1 ;;Quote: Zeno's paradoxes illustrates the problem of relating discrete to continuous

1 ;;Quote: objective experience is discrete but the world hangs together by the grace of continuity

1 ;;Quote: if this becomes that, it does so continuously; but without an hiatus, how is one to distinguish between this and that?

1 ;;Quote: when walking, one step leads continuously to the next yet steps are easily counted

2 ;;Quote: being in a state is being within a bounded region, while being in a transition is crossing a boundary

3 ;;Quote: being in a transition is interpretable as being within a bounded period of change

3 ;;Quote: states and transitions is like a hiker advancing from valley to valley by crossing a series of mountains

4 ;;Quote: a hiker going between valleys is like a clock whose ticks are the hiker's transitions from valley to ridge

7 ;;Quote: between states there are spatial boundaries and no temporal boundaries; the opposite holds for transitions

7 ;;Quote: a digital device is always in some state; so states partition its existential time and transitions are instantaneous

11 ;;Quote: associated with each atomic object is a set of possible states and a set of possible transitions

15 ;;Quote: the boundary of a region is all objects that are neither in the region nor out of the region

21 ;;Quote: a state space of regions and boundaries forms a topology of open and closed points; isomorphic with undirected Petri nets

29 ;;Quote: two regions of state space are 'separated' if their intersection is closed, 'joined' if the intersection is open, and 'inseparable' if same frame

33 ;;Quote: regions in transition space are processes with bounds called "begins" and "ends" instead of "entrance" and "exit"

40 ;;Quote: a object in transition is one state becoming another; neither pre-state nor post-state clearly holds

42 ;;Quote: atomic state can not have duration separate from the duration of the processes that hold the state

43 ;;Quote: an object can only be clearly in one state at a time or one transition at a time

43 ;;Quote: the states and transitions of an object cover its behavior with no gaps in space and time; creates a continuum out of discrete conditions

43 ;;Quote: a state and its bordering transitions are inseparable; can not resolve arguments about being clearly in a state or clearly in transition

43 ;;Quote: if a state clearly holds, then transitions for the state are unclear; and vice versa

46 ;;Quote: there is no boundary between 'clearly' and 'not clearly' yet 'clearly' has formal properties

47 ;;Quote: for atomic objects, a transition can have only one pre-state and post-state while states can have multiple pre/post-transitions