Calculating the Midpoint of Time

Among my favorite tools for raising smart kids are games: Games we play together, games kids can play on their own, games that provide materials and inspiration for new ways of play.

We’ve had our Time Breaker set for more than a year, but somehow I haven’t yet had the opportunity to play this game with anyone except my daughter Lydia, now six years old.  She loves it!  I like setting up the tiles, but the game play doesn’t really grab me….  I guess I just wish we were playing Chrononauts, another time travel game from Looney Labs, which does more to draw you into thinking about moments in history and how they affect one another.  Time Breaker’s timepoints function like physical places which are connected in two ways (to the tiles physically adjacent, and to the tiles that represent the timepoints before and after) but which don’t seem to matter to the course of history.

My indifference to this game makes me much more tolerant of the times Lydia decides to deviate from the rules, than I am with games I actually want to play!  Lately, instead of having each of us operate one agent and compete to arrest the Time Breaker, she’s been convening the five agents as a team that cooperates to surround and overpower the Time Breaker.  She says I need to play this with her, but in fact she’ll play happily by herself while I’m nearby doing something else, as long as I jump in when she calls for specific assistance every five or ten minutes.

Last night, “we” were playing Time Breaker and I was texting with a friend when Lydia called me into a strategy meeting: The team was getting frustrated with our inability to get anywhere near the Time Breaker with the cards we were drawing.  We needed “strong magic” to distract him, she said.

Looking at the agents’ positions, I pointed out that one stood on the Big Bang: “That’s the beginning of Time, so if we can get another agent to the end of Time, we will control all of Time and thus get control of the Time Breaker.”  Sounds promising, right?  The latest tile is 3069, so (ignoring the total lack of evidence that colonization of Alpha Centauri would bring Time to a close) I traced a parabola between the tiles for 3069 and 13,800,000,000 BCE, showing how it would ensnare the Time Breaker from his physically distant position.

Lydia was excited about this strategy until she’d managed to maneuver an agent to 3069: “It didn’t work!  The Time Breaker’s powers are too strong.”

“Hmmm, we’ll have to try something else,” I said vaguely, not looking up from my phone.

“Well,” said Lydia, “We have to lure the Time Breaker to the exact center of Time.  That’s where our grip on Time is strongest.  We have to have a way to get an agent there to arrest him.  Which year is the middle of Time?”

She looked at me trustingly, certain that I would know the answer to this question.

My first thought was that we’d do the math to determine what year is halfway between 13,800,000,000 BCE and 3069.  I could have done this by hand, but Lydia fetched a calculator instead of pencil and paper.  This calculator has an 8-digit display and no scientific notation, so it couldn’t work with such a large number.  I was musing about how to handle this–and thinking that because the Big Bang was so very early, 9.3 billion years before the next notable event, the midpoint of Time was going to be way far back before the existence of our species, which is rather depressing–when Lydia came up with a different approach:

Each tile has arrows that direct you to the next tile forward and backward in time.  Therefore, by moving our agent stationed on the Big Bang forward one and our agent on Alpha Centauri backward one, and repeating these moves until they landed on the same tile, we would locate the midpoint of Time!

This seemed logical because there are 25 tiles, but we were forgetting that one of them is the Time Repair Agency HQ–so there are 24 timepoints, an even number.  Ultimately our forward-going agent got to the Great Wall of China in 210 BCE, where the Time Breaker was–“You’re under arrest!”–while our backward-going agent was at Chichen Itza in 900.  One more step, and they’d switch places and miss each other and skip right over the powerful midpoint of Time!  (Never mind that, by the rulebook, the agent in 210 BCE ought to be able to haul the Time Breaker back to HQ by making the right series of moves–we were way off script here.)

Lydia jumped up and ran out of the room, calling over her shoulder, “You perform the calculations while I get scissors and a pencil!”  I was worried that she was planning to modify the tiles, and I wasn’t going to let her do that, but meanwhile I calculated the midpoint between these two timepoints:

  • 210+900=1110 years between 210 BCE and 900.
  • 1110/2=555 years from one timepoint to the midpoint.
  • 900-555=345.

Lydia returned and assured me that she was planning not to modify the game but to add to it: “We need a tile for 345, and we need a card to get us to 345.”  This was such an urgent task that she was drawing even as I was looking up what happened in the year 345.  The answer is, nothing that seems particularly interesting or lends itself to an easily-recognized graphic.  But Lydia had decided to draw a ship.

A small square of paper with a child's drawing of a ship, placed next to Time Breaker tiles.

Hey, why not?  Whatever else was going on in 345, somebody must have built a ship.  Our local museum has an ancient Egyptian ship; that’s much older, so ships must have been commonplace in 345.  Lydia asked me to do the lettering on the card.

An unevenly-cut slip of paper with a child's drawing of a ship and "JUMP TO... 345" in adult handwriting.

Now I thought we were ready!  The agent in 210 BCE would sneak up behind the Time Breaker and push him through the gate, and he’d think he was escaping to 900, but he’d land in 345 at the apex of our power!  Meanwhile, another agent would draw “Jump to 345” (which Lydia had placed face-down on top of the draw pile) and be there to apprehend the Time Breaker!

Lydia, however, felt that the Time Repair Agency also needed a build-out and some new hires to corral this exceptionally wily Time Breaker.  She brought in her miniature Christmas village, some dinosaurs, and the pawns from another game to assist us in our mission.

Full array of Time Breaker tiles, with the added tile and card nearby.  Almost every tile is occupied by a playing piece--Time Breaker pawns, pawns from another game, small dinosaurs, and Christmas carolers.  Three buildings from a miniature Christmas village are placed alongside.  A child's hand is adding a figure to the scene.

And this is how playing games inspires creativity, logical reasoning, math, etc.

Of course I did have to work out the other midpoint of Time, the point exactly between the Big Bang and the colonization of Alpha Centauri, both to satisfy my own curiosity and to demonstrate to Lydia that I’m sometimes able to do math with my own brain that I can’t figure out how to do on the calculator!

  • 13,800,000,000+3069=13,800,003,069 years between 13,800,000,000 BCE and 3069.
  • 13,800,003,069/2=6,900,001,534 and a half years from one timepoint to the midpoint.  It’s fun to do such a long long-division problem!
  • 13,800,000,000-6,900,001,534=6,899,998,466 BCE.  And to account for the half year, maybe we’d better calibrate our timepoint to 11:59pm on December 31.

But that was a pretty lonely New Year’s Eve, back before Earth or the Sun existed!  We prefer the calculations that place our epic battle on the deck of a ship in 345.  What with all those dinosaurs and Christmas carolers, the Time Breaker will never know what hit him!


2 thoughts on “Calculating the Midpoint of Time

  1. Pingback: 15 Ways to Build a Smarter Kid | The Earthling's Handbook

  2. Pingback: What have kids learned in a year of distance learning? | The Earthling's Handbook

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