I stayed in Edinburgh, Scotland for a few days last year. While there I climbed Arthur's Seat, the extinct volcano near Holyrood Palace. The wikipedia entry to Arthur's Seat says that in 1884 famous mountain climber Émile Rey visited Edinburgh to climb the mountain and, "local tradition stating that before doing so he estimated it would take much of the day to reach the top."
Don't get me wrong, it's not a brisk walk up the mountain, but it's really not that difficult. It took me maybe an hour and a half to get to the top. I would imagine that in 1884, people didn't have the same amount of free time, so the trails might not have been marked as well, and the various steps wouldn't have been built yet. But even without those thing, I don't think it would have taken much longer to reach the top.
My questions are:
I tracked down the citation from Wikipedia (the link is broken on the page), which essentially consists of a local resident reviewing a book by Claude Wilson, 'sometime President of the Alpine Club' in 1933. In surveying some of the anecdotes contained therein, they make the following comment:
By the way, when did Emile Rey visit Edinburgh (p. 26)? Was it not early in 1884? He climbed Arthur's Seat, and the reviewer remembers as a boy hearing the local tradition that Rey estimated beforehand the. ascent would occupy the day, a story also told of other Alpine guides on other British mountains.
Here, two things are already clear. First, that the story is anecdotal in the extreme - second or third hand at best, heard decades prior. Given that this was the climbing equivalent of a celebrity, they are a logical name to attach to an apocryphal story. Second, this same story circulates about other guides on other British mountains - this is just a local version of common tale about foreign climbers in Britain. In fact, when searching I found a version of the same story about Rey in connection with Snowdonia in Wales.
But what was the point of the story - or rather, what's the joke? Another version of the tale in a different alpine journal (Scottish Mountaineering Club) from 1906 makes it clearer:
There is a mention of Arthur’s Seat as a climbing ground in the book on “ Mountaineering ” in the All England Series, by Dr Claude Wilson, and it was ascended by one of the best and most famous of Alpine guides, Emile Rey of Courmayeur, when on a visit to Scotland with Mr C. D. Cunningham in 1886, when the party also climbed Ben Nevis by the path in three hours thirty-five minutes.
As a striking instance of the difficulty of judging distances under unfamiliar conditions, the story is told of how Rey, looking up at the hill from Holyrood Palace, was asked, “ How long did he reckon it would take to gain the top?” He replied, “ Two and a half to three hours,” whereas the party reached the top in twenty-five minutes.
(note: the same Wilson!)
Here, the nature of the story is clearer: even the most experienced climbers have difficulty making good judgements in unfamiliar conditions - a humorous but also important point to make to budding climbers who might overestimate their capabilities in alien terrain, even when conditions are supposedly easier. If even the best climbers of the era can be bamboozled by a small Edinburgh hill, it can happen to anyone, anywhere.
As Edinburgh locals will tell you (I live a block from Arthur's Seat, as it happens), this specific confusion is very common - people generally assume the hill is further away from the centre of Edinburgh than it really is, and thus massively overestimate its height. My own pet theory is that people also mistake the gorse bushes on the side for trees at a distance, further distorting their sense of scale. In my view, this is likely the basis of the anecdote - local climbers would have been well aware of the common error made by visitors, and by attaching it to a famous climber who had once visited the city, the story is enriched.