One of the things I enjoy about having to use public transportation (since I don’t own a vehicle of my own) is the fact that while I’m waiting I get to think a lot.  Thinking is something I enjoy doing, and probably is the one activity that I do more than anything else.

As I’ve mentioned before on this blog, one of the things I like to think about is patterns.  Today, I thought a bit about random patterns and how, in reality, they aren’t “random” at all.

Consider, for example, dice.  One cube has six possible results when cast.  Throwing a die, you have a one in six chance of coming up with a specific number.  Which number will it be?  The answer is random.

It’s random because we cannot predict before hand which one it will be.  We know that the die will be 1, 2, 3, 4, 5, or 6; but we don’t know which one it will be.  So a single toss of a die is a purely random event.

Or is it?

If you cast a die 1,000 times, you will quickly find that the numbers all come up about as equally often as any other number.  For example, I wrote a simple program in Visual Basic .Net that calculated how many times a number on a die would show up after 1,000 rolls, and the first time running it I got the following results:

1 = 148
2 = 194
3 = 159
4 = 173
5 = 151
6 = 176

The range was from 148 to 194 (a difference of 46).  Running it a second time produced the following results:

1 = 159
2 = 186
3 = 154
4 = 154
5 = 168
6 = 180

The range here was from 154 to 186 (a difference of 32).

What happens if we extrapolate further and test 10,000 instead of 1,000?  The first time I got these results:

1 = 1605
2 = 1632
3 = 1745
4 = 1701
5 = 1619
6 = 1699

Now the range was from 1605 to 1745. After 10,000 rolls there was only a 140 difference between the highest number of instances and the lowest.  Running it a second time resulted in:

1 = 1658
2 = 1637
3 = 1695
4 = 1611
5 = 1699
6 = 1701

Here the range was from 1611 to1701—a scant difference of 90 between the lowest and highest frequency.

Despite increasing the total count by a factor of 10, the range between the number with the most instances and the number with the least only increased by 33%.

And just for fun, I did it for 100,000 and got these results:

1 = 16583
2 = 16620
3 = 16358
4 = 16836
5 = 16929
6 = 16675

The range here was from 16358 to 16929 (a difference of 571).

Running it a second time resulted in:

1 = 16788
2 = 16644
3 = 16709
4 = 16635
5 = 16610
6 = 16615

The range here was 16610 to 16788 (a difference of only 178!).

So when you toss a die, despite the fact that you don’t know what the die will come up with, it will tend to pop up on each number an equal amount of time.  The question is: why?

Each toss of the die is completely random.  The die doesn’t “know” what was tossed before it.  It cannot keep track of what number should be coming up.  Yet invariably, each number gets represented to almost the exact same degree.  This means that even though each individual toss is random, the structure as a whole is following an orderly process.  There is a hidden order beneath the randomness that is at work.

Once you realize this is the case in casting dice, it becomes a rather simple matter to realize that it is in all of nature.  Consider the fact that every person has his or her own unique fingerprints—yet everyone can tell what a fingerprint looks like.  There’s a structure to a fingerprint such that it is possible for anyone to identify a fingerprint as a fingerprint instead of a footprint.  Or consider a tree.  Each tree has its own unique branch structure, yet aspen trees always look like aspen trees and pine trees always look like pine trees.

This is even demonstrated in humanity.  All humans have the same bipedal shape—yet no two people are the same.  We each have similar internal organs, yet no two organs are identical.  Each of us is randomly different from one another, and yet each of us follows an underlying structure such that we have a “human-ness” quality to us.

How random are we then?  There is a pattern that we must adhere to.  This is how we can recognize that we are all human while at the same time differentiating between Steve and John.

But can we take it even further than this?  One of the most “random” processes is nuclear decay—and yet it is predictable enough to calculate a half-life for the material.  Each of us is made up of subatomic particles that exist in probabilities (just as it is a probability when you cast a die as to which one will show up).  Thus, it seems that the very fabric of matter and energy itself is made up of these random structures that nevertheless follow an underlying order.  It’s why we don’t suddenly cease to exist because matter “decides” to behave differently.  Matter cannot.  Even though there are “random” processes involved, these processes act as if guided.

Why should that be the case?  What is it that can create the order beneath the random?

I’ll leave it to you, Reader, to think on that.