We’re not in disagreement. If you create an interface with reference to the user’s existing knowledge you are drawing on the conventions they are familiar with. Across a single site you would then (hopefully) maintain consistency. For example, a convention might be logo in the top left of the screen will link to the homepage. To be consistent, this behaviour would be maintained throughout the website.

Consistency does enable a system to be learnt: push lever, get peanut. Adhering to conventions reduces the cognitive burden of learning a new system: last time I pushed the lever I got a peanut, this time I push the lever expecting a peanut, if I get a peanut-great, if not I’ll need to learn a new system.

The worst case is when a convention known to the user is either misused or used inconsistently. This introduces uncertainty. I push the lever once, I get a peanut, twice a lemon, etc. etc.

It’s not necessary to adopt a binary approach to conventions and consistency. They’re complementary approaches/considerations.

When did ‘what people know’ become different from ‘consistency’?

It depends on who is using the word ‘consistency’. Many people interpret it to mean “make things look and behave the same as other things” — independent of what the user knows or needs. (For example, “we need the same navigation across all of our sites” or “we always use ‘OK’ and ‘CANCEL’ on all of our forms.”)

On the outset, this feels like it works for the user, but, as the design inherits any amount of complexity, it quickly starts working against the user and the effectiveness of the design.

“Don’t Make Me Think” come to mind.

Consistency enables a system to be learnt.

Sorry Andy, but I disagree: Consistency is the Wrong Approach

(Even the eye tracking article you provide says so. Just read the bulleted tips at the bottom. They say the intent and context of use far outweighs any consistent use of contextless layout convention.)

Recognising left hand navigation as a convention does not preclude right hand navigation from also being a convention (albeit a convention that has been significantly socialised by blogging software default layouts).

Identifying something as a convention requires that the experience of the thing is common to a community. The size of that community may vary. For example a word may take on meaning that is specific to a region (dialect), ‘Bad’ has both a formal and colloquial meanings. If the word is used consistently, e.g. to mean ‘good’ a person from outside of the community will gradually become aware of the new, context-specific meaning. Consistent use leads to an understanding that may be thought of as conventional.

If there’s one thing usability evaluation reminds you of, its that people learn. We draw on our previous experience when engaged in any activity, including using websites. Consistency enables a system to be learnt. Consistent use of conventions requires less learning as it drawns on prior experience. Inconsistent use of convention is likely to be frustrating. (For example, when underlined text does not denote a link.)

As to right hand navigation ‘being just as good’, without context (i.e. what is meant by ‘good’), such as statement is meaningless. Good as/for what? If by good you mean ‘efficient’ this article on the evaluation of navigation using eyetracking software may provide further food for thought.