Page 3. " wood-walled, Remington-hung "
Fired On
Creative Commons Attribution Share AlikeFired On - Credit: Claire H

Frederic Remington (1861-1909), was an American painter, sculptor and writer, and founder of the Cowboy Art movement. 

To the left is his 1907 oil on canvas, Fired On.

More of his work can be seen here.

Page 4. " the prestigious WhataBurger Southwest Junior Invitational "
Whataburger
Public DomainWhataburger - Credit: Andreas Praefcke

A fictional tennis tournament, but the sponsor is real; Whataburger is a burger chain based in Southwest U.S.A.

 

Page 7. " Neoclassical Assumptions in Contemporary Prescriptive Grammar "

The term 'Prescriptive Grammar' refers to the notion that the rules of grammar should be strictly obeyed. Wallace wrote about the subject for Harper's Magazine in his essay Democracy, English and The Wars Over Usage.

Wallace's mother Sally, a professor of English, would fake coughing fits at the dinner table if her children committed linguistic errors, stopping only when it had been corrected by the perpetrator. Wallace once wrote that he was "slightly chilled by the idea of children being brought up to think that a linguistic error might deprive their mother of oxygen."

Page 7. " Montague Grammar and the Semantics of Physical Modality "

This refers to the American logician Richard Merret Montague (1930-1971), whose thesis was that natural languages (such as English) and formal languages (such as programming languages) can be treated in the same way.

"There is in my opinion no important theoretical difference between natural languages and the artificial languages of logicians; indeed, I consider it possible to comprehend the syntax and semantics of both kinds of language within a single natural and mathematically precise theory."

Page 8. " and based by him on the rigorous Oxbridge Quadrivium-Trivium curricular model "

Oxbridge refers to the two British universities of Oxford and Cambridge. 

The Quadrivium are the four academic subjects of arithmetic, geometry, music and astronomy. The Trivium are three disciplines: grammar, logic, and rhetoric.

Page 9. " I have been coached for this like a Don before a RICO hearing "

RICO = Racketeer Influenced and Corrupt Organizations Act.  This is a statute used to charge organized crime figures in criminal conspiracies.

Page 10. " The Brewster's-Angle light of the tabletop "
Brewster's Angle
Public DomainBrewster's Angle
The angle at which non-polarised light striking a surface will reflect polarised light. Named after Sir David Brewster (1781-1868), a Scottish physicist, mathematician, astronomer, inventor and writer.
Page 18. " And Venus Williams owns a ranch outside Green Valley "

 

Venus Williams
Creative Commons Attribution Share AlikeVenus Williams - Credit: Sascha Wenninger

 

Venus Williams is a professional tennis player. She would have been 16 when Infinite Jest was published. She reached the US Open finals at the age of 17, and has since won 20 Grand Slam titles.

David Foster Wallace was himself a regionally-ranked junior tennis player. In 2006 he wrote an article for the New York Times entitled 'Roger Federer as Religious Experience'.