Among those of us who remember high school math, there’s undoubtedly a consensus that logarithms are trickier to master than addition. So you might be surprised to learn that our brains process sensory input logarithmically. For example, when the level of light or sound around us builds exponentially, we perceive these large increases as simple arithmetic progressions.
John Sun is part of a team of researchers trying to determine why nervous systems may have evolved in this way. In a new paper, he suggests that processing sensory input logarithmically is advantageous because it reduces the expected relative error, rather than expected absolute error. In other words, if your brain compresses information logarithmically, you’ll be less likely to have errors that are large relative to the value of the data. For example, someone caught in a severe storm may hear multiple claps of thunder. The more claps there are, the less difference it makes whether the person believes he heard one fewer clap than was actually heard. The number is large and the storm severe in either case. For a person who believes the weather outside is calm, however, hearing just one thunderclap is significant. Small errors in counting data become more meaningful when the amount of data is smaller. Under most conditions, a system that stores data logarithmically will reduce these types of meaningful errors.
Sun, a graduate student in the MIT lab headed by professor Vivek Goyal, is the lead author of the paper, which recently appeared in the Journal of Mathematical Psychology. His research initially focused on helping engineers design better information compression systems like those employed in JPEGs and MP3s, but now he hopes his work will help bridge technology and biology. As Lav Varshney, a coauthor of the paper, puts it: “Mathematical models of human behavior are crucial to understanding and improving how people work and make decisions.”
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