​Twenty-One Divine Infinities
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There are three kinds of infinities: mathematical, non-mathematical, and metaphorical. Divine infinities are typically non-mathematical and metaphorical, intended to articulate an aspect of God which is immense, boundless, and ultimately incalculable. Below are twenty-one divine infinities which are meaningful to process-relational theologians in different contexts. All are portals for belief in God, and some are more important than others relative to given situations. All are true to Whitehead's philosophy, by which so many of process theologians are influenced. Add your own.

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1. Infinitely Tender: The tenderness of God knows no limits, as the wisdom at the heart of the universe empathizes with and desires the well-being of all beings. God is found in the quiet and loving side of life. This side of God, says Whitehead, "dwells upon the tender elements in the world, which slowly and in quietness operate by love; and it finds purpose in the present immediacy of a kingdom not of this world. Love neither rules, nor is it unmoved; also it is a little oblivious as to morals. It does not look to the future; for it finds its own reward in the immediate present." God is "a fellow sufferer who understands."
2. Infinitely Wild: The primordial nature of God, as distinct from the tender side, is hungry for intense experience and the intensities of the universe (subatomic, atomic, molecular, cellular, organic, and galactic) are satisfying to the divine appetite. It is "wild" in the sense that, like wilderness itself, it is indifferent to the concerns of particular living beings and to issues of their survival. It is a quest for novel intensity. Whitehead writes: "He, in his primordial nature, is unmoved by love for this particular, or that particular; for in this foundational process of creativity, there are no preconstituted particulars. In the foundations of his primordial nature. God is indifferent alike to preservation and to novelty. He cares not whether an immediate occasion be old or new, so far as concerns derivation from its ancestry. His aim for it is depth of satisfaction as an intermediate step towards the fulfilment of his own being. His tenderness is directed towards each actual occasion as it arises."
3. Infinitely Vulnerable: The tender side of God is affected by everything that happens, but this vulnerability is not a weakness. Rather, it represents a strength, as God's openness and responsiveness are not hindered by any limitations. Whereas we humans and other living beings are finitely vulnerable, God is infinitely vulnerable. The vulnerability of God includes divine suffering. Each instance of suffering in the universe is felt by God and shared by God.
4. Infinitely Playful: God is infinitely playful, continuously seeking the actualization of new possibilities and inspiring creativity and growth within the universe. God is Krishna-like.
5. Infinitely Humble: In God's tender aspect, God does not assert dominance over creation but rather exercises a receptive and persuasive power. Receptive in that God receives all that happens with tender care; God is persuasive in that God seeks to be loved as a trusted friend, not recognized as a mighty king, and does not require praise to be God. God is Christ-like. God doesn't mind being hidden and unrecognized, like a kindly grandmother who stands in the background.
6. Infinitely Erotic: At the heart of God is a primordial appetition for intense experience. God represents the Eros of the universe, forever seeking novelty. The infinite eroticism of God coexists with infinite patience and tenderness. Divine eroticism is filled with desire, with subjective aim, with a need to be "at one" with the world.
7. Infinitely Adaptable: God adjusts to each novel situation and responds to the changing circumstances of the evolving universe. God's adaptability reflects a dynamic nature and responsive engagement with the world and with unfolding possibilities.
8. Infinitely Beautiful (Musical and Rhythmic): The musicality of God is similar to an unfinished symphony filled with contrasts. It involves the Sacred Whole gathering all that happens in the universe into whatever harmony is possible, like an unfinished symphony evolving through time. Its rhythms include the rhythms of the universe: the vibrations of molecules, the movements of the heavens, the changing of seasons, the stages of life.
9. Infinitely Ancient: Even as God is new at every moment, God is the most ancient actuality in the universe in that God's ongoing life contains the entirety of the past as if it were yesterday, itself a source of wisdom for the world. God is like a cosmic sage, magnified by infinity.
10. Infinitely Young: God is new at every moment and youthful, too: a source of novel possibilities, constantly surprising and inspiring with fresh insights and creativity, God is like a newborn child, magnified by infinity.
11. Infinitely Temporal: God is infinitely temporal or "everlasting" in what God has no beginning or end and God forever includes what is new in the universe, becoming new.
12. Infinitely Timeless: While God is infinitely temporal, there is a non-temporal or eternal aspect that encompasses pure potentialities, eternal objects. These possibilities exist beyond time, contributing to God's infinite nature.
13. Infinitely Patient: God possesses infinite patience, enduring and persisting in the face of the evolving complexities and challenges of the world. This patience allows God to await the fruition of possibilities and the ongoing process of realization.
14. Infinitely Dependent: God, while inwardly free, is infinitely dependent on every other actuality in the universe to be "God." God is the most related actuality, not the least related, emphasizing the interdependence within the divine reality.
15. Infinitely Deep: It is common for people to imagine God in terms of height metaphors. God is "up in the sky" in some way. But depth metaphors are just as good and often better. God is deeper than the deepest thing we can imagine. Wide as the sea, yes, but also deeper than anything we can imagine: deeper than the ocean, deeper than the core of Jupiter, and deeper than our own unconscious experience, We do not need to look outside us to find God, we can also look within, yet deeper. God is the Deep.
16. Infinitely Wide: As the sacred whole of the universe, God is not an object among objects in our experiential field. We are always already within this whole. but never grasp it as an object among objects in the whole. Rather, God is a non-objective field within which we live, move, and have our being. 
17. Infinitely Mysterious (apophatic): In "Process and Reality" Whitehead writes: "There remains the final reflection, how shallow, puny, and imperfect are efforts to sound the depths in the nature of things. In philosophical discussion, the merest hint of dogmatic certainty as to finality of statement is an exhibition of folly." This is true of God as well, the merest hint as to finality of statement is an exhibition of folly, and any attempts to sound the depths of God are shallow, puny, and imperfect.
18. Infinitely Palpable (cataphatic): Whitehead writes that the world in all its diversity is part of the divine life: "It is as true to say that God is one and the World many, as that the World is one and God many."  God "acquires a consequent multiplicity" from the world itself, such that the world is one and God many. This means that everything we see around us, beyond us and with us, is part of God. Not the whole of God, but part of God.
19. Infinitely Incarnate: God is "incarnate" in each creature (each actual occasion) as its innermost initial aim, its possibility for maximum satisfaction relative to the situation. God is even more incarnate with that creature actualizes the aim. When this happens, the Logos of God, the Word, becomes flesh. There are many kinds of incarnation: subatomic, atomic, cellular, organic, galactic. If spirits exist (angels, ghosts, devils) they, too, incarnate God. The devils incarnate God in the first way. The angels do it in both ways. Most of us humans have a devil and an angel inside us. We are virtuous and sinful at the same time.
20. Infinitely Small: It is tempting for people to think of God in "large" and "grandiose" terms, always "more" than this and that. But part of what makes God beautiful is divine smallness: that is, the way in which God is present in the little, the tiny, the the non-grandiose, the "least of these." Only those who have eyes for the small can see his side of God. 
21. Infinitely Faithful: God's lures and companionship are always present, even in times when God seems absent. The divine presence permeates the fabric of existence, offering guidance, comfort, and companionship at all times, even when it may not be immediately apparent.​

These aspects contribute to the nuanced understanding of the God of process theology, highlighting the interplay between infinity and finitude. They emphasize God's infinite nature in knowledge, experience, adaptability, vulnerability, patience, the non-temporal realm of potentialities, and the intimate relationship with the finite realities of the universe. Additionally, they recognize God's infinite playfulness in the eternal pursuit of new possibilities and the realization of creative potential. Some are in tension with others: for example, the wildness of God is in tension with the tenderness of God. Yet all touch, or seem to touch, some aspect of the divine life and become relevant to people at different times in their lives.

Three Kinds of Infinities

hyperbolic, non-mathematical,
and mathematical

In Greek, ‘to apeiron’ means ‘the infinite’: ‘a’ denotes privation and ‘peras’ the notion of ‘limit’ or ‘bound’. Etymologically, the English word ‘infinite’ comes from the Latin word ‘infinitas’: ‘in’ = ‘not’ and ‘finis’ = ‘end’, ‘boundary’, ‘limit’, ‘termination’, or ‘determining factor’. In contemporary English, there is a range of uses of the word ‘infinite’:
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• In a loose or hyperbolic sense, ‘infinite’ means ‘indefinitely or exceedingly great’, ‘exceeding measurement or calculation’, ‘immense’, or ‘vast’.​
• In a strict but non-mathematical sense that reflects its etymological history, ‘infinite’ means ‘having no limit or end’, ‘boundless’, ‘unlimited’, ‘endless’, ‘immeasurably great in extent (or duration, or some other respect)’. This strict, non-mathematical sense is often applied to God and divine attributes, and to space, time and the universe.
• There is also a strict, mathematical sense, according to which ‘infinite’ quantities or magnitudes are those that are measurable but that have no finite measure; and ‘infinite’ lines or surfaces or volumes are measurable lines or surfaces or volumes that have no finite measure.

- Easwaran, Kenny, Alan Hájek, Paolo Mancosu, and Graham Oppy, "Infinity", The Stanford Encyclopedia of Philosophy (Winter 2021 Edition), Edward N. Zalta (ed.), URL = <https://plato.stanford.edu/archives/win2021/entries/infinity/>.

Beware of Subject-Predicate Thinking
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In process theology, God is infinite in many ways. Some are familiar and predictable: God knows all that can be known and is infinitely wise; God seeks the well-being of each and all and is infinitely loving. But some are surprising and delightful. God is infinitely playful, infinitely incomplete, infinitely vulnerable, infinitely imaginative, infinitely tender, and infinitely unanalyzable.

These less familiar, more surprising infinities are important because they help free the mind from tendencies to make God an object among objects, a mere focal point of the theological imagination. Each infinity provides a portal for experiencing God in fresh ways.
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God is not the subject of a sentence but rather an encompassing Life in whose consciousness the universe unfolds. Instead of saying "God is playful," it is better to say "In the divine life, there is an infinite playfulness." And instead of saying "God is tender," it is better to say "The universe carries within it a deep tenderness." God's infinities are not a property of a separate something called God. They are God godding.

It is also important to note that the many infinities include finitude in ways that elude impulses to praise or flatter God. The impulse to praise God, as if God were merely a monarch in the sky or a bully on a throne, can inhibit a respect for God's finitude: God's presence in the child at play, in the loneliness of the forsaken, in the hunger of the abandoned, in the death of the victims. These events are part of God's own life. They are God, too. Thus infinites are not isolated in a compartment called "the infinite." They include the finite. They are God.

Mathematical Infinity
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Melvyn Bragg and guests discuss the nature and existence of mathematical infinity. Jonathan Swift encapsulated the counter-intuitive character of infinity with insouciant style:“So, naturalists observe, a fleaHath smaller fleas on him that prey, and these hath smaller fleas to bite ‘em, and so proceed ad infinitum.”Alas, the developing utility mathematicians put to the idea of infinity did not find the English philosopher Thomas Hobbes quite so relaxed. When confronted with a diagram depicting an infinite solid whose volume was finite, he wrote, “To understand this for sense, it is not required that a man should be a geometrician or logician, but that he should be mad”.

​Yet philosophers and mathematicians have continued to grapple with the unending, and it is a core concept in modern maths.So, what is mathematical infinity? Are some infinities bigger than others? And does infinity exist in nature? With Ian Stewart, Professor of Mathematics at the University of Warwick; Robert Kaplan, co-founder of The Math Circle at Harvard University and author of The Art of the Infinite: Our Lost Language of Numbers; Sarah Rees, Reader in Pure Mathematics at the University of Newcastle.

History of the the Idea of the Infinite

​History of the Infinite Part I: click here.
History of the Infinite Part II: click here.

University of Oxford professor Adrian Moore explores the philosophical, mathematical and cultural history of the infinite through two and a half millennia. In this first of two episodes, Adrian discovers why the Ancient Greeks abhorred the notion of infinity and introduces us to the Greek philosopher, Aristotle. He describes how the church attempted to stamp its authority on the debate and how that led to some explosive disagreements amongst medieval thinkers, before bringing us to the verge of the modern world and the way we think now. Having looked at the infinite in philosophical and theological terms, Adrian then views it through the lens of mathematics, considering the pivotal role mathematics has played in the quest to understand the infinite.