Logic Diagrams |
|
| As we may or may not have previously discused (depending on the way in which you're bouncing around our web pages), these days we are predominantly concerned with computers, but it's worth noting that there has historically been a great deal of fascination in logic in general. This fascination was initially expressed in the form of logic diagrams, and later in the construction of special-purpose logic machines for manipulating logical expressions and representations. |
| a |
| Diagrams used to represent logical concepts have been around in one form or another for a very long time. For example, the Greek philosopher and scientist Aristotle (384 BC to 322 BC) was certainly familiar with the idea of using a stylized tree figure to represent the relationships between (and successive sub-divisions of) such things as different species. Diagrams of this type, which are known as the Tree of Porphyry, are often to be found in medieval pictures. | Following the Tree of Porphyry, there seems to have been a dearth
of activity on the logic diagram front until 1761, when the brilliant Swiss mathematician
Leonhard Euler introduced a geometric system that could generate solutions for problems in
class logic. Euler's work in this area didn't really catch on, however, because it was somewhat awkward to use, and it was eventually supplanted in the 1890s by a more polished scheme proposed by the English logician John Venn. Venn was heavily influenced by the work of George Boole, and his Venn Diagrams very much complemented Boolean Algebra. |
|
| a | ||
| Venn Diagrams were strongly based on the interrelationships between overlapping circles or ellipses. The first logic diagrams based on squares or rectangles were introduced in 1881 by Allan Marquand, a lecturer in logic and ethics at John Hopkins University. | ||
| a | ||
| Marquand's
diagrams spurred interest by a number
of other contenders, including one offering by an English logician and author, the
Reverend Charles Lutwidge Dodgson. Dodgson's diagrammatic technique first appeared in his book The game of Logic, which was published in 1886, but he is better known to us by his pen-name, Lewis Carroll, and as being the author of Alice's Adventures in Wonderland. |
|
|
| a | ||
| Leaping from one topic to another with the agility of a mountain goat, we might also note that Lewis Carroll enjoyed posing logical conundrums in many of his books, such as Alice's Adventures in Wonderland (1865), Through the Looking-Glass (1872), and The Hunting of the Snark (1876). For example, consider this scene from the Mad Hatter's tea party in Chapter 7 of Alice's Adventures in Wonderland: | ||
| a | ||
"Take some more tea," the March Hare said to Alice, very earnestly. |
||
| a | ||
"I've had nothing yet," Alice replied in an offended tone: "so I can't take more." |
||
| a | ||
"You mean you can't take less," said the
hatter: |
||
| a | ||
| And we would have to chastise ourselves soundly if we neglected the scene involving Tweedledum and Tweedledee in Chapter 4 of Through the Looking-Glass: | ||
| a | ||
"I know what you're thinking about," said Tweedledum; "but it isn't so, nohow." |
||
| a | ||
"Contrariwise," continued Tweedledee, "if it was so, it might be; and if it were so, it would be; but as it isn't, it ain't. That's logic." |
||
| a | ||
| You have to admit, these gems of information aren't to be found in your average history of computers, are they? But once again we've wandered off the beaten path ("No," you cry, "tell me it isn't so!"). | Apart from anything else, rectangular logic diagrams as espoused by Allan Marquand and Lewis Carroll are of interest to us because they were the forerunners of a more modern form known as Karnaugh Maps. Karnaugh Maps, which were invented by Maurice Karnaugh, in the 1950s, quickly became one of the mainstays of the digital logic and computer designer's tool-chest. | |
| a | |
|
|
| These notes are abstracted from the book Bebop BYTES Back (An Unconventional Guide to Computers) Copyright Information |
|
