2017. Paradigm Shift Knuckle Sandwich & other examples of P.N.T (Perverse Number Theory)

The above-mentioned magazine that I was hoping would print a small part of this book in was the late lamented RAMPIKE. Here're the pages I submitted:

When I 1st wrote the book & had an electronic copy of it I listed it online on Goodreads as one of my books & provided this description/review/promotion:


2008.02.01 Paradigm Shift review


Given that this is my bk, this is more of a promotional statement than a review.

The 1st paragraph reads:

"When I was a child, I was a very good mathematician. I was also good at drawing. I remember thinking, when I was 9 yrs old, something to the effect that a mathematician's life was probably too socially isolated & not much fun & I decided that, therefore, it might be better for me to be an artist."

40 yrs passed & while I still played w/ the math that most interested me, such as set theory & imaginary numbers, my math skills largely waned. Then, in 2003, at age 49, I decided to read Simon Singh's bk "Fermat's Enigma" as an experiment in determining what was left of my ability to understand math. That lead to reading more math bks aimed at lay readers.

5 yrs later I thought I might as well try to WRITE a math bk - as an experiment to see if I cd actually do it. I envisioned it as around 160pp. 6 wks later, it was done - 408pp! I was very, very pleased. In some sense, this bk became my most articulated philosophical statement.

The next step was to send out the ms to 2 friends, poet/scholar Bruce Stater & musician/conceptualist 'Charles Boyd' (aka John Berndt), for them to add MARGINALIA to it. It was a part of my design plan to have the marginalia be referred to in the original text & for the 'marginalia' to be printed in the original bk - thusly possibly making this one of the 1st & only bks to be so designed.

The basic idea of the bk is that certain concepts create PARADIGM SHIFTS - thusly getting away from (somewhat) the notion that only technology (such as the printing press & the telescope) produce paradigm shifts. Various turning point mathematical concepts are then explored as examples of this.

The cover of the bk shows a knuckle tattoo that I have that consists of the following variation on a famous equation of Leonard Euler's (expressed here in so-called 'natural language'):

e to the power of pi times i + one to the power of infinity is approximately equal to zero.

"e" & "pi" are both transcendental numbers that serve as constants.

"i" is the symbol for "imaginary numbers" generally represented as the square root of negative one.

The whole shebang is meant to be representative of multiple paradigm shift concepts culminating in an indeterminate form. A "knuckle sandwich" is a punch. I like to think of this knuckle tattoo as a symbol for the punches to worldviews that concepts like "infinity" have brought w/ them.


In the fall of 2008 I gave a reading from it at the Bowery Poetry Club in New York City:


The relevant section starts at 32:15.


The years passed & I finally self-published it in the beginning of 2017. My favorite bookstore bought 2 copies. All the other bookstores would only take it on consignment (or not at all). I'll never get paid for those even if they sell.


Here's the link for Amazon in the US:


Here it is on Barnes & Noble:


Here's a link for Amazon in the UK:


Here's one for sale in Australia on e-Bay:


Here's another bookseller in the US:


Here's one in India!:


It's also available in Rotterdam:


Some of those links might not be any good anymore. I know it's available in South Africa & at Target & Sears. Really.

On March 8, 2017 I gave a short reading from it at Té Café in Pittsburgh. There's a movie from that here:


& here're the YouTube notes for it:

"Paradigm Shift Knuckle Sandwich: March 8, 2017E.V.": I wrote my 'Pataphysics / Math / Humor / Cognitive Dissidence book entltled "Paradigm Shift Knuckle Sandwich & other examples of P.N.T. (Perverse Number Theory)" in the 1st six weeks of 2008 after doing five years of research. For various reasons, I abandoned all hope of publishing it. Nine years later, in the beginning of 2017, I decided to publish it myself & was then aided by a generous donation from my old friend Trevor Blake. I'd read from the manuscript once before at Bowery Poetry Club on November 1, 2008. In honor of finally having a proof copy of the book, I decided to read a short section at the Open Poetry/Prose Mic night at Té Café in Pittsburgh. This is the documentation from that reading. I think this is some of my best writing. As a person who prefers originality & intensity but who rarely or never finds anyone else who does, it's hard for me to say how this brief reading was received. I'm inclined to think that most of my work is outside genre & this book would most likely be hated by most mathematicians & by most poets. Its probable readership is a small group of eccentric hyper-intellectual 'patanational 'pataphysicists & neoists that's scattered all over the world. - March 10, 2017 notes from tENTATIVELY, a cONVENIENCE.

Tags: tENTATIVELY a cONVENIENCE, 'pataphysics, math, humor, cognitive dissidence, Paradigm Shifts, Knuckle Sandwiches, Paradigm Shift Knuckle Sandwich, PNT, Perverse Number Theory, Té Café, Open Poetry/Prose Mic

On April 1, 2017 (exactly a year ago from when I'm making this webpage!), I premiered the book at the Glitter Box Theater. 3 people came, one 5 minutes before the reading was over. Here's the movie from that:


& here're the YouTube notes for it:

"Is this a Black Theorem?": I was a mathematician as a child. I lost interest as an adult. At age 49, I started reading pop math books that centered around what I considered to be paradigm shifting concepts: zero, negative numbers, transcendental numbers, imaginary numbers, & the like. After 5 years of this I decided to write a book springing off from this research, a book extolling the virtues of heretical paradigm shift outlaws. A part of the idea is that, contrary to the conventional notions, paradigm shifts don't just center around the introduction of technologies such as the printing press & the cell-phone but can also center around IDEAS, 'pure' & 'simple' (anything but). A "Black Theorem" is what mathematicians jokingly call a theorem that exposure to causes a person to go insane. Given that the book being read here, my "Paradigm Shift Knuckle Sandwich & other examples of P.N.T. (Perverse Number Theory)", is meant to humorously challenge taking underlying concepts of 'reality' for granted, one could imagine that, for some sensitive types, it might really 'drive someone insane'. Perhaps it was fear of that that made it so that there was only ONE audience member there at the beginning of the reading, another one added halfway through, & a 3rd, & last, toward the end. Sounds like a math problem, eh?! - March 11, 2017 notes from tENTATIVELY, a cONVENIENCE

Tags: tENTATIVELY a cONVENIENCE, reading, math, 'pataphysics, Glitter Box Theater, April 1 2017, humor, cognitive dissidence

& here're stills from that:

Bill O'Driscoll of the Pittsburgh City Paper, someone who's supported my work for more or less the entire 22 years I've lived in Pittsburgh, read the 1st 50 page or less & wrote this review which was published on August 30, 2017:

2017.08.30 Pittsburgh City Paper review of "Paradigm Shift Knuckle Sandwich" by Bill O'Driscoll


Paradigm Shift Knuckle Sandwich, by tENTATIVELY, a cONVENIENCE

By Bill O'Driscoll

PARADIGM SHIFT KNUCKLE SANDWICH. Tapping inspirations including absurdist playwright Alfred Jarry, and Douglas Hofstadter's classic book Godel Escher Bach, local art imp tENTATIVELY, a cONVENIENCE offers this good-humored, self-published 407-page journey into mathy thought experiments, number games, logical conundrums and the nature of language. The general idea is that what we call "reality" can be improved upon, and that "paradigm shifts in consciousness can occur from 'violent' conceptual shocks to the (consensus reality?) system" that induce changes in the physical world. In Tent's view, games where the rules change continuously are not only legit, but preferable to games with consistent rules. Obscure? A bit. But you don't have to understand much math to be engaged by his wide-ranging intellectual curiosity and irrepressible sense of play. As Tent himself writes, "I don't know where I am, but I won't let that stop me from navigating thru the chaos of believing in nothing at the same time I believe in everything."

Paradigm Shift ($20) is available on Amazon and at Caliban Books, Copacetic Comics, and White Whale Bookstore.

& I sayeth unto YOU: Buy the damned book so that I MAY LIVE!!

- tENTATIVELY, a cONVENIENCE note, April 1, 2018E.V.


My friend Brian Gentry, who I've known through various 'underground' connections such as neoism & anarchism bought a copy in 2018ish. He's a physics professor at a university & he sent me this image of a shelf of the books he reads these days. I feel like I'm in good company:

PSKS has requested marginalia built into its design. The 1st printing of it had marginlia by 2 people: Bruce Stater & 'Dr. Charles Boyd'. That's the edition Brian has. For the 2nd printing I removed Boyd's marginalia. Brian took the making of marginalia for the book seriously as a way of participating in the book's extended writing. The following are samples of what he sent me soon after he started reading it. I'm sure that now that he's finished the whole book his marginalia is much more comprehensive.


As of October, 2020, my old friend Brian Gentry, now a biophysicist, gave an excellent review on Goodreads. After 43 years of writing books it's astounding how few good reviews any of my books have gotten. This one is truly extraordinary.


Brian Gentry's review of

Paradigm Shift Knuckle Sandwich & other examples of P.N.T. (Perverse Number Theory)

by tENTATIVELY, a cONVENIENCE (Goodreads Author)

- https://www.goodreads.com/book/show/10789926-paradigm-shift-knuckle-sandwich-other-examples-of-p-n-t

Brian rated it 5 stars

it was amazing

First, I highly recommend this book. It is a book about mathematics, but perhaps not like any other you are likely to read on the subject. Second, this book is not for everyone. Personally, I don't waste my time on books that have "something for everyone" because that usually means they don't have any real substance. This book has plenty of substance, but requires curiosity, open-mindedness, and an appreciation of a highly intelligent, ironic, absurdist sense of humor. You don't have to be a mathematician, but you do need to think that math is interesting. If this is you, then I suggest giving this a thorough read.

The author of this book is not a professional or even amateur mathematician, but rather an intensely creative person with a good deal of natural but untrained mathematical ability. They have produced a large body of highly idiosyncratic, playful, and often deeply intellectual creative work as a musician, filmmaker, writer, and performer. In this book, the author applies their unique approach to the understanding and interpretation of various aspects of pure mathematics, and number theory in particular. They execute this process through reading and review of eight books on popular mathematics, including the notoriously obtuse Gödel, Escher, Bach, biographies of famous mathematicians such as Alan Turing and John Nash, and books on the history and development of the numbers e, pi, and zero. In addition, the author brings their full creative process to bear on the interpretation of these texts, which results not only in playful adaptations and applications of the material but also in extensions of these concepts in new directions. In this regard, the author works in the spirit of the great artist Alfred Jarry, who engaged in a similar approach to modern science that turned physics and metaphysics on their heads, creating his own 'philosophy' of science that extended these fields in absurd, playful, and perceptive directions.

Even though the subject of this book is mathematics, it involves much, much more, including "the history, the politics, the apparent paradoxes, the etymology, the anti-religion, the philosophy, [and] the biography." It accomplishes this through the author's extensive "digressions, tangents, extrapolations, absurd fantasies, [and] convoluted explorations." These include insightful, convoluted, funny, and sometimes bizarre permutations of text, symbols, and images. In addition, various dialogues between the author and his associates serve as commentary and further exploration and expansion of the mathematical concepts. There is even documentation of a film based on creative interpretations and permutations of them. And finally, an extensive glossary manages to tie this all together.

While this mix of elements may seem confusing to some, particularly for an already obtuse subject matter, the author's sense of humor greatly lightens these explorations. Though he is serious about his work, he does not take himself or his subject so seriously that he cannot poke fun at both. He develops extensive running inside jokes that he lets the reader in on that make it fun to read. And despite the many digressions, he always brings the reader back to the punchline. This makes it a good read for those who might otherwise be intimidated by number theory.

The abstract nature of number theory proves fertile ground for a subversive playfulness designed to undermine what the author calls 'reality maintenance traps' (see below) through the creation of his own Perverse Number Theory (P.N.T.). Number theory already presents us with mind-bending abstract concepts and unusual implications, and the author takes these and runs with them, bending the reader's mind even further through a process that is very clever, sometimes convoluted, and often funny. In P.N.T., topics in mathematics such as indeterminant forms, imaginary numbers, infinity, infinitesimals, zero and the empty set, and transcendental numbers get treated to a retooling and reformulation that "point[s] to a flexible 'reality' that evades definition by its very nature."

Reality maintenance traps, as I understand them, are ideas, constructs, and notions we have about the world that operate to limit our thinking about and being in it. Ultimately, they constrain our behavior by limiting what we imagine to be possible. We take them as truth but they are, in fact, the result of social consensus and are absorbed and internalized from the dominant culture. The author develops P.N.T as a kind of antidote to this restrictive normality in an attempt to break its hold on our thinking. It takes aim at the repressive and oppressive aspects of what we take for granted. P.N.T requires the reader to wrestle with concepts outside of the range normally encountered. Thus, the author states that "whatever is NON-AXIOMATIC can be embraced as liberatory." In considering neural processing from an information theory standpoint, they ask "if we are soft machines channeling neurons thru gates of interpretation in order to generate 'true meanings', can we increase & control the number of gate ambiguities to choose 'reality'-manifested outcomes?" The author proposes " 'changing the way one thinks' at a more basic system level [than, for example, by so-called "thinking outside of the box"] by changing the units w/ wch we think." Thus, P.N.T takes the reader into areas of philosophy and ontology that are fascinating and often unanticipated and surprising. Though challenging, this is an enjoyable mix.

A final aspect of the book that I appreciate is that, ultimately, it is a participatory experience.

What you gain from this book and from P.N.T is largely determined by how you engage with it. It operates on many levels and can be approached in different ways depending on what you bring to the experience: as a good introduction to higher mathematics from a non-expert, as a creative exploration from a decidedly outsider perspective, as an thought-provoking, entertaining, and challenging new way to approach "accepted" notions not only of math, but of reality itself. Perhaps one of its most successful aspects is that these different approaches and levels are intertwined and operate simultaneously.







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