The present paper offers a more macroscopic and system-oriented analysis of the tense-taxis-aspect-mood (TTAM) semantics of the Biblical Hebrew verbal system developed within the framework of grammaticalization-based maps and cognitive linguistics. By combining the maps (i.e. qualitative compositions of senses) and waves (i.e. qualitative-quantitative complexes of senses) into higher-level dynamic modules, i.e. currents, and by explaining the global system in terms of such currents, the study designs a possible way of expansion of the semantic maps’ model from a gram-oriented analysis to a more systemic perspective. Accordingly, higher level properties of the sub-modules of the Biblical Hebrew verbal system are postulated, the environments of grams are expanded from their immediate setting (the adjacent waves on the stream) to other, more distant, regions of the verbal organization, and a tentative dynamic model of the entire Biblical Hebrew verbal system is formulated.
Developed within the frame of cognitive linguistics and cognitive science, the present paper argues that the wave-stream model is a more adequate manner of representing verbal grams in Biblical Hebrew than neat models built on discrete, binary and static categories. Taking as examples two Biblical Hebrew verbal grams (WAYYIQTOL and QATAL) and building on the empirical evidence concerning the senses conveyed by these two forms in the book of Genesis, the author demonstrates the following: a) Neat, binary, discrete and static models correspond to “folk” representations of reality; b) A more adequate representation, which preserves the complex nature of language and its components, is provided by the wave-stream model; c) The wave-stream model additionally suggests the psychological reality of the grams or their conceptualizations by speakers. As a result, the wave-stream model has both etic (language centric) and emic (psychological or human centric) dimensions, the latter being derived in a principled manner.
The known standard recursion methods of computing the full normalized associated Legendre functions do not give the necessary precision due to application of IEEE754-2008 standard, that creates a problems of underflow and overflow. The analysis of the problems of the calculation of the Legendre functions shows that the problem underflow is not dangerous by itself. The main problem that generates the gross errors in its calculations is the problem named the effect of “absolute zero”. Once appeared in a forward column recursion, “absolute zero” converts to zero all values which are multiplied by it, regardless of whether a zero result of multiplication is real or not. Three methods of calculating of the Legendre functions, that removed the effect of “absolute zero” from the calculations are discussed here. These methods are also of interest because they almost have no limit for the maximum degree of Legendre functions. It is shown that the numerical accuracy of these three methods is the same. But, the CPU calculation time of the Legendre functions with Fukushima method is minimal. Therefore, the Fukushima method is the best. Its main advantage is computational speed which is an important factor in calculation of such large amount of the Legendre functions as 2 401 336 for EGM2008