Bioinformatics An Introduction 4th Edition (Jeremy Ramsden)

The Nature of Information

The only meaningful way of interpreting the ﬁrst category is to suppose that the

order was implicit in the initial state; hence, it is questionable whether information

has actually been generated. In the second category, the volume of ordering has

increased, but inevitably at the expense of more disorder elsewhere, because of the

physical exigencies of the copying process. ³²Note that copying per se does not lead

to an increase in the amount of information. The third category is of genuine interest,

for it illuminates problems such as that of the development of the zygote, in which

environmental information is given meaningful macroscopic expression, such that

we are indeed more complex than the zygotes whence we sprang.

Problem. Examine the proposition that the production and dissemination of copies

of a document reporting new facts does not increase the amount of information.

6.5

Summary

Information is that which removes uncertainty. It has two aspects: form (what we

already know about the system) and content, the result of an operation (e.g., a mea-

surement) carried out within the framework of our extant knowledge. Form speciﬁes

the structure of the information. This includes the speciﬁcation of the set of possible

messages that we can receive or the (design and fabrication of and way of using the)

instrument used to measure a parameter of the system. It can be quantiﬁed as the

length of the shortest algorithm able to specify the system (Kolmogorov informa-

tion). If we know the set from which the result of the measurement operation has to

come, the (metrical) content of the operation is given by the Shannon index (reducing

to the Hartley index if the choices are equiprobable). A message (e.g., a succession

of symbols) that directs our selection is, upon receipt, essentially equivalent to the

result of the measurement operation encoded by the message. The Shannon index

assumes that the message is known with certainty once it has been received; if it is

not, the Wiener index should be used.

Information can be represented as a sign or as a succession of signs (symbols). The

information conveyed by each symbol equals the freedom in choosing the symbol. If

all choices are a priori equiprobable, the speciﬁcation of a sequence removes uncer-

tainty maximally. In practice, there may be strong syntactical constraints imposed

on the successive choices, which limit the possible variety in a sequence of symbols.

In order to be considered valuable (or desired), the received information must

be remembered (macroscopic information). Microinformation is not remembered.

Thus, the information inherent in the positions and momenta of all the gas molecules

in a room is forgotten picoseconds after its reception. It is of no value.

Information can be divided into three aspects: the signs themselves, their syntax

(their relation with each other), and the accuracy with which they can be transmitted;

32 The creation of disorder could be avoided by doing things perfectly reversibly, but that implies

doing them inﬁnitely slowly and is, hence, scarcely of practical interest.