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Two Generals

I was thinking about the problem regarding my communication with Austin, and it reminded me of The Two Generals' Problem.

It goes like this. There is a fortified encampment on the top of a hill. Let us call it Europe. To the left, is an army, an American army led by General Swartzkopf. And to the right is another army, a British army led by... does Britain have any Generals of note? Patton? No, he was American. Ah.. Admiral Nelson!

So here we have a diagram to illustrate the situation:

Two Generals

Now what Nelson and Swartzkopf both know is that together they can take down Europe. But individually, they don't stand a chance. The hill is more of a ridge, so the only way the armies can communicate is by sending a bloke with the message over the ridge and to the other army. This is a bronzepunk sort of universe where GPS and tanks don't exist, but awesome-looking medieval weapons do. Now, the problem is the runner taking the message has to cross the ridge. There's a reasonable chance that the messages will be intercepted, and the generals cannot necessarily rely on codes (look how well that did for Nazi Germany in the end).

Both armies have agreed to attack, for the only way to avoid being slaughtered is if the both come from each direction at the same time. The thing is, they have not agreed when this attack will take place. The two armies have to attack at exactly the same time, or Europe will slay one, then turn around and massacre the other.

The problem is, Swartzkopf and Nelson need to send messages to coordinate the attack. Simple, no?
Because it is not enough to send a message, the army can't commit itself until it is certain the other army will be there, and that certainty is a receipt of the message.

Nelson sends a message to Swartzkopf to say "we'll attack at 9am if you reply okay".
Swartzkopf will then reply "okay, we'll join you at 9am if you acknowledge".
Nelson: "9am it is then, if you respond".
And so it can continue, indefinitely.

Why? Let's look at a scenario:

  1. Nelson's first message gets through, but there is no reply. Thus, Nelson is not certain if his message was received and he doesn't want to lead his army to slaughter.
  2. Which is also a problem for Swartzkopf. For he did send a reply, but he does not know if this message got through. Should he attack and support Nelson? Or if the message was lost and Nelson holds back, would he be leading his army to certain death?

The logical ones among you might say why not have Swartzkopf send multiple confirmations so one ought to get through? There is no saying the message really will get through. Or, worse, that it won't be tampered. Europe could alter the message to "11am is a better time for us, let's kick ass then". This could cause hesitation, or - better - for both armies to conveniently attack in turn and be utterly decimated.

Yes, I know the meaning of "decimated". I'm using it in italics for ironic effect.

And so to my email to Austin. Which never received a response. Because it never got there. But how could I have been certain of that? I will reply, this time requesting a read receipt, but this is assuming his software supports and doesn't block such receipts. But if receipts are not supported, or are blocked, or he chooses not to allow it, I'll be back to square one. Austin, how does 9am suit you for attacking the city on the hill?


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