The identication of the experienced time te and geometric time tg involves well-known problems. Physicist is troubled by the reversibility of tg contra irreversibility of te, by the con ict between determinism of Schrödinger equation and the non-determinism of state function reduction, and by the poorly understood the origin of the arrow of tg. In biology the second law of thermodynamics might be violated in its standard form for short time intervals. Neuroscientist knows that the moment of sensory experience has a nite duration, does not understand what memories really are, and is bothered by the Libet's puzzling nding that neural activity seems to precede conscious decision. These problems are discussed in the framework of Topological Geometrodynamics (TGD) and TGD inspired theory of consciousness constructed as a generalization of quantum measurement theory. In TGD space-times are regarded as 4-dimensional surfaces of 8-dimensional space-time H = M4xCP2 and obey classical eld equations. The basic notions of consciousness theory are quantum jump and self. Subjective time is identied as a sequence of quantum jumps. Self has as a geometric correlate a xed volume of H- "causal diamond"-dening the perceptive eld of self. Quantum states are regarded as quantum superpositions of space-time surfaces of H and by quantum classical correspondence assumed to shift towards the geometric past of H quantum jump by quantum jump. This creates the illusion that perceiver moves to the direction of the geometric future. Self is curious about the geometric future and induces the shift bringing it to its perceptive eld. Macroscopic quantum coherence and the identication of space-times as surfaces in H play a crucial role in this picture allowing to understand also other problematic aspects in the relationship between experienced and geometric time.