Simple sinusoidal wave can't convey information?

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Hello,

Here http://www.mathpages.com/home/kmath210/kmath210.htm it is written that "...in order to actually convey information, a signal cannot be a simple periodic wave...". I've met this statement in several other places too, this one is just for reference.

What does that mean that a simple sinusoidal periodic wave can't convey information?
 
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A "simple sinusoidal periodic wave" in this sense continues for all time (both in the past and in the future) with the same amplitude and frequency.

That might be different from a "common sense" idea of what the word "simple" means.
 
To convey information, you need at least two "words". One word gives no information - If your answer to every question was "yes", your answers would have no value at all, they would carry no information. A simple sine wave is like one word, it carries no information. If you had two possibilites, a sine wave or no sine wave, then you could transmit information, like "yes" or "no".
 
thanks for the answers.
thank you Rap, that explains it clearly