7.1: The Scribe School
- Page ID
- 47628
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Old Babylonian mathematics was not the high-status diversion of wealthy and highly intelligent amateurs, as Greek mathematicians were or aspired to be. According to the format of its texts it was atught in the scribe school—hardly to all students, not even among those who went through the full standard curriculum, but at least to a fraction of future scribes (or future scribe school masters only?).
The word "scribe" might mislead. The scribe certainly know to write. but the ability to calculate was just as important—originally, wirting had been invented as subservient to accounting, and this subordinated function with respect to calculation remained very important. The modern colleagues of the scribe are engineers, accountants and notaries.
Therefore, it is preferable not to speak naively of "Babylonian mathematicians." Strictly speaking, what was taught number- and quantity-wise in the scribe school should not be understood primarily as "mathematics" but rather as calculation. The scribe should be able to find the correct number, be it in his engineering function, be it as an accountant. even problmes that do not consider true practice always concern measurable magnitudes, and they always ask for a nubmerical answer (as we have seen). It might be more appropriate to speak of the algebra as "pure calculation" than as (unapplied and hence) "pure" mathematics. The preliminary observations on page 7 should thus be thought through once again!
That is one of the reasons that many of the problems that have no genuine root in practice none the less speak of the measurement and division of fileds, of the production of bricks, of the construction of siege ramps, of purchase and sale, and of loans carrying interest. One may learn much about daily life in Babylonia (as it presented itself to the eyes of a professional scribe) through the topics spoken of in these problems, even when their mathematical substance is wholly artificial.
If we really want to find Old Babylonian "mathematicians" in an approximately modern sense, we must look to those who created the techniques and discovered how to construct problems that were difficult but could still be solved. For example we may think of the problem TMS XIX #2 (not included in the present book): to find the sides \(\ell\) and \(w\) of a rectangle from its area and from the area of another rectangle 
\((d,\) 
\((t))\) (that is, a rectangle whose length is the diagonal of the first rectangle and whose width is the cube constructed on its length). This is a problem of the eighth degree. Without systematic work of theoretical character, perhaps with a starting point similar to BM 13901 #12, it would have been impossible to guess that it was bi-biquadratic (our term of course), and that it can be solved by means of a cascade of three successive quadratic equations. But this kind of theoretical work has left no written traces.