CONCEPT
Shannon's Amplifier Theorem
The mathematical result — implicit in Shannon's framework — that no device operating on a signal can improve the signal-to-noise ratio of that signal; amplification increases power but cannot distinguish signal from noise, because the distinction is a property of the sender's intention.
An amplifier increases the power of a signal. It does not distinguish between signal and noise, because the distinction between signal and noise is not a property of the waveform — it is a property of the sender's intention, which the amplifier cannot access. The consequence is a hard mathematical constraint: no amplifier, however sophisticated, can improve the signal-to-noise ratio of what it receives. In the human-AI collaboration, this theorem is the mathematical foundation beneath Segal's central claim in You On AI: AI amplifies what it is given, and no improvement to the model can overcome a low-quality input. The quality of the output is bounded above by the quality of the input. The ratio cannot be raised by the machine; it can only be raised by the human at the source.
In The You On AI Field Guide
The result follows from basic circuit analysis. A real amplifier multiplies its input by
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