Topic: discrete vs. continuous

topics > Group: philosophy


abstraction by name
continuum in mathematics
digital simulation of analog
event time
hardware vs. software
metaphysics and epistemology
quantum mechanics
real numbers and floating point numbers
sensitivity of software to change
symbolic representation
telephone system
what is a computer
what is a number


One can view the world in discrete pieces or as a continuum. Our sensory experience of the world is discrete. We see things and the things are clearly delineated. But the world is undergoing continuous change and at the boundary between things, our distinctions become unclear. We still think with discrete symbols, numbers, and names, but we act in a continuous fashion.

The digital computer is clearly discrete. It has replace the analog computer because it can simulate with analog computer without the errors that are part of analog processes. Language has many discrete aspects such as phonemes and words and morphological structures.

Einstien and Feynman believed that nature is at bottom discrete and not continuous. This conforms with quantum theories.

Holt saw an important aspect of understanding systems was the relation between discrete and continuous. With states and events one can describe a continuum without gaps. The boundaries between states are covered by events and the boundaries between events are covered by states. This is important for coordinated behavior. For example walking is a continuous process made up of discrete steps. (cbb 4/94)

Subtopic: continuum vs. objects up

Quote: objective experience is discrete but the world hangs together by the grace of continuity [»holtAW11_1980]
Quote: understanding humans at physical level is continuous while phenomenologically have objects in an organized field of experience [»dreyHL_1979]
Quote: since the world is a continuum, a network of concepts is at best a workable approximation [»sowaJF_1984]
Quote: a concept is a unit, i.e., it is discrete; e.g., easier to remember discrete relationships than continuous quantities [»sowaJF_1984]
Quote: Complementarity Principle for living systems--nature uses dynamics to the fullest while symbols used sparingly for direction and simplification [»turvMT_1984]
Quote: discrete decisions about continuous values cannot be made within a deadline

Subtopic: quantum mechanics up

Quote: processes are discontinuous in small regions and short times; it is clearly meaningless to speak about one velocity at one position [»heisW_1927]
Quote: quantum mechanics describes discontinuous change by the continuous change of the probabilities of possible states [»einsA_1949]
Quote: atomistic phenomena occurs in discrete states and discontinuous transitions; like stationary waves in an organ pipe or vibrating string (de Broglie) [»einsA5_1940]

Subtopic: physics up

Quote: rule of continuity -- no change takes place by leaps and bounds
Quote: physics must fuse the continuous and the discontinuous; the universal interaction of things and the simplicity of indivisible elements [»debrL_1937]
Quote: can judge incidence between states or transitions but not the coincidence of either; e.g., a clock dial is between 1 and 2 vs. exactly 1; i.e., continuous motion [»petrCA_1996]
Quote: space should be discrete because continuous space yields infinities; so geometry does not extend down into infinitely small space [»feynR_1965]
Quote: reality should have a purely algebraic theory since quantum phenomena are completely described by a finite set of numbers; not a continuous field [»einsA_1956, OK]
Quote: computational systems will become physics-like because of physical constraints such as 3-d and speed of light [»hillWD_1985]

Subtopic: name vs. process up

Quote: the difference between evolution and learning is similar to the different between digital and analog or name and process named [»bateG_1979]
Quote: name vs. process that is named is similar to digital vs. analog
Quote: AI concentrates on discrete aspects of intelligence while AI critics concentrate on the continuous aspects [»sowaJF_1984]

Subtopic: continuous vs. number up

Quote: the universe knows only one musical form--legato, while number is staccato; any attempt to make one the other is a deception [»dantT_1954]
Quote: in physics, action has local effects (e.g., inverse square law); in computation, a tiny program can clear all of memory [»hillWD_1985]
Quote: quantity is approximate; you can never have exactly three gallons of water [»bateG_1979]
Quote: picking a time for "inhabitant of Germany", fixes the number for all eternity
Quote: Zeno's paradoxes illustrates the problem of relating discrete to continuous [»holtAW11_1980]

Subtopic: space and boundaries, states and transitions up

QuoteRef: cbb_1973 ;;(lost) continuous to objects is seeing boundaries
QuoteRef: cbb_1973 ;;3/3/74 discontinuity is the way to represent a finite multi-dimensional space in a single dimension
Quote: if this becomes that, it does so continuously; but without an hiatus, how is one to distinguish between this and that? [»holtAW11_1980]
Quote: when walking, one step leads continuously to the next yet steps are easily counted [»holtAW11_1980]
Quote: states and transitions is like a hiker advancing from valley to valley by crossing a series of mountains [»holtAW11_1980]
Quote: being in a state is being within a bounded region, while being in a transition is crossing a boundary [»holtAW11_1980]
Quote: between states there are spatial boundaries and no temporal boundaries; the opposite holds for transitions [»holtAW11_1980]
Quote: a object in transition is one state becoming another; neither pre-state nor post-state clearly holds [»holtAW11_1980]
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 [»holtAW11_1980]
Quote: a state and its bordering transitions are inseparable; can not resolve arguments about being clearly in a state or clearly in transition [»holtAW11_1980]
Quote: if a state clearly holds, then transitions for the state are unclear; and vice versa [»holtAW11_1980]
Quote: there is no boundary between 'clearly' and 'not clearly' yet 'clearly' has formal properties [»holtAW11_1980]
Quote: the boundary of a region is all objects that are neither in the region nor out of the region [»holtAW11_1980]
Quote: a state space of regions and boundaries forms a topology of open and closed points; isomorphic with undirected Petri nets [»holtAW11_1980]
Quote: two regions of state space are 'separated' if their intersection is closed, 'joined' if the intersection is open, and 'inseparable' if same frame [»holtAW11_1980, OK]
Quote: regions in transition space are processes with bounds called "begins" and "ends" instead of "entrance" and "exit" [»holtAW11_1980]
Quote: general net theory concerns conceptual levels, concurrency, resources, imprecision, and discrete/continuous [»petrCA10_1979]
Quote: an object can only be clearly in one state at a time or one transition at a time [»holtAW11_1980]
Quote: programming is not interested in the state of the machine at every moment; only at prepulses

Subtopic: continuum as overlapping regions up

Quote: the strength of a rope is due to a vast number of overlapping fibers [»wittL_1958]

Subtopic: speech as both continuous and discrete up

Quote: speech has a continuous range of dynamics for expressing emotions (also primates) [»sowaJF_1984]
Quote: speech uses discrete words or morphemes for expressing concepts
Quote: every human language standardizes on a few dozen phonemes even though humans can produce an infinity of sounds [»sowaJF_1984]

Subtopic: biology up

Quote: what atoms belong to a living organism?; vital functions depend an exchange of atoms with the environment

Related Topics up

Group: systems   (17 topics, 530 quotes)

Topic: abstraction by name (29 items)
Topic: change (28 items)
Topic: continuum in mathematics (7 items)
Topic: digital simulation of analog (8 items)
Topic: entities (20 items)
Topic: event time (45 items)
Topic: existence (29 items)
Topic: hardware vs. software (15 items)
Topic: metaphysics and epistemology (99 items)
Topic: quantum mechanics (103 items)
Topic: real numbers and floating point numbers (37 items)
Topic: state (35 items)
Topic: sensitivity of software to change (44 items)
Topic: symbolic representation (26 items)
Topic: telephone system (6 items)
Topic: what is a computer (62 items)
Topic: what is a number
(55 items)

Updated barberCB 5/04
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