“In many cases we can do this and avoid the exponential blowup. Suppose you’re leading a platoon in single file through enemy territory in the dead of night, and you want to make sure that all your soldiers are still with you. You could stop and count them yourself, but that wastes too much time. A cleverer solution is to just ask the first soldier behind you: “How many soldiers are behind you?” Each soldier asks the next the same question, until the last one says “None.” The next-to-last soldier can now say “One,” and so on all the way back to the first soldier, with each soldier adding one to the number of soldiers behind him. Now you know how many soldiers are still with you, and you didn’t even have to stop. Siri uses the same idea to compute the probability that you just said, “Call the police” from the sounds it picked up from the microphone. Think of “Call the police” as a platoon of words marching across the page in single file. Police wants to know its probability, but for that it needs to know the probability of the; and the in turn needs to know the probability of call. So call computes its probability and passes it on to the, which does the same and passes the result to police. Now police knows its probability, duly influenced by every word in the sentence, but we never had to construct the full table of eight possibilities (the first word is call or isn’t, the second is the or isn’t, and the third is police or isn’t). In reality, Siri considers all words that could appear in each position, not just whether the first word is call or not and so on, but the algorithm is the same. Perhaps Siri thinks, based on the sounds, that the first word was either call or tell, the second was the or her, and the third was police or please. Individually, perhaps the most likely words are call, the, and please. But that forms the nonsensical sentence “Call the please,” so taking the other words into account, Siri concludes that the sentence is really “Call the police.” It makes the call, and with luck the police get to your house in time to catch the burglar.”