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The goal of the presented work consists in the construction of the new three-levels scheme of authomatical classification. This scheme is based on the newly introduced notion of volatility of separate clusters as well as of whole classification. The property is exactly defined and efficiently calculated. It describes the stability, exactness, validity of subsets of the given initial set in essence, their possibility (or impossibility) to be selected as clusters. The suggested algorithm finds the clusters with arbitrary levels of volatility, including the conventional case of zero volatility. The clusters in USA, Russia and Sweden stock market (for crisis period of 2008-2010) and deputies clusters based on voting results in the 3rd State Duma between September 2001 and January 2002 (the period including the creation of the party "United Russia" 01.12.2001) were constructed by the suggested algorithm. Analyzing clusters constructed basing on the voting results for every of the considered months, it has turned out that the clustering volatility was equal to zero in September and October, drastically increased in November and slightly decreased in December and January. But several indices (i.e. concordance of parties' positions) did not show sensible jumps near this political "bifurcation point". The other considered various model examples demonstrated the results well-coordinated with geometrical intuition.

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AbstractThis article argues that there are parallels between developments in modern science and in art and culture, including the culture of finance, and that these developments can be tracked by a notion of volatility not just as change, but as how change itself has changed. Describing this paradigm shift requires a language that is precise but indeterminate, a language akin to metaphor, understood as figures of volatility. Three such figures are anamorphosis, anachronism, and catachresis. These figures are major instantiations of volatility, though they do not exhaust all the possibilities. What they indicate is not just that our frames of understanding have shifted, but that we are dealing with problematic, multiple, and overlapping frames: anamorphosis problematizes our experience of space, anachronism of time, and catachresis of language. These figures are not all in play at the same time. In literature, catachresis may be the dominant figure; in dance, anamorphosis; in 'slow cinema', anachronism. The aim is less to arrive at a set of defining characteristics than to follow a series of transformations across different cultural fields. Almost every field in our time is volatile each in its own way, and this has consequences for methodology. If figures are tools to think with, not to regulate thought, a necessary method would be to allow these figures to emerge from the material, not from a checklist. The question of volatility is arguably the key intellectual challenge of our time because it allows us to see deviation from a norm not just as an aberration, but as an indication that established norms are losing their normative value.