How has the date of Easter been calculated over the centuries?

In this article, we will tell you how astronomy was related to mathematics, how many centuries it took modern scientists to catch up with the achievements of ancient astronomers, and how to find that experience and observation confirmed the theory.

When we want to check the date of next Easter today, just look at the calendar and everything will immediately become clear. However, setting vacation dates has not always been so easy.

14 or 15 nisans?

Wielkanoc it is the most important annual holiday of Christianity. All four gospels agree that the Holy Day was Friday and that the disciples found Christ's tomb empty on the Sunday after Passover. The Jewish Passover is celebrated on Nisan 15 according to the Jewish calendar.

Three evangelists reported that Christ was crucified on Nisan 15. St. John wrote that it was Nisan 14, and it was the latter version of events that was considered more likely. However, the analysis of the available data did not lead to the selection of one specific date for the resurrection.

Therefore, the rules of definition had to be somehow agreed Easter dates in subsequent years. Disputes and refinement of methods for calculating these dates took many centuries. Initially, in the east of the Roman Empire, the crucifixion was commemorated annually on Nisan 14.

The date of the Jewish holiday of Passover is determined by the phases of the moon in the Jewish calendar and can fall on any day of the week. Thus, the feast of the Passion of the Lord and the feast of the Resurrection could also fall on any day of the week.

In Rome, in turn, it was believed that the memory of the resurrection should always be celebrated on the Sunday after Easter. Moreover, Nisan 15 is considered the date of the crucifixion of Christ. In the XNUMXth century AD, it was decided that Easter Sunday should not precede the spring equinox.

And yet Sunday

In 313, the emperors of the western and eastern Roman Empire, Constantine the Great (272-337) and Licinius (c. 260-325), issued the Edict of Milan, which ensured religious freedom in the Roman Empire, addressed mainly to Christians (1). In 325, Constantine the Great convened a council at Nicaea, 80 km from Constantinople (2).

Sam presided over it intermittently. In addition to the most important theological questions - such as whether God the Father existed before the Son of God - and the creation of canonical laws, the question of the date of the Sunday holidays was discussed.

It was decided that Easter would be celebrated on the Sunday after the first "full moon" in the spring, defined as the fourteenth day after the first appearance of the moon after the new moon.

This day in Latin is moon XIV. An astronomical full moon usually occurs on Moon XV, and twice a year even on Moon XVI. Emperor Constantine also decreed that Easter should not be celebrated on the same day as the Jewish Passover.

If the congregation in Nice fixed the date for Easter, then this is not the case. complex recipe for the date of these holidaysscience would certainly have developed differently in subsequent centuries. The method of calculating the date of the Resurrection received the Latin name computus. It was necessary to establish the exact date of the upcoming holidays in the future, because the celebration itself precedes fasting, and it is important to know when to start it.

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Earliest methods easter date calculation they were based on an eight-year cycle. The 84-year cycle was also invented, much more complex, but not better than the previous one. His advantage was the full number of weeks. Although it did not work in practice, it was used for quite a long time.

The best solution turned out to be the nineteen-year cycle of Meton (an Athenian astronomer), calculated around 433 BC.

According to him, every 19 years, the phases of the moon repeat on the same days of successive months of the solar year. (Later it turned out that this is not entirely accurate - the discrepancy is about an hour and a half per cycle).

Usually Easter was calculated for five Metonic cycles, that is, for 95 years. Calculations of the date of Easter were further complicated by the then known fact that every 128 years the Julian calendar deviated by one day from the tropical year.

In the fourth century, this discrepancy reached three days. St. Theophilus (died in 412) - Bishop of Alexandria - counted the tablets of Easter for a hundred years from 380. St. Cyril (378-444), whose uncle was St. Theophilus established the dates of Great Sunday in five Metonic cycles, beginning with the year 437 (3).

However, Western Christians did not accept the results of the calculations of Eastern scientists. One of the problems was also determining the date of the vernal equinox. In the Hellenistic part, this day was considered March 21, and in the Latin - March 25. The Romans also used the 84 year cycle and the Alexandrians used the Metonic cycle.

As a consequence, this led in some years to the celebration of Easter in the east on a different day than in the west. Victoria of Aquitaine he lived in the 457th century, worked on the Easter calendar until 84. He showed that a nineteen-year cycle is better than an 532-year one. He also found that the dates of Holy Sunday repeat every XNUMX years.

This number is obtained by multiplying the length of a nineteen-year cycle by a four-year leap year cycle and the number of days in a week. The dates of the Resurrection calculated by him did not coincide with the results of the calculations of Eastern scientists. His tablets were approved at Orléans in 541 and were used in Gaul (today's France) until the time of Charlemagne.

Three friends - Dionysius, Cassiodorus and Boethius and Anna Domini

Do Easter board calculation Dionysius the Lesser (c. 470-c. 544) (4) abandoned Roman methods and followed the path indicated by the Hellenistic scholars from the Nile Delta, i.e. continued the work of St. Kirill.

Dionysius ended the Alexandrian scholars' monopoly on the ability to date the Sunday of the Resurrection.

He calculated them as five Metonic cycles from 532 AD. He also innovated. Then the years were dated according to the era of Diocletian.

Since this emperor was persecuting Christians, Dionysius found a much more worthy way to mark the years, namely from the Nativity of Christ, or anni Domini nostri Jesu Christi.

One way or another, he incorrectly calculated this date, having mistaken for several years. Today it is generally accepted that Jesus was born between 2 and 8 BC. Interestingly, in 7 BC. the conjunction of Jupiter with Saturn occurred. This gave the sky the effect of a bright object, which can be identified with the Star of Bethlehem.

Cassiodorus (485-583) made an administrative career at the court of Theodoric, and then founded a monastery in Vivarium, which at that time was distinguished by the fact that it was engaged in science and saved manuscripts from city libraries and ancient schools. Cassiodorus drew attention to the great importance of mathematics, for example, in astronomical research.

Moreover, for the first time since Dionysius used the term Anna Domini in 562 AD in a textbook on determining the date of Easter, Computus Paschalis. This manual contained a practical recipe for calculating the date according to the method of Dionysius and was distributed in many copies to libraries. The new way of counting the years from the birth of Christ was adopted gradually.

It can be said that in the 480th century it was already widely used, although, for example, in some places in Spain it was adopted only in the 525th century by the reign of Theodoric, he translated Euclid's geometry, Archimedes' mechanics, Ptolemy's astronomy, Plato's philosophy and Aristotle's logic into Latin, and also wrote textbooks. His works became a source of knowledge for future researchers of the Middle Ages.

Celtic Easter

Now let's go north. In Reims in 496, the Gallic king Clovis was baptized along with three thousand francs. Even further in this direction, across the English Channel in the British Isles, the Christians of the Roman Empire lived much earlier.

They were separated from Rome for a long time, since the last Roman legion left the Celtic island in 410 AD. Thus, there, in isolation, developed separate customs and traditions. It was in this atmosphere that the Celtic Christian king Oswiu of Northumbria (612-670) grew up. His wife, Princess Enflaed of Kent, was brought up in the Roman tradition brought to southern England in 596 by Pope Gregory's envoy Augustine.

The King and Queen each celebrated Easter according to the customs they grew up with. Usually dates of holidays they agreed with each other, but not always, as they did in 664. It was strange when the king was already celebrating holidays at court, and the queen was still fasting and celebrating Palm Sunday.

The Celts used the method from the middle of the 84th century, based on the 14-year cycle. Sunday Sunday could happen from moon XIV to moon XX, i.e. the holiday could fall exactly on the XNUMXth day after the new moon, which was strongly objected to outside the British Isles.

In Rome, the celebration took place between moon XV and moon XXI. Moreover, the Celts mentioned the crucifixion of Jesus on Thursday. Only the son of the royal couple, brought up in the traditions of his mother, persuaded his father to put her in order. Then at Whitby, in the monastery at Streanaschalch, there was a meeting of the clergy, reminiscent of the Council of Nicaea three centuries earlier (5).

However, there can really only be one solution, rejection of Celtic customs and submission to the Roman Church. Only a portion of the Welsh and Irish clergy remained for some time under the old order.

5. The ruins of the abbey where the synod was held in Whitby. Mike Peel

When it's not the spring equinox

Bede the Venerable (672–735) was a monk, writer, teacher and choir conductor at a monastery in Northumbria. He lived away from the cultural and scientific attractions of the time, but managed to write sixty books on the Bible, geography, history, mathematics, timekeeping, and leap years.

6. A page from the Venerable Bede's Historia ecclesiastica gentis Anglorum

He also made astronomical calculations. He could use a library of over four hundred books. His intellectual isolation was even greater than his geographic isolation.

In this context, he can only be compared with the somewhat earlier Isidore of Seville (560-636), who acquired ancient knowledge and wrote on astronomy, mathematics, chronometry, and easter date calculation.

However, Isidore, using the repetitions of other authors, was often not creative. Bede, in his then popular book Historia ecclesiastica gentis Anglorum, dated from the birth of Christ (6).

He distinguished three types of time: determined by nature, custom and authority, both human and divine.

He believed that God's time is greater than any other time. Another of his works, De temporum ratione, was unparalleled in time and calendar for the next few centuries. It contained a repetition of already known knowledge, as well as the author's own achievements. It was popular in the Middle Ages and can be found in over a hundred libraries.

Bede returned to this topic for many years. easter date calculation. He calculated the dates of the Resurrection holidays for one 532-year cycle, from 532 to 1063. What is very important, he did not stop at the calculations themselves. He built a complex sundial. In 730, he noticed that the vernal equinox did not fall on March 25th.

He observed the autumnal equinox on September 19th. So he continued his observations, and when he saw the next equinox in the spring of 731, he realized that to say that a year consists of 365/XNUMX days is only an approximation. It may be noted here that the Julian calendar was then "wrong" by six days.

Bede's experimental approach to the problem of computation was unprecedented in the Middle Ages and several centuries ahead of its time. Incidentally, it is also worth adding that Bede discovered how to use sea tides to measure the phases and orbit of the Moon. Bede's writings are cited by Abbott Fleury (945–1004) and Hraban Maur (780–856), who simplified their calculation methods and obtained the same results. In addition, Abbott Fleury used a water hourglass to measure time, a device more accurate than a sundial.

More and more facts don't agree

German Kulavi (1013-54) - a monk from Reichenau, he expressed a completely unsuitable opinion for his time that the truth of nature is insurmountable. He used an astrolabe and a sundial, which he designed especially for him.

They were so accurate that he found that even the phases of the moon did not agree with computer calculations.

Checking compliance with the vacation calendar church problems with astronomy turned out to be negative. He tried to correct Bede's calculations, but to no avail. Thus, he found that the whole way of calculating the date of Easter was wrong and based on faulty astronomical assumptions.

That the Metonic cycle does not correspond to the actual movement of the sun and moon was discovered by Rainer of Paderborn (1140–90). He calculated this value for one day in 315 years of the Julian calendar. He used the mathematics of the East in modern times for the mathematical formulas used to calculate the date of Easter.

He also noted that attempts to list the age of the world from its creation through successive biblical events are erroneous due to an incorrect calendar. Moreover, at the turn of the XNUMXth/XNUMXth centuries, Conrad of Strasbourg discovered that the winter solstice had shifted ten days from the establishment of the Julian calendar.

However, the question arose whether this number should not be fixed so that the vernal equinox falls on March 21, as was established at the Council of Nicaea. The same figure as that of Rainer of Paderborn was calculated by Robert Grosseteste (1175-1253) of the University of Oxford, and he obtained the result in one day in 304 years (7).

Today we consider it to be one day in 308,5 years. Grossetest proposed to start easter date calculation, assuming the vernal equinox on March 14. In addition to astronomy, he studied geometry and optics. He was ahead of his time by testing theories through experience and observation.

In addition, he confirmed that the achievements of ancient Greek astronomers and Arab scientists surpassed even those of Bede and other scientists of medieval Europe. A slightly younger John Sacrobosco (1195-1256) had a thorough mathematical and astronomical knowledge, used the astrolabe.

He contributed to the spread of Arabic numerals in Europe. Moreover, he sharply criticized the Julian calendar. To remedy this, he proposed to omit one leap year every 288 years in the future.

The calendar needs to be updated.

Roger Bacon (c. 1214–92) English scientist, seer, empiricist (8). He believed that experimental action should replace theoretical debate - therefore, it is not enough just to draw a conclusion, experience is needed. Bacon predicted that one day man would build vehicles, powered ships, airplanes.

8. Roger Bacon. Phot. Michael Reeve

He entered the Franciscan monastery rather late, being a mature scholar, the author of several works and a lecturer at the University of Paris. He believed that since nature was created by God, it should be explored, tested, and assimilated in order to bring people closer to God.

And the inability to reveal knowledge is an insult to the Creator. He criticized the practice adopted by Christian mathematicians and calculus, in which Bede, among other things, resorted to approximating numbers rather than counting them exactly.

Errors in easter date calculation led, for example, to the fact that in 1267 the remembrance of the Resurrection was celebrated on the wrong day.

When it should have been fast, people didn't know about it and ate meat. All other celebrations, such as the Ascension of the Lord and Pentecost, were celebrated with a weekly error. Bacon distinguished time, determined by nature, power and customs. He believed that time alone is the time of God and that the time determined by authority can be wrong. The Pope has the right to amend the calendar. However, the papal administration at the time did not understand Bacon.

Gregorian calendar

It was arranged in such a way that the vernal equinox would always fall on March 21, as agreed at the Council of Nicaea. Due to the existing inaccuracy, the Metonic cycle was also made corrections in the lunar calendar. After the introduction of the Gregorian calendar in 1582, it was immediately used only by the Catholic countries of Europe.

Over time, it was adopted by the Protestant countries, and then by the countries of the Eastern rite. However, Eastern churches adhere to the dates according to the Julian calendar. Finally, a historical curiosity. In 1825, the Roman Catholic Church did not comply with the Council of Nicaea. Then Easter was celebrated simultaneously with the Jewish Passover.