New trends in physics teaching, v.4; The ... - unesdoc - Unesco

Entropy and Information
society - one has to switch currents off and on as fast as possible. In each half wave of an alternating
current, one bit of information can be stored (whether or not the half wave is at full
amplitude). Therefore, the feasibility of communication networks was linked historically to the
progress of high-frequency technology. The highest requirements are posed by television. Each
television picture consists of, say, 500 lines containing 600 points each, i.e. a total of 3 X 10’
points. If we assume, for the sake of simplicity, that each point can be either black or white, the
total information content of one picture becomes 3 X IO5 bit. Since 25 pictures have to be
transmitted per second, the total information flow becomes 7.5 X lo6 bit/s. From this we can
easily calculate the band width required for the transmission of television pictures. Since each
bit corresponds to a half wave, the total band width becomes
Af=?hX7.5X 106/s~4MHz.
The frequency f of the carrier signal should be at least f x l0OAf~ 400 MHz. From the relation
fX=c we can now calculate the wavelength used in television:
X=c/f= 3 X i08ms-l/4 X lo8 s-l x 1 m.
Returning to our examples from biology we can calculate to how many seconds of television
commercials the genetic information contained in man corresponds. Since roughly 1 O7 bit can
be transmitted per second we obtain for the time T needed:
lo7 bit/s X T = lo9 bit or T= 100 s.
Therefore it would take about two minutes to transmit the genetic make-up of man in the form
of a television commercial.
In another example using television we can check the proverb: ‘A picture says more than a
thousand words.’ One word contains about 30 bit of information, if we assume that it consists
of six letters. Therefore the information contained in 1000 words is 3 X lo4 bit. Bearing in mind
that one television picture contains about 3 X lo5 bit, it follows that one picture corresponds
to roughly 10 000 words (or about 30 pages).
In conclusion, we refer to another problem which can also be solved with the help of information
theory. Of twelve balls, one ball is either heavier or lighter than the other eleven balls. The
object is to find out, using a balance, which ball is the odd one out and whether it is heavier or
lighter than the rest. This problem is clearly one of missing information, which is to be gained by
using the balance. How many times do the balls have to be weighed in order to supply the missing
information? 171.
ENTROPY AND INFORMATION
With the help of the metric concept of information we can characterize the information missing
about thermodynamic systems. While a detailed knowledge of the initial positions and velocities
of all mass points contained in an n-body problem is assumed in mechanics, the exact positions
and velocities of the numerous molecules contained in a gas or another thermodynamic system
are never known exactly. This lack of information about thermodynamic systems is described
by entropy.
At first it might seem that the lack of knowledge about the initial conditions of the molecules
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