Mind Hacks™: Tips & Tools for Using Your Brain (7 page)

More intense signals cause faster reaction times, but there are diminishing returns:
as a stimulus grows in intensity, eventually the reaction speed can’t get any better. The
formula that relates intensity and reaction speed is Pieron’s Law.

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 +
k
I
-β

Reaction Time
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 1-2
.

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).

Figure 1-2. How reaction time changes with stimulus intensity

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.

All abilities are skills; practice something and your brain will devote more resources
to it.

You can play around with Jaakko Hakulinen’s homunculus applet (
http://www.cs.uta.fi/~jh/homunculus.html
; Java) to see where different bits of the body are represented in the sensory
and motor cortex. There’s a screenshot of it in
Figure 1-3
.

This is the person inside your head. Each part of the body has been scaled according
to how much of your sensory cortex is devoted to it. The area of cortex responsible for
processing touch sensations is the
somatosensory cortex
. It lives in
the parietal lobe, further toward the back of the head than the motor cortex, running
alongside it from the top of the head down each side of the brain. Areas for processing
neighboring body parts are generally
next to each other in the cortex, although this isn’t always possible because
of the constraints of mapping the 3D surface of your skin to a 2D map. The area
representing your feet is next to the area representing your genitals, for example (the
genital representation is at the very top of the somatosensory cortex, inside the groove
between the two hemispheres).

Figure 1-3. The figure shown is scaled according to the relative sizes of the body parts in the
motor and sensory cortex areas; motor is shown on the left, sensory on the right

The applet lets you compare the motor and sensory maps. The motor map is how body
parts are represented for movement, rather than sensation. Although there are some
differences, they’re pretty similar. Using the applet, when you click on a part of the
little man, the corresponding part of the brain above lights up. The half of the man on
the left is scaled according to the representation of the body in the primary motor
cortex, and the half on the right is scaled to represent the somatosensory cortex. If you
click on a brain section or body part, you can toggle shading and the display of the
percentage of sensory or motor representation commanded by that body part. The picture of
the man is scaled, too, according to how much cortex each part corresponds to. That’s why
the hands are so much larger than the torso.

Having seen this figure, you can see the relative amount of your own somatosensory
cortex devoted to each body part by measuring your touch resolution. To do this, you’ll
need a willing friend to help you perform the two-point discrimination test.

Ask your friend to get two pointy objects — two pencils will do — and touch one of your
palms with both of the points, a couple of inches apart. Look away so you can’t see him
doing it. You’ll be able to tell there are two points there. Now get your friend to touch
with only one pencil — you’ll be able to tell you’re being touched with just one. The trick
now is for him to continue touching your palm with the pencils, sometimes with both and
sometimes with just one, moving the tips ever closer together each time. At a certain
point, you won’t be able to tell how many pencils he’s using. In the center of your palm,
you should be able to discriminate between two points a millimeter or so apart. At the
base of your thumb, you’ve a few millimeters of resolution.

Now try the same on your back — your two-point discrimination will be about 4 or 5
centimeters.

To draw a homunculus from these measurements, divide the actual width of your body
part by the two-point discrimination to get the size of each part of the figure.

That’s only two parts of your body. To make a homunculus like the one in Hakulinen’s
applet (or, better, the London Natural History Museum’s sensory homunculus model:
http://en.wikipedia.org/wiki/File
:
Sensory_and_motor_homunculi.jpg
), you’ll also need measurements all over your
face, your limbs, your feet, fingers, belly, and the rest. You’ll need to find a fairly
close friend for this experiment, I’d imagine.

The way the brain deals with different tactile sensations is the way it deals
with many different kinds of input. Within the region of the brain that deals with that
kind of input is a surface over which different values of that input are
processed — different values correspond to different actual locations in physical space. In
the case of sensations, the body parts are represented in different parts of the
somatosensory cortex: the brain has a
somatotopic
(body-oriented)
map. In hearing, different tones activate different parts of the auditory cortex: it has a
tonotopic
map. The same thing happens in the visual system, with
much of the visual cortex being organized in terms of feature maps comprised of neurons
responsible for representing those features, ordered by where the features are in visual
space.

Maps mean that qualities of stimuli can be represented continuously. This becomes
important when you consider that the evidence for each quality — in other words, the rate at
which the neurons in that part of the map are firing — is noisy, and it isn’t the absolute
value of neural firing that is used to calculate which is the correct value but the
relative value. (See
See Movement When All Is Still
on the motion
aftereffect for an example of this in action.)

The more cells the brain dedicates to building the map representing a sense or motor
skill, the more sensitive we are in discriminating differences in that type of input or in
controlling output. With practice, changes in our representational maps can become
permanent.

Brain scanning of musicians has shown that they have larger cortical representations
of the body parts they use to play their instruments in their sensory areas — more neurons
devoted to finger movements among guitarists, more neurons devoted to lips among
trombonists. Musicians’ auditory maps of “tone-space” are larger, with neurons more finely
tuned to detecting differences in sounds,
¹
and orchestra conductors are better at detecting where a sound among a
stream of other sounds is coming from.

It’s not surprising that musicians are good at these things, but the neuroimaging
evidence shows that practice alters the very maps our brains use to understand the world.
This explains why small differences are invisible to beginners, but stark to experts. It
also offers a hopeful message to the rest of us: all abilities are skills, if you practice
them, your brain will get the message and devote more resources to them.