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

Ask adults from the industrialized 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.

Cognitive scientists theorize that that’s because it’s actually more natural for humans to think logarithmically than linearly: 3⁰ is 1, and 3² is 9, so logarithmically, the number halfway between them is 3¹, 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.