This post on Scott Aaronson’s weblog is every internet discussion thread in microcosm (except for ours, which are shockingly polite by internet standards). Scott thought he was explaining the notion of non-constructive proof to a dense but argumentative student. If you read the comment thread, though, you’ll discover that the “student” thought Scott was some sort of nut who imagined he’d invented a computer more powerful than a Turing machine.

That actually made my day.

That one is rather harmless, still. When I started reading science blogs and forums a few years ago, I remember being very intimidated by the behemoth Bogdanov-related threads in which dozens of people with rather spectacular differences in proficiency would take part. Insults, accusations of “intellectual bankruptcy” and “dubious credentials”, phony proofs and counterexamples, all you had to do is ask.

There’s an important point there. More and more people have computation as their model for mathematics and so they have difficulty with the notion of an existence proof. Confusing “there exists…” with “here is a construction of…” is not at all unusual.

“More and more people have computation as their model for mathematics . . .”So Brouwer may have won his argument by default!

Never having heard of an Oracle is the shocking part. How could NP have even been explained to this person?