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> The observation of sunspots predates modern astronomy by at least three millennia.

Any idea how they watched those back then? With the naked eye seems too painful.

Sadly, they don't mention Ham Radio, which (along with other shortwave users) is pretty close to obsessed with sunspots. They have a dramatic impact on HF propagation.
Forgive my ignorance, but what mechanism did they use to not damage their retinas by staring at the sun through a telescope?
A dark filter of some kind ? Can be as simple as smoked glass. The ones manufactured for modern photography are called Neutral Density filters, and they're available in a variety of f-stops, but the intensity reduction is insufficient for observing the sun safely. Higher reduction filters are built for astronomy.
I thought the way that sunspot counting works is that you point a magnifying telescope at the sun, and the image projects on the floor. You look at the image on the floor.

He did have a valid point. For the data to be consistent across a 300+ year data set, he had to use the same method as his predecessors.

However, you could use technology to augment the manual count. They could use the same k-factor adjustment they used to compare multiple human counters, and use the same k-factor adjustment when technology changes.