Invenntiveness

My own little corner of the Intertubes is supposed to be about explaining things, so why not get right down to explaining how to explain things?

Before we go any further, though, we have to get down to definitions. And trying to define ‘define’ can send you thinking in circles if you aren’t careful:

• Reference.com: to state or set forth the meaning of
• Merriam-Webster: to determine or identify the essential qualities or meaning of
• YourDictionary.com: To describe the nature or basic qualities of; explain
• Encarta (MSN): to state or describe something exactly
• theFreeDictionary.com: to state or describe something exactly

In comparing the above concepts, I think we can drill down to a couple of key points. ‘Defining’ something:

1. is a conscious, willful act.
2. is exact.
3. captures essence.

Definitions are an important first step in just about any process. The vast majority of arguments (internet or otherwise) get ugly at the definition phase, and need go no further. If you can’t agree on terms, you can’t even agree to disagree. Yet somehow, most of our educational systems are geared more toward definition instead of cognition, or understanding. Maybe it’s just a function of easier testing, but too many people believe that learning begins and ends with the definitions.

So let me re-wire the way you think about definitions, with an analogy.

A definition is a circle…

I didn’t come up with that on my own. My favorite professor, the late Dr. Daniel Pound, hit us with that bit of wisdom in a graduate-level political theory class. (I’ll write about that in a future post.) Simply put, the circle delineates the boundary that separates what ‘is’ from what ‘isn’t’.

Of course, we can quibble all day about which sheep belong “in the fence” and which ones will forever graze outside, but the circle works. By definition, it does. Three of the five definitions I cited above used the word “describe,” which includes as a definition “to represent pictorially; depict.”

And thus the circle closes back upon itself.

So, what do we do with this snake that eats its tail? Why, we start looping them together! By crossing the fences, we can start looking at ways that objects can share or not share various properties. And we can also seek out new insights and truths.

Okay, I didn’t come up with that on my own either. John Venn, a brilliant turn-of-the-century logician did – and launched what we now know as set theory. You’ll remember him from those diagrams that most hated in geometry, but seem to love in PowerPoint presentations. The interlocking circles provide a quick shorthand.

For starters, we have a nice little color chart.

This, of course, would represent the color mix of visible light, where the primaries are Red, Green, and Blue. Except, of course, for the gray in the middle. If this were completely accurate, I’d have White in the middle, and Black for the background. But I don’t want to break my blog template.

I’m looking forward to the day when I have to explain to my daughter why our perception of mixed light differs from our perception of mixed crayons. (Never mind. That will come in its own post fairly soon, and she can read it for herself.)

I’m rather fond of these myself. In addition to helping you organize your thoughts, they also form the bedrock of understanding Aristotelean syllogisms.

Periodically, when I gather my thoughts in a cohesive and consistent manner, I’ll be posting some Quick Thoughts involving these diagrams. Nothing fancy, no drawn-out explanations. Just some simple cool thoughts to pass the time.

[tags]Ike Pigott, Occam’s RazR, John Venn, Venn diagrams, Daniel Pound, Logic, Syllogism, Aristotle, Definitions[/tags]