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Boolean Logic : George Boole's The Laws of Thought
Ian writes "The Globe and Mail has a piece about the man behind Boolean Logic - George Boole - The Isaac Newton of logic. 'It was 150 years ago that George Boole published his classic The Laws of Thought, in which he outlined concepts that form the underpinnings of the modern high-speed computer.'"
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Let's not forget Lovelace, Ritchie, Knuth, von Neumann, Turing...
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Offtopic: Why did it take me 15 seconds to realize the word "Google" was no where in the story title? Anyone else have that problem?
Set Theory is a Boolean Algebra. Odd there was no (explicit) mention of this. It is important to both mathematics in general, and Computer Science.
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Just as an aside, a mathematical structure is a Boolean Algebra if, and only if, if it contains two operations (generally denoted +, and *), such that for all elements A, B and C in the structure
A + B = B + A
A * B = B * A
(A + B) + C = A + (B + C)
(A * B) * C = A * (B * C)
A + (B * C) = (A + B) * (A + C)
A * (B + C) = (A * B) + (A * C)
and there exists two elements 0 and 1 in the structure such that
A + 0 = A
A * A = A
and for each A an element exists that's the "negation" of A
A + ~A = 1
A * ~A = 0
In logic, + is equivilent to OR, * is equivilent to AND, a Tautology is equivilent to 1, and contradiction is equivilent to 0. ~ is NOT.
Similar comparisons can be made in Set Theory. In the same order of above: Union, Inclusion, Universal Set, Empty Set, and Set Complement.
So, if you prove one algebraic identity in Set Theory, you also proved the same exact identity in
Propositional Logic (and vice versa.)
(shrug)
It's probably the same reason multiplication has a higher precedence than addition. Multiplication and AND are equivalents, and addition and OR are equivalents.
In fact, for most practical purposes, AND *is* multiplication and OR *is* addition. Just compare the truth tables with multiplication and addition tables (one minor technicality, of course, is that addition carries while OR does not; the carry bit is simply the result of A AND B).
It was a really good paper.
Some complain that the intruduction of "null" into some systems (such as databases) ruins the simplicity of Boolean logic. It creates a "3-value logic" which can get messy to grok.
I generally agree. I think nulls are perhaps fine for numeric calculations in some cases, such as the average if there are zero records, but not Booleans and not strings. But sometimes it is hard to limit it to one but not the other. It is a controversial topic nevertheless. Chris Date has written some white papers on how to get rid of null.
Table-ized A.I.
Not to mention that it is unlikely that Hopper ever claimed to find the first "bug".
The comment next to the moth taped in the logbook seems to indicate that the word had been in use for some time, and Hopper was making a bit of a joke.
-- clvrmnky
It appears this "Computer History" attempt overlooks John Vincent Atanasoff, credited by most reliable sources (Smithsonian, etc.) as developer of the first electronic digital computer" years before the ENIAC. In fact, the ENIAC was derived from Atanosoffs's ABC Computer at Iowa State after an ENIAC developer visited Atanasoff (stayed several days in Atanasoff's home), and "stole" his ideas and proposed a larger verssion as the ENIAC to the army. Atanosoff's ABC computer was the first to solve Schroedinger's equation represented by the solution of a 39x39 system of matrix equations. However, time caught up with the ENIAC visitor, and the notebook he kept when he visited Atanasoff was his undoing when the U.S. Court in Minneapolis overturned previous patent rulings for computer developments and ruled they were all derived from Atanasoff's ABC computer. Hopefully, this attempt at a computer museum will soon be updated to accurately reflect the original development of the electronic computer by Atanasoff at Iowa State in 1942.