you'd still probably have one of those coordinates (of the tall mountain) remain the same, then find a tower that goes even further than the second point - although I never assume my logic is correct in geodesy/astronomy, especially when I'm tired

edit* - in practice you're probably right

Laser powered ISPs anyone?

I kid, but is this a possibility?

This exists already, from some pretty serious telecom companies, for distances of a few miles. The problem is that, in optical wavelengths, there's too much absorption and scattering in the atmosphere - fog, rain, storms, smog, smoke - that can disrupt the signal.

But, in radio frequencies, this is how the microwave tower communications network works -- it's line-of-sight from tower to tower. https://www.wired.com/2015/03/spencer-harding-the-long-lines...

Microwave LoS is still widely used to connect cell towers for example. Look at these circular dishes in this picture[1].

1. https://ssl.c.photoshelter.com/img-get2/I0000JUzapOxgCs0/fit...

The microwave network is being resurrected between Chicago and NYC as a way to shorten the communications time for high frequency traders. Even after successively purchasing straighter and straighter rights of way for fiber, the microwave path is still shorter.

Nice article, now I need to plan a hiking trip to see one of the old towers.

wikipedia mentions that the longest microwave link is ~200 miles, but it's 2GHz and from the 1970s. I wonder what the limits for higher frequencies might be.