Using "~keyword" in a search has
nothing whatever to do with Latent Semantic Analysis. That's standard semantics, such as applied semantics, with nothing
latent about it.
The ~ operator is simply used to find synonyms and stem-variants of a given word.
Please tell me that your 37 ebooks on LSA do indeed know what LSA is, and what it is not.
This thread from the Search Engine Watch Forums discusses c-index methods for building up 'thesaurus' of related words by co-occurrence. As Orion states there, c-indexes date back to the 70s at least, and so far predate any existing search engine.
However, these too are mainly about 'active' semantics, not 'latent' semantics. Latent semantics are the things you only tend to spot from a distance, with fractals or some other plotting/graphing analysis.
The best way of explaining the difference might be to look at ways of blocking spam (such as emails).
If we use exact negative matching (allow no email that uses the word 'viagra' for example) this can get a wide range of false positives, blocking emails that were not actually spam at all.
Using semantics, we might look for variants of the word viagra, especially misspellings that are attempting to bypass the first kind of exact matching we just mentioned - like those that use "VlAGRA" (the I there is actually a lower-case L)
Latent semantics is the system that noted you could block over 70% of all spam by just blocking anything that used bold red exclaimation points as punctuation.

Bayesian spam filtering methods are far more along the line of latent semantics than most other systems.