The MIT press release, What number is halfway between 1 and 9? Is it 5 or 3?, doesn't mention Decibels; however, since Decibels are logarithmic, I felt it justified my headline. Adults from the industrial world answer “five,” but when small children and people living in traditional societies were asked the same question they were likely to answer with “three.”
According to the MIT release: “Cognitive scientists theorize that's because it's actually more natural for humans to think logarithmically than linearly: 3^0 is 1, and 3^2 is 9, so logarithmically, the number halfway between them is 3^1, or 3. Neural circuits seem to bear out that theory. For instance, psychological experiments suggest that multiplying the intensity of some sensory stimuli causes a linear increase in perceived intensity.”
Researchers from MIT's Research Laboratory of Electronics used the techniques of information theory in a paper that appeared on-line last week in the Journal of Mathematical Psychology to “demonstrate that, given certain assumptions about the natural environment and the way neural systems work, representing information logarithmically rather than linearly reduces the risk of error.”
The work was led by John Sun, a graduate student in Vivek Goyal's Signal Transformation and Information Representation (STIR) Group. The Group's work typically focuses on signal processing problems in such areas as optical or nuclear magnetic resonance imaging.
“Although this problem seems very removed from what we do naturally, it's actually not the case,” said Sun. “We do a lot of media compression, and media compression, for the most part, is very well-motivated by psychophysical experiments. So when they came up with MP3 compression, when they came up with JPEG, they used a lot of these perceptual things: What do you perceive well, what don't you perceive well?”
The MIT release further noted: “If you're trying to store data in memory, a logarithmic scale is optimal if there's any chance of error in either storage or retrieval, or if you need to compress the data so that it takes up less space. The researchers believe that one of these conditions probably pertains--there's evidence in the psychological literature for both--but they're not committed to either. They do feel, however, that the pressures of memory storage probably explain the natural human instinct to represent numbers logarithmically.”
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