For example, when we use GPS for geolocation, the calculation is made possible by an algorithm. The same can be said when we write a word in a search engine on the web. Its use is vast and varied, from finance, where it might seem obvious, to medicine, to optimize drugs or anti-tumor therapies. In time, however, this term has crossed the boundaries of mathematics, taking on new meanings. We talk about the algorithm to find the perfect match or the perfect vacation.
Schematizing and formalizing our actions today is a common practice useful for ordering our actions and ideas in order to move according to new standards that we impose on ourselves. The following example is interesting.
Despite the lexical suggestions, the term 'algorithm' does not derive from 'algebra' or 'arithmetic', but from the appellation al-Khuwarizmi (originally from Corasmia) of the mathematician Muhammad ibn Musa of the 9th century.
In the archaic version 'algorism', it was used in the 13th century to denote the Arabic numeral system and, subsequently, the methods of arithmetic. Only in more recent times has the term unequivocally taken on the connotation of a formal calculation procedure.
At first, the term algorithm was used exclusively in mathematics, today it has entered common language where it often undergoes a 'fading of meaning', reducing the concept to a method for achieving a goal.
It is now evident how we can find an algorithm even by simply thinking about the actions we perform daily.
An example is the procedure for preparing the moka for coffee, or all the steps for a good laundry,
or even better the procedure exposed in any culinary recipe.
So, our mother's recipe book is a real book of algorithms!
In order for a 'recipe', a list of instructions, to be considered an algorithm, the following requirements must be met:
Finiteness: every algorithm must be finite, i.e. every single instruction must be able to be executed in finite time and a finite number of times
Generality: every algorithm must provide the solution for a class of problems; it must therefore be applicable to any set of data belonging to the definition set or domain of the algorithm and must produce results that belong to the arrival set or codomain of the algorithm
Non-ambiguity: the steps to be executed must be defined in a unique way; paradoxes, contradictions, and ambiguities must be avoided; the meaning of each instruction must be unique for whoever executes the algorithm
Here are the five points you should remember to define the characteristics of an algorithm:
- the constituent steps must be 'elementary', i.e. not further decomposable (atomicity);
- the constituent steps must be interpretable in a direct and unambiguous way by the executor, whether human or artificial (non-ambiguity);
- the algorithm must be composed of a finite number of steps and require a finite amount of input data (finitezza)
- the execution must have a termination after a finite time (termination);
- the execution must lead to a unique result (effectiveness).