Breakthrough realization

Even if they don’t touch, they help to propel other things to force other things off of the hands. So they do wash. But it isn’t hands alone, it’s other parts in the arm and the nerves that tell them to do it.

I agree with your assessment that more is at play than just hands. However propulsion isn’t a necessary component of washing. The necessary component of washing is water- by definition. Specifically to clean with water. It isn’t your hands that are doing the washing. They are a necessary component sure. The movement should of the hands allow the repulsion and manipulation of the electrons in the water and so forth. However using your example- your shoulder propels your hands but you don’t wash your hands with your shoulders. In the end, it is not the hands which are doing the washing regardless. The water does the washing, you move your hands in a washing motion to elicit the effect. Perhaps a better way to put is is that when you are baking, you aren’t heating the cake. In a macro sense the over is heating the cake. So you can’t rightly say you heated the cake so much as your actions led to it being heated- the term for which is baking.

I mean technically the failing point of the nothing touches anything arguement is that the atoms that make you up aren't even touching themselves. Not even on a single atom level. The electrons in the atom don't touch each other nor do the protons touch each other. On an atomic scale protons, neutrons, electrons, quarks, and anti quarks don't ever touch each other. there is always some distance between the parts of the parts of the parts of the parts ad infinitum. Which means that "touching" as is defined in common tongue doesnt actually exist but "touching" as defined in physics is true on all levels including that of washing your hands

I’d say that it’s not a failing point, but more a broadening of the basic concept from just your ability to touch, to all things ability to touch. It makes sense that if subatomic particles don’t touch, that we could apply the same to any object made of subatomic particles, but as it pertained to the OP and their pseudo shower thoughts- ones hands do not touch when washing. What we experience as touch, what we think of as touch, and what actually is going on with a touch are not generally the same. So I thought it fit nicely in the theme of “blow your mind” style memes- the fact that one really doesn’t ever touch anything, and few if anything else vet does either. That most things including us are made of more “empty” space by our physics model than solid space, and in theory should just slide through each other if it wasn’t for such forces or unknown factors is a bonus I’ll throw in for funsies.