This article on today’s MIT front page sketches an argument that I’ve been thinking about for a while, ever since the IBM Watson Jeopardy contest — that natural language processing is hopeless to the extent that there is additional context (side information) not visible to the machine.

Many prominent linguists … have argued that language is … poorly designed for communication [and] … point to the existence of ambiguity: In a system optimized for conveying information…, they argue, each word would have just one meaning. … Now, a group of MIT cognitive scientists has turned this idea on its head … [T]hey claim that ambiguity actually makes language more efficient, by allowing for the reuse of short, efficient sounds that listeners can easily disambiguate with the help of context.

Although this is just talking about homophonic ambiguity at the word level, the same applies to all levels of language, including full messages whose decoding requires potentially deep context.
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t-Mobile has these tiered refill cards for their prepaid mobile phones. The pricing table is here and reproduced below:

$10 for 30 minutes, expires in 90 days
$25 for 130 minutes, expires in 90 days
$40 for 208 minutes, expires in 90 days
$50 for 400 minutes, expires in 90 days
$100 for 1000 minutes, expires in 365 days

So which card should you buy? You could calculate a per minute cost and conclude that $100 for 1000 minutes is the most economical (plus it doesn’t expire for the longest time). Wrong!

It depends on how much you use the phone. The fact that the minutes expire makes the prepaid plan a virtual monthly plan in the regime where you do not use 1000 or more minutes per year, which is highly likely for people who choose prepaid phones to begin with (e.g. temporary visitors, odd occasions, emergencies, etc.). The constraint in that case is the expiration, not the number of minutes. If you blindly purchased $100 refills one after another, you’d have more and more unused minutes piling up. Sure, you could still use them, but even at $0.10/min. it is expensive compared to a straight monthly plan if you really mean to call that much. Of course you don’t, so now what?
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