What number is halfway between 1 and 9? Is it 5 — or 3?

A new information-theoretical model of human sensory perception and memory sheds light on some peculiarities of the nervous system.

Ask adults from the industrialised world what number is halfway between 1 and 9, and most will say 5. But pose the same question to small children, or people living in some traditional societies, and they're likely to answer 3.

Graphic: Christine Daniloff

Cognitive scientists theorise that that's because it's actually more natural for humans to think logarithmically than linearly: 3° is 1, and 3² is 9, so logarithmically, the number halfway between them is 3², 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.

In a paper that appeared online last week in the Journal of Mathematical Psychology, researchers from MIT's Research Laboratory of Electronics (RLE) use the techniques of information theory 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 new work was led by John Sun, a graduate student in Vivek Goyal's Signal Transformation and Information Representation (STIR) Group at RLE. Joining Sun and Goyal on the paper are Lav Varshney, a researcher at IBM's Watson Research Center and a former graduate student in Goyal's group, who remains a research affiliate at RLE, and Grace Wang, formerly a neurophysiologist at the Massachusetts Eye and Ear Infirmary.

Usually, STIR members research signal-processing problems in areas such as optical imaging or magnetic resonance imaging. So publishing a paper in a psychology journal might seem a little out of character.