Bob Schwartz

Tag: binary

The binary and the infinite: What we learn from computers, the I Ching, the Bible and breathing.

We live today and have long lived in what seems to us, at first glance, a binary world. So it seems.

At their most basic, computers are binary machines. Countless combinations of yes/no, on/off decision circuits, adding up, as speed and the number of decisions increase exponentially, to processes that mimic (or exceed) human thought.

The I Ching begins its panoramic presentation of world with a simple binary calculation: either a solid yang line or a broken yin line, combined into eight trigrams and sixty-four hexagrams, from which the entire nature of life and time is profiled, if not actually predicted.

Traditions, such as Taoism, Zen and others, suggest non-duality. That reality exists between those choices we are so attached to. That it is not either/or, not neither/nor. Computers agree. Reduced to each of the billions of digital decisions, binary means nothing. The I Ching reduced to a single line means little. The meanings, all of them, are in the matrix of combinations.

The Bible agrees. It would seem, in its rules and lists, to promote binary behavior. The Ten Commandments are a prime example. But at the literal first moment, if we immerse ourselves in the question of what is between existence and non-existence at creation (contemplation that according to one legendary interpretation drove the Talmudist Ben Zoma crazy), the answer may be everything. The Book of Ecclesiastes, famous for saying that all is ephemeral vapor and listing the binary poles (a time to laugh, a time to weep…), is telling us we live now and ever in the changes in between. Not unlike the I Ching.

Physics has also given up on the binary. Simplistic analysis has given way to acknowledgement that as much as we would like to hold on to a concept of this or that, now or then, the physical world at a foundational level exists in simultaneous multiple states.

Not everything about our organic human lives is binary, but plenty of it is. Ten has its place (fingers, toes), but a distinct second place to two. Two arms and hands, legs and feet, eyes, ears, lungs.

Lungs bring us to breathing, the penultimate binary. Inhale, exhale. There is nothing in between. The failure of that binary leads to the ultimate: life, death. Some do posit an alternative to that binary, a third option. But if we just stick to life/death, what do we learn about either one from this discussion of binary?

Things as they are are not exactly binary, except we make them so. This doesn’t mean that one can think away breathing or death. No inhale/exhale, no life happens. But the values in between—the digital fabric, the I Ching, the space between existence and non-existence, the time between laughing and weeping, the quantum states—are where it is at.

Hanukkah Hexadecimal Code


If four sides of a dreidel and eight candles are proving too simple for you, here is a way to expand the Hanukkah holiday—mathematically and mystically.

The eight-candle menorah is binary, that is, a candle is either lit (1) or unlit (0).

With eight binary places, the menorah is a type of hexadecimal, a code central to digital processing. Each of the eight places in a hexadecimal is occupied by a digit or a letter.

If you assign each of the eight candles, left to right, either a 0 or a 1, you can convert each from a hexadecimal to a numeric value:

First night of Hanukkah = 00000001 = 1
Second night = 00000011 = 17
Third night = 00000111 = 273
Fourth night = 00001111 = 4,369
Fifth night = 00011111 = 69,905
Sixth night = 00111111 = 1,118,481
Seventh night = 01111111 = 17,895,697
Eighth night = 11111111 = 286,331,153

Is this of any use? Some suggestions:

1. A secret code to identify each day of Hanukkah with a number. When greeting someone on the second day of Hanukkah, you might say “Happy 17”. Please be sure to explain the system behind your greeting, lest it is thought you are experiencing a psychological break or are high (assuming you are not).

2. Gematria is a system that assigns numbers to each Hebrew letter in a word, and then calculates a value for each word, which value is then associated with other words of the same value. You can look online to find the gematria associations for each of the above values. In addition to gematria, there are countless systems that assign values to letters and meaning to numbers.

For the larger numbers, you may not find an associated meaning. But you can factor the larger numbers to find smaller associated meanings. So, for example, the eighth night value of 286,331,153 factors to 17 × 257 × 65537. The smaller numbers such as 17 and 257 are widely discussed.

Chag urim sameach! (Happy Festival of Lights). And if I don’t see you, Happy 273!