Today we celebrate the birthday of Gustav Theodor Fechner. He was born in 1801. Anecdotes have it that he was a late-night owl and that, as a young student, he liked to stay in bed daydreaming in the mornings and was notoriously tardy even for ten-o'clock c.t. lectures (Boring EG, 1970). In the German academic system, the suffix c.t. stands for cum tempore and means that the lecture actually begins fifteen minute past the hour.
He must have spent his time with the right thoughts. At the age of 34, he had completed his M.D. and Ph.D. degrees and was tenured as full professor on his way to become one of the first and most eminent experimental psychologists. He believed that the physical world and our perception of it were complementary and set out to find a mathematical relationship between the physical world and its mental image.
While Fechner began to explore methods to quantify mental work, he became aware of Ernst Heinrich Weber's studies. Weber had asked blindfolded participants to compare packages of differing weight placed in each hand. He observed that the smallest weight that could be judged as different changed in fixed proportion with the weight of reference. The heavier the reference weight, the greater the difference in weight had to be to be noticed. The reported change in sensation Δs was a function of the ratio between the difference in weight Δw and the reference weight W multiplied by a factor r:
Integrating function (1) and substituting weight for stimulus R results in:
where sensation S is a function of the natural logarithm of stimulus R multiplied by factor r plus a constant Smin which constitutes the smallest noticeable difference in R. Hence, sensation S increases in direct proportion with the logarithm of stimulus R with the slope of factor r. Consequently, stimulus magnitude had to be doubled for the increase to be noticed.
In reverence of Weber's work, Fechner called the direct proportionality between sensation and the logarithm of stimulus strength Weber's law, proposing that the relationship may apply to all senses. Confirming his hypothesis, he could provide evidence that Weber's law adequately described the relationship between perceived luminosity and the brightness of stars. He believed that the law might open ways to indirectly measure mental processes, trailblazing a science of quantifying mental activity. Alas mind work remained inferred from the participants' judgment. In acknowledgment of the pioneering contributions to experimental psychology of both men, the law is known as Weber-Fechner law today.
One hundred-fifty years later, the direct measurement of mental processes remains elusive. However, methods have been found to measure cerebral work. Brain cells utilize glucose and oxygen to process information. Both have to be supplied by blood flow on demand, since they cannot be stored in the brain tissue. Thus, local cerebral blood flow increases with the increase in nerve cell activity.
Since the 1940's, Seymour Kety, Lou Sokoloff, and others were working out methods to measure local cerebral blood flow with radioactive tracers, initially at the University of Pennsylvania and later at the National Institutes of Health (Sokoloff, 2000). Around 1970, Lou Sokoloff and others succeeded in developing a method with which the rates of local cerebral glucose utilization could be determined in animals (Sokoloff and others, 1977).
With the advent of Positron Emission Tomography (PET), both methods became widely used in humans. Since then, numerous studies have demonstrated that brain work and blood flow indeed increase in logarithmic proportion with the magnitude of stimulation. Electrical nerve cell discharges known as spikes encode stimulus magnitude. My colleagues and I observed with micro-electrode recordings from nerve cells in the cerebral cortex that the cells are limited in their ability to increase the spike rate with increasing frequency of stimulation. Instead, they dynamically scale down their responsiveness with increasing frequency, while continuing to respond time-locked to the stimuli (Melzer and others, 2006). This ability, known as gain control, may underlie the logarithmic relationship between sensory stimulus, brain cell response and mental perception.
Combining PET with functional magnetic resonance imaging (fMRI), Dettmers and others (1996) were able to show a tight association between stimulus-related increases in local cerebral blood flow measured with PET and the blood oxygen level-dependent (BOLD) signal measured with fMRI. Hence, modern non-invasive tomographic brain imaging methods support that the law of Weber and Fechner may apply to brain work. This is not exactly the outcome Professor Fechner had in mind, but he would certainly find the findings exciting, were he still alive today.
- Boring EG (1970) History of Experimental Psychology. Appleton, New York.
- Dettmers C, Connelly A, Stephan KM, Turner R, Friston KJ, Frackowiak RS, Gadian DG (1996) Quantitative comparison of functional magnetic resonance imaging with positron emission tomography using a force-related paradigm. Neuroimage 4:201-209.
- Melzer P, Sachdev RN, Jenkinson N, Ebner FF (2006) Stimulus frequency processing in awake rat barrel cortex. J Neurosci 26:12198-12205.
- Sokoloff L (2000) Seymour S. Kety. Biographical Memoirs. The National Academies Press. Wash. D.C.
- Sokoloff L, Reivich M, Kennedy C, Des Rosiers MH, Patlak CS, Pettigrew KD, Sakurada O, Shinohara M (1977) The [14C]deoxyglucose method for the measurement of local cerebral glucose utilization: theory, procedure, and normal values in the conscious and anesthetized albino rat. J Neurochem 28:897-916.