Rethinking mathematics

 I have seen articles on Mesopotamian mathematics in which authors write about tablets for which there is much literature, sometimes their own. I understand that there are often new ways of viewing tablets within the context of research. My only objection is creating a new scholarly “lingo,” almost a secret language among scholars involved in that field. I prefer transparency. I think the purpose of research is to make information more readily available rather than creating obstacles so other scholars think that both the field of ancient Mesopotamian mathematics and its application are extremely specialized by unnecessary language created by scholars. 

For scholars trying to gain understanding so that they don’t feel simple measurements or mathematics belongs only to specialists, Mesopotamian mathematics must not be obscured by new terminology. Some scholars may have forgotten mathematical terminology (easily accessible by checking a dictionary), formulae, and algebra. Researchers can follow the logic of an article if we write for others and not the very small group who deal with these matters.

French scholars are taught to write their research in French so foreigners can easily read it. This model can provide an important lesson not only for writing about Mesopotamian mathematics but also for almost any sub-category of ancient Near Eastern civilizations.

 I have seen the words area and surface used interchangeably as if they are the same. The difference might be explained in the following way: The area is the measurement of the space occupied by any two-dimensional geometric shape. The surface area is the sum of the areas of all the faces of the three-dimensional figure. Plane might represent the area two-dimensional figures. In Mesopotamian mathematics, the same term is used, because geometry only existed as formulas, not shapes in a three-dimensional space. The sides of a geometric shape are not added together; the use of the word surface for geometric shapes implies that the area of each side is calculated and then all sides are added together. Therefore, the term in Sumerian and Akkadian being the same word should be translated by the same word "area," i.e., the technical meaning of the term.

Translation of mathematical terms

Anyone who has studied languages knows that words often have more than one translation; sometimes these meanings are related by extension, and sometimes they are not. Some words have idiomatic meanings in combination with other words. Also, these same words may have technical meanings. This analysis seems rather elementary, but, somehow, some scholars working on mathematics seem to lack an understanding of basic linguistics. In Mesopotamian mathematics, some scholars have chosen to give a literal translation to get to the “heart” of understanding the text. For example, našû can be translated as “to lift, raise up something” (during a ritual, etc.)➔” “to elevate a person to a high position”➔ “to transport goods,” “to carry,”➔ “to take, accept, receive something from someone, (often in conjunction with ina qāti).” This verb is a rather general verb with multiple meanings, of which I have only stated a few. Then there is the technical meaning, “to multiply,” that is, x našû y išû xy (The verbs are written in the infinitive because they are conjugated according to context.) I will give an example without x and y to clarify the problem of literal translation: 2 “raises up” 3 “has” 6. There are other ways of expressing multiplication, but I am using one common example of a literal translation. Absolutely nothing is gained by a literal translation—the reader/mathematician has not come to a greater understanding of the language of an ancient text. Clearly, the meaning of našû  in this context is “to multiply”; that is, 2 multiplied by 3 is 6. There is an expression in English: “ if it walks like a duck and quacks like a duck, it’s a duck!”

Early Work In Re: Digitilization

Why do the digitalized texts sometimes give more information than the scholars who have copiously cataloged the tablets? For example, Abe Sachs cataloged the mathematical texts at the University of Pennsylvania. Upon a visit to Penn almost 20 years ago, I was kindly given a copy of his work. Robert Englund in a long comment in CDLN 2 010:0004 about publishing and cataloging collections noted this problem, among many, from a different angle: collaborators of research efforts to gather and make available primary cuneiform sources for cuneiform studies, for related disciplines, and for the global community of informal learners are, unfortunately, and unnecessarily, stymied by this lack of publication care, leaving us to do the work of others in cleaning up defective or incomplete catalogs; outsiders like ourselves, however, must work without access to internal resources, for instance, the letters and notes of Goetze, that will have been available to those participating in a collective publication.