Note on the Theory of a Just Noticeable Visual Motion

July 1966

Note on the Theory of a Just Noticeable Visual Motion

J. J. Gibson, Cornell University

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Efforts to determine a just noticeable speed of visual motion have been made for years (Spigel, Readings), but seem to have failed (Gibson, in Spigel). If there is no speed threshold, is there perhaps adisplacement threshold (Graham in Stevensí Handbook)? A displacement of an object in the world (or a spot in an array) is surely detectable. Does it have a threshold?

I believe that the more “sudden” the displacement the less extensive it need be for detection. Conversely, the slower the displacement, the longer it must be (the more angular distance it must traverse in the optic array). Considering a spot of light in an otherwise homogeneous total field, does a perceptible “jerk” occur with either a small displacement in a short time or a larger displacement in a longer time? (Cf. the experiment of Hick). Korte’s third “law” for optimal stroboscopic motion refers to small displacements in a short time and large displacements in a long time (Koffka, p. 292). This suggests constant speed over varying displacements. What is the threshold formula for continuous displacements as distinguished from discontinuous displacements (so-called “real” motion as contrasted with so-called “apparent” motion)?

Perhaps speed has nothing to do with a just noticeable displacement-event. At a very small displacement a high speed (ds/dt) may be necessary whereas a very low speed may be sufficient with large displacement. An event motion of this sort does not really have speed. Perhaps the only threshold for “motion” is for a motion of this sort. And a displacement may go below noticeability by being either too small in optical extent or too slow in time. But perhaps smallness may be compensated by quickness and slowness may be compensated by extendedness.

That is, with a single spot of light in darkness (which is the only case where an optical motion is not a transformation or change of “form” in some sense of that term) one can ask two questions:

1. What is the shortest constant-speed displacement of the spot that is detectable? (This would have to be determined for a whole set of angular speeds).

2. What is the slowest one-degree displacement of the spot that is detectable? (This would have to be determined for a whole set of visual angles).

Neither of these determinations would yield a “displacement threshold” in the exact meaning of that term. But a third question, as formulated above, might receive an intelligible answer. Do speed and displacement trade off?

Let us note that the classical method of trying to determine the just noticeable speed of motion is to hold constant the source of optical motion (an endless belt, a disk, a scope face) and vary the speed of the object.

But this method does not experimentally isolate speed of optical motion since (as the Cornell experiments have shown), it entails a change or pattern or transformation, not simply the rate of change of position with time (ds/dt).

There may be no such thing as a fixed displacement threshold just as (I am convince) there is no such thing as fixed velocity threshold. But if there is anything determined for a single spot in an empty field it might be discovered in the way suggested.