On the Relationships between Psychophysical Laws

Professor Yuri Mikhailovich Zabrodin headed the first Russian laboratory of psychophysics at the Institute of Psychology Russian Academy of Sciences (former AS USSR). He founded the leading school of Russian psychophysics, where innovative ideas for world science, an unconventional research paradigm, were developed. The key idea is that there are not pure sensations, but sensory tasks of the subject. Zabrodin gave a modern definition of psychophysics as a branched field of psychology that studies the laws of sensory reflection, human behavior and activity in perception and evaluation of external signals. He developed the mathematical model of an adaptive suboptimal observer (including other models of the sensory process as special cases), the conception of the sensory space internal structure and, in general, a systematic-dynamic approach to sensory processes analysis. On this basis he founded the general theory of psychophysics, which still has no analogues in the world science. The theory united 4 main sections of psychophysics: sensory sensitivity, decision making, subjective scaling and psychophysical laws. The transition functions between the psychophysical methods indices were found, which made it possible to combine them into a common system. The generalized psychophysical law has been deduced, which describes not only the known logarithmic and power forms of the connection between stimuli and sensations values, but intermediate functions as well. Zabrodin’s theory is multilaterally substantiated experimentally. The contemporary psychophysical paradigm of research has been systematically combined with the activity paradigm, differential-psychological one and functional states studies. Zabrodin’s fundamental heritage of in the domestic and world psychophysics is being developed by his followers and is still far from being fully realized in experiments and practice. Yu.M. Zabrodin became a true generator of new ideas in the field of psychophysics.

His works are known in the fields of organizational and economic psychology, management psychology as well as acmeology. Being a deputy director for science for a number of years, Yu.M. Zabrodin did a lot for the organizational strengthening of the Institute of Psychology of the Russian Academy of Sciences. He made the important contribution to the development of the Moscow State Psychological and Pedagogical University, being vice-rector for scientific and educational work, interdepartmental interaction, for more than 15 years. Zabrodin was the great researcher and organizer of the Russian science.

Artur Nikolaevich Lebedev graduated from the Yaroslavl’ Medical Institute. He was the Stalin Scholarship Holder, and also worked as a tractor driver in the virgin lands. In 1960 he received a medical degree with honors and was sent to graduate school in Moscow. A.N. Lebedev initially studied mechanisms of radiation damage to the brain of animals under the leadership of Academician M.N. Livanov and made his Ph.D. thesis on this topic. At the same time, A.N. Lebedev worked as an ambulance doctor, and then as a psychiatrist in the Kremlin hospital under the direction of I.V. Strelchuk. After defending his Ph.D. thesis, he worked at the Institute of High Nervous Activity and Neurophysiology of the USSR Academy of Sciences (AS USSR) in the laboratory of Livanov, where he defended his doctoral dissertation on the topic of trace neural processes in perception and memory. At the invitation B.F. Lomov, Professor Lebedev organized a laboratory of psychophysiology at the Institute of Psychology of the AS USSR in 1973 and was appointed its head. From 2003 to the present, Lebedev works at the same Institute of Psychology (of the Russian Academy of Sciences now) as a freelance chief researcher at the Laboratory of Psychology and Psychophysiology of Creativity. Under his leadership, ten candidate’s and two doctoral dissertations were defended. In 2008 he was elected a full member of the Russian Academy of Natural Sciences. Artur Nikolaevich Lebedev was the main organizer of the 24th annual conference of mathematical psychologists (Moscow, 1993), the permanent representative of the Japanese Society for High Scientific Technologies in Russia. He has several copyright certificates for inventions, his Hirsch index is 10 points. A.N. Lebedev discovered new fundamental laws of psychophysiology with two neural constants, which determine human behavior with high accuracy in a wide range of conditions of his life and activity. According to instrumental assessments of the biopotentials of the human brain, one can calculate with high accuracy the volume of his operative and long-term memory. A.N. Lebedev has developed original psychological tests: “Mirror” and “Seven”, characterized by their simplicity and high validity. A.N. Lebedev continues his fruitful scientific work actively, and we wish him long years more.

On the Relationships between Psychophysical Laws

 Zabrodin Yu.M.^a, Lebedev A.N.^a*

^aInstitute of Psychology, Russian Academy of Sciences, Moscow, Russian Federation

Zabrodin Yu.M.^a, Lebedev A.N. On the Relationships between Psychophysical Laws. In: Advances in Psychophysics. Ed.: H.-G. Geissler, Yu.M. Zabrodin. Berlin: VEB, 1976.

Abstract: The present paper investigates the relationship between the psychological laws of Weber, Fechner, Pierone, Hick and others. Analysis of these is based on the concept of systemic interaction of psychophysical and physiological mechanisms. New psychophysical equations containing variables and coefficients are suggested, which can be interpreted in terms of psychological and neurophysiological events. At the first sight, the known psychophysical laws are little related and some of them appear to be mutually contradicting, such as the laws of Weber-Fechner and Stevens. But in reality, these laws may be interrelated. The analysis of such interrelationship is the aim of our paper. The concept of systemic interrelationship between psychological and physiological processes was used for our analysis (Zabrodin, 1975).

Keywords: Psychophysical Laws, Stimulus Magnitude, Subjective Magnitude,

Alpha Rhythm, Memory Span, Perception Time.

Introduction

• The systemic character of perception

It has been proposed that perception is a systemic psychophysiological process including a decision-making and a choice strategy (Zabrodin, 1970, 1974, 1975) and at the same time is a result of systemic brain activity (Anоchin, 1973) and systemic space organization of oscillatory neuronal processes (Livanov, 1934, 1940, 1972; Lebedev & Lutsку, 1969, 1972, 1973).

In our opinion, stimulus perception consists of detection, discrimination and recognition. On this basis some revealing hypotheses may be formed.

Quantitative data accumulated in the area of neurophysiology can be used for the analysis of psychological processes of perception. Some of these data furnish evidence on the step-like organization of brain-electrical waves.

• Step-like organisation of neuronal processes of perception

Вerger (1929) was the first to discover the striking regularities of human brain-electrical waves (alpha rhythm) and suggested that these regularities were related to mental state. Livanov (1934, 1940) discovered the step-like structure of the brain frequency spectrum. In his experiments in rabbits the smooth changes in frequency of flashes were accompanied by step-like changes in bioelectrical wave frequency. Livanov (1934, 1940) assumed that the configuration of evoked potentials and spindle-like character of changes of Berger alpha rhythm are the result of the summation of brain-electrical waves. Later Wiener (1949) also assumed that attraction and pushing of bioelectrical waves (i.e., their step-like differentiation) are the fundamental processes of brain functioning. Livanov (1972) discovered regular’ interrelationships between the spatial correlation of brain waves and the probability of reflector movements. Only the narrow frequency band is responsible for such a relationship.

The neurophysiological basis of neuronal oscillatory processes and their quantitative description were studied by Lebedev and Lutsky (1969, 1972). The authors constructed a formal statistical model of the electroencephalogram, evoked potential and neuronal impulse activity which permitted them to analyze the psychophysical laws from the neurophysiological point of view. The results of their investigation testify to the possibility of functional quantitative correlation between the electroencephalogram parameters of the human brain and some quantitative characteristics of human perception. The high speed of perception and decision making, which was suggested by Anоchin (1973) and his colleagues (Shvirkov & Alexandrov, 1974), were quantitatively explained.

• The spatiotemporal organization of neuronal oscillation as a physiological basis of psychological processes

The signals which are processed by perception or reconstructed from memory form, in our opinion, evoke systems of coherent oscillations of neuronal activity. Each system of these waves represents a memory engram, which is first produced by the perceptual stimuli and then corrected by the same or other stimuli.

We assume that the narrow band of alpha frequency has close relationship to memory and perception. Step-like differences between two or three alpha frequencies and phases of alpha waves make it possible to calculate the maximal span of the human operative memory:

• H= (1-αρ / αρ) x log2(1-αρ / αρ),

where Н — the capacity of human operative memory in bit,

α — the mean frequency of alpha rhythm (10 Hz),

ρ — the frequency of refracterity (0.01 sec).

This equation and those below have been described in previous papers (Lebedev & Lutsky, 1969, 1972, 1973).

The mean time (in sec) needed for perception of stimuli is:

(2) (d – p) (1 – ρ) / (d + 1) α2ρ,

where d — the number of simultaneously perceived stimuli,

p = 1- αρ / n — the probability of perception of any stimulus without variable delay, where n denotes the number of equiprobable stimuli (or perhaps the number of neuronal engrams) which are compared with perceived stimuli,

α, ρ — see above.

Equation (2) is adequate for optimum conditions of perception. If stimuli are weak (near-threshold), perception delay, or perception time, is functionally dependent on the physical intensity of perceived stimuli.

The probability of perception without delay is:

(3)  p = 1 / (1+ 1/k lgI),

where p — the probability of perception without delay,

к — a coefficient,

I — stimulus intensity in relative threshold units.

The value of sensation of stimulus intensity should fulfil the equation:

(4) ψt = c,

where ψ — the sensation value,

c — a constant.

Equations (1) and (4) were examined in our own experiments and those of others and according to data contained in the literature.

Method

2. Theory and experiment

2.1. The relation of subjective magnitude to stimulus magnitude

The psychophysical laws of Fechner and Stevens are contradictory. The former says that subjective magnitude is related to stimulus magnitude logarithmically whereas the latter says that the relation is a power function. What is it in reality?

Zabrodin (1974) suggested the simplest relationship between them:

(5) dψ / ψz = g dI /I,

where ψ –the subjective magnitude,

I — the physical magnitude, i.e., intensity of the perceived stimulus,

g — a coefficient,

z — a changing exponent.

Equation (5) expresses the Weber-Fechner law, if z = 0,

but Stevens’ law, if z = 1.

If d = 1, i.e., the number of simultaneously perceived stimuli is one, then according to equations (2), (3) and (4):

(6) ψ = (g lgl + с)2,

where с — the constant,

ψ, g, I — see above.

After integration of the both parts of the equation (5) we obtain

(7) (1 / 1-z) ψ 1-z = g 1gI + c

and therefore, using (6) and (7) we get

(8) ψ1/2 = (1 / 1-z) ψ1-z

for the calculation of z, where: 0 < z < 1.

Equation (6) expresses the psychophysical law according to category scale measurement.

2.2. The latency of sensory motor reaction and the stimulus intensity

The empirical equations (9) and (10) (see below) of Pieгоn (1922) and Коssоv (1971) respectively were analyzed together with equation (11), which is derived from equations (2) and (3). Experimental data of Chocholl (1941) were used for this purpose. The results of the analysis are listed in the Table 1.

The theoretical values were estimated according to equations of Pieron (1922), Коssоv (1971) and the present authors:

(9) t = 417 × E ^-0,47 + 50,

(10) t = 264 × 10 ^-E/20 – 0.006 × 10^E/20 + 120,

(11) t = 295 / (1 + 0.085E)² + 10,

where E — intensity of tones 250 Hz,

t — latency, msec.

We can see that equation (11) is fairly exact.

2.3. The interrelationship between operative memory span and perception time

The operative memory span may be defined as the maximum number of character or numerical symbols which are recalled by the subject after simultaneous perception of these stimuli during a 1–2 sec. period. This span may be defined with the help of equation (1). For this purpose, the maximum value of memory H is divided by the information value of one symbol. The result of this division, the value d, is used in formula (2) and subsequently the time is determined which is needed for the perception of one symbol.

Experiments performed in collaboration with I.A. Komarova are summarized in the Table 2.

The experimental span of the operative memory is equal to 23 bits, according to these experiments, but it is 29 bits, according to formula (1). This difference is in our opinion the result of a poor organization of sensory stimuli. This is obvious from another experiment, where the same Ss were able to remember 20–30 bits of information which was organized as a stochastic chain of syllables.

Our results are in accordance with the data of others (see Lomov, 1966).

Conclusions

The results mentioned above show that there is close interrelationship between psychophysical and neurophysiological processes as well as between the psychophysical laws.

Table 1. Theoretical and empirical values of the simple sensorimotor reaction latency

Table 2. The span of operative memory and perception time

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