1000 Bytes of Pi

2015. 8 Framed and Hammered Sheets of Stainless Steel 8 x 12” x 12” (frame dimensions).

The piece itself is a celebration of Pi and a meditation on texts. When I see a text that I understand (e.g. a book in English) I generally approach it and appreciate it as a source of information and meaning. When I see a text that I don’t understand (e.g. a Chinese scroll, a hieroglyphic inscription, instructions in braille, machine language) I tend to approach it as a thing of mystery and beauty. A lot of my number work therefore has this duality built into it, the ability of a text to be a work of clarification and meaning or of mystery and beauty, or both.

Explicitly, the piece is the first 8,192 values of the binary extension of Pi. We’re all familiar with Pi expressed in the decimal system (ones, tens, hundreds, thousands etc.), namely 3.14159…, but we’re much less familiar with it expressed in the binary system (ones, twos, fours, eights, sixteens etc.), namely 11.0010010…Every “bump” in the piece represents either a one or a zero in this binary extension. The binary system is most closely associated with the digital computer where it is used to store information as ones and zeros (or “on” and “off”). In this digital world, each one or zero is called a bit. Bits are organized into groups of eight, known as a byte, which can contain any value from 00000000 to 11111111 in binary, or 0 to 255 in decimal. I have used this system to organize the ones and zeros of binary pi, and if you look closely at the piece you will see that all the hammer punches in the steel are organized that way, as groups of 8 “bits”, in 8 columns, with 8 row clusters, across 8 sheets.

In this system, “1,000 bytes” is known as a kilobyte (1Kb), and actually represents 1,024 Bytes (2 to the power of 10), not 1,000 Bytes (10 to the power of 3). So the title of the piece is deliberately misleading because it actually contains 1,024 bytes, or 8,192 individual bits or hammer punches or bumps as you see them on the steel, not 1,000. If, however, you think of 1000 in the binary system instead of the decimal system, you will see that it equates to 8 in decimal. So the 1,000 of the title actually means 8 and reflects the number of sheets (or frames). And if you look at the bottom right hand corner of each sheet where I have initialed and numbered it, you will see 1/1000, 10/1000, 11/1000, 100/1000, 101/1000, 110/1000, 111/1000, 10000/10000. This is binary numbering and equates to 1/8, 2/8, 3/8….8/8. Now, the “odd” numbered sheets (1/1000, 11/1000, 101/1000, 111/1000) contain all the hammer punches for the 1s in the binary extension of Pi. The “even” numbered sheets contain all the 0s. So the 8 sheets can be thought of as 4 pairs, an odd and an even numbered sheet. Each pair covers 1/4 of the total.