The poem A Visual Music Exhibit: Mathematical Impressions is based on mathematical impressions of the art exhibition, Visual Music: Synaesthesia in Art and Music Since 1900, held at the Hirshhorn Museum in Washington, DC, June 23 through September 11, 2005.

Before visiting the museum, a randomly selected page of the book The Harper Collins Dictionary of Mathematics^* was assigned to each of the 92 works in the exhibition checklist.^† The pages were chosen from the section of the dictionary that contains entries (i.e. pages 1 through 642). Random page numbers were generated by using a 10-sided die (with faces labeled 0 through 9). First, the hundreds digit was generated by rolling the die repeatedly until the outcome was in the range 0 through 6. Next, the tens digit was generated. If the hundreds digit was 6, the die was rolled until the outcome was in the range 0 through 4. Otherwise, the die was rolled once. Finally, the units digit was generated. If the hundreds digit was 6 and the tens digit was 4, the die was rolled until the outcome was in the range 0 through 2. If the hundreds digit and tens digit were both 0, the die was rolled until the outcome was in the range 1 through 9. Otherwise, the die was rolled once. The random page numbers were recorded on a photocopy of the checklist.

The exhibition was visited on September 10, 2005. It consisted of paintings, photographs, films, light projections, computer graphics, and immersive environments. The poem is based on the paintings and photographs only, because these works were thought to be more interesting than the others.

There were 46 paintings and photographs.^‡ These were visited, roughly speaking, in the order in which they had been arranged in the museum. (Note: This was done with the following items in hand: the copy of the checklist containing the random page numbers and a copy of The Harper Collins Dictionary of Mathematics.) For each of these works, the following actions were performed: (1) examine the work for several minutes, (2) read the page of The Harper Collins Dictionary of Mathematics that was assigned to the work and (3) select one term or phrase for which the definition begins on that page. Generally speaking, terms and phrases were selected that were thought to be interesting and related in some way to the work.

The 46 selected terms and phrases were decomposed into a list of 93 words. In the process, hyphenated pairs of words were separated into their constituent words. A hyphen was placed immediately after (before) each word that had been the first (second) word of a hyphenated pair.

A random 2-digit number was assigned to each of the 93 words. To generate a number, a 10-sided die (with faces labeled 0 through 9) was rolled twice. The first roll was for the tens digit; the second was for the units digit. In some cases, the same number was assigned to more than one word. For such words, the 10-sided die was rolled one more time. The resulting digit was appended as a decimal digit after the word's 2-digit number. Additional decimal digits were generated and appended as needed until a unique number was assigned to each word. The words were sorted in numerical order using the randomly generated numbers.

The 93 words were used (in numerical order) for the words of the poem. Any word followed by a hyphen was combined with the subsequent word to form a hyphenated pair. Similarly, any word preceded by a hyphen was combined with the previous word. (Note: If a word followed by a hyphen was followed by a word preceded by a hyphen, the two words were combined with one hyphen, rather than two.)

The length of each line of the poem was set by rolling a tetrahedral die (with faces labeled 1 through 4). First, it was rolled to determine the number of words to be used in line one; the outcome was 2. (Note: Here, hyphenated sequences of words were counted as one word.) Next, it was rolled to determine the number of words for line two. This process was repeated for subsequent lines until the outcome of the roll was greater than or equal to the number of words remaining in the poem.

The two auxiliary notes given after the poem were arranged randomly. A random 1-digit number was assigned to each note. To generate a number, a 10-sided die (with faces labeled 0 through 9) was rolled once. The notes were sorted in numerical order using the randomly generated numbers.

* The Harper Collins Dictionary of Mathematics, E. J. Borowski and J. M. Borwein (New York: Harper Perennial, 1991).

† The checklist was obtained from the book that was published in conjunction with the exhibition (Visual Music: Synaesthesia in Art and Music Since 1900, Kerry Brougher, Olivia Mattis, Jeremy Strick, Ari Wiseman and Judith Zilczer [New York: Thames & Hudson, 2005]).

‡ For a list of the paintings and photographs upon which the poem is based, see Bibliography.