Does the Brain Work Logarithmically?

New research suggests it does, when it’s the efficient way to process information

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Steven Cherry: Hi, this is Steven Cherry for IEEE Spectrum’s “Techwise Conversations.”

It seems automatic to us that the midpoint between 1 and 9 is 5, but if you think about it, it’s not at all obvious that that our brains are wired for a linear scale. In fact, in many situations, we perceive the world logarithmically.

It makes sense. The difference between 1 and 3 gazelles, if you’re hunting gazelles, is as important as the difference between 3 and 9—and on a log scale, 3 to the first power is halfway between 3 to the zeroth and 3 squared.

As numbers get larger, logarithms tend to flatten things out, and sure enough, add 20, say, and the difference between 29 gazelles and 23—or even 21—is hardly noticeable at all.

To some extent, this has been known for some time. The Weber–Fechner law, actually two laws, goes back more than 100 years and uses a logarithm in giving the ratio of physical stimuli to perceived intensity. But some new research, published in the Journal of Mathematical Psychology, has found a neurobiological basis for this for the first time. And what’s more, it also theorizes that the brain wiring responsible for it has a correlate when it comes to electronic information systems.

The research team is as diverse as the research: four individuals from three institutions, some with joint appointments. The institutions are the Research Laboratory of Electronics at MIT, the Eaton-Peabody Laboratory at the Massachusetts Eye and Ear Infirmary in Boston, and IBM’s Watson Research Center in Hawthorne, N.Y.; and the individuals are John Sun, Grace Wang, Vivek Goyal, and my guest today, Lav Varshney. Varshney has a research affiliation at MIT and still uses his alumni address for e-mail; he earned his Ph.D. from there in 2010 in electrical engineering and computer science. But his day job is at IBM, and he joins us by phone from his office there in Hawthorne.

Lav, welcome to the podcast.

Lav Varshney: Thanks, Steven. It’s good to be on.

Steven Cherry: Let’s start with the Weber-Fechner law. Now, this says as an actual stimulus increases linearly, the intensity of our perception increases only logarithmically. I’m reminded of a question doctors and nurses ask: “On a scale of 1 to 10, how bad is your pain?” And let me say my sister described hour 22 of giving birth to my nephew, and I know if we call that a 10, I’ve probably never even had a 7. But anyway, is pain the sort of thing that increases logarithmically?

Lav Varshney: So, it’s kind of interesting: The Weber-Fechner law has been around for more than 100 years, as you mentioned. Some of the early work was on perception of things like sound intensity, light intensity, and things like that, but one could also study things like electric shock as a stimulus or saltiness or things like that. And so it’s typically these kinds of physically measurable stimuli that are considered. Pain, on the other hand, is a very different kind of phenomenon. It’s modulated by other factors, and so I would imagine that pain is also felt in some kind of logarithmic kind of scale. There’s no stimulus that goes with it, so it’s kind of hard to characterize in this way.

Steven Cherry: Fair enough. Now, if I understand it, your research shows two key things: first, that it would make sense that the brain is hard-wired this way because it’s more efficient in terms of probabilities, and second, that it’s more efficient in terms of signal transmission. Let’s take these one at a time. And for the first, your paper says that the brain is Bayes-optimal. What does that mean, and is gazelle hunting an example of that?

Lav Varshney: Yeah. So, what it means for something to be optimized in a Bayesian sense is that it’s well adapted to the environment in which it’s operating. And so, if one is on the African savannah hunting a gazelle or if one is looking at the natural distribution of light intensities in the world or the levels of sound intensity, so then your system should be well adapted to that in a probabilistic sense. So your internal representation should be well matched statistically to the outside world. So that’s exactly what we’ve asserted as our optimization principle, and it seems to bear out and provide a nice explanation for a lot of this empirical work.

Steven Cherry: So in the second finding, you found that the brain was acting basically like an efficient signal-processing system in terms of maximizing the information passing through a channel. Is that a fair way to put it?

Lav Varshney: Yeah, that’s right. So both things kind of work together, and so we argue that in certain settings there is coding, like in information theory, and so in that setting in fact it doesn’t matter what the natural stimuli distribution is: Perception should be logarithmic irrespectively. On the other hand, if your signal-processing system is just a scalar quantizer due to, say, latency constraints or something like that, then the distribution should be like the ones that we see naturally occurring for the Weber-Fechner law to hold.

Steven Cherry: So, what would be an example of that in the signal-processing world?

Lav Varshney: So in fact, since the Weber-Fechner law itself is so old, it’s been used, for example, at Bell Labs to design speech coders or coders for television, and so these perceptual coding algorithms, they pretty much rescale things logarithmically before they quantize. And so if you’re doing things like speech where there’s a strong delay requirement, then you would not have access to block coding or other fancier kinds of coding that information theory likes to use. And so there you would need the statistics to be power law distributed like they are naturally. On the other hand, if you’re storing things in memory, you can use fancier coding techniques that do incur delay. And there’s actually strong evidence that human memory does use coding techniques, so that’s a setting where it doesn’t matter what the natural distribution is. So it doesn’t matter if there are three gazelles typically or whether there’s a wide distribution: Anything would be perceived logarithmically there.

Steven Cherry: So you mentioned coding schemes—I guess compression algorithms would be the sort of thing you’re talking about?

Lav Varshney: Yeah, that’s right. By coding schemes I mean algorithms for data compression.

Steven Cherry: So the decibel scale would be another example of this?

Lav Varshney: Yeah, that’s right. The decibel scale for speech and for audio is exactly on a logarithmic scale, so it exactly espouses the principles we put forth for how humans perceive.

Steven Cherry: So this line of research—the parallels, pun intended I guess, between the brain and electronic information systems—I gather your dissertation was about that.

Lav Varshney: Yeah, it was in part. So, my training at MIT was in information theory, though I also did quite a bit of theoretical neuroscience there. And so it turns out there are quite a few parallels, especially when one uses the optimization approach to biology. So it’s kind of a theoretical way of putting forth principles for explaining why biological systems are the way they are. And so if one optimizes a technological system or one argues that a biological system is optimized, one ends up with similar principles.

Steven Cherry: So, how do you expect this to be put to use? Do you think that we’re going to learn more about the brain and understand the biology better? Or are we going to use the biology to design even better electronic information systems? Or both?

Lav Varshney: So, I think this work is mostly scientific, so it’s meant to provide an explanation for why things are the way they are. And in fact, it’s not that the Weber-Fechner law always holds; in fact, there’s deviations from it, and so that’s always been puzzling. And so our theory actually explains some of these deviations as well, so it predicts that there will be a breakdown of the law at the edges when there’s smaller and larger stimuli and also things like plasticity. So there’s been a lot of experiments on people that start using hearing aids, and so their perceptual skills actually change after about a month of usage. And so it provides an explanation that’s unified in this way for all of these phenomena.

Steven Cherry: And it does seem like knowing that would enable you to basically create better algorithms on the sort of computation side.

Lav Varshney: Yeah, that’s right. In fact, John Sun and Vivek Goyal, my collaborators, they’ve been looking at that, designing better quantizers for technological systems.

Steven Cherry: What would be an example of that?

Lav Varshney: So again, looking at, say, a speech coder or a codec for video to do a little bit better on taking advantage of these perceptual principles.

Steven Cherry: And so most of the computation examples so far seem to be directly related to human perception. Are there any other areas where this might be of use? I’m imagining maybe in data mining.

Lav Varshney: Yeah. So actually my work at IBM is all about data and things, and so one interesting example is the perception of price. So in business, you try to price your product in a nice way, but it turns out people often perceive the price of things on a logarithmic scale. And so by knowing kind of the Weber-Fechner aspect of pricing, you can actually do things in a better way.

Steven Cherry: And yet there are sort of hard break points when it comes to pricing. People might not notice the difference between, I don’t know, $2.49, $2.79, $2.99—and then you hit $3.00, and the perception changes quite a bit.

Lav Varshney: Yeah. So psychophysics has different aspects to it. One we’re describing is the scaling, but there’s also framing effects, which also impact things as well. So that’s kind of the reason why things are often $1.99 or $2.99—they’ll try to avoid going over that threshold.

Steven Cherry: Well, Lav, thanks. I think we all suspect the brain is a remarkable piece of hardware and firmware design, one that we have a lot to learn from and about, and we’ll learn it through the work of researchers such as yourself. Thanks for joining us today.

Lav Varshney: Thanks for having me.

Steven Cherry: We’ve been speaking with IBM researcher Lav Varshney about how the brain is efficiently wired to sometimes think with a logarithmic scale—just like electronic information processing systems.

For IEEE Spectrum’s “Techwise Conversations,” I’m Steven Cherry.

Announcer: “Techwise Conversations” is sponsored by National Instruments.

This interview was recorded 18 October 2012.
Studio engineer: Francesco Ferorelli

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