Even with a small degree difference, you can do the trig to show the bowling ball would hit first.

I don't mind approximations. At all. It just should be presented in the full form, with the note you can drop the mass of one object from the equation when it is dominated by the other mass. This way people won't learn bad physics.

First....nice, nice.
Second. I get your point. They should have been more clear that they are intentionally ignoring any other forces, such as the force exerted by the objects on the planet and each other, and the pull of the observer, and the pull of the milky way, the sun, the moon, Venus, etc. Because those forces are completely inobservable, even with top notch equipment, it's simpler for most to not mention them at all. They have no bearing on what they're teaching, and the smart children who see farther into the details are smart enough to know what this experiment is designed to show, and what it ignores....or at least smart enough to ask the right questions, while the less science/math minded would only be confused by the mention of them while also ignoring them. it's not exactly the same thing as teaching that 5/0=0, when it's really infinity, the exact opposite of 0.

This experiment was about what's observable, not what's mathematically provable at the tiniest detail level. Those details are for higher level physics. I will agree, it's a disservice to not mention that clearly, but I think it's implied by the parameters and the intent (teaching that acceleration due to gravity is independent of mass).
EDIT: Also, please remember that for all intents and purposes, they are releasing the objects from the same point, so they still 'hit' at 'exactly' the same time because their forces are in line, off by what, perhaps <.0000000001deg?. As you said, all solved by equivocating 'exactly' to 'nearly exactly' or 'approximately the same' or even 'observably exactly the same time'.

Technically correct is the best kind of correct.

The trouble with teaching people that the bowling ball and feather will hit at, quoting the physicist in this clip, "exactly the same time", is that (relativity issues aside making the statement a joke anyway) it leads people to have a faulty understanding of how gravity actually works.

It's fine to teach that bowling balls and feathers will hit at *approximately* the same time, due to one mass in the equation being much higher than the other (allowing us to approximate it out), but it seems to never be taught this way. So these students end up with all sorts of wrong ideas about gravity when they get to me to work on n-body solvers.

It's the same problem, for example, as teaching elementary school kids that 5 divided by 0 is 0. It might make that teacher's life a little easier, but causes problems downstream.

Now I'm starting to think you just want to argue. If you're smart enough to make those technical assertions, you're smart enough to know that's not what the experiment was about, and that you're just adding data to confuse the lesson.
The experiment is about the effect of gravity on the moving objects under 2 conditions, and how their mass means nothing when determining THEIR accelerations/speeds in a vacuum. Period.
You want to introduce other, completely unobservable (and irrelevant to the lesson) forces and movements to say 'nope'. Technically, you may be correct in a way, but you must completely ignore the purpose and parameters of the experiment and assume inobservably small movements to make your point...a point that does not actually change the experimental findings or the lesson, but does confuse it thoroughly.

EDIT: I would note that, by your standards, exactly where the observer is positioned makes MORE difference than the different masses of the bowling ball and feather, as do the exact positions of the two...if dropped from exactly the same position, they hit at exactly the same time because their gravitational forces are in line.

I would also note that if you change it to say, unimpeded, they would cross any imaginary line in space at the same time (essentially what they mean), again your point becomes moot.

If a planet would hit before a feather, then a bowling ball would hit before a feather. The only difference is the effect size.

No...I'm talking in reference to earth (or any 'stationary' gravity source), as is the video. You are talking about relative speeds of moveable, nearly equal gravitational forces. That's why we disagree, we're talking about completely different things.

Yes. You are correct. If you put 3 objects in space, 2 of them being planet masses (not sized, size has nothing to do with it) and the third being the mass of a feather, the planet masses will come together first because they attract each other.

But that's not what this video, or the discussion were about. They are about how mass is irrelevant when discussing/calculating acceleration due to gravity (in the absence of other opposing forces, like wind resistance), and that's still true in your example. It gets MUCH harder to understand when you change the experimental parameters to have the (now multiple) gravitational force(s) also acted upon and moving, but the same rules all still apply. It's just much simpler to use masses of magnitudes so different where you can consider the gravity well a stationary object not attracted towards or effected by either moving object.

You're starting to get it. Except we're not talking about acceleration in reference to earth, we're talking about which would hit first, a massive object or a less massive object.

So if you drop a planet on the earth, it will hit before a feather would from the same distance.

No. The acceleration is exactly as fast, there are simply two of them in opposite directions, so the RELATIVE speed achieved is twice as fast, but actual speed AND the acceleration is the same.
You are confusing 'closing speed' with acceleration, and confusing what was being discussed in the first place, which was that objects are attracted by gravitational acceleration completely independent of their mass or density. You are adding a second gravitational acceleration and trying to say 'see, it's not the same', but of course it's not the same, because it's not the same question.

Right. They will both accelerate towards each other at 9.8 m/s^2. So the total acceleration is twice as fast, and they hit in less time than if you drop a feather.

After our discussion regarding alternative medicine a while ago, I came across this article. I thought you might be interested in it.

http://www.sciencebasedmedicine.org/answering-our-critics-part-1-of-2/

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Have you got a link to that analysis? I'd like to read it too.

In reply to this comment by ShakaUVM:
It's an interesting argument, but I read an analysis of Outliers which showed that Gladwell completely botched the story of the Korean Airlines flight.

So I don't trust anything he says on the topic.