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Yes, you can say it on the air. But should you?
Just last week I started teaching the "Communicating With Other Hams" section from the ARRL Ham Radio License Manual. Since this is the Technician course, I never assume that my students will know how to start and conduct an actual contact on the air. The contact has certain procedural requirements, of course. You need to follow the rules for identification, but aside from that FCC mandate, you do actually have very few restrictions on either what you say or how you say it. A basic contact consists of exchanging callsigns, signal reports, names, locations, and station information. If you are in a contest, you'll do a quick exchange of the required contest information and move on to the next contact. In a net, your contact time may be extended over most of the time the net is in operation, even though you may actually say very little unless you are called upon to handle traffic or do whatever it is the net is all about. In a casual conversation between stations or in a social net, the topic of conversation can vary widely and can go in any direction. It's always safe to talk about the weather, but maybe discussing photography or aviation may be your cup of tea. Go for it!
This brings me to the section in the book entitled "Appropriate Topics". It should go without saying, but indecent and obscene language is prohibited. This is the sort of thing that isn't really defined and is hard to enforce, but most of us generally have no trouble recognizing bad language when we hear it. Then there is the fatal triad: sex, religion, and politics. These three topics are deadly at the Thanksgiving day table because any one of them - or any combination - is guaranteed to offend someone and start a family feud. When I first started my ham radio career, one of the best pieces of advice I received was to avoid talking about sex, religion, or politics on the air. It was good advice then and is good advice now.
Just don't do it!
Yesterday I was listening to an early morning net on 75 meters, and some guy decided to tell a joke about a priest hearing confession and an Obama supporter. In a matter of a few seconds, he managed to offend a major religious group and anyone who voted for the President. This is bad, bad form. The venue - a popular, long-running net, should never have been the forum for this kind of thing, which included two of the three "don'ts": religion and politics.
What's the net control to do?
The introduction of topics in bad taste can put the Net Control Station in an uncomfortable position. Put yourself in the unenviable role of the NCS. You don't know whether to chastise the guy or just move on. It can be tricky, because you have to tread a fine line between blowing the incident out of proportion, thus calling even more attention to it and causing people to start choosing sides, or just doing nothing - which is an implicit acceptance of bad behavior on the net. Since every incident will be unique, it's hard to be ready with the appropriate response.
I would not be afraid to say, "Please avoid topics involving sex, religion, or politics on the (fill in the blank) net." This is a fairly benign reminder to your net participants that you do not welcome certain topics.
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