It's a common illusion
that if you are in a hurry for the elevator you can make it come
quicker by pressing the button harder. Or more often. Or all the
buttons at once. It somehow feels as if it ought to work, although of
course we know it doesn't. Either the elevator has
heard you, or it hasn't. How loud you call
doesn't make any difference to how long
it'll take to arrive.
But then elevators aren't like people. People
do respond quicker to more stimulation, even on
the most fundamental level. We press the brake quicker for brighter
stoplights, jump higher at louder bangs. And it's
because we all do this that we all fall so easily into thinking that
things, including elevators, should behave the same way.
In Action
Give someone this simple task: she must
sit in front of a screen and press a button as quickly as she can as
soon as she sees a light flash on. If people were like elevators, the
time it takes to press the button wouldn't be
affected by the brightness of the light or the number of lights.
But people aren't like
elevators and we respond quicker to brighter lights; in fact, the
relationship between the physical intensity of the light and the
average speed of response follows a precise mathematical form. This
form is captured by an equation called Pieron's Law.
Pieron's Law says that the time to respond to a
stimulus is related to the stimulus intensity by the formula:
Reaction Time
R0 + kI-β
ReactionTime is the time
between the stimulus appearing and you responding.
I is the physical intensity of the signal.
R0 is the minimum time for
any response, the asymptotic value representing all the components of
the reaction time that don't vary, such as the time
for light to reach your eye. k and
β are constants that vary depending
on the exact setup and the particular person involved. But whatever
the setup and whoever the person, graphically the equation looks like
.
Figure 1. How reaction time changes with stimulus intensity
How It Works
In fact, Pieron's Law
holds for the brightness of light, the loudness of sound, and even
the strength of taste.1 It says something
fundamental about how we process signals and make decisions—the
physical nature of a stimulus carries through the whole system to
affect the nature of the response. We are not binary systems! The
actual number of photons of light or the amplitude of the sound waves
that triggers us to respond influences how we respond. In fact, as
well as affecting response time, the physical intensity of the
stimulus also affects response force as well (e.g., how hard we press
the button).
A consequence of the form of Pieron's Law is that
increases in speed are easy for low-intensity stimuli and get harder
as the stimulus gains more intensity. It follows a log scale, like a
lot of things in psychophysics. The converse is also true: for quick
reaction times, it's easier to slow people down than
to speed them up.
Pieron's Law probably
results because of the fundamental way the decisions have to be made
with uncertain information. Although it might be clear to you that
the light is either there or not, that's only
because your brain has done the work of removing the uncertainty for
you. And on a neural level, everything is uncertain because neural
signals always have noise in them.
So as you wait for light to appear, your neuronal decision-making
hardware is inspecting noisy inputs and trying to decide if there is
enough evidence to say "Yes, it's
there!" Looking at it like this, your response time
is the time to collect enough neural evidence that something has
really appeared. This is why Pieron's Law applies;
more intense stimuli provide more evidence, and the way in which they
provide more evidence results in the equation shown earlier.
To see why, think of it like this: Pieron's Law is a
way of saying that the response time improves but at a decreasing
rate, as the intensity (i.e., the rate at which evidence accumulates)
increases. Try this analogy: stimulus intensity is your daily wage
and making a response is buying a $900 holiday. If you get paid $10 a
day, it'll take 90 days to get the money for the
holiday. If you get a raise of $5, you could afford the holiday in 60
days—30 days sooner. If you got two $5 raises,
you'd be able to afford the holiday in 45
days—only 15 days sooner than how long it would take with just
one $5 raise. The time until you can afford a holiday gets shorter as
your wage goes up, but it gets shorter more slowly, and if you do the
math it turns out to be an example of Pieron's
Law.
End Note
Pins, D., & Bonnet, C. (1996). On the relation between stimulus
intensity and processing time: Pieron's law and
choice reaction time. Perception & Psychophysics,
58(3), 390-400.
