Next I try subtracting each number from the one above it in the sequence (that is, 80 – 50 = 30, which gives me the second number in the third column). This is a clever trick that often works for finding simply polynomials (more on this in another post), but it's giving junk here (that -50 in the 3rd column is just a mess).
Saturday, March 20, 2010
“Sensemaking” is what you do when you’re trying to figure out some complicated problem that involves too much data, or the wrong kind of data. It’s problem-solving, but of a particular type. When someone says “I need to make sense of <something…>” generally what they mean is that they don’t get what’s going on in a deep way.
So what do one do? Answer: You start collecting information about what’s going on, then start to organize it in ways that make sense.
That’s kind of abstract, so let me give you the smallest possible sensemaking problem I could think up.
Here’s a number sequence: 80, 50, 40, 90, 70, 60, 30, 20
Now I’ll tell you that the number 10 fits into this sequence. So… where does 10 go?
Think about this for a second. (Really! Don’t read farther until you’ve given it at least 30 seconds of thought.)
If you’ve done problems like this in the past, you might have done what I did and made a table of numbers, with each column showing a different operation on the numbers.
The reason for making a table like this is to try different artithmetic operations, looking for a pattern that you recognize. In this case, we’re looking for a numeric relationship. So first I try dividing the number by 10 (that’s the second column). That’s better, but I still don’t recognize any pattern.
Then I tried dividing the number by 10 and then squaring the result. (80 / 10)^2 = 64.
No such luck. This is just mucking around, and not revealing anything to me. I try a few other operations… and nothing seems to be working. Usually if you just fool around trying different operations on the sequence of numbers, something will emerge.
I step away for a bit, and then realize that maybe this question is NOT a numeric question, it just might LOOK like a math problem. Perhaps, just maybe, it’s a TEXT question. That’s the kind of thing that makes puzzles so hard—you focus intently on one possible solution that you don’t think about anything else.
So I write down all the names of the numbers into my table. Now it looks like this.
And I notice something interesting with this pattern… The names of the numbers are all in alphabetic sequence! It has nothing to do with any mathematical formula at all!
This tells me that the number 10 belongs in this sequence just after 60 (sixty) and before 30 (thirty). So the answer is: 80, 50, 40, 90, 70, 60, 10, 30, 20
As you might have guessed, I’ve been using a spreadsheet to help me figure this stuff out. A spreadsheet is nice for doing this kind of sensemaking task because you can try out lots of hypotheses really quickly. Want to divide everything by 10, just make the formula once, then you can extend it downward with a single keystroke. (It’s control-D, for Down.)
And the really great thing is that if we add 10 (and it’s name “ten”) to the spreadsheet, and then sort the spreadsheet by the “names” column, we’ll get exactly the sequence we want. Namely,
Now let’s pop back up to the question of sensemaking again.
In this case, I’ve been using a spreadsheet because it’s a handy way to keep track of a sequence of numbers. Once you’ve got that sequence, you can do various operations on them quickly and easily. As you can see, I can even sort by alphabetic sequence to verify that everything’s right.
In the language of sensemaking, I’ve been “trying out different representations,” looking for one that explains what’s going on with this small data set. That is, I’m trying to find a way to represent that data in a way that has a neat, simple and correct explanation for what’s going on.
I must have tried 5 or 6 different representations before I figured out that it was the alphabetic sort order that was the best explanation. That’s part of the process too! For almost any sensemaking task, finding the best solution (or interpretation of the data) means trying out different “theories” about what’s going on. I had the “divide by 10 and square it” theory, and that didn’t work at all. I tried others, but nothing really clicked until I got here to the last step. Once I figured that one out, everything fell into place.
As I said, this is just about the smallest sensemaking problem I can think up. It’s not something I can do in my head—I really did have to sit down and fool around with the data for a while, searching for a pattern that explained everything.
And, in the end, the explanation is neat and clean; it explains everything.
This is not the usual case with real-life big & hard sensemaking problems. If I could make sense of the Middle East situation by filling out a table, I’d do so. But in the smaller less geopolitically complicated day-to-day sensemaking tasks, tables and other ways of organizing the data often help by making the data visible and comprehensible. And that’s almost entirely the trick of sensemaking… converting data from a large, intractable mess into something that’s smaller and has a clear underlying explanation.
That makes sense to me so far.