The Beauty of Chaos

Tell me, what comes to your mind when you think of Chaos?

I know it is kinda of a hard word (concept) to address let alone think about, what images rise above your mental horizons?

• It could be raging bulls running down the streets of some Spanish town.
• It could be the panic of being in a building that has caught on fire.
• It could be “spring breakers” parading through a coastal town.
• It could be the immediate aftermath of the Boston Marathon bomb explosion.
• It could be the frenzy on the court after winning the Championship basketball game.

Each one of those a little different from the other one but I would suspect that these examples give you a pretty good idea of what I mean by chaos.

My images and your images probably do not correlate too well with the concept of “beauty” but bear with me because we just got started. And yes, I do understand that beauty is in the eye of the beholder and that what is one man's (or woman) floor is another man's (or woman) ceiling.

So, there is a random nature to beauty or a sort of randomness if you will, somewhat unpredicted and certainly unexpected.

Actually, randomness means lack of pattern or predictability in events.

A random sequence of events, symbols or steps has no order and does not follow an intelligible pattern or combination. Individual random events are by definition unpredictable, but in many cases the frequency of different outcomes over a large number of events (or "trials") is predictable. 

For example, when throwing two dice, the outcome of any particular roll is unpredictable, but a sum of 7 will occur twice as often as 4. In this view, randomness is a measure of uncertainty of an outcome, rather than haphazardness, and applies to concepts of chance, probability, and information entropy or the average amount of information that is contained within each event.


However, in the fields of mathematics, probability, and statistics use formal definitions of randomness.
In statistics:

1. a random variable is an assignment of a numerical value to each possible outcome of an event space.
2. a random process is a sequence of random variables describing a process whose outcomes do not follow a deterministic pattern.

Is the beauty of it all starting to emerge?


So... let's put these two words together and we have RANDOM CHAOS which, on the surface, seems to have made the beauty of it all just disappear.

In my attempt at clarification, let me suggest that create ourselves a data pool from which we are randomly going to extract some type of information and put that extracted data on a virtual white board as it is being randomly collected giving us the appearance of chaos. Ok... and, the data pool that we are going to create is all the women in the United States for example, rather than all the women in a particular State which would work equally as well.


Ok... and, from that data pool of women we are going to collect their height in inches. And, those numbers may look something like this:
60
63
62
59
61
60
60
65
58
58


As you can see, we have 10 numbers and we need to continue to randomly collect our measurement data until we have, at least, 100 pieces of data.


Since height data is collected by using a measuring device, I have referred to it as measurement data so in order to make sure our data is accurate, we have to make sure that our measuring device has been properly calibrated by certified calibration people. Additionally, we must make sure that those people collecting the data using the measure device the same way every time and follow the procedure the same exact way every time.


Ok... so, let's make the assumption that we have randomly collected 10,000 heights of women and while they have been collected in a random sequence, we decide to rearrange them into classes, identified by height ranges, like:
48 – 52
53 – 57
58 – 62
63 – 67
68 – 72
73 – 77


Ok... so, this is relatively easy to follow and let me also share with you that we could, in fact, have more of fewer classes, depending up how we want to look at the date; however, for my purposes here, I would say that if I was to do anything at all, I would create more classes instead of fewer; in fact, I would probably create a class within each inch, breaking it down into millimeters for complete accuracy.
But, let's deal we these classes for right now because it helps to simply the explanation.


Ok... so, over every class, I am going to but a capital X every I reach 100 women whose height fell into that class. And, once this task is completed, I would take a pencil and draw a line that would no doubt be curved up to a high point and then downwards to lower points, from the top of the first column of the first Xs and then to each subsequent column of Xs until I arrived at the last column of Xs.


Standing back and looking at what I had just done, I would be willing to bet my “bottom dollar” that the image that we just drew resembled a BELL SHAPED curve almost exactly. And, I could also say with 99.7% degree of certainty, that

1. 48 – 52 would represent 2.35% of all the data collected
2. 53 – 57 would represent 13.5% of all the data collected
3. 58 – 62 would represent 34% of all the data collected
4. 63 – 67 would represent 34% of all the data collected
5. 68 – 72 would represent 13.5% of all the data collected
6. 73 – 77 would represent 2.35% of all the data collected

And, this my friends is how we can see the beauty in numbers that at first glance seems like it is in chaos and then at second glance, perhaps we see it in random chaos... but, for some of us, we see symmetry and orderliness emerge within the randomness of it all.


At this point, you should be seeing the beauty of chaos... and, you should be understanding how this beauty can be used to predict a series of events in the future.


For instance, let's just say, I went to one State in the US to collect samples just in that State regarding the height of women and I used the exact same methods and made sure my measuring device was properly calibrated.


Before, I started collecting any data at all, I could make the assumption with 99.7% certainty that this new set of data would be almost an exact copy of the data previously collected involving every State in the US.

However, I could not make that statement or be as confident with my predictions, if I decided to conduct this same experiment in Japan, Russia, China, or Ethopia.


Everything... all of life follows a pattern that on the surface at first seem chaotic and just a bunch of randomness. Maybe now, you will see things a little differently.