# What is a Lifelong Word™?

This is in the spirit of the What is a Word/Phrase™ series started by JLee with a special brand of Phrase™ and Word™ puzzles.

If a word conforms to a special rule, I call it a Lifelong Word™.
Use the examples below to find the rule.

$$% \def\Pad{\P{0.0}} \def\Title{\textbf{ Lifelong }} % \def\S#1#2{\Space{#1}{20px}{#2px}}\def\P#1{\V{#1em}}\def\V#1{\S{#1}{9}} \def\T{\Title\textbf{Words}^{\;\!™}\Pad}\def\NT{\Pad\textbf{Not}\T\ } \smash{\lower{29px}\bbox[lightblue]{\phantom{\rlap{rubio.2019.05.15}\S{6px}{0} \begin{array}{cc}\Pad\T&\NT\\\end{array}}}}\atop\def\V#1{\S{#1}{5}} \begin{array}{|c|c|}\hline\Pad\T&\NT\\\hline % \text{girl}&\text{boy}\\ \hline \text{eastern}&\text{northern}\\ \hline \text{right}&\text{left}\\ \hline \text{biological}&\text{dead}\\ \hline \text{master}&\text{slave}\\ \hline \text{stupid}&\text{clever}\\ \hline \text{friendship}&\text{rivalry}\\ \hline \text{bike}&\text{automobile}\\ \hline \text{lunch}&\text{supper}\\ \hline \text{amazing}&\text{everyday}\\ \hline \text{public}&\text{private}\\ \hline \text{situp}&\text{pushup}\\ \hline \hline \end{array}$$

Important: There are some words which cannot be evaluated with this rule. Examples of undefined words:

Japanese, Journalism, Jaw, Injection, Prejudice, Joy, Jaywalk, trajectory

CSV version:

Lifelong Words™,    Not Lifelong Words™

girl,               boy
eastern,            northern
right,              left
master,             slave
stupid,             clever
friendship,         rivalry
bike,               automobile
lunch,              supper
amazing,            everyday
public,             private
situp,              pushup


What is the special rule these words conform to?

Hint #1:

Ironically, "John" can also not be evaluated. But he's nonetheless back on the grid.

This is an impressively complicated one, but I'll do my best to explain it! A Lifelong Word is one where:

If we arrange the letters of the alphabet (except J) into a 5x5 grid and highlight the cells corresponding to the letters which spell the word and then we run the rules of Conway's Game of Life on it within an infinite grid, the resulting simulation either (i) ends in a static state with some surviving cells, (ii) enters an infinite loop, or (iii) sets off a constantly moving but neverending sequence. By contrast, for words which are Not Lifelong their cells all die out within a few generations.

This explains a few peculiarities in the puzzle:

1. The name Lifelong contains a reference to Life and an implication that it is long-lasting.

2. All words in the 'undefined' list contain the letter J - this is the one letter of the alphabet which must be omitted when running the simulation.

3. The mention of 'John' in the hint is a reference to the mathematician John Horton Conway who developed this game. The mention of 'grid' also points towards this game specifically.

The simplest result to show is that for GIRL (I used this tool to check my working), which produces the following:

After one generation, the L, M and N cells are alive, while the G, R and I cells die out. However, in generation 2 the G and R cells resurrect while L and N die out, and we enter an infinite loop known as a 'blinker', forever fluctuating between the two states.

Meanwhile, running the game for EASTERN produces four infinitely-fluctuating blinkers after 9 generations:

RIGHT also produces 4 blinkers (after 11 generations), but BIOLOGICAL produces a static state known as a 'loaf' after 3 generations:

And MASTER results in a 'bee-hive' after 3 generations:

As for the others:
STUPID = 2 bee-hives
FRIENDSHIP = 4 'blocks' (2x2 squares)
BIKE = 1 block
LUNCH = 1 block
AMAZING = 1 bee-hive
PUBLIC = 3 blocks + 1 blinker
SITUP = 1 'glider' - a shape which continually moves onward in a zigzagging (but ultimately straight) line!

Meanwhile the words which are Not Lifelong all 'die out' like so:

• Yes, well done! I chose the infinite option because I wanted to make SITUP behave in the way it does ;) – Lukas Rotter Oct 12 '20 at 19:03
• It was when I realised what shape SITUP made that the truth dawned on me! I had the right idea a little earlier but it wasn't until I twigged the importance of J that I actually made it work. An impressively involved 'What is a Word' puzzle, thank you! :) – Stiv Oct 12 '20 at 19:05