Intersection-reality: where poetry meets mathematics ⇒ JoAnne Growney’s post-contribution in Poetry with mathematics blog

Intersection-reality: where poetry meets mathematics: A Reader’s annotation

Readers, today’s shared post are my homage to the poet and mathematician JoAnne Growney, remembering her excellent contribution and dedication to link up the two beautiful fields in a unified accordion. As a former professor of mathematics and a poet, this introduction speaks very little about the Pennsylvanian woman’s efforts to bridging the most abstracted beauties of human knowledge. JoAnne is now living in Washington DC since 2009 and dedicates her soul to enjoy the sublimed artfulness of both poetry and mathematics to reveal the secret meaning, “what reality does mean to the end.”

Poet like abstraction as like the artists brushed their canvas to upset the reality.

Reality is itself very tricky to define. Each of us having own definition and perception to define the real. It is indeed the effect of consciousness. Reality helps us to comprehend the detail about the real world we’re living now. Problem is that, how can we be sure that our comprehension is true, despite the relative perception of reality. What is the de facto of comprehension? How do we convey the cognition that we have capacity to narrate the reality? What is the barometer of this cognitive reality? Is it the reflector of inter-chained interaction between live-and-inert things existed in the surface? Who build the cognitive sense in our embodied mind, and from when? What is body and mind? What do we meant by this? How do we get sure about the bodied existence, -by mind, by soul, by anything atonal, which we yet not concerned?


Readers, here I just mentioned a few and the questions could be multiplied to the infinite. Each of them has its own chain-relation (and perhaps chained contradiction) to the other. The cognition of reality, comprehension, apprehension (or perception) of existence is utterly abstract rather than to be real. We yet don’t sure about the container of these abstracted words that makes the sense to us that we’re a real being and living in the real. In that case perception of reality truly depends on our perception that how can we explain it by language. Our perception of reality depends on the expansion-capacity of language as so far we could expand it.

Everything is this reality could be explained by mathematics and everything could narrate by the poet, who has great imagination and distortion power to molding the words as newish for human knowledge.

Wittgenstein once commented that, “My language is the limit of my world”. His comment reflects the paradox between seen and unseen, observable and non-observable and perhaps the beyond observable. Anything seen or unseen must have filled the first condition that it should have capacity to express the fact in language. However, what language is, it’s also the questionable matter and we yet not draw any conclusion about the reality of language.


I believe, we certainly exist and interact in the reality as an existed entity and it is happening without any verbal or written interpretation that’s we called language. On other hand, it also is true that we cannot explain (and interpret) the existed reality sans the presence of language. We really need this because the evolution of human species made us remarkably different to the other species, despite the great similarities of genetic subset to many of the other species.

We lived here greatly depended on the reasoning of everything that we think have to be reasonable for the sake of reality, but other species are not alike to us. They lived here just to depend on their instinctive logical capacities that could be necessary for them to survive. This biological distinction makes our journey to the reality even more complicated and abstract in nature. The reality-feature of human race is utterly distinctive to the reality-feature of any species in the world.

The more we analyze the reality even more we able to abstracted it and that is “knowledge”. We’re natural real being just like other but our apprehension of reality now stands far beyond the natural, because we can deliberately think-and-imagine anything observable, can draw the patterns for anything that is non-observable and perhaps relate the patterns with observable to achieve the landscape of reality.

…perception of reality truly depends on our perception that how can we explain it by language.

Our definition of reality is just the byproduct of our deliberate perception to the reality and thousands of definitions now multiply it by thousands divisions. No exterior stranger (perhaps God) helped us here to depict the reality, we depicted it just because the fact that we have bound to do this. There is no alternative for us to escape the reality that, —we have to sprouting on the new models of reality, because our cognitive capacity deserve this. Our knowledge makes us distinctive to the other and now it will never possible for us to back the Savanna or even the billion years back, when everything tangled in a super massive quantum fluctuation.

We cannot back to the past but our reality truly interlinked with the past. We’re “nobody” except comprehend the fact that what was happening in remote past and how we have evolved to the reality we seen today. The thousands comprehensive models of reality (includes the thousand division of knowledge) is invented from this reality. Poetry and Mathematics are just two of them and today’s post offer the readers a new realm where the two divisions linked themselves (despite their unique distinction) to understand the reality of life.


It’s perhaps not hear weird if I say, perception of reality is mathematical and mathematical perception is to be poetical. According to Sir Roger Penrose, we can say the reality (that we existed and observed everything exigent to understand the real) needs mathematics to explain the relation between “physical” and “mental” world. Mathematical Model is necessary to realize the life-evolved past and to infer the upcoming future. Why it’s necessary? Penrose answered it briefly in an interview where the interviewer asked him, I quoted the sequence here:

Interviewer: “Stephen Hawking says that you are a Platonist and that he is a positivist what does he mean and what is your comment?”

Penrose: “I suppose being a Platonist is irrelevant to this. I think realist is the word I would use here. It’s whether you take the view that the physical theory is supposed to describe what the real world does or what. Is there a real world or what. I find myself rather unable to understand Stephen’s view because he says he’s a positivist, which somehow means that you don’t ask what reality is…”

Interviewer: And you are just satisfied with its mathematical representation…

Penrose: Yes, you just say that mathematical theory predicts this or that and you don’t ask questions about what the theory means about reality. Is there a real world at the quantum level or am I just doing a calculation to see what it will produce. I have a lot of trouble with that because it seems to me that if reality is there at all and I have to certainly accept that then your theory should say where does reality begin. If this is not supposed to be a real thing it should give you a statement about what reality is. It has to tell you what real things do.

Interviewer: Like asking is the moon there or not?

Penrose: Yes, if it says the moon is only there in your mind, it’s no good to me the theory has to tell me that the moon is there. And the moon is there when nobody looks at it. And that is a ‘real’ problem of the moon. Same for the electron. If the electron is not real then the theory has to say what is a real thing and what is not a real thing.

It is not good enough to say that theory makes no comments on what is reality. To me reality is what we are after. We need an explanation of how reality behaves. If electrons in our present description are not to be considered real so be it. But you have to have a theory, which tells us what is real.

I think electrons are real but they don’t satisfy the same kinds of laws that we are used to (or they do, but it’s a question of time scales). You could say that the electron doesn’t have a well-defined position in a certain time scale. Actually, ‘does the electron have a position?’ is a wrong question. Standard quantum mechanics will say that if only you measure position. But that’s not very good because if you measure position then it stays dispersed and spreads out with the speed of light. Which is not what electrons normally do. So it is not a good thing to try to assign it a position.

And that’s not what you do. You assign it a wave function as part of a larger construct. But these descriptions, to my mind are still not adequate yet. Because you need to have a description in which the small-scale things do tie in with the large-scale things. At the moment you have a dichotomy, you have the quantum physics of the small and the classical physics of the large. They don’t fit together properly. When I say small I should be careful here I don’t mean small distances because quantum effects are known to stretch over hundreds of kilometers. That’s a large distance. But the amount of mass displacement is still very, very small. So the question is small in the sense of how much displacement of mass is involved.

And if that gets big then you start to have classical situation. But you need a theory, which explains the join between these two worlds. At the moment we have two worlds that do not join very well.”

Source: Impossibilities in the real world have to be possible Times of India, 2011

I know the genius of mathematics-and-quantum field is hugely criticized today by the majority of scientist for his “Orch-OR” (Orchestrated Object reduction) theory and platonic whim to describe the “what reality is, what it was before (object reduction scenarios in quantum level fluctuation, before or after moment of big bang) and what it looks alike in our conscious mind-reality.” I’m not an expert of the field, so commenting about Penrose works is not my issue at all. I quoted him to clarify the fact that, reality needs evidence based proof, but proof means the presence of observer who can observe the proof.

No exterior stranger (perhaps God) helped us here to depict the reality…

So, the theory of existential reality (how it begun, what it limits and be the destiny) could never be completed all these at the same time. Any theory whole like the Curt Gödel’s Incomplete Theorem (just for example: when you say “anything is false” you say wrong, because when you able to prove that it is false means yonder false able to touch the true ground that it’s false and if it’s not false, that means your claim is true).


Our deliberate thoughts and imagination about reality (and so far many relevant subjects) is incomplete and in that sense, they greatly depended on the metaphysical inference, apprehension and assumption. The mathematical model perhaps only the way where we can depict utmost a fine-tuned picture of everything about the reality, as Penrose said in his book:

“…everything in the physical universe is indeed governed in completely precise detail by mathematical principles… Yet, I can well imagine that a good many readers will still have difficulty in accepting that all actions in the universe could be entirely subject to mathematical laws. Likewise, much might object to two other prejudices of mine that are implicit in Fig. 1.3 (his platonic mathematical model of reality). They might feel, for example, that I am taking too hard-boiled a scientific attitude by drawing my diagram in a way that implies that all of mentality has its roots in physicality. This is indeed a prejudice, for while it is true that we have no reasonable scientific evidence for the existence of ‘minds’ that do not have a physical basis, we cannot be completely sure. Moreover, many of a religious persuasion would argue strongly for the possibility of physically independent minds and might appeal to what they regard as powerful evidence of a different kind from that which is revealed by ordinary science.” (Source: The Road to Reality, page 19, 2004)

The necessity of mathematics needed here to depict a pragmatic logical picture that was maybe more metaphysical in poetics and philosophy, but it doesn’t mean or ensure that the poet’s (and philosophers) imagination about reality is false and mathematical model is utterly true. We could say mathematical model sound better to reasoning the reality indeed. This is the “intersection” between poetry and mathematics, which JoAnne Growney mentioned in her blog-site‘s refrain:

“Mathematical language can heighten the imagery of a poem; mathematical structure can deepen its effect.”

This “intersection” of two different subjects, we can see everywhere if we wish to see this. Poets depends on their power of imagination where they desperately try to change the every description of reality by using their intuitive logical capacities. Poetry is that science where familiar words and meaning replaced, transferred and distorted by the new appearance, and that’s the model of poetical wisdom. 

intersection-reality_6_2_2Poets like abstraction as like the artists brushed their canvas to upset the reality. Because, our sense (and comprehension) of the reality is more “inference” based than the “criterion”. What does a mathematician do? He does the same destruction of manipulate the reality by following the previous models and represents new “inference” for the audience, because, reality is incomplete than the “criterion”. When anybody realizes the intersection-relation, his thought-pattern then able to invent the fractals, where poetry intersect mathematics and mathematics be the poetry too.

How do we get sure about the bodied existence, -by mind, by soul, by anything atonal, which we yet not concerned?

Everything is this reality could be explained by mathematics and everything could narrate by the poet, who has great imagination and distortion power to molding the words as newish for human knowledge. JoAnne Growney nicely adapted her “Self” to the both intersections, where poetry and mathematics embrace to lead our “Self” to the reality.

Brief notes: Readers, I choose five poems from the very well-constructed collection of lot other and I reblogged the poetry according her mentioned condition (just put down the introduction section to the bottom of each poetry by adding the title: “JoAnne Growneys prologuein her blog as well. I hope she will never mind for this. 


Brief Reflections on Logic by Miroslav Holub
Translated by Stuart Friebert and Dana Habova

The big problem is everything has
its own logic. Everything you can
think of, whatever falls on your head.
Somebody will always add the logic.
In your head or on it.

Even a cylinder makes sense, at least
in that it’s not a cube. Even a cleft
makes sense, maybe just because
it’s not a big mountain.

A special logic must be assigned to cylinders
that pretend to be cubes. And clefts
that think they’re big mountains.
The logic of these things is in fact that
they strip other things of their meaning.
This reflection isn’t abstract.

It’s in view
of recent history.

JoAnne Growney‘s prologue: Reflections on Logic…
Miroslav Holub (1923-1998), Czech poet and immunologist who excelled in both endeavors, is one of my favorite poets. He combines scientific exactitude with empathy and absurdity. Here is a sample:

This poem and several others by Holub appear in Numbers and Faces: A Collection of Poems with Mathematical Imagery, a group of poems that I gathered and edited for the Humanistic Mathematics Network in 2001. This small anthology is out of print but is available online here.

Originally Posted by JoAnne Growney at 6:45 AM on: poetry with mathematics


Found poetry: words of Dirac

If you are
and humble,

will lead you
by the hand.

In science one tries to tell people,
in such a way as to be understood
                                           by everyone,
something that no one ever knew
before. But in the case of poetry,
                        it’s the exact opposite!

Does Dirac mean (above) that poets
speak of things everyone knows
in language understood by no one?

I think it’s a peculiarity of myself
that I like to play about with equations,
just looking for beautiful mathematical relations
which maybe don’t have any physical meaning at all.
Sometimes they do.

JoAnne Growney‘s prologue: Found poetry: words of Dirac:
The epigraph for Richard Bready’s “Times of Sand” (a stanza of which I posted a few days ago on 21 February) is a quote from British physicist Paul Dirac (1902-1984, founder of quantum theory). This quote reminded me how often we find poetry within well-written prose — and I have gone to WikiQuotes and found more poetic words from Dirac:

Dirac‘s words express thoughtfully the viewpoints of many 20th century mathematicians and scientists.. For more quotable lines from and about him, follow this link.

Originally Posted by JoAnne Growney at 10:21 PM on: poetry with mathematics


After Leviticus by Philip Levine

The seventeen metal huts across the way
from the great factory house seventeen
separate families. Because the slag heaps
burn all day and all night it’s never dark,
so as you pick your way home at 2 A.M.
on a Saturday morning near the end
of a long winter you don’t need to step
in the black mud even though you’re not sober.
You’re not drunk either. You’re actually filled
with the same joy that comes to a great artist
who’s just completed a seminal work,
though the work you’ve completed is “serf work”
(to use your words), a solid week’s worth of it
in the chassis assembly plant number seven.
Even before you washed up and changed your shirt
Maryk invited you for a drink. You sat in the back,
Maryk and his black pal Williams in the front,
as the bottle of Seven Crown passed slowly
from hand to hand, eleven slow circuits
until it was empty and Maryk opened
the driver’s side door and placed the dead soldier
carefully bottom-side down on the tarmac
of the parking lot and then drove you home
or as close to home as he could get
without getting his sedan stuck in the ruts.
Neither Maryk nor Williams had made a pass,
neither told a dirty joke or talked dirty.
The two, being serious drinkers, said
almost nothing though both smoked and both sighed
frequently, perhaps from weariness,
from a sense of defeat neither understands,
or more likely because their lungs are going
from bad air and cigarettes. You’re nearly home
to number seven, where a single light burns
to welcome you back with your pay envelope
tucked in your shirt pocket, the blue, unironed
denim shirt your oldest, Walter, outgrew
eleven years ago. Bernadette Strempek,
let me enter your story now as you stand
motionless in the shadowy black burning
inhaling the first warm breeze that tells you
this endless winter is ending. Don’t go in
just yet; instead gaze upwards toward the stars.
Those tiny diamonds, though almost undone,
have been watching over your house and your kids
while you’ve been away. Take another breath,
a deeper one and hold the air until you can’t.
Do you taste it? You shake your head. It’s God’s
breath, a magical gift carried
all the dark way from Him to you on the wind
no one can see. Seventeen separate huts
hunkered down and soberly waiting, this night
three of you in a ’47 Plymouth four-door
drinking Seven Crown for eleven circuits
until the work was done, one woman alone
beneath the blind sky, standing patiently
before number seven Mud Lane taking
into her blood one gasp after another
of the holy air: the numbers say it all.

JoAnne Growney‘s prologue: The numbers say it all…
The title of my posting today, “The numbers say it all” comes from the final line of “After Leviticus,” by Detroit poet Philip Levine. Levine (1928-2015) died this past Saturday. Often termed “a working class poet,” this fine writer won many awards for his work.“

After Leviticus” is on my shelf in The Mercy, (Knopf, 2000). Another poem by Levine, “M. Degas Teaches Art & Science At Durfee Intermediate School” Detroit, 1942, appears in my blog posting for October 11, 2011.

Originally Posted by JoAnne Growney at 8:11 PM on: poetry with mathematics


Departures in May by Sarah Glaz

Big things crush, inside the brain,
like plaster of Paris on stone;
a taste of splintered metal;
terra-cotta hardness of heart’s desire.
Statues motionless
at railroad depots,
proclaim imitation as life.
A white bird flies low above platforms,
sweeps above train cars;
The Orient Express of boundless motion–
preserved lanterns,
boundless upholstery,
carriages of red absorbency,
soundlessly waiting for late chances.
I had been to Paris-Roma-Venezia,
felt the grid of time
curve in space, fluid,
twined arcs convergent at infinity,
defying Euclid.
Suspended on pale May sky,
puffed-up clouds–
grave formulas,
ominous signs,
white droppings of the aged snow bird,
death white.

JoAnne Growney‘s prologue: Twined Arcs, Defying Euclid
The English language has adopted into current usage many terms from other languages. French terms like coup de grace and haut monde have for many years been found in English dictionaries. Recently, computer terms such as bite and captcha and google have achieved widespread use. In addition, those of us who are fluent in the language of mathematics find that its terms sometimes offer a concise best way to describe a non-mathematical phenomenon.

Mathematician-poet Sarah Glaz weaves mathematical terms into her poem, “Departures in May” — a poem that uses the language of geometry to vivify the presence of loss, death and other dark forces.

This poem first appeared in Ibis Review, 1995. Poet Sarah Glaz is a mathematics professor at the University of Connecticut and her webpage provides (scroll down) a wealth of links to poetry-math resources. News of Glaz’s activity and her poems have appeared often in this blog; enter her name into the SEARCH box at the top of the right-hand column of this blog to find these various items.

Originally Posted by JoAnne Growney at 1:31 PM on: poetry with mathematics


The Progression by Omar Pérez
translated by Kristin Dykstra

When one isn’t enough, you need two
when two aren’t enough, you need four
with four the progression begins, moving toward a number
that schoolteachers will call absurd.
Question: How many men do you need
to put up a house?
Answer: You need absurd men
when one isn’t enough and two can’t do
the work of One.
And how much money should we give these men
to compensate them?
You need absurd coins when one coin
sliced in half and handed out
isn’t enough.
And how many words do you need to
transform them?
Absurd and absurd and absurd words
when silence isn’t enough.
This is what they call progression:
Absurd men aren’t enough for putting up the house,
absurd coins don’t make them happy
absurd words can’t dissuade them.

A bit more poetry of Cuba can be found here at the PoetryInternationalWeb.

JoAnne Growney‘s prologue: When one isn’t enough … words from a Cuban poet
Last week I traveled (as part of an organized people-to-people program) to Cuba. I will need many days to sort and digest and organize the details of that experience.

Neither poetry nor mathematics was part of our Cuba schedule but I did have a chance to visit the sparse collection at La Moderna Poesia in Havana and to purchase their only two bilingual poetry collections (by poets José Martí and Nicolás Guillén). The PoetryFoundation website has introduced me to the work of Cuban poet Omar Pérez (son of Ernesto “Che” Guevara) and I found there, at this link, Pérez’s poem “The Progression” — which includes some mathematical ideas.

Originally Posted by JoAnne Growney at 2.44 PM on: poetry with mathematics

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Reality is itself very tricky to define