[ Continued from last week, and I'm feeling considerably better, thank you. ]
In your mathematics paper, between the equations and the striking new translation of The Canterbury Tales, include some definitions. Begin by defining ``normal'', ``unity'', ``orthogonal'', and ``inner product'', because they've been defined in every mathematics paper ever and what will a couple more definitions hurt? Then you can add clarifications, like ``the unified orthogon is the maximal subset of the minimal superset which covers but does not exclude all the subsets composed of non-unity elements of the power set basis subspace excepting but not excluding the span of the orthogonal dual basis'', which sends readers back to the numbered equations' reassurance that H equals the sum of all the components of H, whether serif or gothic. Some definitions should introduce subscripts, ideally ``5'', ``*'', or the pair ``3, 3'', the most mathematical of subscripts.
You might include graphs, to remind you how awful your paper-writing software makes including graphs. The first should be a wavy scribble with a modest peak, proving the existence of grid marks. Figure two should be an isometric view of a tetrahedron with arrows. Figure three should be disconnected open dots that rise sharply, drop to the bottom, then rise back to level. The fourth figure should be scattered dots on a log-log plot and a dashed line of interpolation never threatening to go near any of them. The fifth picture should be some hypnotic repeating pattern in really old artwork. The eighth picture should be a polygon, making the reader search for the sixth and seventh, the mad fools.
Also try a few tables. The left column should be several Greek alphabet levels with superscripts of + and -, and subscripts of up to four characters. Do not repeat any combination of subscripts. Include several numbers beside each figure, but include a hyphen or ``NA'' in at least one of each row's columns. Repeat until this explains how you've proven the specific heat of clay.
Proofs lie at the heart of most papers, surrounded by a protective layer of boldface, the rib cage, a little filled-in box at the lower right corner, and one or more ventricles. The important part is the declaration of something like ``Unified3,3 rotation star matrices are decomposable into linear diagonalizable rotatable non-star matrices diffeomorphic to the quaternion GL5''. Follow this with between two-thirds and three-quarters of a page of algebra, which can be as simple as factoring 15 in a difficult way, and explain the conclusion is obvious now. Any proofs not having enough words should be called Lemmas and itemized as deductions on your income tax.
Next comes explaining the analysis. For example: you do a Laplace transform, modifying the original equation by turning Pierre-Simon, Marquis de Laplace into a penguin. After some manipulations do the inverse Laplace transform, resulting in a different, angrier penguin. If this is unsatisfying try the z-transform, giving you a napping penguin with angry dreams. Use a Hamming filter, surrounding the napping angry penguin with pork products until it is satisfied. Then run away before it remembers how tired it is of the fetishization of bacon in modern comedic culture.
Spend no fewer than four pages reporting surprises and discoveries. For example, perhaps in the middle of your wall calendar you discovered a sticker page for marking important dates like scheduled oil changes, visits to the Museum Of Art You Will Never Visit, or the expiration date to eat your air conditioner by. Your readers will never imagine the murder was actually a suicide, discovered coincidentally by the man the jilted fiancee was going to elope with, and hastily covered up to protect the vicar, who didn't know anything about it before the police were called.
Remember to passive-aggressively thank your granting organization. Then include six citations per page of your paper; this requires thinking of credible-sounding titles. Journals may be identified by sets of three to five units of one to four letters each, such as ``Am J Diff Let'', ``New Brit Cndy Tree'', ``Sing Or Clap'', and ``Turb Hamr''.
Remember to list one of your co-authors as contact person and submit to any reputable journal, if you find any.
Trivia: The International Geophysical Year was conceived in James Van Allen's home as a Third International Polar Year on 5 April 1950; the closing date for analysis and publication of data collected during the Second Polar Year, 1932-1933, was the 31st of December, 1950. Source: This New Ocean: The Story Of The First Space Age, William E Burrows. (And looking it up on Wikipedia reveals that we did have a Third Polar Year after all, 2007-08. I never got a memo about this. Did any of you?)
Currently Reading: The River At The Center Of The World: A Journey Up The Yangze, And Back In Chinese Time, Simon Winchester.