How's this story/joke/anecdote supposed to go?

It seems there were five Englishmen, one statistician, one biologist, one mathematician, one physicist and one quantum physicist, none of which had ever left England, but were now on board a train headed into Scotland. As soon as they cross the border, they see three black sheep.

“Fancy that”, says the statistician. “In Scotland, all sheep are black.”
“Not so”, says the biologist. “All we know is that in Scotland, some of the sheep are black.”
“Not so”, says the mathematician. “All we know is that in Scotland, there are at least three black sheep.”
“Not so”, says the physicist. “All we know is that in Scotland, there are at least three sheep that are black on at least one side.”
“Not so”, says the quantum physicist. “All we know is that in Scotland, there are at least three sheep that are black on at least one side, at least some of the time.”

That’s the best I can remember it, but it doesn’t seem quite right. There’s something missing, and I’m not sure what. I’ve heard another version with only three characters, but cannot remember that one as well.

How’s it supposed to go? What’s the canonical version?

Priceguy, I tried googling:

“black sheep” mathematician joke

and got a huge number of variations, none of which seemed the least bit funny. I share your sense that something is missing, but I think that it’s as basic as a funny punchline.

Similar but less elaborate anecdotes predate the development of Quantum Physics. I read one such in a book published in 1914 about politics in the 1890s. There was a U.S. Senator (I don’t recall the name) who was famous for being very careful in choosing his words and taking pains never to overstate his case. One day he and a colleage spotted a flock of sheep being driven from one pasture to another. The colleague, thinking he might finally get the senator to take a firm stand on a question said “They sheared the sheep mighty close this year, didn’t they, Senator?” The Senator replied, “It appears so,” but then, fearing he might have said too much, he added, “from this side.”

The humor value, such as it is, lies in the contrast between math types thinking in ways stereotypical of their specialties and the much simpler “real world.”
So, we have the statistitian drawing a false conclusion from a tiny sample; all the way up to the quantum physicist, who is used to dealing with objects that, unlike most, have unusually mutable characteristics.

Well, yeah, but there doesn’t seem to be much of a pay-off, even for a piece of trade humour. Although I at least get the “joke”, unlike some of the mathematical pieces of humour I found in my search.

Then the Doper sees the sheep, and says" When come back, bring pi"

Oliver Wendall Holmes was traveling with his wife by train. Looking out she remarked, “Look. All those sheep have just been sheared.”

“At least this side,” added Oliver.