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December 8, 2003

Paul Grobstein (Biology)
Quantity, Quality and Value: A View From the Brain

Prepared by Anne Dalke
Additions, revisions, extensions are encouraged in the Forum

Some people suspect that both human behavior and its products (culture among them) reflect the organization of the brain (which, of course, in turn reflects human behavior and its products, including culture). With the objective of encouraging a conversation ranging critically and synthetically over the diverse matters that arose during this semester's consideration of "What Counts?", Paul tried to set a context with a brief discussion of brain organization, suggesting that a preoccupation with number and quantification is not only historically an "add on" but an "add on" developmentally and in terms of brain organization as well. More fundamental (unconscious) brain processes do perfectly well in the absence of modern concepts of number and quantification (the preoccupations of consciousness), and are more directly and meaningfully related to "quality" and "value". Along the way, Paul attempted to illustrate the theory and practice of "qualitative science", as well as to lay to rest unfounded claims that he personally dislikes numbers, statistics, and mathematics (he doesn't) and has a nostalgic hankering for the good old days (he hasn't).

Some relevant materials:
Well, it seemed like a good idea at the time - Charles Murray, NYTimes Week in Review, 30 Nov 2003
Why Americans Must Keep Spending, NYTimes, Business, 1 December 2003
An exchange on science between Peter Beckmann and Paul Grobstein, January 2001
An exchange on mathematics and science between Lisa Chirlian and Paul Grobstein, November 2001
Math learning disabilities

Paul began by summarizing his view of where we started, and where we got to, during the course of our semester's conversations about "What Counts?" He thought that it had been established, to the satisfaction of all, that because both the objectivity and the precision of numbers are context-dependent, it matters how and why one counts. Counting is "frequently done because it can be done," not because it adequately characterizes what we seek to measure. Many examples of this were offered during the course of the semester: numbers do a very poor job of fulfilling the purpose, for example, of evaluating our students. And yet we still feel obligated to use numbers in cases where they do not achieve the objective we want. We have a perception that there is no alternative, but there is one. There is a way for deciding when numbers are useful as a measure, and when they are not.

A very large portion of human history took place without numbers. There are a whole series of capacities within us which are not dependent on numbers; the use of numbers reflects a restricted domain of brain processing. But numbers have certainly played a valuable role in the development of human culture; they can open up worlds not reachable in any other way. Paul showed us, for instance, how we can use numbers to figure the distance between two points in a four-dimensional space. Numbers can be used to make meaningful generalizations into spatial dimensions beyond those which we experience; they may actually lead to better descriptions of reality than those we start with, since we may be living in more than three spatial dimensions. Our sense of being limited to three dimensions is a function of a particular part of our brain. When one of us superimposes his hand on another, however, we are actually operating in six dimensions: we displace our hand in three dimensions, and then rotate it around each of three axes. In doing this, we operate like the pilot of an airplane, who in his landing plans needs to correct not only for distance, alignment and elevation, but also for pitch, roll and yaw. All six of these variables are independent of one another (that is actually the definition of a dimension: an independent variable).

Having established the usefulness of numbers (and how much he believes in their value), Paul went on to claim that only a restricted part of our nervous system is interested in counting: that portion which attends to small numbers of variables. In a very well-known paper published in The Psychological Review in 1956, "The Magical Number Seven, Plus or Minus Two: Some Limits on Our Capacity for Processing Information," George Miller showed that humans can remember about seven numbers. This is not a limit on the ability of the nervous system to judge magnitude, however; we can distinguish a pile of "more" from a pile of "less" (if the amounts are different enough to be noticable--the noticability is logarithmic) without actually having to count all the beans in each pile. This is because the nervous system is composed of two parts which work differently. When the unconscious gathers information from the external world, which leads to action and effects, its distinctive processing signals deal directly with quality and value. It is only the conscious portion of our brain which actually counts (using numbers). Consciousness acts at a remove ("most of the time we are sleepwalking"). Value is always a complex multi-dimensional judgment; we use numbers to reduce it to a few variables and simple causal relations. Valuation becomes, in this account, "like pornography: I know it when I see it." We make most judgments unconsciously, and then try to justify or rationalize them using numbers.

Observing that Paul had given us a "useful story," but "no proof," we turned to the question of why we sometimes use one, sometimes another way of processing information. Paul claimed that numbers become necessary when people are separate enough from one another that they need to resort to approximations of what they value. The alternative to using numbers is to share an unconscious. All of us have both conscious and unconscious systems in our brains; we try to conduct our affairs consciously, but should not overprivilege or become preoccupied with that particular processing style. The conscious mind works quantitatively, using numbers; the unconscious has a different mode of operation: it works qualitatively and does not assign numbers. Godel's proof showed us the fundamental limits of everything with numbers.

Questions were raised about what happens when computers enter this story: they can process lots of variables and then reduce their dimensionality; are they translating them into a form our conscious brains can deal with? Turing's test showed us that we do not yet know if our brains are algorithmic. Consciousness wants to "hear relations," to recognize linear causes and effects. Does doubt come to consciousness from the unconscious? Is it the unconscious which notices missing information? When we perform our research in a play, or to music, trying to make it more entertaining to ourselves or to our audience, are we challenging the limits of communication among conscious minds, trying to speak to or activate the unconscious in our audience?

This conversation is invited to continue online. It will resume at noon on Thursdays in the Spring Semester, under a new rubric: "Information, Meaning and Noise: What's the Difference?" We hope you can join us then.

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