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Back to the ancients to find the future of science

The Shape of Space

In  soon to appear book and its appendixes, we have mapped out the foundations of a new kind of geometry based on the right side scientific paradigm. When talking about the shape of knowledge, we must also talk about the shape of geometry. Traditional left side spatiality, like Hilbert space for example, is notable for its lack of shape.. Arguing from the left side perspective, this is seen as a good thing. Space does not have shape; only the objects, which inhabit the space, have shape. Thus, the shapelessness of space is a necessity for left side science. Consequently, one finds that the dimension of a traditional space is the same as the number of degrees of freedom. In the final analysis, the traditional left side geometry leads to a space made up of a formless blob consisting of infinitude of points. Such a space is uniformly dense in structure. One could say that the space is devoid of sparseness. According to the left side scientific paradigm, the only sparseness is the apparent void between any objects that might inhabit the space. However, even that sparseness is illusory as the left side paradigm regards objects merely as ensembles of point-like particles. In other words, such ensembles do not take up any space at all, as each constituent particles is lacking in extent. Right side geometry takes another tack. To begin with, there is no dichotomy between space and the things that inhabit space. Space and the thing are the same stuff.  One space per thing. In this context, space must have shape as the thing has shape. As shown in the book, the thing is made up of a conglomerate of spaces, as spelt out in the Code that describes it. Each space is a particular type of Three-in-One structure corresponding to a codon of the Code. However, each of these micro cum macro spaces can invoke a higher dimensionality. We have mentioned this to explain the so-called degeneracy in the genetic code. If our hypothesis is valid, each elementary space can be coded by different codons from the Code, all according to the observed degeneracy of the code. Thus, even at the micro level, the dimension and degrees of freedom are far from being the same thing. Such space, where the number of degrees of freedom is less than the number of dimensions, can be said to be sparse. Sparseness in form is a prime requirement for shape in form. According to our analysis, any entity whatsoever that exists, is an amalgam of such sparse structures. The specificity in terms of gender typing of these constituents articulates the shape of each organism in question. In addition, to note, there is no absolute dividing line between biological forms and the material forms of physics. They are all constructed from the same generic principles.