How language and cognition interact in thinking? Is language just used for communication of completed thoughts, or is it fundamental for thinking? Existing approaches have not led to a computational theory. We develop a hypothesis that language and cognition are two separate but closely interacting mechanisms. Language accumulates cultural wisdom; cognition develops mental representations modeling surrounding world and adapts cultural knowledge to concrete circumstances of life. Language is acquired from surrounding language “ready-made” and therefore can be acquired early in life. This early acquisition of language in childhood encompasses the entire hierarchy from sounds to words, to phrases, and to highest concepts existing in culture. Cognition is developed from experience. Yet cognition cannot be acquired from experience alone; language is a necessary intermediary, a “teacher.” A mathematical model is developed; it overcomes previous difficulties and leads to a computational theory. This model is consistent with Arbib's “language prewired brain” built on top of mirror neuron system. It models recent neuroimaging data about cognition, remaining unnoticed by other theories. A number of properties of language and cognition are explained, which previously seemed mysterious, including influence of language grammar on cultural evolution, which may explain specifics of English and Arabic cultures
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