Imagining Worlds with Three Hundred and Thirty-Three Dimensions
So far as mere extensiveness is concerned, space might as well have three hundred and thirty-three dimensions, instead of the modest three dimensions of our present epoch. The three dimensions of space form an additional fact about the physical occasions. Indeed the sheer dimensionality of space, apart from the precise number of dimensions, is such an additional fact, not involved in the mere notion of extension. Also the seriality of time, unique or multiple, cannot be derived from the sole notion of extension.
- AN Whitehead, Process and Reality
Imagining Worlds without Arithmetic
We hardly ever apply arithmetic in its pure metaphysical sense, without the addition of presumptions which depend for their truth on the character of the societies dominating the cosmic epoch in which we live. It is hardly necessary to draw attention to the fact, that ordinary verbal statements make no pretence (sic) of discriminating the different senses in which an arithmetical statement can be understood.
There is no difficulty in imagining a world—i.e., a cosmic epoch—in which arithmetic would be an interesting fanciful topic for dreamers, but useless for practical people engrossed in the business of life. In fact, we seem to have been only barely rescued from such a state of things. For amid the actual occasions located in the wilds of so-called ‘empty space,’ and well removed from the enduring objects which go to form the enduring material bodies, it is quite probable that the contemplation of arithmetic would not direct attention to any very important relations of things. It is, of course, a mere speculation that any actual entity, occurring in such an environment of faintly coordinated achievement, achieves the intricacy of constitution required for conscious mental operations.
- AN Whitehead, Process and Reality
Imagining Worlds without Shapes, Dimensions, or Measurability
...the real potentialities relative to all standpoints are coordinated as diverse determinations of one extensive continuum. This extensive continuum is one relational complex in which all potential objectifications find their niche. It underlies the whole world, past, present, and future. Considered in its full generality, apart from the additional conditions proper only to the cosmic epoch of electrons, protons, molecules, and star-systems, the properties of this continuum are very few and do not include the relationships of metrical geometry. An extensive continuum is a complex of entities united by the various allied relationships of whole to part, and of overlapping so as to possess common parts, and of contact, and of other relationships derived from these primary relationships. The notion of a ‘continuum’ involves both the property of indefinite divisibility and the property of unbounded extension. There are always entities beyond entities, because nonentity is no boundary. This extensive continuum expresses the solidarity of all possible standpoints throughout the whole process of the world. It is not a fact prior to the world; it is the first determination of order—that is, of real potentiality—arising out of the general character of the world. In its full generality beyond the present epoch, it does not involve shapes, dimensions, or measurability; these are additional determinations of real potentiality arising from our cosmic epoch.
- AN Whitehead, Process and Reality
Imagining a Vast Nexus of Many Cosmic Epochs
"In these general properties of extensive connection, we discern the defining characteristic of a vast nexus extending far beyond our immediate cosmic epoch. It contains in itself other epochs, with more particular characteristics incompatible with each other. Then from the standpoint of our present epoch, the fundamental society in so far as it transcends our own epoch seems a vast confusion mitigated by the few, faint elements of order contained in its own defining characteristic of ‘extensive connection.’ We cannot discriminate its other epochs of vigorous order, and we merely conceive it as harbouring the faint flush of the dawn of order in our own epoch. This ultimate, vast society constitutes the whole environment within which our epoch is set, so far as systematic characteristics are discernible by us in our present stage of development. In the future the growth of theory may endow our successors with keener powers of discernment"
AN Whitehead, Process and Reality