Let's start with BDL's hypothesis. It's true
When you look at a natural stone finish and contrast it to a synthetic stone finish, you are going from a uniform grit of a synthetic abrasive considerably harder than the steel to something much closer in hardness to the steel - natural abrasives. Furthermore the variance in size of particles, particle hardness and shape are considerably more complex and varied. Thus you look at a scratch pattern of a synthetic stone and it looks like a freshly plowed field - nice neat rows assuming the sharpener is 'stroking' the steel in a consistent manner (no, don't go there
) in one direction. Now look at a natural stone finish - it is a more sandblasted look. Quite different.
So when you go from a synthetic finish to a natural finish, converting the finish could be described as 'scrambling' the finish. It's a reasonable description.
So Arkansas stones (Surgical black and the slightly finer translucent) do pretty well with softer steel knives - not so well with harder or more abrasion resistant steels. Although it is a bit of an apples and oranges comparison, something around a Japanese 4k grit is a reasonable functional comparison.
As an aside, what I've found most interesting lately is to use the Arkansas stone as a platen with some natural stones, using the natural stone as a nagura on the Surgical black. Then you have for instance Aoto mud on the Arkansas stone and the 4k ish surface of the Arkansas stone breaks down the Aoto mud nicely giving a luxurious soft mud on the Arkansas stone. The aoto mud acts as the interface to the steel allowing it to cut the harder Japanese steel quite nicely and also work nicely with softer steels as well.
Utilizing the Arkansas stone as a 4k abrasive to use as a platen for the nagura mud of various natural stones (primarily aoto and various nakado or midgrit Japanese stones) works quite nicely. I'm also exploring this technique with several other non-Japanese natural stones with good effect. The exceptionally slow wear rate of the Arkansas is of considerable advantage in this application.
Lately I've been using the Meara stone - a Japanese natural stone. Finer than the surgical black or translucent Arkansas stones and just a slight bit softer, which is still quite hard. It actually does generate some mud unlike the Arkansas stones and seems to work on a really wide variety of steels.
James has one (Meara) - and of course his Arkansas stones, so it would be fun to get his take on a comparison.
BDL, I think this might be a fun one for you to try. Send me a PM if this interests you.