Victor Vvedensky, Kurchatov Institute

Direct contact with technical devices using human speech implies ability of the computer to understand in some way the idea of the message. The people feel semantic similarity of words and can find the word with close or just opposite meaning. Can one find mathematical description of this ability?

Transistors flop millions times faster then the neurons are spiking, available fast memory is huge in comparison with the working memory of the brain, the software can be sophisticated enough to beat top chess players, and still, computers fail to interpret vocal commands of humans. Special organization of language in the brain is the probable reason of its excellent performance.

We start our study with the analysis of compatibility of different elements of language. Each verb can be attributed with the set of properties. The adverbs, which can be readily used together with this verb in many different contexts, reflect these properties. One can смело прыгать to jump bravely ловко прыгать to jump deftly возбужденно прыгать to jump excitedly

Compatibility values for representative sets of 25 verbs and 25 adverbs of Russian language

2D projections of 900 verbs in first 9 dimensions of the multidimensional space Each verb is presented as a dot. The numbers indicate the order of dimensions. Each 2- dimensional plane shows distributions for the pair of dimensions with numbers indicated for rows and columns. The uppermost square represents projection on the plane in dimensions one and two or X and Y. The scale is normalized to unity

Distributions of verbs and adverbs in first two dimensions of the multidimensional space 900 verbs and 600 adverbs of Russian language in first two dimensions. The distributions nearly mirror each other so that the most compatible verbs and adverbs are close, while incompatible pairs are on the far ends. Sets of verbs compatible with three adverbs are shown as hazel points. Green points indicate fuzzy cases. patiently, industriously, motionlesslyTo cost, to fill over, to throw down, to continue

Compatibility of prefixes with word roots can also be represented as a table for Russian verbs

Distribution of Russian prefixes on the two-dimensional plane, calculated using compatibility table of word roots and prefixes. Since the number of prefixes is much smaller then the number of roots (~20 and ~4000) the distribution of prefixes is accurate enough. The opposite is not true. One needs another approach to analyze the space of roots.

Small cortical patches with a certain function Brain studies, using special functional staining techniques, reveal confined areas performing definite tasks. These portions of the monkey cortex extract visual features with certain orientation. They are about 1 mm x 2 mm large. Rich internal connections can impart this cortical patch with properties reflected as additional dimensions. That is like blowing up the flat soap film making the bulb in the space with multiple dimensions D.H.Hubel, Eye, Brain, and Vision

The principal central connections of hearing

The principal central connections of speech

The corticobulbar tract is a pathway connecting the cerebral cortex to the brainstem

The muscles of the face, head and neck are controlled by the corticobulbar system

Die Liste der häufigsten Wortformen aus den Textkorpora des IDS, absteigend sortiert nach relativer Häufigkeit. Institut für Deutsche Sprache Zipf Law for words Exponential decay for word roots

All the roots can be fit into 2D plot, where they densely fill the portion of the surface. Triangles - roots absent in Czech

Triangles - Russian roots compatible with «На» prefix

Russian roots with initial consonants «К» and «П»

Space of qualities built using frequencies of occurrence of Russian adjectives and adverbs хорошо - well хороший - good прямо - directly прямой - stright сильно - strongly сильный - strong медленно - slowly медленный - slow полный - full полно - completely одновременно - simultaneously одновременный - simultaneous грязно - dirty грязный - dirty поспешно - in hurry поспешный - hasty толстый - thick

Positions of different qualities, expressed in Russian words in respect to the positions of actions and entities. Speech generator should be in the upper right corner.

2D distribution of actions, built using frequencies of occurrence of continuous and completed forms of Russian verbs. понимать-понять to understand получать-получить to get кричать-крикнуть to cry вызывать-вызвать to call покупать-купить to buy носить-нести to carry выполнять-выполнить to fulfil выяснять-выяснить to clear up избавляться-избавиться to get rid

Cortical Representation of Sign Language Cerebral Cortex, Vol. 11, No. 6, , June 2001

Sketch depicting interactions of cortical patches storing different elements of speech

Аналогично можно построить вмещающее пространство для конечных согласных корней немецкого языка. А также многих других языков.