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

New Trends in Physics Teaching IV
some simple cases only, in which all events considered occur with equal probability. Despite this
restriction we will, however, be able to deal with a number of very interesting and relevant
examples from various sciences [ 41 .
With the definition given above, we can discuss several relevant examples of information
storage. Table 1 gives the number of bits contained in various sources of information.
TABLE 1. Information content of the ‘letters’ of various sources of information
Alphabet N=32 n=5
Genetic code N=4 n=2
Numbers N= 10 n = 3.32
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According to this table, one letter of the alphabet contains five bit of information and an average
word - containing six letters - corresponds to thirty bit. For simplicity, we have assumed here
that all letters in the alphabet occur with equal probability. Only in this case can our result
(Eq. 1) be applied. If this is not the case - or if the sequence of letters contains correlations -
the amount of information contained in one letter is less than the result indicated above. This
leads to interesting questions of redundancy, which wil not be dealt with here [ 5 I .
A different type of alphabet is contained in the genetic code [6]. The genetic information
contained in DNA is encoded into the sequence of the four different bases (thymine, adenine,
cytosine, and guanine). One base corresponds to two bit of information, since there are four
different possibilities. The double helix of Drosophila (the fruit-fly) is a giant molecule with
a length L = 1.2 cm. Each of its subunits containing two bit of information has a length of
approximately 1 = 1.2 X lU7 cm. The total information contained in the genetic code of
Drosophila is thus
n = 2L/Z = 2 X lo7 bit. (Eq. 3)
In a similar way the information content of various other organisms can be calculated (see
Table 2). With the help of Table 1, we can translate this into various other types of information.
How many pages are needed for a ‘build-your-own-man’ book? If one page has 30 lines with 70
characters to a line then its information content is
TABLE 2. Information content of various organisms
Organisms
Virus
Drosophila (fruit fly)
Mm
n (1 page) = 30 X 70 X 5 = lo4 bit. (Eq. 4)
Information
2 X lo4 bit
2 X lo7 bit
lo9 bit
Thus the genetic information contained in a virus corresponds to two pages, while for Drosophila
2000 pages are needed and for a man lo5 pages, i.e. the content of about 500 books. It is rather
surprising that so little information is needed to build a virus. Maybe this can help in understanding
how life originated.
This result brings us to one of the most important technical problems in communication
theory. If we want to communicate information at a great rate - as is required by modern
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