The Mayan Venus Tables
Cracking the Bars and Dots of the Dresden Codex on Honeymoon
Pages 46 through 50 of the Dresden Codex—an eleventh-century Mayan screenfold book painted on beaten fig-bark paper that survived the Spanish conquest of Yucatán—consist of dense columns of red and black numbers arranged beneath hieroglyphic headers. In the Mayan vigesimal (base-twenty) numeral system, a single circular dot stands for 1, a horizontal bar stands for 5, and a stylized shell glyph stands for 0. Numbers are stacked vertically in powers of 20 from bottom to top. In calendar day counts, however, the third vertical position multiplies by 18 instead of 20. That modification makes the third place equal $18 \times 20 = 360$ days, close to the length of the solar year.
In 1952, Feynman returned from a honeymoon trip through Mexico with his second wife, Mary Louise Bell, who studied Mexican art and archaeology. Soon after, he bought a facsimile copy of the Dresden Codex. True to his lifelong dislike of spoilers, he covered up the Spanish and German scholarly commentaries. He refused to read what the astronomical tables represented until he had worked them out himself. Just as he had treated the three-wheel Mosler safes at Los Alamos as mechanical puzzles, he spread the bark-paper tables across his desk in Pasadena. He wanted to see whether he could crack an ancient civilization's astronomy from raw numerical patterns alone.
In Surely You're Joking, Mr. Feynman!, he recounted how he acquired a facsimile of the Dresden Codex and decoded the bars and dots on its pages exactly as if he were cracking a new safe combination.
First, Feynman verified the carry rules of the vertical columns on page 24 and pages 46 through 50. That check allowed him to reconstruct missing bars where rainwater or wear had flaked away the lime plaster on the original manuscript in Dresden. Next, he took the first differences between consecutive cumulative day totals across the bottom of pages 46 through 50. He immediately spotted a repeating four-part sequence of intervals: 236, 90, 250, and 8. Added together across any horizontal row, those four intervals always summed to 584 days:
- * Morning Star phase (236 days): The interval during which Venus shines in the eastern sky before sunrise following heliacal rising.
- * Superior conjunction (90 days): The interval when Venus passes behind the far side of the Sun and vanishes in solar glare.
- * Evening Star phase (250 days): The interval when Venus reappears in the western sky after sunset.
- * Inferior conjunction (8 days): The brief window when Venus passes between Earth and the Sun before emerging again in the east.
The cycle total of 584 days immediately identified the physical subject of the five pages. It is the synodic period of the planet Venus (583.92 days). Across the five pages of the table, five consecutive 584-day Venus cycles totaled $2{,}920$ days. That sum equals exactly eight solar Haab' years of 365 days ($5 \times 584 = 8 \times 365 = 2{,}920$). Furthermore, cycling through all thirteen rows of the five-page table required $13 \times 2{,}920 = 37{,}960$ days (104 solar years). That grand cycle brought the 584-day Venus cycle, the 365-day solar calendar, and the 260-day sacred Tzolk'in ritual calendar back into exact alignment.
Yet Feynman noticed an intriguing numerical anomaly on page 24, the introductory multiplication table preceding the five Venus pages. Alongside standard multiples of $2{,}920$, the Mayan scribes had recorded strange non-multiples such as $9{,}100$, $33{,}580$, and $35{,}040$. Working out the modular remainders, Feynman saw why those irregular offsets were engineered into the table. Because the true astronomical synodic period of Venus is 583.9213 days rather than 584.00, the nominal 584-day table slips behind the real sky by 0.08 days per cycle. Over 60 cycles, that error reaches 4.8 days. By subtracting four days every sixty-one Venus cycles and eight days at the end of every three hundredth cycle, the Mayan astronomers in the Dresden Codex kept their Venus table accurate to within two hours over five hundred years.