The first few seconds of a nuclear blast.

You're far enough away from a nuke if you can't see the explosion after holding a finger in front of your face. But no one said how close the finger was supposed to be

Arms length.

That is not true at all. Whose arm? How is your tolerance to radiation? It was a joke, it means you aren't able to be safe from a nuke.

Your own arm, obviously. As a general rule the proportions of the human skeleton remain relatively constant, so a finger held at arm's length will appear approximately the same size for everyone, provided they are not significantly deformed. And again, there's not that much variation in radiation tolerance from person to person, Also, it's not a joke, you can be safe from a nuclear explosion provided you are sufficiently far away, which is what the covering-with-a-finger method supposed to measure.

The thing is that you could see the Castle Bravo explosion on Bikini Atoll from the battleship 800 miles from it, they got showered with fallout. And the Russian nukes are 6+ times that powerful

And? Fallout is not automatically lethal, you can take shelter, wash yourself off, and get the hell out of there. Fallout also depends on wind currents, and the amount any one location receives decreases with distance. The cover-it-with-a-finger rule is not even about fallout, it's about radiation exposure from the explosion itself.

My point is when our explosions are big enough to create a 200 foot deep crater in a coral reef and the Russians have a nuke 6+ times that big, why the fuck are we standing close enough to see it go boom

A fair point, but not the original point.

It was a joke from the people on said battleship