Abstract
In physics, we have been seriously confronted with the question of continuous vs. discrete since the beginning of the last century. Why is it still with us, and increasingly so in the last sixty years? The title of the essay suggests the reason: so far, we have relied on the "continuous", or vector space, mathematics (of spatial origin), the only one we have, while the experiments suggest that, at the bottom, the nature is non-continuous, or discrete, albeit in a sense unfamiliar to us. We have tried to save the situation by "discretizing" our conventional models, but for the reasons I discuss here such desperate attempts to transform our basic formalism (by destroying its integrity) are not meaningful. We may have no other choice than to set aside for a while the millennia-old numeric, or spatial, forms of representation and the associated measurement processes and to begin completely anew, by shifting to a non-numeric-- relational, or temporal--representational formalism, which should give the meaning to the nebulous concept of discreteness and, even more importantly, should remove the enormous present gap between the physical and the mental.
Lev Goldfarb