To people who don't know what the parent is talking about.

Take a simple example.

http://en.wikipedia.org/wiki/Two_Generals_Problem

My summary:

The two generals problem proves that, if there exists any nonzero probability of packet loss, two people cannot even coordinate to both have a state 1 at sunrise tomorrow (attack!!!) or both have the state 0 if it is not 100% mathematically guaranteed that they both believe this has been coordinated (since an uncoordinated attack will be a catastrophic loss for them).

(In other words, the guarantee must be such that by sunrise tomorrow state 0-1 or 1-0, in other words one general thinking the attack has been coordinated with certitude and attacks, but the other general thinking the attack has not been confirmed with certitude and does not attack, must be a mathematical impossibility.)

Take a simple approach. The following packets are all encrypted, but any or all may be lost.

1) first general sends: "Let's both be in state 1 tomorrow (coordinated attack). Since an uncoordinated attack is so catastrophic to us, I will only enter state 1 if I receive your reply. Please include the random number 25984357892 in your reply. As soon as I get this the attack is ON. If I don't get such a packet within the hour I will assume this post was intercepted (lost), and I will send another. I will remain in state 0 until I receive that packet."

2) second general sends: "Got your packet with 25984357892. This is my acknowledgment! I will attack as well. In case you don't get this, I know you won't attack thinking I didn't get your message, so I am sending this message continuously."

Great. But what if all messages from the second to the first are intercepted. Now the first thinks all of HIS were intercepted (has received no acks) and doesn't attack, but the second one does. Failure.

So, we have to emend 2) to:

2) second general sends: "Got your packet with 25984357892. This is my acknowledgment! I will attack as well. In case you don't get this, I know you won't attack thinking I didn't get your message, so I am sending this message continuously. In case you don't get any of THESE messages, however, I will not attack. Therefore acknowledge ANY of them with random number 458972984323..."

Ooops. What if all the first general's ack's of the acks are intercepted or lost? (Perhaps the first general is able to send messages until receiving (2), but just as the first general gets 2) conditions change and the general no longer has any of his messages delivered.)

Now the first general thinks he has acknowledged the ack, but the second general doesn't even know if his ack-(cum-request-for-an-ack-back) message was even delivered...

and so it goes...

Of course, in practice you can simply say: "Let's do this for a certain number of acks of acks of acks, 3 let's say, and then just keep sending the same ack to each other, assuming that if the connection was reliable enough to get to three deep, then it will be reliable enough for one of the final acks to make it through." That's a false assumption (mathematically - what guarantee do you have that if 3 of your encrypted messages made it across, at least one of the next 217 that you send by sunrise all with the same message will), but a reasonable one.

So it is not a practical problem. This is a mathematical problem. Although you cannot even do something as simple as "let's agree to both be in state 1 (or neither if we fail to agree), OK?" over a less than guaranteed reliable connection, if the connection has any reliability at all you can get to within a practical level.

once you reliaze that, PROVABLY, you can't even do the most mundane things no matter what, the mathematics the parent is talking about do not seem all that interesting anymore. :)