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This Concept Map, created with IHMC CmapTools, has information related to: p-Adic manifold.cmap, THE NOTION OF P-ADIC MANIFOLD is needed in order to fuse real physics and various p-adic physics to a larger structure, in order to fuse real physics and various p-adic physics to a larger structure which suggests that real and p-adic number fields should be glued together along common rationals, to be based on chart maps from p-adics to reals rather than to p-adics! Also reverse maps make sense. interpreted as cognitive maps, "thought bubbles", to be based on chart maps from p-adics to reals rather than to p-adics! Also reverse maps make sense. and realized in terms of canonical identification or some of its variants, p-adic manifold structure is induced from that for p-adic imbedding space with chart maps to real imbedding space and assuming preferred coordinates made possible by isometries of imbedding space: one however obtains several inequi- valent p-adic manifold structures depending on the choice of coordinates: these cognitive representa- tions are not equivalent, canonical identifi- cation is continu- ous but does not map smooth p-adic surfaces to smooth real surfaces requiring second pinary cutoff so that only a discrete set of rational points is mapped to their real counterparts by chart map, breaks general coordinate invariance of chart map: (cognition-indu- ced symmetry breaking) minimized if p-adic manifold structure is induced from that for p-adic imbedding space with chart maps to real imbedding space, cognitive maps, "thought bubbles" with reverse map interpeted as a transformation of intention to action, THE NOTION OF P-ADIC MANIFOLD is suggested to be based on chart maps from p-adics to reals rather than to p-adics! Also reverse maps make sense., second pinary cutoff so that only a discrete set of rational points is mapped to their real counterparts by chart map requiring completion of the image to smooth preferred extremal of Kaehler action so that chart map is not unique in accord- ance with finite measu- rement resolution, THE NOTION OF P-ADIC MANIFOLD involves some problems: canonical identifi- cation is continu- ous but does not map smooth p-adic surfaces to smooth real surfaces, THE NOTION OF P-ADIC MANIFOLD is problematic because p-adic topology is totally disconnected, canonical identifica- tion does not respect symmetries since it does not commute with arithmetic operations which requires pinary cutoff below which chart map takes rationals to rationals so that commutativity with arithmetics and sym- metries is achieved in finite resolution: above the cutoff canonical identification is used, THE NOTION OF P-ADIC MANIFOLD involves some problems: canonical identifica- tion does not respect symmetries since it does not commute with arithmetic operations, because p-adic topology is totally disconnected implying that p-adic balls are either disjoint or nested, real and p-adic number fields should be glued together along common rationals bringing in mind adeles, THE NOTION OF P-ADIC MANIFOLD involves some problems: breaks general coordinate invariance of chart map: (cognition-indu- ced symmetry breaking), p-adic balls are either disjoint or nested so that ordinary definition of manifold using p-adic chart maps fails
