Information Technology Reference
In-Depth Information
complex. No system can exhibit a complex behavior, without a reliable system of
data processing. This is the reason why living organisms need sophisticated mecha-
nisms of data manipulation.
Information occurs with data transformations, while energy occurs with states
transformations. Information needs energy for transforming, sending, receiving, and
storing data, but simultaneously, it may control actions. In those cases where it does
not provide a direct control of actions, it can be always located in a chain of effects
which terminates with a control, or a potential control. For example, some keys in
a computer keyboard send signals with direct effects to some device (for example,
a printer), while pushing other keys provides only the memorization of characters
somewhere (by forgetting their side effects on the screen). Typically, a document
does not have a direct effect of data transformation, but it is aimed at provoking
or evoking actions. Moreover, very often, the effects of some data are not easily
definable, because their information can act at different levels. For example, the
production of a topic could have effects at the level of the topic market, but also
effects in the diffusion of ideas and consequent behaviors.
The term “discrete” in mathematics refers to any aggregation of objects where
components are clearly distinguishable. A finite set of objects is the simplest exam-
ple of a discrete structure. A segment, considered as a subset of points on a line is an
example of “continuous” structure, because the geometrical representation of lines
assumes that in the middle between two points there are other points, and moreover,
that infinite intermediate points can be found with an endless process of resolution
refinement. Space and time are usually modeled as continuous magnitudes. This is
probably an idealization, with respect to the physical reality, but it provides pow-
erful mathematical concepts for their analysis. The surprising results of classical
physics (mechanics and electromagnetism) are based on continuous mathematical
structures (real numbers, limit process, differential calculus). The 19th century con-
cluded (Planck's famous quantum theory is dated November 1900) with the discov-
ery of the discrete nature of matter and energy (the origin of Dalton's atomic theory
is dated September 1803).
Information is discrete when data are based on discrete mathematical structures
(the fundamental ones are presented in the second part of this topic).
Digital infor-
mation
is the discrete information, which refers to data realized by sequences of
digits
(elements of a finite set).
Data are represented by means of symbols, which are physical entities. Their
physicality is an intrinsic aspect of their nature; even the abstract symbols of math-
ematics introduced for algebraic manipulation need a physical realization, that is, a
quantity of matter/energy in order to be produced and perceived. A finite set of
sym-
bols
(digits, characters, letters, signs) is called an
alphabet
. The English alphabet
has 26 letters. Most alphabetic writing systems have around 20-30 characters (Ar-
chaic Latin has 21 letters). The chemistry alphabet of Mendeleev's table is given by
the symbols of atomic species (around 100 elements):
.
The alphabet of amino acids is of 20 symbols (21 including one stop symbol). The
alphabet of the usual Indo-Arabic decimal notation has ten digit symbols.
{
H
,
He
,
Br
,...,
C
,
O
,
N
,...}
