It is well known that the African Tectonic Plate has been drifting relatively slowly compared with many of the surrounding plates. On the opposite side of the globe, the Pacific Plate also appears exceptional in several respects. At its center lies Hawaii, one of the most volcanically active regions on Earth.
Theoretic Pacific-centered tectonic map emphasizing the approximately equal spacing of the Mid-Atlantic Ridge and Mid-Indian Ridge relative to Hawaii.
The S-shaped red lines show the location of the divisions, according to the mantle convection rolls model, associated with the minor and major axes of Antarctica. When the globe is viewed from a Pacific-centered perspective, with Hawaii near the middle of the map, an interesting geometric relationship appears. The theoretical central axes of the Mid-Atlantic Ridge and the Mid-Indian Ridge lie at equal distances from Hawaii. This relationship can best be illustrated with a world map centered on the Pacific Ocean.
In such a representation, the three major mid-ocean ridge systems — the Mid-Atlantic Ridge, the Mid-Indian Ridge, and the East Pacific Rise — together with the principal subduction zones of the western Pacific, appear geometrically connected with the endpoints of the major and minor axes of the elliptical form associated with the Antarctic Tectonic Plate.
Within this framework, Hawaii occupies a particularly central position. It lies midway between the axial region of the Pacific spreading system, represented by the East Pacific Rise, and the extensive subduction systems of the western Pacific Ring of Fire. Seen in this way, Hawaii becomes part of a broader large-scale geometric arrangement linking the Pacific basin, Antarctica, and the global mid-ocean ridge network.
This concept can be illustrated effectively with a Pacific-centered world map, where Africa appears on both outer edges of the projection, emphasizing the symmetry and large-scale relationships of the global tectonic system.
Comparing the geometry of Indonesia and the Caribbean reveals a remarkable degree of similarity. Although these two tectonic systems are located on opposite sides of the Pacific realm, many of their large-scale structural relationships appear comparable.
The Identical Shape of Indonesia and the Caribbean: Comparable Subduction and Transform Geometry on Opposite Sides of the Ring of Fire
First, both systems are closely associated with the equatorial region. The Indonesian arc faces southward, with one important eastern endpoint located near the coast of Sumatra. Another major subduction-related crossing appears roughly 30° farther east along the equatorial zone, connected with the subduction framework surrounding the Philippine Plate.
A similar arrangement can be observed in the Caribbean region, although shifted slightly north of the equator. The Caribbean basin is associated with another pair of crossings of lower-mantle flow structures, where subduction-related zones occur at points approximately 30° apart, comparable to the Indonesian case. The Caribbean arc also extends outward in a manner resembling the Indonesian arc.
The Central American Trench stretches from the inner part of the Ring of Fire toward its outer margin, where the division line appears to turn toward the key region of the Peru–Chile Trench near the equatorial framework. This geometry resembles the relationship between the New Guinea Trench and the continuation of the Philippine Trench on the Indonesian side of the Pacific.
In this way, many aspects of the Indonesian and Caribbean plate-boundary systems appear strikingly similar, although effectively rotated by 180° relative to one another.
Considering that these two tectonic regions connect the Pacific Ocean with the Indian Ocean and the Atlantic Ocean respectively, the broader function of this arrangement becomes important to examine. The fundamental span of a 30° convection-roll unit, together with an additional extension east of the eastern crossing points, may help explain the tectonic importance of these paired regions on opposite sides of the Ring of Fire.
South of Indonesia, subduction is the dominant tectonic process, whereas in the Caribbean region transform motion and tectonic transition play a larger role, especially along the northern boundary of the Caribbean Plate. Even so, both systems appear to participate in a broader structural unity within the Ring of Fire.
The anticlockwise rotational tendency associated with the North American sector of the Ring of Fire is consistent with the northward-facing curvature of the Caribbean arc and the southward-facing curvature of the Indonesian arc. At the same time, the long-term expansion of the Atlantic Ocean on one side and the Indian Ocean on the other appears to be buffered near equatorial latitudes by these major subduction and transform systems situated between the large ocean basins.
The similarities are therefore sufficiently striking that they may partly reflect an underlying large-scale geometric organization. At the same time, this comparison leaves many important questions unanswered and suggests several directions worthy of further investigation. Further information: https://pangea.stanford.edu/ERE/db/GeoConf/papers/SGW/2024/Thorbjarnarson.pdf
All of these characteristics of the two archipelagic systems are, of course, well known. They can first be summarized as follows:
Both archipelagos are associated with the Ring of Fire.
Both archipelagos are located close to the equator.
Both archipelagos have a predominantly east–west orientation.
However, when compared within the framework of the mantle convection rolls model, several additional observations can be made:
When the tectonic features of Central America are included, the overall mathematical framework becomes directly comparable to that of Indonesia.
The width of both archipelagic systems is comparable when measured in degrees of longitude along their respective latitudes.
The relative position of both archipelagos appears comparable in the context of the large-scale convection-roll geometry proposed in the mantle convection rolls model.
The influence of mantle convection upon the Earth’s surface can be examined through the tectonic patterns that develop above it. In this study, several recurring geometrical expressions are considered. First are the division lines between convection rolls. Second are the polygonal regions enclosed by those division lines, where geological structures frequently develop from one corner of a polygon to another, commonly in north–south or east–west directions. A third recurring expression is the appearance of elliptical forms under certain large-scale conditions.
The Ring of Fire and Antarctica.
These observations suggest that many aspects of geology may be investigated through geometric analysis. Once geometric consistency is identified, detailed geographic and geoscientific data can be used to further evaluate the resulting patterns and their possible physical significance.
The Pacific Ring of Fire provides an important example. Although the exact physical processes governing its overall geometry remain uncertain, the arrangement itself displays remarkable large-scale regularity. Antarctica presents a similar challenge. Its tectonic framework is difficult to explain in simple terms, yet its geometry also appears highly organized.
Antarctica is particularly difficult to examine because most world maps distort the continent, stretching it along the southern edge of the map projection. When viewed directly from above the South Pole, however, its remarkably circular form becomes evident. It is also well known that Antarctica can be divided into East and West Antarctica, with the western sector being considerably more tectonically and volcanically active.
The boundary between East and West Antarctica appears to coincide closely with the center of the minor axis of the system of mid-ocean ridges encircling the continent. Near this axis lies the famous volcano Mount Erebus, one of the most persistently active volcanoes on Earth. Because Erebus is located at approximately 77.5°S latitude, its distance from the inferred minor axis is only about 100 km.
Another important geometric relationship emerges offshore from Erebus. At this location, the minor axis of the Antarctic system appears to intersect the minor axis of the Pacific Ring of Fire. Thus, the most active volcano in Antarctica occupies a position where two large-scale tectonic geometries appear to converge: the minor axis of the Antarctic ring of mid-ocean ridges and the minor axis of the Ring of Fire.
This geometric axis can then be examined further in relation to external geological conditions. When the Antarctic minor axis is extrapolated northward, it intersects the inner margin of the Ring of Fire at the location of the Valley of Geysers on the Kamchatka Peninsula. A similar relationship appears when extending the major axis of Antarctica northward toward the East Pacific Rise, where the projected line crosses the region of Yellowstone National Park, also situated at the geometrical margin of the Ring of Fire.
These two regions, Kamchatka and Yellowstone, contain by far the greatest concentration of geysers on Earth. Beyond them, only a few additional major geyser regions exist worldwide, and these too may potentially be interpreted within a similar geometric framework, such as Iceland. New Zealand is another obvious example.
The implication is not necessarily that geometry alone explains tectonic activity, but rather that persistent mantle organization may leave detectable large-scale geometric expressions at the Earth’s surface. Such relationships may provide an additional tool for examining the long-term structure of mantle convection and its connection to volcanism, tectonics, and geothermal activity. The degree of accuracy is very high, only to be understood in context with the mathematics of the shape of the Earth.
Everyone notices that Antarctica is centered around the South Pole. It has not always occupied this position, and over geological time it will eventually drift toward other latitudes. So why should its present location matter? Many people may consider it coincidental, yet the degree of regularity surrounding Antarctica is nevertheless worth examining.
The mainland of Antarctica is not perfectly circular, but a circle drawn around the coastline of East Antarctica, centered on the South Pole, also broadly encompasses the Antarctic Peninsula. This gives the continent as a whole a remarkably regular appearance https://www.sciencedirect.com/science/article/pii/S1674984722000775.
Antarctica is also almost completely encircled by mid-ocean ridges. The Antarctic Plate can therefore be regarded as a growing tectonic plate, since mid-ocean ridges expand outward on both sides according to the standard plate-tectonic model accepted by most geologists.
When the oceanic part of the Antarctic Plate is examined, it roughly fits an elliptical form centered on the South Pole, with one side extending from East Antarctica and the other from West Antarctica, along the geometrical major axis. Tracing the East Pacific Rise, and the Mid-Indian Ridge, they connect closely with the endpoints of the ellipse’s major axis.
Looking at the minor axis, the Mid-Atlantic Ridge approaches one endpoint rather closely, while the Puysegur Trench subduction zone, extending from New Zealand, connects near the opposite endpoint. Another major subduction system, along the western margin of South America where the Nazca Plate meets the South American Plate, touches the elliptical form at a position approximately equidistant from the Pacific and Atlantic ridge systems.
This degree of regularity can be observed directly on a simple world map. In addition, it fits well with the convection-roll framework examined here, since mid-ocean ridges outside this elliptical form around Antarctica, mainly tend to follow north–south alignments inherent in the mantle convection rolls model.
Within this interpretation, Antarctica is confined within the polar portion of the convection-roll system, bordering the transition zone of the model between 60.7°S and 67.3°S. From this perspective, the present position of Antarctica becomes relevant not only because of the regularity visible on the world map itself, but also because of the way these large-scale features appear to correspond with the mantle convection-roll model being explored here.
In addition, comparing with the Icelandic elliptical form, the minor axis is found along the same longitude.
Location of Hekla (red circle) and the Elliptical Outline of the Continental Shelf of Iceland.
Those two elliptical forms of the Antarctic and Icelandic continental shelfs, which can be identified with reasonable accuracy, both have a minor axis along 19°40′W. The Mid-Atlantic Ridge is obviously north-south oriented, but this consistency between Iceland and Antarctica clearly adds to that concept.
Major and minor axes of the Antarctic continental shelf, centered around the South Pole and reflecting the large-scale elliptical geometry of the Antarctic Plate margin.
The Icelandic continental shelf is indicated on the map. This interpretation is based on the mantle convection rolls model and the related large-scale structural pattern. The minor axis coincides with the transition zone between polar- and equatorial-related convection rolls, while the major axis extends toward the central part of the equatorial convection rolls. Map base: https://oceanobservatories.org/2022/11/nature-review-paper-reveals-new-understandings-of-mid-ocean-ridge-systems/
Comparing large-scale convection rolls with the shape of the Pacific Ocean reveals several intriguing geometrical structures. The first step is to consider the equator itself. It forms a simple reference line, but one with important physical implications, because the effects of Earth’s rotation differ there from those at other latitudes. At the equator, the clockwise deflection characteristic of the Northern Hemisphere, and the tendency of horizontally moving particles to turn anticlockwise, do not apply in the same way.
The Geometry of the Pacific Ocean.
The presence of major subduction zones on either side of the Pacific, Indonesia in the west and South America in the east, approximately 150° apart, provides two stable reference points.
As the Ring of Fire is a well-established concept, the volcanic regions can be outlined in a relatively simple way, beginning from these two equatorial reference points. The San Andreas Fault provides particularly strong support for this geometry, as it forms the sliding boundary between the Pacific Plate and the North American Plate. https://www.youtube.com/watch?v=YQtMBmS49Ew It thereby marks the approximate position of the minor axis of the elliptical form that appears when the Ring of Fire is sketched onto a map. This essay contains a lot of details:
Several principal lower-mantle division lines from the mantle convection rolls model are also drawn on the map. It should perhaps have been mentioned earlier that the major intersections between the main lower-mantle convection rolls coincide with the subduction regions on both the Indonesian and South American sides of the Pacific (shown with red dots). This observation alone deserves attention when comparing the model with the map.
Additional features emerge when examining the northeastern section of the Ring of Fire. When the outer limits of the Ring of Fire are outlined, the resulting elliptical form crosses Yellowstone National Park, a volcanic region unlike any other. Within the model, the pattern created by the division lines between convection rolls of different mantle layers produces a north–south axis between the predominantly north–south-trending rolls. Yellowstone is located directly on such a north–south axis.
With this in mind, the position of Hawaii also becomes significant. Hawaii is located not only on the north–south axis emerging from the convection-roll division pattern, but also on the central north–south axis of the Ring of Fire as represented on this map.
Looking at the western side of the Pacific, one of the first indications of a broader geometrical structure is the position of New Zealand along the minor axis of the elliptical form, opposite the San Andreas region and Yellowstone on the same axis. The Taupō Volcanic Zone is located where this minor axis intersects a principal lower-mantle division line. On the map, that mantle division line is drawn somewhat exaggerated in order to emphasize its significance.
The western Pacific is subject to intense geophysical and tectonic stress, and this particular division line — extending from Japan to New Zealand — appears to accommodate much of that stress. Comparing the Northern and Southern Hemispheres, New Zealand and Japan, together with the subduction systems extending southward and northward from them respectively, display a mirrored relationship. Because stress is concentrated along this division line, and because rotational effects differ symmetrically between the hemispheres, New Zealand appears within the inner elliptical form of the Ring of Fire.
Further similarities emerge when examining the convection-roll division lines. Not only do Japan and New Zealand occupy corresponding positions within the model, but major volcanic centres such as Mount Fuji and Taupō are also found in analogous hemispherical settings on opposite sides of the globe. Likewise, the Kermadec Trench and the Izu–Bonin Trench display mirrored alignments.
The circular — or more precisely elliptical — geometry of the Pacific can therefore be compared with many details of the mantle convection rolls model. At the same time, the dimensions and shape of the Pacific have continually changed through tectonic drift. Over geological time, plate motion gradually alters the geometry of the basin itself.
The geological development of the region is equally revealing. Research has shown that much of the crustal material now forming southern Alaska originated at far more southern latitudes and has since been transported more than a thousand kilometres toward the northwest. The Denali Fault and Tintina Fault systems appear to have played a major role in this transport after island arcs had been sutured onto the North American continent. This partly illustrates how the Ring of Fire functions and why it extends across a geometrically well-defined region composed primarily of two concentric elliptical forms and the area enclosed within them.
This perspective also suggests that subduction zones may remain relatively fixed once established within the mantle convection rolls system. As the geometry evolves through tectonic drift, slabs descending into the mantle may become detached from their original surface plates, while new subduction zones eventually develop elsewhere.
It should be added here, tht there is a possible explanation for the formation of north–south axes within the framework of convection rolls. This becomes apparent when examining the detailed geometry of the division lines and polygonal regions formed between them. These polygons often tend toward a diamond-shaped geometry, with corners aligned approximately east–west and north–south.
Pressure exerted along the sides of such polygons may then create preferential lines of weakness or activity extending from one corner to the opposite corner. When this process is repeated across many adjacent small polygons, the resulting alignment can be extrapolated into the large-scale north–south patterns observed across the Pacific and elsewhere.
A particularly clear example of this type of geometry can be examined in Iceland. There, the North Volcanic Zone forms a pronounced north–south volcanic alignment, while the South Iceland Seismic Zone follows an east–west-oriented structural trend. Together, these systems illustrate how polygonal stress geometry within the mantle convection rolls framework may influence both volcanic and seismic alignments on the surface.
Magic Magma 