**Radio Programs, Set Theory
and Individuals**

**5/27/08**

I was
listening to a National Public Radio program today, *Talk of the Nation*,
and the hosts were discussing various topics with guests, and encouraging
listeners to phone in or email them. The programs motif so to speak is based on
allowing listeners to be *heard* by as the name implies--the whole country
at large. But, as I listened to the callers that actually were put on air, an
idea of how many listeners actually could be heard on this program began to
form in my mind. The fact is very few listeners actually get the chance to *speak
to the nation.* This fact is not very hard to see. Lets take a fictitious
example to illustrate it.

We have a
radio called *You might get on the air. *It has 10,000 listeners. Now lets
see how many of that 10,000 can speak to the nation in one hour.

Radio *You
might get on the air* =10000 listeners

Maximum number of listeners that can speak per minute if we assume the whole hour is devoted to listeners speaking is

10000/60=166 listeners per minute. This is a limit that the program will never reach. It is clear the 166 people couldn’t be broadcasted in series speaking in one minute.

But course listeners aren’t given 1 minute speak each, so lets say we assume that each listener is given (at minimum) 10 seconds to speak. Ignoring access time, credits (even public radio has beginning and ending credits, though no commercials), we can see that if 10 seconds per call was the limit then we have:

10 sec *6=60
seconds which equals 1 minute, thus 6 callers speak per minute. 6 calls per
minute * 60 = 360 callers get to speak on *You might get on air*.

The
percentage becomes 360/10000=4% (approx) spoke on air on Radio program *You
might get on the air*.

These
percentages are also the probabilities of your getting to speak. It is
undeniably clear from this simple arithmetic that most of the people listening
to *You might get on air *are never heard when they attempt to call in.
And the fact is that most radio programs like this one that is nationwide have
many more than 10,000 listeners. Also, note I'm telling the probability if the
entire hour were devoted to listeners calling in. Of course, it's not. If we
factor in the time the hosts take running their mouths, the probability is even
less. You just have to count how many people you hear on air during a program
like *Talk of the Nation* and do the arithmetic with an appropriate guess
of how large the listening audience is, to see--very, I repeat very few are
heard by the nation at large. My count is about 6 to 7 at most! I need to
qualify the analysis just given. First, I am sure there are those who will cry
no! no! no! He's wrong. Suppose only
500 of the 10,000 attempt to call in, then the odds are much better? I've thought of these objections too, and
looked at what I project with differing numbers and probabilities, but still
the percentage is small and another example illustrates. If only 500 of a
possible audience size 10,000 attempts to call, and we assume that say
maybe...uh 30 minutes of the 60 are given over to call-ins, then we have the
probability of any one of the 30 getting to speak as 30/500=6% per minute. That's
not a good chance again. The only way to increase the probability of a caller
getting on air, is to increase the time allotted to call-ins, or a decrement in
number of calls coming in. Both changes are unlikely in my opinion. But, on the
rare occasions when the topic is uninteresting and few call in, then more are
heard. The greatest probability would be if only 30 callers phone in the 30
minutes, then every caller should be heard if we ignore the obvious
constraints, access time, the screeners querying you before going on air, etc.
But, that is not likely. I have heard on many PBS radio programs that have
contests where you can submit an answer to a question they ask on weekly
broadcast, that they receive thousands of emails and calls. This is analogous
to the numbers of callers phoning in during these programs. So, fiddling the
numbers of my above estimation doesn't change the conclusion: most people are
not heard on air. The producers, hosts,
and all others connected with these programs know this! For them to suggest
their program as some kind of vehicle for you, the individual to be heard by
the whole country is such a lie it makes me angry. And its even worst than the
simple arithmetic implies, if you don’t play the game their way, even if you
are chosen you wont have the chance to speak to the country. for instance if
you use profane language or expressing opinions they consider not appropriate
you STILL won’t have your cherished chance to speak to their 50,000 or so
listeners. It borders on false advertising to me. It is a lie that is foisted
upon listeners to tell them to call in and well let your voice be heard when
the probability at most (drawing from the fictional example above) is 4% that
they will be heard. Though I think its deceptive and unfair to make these false
attributions to listeners, I am much more interested in what the radio
broadcaster/listener experience implies about human relations. It should go
without saying that whatever I write about radio as a media will apply to any
other *one-to-many relationship*, such as TV, the Net, magazines,
newspapers. We will see using database theory terms and set theory methods,
that individuals have a special relationship with the multitude.

As
individuals we are anonymous to the broadcasting world of radio. Of course,
they have all sorts of sophisticated methods of knowing us in general. They
typify us by race, age, stations we listen to, income, geography, consumption
patterns, sex etc. Yet even with these data the broadcasters (I mean the entire
organization by that term) don’t know us as individuals. That is to say, when
we tune in a program, there is no person or persons there to see, oh that’s X,
who is now lighting a cigarette, and okay he told his wife to be quiet, and uh
he’s going to take a uh lemme see oh yeah he’s taking a piss before we start
broadcasting that's old X, he always takes his piss before listening to
us...etc. Thank the non-existent God they don't have that power yet, huh? No, we are for them the amorphous, anonymous
audience out there. We are the *Many *dialing into the *One*. The *One*
has the Godlike power to reach the multitude, while the *Many *is defined
by being a supplicating hoard seeking to speak to the *One.* Yes if you
noticed, this relationship is the same one that is characteristic of religious
experiences. When the *Many *at last finds and can talk to the *One*,
well what happens then? This is equivalent in the radio example to a caller
having his chance to talk to the nation.

If you’ve
ever had the experience of being chosen to give your opinion on a call-in radio
show, you’ll no doubt know that it’s an overwhelming one. When you hear your name announced on some
radio program from such and such place, and then the hosts ask you to speak,
you are at first shocked to hear your NAME called out and knowing you will be
speaking to tens of thousands of people, you are nervous and apprehensive. If
you pull it off, you feel a sense of worth and accomplishment. What has really
happened in these cases is the *many* has become a part of the *one*.
You, the individual for those brief seconds, become like the radio show host,
touching the multitude out *there*. You feel something akin to *stage
fright*, your voice may crack, and you might ramble, and completely forget
what you had composed in your head, that important point you were going to
make, it now seems so small. Or contrarily, you may take control of yourself
and speak clearly, and put your point across eloquently. In either case, you
feel as if you’ve been given a power: the power to communicate with some many,
many others. And you also sense something comes with this. You lose you
anonymity in doing this. You are not a private person any longer. This is
disturbing to you. And why is that?

We are, all
of us private beings. We share the knowledge of our private states of mind, by
choice. We think in our heads and have experiences only known to us. Privacy is
a part of our existence we have from birth. The child sliding out of its
mother’s womb is a child experiencing that occurrence alone. That same child
while in the womb, if it has a rudimentary thought process anything like it
will have as an adult *its still doing this alone*. Even its mother
carrying it doesn’t know that it might be developing thoughts. So you see, we
are by our very nature as living beings in this world-alone. And to be alone
means to be private. Not even a most fundamental bond like that of the pregnant
mother to her infant can break that necessary divide of being a living thing
alone and private unto itself. Is it any wonder that when we are called upon to
share ourselves through something like a radio broadcast, we feel a cringing in
ourselves?

Then there
is this need we feel to communicate with others. We are unto ourselves a unified agency of states of mind. Still,
we do want to know others and communicate with them. I would venture to say,
most of us want to touch many others too. We want to be heard, by the *many*
if you will as the *one*. Most of the time, we only want to communicate as
a *one-on-one* relationship. Again another term from database theory, I’m
using. We meet and know others as individuals like ourselves, and are
themselves alone as human beings in this world. So what would ever make us want
to know more than our individuated experiences can offer? It is the social
nature of our being in the world that does this.

We are mix of several types. Humanity is not one individual or type of individual. We are in our genetic combinations so many types (members) of one set. The human set, which is outward and forming new relationships, and thus new sets from its generating set, is a process that defines our social world. This behavior in human beings makes me think we are somehow doing this from something more basic. Lets see if we can build a model of human communications as a relationship of sets, then apply it to the radio broadcast example above.

If we take
the set of integers, {0, 1,2, 3∞}, then the only element of that set that
under the operation of + has relation to every other member of that set is 0.
And every element of the integer set has a *one-to-many* relationship with
the number 0 called Identity. So, 0 is like the broadcaster above, and we are
like the other integers. The problem here, is when we call 0, we get ourselves
as the result. This is a very simple set with rules that map in a way that the
broadcaster never lets the members in the set talk to anyone but themselves.
Not a very fruitful example. So, lets consider a set relation that widens the
field and somewhat approximates the radio call-in experience. Logarithms of
base 10 can capture this idea.

Consider the series below:

0 log 10= 1

1 log 10 =10

2 log 10 =100

3 log 10 = 1000

4 log 10 = 10000

It is clear if we keep going on a set integers would be produced from increasing powers of the logarithms of these base 10 numbers. It is also clear that series would be the set of integers. Now go back to my original example. If we consider the callers as the result of a logarithmic set, then we have the following equation.

F(x) =xlog_{10}

This set
would generate every integer to infinity for powers of 10. What does this mean?
It means in simple terms, smaller numbers would be mapped to larger numbers.
This mapping approximates the *one-to-many*
nature of radio broadcasting.

For example take 4 log 10 = 10000. We could see this as indicating 4 people (the host and a small staff) communicate with 10,000. In this manner, the radio broadcast experience can be said to have a logarithmic relation. Though, to be more accurate about it, we’d probably have to change the base of the logarithm. But, there are other ways to capture the relationship between broadcaster and audience. Few examples will get us started.

Take the equation

F(x) =√x for x≠1 and x is an integer

This
relationship is a function for all integers greater than 1. In other words it
is a *one-to-one *mapping. This
relationship is said to be isomorphic, since every input begets a unique output
within the set of integers. This relationship is more like a conversation
between individuals than a broadcast. Though, one person starts all the
communicating, that is x starts conversations.

Composite
functions also approximate *one-to-one*
mappings, though less uniformly.

Take the equations

F(x) = 2x
+1/x^{2}

G(x)
=2(f(x)) +1=2(2x + 1/x^{2}) + 1= 4x +2/ x^{2} + 1= 2/x^{2}
+ 4x + 1

Here for every input to F(x) we get a unique output in G(x), often called the image of F(x). These sets are like the above isomorphic mapping and would be another person-to-person sort of communication. However a subclass of composition known as iteration is very much like an exchange in which one speaks and the other responds using the information that was given from the original speaker.

Take the iterative equation

F(F(x)) for F(x)= 1/√√x-1.
At 0, it’s *1*/√*i-1.
*And at 1 it’s *–1. *Beyond
these values, this equation is a real-valued function.

As a non-iterated function, this set approaches from the left the value of zero as shown below:

F(x) = 1/√x-1 = 0

_{Lim
x->∞}

Which means
conversation dies off between the two mapped sets. It would be like a *one-to-one *mapping, where one side stops
communicating.

Embedding this function in itself and taking its limit leads to again a slow slide to 0. F((F(x)) will take longer no doubt, but the conservation eventually dies off. It doesn’t help to keep iterating this function either. Try it and see. You still go to 0.

None of the above set mappings really captures what happens in the radio broadcast I started this article with. But there is way to make the exchange between the broadcaster and audience more symmetric.

We now come
back to the *one-to-many *set mapping
we started with using base 10 logs. But instead of base 10 logs we will use
base 2 logs. This set relation provides a much more realistic model of the
broadcaster to a wide audience for instance look at this:

F(x) = 20
log_{2 }= 1,048,576.

Now that is
much closer to the kind of relationship a show like *Talk of the Nation* has with its listeners. This mapping is
saying that a staff of 20 can reach 1,048,576, but they don’t talk back much.
So, now here is what I’ve been leading up to.

Why not let groups of listeners form sets
that can talk back to the broadcaster as groups. The broadcasters will of
course still decide what listeners will have the chance to speak, but the basis
for this decision is fair, and much more representative of the audience tuned
in. This model can be easily made with set theory methods.

We can use the base 2 log above to develop a model that would allow callers to radio programs like Talk of the Nation to voice their opinions in large numbers. The model utilizes the database theory idea of one-to-many, as I’ve described, but its converse, that is many-to-one. I must point out for my model to be realized, the radio shows producers would have to do more preparation to accommodate their mass of callers. Actually, it would take virtually an entire week before the broadcast airs for the shows producers to set-up what my model will illustrate. I don’t feel it is asking too much of them. After all, the program am I using to create my model claims to be the Talk of the Nation, thus it should attempt to allow its many callers to be heard.

Go on to next section Sets, Radio programs and Individuals

Ken Wais