Integration

At a higher altitude the flag unfurled, we reached the dizzy heights of that dreamed of world—Pink Floyd

AUTHOR'S NOTE: A few weeks ago, I wondered what was behind my recent spate of posts. After some reflection, it's clear I've been searching for a theme for the 2011-2012 ski season. Past themes have included uncertainty and psychology, but this year I'm going to write about complexity. Very often complexity is managed by breaking things down into constituent elements. As we shall see, this has benefits and drawbacks.


This post compares simplicity with complexity; specifically whether or not it is desirable, possible, or necessary to simplify complex information. This post will require significant patience, so if you're not feeling patient ... please come back when you are.

Experiment #1

Maybe you don't often think about linguistics, but it's pervasive, and you rely on linquistic techniques every time you read, write, and communicate. In this experiment, we're going to borrow a few tricks from linguistics and engage in a thought experiment or two. Consider the following sentence:

• The snow is between the sky and the ground.

Figure 1.1. The sentence is a system composed of individual elements ( called words ) and we could say that meaning emerges from the system. Spend a moment thinking about alternate word arrangements. While you're at it, take a long, hard look at the sentence and see if you can extract additional meaning from the arrangement of the words. Does rearrangement affect your perception?

• The ground and snow are below the sky.
• The sky is above the snow and the ground.

Figure 1.2. What about removing individual letters? Sometimes it matters and sometimes it doesn't, but having not seen the original, how many people can reconstruct the original phrase from the phrase below?

• The now is betwen he ky an te grond.

Figure 1.3. If removing letters doesn't work very well, what about reducing the system to its constitutent elements? You can still extract meaning from the individual words, and it may be possible to extract a general concept from the words themselves. But ask yourself, do the individual words have the same meaning as the original or has something has been lost in the simplification? How would you describe the change in meaning for this diagram?

• And
• Between
• Ground
• Is
• Sky
• Snow
• The

Figure 1.4. What about the individual letters? Do you feel like this representation is much simpler than the original sentence? If so, you can test the hypothesis by comparing the time required to memorise the string of letters with the time required to memorise the original phrase. One thing we can say for sure is that the original meaning has been lost entirely. Still, the individual letters are very easy to understand in the sense that you know what the letters themselves represent. How would you describe the change in meaning for this diagram?

• A, B, D, E, G, H, I, K, L, N, O, R, S, T, U, V, W, Y

Figure 1.5. I hate to take you back to grammar school, but this is a diagram of the sentence. It's another model of the system and it gives you an idea of how to simplify the system in a way that preserves its essential meaning: snow between sky and ground. If we want an even simpler representation, we can use the following: sky snow ground. In this case, we've kept the three essential nouns and we're encoding the position of the snow ( between ) in the structure of the phrase itself. Neither simplification constitutes a proper sentence, but we aren't interested in grammar at the moment. As it turns out, the really essential elements are three nouns, but counter-intuitively, adding an adjective and a conjunction significantly increases understanding. All this might sound nutty, but you probably do it almost every day. How many times have you revised an email and wondered if you're still getting your point across? Do you add or remove information to simplify and increase clarity? My guess is that you do both.

Off The Philosphical Deep End

Well not really, but here's a question that seems very philosophical: why does writing work? How is it possible to take 26 characters and produce the works of Shakespeare, The Avalanche Handbook, and this blog? The science of physics provides a very reasonable answer.

Writing works because of a concept called mixing. The origin of mixing depends on who you ask, but classically, mixing is used to describe irreversible processes such as mixing ink in water or mixing vodka, water, and vermouth. Literature, which is an execellent example of complexity in its own right, emerges from the alphabet because we can mix the letters into words, we can mix words into phrases, and we can mix phrases into sentences. You can even mix letters and make up your own words, which might sound a little ridiculous, but it happens every day.

But anyway, this is where scale comes in.

In addition to the concept of meaning, we are also working with the concept of scale. Where is meaning encoded? At the scale of a sentence, clause, word, or letter? Actually, meaning is encoded at all scales. A is not the same as B just as apple is not the same as bat and I like apples is not the same as I like bats. Yes, you can file this under useless philosophical controversies, but it's quite true nonetheless.

This blog post also exploits mixing. Not only am I mixing letters, phrases, and words into a novel work, I am also mixing concepts from linquistics, physics, mathematics, and meteorology. But let's go back to the word exercise for a moment: you can see that simplifying a system doesn't always make it easier to understand.

So, why is that?

When you simplify something, you create something novel, and there is a very significant chance that new complexity will emerge from your novel creation. In many cases, the complexity that arises from simplifications actively prevents clear understanding. Sound like a stretch? Go back to the sentence experiments and do them again.

Or just ask yourself how many times you've requested clarification from the author of a five word email.

Experiment #2

This experiment is designed to test your patience ( and powers of observation ).

Figure 1.6. Watch this video of the environment, but pretend that it's snowing and you have magical binoculars that allow you to see through the storm. Rather than thinking about terrain, snowpack, and weather, just think about the environment containing the terrain, snowpack, and weather. The interaction between the systems produces remarkable variations.



Write three words that describe what you've observed. Mixing makes things quite complicated, doesn't it? Three words aren't quite enough? Alright then, start by explaining the phenomena you've observed with a single sentence of up to 10 words. If that's not enough, then feel free to use a paragraph. If you still feel constrained, use three paragraphs: introduction, body, and conclusion.

Samples

Here are several sample models of the phenomena at play. Mixing is represented by the arrows, and the on-going nature of the phenomena are represented by the continuous cycle diagram.

Figure 1.7. Here's my three word version of my observations from the video. You'll notice that it's wrapped up in a conceptual model that integrates the elements. I spent a week thinking about this and actually consulted several outside experts. By itself, this model is very easy to understand. But as in the real world, the factors in this diagram are mixed with the factors in the following diagram.

Figure 1.8. Here's a model of what's going on in the snowpack. Again, by itself snow metamorphism isn't particularly difficult to understand. And again, complexity arises because the factors in this diagram are mixed with the factors in the preceding diagram and the following diagram.

Figure 1.9. Here's a model of what's going on with the weather. When viewed alone, these weather trends are very easy to understand. But again, complexity arises because weather factors are mixed with factors from the preceding diagrams. This means that, ultimately, the direction of instability corresponds to the magnitude, rate, and duration of each factor, which is determined by a complex mix of other factors ( and so on ).

This post probably seems a bit strange, but I want to make a point.

Simplicity and complexity are not mortal enemies. They're not at opposite ends of a spectrum. In fact, comparing simplicity with complexity is like comparing apples and oranges. As a backcountry skier, it's important to ask yourself if you really understand the sources of complexity.

HINT: It's not the science.