I mean something like the difference between, "You believe in UFOs?  You are deluded, my friend" and "Have you ever seen a UFO yourself?  You have?  Where was that?  What happened?" etc.

A false dichotomy. You forget that it is entirely possible to say "a bottle of beer says that what you saw was an optical illusion." It would be a sad world, were we left with a choice between uncritical rejection of personal experience and equally uncritical acceptance of it.

I think it is better to say that we cannot currently conjure up sensible models for what his happening--sensible to our understanding of spacetime...and here come the New Agers, saying that they don't have your understanding of spacetime...so the model (as they have understood it) makes sense to them...maybe...

You have just concisely described why people fall for newage bullshit. The problem, which has been explored at some length here and elsewhere, is that they have no model, and they have no concept of 'spacetime' - it's just a fancy word that they can use to give their text a superficial appearance of erudition.

The point being that the search for accurate measurement hits the "inner" wall, as Zeno's paradox hits the inner wall of infinite division...

Nonsense. We have hit no such wall, misguided allusions to Heisenberg uncertainty notwithstanding.

....to the point where it will even tunnel its way out--which should be impossible

Not at all impossible. It is a standard effect in wave mechanics and the equations describe it very elegantly.

These strange facts about nature (and I agree with DoDo's comment above, basically--that nature is stranger than strange) clearly tie nicely to people's various experiences of things happening that are "impossible"!  However, there is a lack of basic empirical data about these impossible events (e.g. ESP) [where I'll take "S" to mean our five senses], and what data there is points to no such impossible yet actually existent phenomena.

Key point: typically, people who are convinced of "unacceptable to science but nevertheless true" processes often don't know much about what science currently says regarding a particular topic.

Bingo. Can I nominate this for the 'most concise summary of the year' award?

This creates an imbalance--and I think the best scientific approach is to (kindly rather than angrily) point out where current scientific knowledge disagrees with their thoughts about what current scientific knowledge is

In principle I couldn't agree more. What is frustrating, however, is that those false impressions that we are supposed to be correcting are often so poorly formed as to be unintelligible - and hence incorrectable. 'Folk science' versions of quantum mechanics, in particular, can require years of study to shake off - and that's assuming that the student is interested in learning the non-folksy version in the first place! Throw in the emotional comfort of using folk science to underpin people's preferred mythology, and you have an industrial grade nightmare.

for those who aren't interested, I don't think judgements are necessary--unless there are claims that this development leads to "better" outcomes (or humans.)

Important take-home point!

I think this is what Jake was referring to the other day when he talked of the dangers of believing that, say, mass praying can prevent a cholera outbreak.

Something like that, yes.

However, this argument should only (I think) be aimed at those who are denying that water supplies should be kept uncontaminated.  In the same way, western medicine has much information about nervous systems, and it is worth arguing with a person who denies the results (e.g. about chemical and electrical interactions.)

I think it's worth pointing out whenever someone makes an unjustified claim. Tagging a 'this remedy should only be taken as a supplement to real medicine and cannot substitute for consulting a competent doctor' disclaimer on your bottle of homeopathic medicine magic water strikes me as dishonest and insincere: Either you think you can produce clinical effects - in which case you should submit your findings for clinical trials - or you do not think that you can produce clinical effects - in which case you shouldn't prey on the fears of ill people.

- Jake

If you only spend 20 minutes of the rest of your life on economics, go spend them here.