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Topic: Lambda Dance
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Mandos
rabble-rouser
Babbler # 888
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posted 24 March 2003 05:12 PM
It's a logic geek joke (ie, geeks who've never studied higher-order logic or never programmed in Lisp or some other functional programming variant wouldn't get it either--and that's a lot of geeks). Lambda is a logical abstraction operator. Basically, you use lambda to generalize a statement over some variable. Then you can apply the statement to some object in order to evaluate its validity. Or you can quantify the variable and evaluate it that way. Example: Suppose I have a plain statement like "I like green food if the food is sweet." I can perform a lambda-abstraction like this: X = (lambda x.I like green x if x is sweet) Then I can apply X to some object. Like
X(keyboards) = (I like green keyboards if keyboards are sweet). (Usually, we use symbols, but for the example there's no reason why we shouldn't use English sentences.) This is called a beta-reduction (I think--I sometimes get them confused with alpha-reductions...). Anyway, you can abstract over multiple variables as well. This has zillions of uses, including being (by Alonzo Church's unprovable hypothesis) a complete model of computation equivalent to a Turing Machine or the PC on your desk. It also allows us to discuss the relationship between statements and meanings in a very flexible way, especially if you throw in a bit of model theory... 
From: There, there. | Registered: Jun 2001
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DrConway
rabble-rouser
Babbler # 490
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posted 24 March 2003 05:25 PM
The only things I know about lambda are threefold:  1. Wavelength 2. It is the variable used to derive eigenvalues and eigenvectors. 3. It is used to set-up Lagrange multiplier optimization problems.
From: You shall not side with the great against the powerless. | Registered: May 2001
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