aa r X i v : . [ c s . D L ] J u l THE GAME OF CIPHER BEADS
S. S. KUTATELADZE
Abstract.
Comparison between the various impact factors of a few Russianjournals demonstrates the deficiencies of the popular citation indices.
Since recently there has been much ado invoked in science by incessant attemptsat replacing expertise with numerical manipulations. Of especial relevance to theRussian mathematical community are the following indices: • MCQ, the Mathematical Citation Quotient of the American MathematicalSociety which utilizes the database of
Mathematical Reviews (abbreviatedto MR); • IF or ISI, the classical impact factor of the Institute for Scientific Infor-mation (which is a part of the Thomson Reuters Corporation); • RISC, the Russian Index of Scientific Citation which rests upon thedatabase of the Scientific Electronic Library; • MNRU, the impact factor of the All-Russia Mathematical Portal Math-Net.Ru which uses its own database. These indices are calculated for each journal one by one. Let Q N,k be the numberof citations in year N of the articles published in the journal in year N − k . By P N we denote the number of the articles published by the journal in year N . Note inpassing that N is the number of a year in the Gregorian calendar, and so N is atleast six since N is greater than thousand. In this notation MCQ N , the MCQ ofthe journal in year N , is calculated as follows:MCQ N = Q N, + Q N, + . . . + Q N, P N − + P N − + · · · + P N − . Denote the impact factor in year N by IF N . By definitionIF N = Q N, + Q N, P N − + P N − . Thus, MCQ and IF are defined by the same scheme covering the different time spansof the relevant databases. The first takes the citations of the previous five years;whereas the second, of the last two years. The RISC and MNRU impact factors arecalculated by the classical two-year formula for IF suggested by Eugene Garfield, the founder of the Institute for Scientific Information. It is worth observing thatall four indices use different although intersecting databases. Date : May 20, 2009. Cp. [1] Cp. [2]. Cp. [3]. Cp. [4].
Let us assume that all articles in some journal are of the same high quality andhas the same number of citations. Assume further that the number of articles inany volume is the same every year. In other words, suppose that Q N,k and P N areindependent of N and k . In this model case, the MCQ and IF of the journal mustcoincide with one another as well as with the remaining two indices. Fluctuationsare inevitable in practical situations, but the trend to coincidence should prevail forsufficiently full databases. However, we observe nothing like this for the real indices.The discrepancies in their actual values for a particular journal seem improbablefor random fluctuations. For instance, IF is twice as much as MCQ for a fewoutstanding mathematical journals.By way of illustration let us compare the current impact factors of the two pairsof prestigious journals on algebra and logic: IF MCQJ. Algebra 0.630 0.64J. Pure Appl.Algebra 0.666 0.59J. Symb. Logic 0.609 0.31J. Pure Appl. Logic 0.613 0.30Using MCQ it is possible to conclude that the two logical journals are twice as“feeble” as their algebraic counterparts. In fact, the practical coincidence of the IFand MCQ of the two algebraic journals demonstrates most likely that the articlesof these journals primarily attract the scientists that publish their papers in thejournals covered by MR. At the same time, more than a half of the citations of thetwo logical journals appears in the sources that are not scanned by MR. Therefore,the scope of influence of the logical pair on the flux of scientific information issubstantially broader than that of the other pair. Moreover, the narrow audienceis hardly a merit of any scientific journal.The differences in databases greatly effect the calculation of the indices of Rus-sian periodicals. Let us take a look at the current values of the above-mentionedindices for a few authoritative journals of the Russian Academy of Sciences. Thefirst four of them publish papers in all areas of mathematics, and the fifth is inter-disciplinary. IF MCQ RISC MNRU Founded inSb. Math. 0.359 0.44 0.113 0.399 1866Russ. Math. Surv. 0.309 0.35 0.103 0.382 1936Sib. Math. J. 0.208 0.18 0.108 0.269 1960Math. Notes 0.251 0.18 0.030 0.244 1967Theoret. Math. Phys. 0.622 0.12 0.107 0.601 1969The obvious conclusion is in order that, taken per annum , all indices under con-sideration primarily characterize the respective databases, slightly reflecting a minorpart of few phenomena of the real functioning of science.The dynamics of citation indices may be more informative. For instance, look atthe impact factors IF and MCQ of the
Russian Journal of Mathematical Physics : Cp. [5].
HE GAME OF CIPHER BEADS 3
IF MCQ2003 0.291 0.232004 0.348 0.192005 0.394 0.262006 0.493 0.342007 1.012 0.35Viktor Maslov, Editor-in-Chief of this journal, indicates that a few publica-tions on economic applications of the ideas of mathematical physics might be areason for the almost two-times raise of IF in 2007. Incidentally, MCQ neglectsthis phenomenon completely.Traffic congestion never reflects the artistic gifts of jammed drivers. By anal-ogy, there are insufficient grounds to correlate rather arbitrary numerical indices ofthe dynamics of scientific information in a particular database with the quality ofpublications, all mystical hypotheses of the bureaucracy of science notwithstanding.Science is not the glass bead game despite whatever ciphers.
References [1] Pislyakov V. and Gokhberg L. (2008) “Assessing the Relative Standing of Russian Sciencethrough a Set of Citation and Publication Indicators,” In:
Excellence and Emergence. Bookof Abstracts. 10th International Conference on Science and Technology Indicators
Encyclopedia of Library andInformation Science . New York: Marcel Dekker, Vol. 5: 16-41.[4] Garfield E. (1979)
Citation Indexing: Its Theory and Applications in Science, Technologyand the Humanities . New York: Wiley Interscience.[5] Khaitun S. D. (1983)
Scientometrics. State of the Art and Vistas. Moscow: Nauka Publishers .[In Russian]
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