I wouldn't use the tool in question, but I relate to the motivation.
So as others have suggested the response can be prioritised according to importance and urgency.
While flow is critical for productive work, it should be directed to the highest priority tasks.
please don't think I'm
being rude
By saying that you remind the interlocutor that being rude is in fact an option (indeed a widely used one) and you may simply be rude ... ah the subtleties of communication.People tend not to think themselves or what they're doing as important for whatever reason.
It also sets the scene for future interactions. Oh and sometimes it really is important..
I agree with the sentiment though, that it does often give the impression of being bad mannered.
Perhaps to address both issues, there could be a version of this that doesn't actually make a physical call? Perhaps a pairing of an iOS/Android app to a button on the browser which send a standard in app message (free) to the phone associated with the button. The app could then simulate a ring tone, which would be enough to complete the illusion of an incoming call?
There's quite a few versions of this. I think a cheaper option is an app on your phone that imitates a phone call.
I used the Skype API with VB6 and some natural voice libraries from AT&T. We mostly got used for prank calls with pre-recorded messages we had. Worked OK. But cost us money and I got bored once it was built. We got maybe 60,000 sign ups I think.
Usually a phone call is the only detractor for them to interrupt me. at the end it ended up being just to let me know something like i got this to compile!! which could have been done on slack or lync.
We got an offer from Madrona Ventures for it that I never ended up following up on.
Plus, it's not like HN is anti-commercial either.
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Great job.