Holes Cannot Be Counted as Immaterial Objects

Verifying Reference Counted Objects

Reference counting is a pervasive resource management idiom where each resource contains a count of the number of clients that hold a reference to it, and each client increments (resp., decrements) the count on acquiring (resp., releasing) the resource. If the reference count falls to zero, the system can reclaim the resource. Reference counting is often a source of subtle bugs, ranging from le...

Not everything that counts can be counted; not everything that can be counted counts.

Objects Counted by the Central Delannoy Numbers

The central Delannoy numbers, (dn)n≥0 = 1, 3, 13, 63, 321, 1683, 8989, 48639, . . . (A001850 of The On-Line Encyclopedia of Integer Sequences) will be defined so that dn counts the lattice paths running from (0, 0) to (n, n) that use the steps (1, 0), (0, 1), and (1, 1). In a recreational spirit we give a collection of 29 configurations that these numbers count.

Measuring research impact: not everything that can be counted counts, and not everything that counts can be counted

Why Machines Cannot be

Mental processes are abstracted from a subset of the physical universe ; these, in turn, lead to the world of ideas. Although these ideas include quantum logic, no credible way has yet been found that constructs machines which use superimposed possibilities in the style of quantum logic, more general in computing power to machines based on classical logic. Machine theories are based exclusively...