Terence Tao on Nostr: Finally, mathematical negative results can provide theoretical upper bounds for ...

Finally, mathematical negative results can provide theoretical upper bounds for various desirable outcomes, which can then provide targets for practical designs. Energy conservation prevents energy efficiency from exceeding 100%, but instead sets the target goal of getting as close to 100% as possible. Information theory sets theoretical limits on the communication capacity or error-correcting capacity of a channel, but again this sets the very useful target goal of developing compression and encoding protocols that come close to such limits. And so forth. It is only through the combination of both positive and negative results that we can fully understand and exploit the space of possibilities. (7/7)