In discussing the Edge question of the year yesterday, SC set aside one article for separate discussion, because it's the only one that he can really claim deep professional expertise in. That would be Marti Hearst's assertion that "The Search Problem is solvable".
As a matter of believing something that can't be proved, this isn't exactly a strong claim. Your host doesn't doubt it in the slightest, depending on what is meant by the "Search Problem", which is rather ill-posed. Reading Prof. Hearst's extended comments, it's clear that there are actually several different problems under discussion.
The problem that SC takes for granted as ultimately solvable is "Advances in computational linguistics and user interface design will eventually enable people to find answers to any question they have, so long as the answer is encoded in textual form and stored in a publicly accessible location." As far as your host is concerned, this is reasonably close to true already as long as you're looking for something in English, and have a little patience in combing through Google's results. The best answer isn't always on the first page, but SC would wager that if you've got a question that you can't answer with Google + patience, it probably doesn't meet one of the two conditions Prof. Hearst laid down.
But then there's another version of the problem, implied in a statement Prof. Hearst makes about translation systems. She didn't restrict her original posing of the problem to English, and this belief requires a bit more faith than the previous one. Cross-lingual information retrieval is not at all up to the standards of monolingual information retrieval; the last time it was evaluated at TREC (Text REtrieval Conference), the benchmark of success was getting back documents on the same topic, not necessarily answering specific questions. Defining the task is an ongoing problem; see the Cross-Language Evaluation Forum's homepage for current work.
Another version of the problem is what we might call the "answer on a plate" goal, or, "Google + patience, minus patience". Question-answering is the technical term, and that's a field that's advancing rapidly (again, in the monolingual English context; here's the TREC page). But unlike the goal of being able to get documents on a given topic across languages, it's less clear that question-answering is important to search. If I pull up Google because I want to know the total land surface of the Hawaiian islands, that's a case where a question-answering system would improve on having to read through a page full of links. If I just want to read about Hawaii, though, and don't have a specific question, then it's not clear that Google doesn't already represent a satisfactory solution.
One area that Prof. Hearst pays considerable attention to is the notion of user interface design. Strictly speaking, this doesn't affect the problem of finding answers to questions. But it does affect the happiness of users. She's quite right to point out that search engine providers have "enormous, albeit somewhat impoverished, repositories of information about how people ask for information". Any blogger who looks at their referral logs knows that there are a wide range of ways in which people reach the same pages. Some people seem comfortable feeding Google whole questions in natural language, even though they have to know by now that Google will strip the punctuation out and many grammatical-function words. Other people just put in a list of terms with no operators. Some people (like SC) insist on explicit operators before every term in a query, even though they may not always be necessary (if you aren't using "-", it really doesn't matter much). Some people always use grammatical phrases, and some people put their terms in apparently random order. Google is probably using the most robust technique to handle all these variations -- throw out everything but keywords -- but people wouldn't use all these different variations if they weren't expressing (sometimes subtle) differences in how they wished they interacted with search engines.
Like SC (see here), Prof. Hearst is skeptical about the Semantic Web -- but she seems fairly positive on the contribution that ontologies can make to search engines. Your host is only half-sure about this -- while he likes ontology-building, and believes it has all sorts of uses, it's not clear to him what purpose ontologies serve in searching unless it's for Semantic Web-like uses. If you have a comprehensive organization of concepts that's only relevant to you and perhaps some particular community of interest, then it can't be useful for browsing the data put out by other people and communities.
Finally, Prof. Hearst suggests that ultimately, we'll want something better than the text box interface for searching. SC isn't so sure about that. It's the simplest user interface possible -- much like the command lines that SC vastly prefers to rodent-based window systems -- and in SC's opinion, that makes it attractive to users of all levels of technical competence. The presentation of results might be improvable in some respects, but unless this sort of thing is your idea of an improvement, SC isn't sure that pages full of links will ever be wholly replaced. On the other hand, Prof. Hearst has some interesting demos up that represent useful enhancements to the basic text-box paradigm. You can see the ontology at work underneath her projects, which means the technology can't be transferred without considerable new effort. But maybe that's not such a bad thing. Maybe the real future is in meta-search engines that then direct you to purpose-built search engines which are more robustly engineered for what you're really interested in. The history of search engine development so far is the development of bigger and better general-purpose techniques for culling information from essentially universal databases. Looking at how elegant Prof. Hearst's work is when it's restricted to one domain, though, it might have been more daring for her predict the demise of general-purpose search engines.
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