Time, memory, illusions and mathematics

In a recent post on the Scientific American blog network, George Musser reported on talks given by neuroscientists at a conference, organized by the Foundational Questions Institute on how the brain works to construct our sense of past, present and future.

Musser’s post made some observations that were familiar to me – like the idea that when we retrieve a memory, we also rewrite it since memories are made from “a smattering of impressions we weave together into what feels like a seamless narrative.”  And so we’re actually always retrieving the last one we recollected, calling the accuracy of any memory into question.

But Musser also made mention of work I knew nothing about that uses electric fish to understand something about sensation.  Malcolm MacIver has taken note of the fact that when one of these fish species is hunting, it swims at a thirty-degree angle to its body which, while tripling the water drag, also increases the volume of water sensed by its electric field.  For these fish the volume of the region it can scan is about equal to the volume of the region it can reach directly. They’ve found a way to maximize the range of their perceptions.  But MacIver goes on to explain that for land animals, given how far light can travel, what we can see extends far beyond our immediate grasp.  MacIver imagines that this is directly related to the development of consciousness since it gave our ancestors the opportunity to plan and deliberate before making a move.   I have also thought that changes in primate vision are related to the development of the analytic and deliberative skills that are our nature but I’ve never used electric fish to think about it.

In the end, the observation I found most interesting was the one Musser makes about the talk by David Eagleman.  Eagleman demonstrated that our consciousness lags 80 milliseconds behind actual events.  Musser explains:

the brain tries to reconstruct events retroactively and occasionally gets it wrong. The reason, he suggested, is that our brains seek to create a cohesive picture of the world from stimuli that arrive at a range of times. If you touch your toe and nose at the same time, you feel them at the same time, even though the signal from your nose reaches your brain first. You hear and see a hand clap at the same time, even though auditory processing is faster than visual processing. Our brains also paper over gaps in information, such as eyeblinks.

There are some interesting details cited:

The 80-millisecond rule plays all sorts of perceptual tricks on us. As long as a hand-clapper is less than 30 meters away, you hear and see the clap happen together. But beyond this distance, the sound arrives more than 80 milliseconds later than the light, and the brain no longer matches sight and sound. What is weird is that the transition is abrupt: by taking a single step away from you, the hand-clapper goes from in sync to out of sync. Similarly, as long as a TV or film soundtrack is synchronized within 80 milliseconds, you won’t notice any lag, but if the delay gets any longer, the two abruptly and maddeningly become disjointed. Events that take place faster than 80 milliseconds fly under the radar of consciousness. A batter swings at a ball before being aware that the pitcher has even throw it.

The cohesiveness of consciousness is essential to our judgments about cause and effect—and, therefore, to our sense of self. In one particularly sneaky experiment, Eagleman and his team asked volunteers to press a button to make a light blink—with a slight delay. After 10 or so presses, people cottoned onto the delay and began to see the blink happen as soon as they pressed the button. Then the experimenters reduced the delay, and people reported that the blink happened before they pressed the button.

But, more importantly, Eagleman also points out that physics is built “on top of our intuitions,” and that it begins with sense data. Musser elaborates by saying that physics is built “on a recognition of the limits of perception.”

The whole point of theories such as relativity is to separate objective features of the world from artifacts of our perspective. One of the most important books of the past two decades on the physics and philosophy of time, Huw Price’s Time’s Arrow and Archimedes’ Point, argues that concepts of cause and effect derive from our experience as agents in the world and may not be a fundamental feature of reality.

What I find striking about the whole discussion is that, except for this reference to Archimedes, no mention is made of the role mathematics plays in this endeavor to “separate objective features of the world from artifacts of our perspective.”  Certainly it is true that mathematics is not physics.  But their tight relationship should, at the very least, provide the opportunity to consider the way the mathematics is used to disarm our mental habits, prejudices, and expectations, or how it is that mathematics can reveal sameness, equivalence, where none is perceived.  One of the best pieces of information for me from Musser’s post is the presence of the  Foundational Questions Institute Community where an initiative is driven by individuals asking a number of questions in physics and cosmology.  Among their questions are these:

What is the relationship between physics, mathematics and information? What determines what exists? How “real” is the world of mathematics—and how “real” is the world of matter?

Why does the universe seem so complex, given its simple initial conditions, and the elegant mathematics that describes it? Is life ubiquitous in the universe (or beyond)? How does matter give rise to consciousness—or does it?

The argument is often made that, for the average individual, the value of mathematics can best be seen when we use it to calculate our savings or our mortgages.  A case is point is this suggestion in a recent NYTimes article on math education:

In math, what we need is “quantitative literacy,” the ability to make quantitative connections whenever life requires (as when we are confronted with conflicting medical test results but need to decide whether to undergo a further procedure) and “mathematical modeling,” the ability to move practically between everyday problems and mathematical formulations (as when we decide whether it is better to buy or lease a new car).

While we certainly want students in our education systems to be able to handle these life decisions, if we make no effort to educate them about mathematics itself, we rob everyone of an important opportunity.  Mathematics tells the story of how the body/mind manages to keep looking, at what light cannot illuminate, trying to get past fragmentary perceptions and closer to the whole.  It’s a fascinating story.