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Intuitively, and based on the principle of parsimony, it is extremely tempting to seek to reduce the theory of all matter in an S4 universe to submanifold geometry.  I have already proposed that electromagnetism is not a $U(1)$ gauge theory but rather an effect of normal circles and the submanifold covariant derivative naturally has the form of a connection in the sense that $\nabla_XY = \tilde{\nabla}_XY+h(X,Y)$ through the second fundamental form using the ambient and submanifold covariant derivatives.  A further natural expectation is that ‘matter’ in the physical world be described in terms of spherical harmonic expansions and also uncertainty principles.  Note that on S4, there is a natural Hopf fibration which leads to $SU(2)$ gauge theories.  The prospect of full geometrization could be realized by understanding in more detail how deterministic physics leads to quantum mechanical approximations on S4.  These are ambitious projects without a doubt but since I have already shown that the universe must be a scaled S4, they are worth undertaking.