Table 1.

Indices used for evaluating circadian rhythms in human estimations of spans ranging from minutes to hours or days – applicable to “intuitive” (empty) estimations or to “rational” ones (eg, by counting)

Index N	Units entering index	Relation of environmental time to “subject” time when given	Examples
		Estimation of “short durations”
1	Seconds elapsed (during estimation) (seconds estimated not stated)	Environment seconds only (corresponding to fixed N of subject seconds)	eg, 240 seconds (elapsed during count from 1–120)
2	Seconds elapsed (during estimation) Seconds estimated (by subject)	$\frac{\mathit{\text{Environment seconds}}(\mathit{\text{or minutes}})}{\text{Subject seconds}(\text{or minutes})}$	$\text{eg},\frac{240}{120}=2(\text{seconds}\text{per}\text{count})$
3	Seconds estimated (by subject) Seconds elapsed (during estimation)	$\frac{\mathit{\text{Subject}}\mathit{\text{seconds}}}{\text{Environment}\text{seconds}}$	$\text{eg},\frac{120}{240}=0.5(\text{counts}\text{per}\text{second})$
		Estimation of “longer durations”
4	Hours *thought to be elapsed (by subject) Hours *elapsed in environment	$\frac{\mathit{\text{Subject}}\mathit{\text{hours}}}{\text{Environment}\text{hours}}$	$\text{eg},\frac{1}{2}=0.5$
5	Days thought to be elapsed (by subject) Days elapsed in environment	$\frac{\mathit{\text{Subject}}\mathit{\text{days}}}{\text{Environment}\text{days}}$	$\text{eg},\frac{40}{60}=0.667$

^*Notes: Converted to minutes prior to division; Index 1 is simple to record, but has shortcomings: (a) The index does not indicate the time span believed by the subject to have elapsed (“subject time”); it denotes only a span of environmental time, corresponding to a (not stated) span estimated by the subject. Therefore, the time estimated (ie, the equivalent of subject time) must be given separately, with each value. For example, in using the index, one must separately specify the estimation of 120 secs (of subject time) for which a given interval, say of 240 secs (environment time) has elapsed during a test. (b) Since, as indicated above, index 1 does not establish a relation between subject time (not explicitly contained in the index) and environment time, it is not comparable, without transformation, among tests involving even slight differences in the time span estimated by a given subject. (c) The index is inversely related to the passage of subjective time; it will assume a higher value when “subject time” passes more slowly than “environment time” and vice versa. Thus, the index is physiologically somewhat confusing in that a number of other biological variables with which this index might be compared, such as heart rates, assume higher values when a process speeds up and lower ones when it slows down. Shortcomings (a) and (b) above do not apply to indices 2–5. None of the above-listed shortcomings applies to indices 3–5, all constituting ratios of $\frac{\text{Subject}\text{time}}{\text{Environment}\text{time}}$.