Papers by Giuseppe Marino
Discrete Mathematics
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Lo sviluppo delle tecnologie informatiche impone di rivedere i modelli comportamentali sia sogget... more Lo sviluppo delle tecnologie informatiche impone di rivedere i modelli comportamentali sia soggettivi che collettivi per adeguarli alla complessità della realtà digitale interconnessa. In questo contesto le tecniche di misurazione del tempo diventano sempre più necessarie, condivise e sofisticate. Si è passati da strumenti semplici come i quadranti solari e le meridiane, a strumenti più complessi come l’orologio meccanico, quello a pendolo e quello atomico. Dal tempo misurato in giorni si è arrivati a quello misurato in nanosecondi, dal tempo locale a quello universale, dalla cronologia alla cronografia e al cronometraggio, dall’orologio analogico al timer digitale. Il tempo non è più scandito da un ticchettio, ma è cronometrato fino a quantità infinitesimali. La misurazione del tempo è un assemblaggio di varie componenti culturali e tecnologiche. Il cambiamento investe sia la sfera personale e individuale che quella sociale ed economica. Una conoscenza di base di questi nuovi strumenti è necessaria per utilizzarli con maggiore consapevolezza.
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Giuseppe Marino, 2022
The development of information technologies requires reviewing both subjective and collective beh... more The development of information technologies requires reviewing both subjective and collective behavioral models to adapt them to the complexity of the interconnected digital reality. In this context, time measurement techniques become increasingly necessary, shared and sophisticated. We have gone from simple instruments such as sun dials, to more complex instruments such as mechanical, pendulum and atomic clocks. From time measured in days to time measured in nanoseconds, from local to universal time, from chronology to chronometry and at the timekeeping, from analog clock to digital timer. Time is no longer marked by a ticking, but is timed in infinitesimal quantities. Time measurement is an assemblage of various cultural and technological components. Change affects both the personal and individual sphere as well as the social and economic one. A basic understanding of these new tools is necessary to use them with greater awareness.
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The dating system currently in use is that of the Gregorian calendar, which reformed the Julian c... more The dating system currently in use is that of the Gregorian calendar, which reformed the Julian calendar by abolishing 10 days in October 1582 and reducing leap years every three centenary years out of four, to realign the equinox and the full moon at solar and lunar cycle. The discontinuity of the 10 days is bridged extending backward the calendar, in the period before its introduction, obtaining the Proleptic Gregorian Calendar. The date identifies each day in this calendar with three integers, year/month/day. Below is a problem that seems simple but is actually quite complex, an algorithm to determine the days between two dates in the Proleptic Gregorian Calendar, which allows you to control the type of calculation performed and extend the limits of some current procedures.
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In ancient times the Ionian Coast of the Italian peninsula was a crossroads of contacts and conne... more In ancient times the Ionian Coast of the Italian peninsula was a crossroads of contacts and connections between the West and the East, which led to the consolidation of small primitive merchant centers, linked to the activity that the Greeks called emporía, that is the practice of going by sea to exchange and trade.
Two of the ethno-cultural entities formed through these ties with the Mycenaean Achaean culture are that of the ethnos Italo enotrio (XIV-XII century BC) and that of the ethnos chonio enotrio (end XII-VIII century BC).
The Choni Enotri area was overlaid, after the colonization of the 8th century BC, by the colonies founded by the Achaeans from Achaia, a region of the Peloponnese, which formed the cultural ethnic identity of the Achaeans of the West.
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The Gauss formula of the day of the week is a simple and reduced algorithm that lends itself to b... more The Gauss formula of the day of the week is a simple and reduced algorithm that lends itself to both the automatic and the manual-mental calculations. The following is a revised version of the formula and a procedure for obtaining it.
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In the Renaissance, with the Gregorian calendar reform, adopted on a proposal of the astronomer A... more In the Renaissance, with the Gregorian calendar reform, adopted on a proposal of the astronomer Aloysius Lilius and implemented by the Jesuit mathematician Christopher Clavius, the studies focused on the computational procedures in algebraic form, at the time executed mainly with tabular methods. Following the procedure initially proposed by Aloysius Lilius, adopted with the reform, it is possible to compose an algorithm in which the operations reproduce the rules and principles of the reform itself, in which the structure of the calendar equations is distinct and the time elements of the calculation are defined.
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The chronological dating system currently in use is that of the Gregorian calendar, introduced in... more The chronological dating system currently in use is that of the Gregorian calendar, introduced in 1582, which reformed and corrected the Julian calendar, creating however a break in the chronological sequence with the cancellation of 10 days.
The date, which identifies each day with three integers, year/month/day, gives no indication on the periods of the two calendars and on the day of the week, essential in some cases, for instance, whether it is a holiday or a working day.
The following is an algorithm, easy to implement, which relates the calendar date with the day of the week and the periods of the Julian and Gregorian calendar, through two procedures: End-year method and March-first method.
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Questo studio riprende e completa, precisando meglio alcuni aspetti, quanto esposto nei precedent... more Questo studio riprende e completa, precisando meglio alcuni aspetti, quanto esposto nei precedenti saggi sulla riforma gregoriana del calendario e su Aloysius Lilius.
Qui viene sviluppato nello specifico l’aspetto della struttura matematica del calendario gregoriano, con l’esplicitazione delle relazioni che ne caratterizzano la forma, il contenuto e le regole di funzionamento. L’elaborazione di tutti questi elementi ha rappresentato un’importante applicazione matematica che ha dato impulso allo sviluppo dell’aritmetica modulare e del calcolo nel discreto.
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Con il varo della riforma del calendario, adottata da Gregorio XIII nel 1582 su proposta di Aloy... more Con il varo della riforma del calendario, adottata da Gregorio XIII nel 1582 su proposta di Aloysius Lilius, fiorirono gli studi per rendere in forma algebrica i procedimenti di calcolo, allora eseguiti soprattutto con l’uso di tabelle. Lo scopo era duplice, uno pratico tendente a semplificare i calcoli, l’altro teorico tendente a dimostrare che le procedure potevano ridursi a operazioni matematiche semplici. Così come nel Medioevo quella del computo lunare era stata l’applicazione aritmetica più importante, con la riforma l’analisi delle regole del calendario e il calcolo della data della Pasqua hanno rappresentato una rilevante applicazione matematica, che ha contribuito allo sviluppo del calcolo dei numeri interi e nel discreto.
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Summary of the proposal by Aloysius Lilius used for the Gregorian reform of the calendar. Latin ... more Summary of the proposal by Aloysius Lilius used for the Gregorian reform of the calendar. Latin text and Italian translation.
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Papers by Giuseppe Marino
Two of the ethno-cultural entities formed through these ties with the Mycenaean Achaean culture are that of the ethnos Italo enotrio (XIV-XII century BC) and that of the ethnos chonio enotrio (end XII-VIII century BC).
The Choni Enotri area was overlaid, after the colonization of the 8th century BC, by the colonies founded by the Achaeans from Achaia, a region of the Peloponnese, which formed the cultural ethnic identity of the Achaeans of the West.
The date, which identifies each day with three integers, year/month/day, gives no indication on the periods of the two calendars and on the day of the week, essential in some cases, for instance, whether it is a holiday or a working day.
The following is an algorithm, easy to implement, which relates the calendar date with the day of the week and the periods of the Julian and Gregorian calendar, through two procedures: End-year method and March-first method.
Qui viene sviluppato nello specifico l’aspetto della struttura matematica del calendario gregoriano, con l’esplicitazione delle relazioni che ne caratterizzano la forma, il contenuto e le regole di funzionamento. L’elaborazione di tutti questi elementi ha rappresentato un’importante applicazione matematica che ha dato impulso allo sviluppo dell’aritmetica modulare e del calcolo nel discreto.
Two of the ethno-cultural entities formed through these ties with the Mycenaean Achaean culture are that of the ethnos Italo enotrio (XIV-XII century BC) and that of the ethnos chonio enotrio (end XII-VIII century BC).
The Choni Enotri area was overlaid, after the colonization of the 8th century BC, by the colonies founded by the Achaeans from Achaia, a region of the Peloponnese, which formed the cultural ethnic identity of the Achaeans of the West.
The date, which identifies each day with three integers, year/month/day, gives no indication on the periods of the two calendars and on the day of the week, essential in some cases, for instance, whether it is a holiday or a working day.
The following is an algorithm, easy to implement, which relates the calendar date with the day of the week and the periods of the Julian and Gregorian calendar, through two procedures: End-year method and March-first method.
Qui viene sviluppato nello specifico l’aspetto della struttura matematica del calendario gregoriano, con l’esplicitazione delle relazioni che ne caratterizzano la forma, il contenuto e le regole di funzionamento. L’elaborazione di tutti questi elementi ha rappresentato un’importante applicazione matematica che ha dato impulso allo sviluppo dell’aritmetica modulare e del calcolo nel discreto.