@pyrodactyl: You might want to consider wearing glasses.
That way you'd get the benefits of being a cyborg and not living with unaugmented vision. A healthy young person without major optical issues should be able to get to 20:12 vision (if you're lucky, 20:10 is very much attainable). and so be able to see things with the clarity of a "naked eye" from 20ft away from a screen that 20:20 vision only resolve when 12ft away. So half the angular resolution of any calculation you're making for people who care about getting the most out of their optical system (the future is cool and so many people live with augmented vision).
And then read this and realise that all of that doesn't matter because your optical system actually cares about hyperacuity. The interesting follow up article to that makes a good case for requiring about 4x linear resolution vs visual acuity for the screen (the other shortfall in getting to hyperacuity can be made up with super-sampling the source image so great anti-aliasing gets us there, probably). It's all interesting research that's going to get really nailed down as we get better VR tech and more research about screens that can get impressive pixel densities to us.
So we're talking about someone with good corrective glasses to maximise their optical system (20:10, half an arcminute, 0.00833(recurring) degrees to be precise) and a screen needs to fit four pixels into that, so about 0.0021 degrees. 68*tan(0.0021 degrees) ~= 0.0025 inches.
Looks like your TV doesn't have nearly enough dots if you're sitting 68 inches away. At least according to reasonable science and maths. Maybe not (this is conjecture), but it's not an unreasonable requirement. It obviously won't be apparent for every possible image what the limits of your vision even are (looking at a pure white screen, the pixel count is functionally 1 - we have brains that are good at adding detail that doesn't exist as many optical illusions show where eg things you're not looking directly at can have their saturation changed without you seeing because your brain makes up the colour of things your cones are not actually pointing at towards the edge of your vision) but as the first link makes clear, you can see an aliased line far further away than you can resolve a single pixel of black in a sea of white.
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