`review of `

`Joel Chace's "Maths" `

2190. "review of Joel Chace's "Maths""

- the complete version of my review

- credited to: tENTATIVELY, a cONVENIENCE

- published on my "Critic" website September 28, 2023

- http://idioideo.pleintekst.nl/CriticChace.html

review of

`Joel Chace's "Maths"
`

`by tENTATIVELY, a cONVENIENCE - September
26 - 28, 2023`

`For the complete review go here: `http://idioideo.pleintekst.nl/CriticChace.html

https://www.goodreads.com/review/show/5873904871

https://www.goodreads.com/book/show/181865410-maths

I rc'vd an email ad for this bk. I replied that I wasn't sure why the bk was being advertised to me but that if a copy were to be sent to me that I wd review it. I also informed the sender that it might take me a long while b/c I have stacks of bks in the high-priority-to-review category, bks either relevant to an immediate interest of mine &/or bks written &/or published by friends. Since this bk turned out to be small I got to it faster than I expected.

There're 3 capsule reviews of "**Maths**"
on its back cover. They're by Nico Vassilakis, whose Visual Poetry I've
seen; Rachel Blau DuPlessis, whose name I've at least encountered; &
Kit Robinson, who I've known of & probably read poetry by. All reviews
are very positive. In the past I've pointed out that on Goodreads poets
tend to give bks by their friends 5 star ratings w/o ever writing anything
to substantiate this praise. This, to me, is an indication that in what
I call "Poetry World" people are careful to take no chances of
receiving a 'revenge review' for their own work. In other words, everyone
praises everyone else in expectation of being similarly praised. There
are, of course, exceptions for poets who dare to be outlaws, writers outside
of a safe community. SO, I wondered: Are Vassilakis, DuPlessis, & Robinson
published by the same press that published "**Maths**", Chax,
& is that part of the reason why they were chosen to be reviewers?

Vassilakis?: YES: His "DIESEL HAND" is published by Chax.

DuPlessis?: YES: Her "Selected Poems 1980-2020" is published by Chax.

Robinson?: YES: His "Leaves of Class" is published by Chax.

I was hoping I'd like "**Maths**" to write
an enthusiastic review. But, really, what wd I write that wd better this
back-cover blurb by Robinson?:

"The title poem of Joel Chace's *Maths* calls
to mind such adventures in concrete poetry as Apollinaire's *Calligrammes*,
the typographical works of the Dadaists and Russian futurists, the 60s cut-ups
of English poet Bob Cobbing, and the contemporary Vispo of Nico Vassilakis.
In an explanatory note, Chace says he is interested in potential connections
between the languages of mathematics and physics and that of poetry. In
*Maths*, he seems to have found a common ground in the aesthetic dimension:
the reader is challenged to combine reading with looking. Propositions,
lyrics, and formulae are decoupled from their sources and permitted to float
free on the page, where they swim like giant sea creatures or stretch and
twirl like dancers on an open stage. The uncertainty provoked by open-ended
lines and fragments shorn of context is this relieved as one visually surfs
the angular typographic topologies and hand-jotted equations within the
margins of each page. The result is as satisfying as a walk in a park,
"replete with approximations." Through these poems, conceived
"to unite highly speculative abstraction and the concrete richness
of phsyical phenomena," one feels the world in all its dynamism: "No
ideas except / in events, often mistakenly called / things."

Whew! Robinson must *really love Chace's writing*.
He waxes *ssssooooooo* poetic! But did he actually read the bk?
I find that to some reviewers, including one poet of my acquaintance, reading
the bk isn't necessary. Instead, just letting loose w/ some eloquent praise
is enuf. 1st, his comparisons seem to be really stretching the truth to
me. Bob Cobbing's cut-ups annihilated syntax, Chace does nothing of the
sort. The dadaists & futurists used a large variety of typefaces &
dramatic composition as an integral part of their poetry, Chace doesn't.
The work that I see by Vassilakis in "**Anthology Spidertangle**"
is much closer to Cobbing formally than to Chace. The more Vispo type works
of Apollinaire's that I've read have calculated layouts that differ from
poem to poem. The 1st section of Chace's bk, the only section to have a
slight Vispo element, uses the same aesthetic approach in every poem.

I, at any rate, read "**Maths**" in its entirety
& will actually write about what I read instead of writing I-scratch-your-back-you-scratch-mine
salesperson hyperbole. It begins w/ Chace's "Building *Maths*:
a Preface" from wch I quote:

"I have become increasingly intrigued by the languages of advanced, creative mathematics and of physics. In previous years, certain of my poems have briefly referenced potential connections between these languages and that of poetry."

[..]

"The method I settled upon is to begin each page with a poetic text"

[..]

"I then add to this be interfacing it with complementary mathematical commentary"

- - iv

I'm fine w/ that, in fact it interests me. Mathematics & poetry are both abstruse to non-mathematicians & non-poets. The difference, for me, is that mathematics usually attempts to describe things w/ an accuracy that can lead to practical applications while poetry is sometimes claimed to do something similar w/o coming thru on the practical application end of things. As such, I tend to think of mathematics as being abstruse language for non-bullshitters & poetry as abstruse language for bullshitters.

The 1st 40 poems constitute the "Maths" section. Each page is one poem, or one part of a 40pp poem, & each is structured basically the same way: There's the main text, the easiest thing to read, apparently what the author terms the "poetic text" in his preface. This is surrounded & interlaced w/ lines of text cut-out & placed in a less straight-forward manner, sometimes w/ parts of words cut off, making fragments. Despite this, the text is also fairly straight-forward & can be read in a linear way. Finally, there's the mathematical notation. I'm interested in math & have written a bk inspired by reading math bks for the lay-reader but I don't understand the majority of the notation. If I DID understand it perhaps the whole poem wd coalesce for me into a transcendental experience. Hence, I accept the possible responsibility that my overall lack of full appreciation for these poems is at least possibly caused by my ignorance.

Instead, my reviewer's note to self about the 1st poem is: "maths - fuzzy resolution - jumbles", wch tells you next-to-nothing. What it tells me is that it looks like what something looks like when it's enlarged w/ inadequate original resolution, it's fuzzy. One might think from that that the poem is large type but, no, it's small. In fact, the entire "maths" section is small enuf to make it a challenge for even good eyesight. I'm 70 & my eyesight's still good enuf to not require glasses - but when font sizes get down to 9 point or lower it's harder for me to read w/o putting more light on it than I'd need if it were what is to me a more reasonable font size of 12 point or above. The decision to make these poems so small was presumably made by the press to save money. Perhaps the original poems were written in 8&1/2 X 11" confines. They're now reduced to broad-margined 5&1/2 X 7&1/4".

"Maths 2" describes a train passing by 2 small watching boys. The engineer throws them some candy. This appears to be something he's done before. Shortly thereafter, the train derails & people die. This 1st part of the poem ends w/ "Every horrifying word-problem, each one with a train in it." Now, that interest me, what does he mean by that? Is he reading a series of word problems or is he making some sort of philosophical statement about writing? The fragments of text laid out around this central text include: "derailments in this study", "mathematical prediction model", "Bayesian Model (HBM)", & ends w/ "Broken symettries are necessar".

"**Bayesian hierarchical modelling** is a statistical
model written in multiple levels (hierarchical form) that estimates the
parameters of the posterior distribution using the Bayesian method."

[..]

"The assumed occurrence of a real-world event will typically modify preferences between certain options. This is done by modifying the degrees of belief attached, by an individual, to the events defining the options.

"Suppose in a study of the effectiveness of cardiac treatments, with the patients in hospital j having survival probability ?j, the survival probability will be updated with the occurrence of y, the event in which a controversial serum is created which, as believed by some, increases survival in cardiac patients."

- https://en.wikipedia.org/wiki/Bayesian_hierarchical_modeling

If, then, the abbreviation for Bayesian hierarchical modeling is HBM does that mean that the term originates in a language where adjectives & nouns are in different positions than they are in English? Has Chace made a mistake? Is it really BHM?

None of the equations presented in Chace's poem match the equations presented in the Wikipedia entry. That doesn't necessarily tell me anything, his equations might be specific to the derailment statistics. One of his equations begins w/ the word "Risk" followed by an "=". I did a search online for "risk equations" & got this brief definition: "Risk = Likelihood ? Impact". I then did a search for "Bayesian hierarchical modeling risk equations for train derailments" wch yielded some scholarly papers. One of them is called:

"Rail Accident Analysis using Large-Scale Investigations of Train Derailments on Switches and Crossings : Comparing the Performances of A Novel Stochastic Mathematical Prediction and Various Assumptions"

& is by: "SERDAR DINDAR, Sakdirat Kaewunruen, Min An" & has this abstract:

"Each day tens of turnout-related derailment occur across the world. Not only is the prediction of them quite complex and difficult, but this also requires a comprehensive range of applications, and managing a well-designed geographic information system. With the advent of Geographic Information Systems (GIS), and computers-aided solutions, the last two decades have witnessed considerable advances in the field of derailment prediction. Mathematical models with many assumptions and simulations based on fixed algorithms were also introduced to estimate derailment rates. While the former requires a costly investment of time and energy to try and find the most fitting mathematical solution, the latter is sometimes a high hurdle for analysists since the availability and accessibility of geospatial data are limited, in general. As train safety and risk analysis rely on accurate assessment of derailment likelihood, a guide for transportation research is needed to show how each technique can approximate the number of observed derailments. In this study, a new stochastic mathematical prediction model has been established on the basis of a hierarchical Bayesian model (HBM), which can better address unique exposure indicators in segmented large-scale regions. Integration of multiple specialized packages, namely, MATLAB for image processing, R for statistical analysis, and ArcGIS for displaying and manipulating geospatial data, are adopted to unleash complex solutions that will practically benefit the rail industry and transportation researchers."

- https://salford-repository.worktribe.com/preview/1489586/Paper%20-revised.pdf

Note that it uses the abbreviation "(HBM)" thusly increasing my data set that Chace's usage is standard. None of the equations shown resemble Chace's. Given that I can't read the equations & don't even know how to write them on my computer my ignorance is definitely a big hurdle here. If I cd understand the equations I might be able to see how they develop the 1st 2 parts of the poem. That sd, my trying to understand it has at least given me a superficial awareness of HBM, wch I wasn't previously familiar w/.

In my understanding of the terms "Concrete Poetry" & Visual Poetry" (henceforth "Vispo") these poems are neither b/c if they were Concrete Poetry the form of the way the elements are presented wd add to the overall meaning. I find that these don't do that. If it were Vispo, all elements might be used more for their visual impact than for their semantics. Again, I don't find that these do that. Instead, they use 3 different types of language, somewhat haphazardly arranged. I think that's interesting in & of itself. I suspect, tho, that I'd prefer a more explicative presentation - i.e. one in wch the differences between the 3 modes were commented on in order to explain the significance of their differences.

"Maths 4" has this as its kernel:

"They called it an accident. Between the two

poles, as usual, the strung the thin rope, tightening it

around high wooden knobs. Then came the fabric,

dyed crimson, gold, cerulean. They began to hook and

spread it across the tautness. But something caught. A

tug. Another. A wrench, and the worn cloth rents, its entire

width. Beasts that his in the hills rushed among them, to gnash,

tear - not flesh, but the ruined banner - and then

speed away, leaving a ground strewn with tatters,

strips, which are gathered, bundled, tied, and laid away."

I find that very interesting. It evokes for me beasts performing a cloth ripping service of sorts that humans then take advantage of somehow. The 2nd level of meaning, provided by the diagonally placed strips from another text, ends w/:

"mathematical concept capable of serving as a threshold between modern and contemporary mathematics, it is that of the mathematical sheaf, which is indispensible for reintegrating adequate local compatibilities into a global gluing."

So, I ask the internet: "What is a mathematical sheaf?":

"In mathematics, a **sheaf** (pl: **sheaves**)
is a tool for systematically tracking data (such as sets, abelian groups,
rings) attached to the open sets of a topological space and defined locally
with regard to them." - https://en.wikipedia.org/wiki/Sheaf_(mathematics)

Again, I find that interesting. The 1st part of the poem ends w/ "tatters, strips, which are gathered, bundled, tied, and laid away" suggestive of the way "sheaves" are used in agriculture to refer to plants bundled together. Then Chace moves on to the mathematical use of "sheaves". From there, there's only one small equation that begins w/ "r =". Perhaps the "r" stands for "radius", perhaps the radius is arrived at in a sheaf meeting specific conditions. Is this pure or applied? It seems likely to me to be applied. I don't know Chace's mathematical background, perhaps he's a math student, perhaps he has a job where certain practical things are to be arrived at w/ statistical analysis.

"Maths 5" has an equation that I can at least write out in a text program w/o needing more esoteric symbols: "y=xt+ax+bx2". Alas, when I do a search for that, the superscript is lost & the meaning changes. SO, I try "y = x(superscript t) + ax + bx(superscript 2)". This at least leads to "A superscript T denotes the matrix transpose operation; for example, AT denotes the transpose of A." ( https://atmos.washington.edu/~dennis/MatrixCalculus.pdf ) THEN, I wonder about "transpose" in math:

"In math, to *transpose* is to move something
from one side of an equation to another. In the equation x + 3 = 2y, you
can solve for x by transposing the 3 to the other side of the equation,
which will change its sign and give you x = 2y - 3." - https://www.vocabulary.com/dictionary/transpose#:~:text=In%20math%2C%20to%20transpose%20is,the%20order%20or%20arrangement%20of

Again, my ignorance interferes. If y=xt+ax+bx2 can be stated in 'natural' language as "y = x transposed + a times x + b times x squared" what's the point of having "xt" presented this way instead of just transposing it? In other words as "y-x=ax+bx2". The poem kernel starts w/ "Not hearing the joke even while listening to it." That's apparently what I'm doing here.

In "Maths 6" the 2nd level text begins w/:

"In fact, hat comes to light in these readimgs is that the questionsconcerning an absolute 'what' or 'where' - whose answers would supposedly describe or situate mathematical objects once and for all (whether in a world of 'ideas' or in a 'real' physical world, for example) - are poorly posed questions."

Then what I've been calling the poetry kernel ends w/:

"*Now, ask the right *

*question.*

So. Of the two

remaining methods, will

b) work, asshole?"

This not only expresses the importance of asking the right questions but also appears to express the author's exasperation w/ a professor whose style of teaching feels sadistic.

"Maths 10" contains an equation that's initially straight-forward for me but then I get loss in my not understanding:

"1/3=.33333->/=.9999"

Yeah, I don't get it. "1/3=.33333" is common enuf, albeit problematic. It seems simple enuf that "1/3", the expression of one third as a fraction, "=.33333", the expression of one third in decimal notation. But then that brings up the problem of 3 X 1/3 = 3/3 = 1 whereas 3 X .3333 = .9999 1. Therefore, 1/3.33333 . It's possible that what I read as a slash, "/" in Chace's handwriting is meant to be a one, "1". If that's the case then I understand the equation to read as 'one third equals .3333 implies that 1 equals .9999'. A problem in the inadequacies of decimal notation. For most practical purposes, .9999 probably can be substituted for 1 until the problems reach a larger scale. If one used .9999 in a calculation instead of one for adding together, say, 1,000 inches w/ each being .9999 instead of 1 then there wd be an error of < 1,000 inches. Then again, .9999 is implied to go infinitely, in wch case the error wd be infinitesimal. So when do we decide that it makes a practical difference? Wd we still get away w/ substituting .9888?

"Maths 12" has this equation:

"(256/243)2=1.110"

Is that so? According to my computer's calculator: 156 divided by 243 = 1.053497942386831 . This squared is then 1.10985791461 . Chace has, then, rounded off 1.1098 to 1.110 . Fair enuf.. but why? & what does it mean in relation to the rest of the poem? The poem's kernel begins w/: "Milton's cartoon cosmology drops chaos into place." - in other words, John Milton (author of "Paradise Lost" & "Paradise Regained") makes heavenly & hellish geography somewhat specific. The kernel ends w/:

"And his math as such: Evil's Army one-third the angels in Heaven; Army of Good two-thirds the angels in Heaven; number of angels in Heaven, infinite."

I'm in the midst of reading "Paradise Lost" so I find that funny. What's one third of infinity? According to most, it wd still be infinity - in wch case there wd be the same amt of devils as there are of angels - regardless of this 1/3rd vs 2/3rds business. Then again, it gets more complicated once one starts getting into the notion of different sized infinities. & how does dropping "chaos into place" tie into rounding off?

"Maths 16":

"With her parents, she, at three (years and

p.m.) enters that living room she's never

seen before, The older couple rise

from chaies to greet unexpected guests. As

the grown four freeze, she snatches a woodsman

Hummel - red, brown, tall, invaluable - then

smashes it down against the hearthstone. The odds?"

That kernel has to its upper left an equation signifying 'df is isomorphic to 2.5'. This might further be interpreted as 'the degree of freedom is isomporphic to 2.5'. This presumably ties into statstics & probability.

"**Degrees of freedom**, often represented by v
or df, is the number of independent pieces of information used to calculate
a statistic. It's calculated as the sample size minus the number of restrictions."
- https://www.scribbr.com/statistics/degrees-of-freedom/#:~:text=Revised%20on%20June%2022%2C%202023,minus%20the%20number%20of%20restrictions.

More & more, this math of Chace's comes across, to me, as problems presented to him in a class. Still, the choice of a Hummel figurine in the kernel is suspect as a humorous jab at kitsch by the author rather than an academic problem presenter. The mid-level content has this bit:

"the stochastic process becomes a set of measurable functions on which a probability measure is defined"

The child becomes a sort of natural force whose presumed lack of knowledge about &/or respect for the economic value of an artwork, kitsch or not, is potentially calculable stochastically.

"Maths 18" cd be sd to end w/ a fragment of Fermat's Enigma:

"an + bn = cn

[no solution in posit

integers if

n - "

Or is it? It's certainly similar but its presentation as a fragment makes it ambiguous. It cd be completed as something like "[no solution in positive integers if n - a = b] Here's Fermat's Enigma aka Fermat's Last Theorem:

"In number theory, **Fermat's Last Theorem** (sometimes
called **Fermat's conjecture**, especially in older texts) states that
no three positive integers *a*, *b*, and *c* satisfy the
equation *an* + *bn* = e*n* for any integer value of *n*
greater than 2. The cases *n* = 1 and *n* = 2 have been known
since antiquity to have infinitely many solutions." - https://en.wikipedia.org/wiki/Fermat%27s_Last_Theorem

The bottom math notation in "Maths 21" seems to be Grassman Numbers in Matrix Notation, in this case a 5 X 4 matrix. Or maybe not? I'll try to quote it below w/o having the correct graphic tools:

_a b c d e_

1 | 1 -1 0 0 0 |

2 | -1 0 1 -1 0 |

3 | 0 1 -1 0 -1 |

4 |_0 0 0 1 1_|

The vertical straight lines & the underscore lines are meant to represent a large set of brackets enclosing the zeroes & ones, the columns are desired to be evenly spaced. I don't know what kind of mess that'll be when it makes it online but I imagine that what little neatness I've accomplished will be destroyed. The kernel poem is about a ritual signifying closeness between lovers. How the math relates to this I won't speculate.

"Maths 23" may express something similar to how I react to this bk:

"Barely cracking the text; not

attending a single class. Exam

eve: skimming pages. Next morning

everything falls into place, each

beautiful number and function.

The prof comments, *I make little *

*sense of your shown work; however*"

- wch isn't to say that I barely cracked the text, etc. I read the bk carefully, looking for what I cd find in it that wd spark the most response in me. It didn't exactly fall into place but I still managed find some "little sense" in it.

"Maths 25" has 2 equations in it that I note to myself that I shd "solve". Ha ha! Fat chance. The 1st reads as 'de to the x power divided by dx equals e to the x power'.

"Differentiation of e to the power x is a process of determining the derivative of e to the power x with respect to x which is mathematically written as d(ex)/dx. An exponential function is of the form f(x) = ax, where 'a' is a real number and x is a variable. e to the power x is an exponential function with base (a) equal to the Euler's number 'e' and the differentiation of e to the power x is equal to e to the power x, that is, itself. It is written as d(ex)/dx = ex." - https://www.cuemath.com/calculus/differentiation-of-e-to-the-power-x/

The 2nd reads as: 'e to the power of i times Pi + 1 = 0'. That's Euler's famous elegant equation. I have a variation of it on my knuckles that reads "e to the power of i times Pi + 1 to the power of infinity is approximately equal to 0". That's what I call my "Paradigm Shift Knuckle Sandwich". Neither of these make any sense to me whatsoever in relation to the kernel poem. Still, Chace might be making a pun b/c the kernel makes reference to a "root cellar" so perhaps there's a double meaning that refers to mathematical roots as well as physical ones.

The 'mid-level' section of "Maths 28" reads as follows:

"The situation of an object cannot be anything but relative,

with respect to a certain realm (geography) and

moment of that realm's evolution (history)."

The overlaps & covered-over words make the next section of this a bit hard to decipher. Here's my try:

"Discovering and s"[ort]"ing out - that

these things that we are in the midst of

reticent structure towards which we

try to grope" [a] "way" [in] "a

perhaps still-babbling language

"in this search for a continuous articulation included dialectical

balance, diagrammatic cuts, screwdrivers, torsions

and articulating incisions of the successive and the lateral"

In "Maths 33" there's a novel twist on heaven:

"On a visit to paradise, he

saw the body-parts room.

After he met the angels, the first human he saw

was his high school girlfriend, decapitated in

an accident. There she was, without her

head. He recognized her right away."

The 1st of the "Physics" poems starts on page 43. Despite the "Maths" section being more original, I can relate to the "Physics" section more easily. Here's the 1st of those in its entirety:

"On Not Taking Physics

"I never took a course in physics, at any level. I retain few memories of high school chemistry; there was, hoever, one curious incident. My friend Tim and I stood at our assigned lab station, where a test tube was heating over a Bunsen burner. We noticed our teacher strolling over from his desk at the front of the room. Thin and tall, Mr. Dries never said or did anything in haste. He stopped beside us and bent at the waist to bring his eyes level with the orange flame. For maybe three seconds he stared and then, in a blur, grabbed the test tube by its lip and dashed it to smithereens against the cinderblock wall behind the lab table. In a moment or two, he phased back into focus, back into his languid body pace, and slid over to the next pair of students, without uttering a single word. That was my introduction to scientific uncertainty.

"Thank you, Albert Einstein, Anaximander, Carlo Rovelli, Chaucer, Democritus, Erica Segre, Giulio Galetto, Hofmannstahl, Horace, Jerome Kern, John Milton, Ludwif Boltzmann, Maimonides, Nelso Goodman, Oscar Hammerstein II, Plato, Richard Strausse, and Simon Carnell."

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