"If someone tells you a fact you already know, they’ve essentially told you nothing at all."<p>I think it's interesting to consider how this is/is not true in a real life context.<p>If someone tells you a fact you already know, then it could be communicating several different things.<p><pre><code> 1. It might mean *they think* you don't know it.
2. It might mean they want to make sure *you know* they know you know it.
3. It might mean they believe you know it and want to communicate they agree.
4. It might mean they are hoping for you to (or not to) contradict/argue/refute it.
</code></pre>
If, however, you can't tell which of those (or some other alternative) is intended, <i>then</i> no information was communicated at all.<p>Except...there is a message communicated that they have <i>some</i> interest or concern regarding the topic, which is different from remaining silent.<p>Whenever someone says <i>anything</i>, true, false, nonsense, lie, they are communicating a true and possibly significant fact - that they chose to say that thing, in whatever circumstance.<p>I am thinking of "Gödel, Escher, Bach", if you can't tell.