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November 10, 2003 Liz began this session on the "frustration and mysterious qualities of numbers" by claiming that they are used in (at least!) two ways by physicists: in the context of how the world IS (i.e. there are three families of fundamental particles) and in the context of how we REPRESENT the results of measurements ( i.e. as an exercise in counting). She described her own Ph.D. experiment, which was "all about getting a number"--in this case obtained by counting charged particles while tuning the energy of a laser. When laser light was introduced into a beam of hydrogen molecules, the energy at which the molecule broke apart was indicated by the production of charged particles. In this project, Liz was attempting, as all physicists do, to make a measurement by counting a physical quantity: the number of charged particles produced in a reaction that signified an event at a certain energy. Liz's focus, in this presentation, was on the connection between the numbers we use to count physical things and the theories we use to express them in terms of mathematical models (what--picking up from last week's session on the Pythagoreans--she called "the Platonic world"). These were the major points she wanted to make about measurement in physics:
Physicists use numbers to talk about how they know; they write down equations to describe motion. Those measurements, put in a larger framework and compared to other measurements, give a self-consistent picture of the world--one that includes a number of mysterious numbers. Why is it, for instance, that there are three--why three?--families of fundamental particles? Why do historians model tensions in terms of dyads (with triangles understood, perhaps, just as "coupled dyads")? Is the number two "fundamental" and "always there"? Do these numbers communicate and represent real measurements? Are we observing numbers that are actually "out there," or are we always using numbers in a relative (comparative) way? What do we have, when we arrive at a "signature," an indication of the property we are trying to probe? Certainly all numbers are a representation of change, in all disciplines: Physics is not about static equilibrium, but about dynamic change; and in literature, plots work the way differential equations do, in accounting for change. But what can we infer from the measurements we make? If we say that objects with a given shape have a certain behavior, is that an interpretation? a prediction? Physicists continually work to construct and improve their apparatus in order to measure the world more precisely, but isn't it an incredible leap of faith (or hubris?) for them to move from that count to claims about reality? Discussion began with the account of a rider on the bus, years ago, known as "Number Two," who said repeatedly, "Two is fundamental. Two is all there is." (Perhaps he was right?) We explored the "disconnect" between what we can perceive (particularly on a molecular level) and the stories we have to tell to make sense of what is happening. There was much discussion of whether all our interfaces with the physical world could be reduced to counting (of individual, quantifiable particles), or whether, on a more "primal level," the brain rather perceives "bigger/smaller/equal to" without actually resorting to counting (we notice, for instance, the quality of brightness in terms of "more light," rather than in terms of numbers of photons coming from one direction). Is this just a matter of noting a threshold? Of acknowledging a sensitivity to frequency of nerve firings? The deep issue here seemed to be one of quantization: is the quantum character of things primary or derived? Are physical structures fundamentally quanitized--that is, appear only in certain configurations at some base level (with us just unable to observe those numbers)? Or are our primary perceptions simply comparisons (in the way a yard stick is always measuring one thing against another)? Are such perceptions always reducible to integers/rational numbers? Or are there things that are "classical," not quantifiable in terms of countable units? Theories in physics are increasingly insisting that everything is quantizable. Does that means that there are no irrational numbers? No irrational values of energy? Can't you take any two points, no matter how close together, and always find a point between them? It was claimed that continuous number lines and quantization (in which measurement can always be done in "chunks," like inches) are incompatible stories, not unifiable. In contrast, descriptions of light as a wave and particles are not conflicting, as two candidate stories about the nature of the world: they are simply products of the same thing seen on different scales--scales which are themselves arbitrary, needing only a "third story" to translate between them. (A project on the work of Richard Feynman suggests as much.) But how can we integrate accounts of general relativity (with its description of continuous space/time, in which a point can always be found between two points) and quantum mechanics (in which space and time are quantifiable)? Is there a fundamental (and shared) set of suppositions that apply? There was some discussion about whether our claims are about the nature of the universe itself, or the nature of the brains that are observing it. When we recognize the equivalence of two models (though total equivalence is never possible) are we recognizing something that is "real" or that we have constructed? What does it mean to apply the Platonic system (closed mathematical concepts) to the physical world? There was considerable effort put into defining the "Platonic world": is it a "fun playground in your mind," with no relation to the real world? Or an ideal system with a (however problematic) connection to the real world? There was much discussion, in this context, of Planck's Constant (=6.626068 A 10 kg/s2 m-34). What, finally, is the relation between phenomena and schema? Liz was insisting on the existence of the physical world; we can "subtract ourselves out of it" and make measurements that are comparative and reproducible. Aren't these stories real, rather than just conventions used, then discarded for newer, more "parsimonious" stories? This, Liz insisted, is the "mystery of numbers": they are NOT just a convenience. Her explanation for the "economy of stories" is their ultimate reference to a physical world--from which the Platonic world is an abstraction. There is a consistant story to be found in the real world, which measurement can describe, and it is the job of physicists to continually cross that boundary. The stories we create in our heads have the capacity to explain the world: this is the easiest way to make sense of the correlation and consistency between measurements made by different people. Any alternative explanation is not as persuasive. Liz ended the session by describing herself as a realist who believes both that reality is out there, and that it has Platonic qualities (that is, is describable in consistent, replicable and sensible--if not simple--ways). This conversation is invited to continue online and will pick up again on a "different level" next Monday, November 17, when David Ross (Economics) will discuss "Bucks, Values and Happiness." Return to Brown Bag Home Page |
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