Did You Know?
Bits and Pieces from the NR Trivia Collection
#14: PI in the 'Face

by Eric Platel, with Jens Kreutzer
using material by Scott Dickie
with support by Nils Kreutzer

Though it is the only card with the keyword "DecKrash" in the base set (v1.0) of Netrunner, PI in the 'Face is somewhat of a staple among sentry ice: If all you want is an end-the-run subroutine on a sentry ice to complement your mix of code gates and walls, PI in the 'Face is the natural candidate. It's a simple but effective little piece of code, and always a good choice in Sealed-deck tournaments.

First of all, the name of this card is a pun between pie (as in 'cake') and the Greek letter pi, which is of course the symbol for and the name of a mathematical constant. Further, 'face is a pun between face and interface. Like so many concepts of Netrunner, this card's design can be traced back to R. Talsorian's Cyberpunk 2.0.2.0. Roleplaying Game. Interestingly, in Cyberpunk, PI in the 'Face is not a defense program for data forts, but an attack program used by Runners to fry a data fort's CPU. Here is the description that can be found in Cyberpunk's Chromebook 3 supplement, on page 73:

"An improved Krash. If the program makes a successful attack, the CPU will be trapped calculating Pi. This paralyses the CPU for 1D10+1 net turns. ICON: A LARGE cartoon pie, for throwing."

Bartmoss' Brainware Blowout (BBB, p. 47) has basically the same information, but adds the following reference to clowns: "Guess which buncha bozos loves this one?" These two quotes explain the inspiration for the artwork by Robert McLees (though BBB was released after Netrunner v1.0). Also, we learn that the keyword DecKrash is indeed an indication of the fact that the Corporation ice card PI in the 'Face and the Runner icebreaker Krash use similar attack strategies!

The beginning of the decimal expansion of the mathematical constant pi (3.141592654...) is shown in the card artwork background - look at the space directly above the pie in the clown's hand to spot the "3.1" that starts it off. Incidentally, if you look closely at the artwork on the card Test Spin, you might be in for a surprise.

Scott Dickie has made some additional remarks to elucidate the flavor text of this card: "Nyuk, nyuk, nyuk...". This is what Curly of the Three Stooges says when something amuses him, such as throwing pies at other people's faces. The French version of this card is called "PiGnon" and has the flavor text, "Heu, le code c'est 3.14159 et ... vous voulez vraiment toutes les decimales? Je peux pas vous le faire au PI-fometre? Non pas dans la tete!�h The word pignon in French means either a house gable, or a pinion gear. The word gnon is slang for a strong blow or impact - so the title could be translated as "Pi Hit". Pif also is French slang and means 'nose'. Therefore, pifometre could be translated into English as 'nosometer'. The term au pifometre means guesstimating, or following intuition (i. e., your nose, as it were). The full translation of the flavor text could read: "Uh, the code is 3.14159 and ... do you really want all the decimal-places? Can't I just take a wild guess (to do it for you)? No! Not the head!"

Weirdly enough, the computation of pi summarizes 4000 years of the story of humanity, covering different fields of fundamental research in mathematics like geometry, algebra and analysis.

The definition of pi is really simple: It's a constant that is equal to the ratio of the circumference of a circle to its diameter.

The hunt for ever more precise definitions (meaning more decimals after the point) started around 2000 BC: On a old parchment in cuneiform writing, the Babylonians gave the very first approximation of pi = 3 + 1/8, which is 3.125.

Archimede of Syracuse developed his own method (using inscribed 96-gons) and stated that pi was bounded by 3 + 10/71 and 3 + 1/7, giving the second correct decimal: 3.142857143...

Using Archimede's works, Ptolemy of Alexandria (Egypt, 150 AD) gave the value as 377/120 (3.14166667...), and Tsu Ch'ung Chi of China (500 AD) set it to 355/133, which is 3.14159292. They respectively defined 3 and 6 correct decimal places.

Around 1450 AD, Al'Kashi managed to compute 14 decimals. In 1609, van Ceulen was the last mathematician to base his research on Archimede's works, and after having dedicated a part of his life to the computation of pi, the 34 decimal places he discovered were engraved on his tombstone.

The 17th century brought renewed efforts to study pi and its properties, not using geometry anymore, but analysis. Leibniz (1646-1716) and Euler (1707-1783) used Gregory's work to devise some formulae that were based on the following serial computation:

[I'm sorry, but I can't display this formula in HTML text. If you'd like to see it, you'll have to download the Word version of this TRQ issue.]

It's obvious that the more iterations you have, the more exact the value of pi you get will be. Unfortunately, you don't get a whole lot of new decimals after each iteration (slow convergence), meaning you have to do a lot of calculating.

In 1706, John Machin discovered another formula, which for the first time in history allowed the manual computation of 100 decimal places, a formula that is still used nowadays:

[omitted]

Euler defined the symbol for pi (the Greek letter of the same name) in 1737.

In 1761, Johann Heinrich Lambert proved that pi was irrational, i. e. it cannot be the exact ratio of two integer values.

William Shanks achieved immortality in a very curious way: In 1864, he computed 707 decimal places, but in 1945, Ferguson discovered (due to a suspicious shortage of sevens) that Shanks made a tremendous error starting at the 528th place!

The German mathematician Lindemann proved in 1881 that pi was transcendent, i. e. that it cannot be the solution of a polynomial with an integral coefficient. This result proved that it was impossible to 'square a circle', i. e. that it is impossible to draw a square whose area is equal to the area of a given circle. This problem was posed by the Greeks 2000 years ago, but had never been solved up till then.

Buffon proposed a curious experiment: Suppose a needle of length k is thrown at random on a plane marked by parallel lines of distance k apart. He estimated that the probability of the needle landing between two lines (i. e., not crossing any line) is 2k/pi. Based on this idea, Lazzerini threw 34,080 needles in 1901 and got the value of 3.1415929 as the result, which was the value calculated by Tsu Ch'ung Chi.

During most of the 20th century, no real progress was made regarding the study of pi. Nevertheless, the massive use of computers caused an explosion of the number of known decimal places, and the amazing number of 1 million was reached in 1973 - still using Machin's formula.

Fortunately, the 1980's saw the birth of many new formulae. The most important step was the discovery of formulae that were able to double the number of correct decimals after each iteration. This new generation of formulae was based on the work of the Indian mathematician Srinivasa Ramajujan, who came to fame only well after his death (1920) because he wrote all of his theories in Indian, i. e. it took a lot of time to decipher it.

On September 19, 1995, Canadian Simon Plouffe (with the help of mathematicians David Bayley and Peter Borwein) found this one:

[omitted]

It allows the computation of any digit of pi either in binary or in hexadecimal code. Moreover, it proves that it is possible to compute a given decimal place without knowing the previous ones.

Using Plouffe's formula, the French student Fabrice Bellard managed to calculate the 1000 billionth decimal place in September 1997, and Colin Percival calculated the 40,000 billionth digit in February 1999, with the help of the Internet community.

It should have become obvious by now that pi is infinite - there is no last decimal place to be found, and attempting to calculate it in its entirety is a hopeless effort that would last into all eternity. And that is precisely why PI in the 'Face is so nasty: Sooner or later, any CPU will be brought to its virtual knees by this.