Alan Sondheim on 21 Nov 2000 00:49:59 -0000 |
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[Nettime-bold] Bridging |
- Bridging from Albert A. Bennett, The Interpolational Polynomial, in Bennett, Milne, and Batement, Numerical Integration of Differential Equations, 1931. "If, as often happens in engineering problems, a function is adequately given by two separate simple algebraic formulas over adjoining parts of the range, a single polynomial of low order may afford a poor method of representing the situation even approximately. Thus if one is given the table," [Which can be summarized: As x takes successive values from -5 to 5, y successively equals 0,0,0,0,0,0,1,2,3,4,5.] "then, by the use of a single polynomial, the value assigned to y at x = -6 is zero if one uses only the data from x = -5 to x = 0 inclusive. Using all the given data, however, one obtains y = 126 at x = -6. Similarly one obtains y = 798 at x = -7. Similarly one has for x = 6 y by the polynomial the value 132. These 'unreasonable' values are not confined to the results of extrapolation. The polynomial gives as the value of y at x = -4.5 the number -22. In examples of this sort, the engineering practice of using an 'easement' or 'transition' curve or 'bridging formula' over a critical region without regard to distant portions of the table is to be recommended for purposes of graduation or subtablation, if the evidence seems to justify a smooth graph. If a concentrated irregularity is to be preferred, interpolation formulas should be applied to the two sides of the break separately, ascending differences being used above the break, descending, below." This very critical example is intimately tied to the bundling of heuris- tics used in practice and salvaging natural law, described by Nancy Cart- wright in How the Laws of Physics Lie. I often use the example of x = 0,1,2,3,4,... and y = 0 except for, say, x = 84927, when y = 1. This may be the case on one hand with noise or random error; on the other, the ratio is meaningful - generates meaning - in particle physics experiments. (The whole phenomenology of meaning in relation to theory, organism, anom- aly, and domain is at work here.) Given the latitude of the real, in other words, meaning and interpretation are found at the heart of facticity. Although this is clearly evident in postmodernity studies, it's interesting to find it treated as a minor but prevalent problem, circumscribed as 'bridging,' in 1931. Think of it this way. There is no bridge, no gap; within the bridge or gap, meaning is generated - and it is meaning which has generated (the perception of) the bridge or gap as well. Resident in organsim, meaning is the weighted, cathected, intended real. Think of it this way: the real as shamed, smudged, spoiled - therein lies the boundary, culture and civil- ization as well. The bridge as bridging transcendentals is problematic; the bridge as meaning's interstice provides space and place for signifier and signification. It's the mouth. It's always the mouth. _ _______________________________________________ Nettime-bold mailing list Nettime-bold@nettime.org http://www.nettime.org/cgi-bin/mailman/listinfo/nettime-bold