I was in a client meeting on Thursday; the topic was “taxonomies” of various sorts and the question arose as the relationship between different taxonomies of users. The answer: “they are orthogonal.” Talk about about term that makes my head hurt. I first heard “orthogonal” when I joined Digital Equipment Corporation; my first project was on the storied VAX/VMS. I was writing a system services manual and attending a lot of the hardware and software design sessions. They talked about orthogonality a lot. Official definitions of orthogonal indicate that it means “at right angles” or “statistically independent.” The closest definition to how it relates to the VAX is (not surprisingly) in the Jargon File:

adj. [from mathematics] Mutually independent; well

separated; sometimes, irrelevant to. Used in a generalization of

its mathematical meaning to describe sets of primitives or

capabilities that, like a vector basis in geometry, span the entire

`capability space’ of the system and are in some sense

non-overlapping or mutually independent. For example, in

architectures such as the PDP-11 or VAX where all or nearly all

registers can be used interchangeably in any role with respect to

any instruction, the register set is said to be orthogonal. Or, in

logic, the set of operators `not’ and `or’ is orthogonal, but the

set `nand’, `or’, and `not’ is not (because any one of these can be

expressed in terms of the others). Also used in comments on human

discourse: “This may be orthogonal to the discussion, but….”

Got it? Okay, so understanding the distinction “orthogonality” is something that made my head hurt in 1976 and it still makes my head hurt. What is it about head hurting? Last week, on the wonderful discussion led by David Hawthorne on AOK about Knowledge Markets, Bernice Johnson and Verna Allee exchanged messages about a 3rd cost factor in deciding about knowledge acquisition and program implementation (the first three are time, energy, and money): the hurt factor:

“I don’t know yet and it hurt too much to think about for long.”

That conversation got me thinking about wobbling while learning something new (which David Hawthorne had referenced in one of his posts). Gaining a distinction, like orthogonality, is like gaining the distinction for balance, which is what you need when you learn to ride a bike. You wobble on that bike until you “get it” — balance — and then you never have to learn it again. (This analogy is not original; I first heard it about 12 years ago, and many times since.)

Taking on something that makes your head hurt is in the nature of wobbling, a new concept or set of ideas that you haven’t quite made sense of yet. Sensemaking comes through connecting new things with things that you already know and have language for. This hurt factor adds a dimension of choice: you have a choice to go into new territory, knowing that you are bound to wobble.

Or you can not think about orthogonality for a really long time and have to wobble again when it comes unbidden back.