I hear your concern for our future engineers! They should have the best educational opportunities we can offer them, and I'm not it! Fortunately, I have no plans to go into teaching. Rather, I thought that the context of the discussion up to that point was sufficient to make clear what I meant by "sin^2x + cos^2x = 1", and not imply anything "= 0" that doesn't. Unfortunately, I've noticed the conversation drifting from the point I was trying to make (which I was making an effort to support). I meant to be addressing...

Pointer to connected thread

The car does have a speed module that happens to be a good analog for a hypothetical free-will module in humans. The speedometer produces an output based on the internal workings of the vehicle. It is also an excellent example of how maps can give outputs that are not necessarily grounded in the state of the territory.

How many conditions can you think of where a driver should ignore the report of the speedometer?

It sounds like you put a higher weight of probability on "meditators can turn off or ignore a brain module that let's them sense their free will" than "meditators can learn to turn off or ignore a brain module that applies a narrative of free will to a deterministic process".

Is that correct? If so, why?

When performing first aid, you must never leave a patient until you have passed them off to someone more qualified than yourself.

How did I get almost 40 years into my life before encountering these words?! Seems like they should be engraved on the box of every first aid kit ever. I spent a few years with the freaking Boy Scouts, for crying out loud, and nobody ever explicitly taught this!

(I notice I am confused) ... (and a little angry)

Absent the preferred evidence, we have to work with what we've got. Dentists keep detailed records on their clients, including notes related to their medical situation so that they know e.g. "Alice has [condition] and should get this kind of care but not that.". Look at the state of evidence regarding flossing and gum health: I remember reading that the statement "flossing is good for your gums" is supported by exactly one study that's over 50 years old and followed a dozen people for two weeks, then had them self-report their flossing habits over that time. That's terrible, but my hygienist can accurately divine if I've been flossing or not just by looking at my gums for about 2 seconds, and I have less pain and taste less blood during cleanings if I have been.

Some of dentistry certainly might have developed how it did because somebody thought it seemed like a good idea at the time and nobody's had the good sense to check the facts. But, absent studies, I don't have another way that's quite as robust of discerning that stuff from the dentistry that represents over a century of increasingly trained medical specialists noticing that their patients get better when they do X. And neither category represents a guarantee that a practice is good or bad for my health and wellbeing, nor does it identify short-term-gain-long-term-loss situations. So I have to treat everything my dentist says as at least slightly sus; but for a slightly sus claim about (e.g.) how taking care of my teeth and gums (which are connected to the blood supply) for a couple minutes every day can reduce my risk of heart problems later in life, the risk is large enough and the cost is small enough that I'm willing to brush, floss, and use that gum stimulator thinggie to get at the back surfaces where my wisdom teeth used to be every night just in case the claim is correct.

"Unsupported by science" doesn't necessarily mean a practice is bad or a claim is wrong. It can also mean simply that nobody has bothered to publish a paper in the subject. I can think of a few simple reasons why that might be the case, and there are probably more.

• Nobody who might publish new research has really been interested in the topic before now
• Scientific journals aren't publishing that sort of thing for whatever internal reasons they have
• The claim seems so obviously true/false that nobody feels it's worth their time to actually do the study
• There's a small pool of existent literature that tends to cause people to extrapolate a larger scientific presence whose lack of actual existence has gone largely unnoticed, at least by those who might do something about it

You're absolutely correct to ask the questions and investigate the answers. And there comes a point where you've collected all the available evidence and you have to decide if a procedure is right for you at this time. In the case of dentistry, the current best source of evidence in many cases is dentists. That's suboptimal for a bunch of reasons, but it's what we've got to work with. In the end, you choose whether to follow or ignore their advice, and you own the outcomes.

To address your clarifications:

Nobody seems to do proper studies on dentistry, so we don't have any gold standard evidence that I've ever seen. But, discounting institutional knowledge out of hand is foolhardy. I'd call the story the dentists tell about this "moderately strong" evidence for a causal connection, but (all together now!) more research is (obviously) needed.

I know a guy who had thyroid cancer. They took the gland out and he has to take a daily pill to replicate the function, but from about two weeks after the surgery I haven't heard him complain in the years since. So, seems manageable from a quality of life angle.

5. More logical still would be to have two periods, one marking the end of the quoted sentence and the other the end of the top-level sentence. But that would be redundant and also look ugly.

This style feels much better when the embedded sentence requires a different punctuation type than the parent sentence, such as "Don't you think?". I expect it only looks "ugly" because we don't typically see things done this way.

Big thanks for doing this for large magnitudes!