Alice and Bob, both logicians, met at the company coffee bar just before Covid struck. Both wanted to see each other again, but safety is paramount, so they agreed to meet for lunch outdoors, at a safe social distance, in a local park.
Being detail oriented both instantly realized that they would need a way to cancel just in case of a rainy day (unlikely in Silicon Valley, but not impossible). This led to the following plan: Alice, who was in the habit of checking the weather each morning, would email Bob if conditions looked good. Bob, a late riser, would confirm her email (once he was awake and read it), and on this basis they could be sure to actually go forward with the plan only if the skies would be blue, the birds happily chirping, and only if both were definitely aware that the rendezvous was on.
Months later, they happened upon one another in Trader Joe’s, and it was love. Yet they had never once managed to meet on a lunch date, although it had been sunny without exception for the entire time since their first meeting! Your task is to explain why this happened.
This being a puzzle, it wouldn’t be right for me to go ahead and solve it for you, but I should provide a little more information. First, it may help to know that although both followed the protocol to the letter, neither was the kind of person to engage in useless activities. And thus Alice had never once sent Bob an email confirming the promising weather. Bob, who fully appreciated Alice’s dilemma, didn’t blame her: after all, he could easily confirm her reasoning. Indeed, they both quickly concluded that it is impossible for committed logicians to meet for a lunch date, and this shared insight only increased their affection!
As Bob explained it later, when Alice failed to send that first email, he realized that she was the one.
Explain their conclusion. Is there a protocol that would have worked? If you need a hint, I recommend watching the Princess Bride: a wonderful family-friendly holiday movie that just happens to feature a related puzzle!
I’ll have a bit more to say about the answer and what it teaches us about distributed systems in a week. (As for Alice and Bob, no worries. They’ve set a date for the wedding, and plan for it to go forward rain or shine!)
A problem in temporal logic? Each can comfirm the conditions at the moment of checking and no farther. After every round of communication the problem of whether it will rain remains as unresolved as at the start of the day. Yes, the window of uncertainty is narrowing but so is the time remaining to conclude the protocol. Realizing this, A did not waste B's time, and knowing A's reasoning, B didn't expect any different.
ReplyDeleteAlice knew that their methodology to reach consensus was flawed. She, realizing that there's no solution to "Two Generals Problem", didn't send message to Bob. Bob also knew this and trusted Alice's reasoning.
ReplyDeleteBoth Alice and Bob had the following logical activities assigned as per their plan:
ReplyDeleteAlice: Send email confirming good weather
Bob: Read and confirm/Acknowledge the email
Alice and Bob: Go and meet for lunch.
However nothing was decided upon who would initiate the request (or initiate the thought of going on a lunch date on a particular day)? since neither Alice nor Bob were the kind of people who would engage in useless (I am reading this as undefined) activities, hence the email never happened.