May 1, 2024

In Episode 12 of Carl Sagan's PBS television series Cosmos: A Personal Voyage, there was a famous sentence: "Extraordinary claims require extraordinary evidence." I quoted it in my recent video regarding UFOs. But when cross-checking, I noticed with surprise that the companion book of the series, Cosmos, doesn't have this sentence. This is the second time I encountered such kind of omission in books of this type (the first being in a Lawrence Krauss book), somewhat disappointing as a book lover.

As a reference, below are the television and book versions in comparison. Although the book version is not without its own merit, but what was omitted was by far the best sentence, the gem of the paragraph:

[Television Version] What counts is not what sounds plausible, not what we'd like to believe, not what one or two witnesses claim, but only what supported by hard evidence, rigorously and skeptically examined. Extraordinary claims require extraordinary evidence.

[Book Version] The critical issue is the quality of the purported evidence, rigorously and skeptically scrutinized ‒ not what sounds plausible, not the unsubstantiated testimony of one or two self-professed eyewitnesses.

May 9, 2024

Mathematics is best known for its certainty and strictness, both of which are unmatched in any other areas of human reasoning. It is therefore a big surprise to not only ordinary minds but most mathematicians that it can be proved that many, in fact most, mathematical systems have statements that can neither be proved nor disproved, and that one can't even prove what seems to be the prerequisite of the strictness, namely the consistency of those systems. These are called Gödel's incompleteness theorems in case you are curious.

What about the mathematical systems that are immune from those theorems? Will they stand out as the most interesting systems? Not at all! According to logician Hao Wang (in his book Reflections on Kurt Gödel), those systems are immune "only because so little can be expressed in it that its deductive power catches up with its expressive power.". Theoretical computer scientist Scott Aaronson (in his book Quantum Computing since Democritus) puts it in a different but equally discouraging way: "the only mathematical theories pompous enough to prove their own consistency are the ones that don’t have any consistency to brag about!".