In my Xenosystems review, I discussed the Orthogonality Thesis, concluding that it was a bad metaphor. It's a long post, though, and the comments on orthogonality build on other Xenosystems content. Therefore, I think it may be helpful to present a more concentrated discussion on Orthogonality, contrasting Orthogonality with my own view, without introducing dependencies on Land's views. (Land gets credit for inspiring many of these thoughts, of course, but I'm presenting my views as my own here.)

First, let's define the Orthogonality Thesis. Quoting Superintelligence for Bostrom's formulation:

Intelligence and final goals are orthogonal: more or less any level of intelligence could in principle be combined with more or less any final goal.

To me, the main ambiguity about what this is saying is the "could in principle" part; maybe, for any level of intelligence and any final goal, there exists (in the mathematical sense) an agent combining those, but some combinations are much more natural and statistically likely than others. Let's consider Yudkowsky's formulations as alternatives. Quoting Arbital:

The Orthogonality Thesis asserts that there can exist arbitrarily intelligent agents pursuing any kind of goal.
The strong form of the Orthogonality Thesis says that there's no extra difficulty or complication in the existence of an intelligent agent that pursues a goal, above and beyond the computational tractability of that goal.

As an example of the computational tractability consideration, sufficiently complex goals may only be well-represented by sufficiently intelligent agents. "Complication" may be reflected in, for example, code complexity; to my mind, the strong form implies that the code complexity of an agent with a given level of intelligence and goals is approximately the code complexity of the intelligence plus the code complexity of the goal specification, plus a constant. Code complexity would influence statistical likelihood for the usual Kolmogorov/Solomonoff reasons, of course.

I think, overall, it is more productive to examine Yudkowsky's formulation than Bostrom's, as he has already helpfully factored the thesis into weak and strong forms. Therefore, by criticizing Yudkowsky's formulations, I am less likely to be criticizing a strawman. I will use "Weak Orthogonality" to refer to Yudkowsky's "Orthogonality T...

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