The Random Walk.. and what it means to you.

A first grader knows that the probability of flipping heads on a coin is 50%. With 3 flips, you have a decent (1/8) chance of all heads, but as the number of flips increases towards infinity, so does the flip average towards 50%. Consequently, infinite heads becomes infinitely impossible.

At first thought, you might suppose 50.0000->% of the total flips landing on heads now means that the quantities of heads and tails become increasingly identical. Quite the contrary: With nearly infinite flips, quinitillions more heads than tails becomes a negligible surplus of increasingly minute proportions. The point being, as the average converges towards 50%, the total numeric tally skews wildly, and in great proportions.

A dojo on the morning after
by Blaine Fontana

If the same number of flips are repeated, we are just as likely to incur quintillions more tails. What happens is as the coin is flipped infinitely, the total tally skews distantly towards one outcome, and then, eventually (but at random), swings back to the other. The, perhaps, surprising outcome is an infinite cycling. All of this occurs as the total outcome average approaches exactly 50%.

Now let’s suppose you’re drunk, live in a one dimensional world (a straight line), and decide to flip a coin infinitely. Heads means one step the right, and tails one to the left. With infinite flips, it turns out that you will cross every point you’ve already stepped on an infinite number of times! Given infinite time, every event (position) will occur infinite times! What are the philosophical implications of this?

Lets try this experiment again, but in two dimensions. You’re drunk at the bar, but this time decide to walk home, taking steps equally randomly in the cardinal directions. The math ends up working out the same as it does in one dimension. Given infinite repetitions, you’ll cross every point you already stepped on an infinite number of times. You’ll find your home an infinite number of times!

Philosophically speaking, does this mean that in a hypothetical reality of infinite time, we’d end up repeating each action an infinite number of times? Sounds tiring, if not downright miserable or worse. Don’t forget, though, that you will infinitely push your boundaries in one or two dimensions and reach infinite new places as the infinite flips go on. And this is a profound truth alone: the infinite provides for infinite experiences.

The only downside to this reality seems to be having to repeat the experience of each experienced position infinite times! If, for example, one of those points contains an angry panda who wants to bite you every time you cross its path, you’re going to have to endure a vicious panda bite infinite times! So, is there any way to avoid repeating an event that’s blocking your path? Turns out there is.. welcome to the third dimension.

What makes the third dimension different from a one and two dimensional world is the existence of infinite planes. If the panda is located at the X,Y,Z position (10,20,5), you can get around the panda on a different plane, such as (10,20,4.999). If you’re not familiar with Z coordinates, just imagine jumping over the panda or floating underneath it. Obstacle avoided. Consequently, a lost bird traveling at random can fly around infinitely and never find its nest.

Hopefully, the bird didn’t leave anything sentimental in there, but more importantly, this immortal bird has plenty of time to craft a much better nest. So if there does exist a heaven which spans the infinity in more than two dimensions, take comfort in knowing that you may never have to repeat an unpleasant event twice. Likewise, don’t discount a beautiful moment in time. You may never experience that feeling again.