### Physics as number theory and number theory as physics

It seems that also mathematicians are discovering the number theoretic vision about physics - or rather - the physics inspired vision about number theory (see the article in Not Even Wrong). In TGD I call this M

^{8}-H duality, H=M

^{4}×CP

_{2}. Arithmetic geometer Minhyong Kim is realizing that rational points of certain exotic spaces encountered in number theory are very special: the space of paths emanating from rational points is speculated to have additional symmetries analogous to gauge symmetries.

In TGD the world of classical worlds (WCW) as as its points pairs or 3-surfaces with members at boundaries of CD and paths between membees correspond to what I call preferred extremals - space-time surfaces.

- At the level of M^8 - the arithmetic side - space-time surfaces are algebraic varieties of certain kind and satisfy algebraic equations plus associativity conditions coding quantum criticality.

- At the level of M^4xCP_2 - the physics side - the preferred extremals satisfy an infinite number of gauge conditions: gauge symmetry again!

See the article Does M8-H duality reduce classical TGD to octonionic algebraic geometry?.

For a summary of earlier postings see Latest progress in TGD.

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