83. Motion, Divisibility, and the Nature of the Now

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Lecture Notes

Main Topics #

• The Now as Limit: The present moment is the indivisible boundary between past and future, analogous to how a point is the limit of a line
• Continuity and Divisibility: Everything continuous (time, motion, bodies) must be divisible; the indivisible cannot compose the continuous
• Motion Cannot Occur in the Now: Since the now is indivisible, no actual motion can take place within it—motion requires divisible time
• The Divisibility of the Mobile: Whatever moves must be divisible into parts, as demonstrated through the analysis of bodies in transition
• The Minimal Reality of Motion: Motion “barely is” because it is never fully present—it exists imperfectly between potency and actuality

Key Arguments #

Why the Moving Thing Must Be Divisible #

• When a body moves from position AB to position BC (where both regions are equal to the body’s length):

  • When the body is wholly in AB, motion has not yet begun
  • When the body is wholly in BC, motion is complete
  • Therefore, during motion, the body must be partly in AB and partly in BC simultaneously
  • This requires the body to be divisible into parts

• The same principle applies to qualitative change (alteration):

  • A body changing from white to black must pass through intermediate states (e.g., gray)
  • When entirely white, alteration has not begun
  • When entirely gray or black, the alteration progresses
  • The changing thing must be partially in both the initial and intermediate states

Why Motion Cannot Occur in the Now #

• The now is indivisible (it is the boundary between past and future)
• If motion occurred in the indivisible now, two bodies of different speeds could traverse different distances in the same indivisible instant
• This would require the now to be divisible to account for the difference in speeds
• Since the now cannot be divided, motion cannot occur within it
• Motion necessarily requires divisible time

Important Definitions #

• The Now (τὸ νῦν): The indivisible limit of both past and future time; the present instant that serves as the boundary of temporal division
• Continuous Quantity: That whose parts meet at a common boundary or limit; characterized by divisibility
• Motion: Imperfect actuality; actualization of potency as such; change from one state to another
• Divisible: Capable of being divided into distinct parts; possessing extension or magnitude
• Change (ἀλλοίωσις - alteration): Qualitative transformation from one quality to another (e.g., white to black)

Examples & Illustrations #

The Train and Track Example #

• A train occupies a length of track equal to its own length
• When the entire train occupies the first section of track, it has not yet begun to move
• When the entire train occupies the second section (equal length), motion is complete
• During the motion between these two states, the train must occupy both sections—part in the first, part in the second
• This demonstrates that what moves must be divisible

Color Alteration Example #

• A body changing from white (the initial state) toward black (the final state)
• Gray serves as an intermediate state between white and black
• When entirely white, alteration has not begun
• When entirely black, alteration is complete
• During the transition, the body exists partially white and partially in the intermediate or darker state
• This is less clear than local motion but illustrates the same principle

Growth Example #

• When something grows from five feet tall to six feet tall, at what point is it exactly five feet? At what point is it exactly six feet?
• During the growth, it must be “in between”—it is neither fully one height nor the other
• This again demonstrates divisibility of the changing thing

Notable Quotes #

“Everything changing necessarily is divisible, for since every change is from something to something, and when it is in that to which it has been changed, it is no longer changing…” — Aristotle, cited by Berquist

“The now is the limit of the past in this direction, and the limit of the future in the other direction.” — Berquist, explaining Aristotle’s concept of the now

“Motion hardly is… because it isn’t in the now.” — Berquist, reflecting on motion’s paradoxical minimal existence

“If no one asks me what time is, I know what it is, but if someone asks me what it is, I don’t know.” — Augustine, Confessions (cited by Berquist)

Questions Addressed #

Why must the moving thing be divisible? #

Because during motion, a body must simultaneously exhibit characteristics of both its initial position/state and its final position/state. This simultaneous presence of contraries is only possible if the body is divisible into parts, with different parts in different states.

Can motion occur in the now? #

No. The now is indivisible, and motion requires time, which is divisible. Since nothing can be in motion in an indivisible instant, motion necessarily occurs over divisible time (the past and future).

What does this reveal about motion’s nature? #

Motion is an “imperfect act”—it barely exists. It is never fully present because the past is no longer, the future is not yet, and the now contains no motion. This makes motion difficult to understand philosophically.

Connections to Modern Physics #

• Instantaneous Velocity: Modern physics speaks of instantaneous velocity as a limit (not as actual motion occurring in an indivisible instant), which may be a useful fiction based on Aristotelian principles
• Quantum Theory: The development of quantum mechanics led modern physicists back to Zeno’s paradoxes and the classical problems of divisibility and motion
• Uncertainty Principle: The impossibility of simultaneously pinpointing both a body’s exact position and its dynamic properties parallels Aristotle’s insight that motion cannot occur in the indivisible now
• Louis de Broglie: Referenced for discussing the connection between quantum theory discoveries and classical philosophical problems of motion