re: #777 lostlakehiker

The bottom does not fall out. Mathematics is the art and science of knowing something about what logically follows from what. What Goedel observed is that mathematics is not powerful enough to let us know EVERYTHING that is mathematically true. There will be some things that are true even though we cannot prove them.

That’s par for the course. There are physics observations we cannot make. Chemistry experiments we cannot conduct. And the reach of human folly and majesty, we aren’t going to understand either, because that too is self referential. If we were bright enough to understand each other, we’d be too bright to be understood by each other.

The difference between Heisenberg’s Uncertainty Principle and Godel’s Incompleteness Theorem, besides their area of application, is that Heisenbergian Uncertainty is a pragmatic and physical constraint dictated by the limitations of the means of measurement available to us (light waves of various frequencies and energy levels and their unavoidable effects upon very small objects), while Godelian Incompleteness is a theoretical constraint built into the very fabric of self-referential systems.