Search NKS | Online
121 - 130 of 188 for Sort
The pictures immediately remind one of the overall branching patterns of all sorts of plants—from algae to ferns to trees to many kinds of flowering plants.
And indeed, in any multiway system with a limited set of rules, such sequences must necessarily be subject to all sorts of constraints.
But what is most relevant here is that it seems likely that—much as for non-planarity—nonzero values of quantities conserved by network evolution rules can be thought of as being associated with some sort of local structures or tangles of connections in the network.
In general the result could be very complicated, and could for example involve all sorts of different forms of curvature and other characteristics of space.
But there are all sorts of phenomena in quantum theory that seem to indicate that electrons do not in fact behave like ordinary objects that have definite properties independent of us making observations of them.
In general, the equations of quantum field theory seem to imply that there can be all sorts of complicated configurations in the field, even in the absence of actual particles.
And certainly in writing this book I have relied heavily on our ability to make all sorts of deductions on the basis of looking at visual representations.
But even if one does all sorts of parallel processing this approach presumably in the end becomes quite impractical.
I suspect that it has to do with the fact that in mathematics one usually wants axiom systems that one can think of as somehow describing definite kinds of objects—about which one then expects to be able to establish all sorts of definite statements.
But it also means that it is not clear whether the axiom system actually describes only the objects one wants—or whether for example it also describes all sorts of other quite different objects.