Tale of Binary
And God called the light, Day, and the darknesse he called Night: and the euening and the morning were the first day.
It makes no sense to think of binary as something someone somewhere invented. If you’re interested in history, I recommend reading Anton Glaser’s History of Binary and Other Nondecimal Numeration. Donald Knuth also has a nice bit in the first volume of TAOCP at the start of section 1.2.6 on Binomial Coefficients.
But if you’re like me, and you’re just interested in how it came into common usage with computers, keep reading.
De Augmentis Scientarium
Bacon of Bacon, or as he is known to some, Saint Frankie Bacon, was fairly certain he knew all the things. But being the careful fellow he was, and just in case something was missing, he wrote them into a long list. To check for gaps.
One of the things on that list was an example Alphabeti Biliterari. A binary encoding for text (if you’re skipping ahead in your reading, it’s on page 350 or so of the Latin edition, in book six).
[Public domain],
via Wikimedia Commons
I like to imagine Henriette Avram thought about Bacon when she was at the Library of Congress inventing a binary text encoding of her own. I imagine the Francis Bacon statue in the main reading room looked down on her with some awe, thinking perhaps there had been a thing or two left off of his list. Bacon’s encoding was published around 1605
Arithmétique Binaire
Gottfried Wilhelm von Leibniz (known to we his friends as “Gary”) had a thing or two to say about binary, but he didn’t love the words like Bacon.
the Library of Congress
Rare Books Division
http://www.loc.gov/pictures/item/2006690495/
In 1703, he published a little pamphlet about binary arithmetic that outlines his plan for using binary for all calculating. For whatever reason, he still built his computers to use decimal, probably to avoid all the nasty floating point conversion stuff that we didn’t figure out until a couple centuries later.
Laws of Thought
A century and a half went by with more people designing and building computers, and more people thinking about binary. George Boole was one of those people, and in 1854 he wrote a book about it. I found the book totally inscrutable. As far as I can tell, Claude Shannon is the one person who ever read it. But that’s getting ahead of the tale.
Until this moment, I don’t believe I had ever read to the end of the title of the book, which is itself a bit inscrutable:
An Investigation
of the Laws of Thought
on Which are Founded
the Mathematical Theories
of Logic and Probabilitie
I am told the book dealt with what we now call “Boolean Logic” which is the reduction of logic to TRUE and FALSE values (see the binary there?) and the use of mathematical operations to calculate with them. This is something anyone who ever used the Altavista search engine gained some experience with. “Search for ‘(David AND Brunton) NOT (England OR Wales)’ to find me” used to mean something on the Internet.
If Claude Shannon hadn’t come along, poor George Boole would still be stuck in the stacks, ignored by people like me who are scared of long titles.
A Symbolic Analysis of Relay and Switching Circuits
What should have been on Frankie Bacon’s list, but wasn’t, is Claude Shannon’s Master’s thesis. Not only is it completely readable, but also it’s still mind-blowing, 75 years later. He figured out that circuits and boolean logic have a one-to-one correspondence.
I suppose there are a few missing pieces to this tale, but this is my best understanding of how letters, numbers, and logic all came to be represented using binary in modern computing.
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