2004: Paradigm Shift Knuckle Sandwich

When I was a child I was a mathematician, probably not a prodigy but closer than most. Even by the time I was in my late teens I could still perform substantial math operations in my head. I remember using rounding-off methods to make the calculations quicker. Once I got into my 20s I used my mathematical abilities less & less until I reached my pathetic decrepit state of the majority of my adulthood. I still retain a love of math anyway, though, even though I can barely add my way out of a paper bag (huh?).

In 2003 I decided to start reading some layperson math books.. but not just any old layperson math books. I wanted to only read the ones about what I consider to be Paradigm Shift concepts: things like "imaginary numbers" & "transcendental numbers" & "zero", etc.. Along the way I started making things inspired by my readings - culminating in my writing a book in the 1st 6 weeks of 2008 called "Paradigm Shift Knuckle Sandwich & Other Examples of P.N.T. (Perverse Number Theory)".

I thought the book might be about 160 pages when I started writing it. It turned out to be 410 pages. I think it's by far one of the best things I've ever written. It's also got a potential readerhip of maybe 5 people (or less). 8 years later I haven't even bothered to try to get it published. NOW, I may FINALLY publish it myself, possibly with help from my old pal Trevor Blake of OVO ( ovo127.com ).


One of the earliest things I did, before I wrote the book, was design math rubber stamps that expressed 'P.N.T.' ideas. The above equation is an example that I had made into a self-inking rubber-stamp so that I could graffiti with it. Perhaps a literal reading of it into 'natural language' might be: "For all "x", x = for all "x", x" or, in English, Anything equals Anything - which is one of my mottos.


The follow-up to that was "Enough is Enough" rendered above as a photograph of admitted abstruseness.


I won't get into the meaning of these things here given that I want you to read my book instead (if & when it comes out). Above is the self-inking rubber-stamp version of "Enough is Enough".


I've always been interested in knuckle tattoos. Perhaps the most 'classic' one is the one where "l o v e" is tattooed on one hand & "h a t e" is tattooed on the other. I worked in a bookstore where a guy who had that tattoo would come in. Whenever he extended a hand to give me money or to receive a book he was always careful to only show the "l o v e" hand. I was touched.

Of course, I didn't want to have a cliché knuckle tattoo, I wanted to 'up the conceptual ante'. The above drawings are early studies for my knuckles tattoo. The upper left, obviously, is an attempt to make my "Anything is Anything" into a knuckles tattoo but the non-translation into 8 units was too awkward.

The lower right non-commutative anti-axiom of m + n does not equal n + m was also awkward. What I finally settled on started out as a straight quote of Leonhard Euler's famous elegant equation: "e to the power of pi times i = -1". At 1st, in order to make that 8 symbols, I changed it to "e to the power of pi times i + 1 = 0".


Then I decided that wasn't interesting enough & I wanted to make it more 'mine' so I changed it to "e to the power of pi times i + 1 to the power of infinity is approximately equal to 0". This latter tweak was inspired by my reading about "indeterminate forms"

[The term "indeterminate" is sometimes used as a synonym for unknown or variable (Becker and Weispfenning 1993, p. 188).

A mathematical expression can also be said to be indeterminate if it is not definitively or precisely determined. Certain forms of limits are said to be indeterminate when merely knowing the limiting behavior of individual parts of the expression is not sufficient to actually determine the overall limit. For example, a limit of the form 0/0, i.e., lim_(x->0)f(x)/g(x) where lim_(x->0)f(x)=lim_(x->0)g(x)=0, is indeterminate since the value of the overall limit actually depends on the limiting behavior of the combination of the two functions (e.g., lim_(x->0)x/x=1, while lim_(x->0)x^2/x=0).

There are seven indeterminate forms involving 0, 1, and infty:


(Thomas and Finney 1996, pp. 220 and 423; Gellert et al. 1989, p. 400). Note, however, that there is a certain ambiguity in this enumeration in the sense that symbolic expressions of the form infty/infty can perhaps be written as inftyinfty^(-1), etc.

If complex infinity infty^~ is allowed as well, then six additional indeterminate forms result:


The Wolfram Language returns the symbol Indeterminate upon encountering such expressions in the course of an evaluation.

The Wolfram Functions Site uses the notation > to represent an indeterminate quantity. - http://mathworld.wolfram.com/Indeterminate.html ]


While the equation's use of "approximately equal to" would probably be considered ludicrous or, at the very least, incorrect by any serious mathematician I like it. After all, I'm trying to use math as a springboard here & not trying to be a 'real' mathematician - which definitely is NOT what I am.


Having decided on what symbols to use I enlisted the aid of my friend Nathan Mould. Nathan was the person I'd loaned my tattooing equipment to after I'd repossessed it from 'the-woman-who-couldn't-tattoo-a-splotch'. As the tattoo I got in trade from Nathan the above was created. It was hard to do the fine line work that my mock-up called for & the tattoo ink has since bled a bit so it's not quite as readable as I'd like it to be. People often think that the right hand spells "exit". One bank teller copied the symbols, I think he thought it was a gang tattoo.


Of course I love insinuating this equation into any footage that my hands are in - as a sort of subliminal paradigm shift. My friend Florian Cramer made a short movie of it & posted it on Vimeo here: https://vimeo.com/44331577 . The 3 photos above are prime examples of this insinuation. They were taken by my, at that time, new photographer friend Julie Gonzalez.






idioideo at verizon dot net


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