If the two generals problem is unsolvable how can we human beings agree on things?

If the two generals problem is unsolvable how can we human beings agree on things?

I mean, we communicate everyday and have the same limitations as any communication problem handled by computer science. Why doesn’t it affect us?

Answer

I disagree with other answers that the communication channel needs to be modelled differently. Malice is irrelevant, simple lost messages with any non-zero probability are sufficient to create the two generals problem. e-mail and IM, for example, have a low but not zero chance of dropping messages. Phone calls can suffer interference, so as with the two generals problem you need to somehow confirm whether the other person heard what you said, ad infinitum. And yet I frequently use these channels to make agreements with other people.

What the insoluble “two generals” problem fails to solve, is to get guaranteed common knowledge. In real life we don’t require formal common knowledge in order to proceed. Therefore the goal in most practical situations needs to be described differently from the goal in the two generals problem.

We settle for agreement being “sufficiently likely”. I might not be willing to attack unless I’m certain you will attack, but I’m willing to walk to the coffee shop to meet you provided that the probability of a communications failure isn’t grossly higher than the probability of you failing to arrive due to traffic. Unlike the generals, I’ll take a chance on you meeting me.

If you’ve ever had someone explain something three times to you in different ways when you got it the first time, or ever had someone ask you to confirm something that you’ve already confirmed twice, then it’s because you reached your threshold of “sufficiently likely” before they reached theirs.

Take your pick of psychology, philosophy, or evolutionary biology as the correct realm in which to look for an answer to the next question, why we don’t really need a full guarantee of common knowledge 🙂

It also relates back to practical problems in computing. For example when we use a single-error-correcting code to “validate” that a symbol in a message has arrived correctly, all we’re doing is accepting that the probability of a double-error is negligible for the time being. Then later in the protocol we might have a CRC, to further reduce the probability of undetected error. None of this solves the two generals problem, but it is sufficient for me, my bank and a merchant all to “agree” that a credit card transaction has occurred, with a small probability that we disagree.

Attribution
Source : Link , Question Author : user1508072 , Answer Author : Steve Jessop

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