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" ... Although applications of the octonions to physics are conjectural, there are many good reasons to be interested in these ideas. The octonions teach us, theoretically, how many spacetime dimensions you need to construct a supersymmetric quantum field theory. They are tied to the exceptional Lie groups which are used to construct GUTs and which play a role, through the E(8) group, in superstring theories. ... "
" ... Visualizing the multiplication of the unit octonions, of which there are 8, requires thinking in... [+] higher-dimensional spaces (left). The multiplication table for any two unit octonions is also shown (right). Octonions are a fascinating mathematical structure, but offers non-unique solutions to a myriad of possible applications. ... "