Can you solve the Big Bang riddle? - James Tanton
It’s moments after the Big Bang
and... wow, you’re still reeling.
You’re a particle of matter,
amidst a chaotic stew of forces,
fusion, and annihilation.
If you’re lucky
and avoid being destroyed by antimatter,
you'll be the seed of a future galaxy.
You gravitate towards a ring of particles
that have devised a game.
A friendly gluon explains:
there are an equal number of matter
and antimatter particles.
At the blow of a cosmic whistle,
every particle of matter with a particle
of antimatter to its immediate right
will merge with that anitparticle
to—poof!— both annihilate.
The circle will tighten
to make a smaller circle,
and the process will repeat
until just one particle of matter remains.
They’d been waiting for someone like you,
as with a perfectly balanced setup,
no one would be left in the end.
As guest of honor, they’ll let you choose
where to insert yourself into the ring.
What spot should you choose to make sure
you’re the last particle standing?
Pause here if you want
to figure it out for yourself.
Explanation in 3
Explanation in 2
Explanation in 1
A general strategy can’t rely on knowing
what the circle looks like.
But we can rely on how it should end:
with you as the last particle standing.
Let's start there and work backwards.
Just before this, there were also
some matter/antimatter pairs.
Here’s 3 for the sake of example.
This right away suggests a strategy.
You can simulate annihilations
in any circle
by marking all pairs
of adjacent particles,
then the newly adjacent pairs, and so on,
to reach this final set.
If you map them back
to the original circle,
standing to the immediate left
of those final matter particles
or the immediate right
of final antiparticles
means you’ll reach this endgame state
and survive.
So here are the safe spots
in all three given circles.
You find a good position and experience
the bittersweet radiance
of your new friends pairing off
and becoming pure energy.
You’re soon left alone.
But wait a minute!
Today’s the big day.
You’re an intelligent creature of matter
amidst a chaotic crowd of alien races.
Every hundred million years,
sentient species of the galaxy
send emissaries to the core
to pay tribute to the galactic seed
you’re all descended from.
Each of the 27,182 attendees
has brought a cube of matter
and a cube of antimatter.
Except you: you’ve been chosen
to represent your famed ancestor
and reenact its moment of choice.
Everyone places their matter
and antimatter cubes in a ring.
Your job: pick a spot to stand
where you won’t be annihilated.
The ring is too large to simulate
annihilations like before,
but you have a programmable device
you can point at spots between cubes.
The device can detect the full sequence
of cubes around the circle,
count cubes of each type,
perform arithmetic,
and carry out simple logical commands.
How do you program your device
to identify safe spots?
Pause to figure it out for yourself.
Answer in 3
Answer in 2
Answer in 1
Let’s go back to our earlier approach:
running time backwards
starting from you alone,
then a sequence of pairs of cubes.
A second step back produces more pairs
nestled between existing cubes.
As does the next, and the next,
each adding nestled pairs
like a Russian doll
of fundamental particles.
A pair never forms around an existing cube
because only adjacent cubes annihilate.
Your survival depends
on the matter particles to your right
buffering you from antimatter.
We can mathematically model this idea
with a sum, starting with your +1.
For instance, this would be +1+1-1+1-1.
From your perspective,
no matter how far you look,
this sum will be positive.
Considering how we introduced pairs,
this makes sense—
each inserted plus was immediately
followed by a minus.
If we examine the starting position
of any other matter cube,
its sum will eventually hit zero.
The moment that happens
marks its exact annihilation partner.
Again, our introduction of pairs
reflects this;
nestled pairs only delay the inevitable
for the outer cubes.
We can now program the device.
Start a running sum with +1,
representing you,
and scan around the circle.
For each matter cube, add one,
and for each antimatter cube,
subtract one.
If all 54,364 cubes have been scanned
without the sum ever hitting 0,
that spot is safe.
Nothing left to do
but enjoy the fireworks.
