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.

Comments:

The importance of distinctions

Over time I've come to appreciate the fundamental role that language and distinctions play in learning. Seems you can only 'get' a new concept if you can assimilate and relate it to something you already know.

To learn something new, means you have to understand why this new 'thing' (concept, thought, idea, meme) is different - that is making a distinction.

Distinction making is a key basic social knowledge practice that we do not talk enough about IMO.

Enjoyed your post

# posted by  Denham : 11:50 AM

 

orthogonality: at a first glance, isn't that the opposite of your theme: relatedness? the fact that the things are "totally" independent? And, at a second glance: is this condition not - in itself - something like a negative mutual definition, thus relating the things together? Because for any random "things", true orthogonality is very unlikely.
Wobbling and vexing: hence simplicity is at least as interesting as complexity, and possibly more useful. And thinking CompleXimple is in itself of that kind - aha, another theme re-appears, reflexive recursion. Let's stop here.
Christianhauck (signed here in the content since I don't have a blogger account)

# posted by  Anonymous : 2:28 AM

 

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