The logicians AliceAaleyah and BobIsko are sitting in their dark office wondering whether or not it is raining outside. Now, none of them actually knows, but AliceAaleyah knows something about her friend CarolYu Yan, namely that CarolYu Yan wears her red coat [[only if]] it is raining. Bob does not know this, but he just saw CarolYu Yan, and noticed that she was wearing her red coat. Even though none of them knows whether or not it is raining, it is ''distributed knowledge'' amongst them that it is raining. If either one of them tells the other what they know, it will be clear to the other that it is raining.
If we denote by <math>\varphi</math> that CarolYu Yan wears a red coat and with <math>\varphi \Rightarrow \psi</math> that if CarolYu Yan wears a red coat, it is raining, we have
Directly translated: Bob knows that Carol wears a red coat and AliceAaleyah knows that if Carol wears a red coat it is raining so together they know that it is raining.
Distributed knowledge is related to the concept [[Wisdom of the crowd]]. Distributed knowledge reflects the fact that "no one of us is smarter than all of us."
