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No. 3301:
The Dawn of Psychophysics

Today, Gustav Fechner and the mathematics of the senses. The University of Houston presents this series about the machines that make our civilization run, and the people whose ingenuity created them. 


Our eyes and ears tell our brain what is going on in the world. But how is what our senses measure translated into what we perceive?  The field of psychophysics was founded less than 200 years ago to answer this question. 

The German scientist Gustav Fechner was a founder of psychophysics. A few years after starting as a professor in Leipzig in 1834, Fechner studied afterimages, the lingering impressions that remain after we stare at something bright. And Fechner did exactly what we tell our children not to do: He stared directly at the Sun. His eyes became so sensitive that he could neither read nor write. He suffered from insomnia for nearly four years after. Doctors prescribed a hallucinogenic substance which probably only worsened his condition. By all accounts, these four years suffered in near complete isolation were hellish for Fechner. But he emerged transformed – his sight restored, and brimming with new ideas. He wrote on a variety of topics for the rest of his life. 

One of Fechner’s greatest insights was what is now known as the Weber-Fechner Law. Fechner’s mentor, Ernst Weber, already observed that the more intense a sensation, the larger the change required for us to notice a difference. If you hold a one ounce weight in your hand you will notice easily if I add another ounce. But, if you hold a ten pound weight, it is much harder to tell the difference when I add an ounce.   

Fechner took this observation, and extended it. He suggested that our perception of the intensity of a stimulus is proportional to the logarithm of its true, physical intensity. For example, when we double the physical intensity of a sound, we perceive it as less than twice as loud. This law holds approximately in many circumstances, and it was one of the first attempts to mathematically formulate how our minds make sense of the world. 

Fechner also wrote on religion, philosophy and other topics. His ideas influenced many others, but he was often not taken literally. Although they sounded fantastical, his speculations were often right: For example, he suggested that if the two halves of the brain are separated, the patient would have two consciousnesses residing in one body. This far-fetched idea has now received strong experimental support from neuroscientists. Neurosurgeons will split the brain in rare cases of severe epilepsy. When dressing, one such patient would sometimes pull up his pans with one hand, and pull them down with the other. 

Yet Fechner’s most influential idea is that our perception can be studied rigorously, and described using mathematical laws. I may not know exactly what goes on in your mind. But, the work of Fechner and his successors tells us that our minds follow similar rules when making sense of the world. 


This is Krešo Josić at the University of Houston where we are interested in the way inventive minds work.

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This is a good article about how scientific progress often starts with questions that seem to have answers that were obvious at the time: Often, these obvious answers are wrong, or not obvious at all.

Here is an entry on Fechner with more details:  Part 3 describing his breakdown is particularly harrowing. Fechner wrote about his findings in his 1860 book entitled Elements of Psychophysics

For more information about patients whose brain is split by cutting the corpus callosum which connects the two halves, in most cases as a last resort treatment for intractable epilepsy, see Michael Gazzaniga’s work. Here is an early account:


This episode first aired July 9, 2024