WolframAlpha is a "computational knowledge engine" rather than a general search engine. It doesn’t just aggregate url’s and match keywords. Instead, it seeks to find relevant answers to real questions using its internal collection of equations, facts, comparisons, and figures. If you put in "weather NYC" it doesn’t just find pages that have those words and show them to you, hoping those pages contain what you are looking for. It understands that you are looking for weather information about New York, and offers you a view of the actual data rather than pages that contain it.

Where Google might be equivalent to asking a librarian "which books contain information about weather, specifically about New York?", WolframAlpha is more like asking a weatherman from New York what the weather is like there. Big difference.

Topsy.com is a search engine trying to capitalize on the popularity of Twitter. Instead of scouring the web for all web pages it can find and indexing the words on each page, it "listens" to all tweets on Twitter and pulls out the keywords and url’s posted with them. It associates the words with the url and aggregates the results.

Searching Topsy for "weather nyc" gives you back nothing useful. But that’s because it’s not meant for that. Instead, Topsy is a view into pop culture and the stream of public consciousness. Searching Topsy for "obama" won’t give you a summary of the President’s actions or all the important news of the day. It will give you a view into what url’s people think are interesting and related to Obama right now. It will also show you who is mentioning the search terms, how many there are, etc. This is a great way to monitor a brand, a current event or issue, or a technology. These things will be tweeted about often, and the way Topsy aggregates the information and presents it can be very interesting.