Pythagoras, having migrated from Samos to Croton, has established a philosophical and religious school here that, from about 525, attracts many followers.

Many of the Pythagoreans reside in quasi-religious communities centered in Croton.

Holding the belief that the soul is immortal, separable from the body, and reincarnated in different animal bodies until it completes the cycle of all creatures, Pythagoreans practice vegetarianism for this reason and seek to release their souls through the leading of a pure life.

The strongly math-oriented Pythagoreans believe the universe was created when the One or the Limit "breathed" in some void and separate things were distinguished.

The two basic principles of all things are the Limit and the Unlimited; the foundations of the cosmos are the musical ratios 4:3, 3:2, and 2:1.

The Pythagorean School studies medicine and astronomy in addition to musical scales and mathematics.

Mediterranean Southwest Europe (1276–1287 CE): Sicilian Vespers, Papal-Aragonese Conflict, and Intellectual Developments in Iberia

The era 1276–1287 CE in Mediterranean Southwest Europe is marked by significant political upheaval in Sicily, papal conflict with the Kingdom of Aragon, increased persecution of Jews in Castile, and important mystical and intellectual developments among Iberian Jewish communities.

The Sicilian Vespers and the Aragonese Crusade

The period sees the outbreak of the War of the Sicilian Vespers in 1282, triggered by an insurrection of the Sicilian populace against Charles of Anjou's rule. The rebellion rapidly escalates into an international conflict, leading Pope Martin IV to declare the Aragonese Crusade (1284–1285) against Peter III the Great of Aragon, who had recently seized Sicily. The Pope justifies this crusade by asserting papal overlordship of Sicily, officially deposing Peter III and dramatically intensifying regional hostilities.

Persecution and Exclusion in Castile

In Iberia, persecution against Jewish communities intensifies significantly under the reign of Alfonso X of Castile. In his influential legal code, Las Siete Partidas (“Seven Sets”), Alfonso X formalizes church doctrines that systematically marginalize Jews, explicitly excluding them from public offices and reinforcing their subordinate status. These measures heighten tensions, marking a significant escalation in the persecution of Iberian Jews, setting the stage for later expulsions and repressions.

Mystical Innovations: Sefer HaTemunah

Amidst this turbulent era, the Jewish mystical text Sefer HaTemunah (“Book of the Image”) emerges in Spain, composed anonymously around the 1270s. The work introduces innovative concepts, such as the existence of cosmic cycles, each governed by distinct divine attributes—namely “grace,” “judgment,” and “mercy.” Each eon, the text argues, possesses its unique Torah, rendering Judaism adaptable to cosmic epochs rather than presenting immutable truths. The book imbues Hebrew letters with profound mystical significance, suggesting hidden, esoteric dimensions of the Torah. This influential mystical tradition significantly enriches Kabbalistic thought and spirituality throughout the Jewish diaspora.

Continued Maritime Rivalries and Economic Strength

Mediterranean maritime republics, especially Genoa and Venice, maintain fierce competition for naval dominance and trade supremacy. Their conflicts influence broader geopolitical dynamics and economic conditions in the Mediterranean, contributing to ongoing regional rivalries and economic vitality.

Architectural Continuity and Urban Development

The region continues its ambitious Gothic architectural projects, particularly in Italy and Iberia, where cathedrals, palaces, and public buildings remain enduring symbols of civic pride, religious devotion, and cultural identity.

Legacy of the Era

The era 1276–1287 CE significantly shapes Mediterranean Southwest Europe through the profound political shifts initiated by the Sicilian Vespers, papal conflicts with Aragon, intensified persecution of Jewish communities, and significant intellectual and mystical contributions in Iberia. Collectively, these events influence the region’s religious, political, cultural, and intellectual trajectory, deeply affecting subsequent European historical developments.

Pierre d’Ailly: Theologian, Church Reformer, and Cosmographer (1395–1418)

Pierre d’Ailly (1351–1420) was one of the most influential theologians and churchmen of his time, playing a pivotal role in resolving the Great Schism (1378–1417) and shaping conciliarist thought. A strong advocate for church unity and reform, he was also a prolific writer on astrology, geography, and ecclesiastical power.

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I. D’Ailly’s Role in the Great Schism and Church Reform

• The Western Schism had divided the Church, with multiple rival popes claiming legitimacy.
• D’Ailly was slow to embrace conciliarism but later became a key participant in the major councils seeking to resolve the crisis:
  • Council of Pisa (1409): Attempted to depose the rival popes but inadvertently created a third papal claimant.
  • Council of Constance (1414–1418): Successfully ended the Schism by deposing all competing popesand electing Martin V.
• D’Ailly dominated the early sessions of the Council of Constance, working alongside Jean Gerson to promote reform and the supremacy of a general council over the papacy.

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II. His Ecclesiastical Career and Political Influence

• D’Ailly’s theological and political versatility helped him rise through the ranks of the Church:
  • Bishop of Le Puy (1395).
  • Bishop of Noyon (1397).
  • Bishop of Cambrai (1397).
• In 1411, Antipope John XXIII made him a cardinal, earning him the title Cardinal of Cambrai.
• His connections with both the French monarchy and various papal factions made him a valuable mediator during the Schism.

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III. Writings on Cosmography, Astrology, and Prophecy

• Imago Mundi (1410):
  • A cosmographical treatise that attempted to synthesize geographical knowledge.
  • Influenced Christopher Columbus, particularly in his estimates of the world’s landmass, contributing to his belief that Asia was much closer to Europe than it actually was.
• Astrology and Free Will:
  • D’Ailly sought to balance divine omniscience with human free will, arguing that astrological influences did not override moral responsibility.
• The Schism and the Apocalypse:
  • He placed the division of the Church within an apocalyptic framework, speculating on whether the Schism was a sign of the coming of the Antichrist.

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IV. After the Council of Constance: Return to Paris

• Following the successful resolution of the Schism, d’Ailly returned to Paris, continuing his writings and advisory roles.
• His conciliarist views and support for Church reform remained highly influential, helping shape later debates on the authority of councils versus the papacy.

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V. Legacy and Influence

• A leading figure in the Church’s most turbulent period, d’Ailly was instrumental in ending the Great Schism and reinforcing the role of general councils.
• His writings on cosmography influenced early exploration, particularly Columbus’ assumptions about the shape of the world.
• His theological and astrological works reflected a deep engagement with the spiritual anxieties of his time, bridging scholasticism, humanism, and reformist thought.

D’Ailly’s career, spanning church politics, theology, astrology, and cosmography, made him one of the most versatile intellectuals of the late medieval period, shaping both the Church’s political future and the intellectual currents that led to the Age of Exploration.

Florentine Paolo dal Pozzo Toscanelli creates a world map in 1457 that perpetuates an error made by Ptolemy nearly fifteen hundred years earlier, thus severely misrepresenting, by shortening, the globe’s actual circumference.

Alberti’s smaller studies, pioneering in their field, include a treatise in cryptography, De componendis cifris, in which he describes a cipher disk capable of enciphering a small code, and the first Italian grammar.

With the Florentine cosmographer Paolo Toscanelli he collaborates in astronomy, a close science to geography at this time, and produces a small Latin work on geography, Descriptio urbis Romae (The Panorama of the City of Rome).

Just a few years before his death, Alberti completes De iciarchia (On Ruling the Household), a dialogue about Florence during Medici rule.

Spain and Portugal agree by the 1494 Treaty of Tordesillas to divide the non-Christian world between them; all territories to the west of the demarcation line in the Atlantic Ocean are to be Spanish; all those to the east, Portuguese.

The shift makes possible the successful Portuguese claim to Brazil, officially “discovered” in 1500 by Pedro Cabral.

Once European cosmographers become aware that a "new world" indeed exists, the entire Western hemisphere becomes known as America, a name that they use on their maps supposedly in honor of the Italian navigator Amerigo Vespucci, who conducts some mapping of the area.

John Michell is the first person to apply the new mathematics of statistics to the study of the stars, and demonstrates in a 1767 paper that many more stars occur in pairs or groups than a perfectly random distribution can account for.

He focuses his investigation on the Pleiades cluster, and calculates that the likelihood of finding such a close grouping of stars is about one in half a million.

He concludes that the stars in these double or multiple star systems might be drawn to one another by gravitational pull, thus providing the first evidence for the existence of binary stars and star clusters.

His work on double stars influence Herschel’s research on the same topic.

Michell follows his work in seismology with work in astronomy, and after publishing his findings in 1767 he serves on an astronomical committee of the Royal Society.

John Michell first proposes the idea that there are such things as black holes, which he calls "dark stars", in a paper for the Philosophical Transactions of the Royal Society of London, read on November 27, 1783.

Having accepted Newton’s corpuscular theory of light, which posits that light consists of minuscule particles, he reasons that such particles, when emanated by a star, would be slowed down by its gravitational pull, and thought that it might therefore be possible to determine the star's mass based on the reduction in speed.

This insight led in turn to the recognition that a star's gravitational pull might be so strong that the escape velocity would exceed the speed of light.

Michell has calculated that this would be the case with a star more than  five hundred times the size of the Sun.

Since light would not be able to escape such a star, it would be invisible.

 In his own words:

    If there should really exist in nature any bodies, whose density is not less than that of the sun, and whose diameters are more than 500 times the diameter of the sun, since their light could not arrive at us; or if there should exist any other bodies of a somewhat smaller size, which are not naturally luminous; of the existence of bodies under either of these circumstances, we could have no information from sight; yet, if any other luminous bodies should happen to revolve about them we might still perhaps from the motions of these revolving bodies infer the existence of the central ones with some degree of probability, as this might afford a clue to some of the apparent irregularities of the revolving bodies, which would not be easily explicable on any other hypothesis; but as the consequences of such a supposition are very obvious, and the consideration of them somewhat beside my present purpose, I shall not prosecute them any further.
     ("On the Means of Discovering the Distance, Magnitude, &c. of the Fixed Stars, in Consequence of the Diminution of the Velocity of Their Light, in Case Such a Diminution Should be Found to Take Place in any of Them, and Such Other Data Should be Procured from Observations, as Would be Farther Necessary for That Purpose. By the Rev. John Michell, B. D. F. R. S.” In a Letter to Henry Cavendish, Esq. F. R. S. and A. S." (PDF), Philosophical Transactions of the Royal Society of London 74 :35-57)

Michell suggests that there might be many "dark stars" in the universe, and today astronomers believe that black holes do indeed exist at the centers of most galaxies.

Similarly, Michell proposes that astronomers can detect "dark stars" by looking for star systems that behave gravitationally like two stars, but where only one star can be seen.

Michell argues that this will show the presence of a "dark star".

It is an extraordinarily accurate prediction.

All of the dozen candidate stellar black holes in our galaxy (the Milky Way) are in X-ray compact binary systems.

A dozen years after Michell comes up with the concept of black holes, the French mathematician Pierre-Simon Laplace will suggest essentially the same idea in his 1796 book, Exposition du Système du Monde.

Michell has become known more recently for his letter to Henry Cavendish, published in 1784, on the effect of gravity on light.

This paper will be rediscovered in the 1970s and is now recognized as anticipating several astronomical ideas that had been considered to be twentieth century innovations.

Michell is now credited with being the first to study the case of a heavenly object massive enough to prevent light from escaping (the concept of escape velocity is well known at this time).

Such an object, which he calls a dark star, will not be directly visible, but can be identified by the motions of a companion star if it is part of a binary system.

The classical minimum radius for escape assuming light behaves like particles of matter is numerically equal to the Schwarzschild Radius in general relativity.

Michell also suggests using a prism to measure what is now known as gravitational redshift, the gravitational weakening of starlight due to the surface gravity of the source.

Michell acknowledges that some of these ideas are not technically practical at this time, but writes that he hopes they will be useful to future generations.

By the time that Michell's paper is rediscovered nearly two centuries later, these ideas will have been reinvented by others.

Alexander von Humboldt, who has spent the last fifteen years writing his great work, Kosmos, an attempt at a comprehensive description of the universe, publishes the first volume in 1845 at the age of seventy-six.

Humboldt believes that the universe is an inseparable organic whole and that all phenomena are interdependent.