Scrabble’s Two Letter Words – Pe & Pi

Pe

The seventh letter of the Hebrew alphabet. Pe is written as ‘פ‘ when it is used at the beginning or inside a word, but is written as ‘ף‘ when it is the last letter of a word. Wikitionary also tells me that pe is the 17th letter of the Aramaic, Phoenician, and Syrian alphabets as well. It is equivalent to the letter ‘p’ in English or, situationally, the letter ‘f.’ The shape of pe originated from a hieroglyphic image of a mouth, which matches the plosive nature of the two letters it’s meant to represent. In Hebrew, the connection to the mouth continues, as pe also means ‘blow’, ‘open’, ‘edge’, and ‘speak’.

Within the Hebrew alphabet, the letter pe is important because it symbolizes words themselves, and words are powerful. They are the orders of a king, and the whims of a poet. The letter pe can save a life or crush it, or save or crush millions of lives. According to Hebrew scriptures, God created the universe by speaking ten utterances. Those ten words are the garments through which divinity is translated into the real.

The Phoenician alphabet, which early Hebrew borrowed from and influenced, also contains the letter 𐤐 or pe. 𐤐 evolved into the Greek letter π or pi, the Roman letter P, and the Cyrillic letter П or pe. It’s not lost on me that many Scrabble dictionaries define ‘pe’ as a Hebrew letter, but recognize ‘ya’ as a Cyrillic letter in the absence of any other alphabet. How very Western Culture of us. I’m going to do the same and focus on Hebrew, but only because Cyrillic will get it’s turn later when we talk about ‘ya.’

While many texts continued to be written in Ancient Hebrew, the language was considered dead and mostly supplanted by Aramaic in the third century BCE. Then, after two millennia, Hebrew made a miraculous recovery and did what no other natural language ever did. It went from zero native speakers to over five hundred native speakers, and it continued to defy expectations. A once dead language is now spoken by nine million people.

Modern Hebrew developed around the fourth quarter of the 19th century. As globalization tied distant Jewish sects together, there was a push for Hebrew to not only be a language for liturgy, but also for literacy among an ever connected Jewish population. Newspapers, pamphlets, and books were printed and shipped to bookstores and newsstands for this new Jewish audience. And one of the more common themes in these publications was the Zionist need for a new homeland. This Zionist movement led Jewish pilgrims to settle in Canaan, The Holy Land, and Palestine. While the diversity of cultures filtering into the flowering nation of Israel was incredible, and while it was encouraging that Jews from around the world could all contribute to this new nation, the new Israelites needed a common language to communicate among themselves. Many of these pilgrims were already advocates of Zionist newspapers written in Hebrew, and were taught Hebrew in order to read ancient texts, so Hebrew became the lingua franca and eventually the national language to the nation of Israel.

Pi

The seventeenth letter of the Greek alphabet, written as π. Also, the most famous irrational number in the world. Pi to the 1,000th decimal place is:

3.1415926535 8979323846 2643383279 5028841971 6939937510 5820974944 5923078164 0628620899 8628034825 3421170679 8214808651 3282306647 0938446095 5058223172 5359408128 4811174502 8410270193 8521105559 6446229489 5493038196 4428810975 6659334461 2847564823 3786783165 2712019091 4564856692 3460348610 4543266482 1339360726 0249141273 7245870066 0631558817 4881520920 9628292540 9171536436 7892590360 0113305305 4882046652 1384146951 9415116094 3305727036 5759591953 0921861173 8193261179 3105118548 0744623799 6274956735 1885752724 8912279381 8301194912 9833673362 4406566430 8602139494 6395224737 1907021798 6094370277 0539217176 2931767523 8467481846 7669405132 0005681271 4526356082 7785771342 7577896091 7363717872 1468440901 2249534301 4654958537 1050792279 6892589235 4201995611 2129021960 8640344181 5981362977 4771309960 5187072113 4999999837 2978049951 0597317328 1609631859 5024459455 3469083026 4252230825 3344685035 2619311881 7101000313 7838752886 5875332083 8142061717 7669147303 5982534904 2875546873 1159562863 8823537875 9375195778 1857780532 1712268066 1300192787 6611195909 2164201989…

And it keeps going forever. That’s what makes a number irrational. It’s a number that can’t be written as a fraction, because it never ends and never repeats. We can’t know all the numbers of pi, so we can’t compare them all to check and see if pi ever repeats. But the fact that pi never repeats can still be proven. This… um… requires calculus to prove. And my calculus is very rusty. Not that I think the majority of my audience would be able to follow even if I could trot out the calculus. But I like morphism’s mental exercise in response to the question in a post in r/askscience, so I’m going to quote them directly.

For the sake of simplicity, consider marbles instead of atoms. Imagine that you have a bag of marbles with a size of 1cm each (about the width of your index finger). Now, imagine that you want arrange your marbles into a circle with a diameter of 10cm. How many marbles do you need? The answer is: 31 marbles will fit on a circle with a diameter of 10cm. (32 won’t fit anymore and 30 is too few.) Note that they are almost touching each other, but there is a wee bit of space between them.

Does that mean that you need 310 marbles for a circle of a diameter of 100cm? No! Now you can fit 314 marbles, no more and no less. The 4 additional marbles come from the space that you couldn’t fill in the previous example.

It goes on and on:

1000cm diameter -> 3141 marbles
10000cm diameter -> 31415 marbles
100000cm diameter -> 314159 marbles

etc. The question is: will you always be able to fit a few additional marbles in there the larger the circle gets? Or will this end at some point? The answer, which is not obvious, is: it’s the former, not the latter. This was proven in 1761 by Lambert.

It should be pointed out that Morphism doesn’t explain why pi doesn’t irrationally repeat, just how pi can keep becoming more and more exact the more we scale out, indefinitely. I can’t say that I can understand the math behind why pi never repeats. But I think I understand the principle. Pi is a lot like a spiral, forever spinning, further and further out. As long as it obeys the set of rules it follows, it will never turn back in on itself and cross over the same point twice. It is a perfect mathematical ideal that spreads beyond every limit imaginable, up and out forever.