when learning how to surf, people don't sit at home reading a technical manual about how to measure velocity, steepness, and hollowness to predict where to position themselves to catch a wave.

No.

They go out and learn the rhythm of the ocean by being in the water.

I think the same applies to learning musical rhythm.

nerd vs. practitioner: cart before the horse

In trying to improve my sense of rhythm, I've seen very mathematical approaches to this. Teachers show numbers and intervals and fractions (4/4, 3/4, 6/8, etc.) and it all makes total sense but doesn't work. If I try to visualize the numbers and count while playing music, it all breaks down the same way I'd be miserable if I wanted to run calculations while surfing Third Point.

But how about those proficient guitar instructors that show intricate strumming patterns while counting aloud? How are they able to do it? They suggest we learn to keep rhythm by counting aloud just as they demonstrated. Just as they learned it...but is that really how they learned?

These guys very likely have the arrow pointing in the wrong direction:

Nerd vision of reality: count aloud → develop rhythm
Reality: count aloud ← develop rhythm

Someone like Nassim Taleb would call the first arrow the soviet-harvard approach to learning music or lecturing birds how to fly. Birds watch a tenured professor explain the physics of how birds can fly, then they fly away.

Aha! They listened to my lecture and learned to fly!

To further support this hypothesis, I found this morning in YouTube:

Why Counting Rhythms Doesn't Teach Rhythm

As for Bonzo, he always takes the number 1 spot: