HvF, Recursion and Multidimensional Visualization Magic - Alfred Inselberg

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        To iterate is human ... but to recurse is divine.
      
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        HvF stressed the crucial role of recursion in learning and epistemology. Our visual 
        experience, which is limited by our 3-dimensional habitation, can also be recursively 
        augmented to \perceive" multidimensionality. Following our 2003 HvF Congress presentation, 
        the representation of a multidimensional object (hyper-surface) S is constructed 
        recursively one dimension at a time. Starting from points in S, lines contained in S are 
        constructed, followed by 2-D planes, 3-D planes and so on until the hypersurface is 
        obtained as the envelope of its tangent hyperplanes. In general, such a process performed 
        on a multivariate dataset concentrates the relational information into clear 2-D patterns 
        corresponding to hypersurfaces. We will see that the interactive navigation of these 
        patterns is equivalent to the exploration of the complex multidimensional relations they 
        represent.  
      
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        P.S. Do not be intimidated by this formalistic description. The speaker is also well known 
        for his numerological anecdotes and palindromic digressions! 
      
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