"The windmill proof" by Stephen Payne (HappenStance, 2021)

Poems from The Dark Horse, Magma, The North, Rialto, etc.

An aside

At the book launch in August we learnt that the author was a keen mathematician until he switched to pyschology at 19, becoming a professor. I kept going with maths beyond 19, ending my maths degree with a course run by a Philosophy lecturer. I go to public lectures on Pure Maths. I knew about the Gobi Desert diagram alluded to in this book. In short, I'm not a typical reader of this book. My Poetry, Mathematics, and Computing article summarises my views on attempts to merge poetry and maths.

It's not enough to measure the sides of many right-angled triangles and discover that a²=b²+c² was true for all of them - the next triangle measured may break the rule. This may sound unlikely but such things have happened before in maths. That's why proofs are important, and why mathematicians spent time seeking proofs. Because of the windmill proof (and other proofs) we know that every right-angled triangle has this property.

However, the proof may contain a mistake (this too has happened in maths). Worse still, it's been proven that there are true statements in maths that maths can't prove. This is distressing - a mathematician might spend a lifetime searching vainly for a proof.

In other universes I'd think that if anything is in common with our universe, it will be maths. Primes often appear in messages that SETI send out, because Euclidean geometry isn't considered sufficiently universal.

Coincidences

His "Cone" poem has "touched by the rays emitted from the eyes ... his searchlight reaching into dark". My "Eyes" poem begins with "Sight is to eyes as soul is to the body - Aristotle// They glowed like pleading searchlights for centuries", ending with how the cone idea is used in modern computer animation by Pixar, etc.

He has poems called "Point", "Line", "Plane", "Angle", "Triangle", "Square", "Hexagon", "Circle", "Ellipse", "Cube", "Tetrahedron", "Cone", "Parabola", "Cylinder", "Prism" and "Sphere". By chance I combined several of those in

The Shape of Lost Love A plate may cast a sphere's shadow, chancing upon perfection as it moves, but it can never be love. Don't be fooled by the light, there aren't infinite sides. When the die stops spinning with its point towards you, it becomes a hexagon in silhouette, hopes trapped in a pentagon of senses. Within the four walls of your flat the eternal triangle seems as far away as Bermuda. It's time to draw the line but what's the point - there's nothing left.

Needless to say, it's unpublished.

Some maths notes

• "This Poem is about self-reference". Gödel's "proof by contradiction" in the end produces a maths statement equivalent to This sentence is not true. Bertrand Russell produced problem cases involving self-referential sets which caused a rethink in the logic of the time. "The Barber's paradox" derives from it, which may explain why "Shave" (about someone who shaves himself) is the poem before this one.
• "Commute" is a mathematical term. I can't see the maths element here though.
• "The riddle of the Buddhist Monk" is an example of how a seemingly difficult maths problems can sometimes be solved simply by looking at the problem differently.

Now the write-up

It's lucid in the way that Holub is, or Magritte whose visual puns are replaced here by verbal ones.

I like "The big leap" and "The pool" most, and "Poem", a twist on the idea that

• "[a poem is] a kind of machine for producing the poetic state of mind" - Valéry
• "A poem is a small (or large) machine made of words" - William Carlos Williams
• "The poem, in a sense, is no more or less than a little machine for remembering itself" - Don Paterson

"Analogy" contains a few explicit analogies - "mind is home", "happiness is a hotel room", "locking oneself out of a hotel room is comedy". But what if you lock yourself out of your home/mind? It could be more serious. You may need to search for an open window, or find a friend/lover with a key.

Several poems are in standard forms. "Lines in Denver" has an "abba" rhyme scheme. "Vie de Joie" is in rhyming couplets. "Concrete Poem" is shaped (like a concrete tower). "Crown Green Bowls" has "abcabc" stanzas. "The Nylon Tent" is a sonnet, etc.

Sub-themes

• hidden truth - "Line" mentions something that other poems hint at - that what you see is only an approximation. A mathematical line has no width so you can't see it. In "Origami", the paper has a "latent third dimension: that it contains a dragonfly, or a boat". A "Point" is "Pure place, no space for even a single angel".
• machines - In "Message", the windmill concept might puzzle aliens - after all, a windmill built to the design and size of the Siberian drawing would fail. But the geometry message would get through. I wonder if "Friend, our machines might not work for you" is anything to do with the "poems=machines" idea earlier?
• strangers - In both "The mousetail man" and "Praca XV de Novembro" the narrator meets a friendly male stranger. In "Stoney Littleton Long Barrow" a stranger is imagined.
• water therapy - Both in "The pool" and "The river swimmer" water is therapy.

Other reviews

• Mat Riches (For all of the shapes and patterns at play here, The Windmill Proof is ultimately a collection that dwells on memory, on recollections and the impact of time as we get older)
• Adele Ward (‘Shop Window with Rats’ ... is a stand-out poem for me in a strong collection)