Thomas Brodhead – American, born 1968 – Stomachion –2013 – acrylic on wood panel – 24" x 24" x 0.25" (60.96cm x 60.96cm x 0.64cm)
Before Archimedes ran naked through the streets of ancient Syracuse screaming “Eureka!”, he contemplated the combinatorics of the stomachion, an ancient tangram puzzle whose Greek name means “belly-ache” because of its difficulty: How many ways can the differently-colored internal shapes (as shown here) be rearranged to form another perfect square?
It took 2,250 years before a modern mathematician solved this problem using computers (and the answer is 536), but recently (1999) it was discovered that Archimedes had attempted it far earlier than anyone had imagined. That attempt constituted the earliest exploration of combinatorics (albeit, sans a solution to the stomachion), and had been preserved in a palimpsest (a medieval form of book recycling) in which the original text had been all but scraped away for reuse as a Christian hymnal that was kept in a monastery in Syria for hundreds of years. We therefore know that combinatorics had been explored by Archimedes during Alexandrian times, some 1500 years earlier than when Europeans were first thought to have explored the subject in the Middle Ages.
Thus, it’s now fair game to use this puzzle for more prosaic purposes, such as done here by the artist. Using the “canonical” arrangement of the internal figures, the artist applied contrasting colors in a paint-by-numbers fashion, highlighting some of them with whites (and off-whites) that suggest the ejaculation of farm animals who couldn’t give a shit about mathematics and would rather eat slop and fuck each other when not licking the afterbirth off their progeny.