Time as the Number of Motion, and the Problem of the Now

Orientation #

He picks up at “the second paragraph of the seventeenth reading” and later turns to “the eighteenth reading,” recalling “the problem we had about the now” (prev. lecture: the puzzle whether the now is the same or always other). He promises “let’s wait till we see the definition of time” for why before-in-time is the central sense. The previous class refuted the opinions that time is the heaven’s motion or the sphere and established time as “something of” motion; the next develops the now/mobile proportion.

The class, in order #

1. Continuity and before-and-after pass from magnitude to motion to time (“proportional to those there”) #

Point: as the continuous is first in magnitude and hence in the motion over it and hence in the time the motion takes, so before and after is first in magnitude (in place, in position), then proportionally in motion, then in time.

• Reading: “since there is a before and after in the magnitude, necessarily there is a before and after in motion proportional to those there; but also in time, because always one of these follows the other.”
• Proportion, his usage: he follows Euclid, not Thomas (who, “taking into account that people tend to use the word proportion for what is ratio,” uses it for ratio). Euclid: proportion (Greek “analogy”) is a likeness of ratios. 2:3, 3:4, 4:6 are three ratios; 2:3 is not as 3:4, but 2:3 is as 4:6 — four terms, first to second as third to fourth; then alternating proportion: first to third as second to fourth.
• Road example: on a road A–C, AB comes before BC (place); the motion from A to B is before the motion B to C; the time likewise. “If AB is to BC, so the motion over AB is to the motion over BC,” and the times the same — unless you complicate it by going faster and slower.

2. Why before-in-time is the central sense though before-and-after is first in place (“things in motion sooner catch the eye”) #

Point: Aristotle gives before in time as the first sense and reduces before in motion and before in magnitude to it, because before and after in motion is what comes to mind first — we name things as we know them.

• Shakespeare, Troilus and Cressida: “things in motion sooner catch the eye than what not stirs.” His grandchild’s wind-up mobile (music plus little animals moving) distracts the baby; Aristotle on the rattle — babies’ limbs always moving when awake (muscles developing, he supposes).
• “The sense in which one is before two is much more abstract,” not as concrete to the senses.
• Third paragraph read: before and after is first in place, “in position,” a firm position because places are not moving.
• Question he raises: why make time the central sense when before and after is first in place? Answer deferred to the definition of time: before and after is in the very definition of time, whereas the definition of motion did not use before and after. Contrast with the word in: there place is the central sense and time attached to it, because being in a place (“I’m in this room”) is clearer to us than being in time, which is “at first a little bit obscure.”
• Daily usage as sign: “I’m going to do this before I do that” — you think of time, not place; “afternoon” is common, “forenoon” less so.
• Student: before and after in magnitude presupposes motion — why is AB before BC unless you think of a motion? He grants it: in magnitude it is “a little more arbitrary” which end is beginning. Time, by contrast, is one-directional (even physicists wonder at this): over a distance I can go and come back; in time I can’t get younger — “except in the movies.”

3. Before-and-after in motion: the same thing as motion, but not its definition (“as regards that which it is, is motion”) #

Point: the fourth paragraph — “the before and after in motion, as regards that which it is, is motion, but to be that is other” — means the before-and-after is not a different thing from the motion, yet it is not what motion is by definition.

1. The definition of motion was “the act of what is able to be, as such”; it contains no before and after.
2. So before-and-after in motion is not something other than the motion, but is not motion by definition.
3. What he is leading to: time is something of motion, but of the before-and-after in motion rather than of the definition of motion — which is why the reference to before and after is explicit in time and not in motion’s definition.

4. How we know time: dividing motion by the now; the definition (“the number of motion according to the before and after”) #

Point: we know time when we divide the motion, separating before and after, and “the soul says the nows are two.”

• Even talking of the now: unless you realize this now is not the now in which I fell asleep — one before, one after — you are not aware of time.
• Reading: we divide by taking the extremities as other with something in between; when the soul says the nows are two, the one before and the other after, then we say this is time; “what is divided by the now seems to be time, and let this be supposed.”
• The now is to time a bit like the point to the line: if this point is not that point, there is a distance between; if this now is before that now, there must be a time between.
• You have to see a number, “because two is the first number.”
• When we sense the now as one, neither time nor motion seems to have been; when as before and after, “and therefore as two,” we speak of time.
• Definition read: time is the number of motion according to the before and after; time is not motion but “as motion has a number,” as you number the before and after in it.

5. Concrete: ten days, Robinson Crusoe’s stick, the watch (“what is time, right?”) #

Point: any amount of time is really a number of some motion according to the before and after in that motion.

• He was gone (to Massachusetts, Friday to Monday night): the time he was gone is a number — “ten days,” as he puts it [ed.: the transcript’s count; kept as spoken] — days being the sun going around.
• Robinson Crusoe, stranded, keeps a smooth piece of wood and makes a mark at each sunset: one sunset before, another after — numbering the before and after of the (apparent) motion of the sun around the earth.
• Timing a run with his watch: one minute, two, three, four, five — counting circulations, one before the other, imitating the sun’s motion.
• Hours: dividing one circulation of the sun “kind of arbitrarily” into twenty-four parts; still the motion from here to here is before the motion from here to here.
• Aside: the modern physicist doesn’t ask “what is time” but “what time is it” (three thirty-three); we ask what time is — always a number, of a before and after in some motion, often the sun’s, and “we’ll see why he takes that particular motion.”

6. Time is a numbered number; long and short, more and less (“the vulgar distinction”) #

Point: the sign that time is some number is that we judge more and less by number, but motion more and less by time; the number time is, is the numbered, not that by which we number.

• Reading: number is twofold — the numbered/numerable, and that by which we number; time is the numbered; arithmetic is about the number by which we number (the abstract number); the two are other.
• John of St. Thomas calls this “the vulgar distinction between numbering number and numbered number”; his history teacher, whose thesis concerned number, was puzzled by it.
• Seven vs. seven dogs: seven dogs is the numbered number; seven, the number by which we number. Time is like seven dogs — but the number of something continuous, like “three yards, three feet.”
• Distinction: more/less (discrete quantity, cf. the Categories; seven is more than five, not longer) vs. long/short (continuous; one line longer than another). Time takes both — “a long time,” “less time” — because it is a number (more, less) of something continuous (long, short).
• Aside: “as Heisenberg said,” it takes more time to ask the right question than to get the answer once asked.

7. The eighteenth reading: the problem of the now restated (“the now is the same as regards what it is”) #

Point: the problem is whether the now is the same throughout all time or always different, and either horn looks impossible.

• Same now throughout: then all events are in the same now — the American Revolution would be taking place now, along with the war with the terrorists in Afghanistan.
• Always different: when does a now cease to be? Not in the now when it is; not in a later now, for there is no next now — any later now you name, the earlier would be simultaneous with all the nows between.
• Text read: as motion is always other and other, so is time; the now is the same as regards what it is, but “being for the same is other”; the now determines times insofar as it is before and after; insofar as it is other and other it is different, “for this was being for the now itself,” but as some thing it is the same.
• Aristotle solves this “by the ability to see a proportion.”
• Aside: reading the newspaper, “another crazy thing going on” on every page.

8. Digression: Euclid Book V and the power of seeing proportions (“Incommensurable magnitudes”) #

Point: the ability to see a proportion is “so important in the whole philosophy,” and you first meet it in Euclid’s theory of proportions.

• Books I–IV go along; Book V is “something kind of new.” Before it came a scandalous discovery: incommensurable magnitudes — two lines that don’t have the ratio of a number to a number, so ratio among lines can’t simply be assimilated to ratio among numbers. Stories that the man who revealed it drowned, punished; “irrational.”
• After Book V establishes proportion for the continuous, Book VI redoes geometry in its light and it becomes astoundingly powerful: the Pythagorean theorem, the completion of Book I, is shown true for every figure — equilateral, equiangular pentagons on the sides of a right triangle, hexagons likewise.

9. The proportion: as time to motion, so the now to the thing in motion (“Better be”) #

Point: “the thing carried along is similar to the point by which we know motion and before and after in it”; the now stands to the mobile as time stands to motion.

• Baseball: is it the same ball hit in the infield and caught in the outfield? “Better be, or something’s very fishy.” Yet the ball is always other, because it is always somewhere other. Same as regards what it is (a baseball, not a football), other in position.
• Proportion stated (at a student’s request, repeated): time is to motion as the now is to the thing in motion. So the now is always the same as regards what it is — never ceases to be what it is, hence incorruptible — but always other in position, before and after; and as the ball in motion makes motion insofar as it is always other in place, so the now makes time insofar as it is always other.
• Student: can we replace the thing in motion with a point? “No, no” — it is a comparison, but it reminds him of what the Platonists say, that a point by its motion makes a line (the point has no length, is always the same point, but here and then there) — “so you can compare it a bit to that.”

10. Digression: definition in geometry against “define it how you want” (“the diagonal of a circle divides the circle”) #

Point: you know the diameter bisects the circle not from the definition of diameter but by resolving to the definition of circle, and ultimately to the point; the modern mind treats definition as arbitrary.

• Euclid defines circle, defines “diagonal” [ed.: diameter, as he himself says once], and states without proof that it divides the circle into two equal parts. His students say “that’s the definition” — but the definition is only a line drawn from a point on the circumference through the center to the opposite side; equal parts are not in it. (Contrast: the triangle has three sides by what a triangle is.)
• Thales’s way: lay one part on the other, same base; if the arcs coincide they are equal; if one fell above or below, the radii would not all be equal, contradicting the definition of circle (plane figure contained by one line, every point equally distant from the center). Without knowing the circle by its definition you could not see something so obvious.
• Student-type objection: isn’t “all radii are equal” itself arbitrary? Reply: go back to the generation of the circle — rotate a straight line around one end (as Euclid defines the sphere by rotating a circle around its diameter, though he doesn’t define circle that way in Book I); then it is obvious, not arbitrary.
• One step further: the line has no width — arbitrary? Answer either “the limit of a surface” (only a proportion, he grants) or, as the Platonists, a point by its motion makes a line; the point has no width, so neither does the line; rotate the line, a circle; the circle, a sphere. “Everything is clear”: in geometry you go all the way back to the point to imagine things as you should.
• Story: his freshman mathematics class at the College of St. Thomas, the cigar-smoking ex-parachutist teacher arguing with his brother Marcus: “I can define anything I want to define, and see where you go from there” — foreign to what Euclid is doing, but “the way the modern mind thinks.”
• Student: they think of giving a meaning to a word, whereas you are saying what something is. He agrees: not “resolving the imagination.”
• Modern mathematicians: “a straight line meaning itself” — he put the book down; “a triangle can have more than two right angles” (lines of longitude meeting the equator on a sphere) — a fallacy of equivocation on triangle and right angle; there is a likeness, “but not exactly the same meaning.”
• Shooting light beams between mountains to test whether interior angles equal two right angles: confusing math with natural philosophy — geometry is about quantity in separation from sensible matter, not measuring the sensible world.
• Aside: a lawsuit by homosexuals to be admitted as a marriage — “you can define marriage any way you want to.”

11. Return: the now, same and other, proportionally to the mobile (“the now is to the thing in motion”) #

Point: the now is to the thing in motion as time is to motion; we must understand how the now is always the same in one way and always other in another, proportionally to the mobile, same as regards what it is, other as to where it is. He leaves it there.

His words #

• proportion: Euclid’s sense, a likeness of ratios (Greek “analogy”), not Thomas’s usage for ratio
• alternating proportion: first to third as second to fourth
• before and after “first in place, there in position”
• definition of motion: “the act of what is able to be, as such”
• the now: divides motion; “the soul says the nows are two”
• time: “the number of motion according to the before and after”
• numbering number vs. numbered number: John of St. Thomas’s “vulgar distinction”; time is a numbered number
• more/less (discrete) vs. long/short (continuous)
• “being for the same is other” / “this was being for the now itself” [ed.: the esse of the now]
• “diagonal” of a circle [ed.: diameter]
• resolving the imagination: going back to the point

Texts #

Read in class:

• Aristotle, Physics IV, in Aquinas’s commentary, seventeenth reading, paragraphs 2–4 and the definition of time (verified: lectio 17)
• the “eighteenth reading,” opening paragraphs on the now (his numbering; the verified match is lectio 17)
• handout: “The First Definition of Reason,” p. 18 (verified read from it)

Mentioned:

• Shakespeare, Troilus and Cressida (“things in motion sooner catch the eye”)
• Aristotle on the rattle (no locus given)
• Aristotle, Categories (more and less as discrete quantity)
• Aristotle on the senses of in and of before (no locus given)
• Euclid, Elements: Book I (circle, diameter, Pythagorean theorem), Book V (proportions), Book VI, definition of sphere
• John of St. Thomas on numbering and numbered number
• Thales’s proof that the diameter bisects the circle
• Heisenberg (remark on asking the right question)

His questions #

• Why does Aristotle make before-in-time the first sense, when before and after is first found in place? Deferred: because before and after enters the very definition of time and not of motion; time is more explicit to us in daily usage.
• What does he mean: the before and after in motion “as regards what it is” is motion, but “to be that is other”? It is not a different thing from motion, but not what motion is by definition.
• Would you say I was gone for some time? How many days? Ten days — a number of the sun’s motion, before and after.
• Why do we say both “more/less time” and “long/short time”? Because time is a number (more, less) of something continuous (long, short).
• What was the scandalous discovery before Book V of Euclid? Incommensurable magnitudes.
• Is it the same ball hit in the infield and caught in the outfield? Yes, same as to what it is, always other as to where it is.
• Can we replace the thing in motion with a point? No; it is only a comparison, though like the Platonists’ point making a line.
• How do you know the diameter divides the circle into equal parts? Not by definition; by superposition resolved to the definition of circle (Thales).
• When does a now cease to be, if it is always different? Left open here; to be solved by the proportion of now to mobile.