1.0

0.7

0.5

λτ

FIG. 16 Efficiency for the Memory Processes in PC Experiments.

FIG. 17 Data for PC Experiments with Memory Time as a Variable.

where по is a term representing an efficiency loss as a result of internal noise and c is a time constant which may be related to the transducer. The efficiency for an experiment is the product of the three terms producing the number 2E/N. Their respective roles are illustrated in Fig. 16, which shows the relation between ʼn for the experiment and r, the time the measure must be stored in the memory.

cr

The general plan is to determine the curve for 1() from values of r sufficiently long that (1 - e ) can reasonably be expected to be very close to 1.0, and then obtain the value of c. The procedure is not quite as simple as it sounds. All three parameters enter every stage of the fit. A set of results is illustrated in Fig. 17, showing the values of the parameters describing the curve. Eight data points have been used to determine these parameters. In this experiment there were more than 1000 observations per point, although the form of the curve was established from a previous experiment in which there were nine points and three thousand observations per point.

However,

Now we want to carry these parameters into the CW experiment. first let us consider some of the mathematical aspects of starting time uncertainty. In Peterson, Birdsall, and Fox (Ref. 6), this problem was considered as one in which a signal specified exactly might occur in any one of M non-overlapping orthogonal intervals of time. They showed that the detectability of a signal of this sort can be described by the equation

However, it seems intuitively more pleasing to think of time uncertainty as being distributed continuously over time rather than discretely. In this case, M would represent the maximum number of orthogonal intervals which can be included over the time during which the signal might occur. In a study not yet reported, Dennis Fife has simulated this condition. The results show that equation (17) becomes

For the CW

However, in Fife's study M was always at least as large as seven. experiment, the effective 2E/N is considered to be the value of (d')2 obtained

for the particular observer in the PC experiment. I have attempted to describe this data both by Eqs. (17) and (18). The data is plotted in Fig. 18 in two

2E

ways, (d')2 vs and (d') vs (d')2. N

CW

pc

)2. The shift in the position of the

2

curve is to be noted. The plot of the data for (d')2 vs (d')2 can be

CW

pc

described by either Eq. (17) or Eq. (18), with values of M = 4 and 1 M 2 respectively. In the second case, one gets the impression from the data that they would be better described by an exponent somewhere between E/N and

2E/N and one can build a strong argument to show that if M is small, the expofient is a function of M. It is 2E/N if M is one and approaches É/N if M is large. Birdsall and I have looked at the case for M being 1 + E, and the exponent for this case is very close to 2E/N.

The next step in the procedure is to move into the detection experiment using (d') as the effective value of 2E/N. The results are illustrated in Fig. 19. Again the data is plotted in two ways: (d'

(a' det

'det)2

det

2 2E
V8

and

Again the second way can be described by either of the two equations. By the first, M is of the order of 5 or 6, by the second approximately 2. The two equations place bounds on the uncertainty introduced by this observer's memory for the particular experiments conducted, assuming the model. The restricting conditions are a single noise level, a single amplitude for the CW and the PC, and a 2AFC experiment in which a flash of light marks the observation intervals. When the signal occurs, its starting time is coincident with the light flash.

Summarizing the results for this observer and their interpretations:

1) The fact that no = .7 can be interpreted as the observer having a noisy

O

transmission channel which effectively increases the noise introduced in this experiment by a facter of 1.4. The extent to which is a function of the particular value of N employed in this particular experiment was not directly investigated. However, related experiments carried out at our laboratory suggest that is constant over a wide range of noise levels. 2) The transducer time constant used to describe the data is .5 seconds. One might get the impression from other studies reported in the literature that this number is too high. It is possible that the constant is not precisely determined from the data in the experiments I have reported. It is also possible that the constant as determined is not purely attributable to the transducer.

No

3) The value of λ at 2/3 again can be a function of N

It says that in

every 1.5 seconds the cut-off adds a variance equal to that introduced by the external noise used in this experiment. Again this might be a constant over noise levels, or may be a function of the noise level. 4) The 50 millisecond signal appears to be positioned within a time interval extending over as little as 75 milliseconds or as long as 200 milliseconds. 5) The frequency memory in the detection experiment places the 50 millisecond signal within as little as 40 cycles around its 1000 cycle frequency to within a range as great as 100 cycles around its 1000 cycle frequency.

In Fig. 20 there is presented what might be considered a descriptive model of a human observer as he performs in the 2AFC. Prior to the experiment, SW is in position 1. At this time there are several presentations of the signal without noise, and these are fed into the analyzing devices so that parameter values can be stored in the memory. When the experiment starts, SW

goes to position 2. In the first observation interval, SW2 is in position 1

and a value stored in the memory. In the second observation interval,

SW2 is

FIG. 20

Block Diagram of a Descriptive Model of an Observer Which Would
Behave in the Same Way as the Observer Over the Set of Experiments.

moved to position 2. At the end of this interval, both the memory and the output of the likelihood ratio computer are fed to the comparater. The comparison is fed to the decision computer which uses this value to determine a decision.

This paper has been concerned with those operations performed by the blocks enclosed in the dotted lines. There are a number of operations still untouched, and still much to be known about those blocks which have been treated here.

C. D. Creelman, in our laboratory, has been conducting an experimental program on duration discrimination. These studies may furnish the basis for describing a mechanism which measures duration.

In closing, I must point out that there is not necessarily any relation between the nervous system and the descriptive model I have presented beyond the fact that in the experiments I have described they yield similar results. The model describes the data, not the nervous system. It may, however, serve a purpose for one interested in describing some nervous sytem operations.

ACKNOWLEDGEMENT

The work discussed in this paper was initiated under a Signal Corp contract. The later work has been supported by the Operational Applications Laboratory of the Air Force Command and Control Development Division and by the Behavioral Sciences Division of the Air Force Office of Scientific Research. The new memory data was collected under contract AF 49 (638)-369.