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====== - 7.2 History of mapping the worlds ======

===== - Geocentric models =====
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Early geocentric models placed the Earth at the absolute center of the universe, a view championed by Plato and Aristotle. The diagram illustrates this perspective through a series of concentric circles representing the celestial spheres. In this system, the Earth sits stationary in the middle, surrounded by the orbits of the Moon, Mercury, Venus, the Sun, Mars, Jupiter, and Saturn. This visual representation reinforced the idea of a stable, human-centered world governed by mathematical order and divine influence.

The diagram specifically labels these spheres with Latin names like LVNÆ, MERCVRII, and SOLIS, reflecting the Ptolemaic system. A central challenge for this model was retrograde motion—the apparent backward movement of planets against the stars. Ptolemy solved this by introducing epicycles: small circular paths that planets traveled along while those circles themselves orbited the Earth on a larger path called a deferent. This complex geometry successfully predicted planetary positions despite its flawed premise.

The transition from geocentricity involved a conceptual shift where the Earth was no longer unique in its position. Even before full heliocentrism, variations of these nested circles began to reorder the heavens to resolve observational inconsistencies. These early maps highlight a growing need to align visual models with more precise observations of planetary motion. While still confined to circular paths, the shift in the center of these diagrams began to simplify the complex geometry required to explain the retrograde paths.

===== - Heliocentric models =====
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Heliocentric models revolutionized mapping by placing the Sun at the center, a monumental shift initiated by Nicolaus Copernicus. The diagram shows the Sun, labeled SOL, as the heart of the cosmic structure. Surrounding it are the orbits of the planets in their now-familiar order: Mercury, Venus, Earth with its Moon, Mars, Jupiter, and Saturn. This visual rearrangement provided a much more elegant explanation for the varying brightness and paths of the planets as observed from our own moving platform.

Copernicus explained retrograde motion as an optical illusion caused by the Earth overtaking slower-moving outer planets in their orbits. However, his insistence on perfect circular motion forced him to retain some epicycles to maintain accuracy. It was Johannes Kepler who later realized the ultimate shape of these orbits was the ellipse. By studying the precise observational data of Mars, Kepler discarded circular paths, finally providing a mathematically perfect description of the solar system without the need for artificial geometric corrections.

As heliocentrism matured, the diagrams began to account for the vast distances between the Sun and the stars. The orbits are no longer just symbolic circles but represent physical elliptical paths through space based on observational evidence. This progression in mapping reflects a move away from purely philosophical arrangements toward models based on physical laws. The Sun became the anchor for a system that was beginning to expand its boundaries beyond the immediate solar neighborhood, setting the stage for deeper stellar exploration.

===== - Acentric models =====
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Acentric models represent a bold leap where the universe no longer has a single, privileged center. The diagram, based on the work of Thomas Digges, illustrates an infinite extension of stars, moving away from a closed, spherical shell. It depicts the "Orbe of Starres Fixed Infinitely Up," suggesting that the suns and worlds beyond our own are countless. This map challenges the viewer to see our solar system as a small part of a much larger, perhaps boundless, celestial architecture.

The visual style of this diagram combines traditional orbital rings with an outer region filled with stars stretching toward the edges of the frame. Digges described this outer realm as "garnished with perpetual shining lights," far excelling our own Sun in quantity. This transition in mapping reflects the realization that the stars are not just lights on a ceiling but distant suns. The center of the map becomes a matter of perspective rather than an absolute, physical location in space.

By removing a fixed center, these maps paved the way for modern cosmology and the principle of mediocrity. They shifted the focus from where the universe is centered to how it is structured on a grand scale. This expansion of the horizon highlights the growth of human knowledge, preparing the intellectual ground for understanding the universe as a vast expanse. In this view, every point in space could potentially be considered a center of observation for a distant astronomer.

===== - Topocentric models =====
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Topocentric models in modern cosmology map the universe across time and scale, rooted in the theories of Einstein, Friedmann, and Lemaître. The final diagram shows a horizontal timeline beginning with the Big Bang and moving through the "Dark Ages." This is a map of the entire observable universe, where the "center" is our current moment in time looking back through billions of years of evolution. It reflects the expanding space-time metric described by the Friedmann-Lemaître-Robertson-Walker models.

The diagram uses color and density to illustrate different eras, such as the Recombination period and the subsequent Reionisation. It tracks the redshift of light, a phenomenon that Georges Lemaître famously linked to the expansion of the universe. This mapping technique prioritizes the history of matter and light over simple spatial arrangements. It provides a visual narrative of how the simple, hot early universe became the complex web of galaxies and structures we observe in the present day.

This final stage in mapping the worlds represents the ultimate progression from local spheres to a temporal cosmos. We no longer just map where things are, but when they occurred in the life of the universe. By integrating time and space into a single visual flow, these models show the total context of our existence. Mapping has moved from the Earth to the Sun, to the stars, and finally to the very origin of time and space itself.