You're wrong in saying "there are two sets", there's only one set that increments in steps of sqrt(2). Of course, sqrt(2) * sqrt(2) is... 2, so some of the numbers are clean multiples of 2.

It's a way to explain the f/stop range to those who are unfamiliar with it without having to teach them math. Rather than saying that you multiply or divide by multiples of the sqrt(2), or by 1.4.

Once you learn full stops, it's not that complicated to use.

The "f-stop" system photographers use are actually rounded down. The "actual" f-stops are something like:

f/1, f/1.414213..., f/2, f/2.828427..., f/4, f/5.656854..., f/8, etc.

Hell, notice that it should actually be f/5.7 not f/5.6, but photographers are dumb.

I'm aware of the rounding. It doesn't mean photographers are dumb, because photographers don't design cameras, engineers do.

The same thing actually happens with shutter speeds. If you look at your camera, it goes something like:

1 sec, 1/2 sec, 1/4 sec, 1/8 sec, 1/15 sec, 1/30 sec, 1/60 sec, 1/125 sec, 1/250 sec, etc...

Unfortunately, anyone who actually looks at these numbers should realize that 1/15 isn't a multiple of 1/8, and 1/125 isn't a multiple of 1/60.

Do you think you are the first person to notice that shutter speeds aren't a strict doubling?

Photographers are just lazy at figuring the actual numbers, which are all multiples of 2.

Again with the lazy photographers comment. Did you design and build your camera with 'proper' shutter speeds, or do you use it as designed by someone else?

The actual numbers that the cameras use internally are:

1 sec, 1/2 sec, 1/4 sec, 1/8 sec, 1/16 sec, 1/32 sec, 1/64 sec, 1/128 sec, 1/256 sec, 1/512 sec, etc.

And the actual values are fractions of a second that don't matter for photography.

The difference be 1/500 and 1/512 is .000047 seconds. 1/60 and 1/64 is .00104 seconds. 1/15 and 1/6 is .0041 seconds.

So tell me the practical difference that .0041 seconds makes.