Biomedical Engineering Reference
In-Depth Information
F
max
= 1 + B/2.
[29]
For any given value of perceptual accuracy B, the payoff converges to a maxi-
mum as a result of perceptual error. Increasing the number of signals increases
the number of objects that can be communicated about, but at the cost of in-
creased ambiguity. We have called this the
linguistic error limit
. It is our hy-
pothesis that phonology, word formation, and simple grammar evolved through
a need for greater robustness in response to inevitable errors of communication.
The key to understanding how this works is to think in terms of composite
words, in which a word
W
ij
consists of phonemes
i
and
j
. The similarity between
words
W
ij
and
W
kl
is given by
s
ik
s
jl
. The payoff to a language that contains
n
2
words to describe
n
2
objects is
¬
-
n
n
1
-
-
F
=
-
-
n
n
-
-
ss
-
i
==
=
1
j
1
®
ik
jl
j
1
l
=
1
2
¬
-
¯
¡
-
n
1
-
=
¡
°
,
[30]
-
-
¡
n
°
-
-
s
-
¡
i
=
1
®
°
ij
¢
±
j
=
1
and for words of length
L
L
¯
¬
-
¡
°
-
n
1
-
¡
°
=
.
[31]
-
-
¡
°
n
-
-
s
-
¡
i
=
1
®
°
ij
¢
j
=
1
±
Hence, the total payoff can now grow exponentially with the length of words.
Words, according to this formulation, are a cultural robustness mechanism.
5.
AWAITING A SYNTHESIS OF ROBUSTNESS IN
BIOLOGICAL SYSTEMS
I have presented a superficial overview of various research projects aimed
at understanding robustness in biological systems. I have tried to organize this
work into a number of principles of robustness—a theoretical taxonomy—so
that common patterns and mechanisms might become apparent to the reader. It
is unfortunate that there does not exist a single theory of biological robustness
that might be applied to these several different problems. The historical, and to
