), approximately 0.693. At I = 40, S = ln(4), approximately 1.386. At I = 80, S = ln(8), approximately 2.079. Each doubling adds approximately 0.693 to the modelled value.
The physical increments are 10, 20 and 40. The modelled increments are equal. This is the distinction that the logarithmic representation captures. Changing the logarithm’s base would rescale the coefficient; it would not change the underlying equal-ratio structure.
The reference inside I/I₀ also matters. A logarithm is applied to a dimensionless ratio, not to an unexplained number bearing a physical unit. If the physical unit changes consistently in both numerator and denominator, the ratio remains unchanged. Forgetting the reference can make a formula look simpler while making its interpretation less clear.
Do not extend the example below the stated reference and announce negative conscious experience. The expression and its interpretation have a domain. Historical equations should be read with their boundary conditions, just as current equations should. A model that provides a useful account in one region need not be an adequate account at every possible intensity.
CHAPTER 5 OF 14 · Logarithms, thresholds and procedures
5. A threshold is an operational result, not a single magical boundary
The word threshold invites a misleading picture: below one exact value nothing is perceived; above it perception is certain. Repeated responses often require a more careful description. A threshold estimate depends on the task, the chosen performance criterion and the procedure used to gather observations. The modern Psychophysics guide develops this distinction in detail.
For historical reading, recover what crossing the threshold meant in the original procedure. Did the observer first say “yes” during an increasing sequence? Did a specified fraction of trials receive correct responses? Was the value an average across several runs? Those definitions can produce different numbers even when the subject of investigation is similar.
Worked case: interpolate only after naming the criterion
Suppose a fictional two-alternative task produces 14 correct responses out of 20 at intensity 6 and 16 out of 20 at intensity 8. The observed proportions are 0.70 and 0.80. If the chosen threshold criterion is 0.75, a straight-line interpolation between these two observations gives intensity 7.
That answer depends on the interpolation rule and the criterion. It is not a directly observed event at intensity 7, and twenty trials at each level leave sampling uncertainty. A fitted curve could give a different estimate, especially if additional observations showed curvature. Reporting “threshold = 7” without these qualifications would hide how the number was obtained.
The chance baseline also matters. In a balanced two-alternative task, random guessing produces 50% correct on average. A 75% criterion is therefore not equivalent to 75% “yes” in a yes–no task. The response categories and opportunities for guessing differ.
The repair is straightforward: attach the operational definition to the number. A historical table becomes much more useful when its entries are described as estimates under a particular method. That wording preserves the achievement of measurement while preventing an estimate from becoming a context-free property of a person.
CHAPTER 6 OF 14 · Logarithms, thresholds and procedures
6. Order, expectation and the organisation of trials
A stimulus sequence is part of an experiment. If intensity rises on every trial, the observer may anticipate that the next presentation will be easier to detect. If the same comparison is always shown second, memory and order can become entangled with the physical difference. Historical apparatus and instructions therefore deserve as much attention as the final formula.
This chapter uses a modern reconstruction exercise rather than attributing one universal procedure to all nineteenth-century researchers. The aim is to show what kinds of information a reader needs to evaluate an older threshold estimate. A diagram of an instrument is not enough if the record omits how it was operated.
Worked case: averaging two directions
Imagine an increasing sequence in which an observer first reports a target at level 9. In a decreasing sequence, the observer last reports it at level 5. A simple midpoint summary is (9 + 5)/2 = 7. The arithmetic is correct. But it does not establish that either sequence measures an unchanged, sharply defined boundary.
The four-unit difference between directions is evidence to investigate. Anticipation, persistence in a previous response, adaptation, timing or other procedural differences might contribute. The midpoint does not identify which explanation is responsible. Repeating the sequences and varying their order would provide more information than calculating additional decimal places from the same two values.
If a historical account reports only the midpoint, say what cannot be reconstructed. If it supplies the trial sequence, examine whether the responses show systematic patterns. A useful analysis can remain descriptive when the available evidence does not support a stronger causal conclusion.
This distinction also changes how we think about precision. More careful arithmetic cannot compensate for an undocumented procedure. A number reported to three decimal places may contain less interpretable information than a coarser value accompanied by clear instructions, calibrated settings and complete response records. The history of experimental method is partly the history of making those conditions available for others to inspect.
CHAPTER 7 OF 14 · Debates, comparisons and scaling
7. James in 1890: discrimination belonged to a wider psychological debate
William James’s 1890 chapter on discrimination and comparison places the problem within a broad discussion of psychological theory. The chapter also discusses Fechner’s work. Its importance for a historical reader is that a quantitative proposal entered a field of arguments about attention, comparison and the structure of experience; it did not circulate as a detached equation accepted in silence.
Read a contemporary discussion differently from a modern retrospective summary. James is a participant in the intellectual world being investigated. His descriptions and criticisms are evidence of that discussion, not an automatic final verdict on every issue. A later reader should distinguish the account of another author’s position from James’s own evaluation of it.
A source-reading exercise
Take a paragraph that describes an experiment and another that argues about its meaning. In the first, underline the observable actions: a stimulus is presented, a comparison is made, an answer is recorded. In the second, identify the proposed explanation. If the explanatory paragraph adds a claim about the nature of sensation, mark that addition explicitly.
Now ask whether the observation could be compatible with more than one explanation. A participant’s difficulty distinguishing two stimuli might involve the sensory information, attention to the relevant dimension, memory for the first presentation or the decision rule. Listing alternatives does not prove they all mattered. It shows what the experiment would need to distinguish before one explanation became compelling.
This exercise avoids two unhelpful readings of history. One treats disagreement as proof that no knowledge was gained. The other treats a famous author’s confidence as sufficient evidence that the matter was settled. Productive disagreement can expose hidden assumptions and motivate a better procedure.
For a learner, the deliverable is a short argument map: observation, interpretation, alternative and proposed discriminating test. That is more useful than memorising which historical figure “won” a debate whose terms and evidence changed over time.
CHAPTER 8 OF 14 · Debates, comparisons and scaling
8. Thurstone in 1927: variability becomes part of comparative judgement
Louis L. Thurstone’s 1927 paper, A Law of Comparative Judgment, developed a quantitative treatment of comparative responses. It considered examples extending from physical stimuli to judgements of specimens and discussed different simplifying cases. Variability across judgements became part of the representation rather than merely an inconvenience to be ignored.
The historical connection with psychophysics is clear: comparisons can supply evidence for a scale, but the move from responses to scale values requires assumptions. A count of preferences is an observation. A distance on a psychological scale is a result of a model applied to such observations.
Worked case: the same count can come from different designs
Suppose A is judged brighter than B in 24 of 40 comparisons. The observed proportion is 24/40 = 0.60. If forty different observers each made one comparison, the result summarises variation across those observers. If one observer made forty comparisons, it summarises that person’s responses across occasions. If ten observers each made four comparisons, both sources of variation may matter.
The numerator and denominator are identical in all three descriptions. Their evidential meaning is not. Treating repeated responses from one person as forty independent people would change the interpretation of uncertainty and generalisation. Conversely, a group average can conceal meaningful differences between individual response patterns.
The count does not show that A contains 60% more light, appears 60% brighter or is brighter for every observer. Those are different claims. To move towards a modelled scale, specify the task, sampling, dependence structure and assumptions connecting comparison probabilities with positions on the scale.
For historical work, inspect how the original investigator combined observations. A table of pooled responses may be adequate for one question and insufficient for another. The modern lesson is not to distrust aggregation automatically, but to retain enough information to know what was aggregated and why.
The neighbouring History of Psychometrics follows related questions about scoring, constructs and validity in psychological and educational measurement.
CHAPTER 9 OF 14 · Debates, comparisons and scaling
9. Competing scaling forms: logarithms and powers ask different questions
The bibliographic record for S. S. Stevens’s On the Psychophysical Law identifies its publication in Psychological Review in 1957. It is a useful later landmark in the history of scaling. The calculation below compares mathematical forms as an original teaching exercise; it does not reproduce Stevens’s experimental results or assign an empirical exponent to a particular sense.
A power form can be written P = aIⁿ for positive I, with coefficient a and exponent n. A logarithmic form can be written S = K ln(I/I₀). They transform changes differently. Under the power form, multiplying intensity by a factor r multiplies the modelled response by rⁿ. Under the logarithmic form, the same multiplication adds K ln(r).
Worked calculation: quadrupling input under a power model
Let a = 1 and n = 0.5 in a fictional model. At intensities 4, 16 and 64, the predicted values are 2, 4 and 8. Multiplying the input by four doubles the output. If instead n = 1, multiplying the input by four multiplies the output by four. If n = 2, it multiplies the output by sixteen.
These are properties of the chosen functions. They do not establish which function fits observations, whether the scale permits ratio interpretations, or whether the same parameters hold across conditions. A polished curve can be mathematically coherent and empirically inappropriate.
To compare candidate models, first make the response task explicit. Direct numerical judgements, pairwise choices and threshold estimates are not interchangeable datasets. Then inspect the range of inputs, the fitting method and the departures between observations and predictions. A narrow range may make different curves look deceptively similar.
Historical debates about psychophysical laws should therefore be read as debates about observations, procedures and measurement assumptions as well as equations. Do not turn the history into a simple replacement story in which one formula instantly made every earlier question disappear. Different tasks can continue to demand different explanations and different forms of evidence.
CHAPTER 10 OF 14 · Decisions, instruments and transfer
10. Detection and decision: a response is not a transparent window
The established Psychophysics root introduces a modern distinction between sensitivity and response strategy. It is a useful endpoint for this historical route: researchers must account for how an observer decides what answer to give under uncertainty. This chapter explains that distinction through counts, without claiming a complete history of signal detection theory or assigning an unverified priority date.
Worked case: more detections, but also more false alarms
In a fictional task, there are fifty target-present trials and fifty target-absent trials. Observer A says “present” on forty target-present trials and twenty target-absent trials. Observer B says “present” on thirty target-present trials and five target-absent trials. A’s hit rate is 40/50 = 0.80 and false-alarm rate is 20/50 = 0.40. B’s corresponding rates are 0.60 and 0.10.
It would be incomplete to declare A better solely because A detected more targets. A also reported targets more frequently when none was presented. The two rates must be considered together, and a formal sensitivity comparison would require a specified model. The example does not calculate such a parameter.
The instructions can also matter. Asking observers to report anything they might have noticed differs from asking them to respond only when confident. The physical presentation can remain unchanged while the balance of responses shifts. Whether that happened in an actual study requires evidence; it should not be assumed from the result alone.
For an old detection report, look for trials without the target, the wording of instructions and the consequences attached to errors. If only successful detections survive in the record, explain why a fuller evaluation is impossible. Missing observations should not be silently treated as zero false alarms.
The repair is to preserve the full outcome structure. A yes–no task has more to tell us than one total of correct responses. Its mistakes can help identify the assumptions behind an interpretation, which is why experimental records are part of the knowledge rather than disposable material left over after a summary has been computed.
CHAPTER 11 OF 14 · Decisions, instruments and transfer
11. Instruments, adaptation and the reproducibility of an experience
An apparatus produces a stimulus under conditions. It does not deliver a context-free experience. A historical study may specify a physical setting precisely while leaving uncertain the viewing distance, background illumination, timing, observer preparation or maintenance of the instrument. Those omissions limit what can be reconstructed.
The same concern applies when an old experiment is simulated on a modern screen. A digital setting is a command to a device, not a measurement of the physical output reaching the observer. The display, ambient conditions and presentation geometry can change the stimulus. Reproducing the appearance of an apparatus in a diagram is therefore different from reproducing its measurement conditions.
Worked geometry case
Imagine a small target of height 1 centimetre viewed from 100 centimetres. For small angles, its angular size in radians is approximately height divided by distance: 1/100 = 0.01 radians, or about 0.573 degrees. At 200 centimetres, the same target subtends approximately 0.005 radians, or 0.286 degrees. The physical target did not shrink; the angle at the observer changed.
A claim that the “same target” was used is consequently insufficient for a question sensitive to angular size. The approximation is suitable for these small ratios, and it is explicitly an approximation. A reconstruction requiring greater accuracy would use the appropriate geometry and a clear definition of the target’s position.
For a practical audit, record the intended physical variable, how it was measured, the presentation conditions and what could drift. If a value cannot be recovered from the archive, identify it as unknown. Sensitivity analysis can then ask how conclusions would change over plausible values, rather than choosing one silently.
This approach respects the historical achievement without demanding that every old record contain modern documentation. It also resists the opposite mistake: assuming a computerised procedure is automatically more reproducible simply because its settings are stored in a file. The file must still be connected to a verified physical presentation.
CHAPTER 12 OF 14 · Decisions, instruments and transfer
12. Changed-context exercise: when improved performance has several explanations
A fictional researcher compares performance before and after practice on a visual discrimination task. The proportion correct increases from 30/40 to 36/40: from 0.75 to 0.90, a rise of 0.15, or fifteen percentage points. The researcher concludes that practice improved perception. What additional information is needed before accepting that explanation?
Begin with the observation. Performance on the recorded task improved. That is a defensible description of the two proportions. A claim about the underlying change is stronger. The observer might have learned to use a relevant visual cue, understood the response mapping better, become more familiar with the task, or benefited from a changed stimulus presentation. The proportions alone do not select among these possibilities.
Introduce a changed condition
Suppose the second session also used larger targets. Chapter 11 showed how a changed viewing geometry can alter the stimulus even when the nominal task remains the same. The practice comparison now combines at least two changes. Keeping the target size constant in a further comparison would address one ambiguity, but other design questions would remain.
Now suppose performance improves on the practised orientation but not on a new orientation. That pattern would be informative about the scope of the observed improvement. It would not justify saying that the observer’s entire visual system improved, nor would it make the original improvement worthless. Transfer needs its own observations.
The Perceptual Learning guide provides a practical continuation into learning to extract relevant information. Use it alongside the historical habit developed here: define the task, preserve the conditions and distinguish demonstrated performance from a proposed mechanism.
The exercise is complete when the answer contains both a positive finding and a boundary. “Accuracy increased from 75% to 90% in these sessions; the design does not isolate practice from the change in target size” is stronger than either an inflated success claim or a blanket dismissal. It says exactly what was learned and what a better comparison should resolve.
CHAPTER 13 OF 14 · Learning projects and source routes
13. Build a small historical investigation
Choose one question narrow enough to answer with accessible sources. For example: how does Fechner distinguish the limits of Weber’s law from the possibility of measurement? Or: what assumptions connect a comparative response proportion with a scale? A focused question produces a more useful investigation than a list of every scientist associated with perception.
Begin with the primary text and identify the edition. For Fechner, the linked page contains selected sections translated in 1912 from the 1860 work. For James, the linked chapter belongs to the 1890 Principles of Psychology. For Thurstone, identify the 1927 paper rather than treating all his work as one undated contribution. Publication dates, translations and later reproductions play different roles.
A workable evidence note
Write a short statement of the author’s problem. Next, describe the observations or comparisons involved. Then identify the mathematical or conceptual step used to interpret them. Finish with one limitation stated by the author and one question raised by your own reading. Clearly label which is which; a modern criticism should not be disguised as a historical quotation.
Add one original calculation. You could reproduce the relative-change exercise using different baselines, compare logarithmic increments or show how a threshold estimate changes when the criterion changes. State all assumed values. The purpose is to understand the structure of an argument, not to manufacture a historical result.
Finally, connect the source to a present-day mechanism through the Psychophysics guide or How Vision Works. Explain the connection without claiming that the historical author possessed every later concept. A good comparison recognises continuity in the question while preserving differences in evidence, apparatus and interpretation.
This project can be completed without collecting anyone’s sensory or medical data. It develops mathematical reading, source criticism and experimental reasoning together. Its success is visible in the final note: another reader should be able to distinguish what the source says, what the calculation proves and what remains an open empirical question.
CHAPTER 14 OF 14 · Learning projects and source routes
14. Frequently asked questions and further reading
Is psychophysics the same as psychometrics?
They overlap in questions about measurement, but their emphases differ. Psychophysics centres on relations between physical stimuli and perception. Psychometrics includes broader psychological and educational measurement problems. The History of Psychometrics follows the latter route through tests, score structure and validity arguments.
Did Fechner prove that all sensations follow a logarithm?
No such unrestricted conclusion should be drawn from the selected text. It explicitly discusses limits to Weber’s law and distinguishes the broader possibility of measurement from one formula’s range of usefulness. The logarithmic derivation is important because of its structure and assumptions, not because it removes the need to investigate particular tasks and conditions.
Is a just-noticeable difference an exact universal unit?
A difference threshold requires an operational definition and experimental conditions. It should not be treated as a universal quantity that is identical across tasks, intensities and observers. Nor does successful discrimination alone establish every property needed for a scale of subjective magnitude.
Why are repeated trials needed?
One response cannot describe a response pattern. Repetition helps reveal variability, but the design still matters. Forty responses from one person and one response from forty people address different questions. More observations do not automatically repair a confounded procedure or an unsuitable interpretation.
Can I reproduce historical results with a phone screen?
You can use a screen to illustrate questions and calculations, but reproducing a quantitative result requires control of the relevant physical presentation and procedure. Pixel values alone do not certify luminance, angular size or timing. Treat an informal demonstration as a demonstration unless the required measurement conditions have been established.
Which sources support this route?
Read Fechner’s selected sections for the measurement programme and mathematical argument; James’s discrimination and comparison chapter for a contemporary discussion; and Thurstone’s 1927 paper for comparative judgement. The Stevens publication record identifies the 1957 scaling landmark; it is a bibliographic route, not a substitute for the full paper. The calculations and reconstruction cases in this guide are original teaching examples with explicitly stated assumptions.
Return to the Education parent to apply the same standard to learning: a useful explanation should remain useful when the task changes, and its limits should remain visible when the reader carries it into a new setting.