Readers Write: October 2001

I WOULD LIKE TO COMMENT ON THE “Four Fours” letter that appeared in the February 2001 issue (p. 340). I have assigned this problem several times in the course of teaching middle school students and have always been impressed with the results. One year, I challenged the students to generate the numbers between 0 and 100 using only four 4s and the basic operations, as well as factorials, square roots, and exponents. (I had not heard of the “next to” operation that was discussed in the letter but will allow its use in the future.) In the letter, Barry D. Cohen writes that he does not believe that 19 can be made using any of the regular or special operations and suggests that it requires the use of .4. I was not sure how to generate 19 with .4, but one of my eighth-grade students was able to generate it in this manner: 19 = 4! −(4 + 4/4). This student was unable to find solutions for a few other numbers between 0 and 100, including 35, 37, 43, and 51, and several in the 70s and 80s. I would love to hear if anyone has results for these numbers. Thank you for putting out such a fine publication.

Turkish Kilims

In every aspect of Turkish studies, the non-Turkish scholar is at a disadvantage in trying to understand the complexities of the Turkish heritage. However hard we may try to learn and understand the language, customs, arts and crafts, through a lifetime of labour, enthusiasm and long residence, our Turkish colleagues should be able to do this better and with greater understanding. During the nineteenfifties, while living in Ankara, one used to regret the lack of interest in Seljuk art and architecture and complain about the absence of any reliable information about the flat woven rugs known as kilims that were just starting to appear in the market.Things have greatly changed in the thirty years that have since passed; and there is a healthy revival in Turkish art of the Seljuk and Ottoman periods, not only in Turkey, but at last also in the West. The interest in Turkish kilims is a modern phenomenon; we have valuable studies on the Türkmen nomads of Anatolia, which never even mention the word kilim. In Turkey also few scholars, except Yusuf Durul who has devoted his life to the study of Yörük textiles, were attracted by kilims. Samples of Old Turkish carpets and kilims, published by the Sümerbank, Istanbul, 1961 broke the ice, at least in Turkey. Then came an exhibition at the Textile Museum, Washington D.C. in 1969 and its fine publication by A. N. Landreau and W. R. Pickering entitled From the Bosporus to Samarkand. Flat woven rugs (1969), followed in rapid succession by three publications by the Akbank in Turkey: C. Kerametli and Z. Güvemli: Türk ve Islam Eserleri Müzesi (1974); Belkis Acar's Kilim ve düz dokuma yaygilar (1975) and Yusuf Duru's Yörük kilimleri (1977) all published in Istanbul. Then came a kilim exhibition in London, published by D. Black and C. Loveless in The undiscovered kilim, London 1977, followed by W. T. Ziemba, A. Akatay and S. L. Schwartz: Turkish flat weaves, London 1979, and now we have a sumptuous book by Yanni Petsopoulos: Kilims, Thames and Hudson, London 1979 (price £38.00) with not less than 278 illustrations of Anatolian kilims alone, many in colour and all old, i.e. before the introduction of chemical dyes, tentatively put at 1900, and nearly all in western collections, many private.