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237 Notes Chapter 1 1. The applicability of the zero-one rule hinges on the nature of the gain function describing processing time and load utility. If the gain function is linear, then a zero-one rule applies. If the function is curvilinear down, the zero-one rule no longer applies, and partially processed loads become optimal. 2. In chapter 6, it is shown that the second prediction is incorrect. The optimal size for tool blanks is 1.5 to 2.0 the minimum usable portion, depending on the way utility is measured. This may seem odd since I have argued that logically speaking, formal models have predictions that must follow from their assumptions. Of course, this is true only if no errors are made in calculations or in manipulations of equations. 3. As is the case for much of oral folklore, I do not know the original source of this joke. It was told to me by John Moore, professor of chemistry at the University of Wisconsin–Madison in the early 1990s. Chapter 3 1. Following Deboer (1974), I have generalized David’s (1972:142) equation, which was originally written to calculate the number of pots discarded after one hundred years, and I have modified the notation so as to be consistent with Schiffer’s (1975a,b) discard equation. 2. It is a simple matter to show that this equation is a modified version of Schiffer’s (1975a,b) discard equation (equation 3.2 in this chap.). If the term S in Schiffer’s equation (the number of artifacts in systemic context) is replaced with p • a representing the number of site occupants multiplied by the number of artifacts maintained per person, the equation becomes: d p a L t t 5 . Therefore, the number of artifacts discarded is equal to the product of the number of site occupants (p), discard rate (a/L), and occupation span. 3. There is one small caveat to this statement. If two types of artifacts have discard rates that change proportionally, artifact ratios will remain constant. For this approach to be used, the discard rate of at least one of the artifact types must change with time and the discard rate of the other artifact type must not change proportionally. 4. I use a nonparametric correlation coefficient because Pearson’s r is very sensitive to outliers. If one point in a Monte Carlo run was a severe outlier, a strong correlation would result. In contrast, Spearman’s r is completely insensitive to outlying values. Chapter 5 1. For additional realism, equation 5.7 could be multiplied by a constant representing the probability of a lithic deficit if no surplus is maintained. Presumably, the variable p should never be equal to 1 because even if no surplus is maintained, there is a decent chance that on any given day a deficit will not occur owing to a low rate of lithic consumption. Therefore, the maximum value of p in actuality should be somewhat less than one. In general, this constant should be governed by the degree of dispersion in both rates of supply and demand. 2. It is fairly straightforward to show that artifact proportions are independent of the number of site occupants, that is, they are per capita measures. If every individual maintains a surplus, the size of the surplus (the numerator of equation 5.12) would be multiplied by a variable representing the number of site occupants. If every individual is also responsible for consumed raw material, the denominator of equation 5.12 would be multiplied by the same constant. Thus, the number of individuals cancels out. 3. The following artifact types were considered to represent “surplus raw material ”: types 1a (large cores, 1 striking platform), 1b (horse hoof cores), 1c (large cores, .1 striking platform), 2a (large flake scrapers with retouch), 2b (spokeshaves), 3a (tula adzes), 3c (non-tula adzes). Included within “consumed raw materials” were types 1d (micro-cores, 1 striking platform), 1e (micro-cores, .1 striking platforms), 3b (tula adze slugs), 3d (non-tula adze slugs), 3e (tula micro-adzes), 3f (tula micro-adze slugs), 3g (non-tula micro-adzes), 3h (non-tula micro-adze slugs), 3i (small endscrapers), 4a (lunates), 4b (Bondi points), 4c (backed blades of irregular shape), 9 (retouched frag. and utilized flakes), and debitage. 4. Here is where formality meets informality. I am stumped by the problem of coming up with a formal definition of the distinction between “surplus” and “consumed ” raw material. The 5...

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