Mathematics and Love Poetry

A Poem by Haipeng Guo

Sometimes, when two people fall in love, they are drawn to the unique qualities that each possesses. For instance, one may be a pragmatic problem-solver, while the other is a dreamer with a penchant for the abstract. What makes their connection intriguing is how these differences complement each other, adding depth to their relationship. Their differences make the whole richer.

Haipeng Guo,* a distinguished academic with multiple roles and accolades at United International College in Zhuhai, China, presents a unique perspective on this theme in his award-winning poem, "When a P-man Loves an NP-woman." His poem is featured in "Strange Attractors: Poems of Love and Mathematics," edited by Sarah Glaz and Joanne Growney in 2008. I've been given permission to reprint it here, as below. In what follows, I offer a brief word about the P versus NP problem and then offer a Whiteheadian interpretation of Guo's poem, in honor of his position as Executive Director of the UIC Center for Whitehead Studies.

*

The question of whether P equals NP is an enduring and as yet unsolved problem in the field of computer science. "P" represents polynomial time, where an algorithm's runtime increases predictably as the problem size grows. In contrast, "NP" signifies nondeterministic polynomial time, indicating that verifying a proposed solution may be relatively quick, while finding the solution itself could be exceptionally challenging, perhaps even impossible within a reasonable timeframe. The precise duration for finding the solution remains uncertain. This question ranks among the most pivotal in theoretical computer science and is one of the seven problems for which the Clay Mathematics Institute offers a million-dollar prize for proof, either way. In essence, P represents a set of relatively straightforward problems, while NP encompasses seemingly insurmountable challenges. If P were indeed equal to NP, it would imply that these formidable problems have surprisingly simple solutions. But the reality is far more intricate. For more details on the intricacy of the problem, I refer readers to an essay on it offered by MIT (click

From a Whiteheadian perspective, poetry and mathematics consist of what Whitehead calls propositions, much like all forms of language. In "Process and Reality," Whitehead suggests that propositions, including mathematical and philosophical ones, are not solely logical but also serve as "lures for feeling." This means that propositions can be conceptual objects that evoke subjective feelings and insights within and beyond their original contexts. Propositions need not be true to be meaningful or captivating. Mathematical propositions, in particular, can possess poetic qualities and shed light on aspects of human life that extend beyond the realm of mathematics. Guo's poem is illustrative of this extension.

Guo's work embodies another concept from Whitehead's philosophy – that of "contrasts." Contrasts, as described by Whitehead, are not contradictions but rather diverse facets of reality that enhance and complete each other through their differences. These contrasting elements form wholes greater than the sum of their parts, enriching the experience of a living subject. Whitehead believes that throughout life we are in search of meaningful contrasts to live by, and contrasts of contrasts of contrasts. Indeed, for him, "contrasts" are among the fundamental features of ontology.

In "When a P-man Loves an NP-woman," the contrast lies in the experiences of two individuals: one with a "polynomial brain" and a preference for "NP orientations," and the other, equally polynomial but possessing a non-deterministic NP wit. Moreover, the evolution of this contrast, both intellectually and emotionally, involves what Whitehead terms "decision." In Whitehead's philosophy, a decision encompasses the active consideration, consciously or unconsciously, of various possibilities in a given moment for responding to what is given to experience, the actualization of some while the abandonment of others.

Guo's poem depicts a man making such a decision, mirroring the indecisiveness surrounding the P=NP problem. This decision carries inherent risk, as the man, like Whitehead's perspective, acknowledges the uncertain and open-ended nature of the future. The poem subtly suggests that even the Almighty might find it futile to seek a definitive resolution to the P=NP question. The assumption is that there might exists an element in the fabric of existence, an element Whitehead calls "creative advance into novelty," which transcends the boundaries of both mathematics and poetry, and which in some ways transcends God, too. Decision-making signifies that there is an element of randomness in the depths of reality that can never be "solved" like a mathematical equation. P needs NP.

Whitehead's philosophy is itself a philosophy that seeks to integrate and affirm both P and NP: the determinate and the indeterminate, the finite and the infinite. Mathematics often points us toward the indeterminate side of life. It deals with patterns of connection, some of which may emerge from what Whitehead calls "eternal objects" or "pure potentialities" in the mind of the divine. These matters include numbers, algebraic relations, topologies, infinities, and much more. Pure mathematics is an exploration of these pure patterns of connection abstracted from their embodiment in life; and thus, in its own way, an exploration of infinity in the form of patterns. But value, says Whitehead in "Mathematics and the Good," is the gift of finitude. Finitude "vivifies" or brings to life the infinite.

A willingness to accept the indeterminate in life, the not easily resolved, is itself a doorway into the infinite, just as mathematics is a doorway. The infinite, always beyond our grasp, becomes concrete through the creativity of feelings and decision. Whitehead puts it this way in his essay Mathematics and the Good: "Creativity involves the production of value-experience, by the inflow from the infinite into the finite, deriving special character from the details and the totality of the finite pattern."

The narrator of the poem, in wrestling with P and NP in the poem is vivifying the infinite in a small but eminently human way. He is, as it were, bringing heaven down to earth, infinity into finitude, abstractness into concreteness. Such vivification is occurring anywhere and everywhere in the universe. Atoms and molecules, plants and animals, solar systems and galaxies are vivifications, as are the emotions and energy of they are expressions.

When a P-man loves an NP-woman, the love itself, and the commitment that accompanies the love, is an expression of the infinite in a particularized, finite way. There is nothing to be 'solved,' but there is a journey to be undertaken. The "happy deterministic man" begins a journey, becoming a new man, thanks to the "polynomial woman with a deterministic wit." And, who knows, she may become a new woman. Whitehead would surmise as much. A marriage, like everything else, is a creative advance into novelty.

- Jay McDaniel

* Guo is a Professor & Ph.D. in Computing and Information Science, Associate Dean of the School of General Education (SGE); Acting Head of the English Language Centre (ELC), Executive Director of the UIC Center for Whitehead Studies. It was written while he was in graduate school many years ago.

Haipeng Guo,* a distinguished academic with multiple roles and accolades at United International College in Zhuhai, China, presents a unique perspective on this theme in his award-winning poem, "When a P-man Loves an NP-woman." His poem is featured in "Strange Attractors: Poems of Love and Mathematics," edited by Sarah Glaz and Joanne Growney in 2008. I've been given permission to reprint it here, as below. In what follows, I offer a brief word about the P versus NP problem and then offer a Whiteheadian interpretation of Guo's poem, in honor of his position as Executive Director of the UIC Center for Whitehead Studies.

*

The question of whether P equals NP is an enduring and as yet unsolved problem in the field of computer science. "P" represents polynomial time, where an algorithm's runtime increases predictably as the problem size grows. In contrast, "NP" signifies nondeterministic polynomial time, indicating that verifying a proposed solution may be relatively quick, while finding the solution itself could be exceptionally challenging, perhaps even impossible within a reasonable timeframe. The precise duration for finding the solution remains uncertain. This question ranks among the most pivotal in theoretical computer science and is one of the seven problems for which the Clay Mathematics Institute offers a million-dollar prize for proof, either way. In essence, P represents a set of relatively straightforward problems, while NP encompasses seemingly insurmountable challenges. If P were indeed equal to NP, it would imply that these formidable problems have surprisingly simple solutions. But the reality is far more intricate. For more details on the intricacy of the problem, I refer readers to an essay on it offered by MIT (click

**here**) and to the scholarly discussion below, offered by the BBC. Now, on to Guo's poem.From a Whiteheadian perspective, poetry and mathematics consist of what Whitehead calls propositions, much like all forms of language. In "Process and Reality," Whitehead suggests that propositions, including mathematical and philosophical ones, are not solely logical but also serve as "lures for feeling." This means that propositions can be conceptual objects that evoke subjective feelings and insights within and beyond their original contexts. Propositions need not be true to be meaningful or captivating. Mathematical propositions, in particular, can possess poetic qualities and shed light on aspects of human life that extend beyond the realm of mathematics. Guo's poem is illustrative of this extension.

Guo's work embodies another concept from Whitehead's philosophy – that of "contrasts." Contrasts, as described by Whitehead, are not contradictions but rather diverse facets of reality that enhance and complete each other through their differences. These contrasting elements form wholes greater than the sum of their parts, enriching the experience of a living subject. Whitehead believes that throughout life we are in search of meaningful contrasts to live by, and contrasts of contrasts of contrasts. Indeed, for him, "contrasts" are among the fundamental features of ontology.

In "When a P-man Loves an NP-woman," the contrast lies in the experiences of two individuals: one with a "polynomial brain" and a preference for "NP orientations," and the other, equally polynomial but possessing a non-deterministic NP wit. Moreover, the evolution of this contrast, both intellectually and emotionally, involves what Whitehead terms "decision." In Whitehead's philosophy, a decision encompasses the active consideration, consciously or unconsciously, of various possibilities in a given moment for responding to what is given to experience, the actualization of some while the abandonment of others.

Guo's poem depicts a man making such a decision, mirroring the indecisiveness surrounding the P=NP problem. This decision carries inherent risk, as the man, like Whitehead's perspective, acknowledges the uncertain and open-ended nature of the future. The poem subtly suggests that even the Almighty might find it futile to seek a definitive resolution to the P=NP question. The assumption is that there might exists an element in the fabric of existence, an element Whitehead calls "creative advance into novelty," which transcends the boundaries of both mathematics and poetry, and which in some ways transcends God, too. Decision-making signifies that there is an element of randomness in the depths of reality that can never be "solved" like a mathematical equation. P needs NP.

Whitehead's philosophy is itself a philosophy that seeks to integrate and affirm both P and NP: the determinate and the indeterminate, the finite and the infinite. Mathematics often points us toward the indeterminate side of life. It deals with patterns of connection, some of which may emerge from what Whitehead calls "eternal objects" or "pure potentialities" in the mind of the divine. These matters include numbers, algebraic relations, topologies, infinities, and much more. Pure mathematics is an exploration of these pure patterns of connection abstracted from their embodiment in life; and thus, in its own way, an exploration of infinity in the form of patterns. But value, says Whitehead in "Mathematics and the Good," is the gift of finitude. Finitude "vivifies" or brings to life the infinite.

A willingness to accept the indeterminate in life, the not easily resolved, is itself a doorway into the infinite, just as mathematics is a doorway. The infinite, always beyond our grasp, becomes concrete through the creativity of feelings and decision. Whitehead puts it this way in his essay Mathematics and the Good: "Creativity involves the production of value-experience, by the inflow from the infinite into the finite, deriving special character from the details and the totality of the finite pattern."

The narrator of the poem, in wrestling with P and NP in the poem is vivifying the infinite in a small but eminently human way. He is, as it were, bringing heaven down to earth, infinity into finitude, abstractness into concreteness. Such vivification is occurring anywhere and everywhere in the universe. Atoms and molecules, plants and animals, solar systems and galaxies are vivifications, as are the emotions and energy of they are expressions.

When a P-man loves an NP-woman, the love itself, and the commitment that accompanies the love, is an expression of the infinite in a particularized, finite way. There is nothing to be 'solved,' but there is a journey to be undertaken. The "happy deterministic man" begins a journey, becoming a new man, thanks to the "polynomial woman with a deterministic wit." And, who knows, she may become a new woman. Whitehead would surmise as much. A marriage, like everything else, is a creative advance into novelty.

- Jay McDaniel

* Guo is a Professor & Ph.D. in Computing and Information Science, Associate Dean of the School of General Education (SGE); Acting Head of the English Language Centre (ELC), Executive Director of the UIC Center for Whitehead Studies. It was written while he was in graduate school many years ago.