the nature of information

Today’s lesson: What does “information” mean? How do you know when something has “information”? And how can you prove that radio shows like Sean Hannity’s and Rush Limbaugh’s have none?

Pattern and RedundancyTextbooks will tell you that information is “pattern” or “redundancy,” but it is a particular kind of redundancy.

Information is always about something. Information happens when looking at one thing (let’s call it a “message”) allows you to come to a conclusion about another thing (let’s call it the “topic”).

When someone utters the words “I am happy”, those words contain information. The reason the words contain information is that hearing the words allow you to conclude something about a person’s internal emotional state. You can’t directly experience someone else’s emotions, but you can conclude something about the person’s emotions based on the person’s words. The person’s words therefore contain information about the person’s emotional state: the words are the message, the emotional state is the topic.

Information doesn’t have to be man-made, or even intentional. You know the expression “where there’s smoke, there’s fire.” The fact that you can guess the likely presence of fire when you see smoke means that the smoke contains information about the presence of fire. The smoke is the message; the topic is the fire.

For information to exist, there has to be variability in both the message and the topic, and they have to vary together. It is this “co-variation” between the message and the topic that allows information to exist.

Think about it this way: the only reason the words “I am happy” contain information at all is that sometimes you are happy and sometimes you are not, and on those occasions when you are happy you say “I am happy” and on those occasions when you are not happy you do not say it. If you said “I am happy” all the time, regardless of how you felt, people would quickly learn that they could not be sure of what your feelings were based on your words: your words would contain no information.

If your dog only barks when there is someone trying to break into your apartment, then the dog bark contains information about whether there is an intruder around. If your dog barks all the time, then that bark contains no information.

Obviously, there can be varying degrees of information and varying strengths of certainty and the whole matter can become quite complex. There are in fact entire sub-fields of mathematics and science dedicated to studying information. But this basic principle of variation and co-variation applies no matter what kind of information you are talking about:

  • MP3 files contain information about music because you can figure out the sounds of the song based on the electronic bits in the MP3 file. (Of course, when I say “you can figure out” what I mean is “your MP3 player can figure out”… that’s how it converts the file from bits to music in order to play the song for you.)
  • A guy’s gaze at the bar contains information about who he is attracted to because you can get an idea of who he is attracted to by looking at who his eyes linger on. (This is a good example of “imperfect information”, though, since he also might look at people who are dressed strangely.)
  • A stop sign on a street corner contains information about the legal proscriptions about what you do when you come to that corner in your vehicle, which in turn contains information about how a policeman might act if you don’t follow that rule.

In all of these cases, the information only exists because there is variation. If stop signs existed on all street corners, even on those corners where you didn’t have to stop, then they would contain no information. If you really want to make sure that nobody knows who you are attracted to at a bar, then you look at everyone for exactly the same amount of time: that way, your gaze will contain no information about who you are attracted to.


What does this have to do with talk radio?

I listen to Sean Hannity’s and Rush Limbaugh’s radio shows regularly, and every time they criticize something that the President has done I ask myself: “If the President had done the opposite thing, would this talk radio host have complimented the President’s actions?”

Now of course this gets into the realm of hypotheticals. You can never prove an argument based on a belief about “what would have happened if….” However, it takes very little imagination to consider these scenarios:

Sean Hannity says President Obama hesitated too long before speaking up about Lybia. If President Obama had spoken out immediately, would Mr. Hannity have said “Good job!” or would he have criticized the President for jumping in without thinking?

During the first year of President Obama’s presidency, Sean Hannity said that President Obama was trying to do “too much”. If President Obama had picked just one or two things to do, would Sean Hannity have complimented him for his focus? Or would he have critcized him for neglecting things?

Rush Limbaugh criticized President Obama for not going to Wisconsin to support the protesters. If the President had gone, would Rush have complimented him for his consistent ideology and for standing up for his beliefs? Or would he have criticized the President for getting involved in a state issue?

Rush Limbaugh said that the health care bill was unreasonably long and detailed. If the bill had been shorter than the average bill, would Rush have complimented the President on his pith and precision? Or would he have criticized the bill for being too general, too under-specified, or too vague?


Of course, hypotheticals can’t be proven. But what do you think?

I think that Sean Hannity’s and Rush Limbaugh’s criticisms contain no information. For any scenario we have seen so far, they have criticized the president when he did A and they would have criticized him had he done not A. When he talks about defense they criticize him for not talking about jobs, and when he talks about jobs they criticize him for not supporting our allies overseas. Their radio shows fail the test of information: If I told you, “Sean Hannity thinks the president gave the wrong response to the crisis in Japan,” would you be able to tell—based on that—what the president did?

Of course not. Sean would have said that any response was wrong, as long as the President did it. He is like the dog that barks all the time. The sounds are there: but there is no information.