# What is Roman infinity?

The concept of infinity played an important role in ancient Roman mathematics and philosophy. The Romans used a specific symbol to represent infinity, which was the letter I enclosed in a circle or oval – ∞. This symbol was called the lemmaton or the auriphorma. The lemmaton was first used by Roman mathematicians to represent infinitely large quantities and endless processes in geometry and arithmetic. Philosophers later adopted the symbol to convey abstract concepts of boundlessness and eternity.

## Origins of the Roman Infinity Symbol

The origins of the Roman infinity symbol can be traced back to the mathematics of the ancient Greeks. Greek mathematicians such as Archimedes and Apollonius of Perga explored the properties of infinitely large quantities in their studies of geometry and calculus. For instance, Archimedes calculated the area enclosed by a spiral by considering the limit as the number of rotations approached infinity.

The Greek letter omega – Ω – was sometimes used by Greeks to denote infinity. The connection is clear – omega is the last letter in the Greek alphabet, just as infinity represents an unending limit. Omega depicts this circular meaning, while also evoking the shape of a snake eating its own tail in the ouroboros symbol of cyclicality.

Roman mathematicians adopted the concept of infinity from the Greeks. However, they represented the notion in their own way by enclosing the letter I in a circle or oval. Some historians suggest the Romans chose the letter I because it is the first letter in the word for infinity in Latin – Infinitas. The loop enclosing the I signifies the boundless, endless nature of infinity.

### Use of the Lemmaton in Mathematics

Roman mathematicians used the lemmaton symbol ∞ to represent infinity in various contexts.

In geometry, it was used to denote an infinitely large quantity. For example, the lemmaton was used to represent a line of infinite length. Apollonius of Perga had shown that as a circle grows larger and larger, its circumference approaches a straight line. The Romans saw this infinite straight line as being represented by the symbol ∞.

The Roman infinity symbol was also used in the context of limits and infinite series in arithmetic. Mathematicians such as M. Terentius Varro and T. Manlius Boethius explored infinite sequences and how variable quantities approached limits.

Boethius, for instance, considered a sequence where each term was generated by adding an extra unit to the previous term. He showed that as this sequence progressed, the terms could become infinitely large, represented by ∞.

Thus the lemmaton found various applications in Roman era mathematics to represent infinity and infinite processes.

### Use in Philosophy

Besides mathematics, Roman philosophers also used the infinity symbol ∞ in their metaphysical speculations. The Stoics, Platonists and Neoplatonists adopted the lemmaton to represent abstract ideas of boundlessness, eternity, and the infinite nature of time and space.

The Stoic philosopher Seneca, for example, used the infinity symbol to represent the unlimited extent of the cosmos. In his Natural Questions, Seneca argues that the universe has no boundary and stretches without limit in all directions – encapsulated by the infinite symbol.

Plotinus, the founder of Neoplatonism, used the lemmaton to represent the infinite and eternal nature of the cosmos and the absolute perfection of the One (or God). He claimed that while numbers and mathematical concepts have limits, the spiritual realm of the One is infinite, transcending all boundaries.

Boethius, in his theological work The Consolation of Philosophy, uses the infinity symbol ∞ to convey the boundless nature of God’s eternity. To God, being outside of temporal flux, past, present and future are joined in an eternal present – reflected in the endless loop of the lemmaton.

Thus Roman philosophers used the mathematical concept of infinity to convey rich metaphysical and theological ideas – adding additional layers of meaning to the symbol ∞.

## Evolution of the Infinity Symbol

The Roman infinity symbol continued to evolve in the medieval era.

In the 12th century, the lemmaton evolved into a figure eight shape – ∞ – which is closer to our modern infinity symbol. The 8-shaped variant became known as the lemniscate.

Mathematicians such as Jacob Bernoulli began to use the lemniscate to denote infinite quantities and processes in calculus. For instance, Bernoulli employed the lemniscate to represent infinitesimals – quantities that approach zero.

In 1655, John Wallis published his seminal work Arithmetica Infinitorum which established the foundations of calculus. In this work, Wallis used the infinity symbol ∞ in its modern form to represent infinitesimals as well as infinite limits.

Wallis explains that just as a circle has “neither beginning nor end”, the lemniscate infinity symbol represents infinitesimal quantities having “no absolute minimum” and infinite quantities having “no absolute maximum”.

Wallis’ consolidation of the infinity symbol ∞ contributed to its adoption in modern mathematics. Today it remains a ubiquitous symbol to denote the endless and the unbounded across all branches of mathematics.

### Infinity in Other Cultures

The early symbol for infinity in ancient Indian mathematics was a dot within a circle – similar to the Roman lemmaton. This was first seen in the works of Brahmagupta where it denoted indefinite quantities.

In Jainism, the shape of the Swastika symbol reflects ideas of infinity and eternal cyclicity. It is sometimes thought to represent the infinity of space and time.

In Chinese Buddhism, the Endless Knot – an intertwined figure eight – represents the infinite wisdom and compassion of the Buddha. The knot has no beginning or end, symbolizing boundlessness.

Thus cultures around the world developed their own symbols for infinity drawing from either circles or interlocked shapes to convey endlessness and limitlessness.

## The Meaning and Significance of Infinity

The Roman infinity symbol represents one of humanity’s earliest forays into understanding the mathematically infinite. Their lemmaton ∞ and its evolution into the lemniscate symbol created a powerful visual representation of infinity.

In mathematics, this unlocking of the infinite allowed Roman and Greek mathematicians to push the boundaries of geometry, arithmetic and calculus. They could now mathematically reason about infinitely large quantities and infinitesimally small ones in their calculations.

In philosophy, the concept of infinity allowed philosophers and theologians to grapple with metaphysical questions of eternity, boundlessness and the limitlessness of time and space.

The infinity symbol continues to be a source of fascination and mystery in modern mathematics. Some types of infinity are larger than others, and the nature of the infinite remains elusive. As mathematics continues to explore this enigmatic concept, the legacy of the Roman infinity symbol endures.

Thus the early Roman symbol for infinity gave form to one of the most profound and far-reaching concepts in all of mathematics and metaphysics – one that continues to inform our understanding to this day.

## Conclusion

The Roman infinity symbol known as the lemmaton originated as a visual representation of infinite quantities and processes in Greek and Roman era mathematics. Over time, it evolved into the modern lemniscate symbol for infinity – ∞. Philosophers used the symbol to represent metaphysical concepts like endlessness and eternity, adding philosophical layers of meaning.

The unlocking of infinity allowed mathematicians to explore geometrical problems and calculus involving the infinitely large and small. It enabled philosophers to speculate on the limitless nature of time, space and knowledge. Across mathematics, philosophy and cosmology, the Roman symbol for infinity created a foundation for understanding the boundless and endless.

While the modern mathematical concept of infinity has grown more complex and subtle, the Roman lemmaton retains its power as an elegant symbol of infinity. It encapsulates the sophisticated concept of endlessness within the simple visual metaphor of a loop or figure eight.

The next time you see the infinity symbol, remember that its origins can be traced back to the innovative Roman mathematicians and philosophers who first gave visual form to the endless unknown.

## The Table of Roman Numerals

Arabic Number Roman Numeral
1 I
2 II
3 III
4 IV
5 V
6 VI
7 VII
8 VIII
9 IX
10 X

This table shows the Roman numerals for the first ten Arabic numbers, demonstrating how the Romans represented numbers before the introduction of the Hindu-Arabic numeral system.

### What shape was the earliest Roman infinity symbol?

The earliest Roman symbol for infinity was the letter I enclosed in a circle or oval known as the lemmaton – ∞. This originated as a representation of infinite quantities in Greek mathematics.

### When did the infinity symbol change to a figure eight shape?

In the 12th century, the lemmaton evolved into a figure eight shape known as the lemniscate – ∞. Mathematicians like Jacob Bernoulli began using this version to represent infinitesimals and infinite limits.

### Who first used the modern infinity symbol?

In 1655, John Wallis published Arithmetica Infinitorum where he consolidated the use of the figure eight infinity symbol – ∞ – in its modern form as a representation of infinitesimals and infinite quantities.

### What philosophical concepts was infinity used to represent?

Roman philosophers like Seneca and Plotinus used the infinity symbol to represent metaphysical concepts like the eternity and boundlessness of time, space and knowledge. Boethius used it to convey the infinite nature of God.

### Are there non-Roman symbols for infinity in other cultures?

Yes, ancient Indian mathematics used a dot in a circle for infinity. In Chinese Buddhism the Endless Knot represents infinity. The Jain Swastika symbol also conveys notions of cyclicity and infiniteness.