Washington Park π

In the Portland area, where I live, there is a light rail with a particular station, Washington Park Station^[1]. The station, commendably, has a bunch of artwork to liven it up. One is a block of digits clearly intended to be π (you know, π, the wrong circle constant) (Figure 1). Unfortunately, only the first 11 decimals are correct (and the 11th being right turns out to be coincidence).

I noticed this instantly, of course, since as a child I memorized a good 200 digits or so to cope with the boredom induced by what passes for the American public school system, and the first thing anyone who's memorized any π does is check every listing of π they ever see, forever after^[2].

The question then arises as to where the digits come from. The first row is correct. The second row is wrong, although I noticed that its first 10 digits are digits 100–110 in the actual value. This gives us something of a clue as to what went wrong.

The newsletter for what is now Oregonians for Science and Reason (O4SR) provides a vital piece of information^[3][4]:

According to Rebecca Banyas of Tri-Met’s Westside Light Rail, the artist, Bill Will, “got his information on pi from a reference book called The History of Pi(8). The numbers that appear on the wall are the same as those in the book.”

[...]

8. Beckmann, Petr. 1971. A History of Pi. The Golem Press. [...]

The source says this in juxtaposition to the digit listing from said book, as if the problem is self-evident, but we'll spell out exactly what happened here.

I couldn't find a convenient copy of the 1971 edition, and it's not clear that's the one that was even used. The digits do not appear in the 1970 edition, but they do occur in the 1993 edition (see what would be pg. 201, following the index). The decimal digits are presented in rows of 100 digits, separated horizontally into groups of 10, and vertically every 10 rows, for visual clarity (Figure 2).

Although this does make the seas of digits easier on the eyes, it also has the tremendously unfortunate effect of producing 10⨯10 'tiles' of digits that seem to stand alone. The artist apparently mistook the text as flowing within the tile before moving on to the next one (Figure 3), instead of the correct way (reading left-to-right all the way across before proceeding to the next line). That is, the text on the wall is the digits of π, read 10 at a time from an incorrect column-major view of π, where each column was formed accidentally from spacing after wrapping at 100 digits, and then regrouped into lines of 12 characters each.

#Given: 910+ decimals of π in `s`
from textwrap import wrap
print( "\n".join( wrap( "3." +
	"".join([ s[ k//100*10 + k//10*100%1000 + k%10 ] for k in range(106) ]),
	12
) ) )

While the few other spots on the internet that have covered the error are understandably rather miffed at its very existence, in my view we can absolutely forgive the artist this. The grouping of tiles does visually seem much tighter than the grouping into rows. It makes considerable sense to traverse the list of digits this way.

Moreover, it's actually quite difficult to realize this problem, if you're stuck within its context. All your references will seem to agree because you're reading all of them wrong, in the same way. Given that the station and presumably the carving opened in September 1998^[5], those references would probably have been a few books, rather than very many websites, which makes it all just that much more difficult.

Even in modern times, the error could still be made; presentations of this ilk remain common today^[6]. If you unluckily picked an ambiguous source, you'd basically only get wise to the possibility of misreading by disagreeing with someone who happened to have read it correctly themself^[7][8], because an error starting from the 12th decimal place is not noticeable in almost any context.

Alas.

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