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Dimensional decoupling

The latter one. It follows the same pattern as this diagram.

Dimensional decoupling

Yes, the failure modes are mentioned in the last part of the post: trying to decouple identical things, and trying to decouple unrelated things.

Dimensional decoupling
How do we identify situations where we are using some concept which may be usefully decoupled? Or, alternatively: which of our concepts in fact constitute couplings of two (or more?!) orthogonal[2] concepts—and how do we tell?

Great catch. This is something I didn't mention in the article because I typical-minded. Here's a description, which I will add back to the article later probably:

1. Whenever you come across something that seems like it is logical, but violates your intuitions, then there's a high chance that this technique can help. This is an easy situation to use dimensional decoupling and it comes naturally, because we are already in 'interrogative' mode.

2. When you're stuck on a problem, go through your assumptions and try to decouple them one by one. Often you will find that some assumptions can be decoupled and then one of the resulting parts can be relaxed. This is relatively harder and needs practice, because it's not natural to examine our assumptions like this.

Having identified a concept which is, in fact, a coupling, just how do we decouple it? Ok, so we have some concept X which we have (somehow) decided may be decoupled into two (or more!) orthogonal concepts Y and Z. Now, how do we identify Y and Z? (And how do we verify that Y plus Z is, in fact, what we originally thought of as X?)

I believe that the hard work is in identifying the object that needs decoupling. Once it's identified, the decoupling method is relatively simpler.

1. The easiest one is with opposites. Happy vs sad, masculine vs feminine, straight vs gay. These are really easy to decouple. To verify them, we just see whether the two new "corners" make sense. E.g. Is it possible for someone to be interested same-sex and opposite-sex people simultaneously? Is it possible for someone to be interested in neither? Y and Z are just the two poles of the spectrum.

2. For non-opposites, make them into poles. Bias vs accuracy. Bias is one pole, so the other pole is "unbiased". Accurate is one pole, so the other pole is "inaccurate". To verify them, again we see whether the two new "corners" make sense.

Note that some pairs { Y, Z } in such situations may not be entirely orthogonal, i.e. there may be a systematic(perhaps because causal) correlation between them.

Yes! They are almost certainly correlated - that's the entire reason that they are so often seen as entwined. Counterintuitively, higher correlations are often more valuable to decouple. On the last graph, we can also think of it in terms of correlations:

1.0 correlation - this is the 'red zone' where we say crazy things like "loud isn't high volume". The correlation is so high that they shouldn't be decoupled.

0.5-0.9 correlation (roughly) - this is the valuable area. The high correlations means that the two concepts frequently go together. But in the situations where they differ, it's super easy to miss.

0.0-0.5 correlation (roughly) - this is not as valuable. Because the correlation is low, it means that we wouldn't naturally think of them as going together. Therefore, there is low risk that we are incorrectly coupling them.

Dimensional decoupling

You're right, bucket errors are the result of entwining things. Dimensional decoupling is a way of reducing bucket errors. In my personal experience, once I used dimensional decoupling regularly, it became second nature and automatic. I think it's important to have low-friction ways of reducing bucket errors.

And yes, the most valuable decouplings are ones where they aren't identical but we think they are. But until we try to decouple them, we don't know whether they are or not!

Dimensional decoupling

Which diagrams disagree?

The pattern is an application of dimensional decoupling - the dimensions are the in the headers of the diagrams.

Top left: sad and not happy.

Top right: sad and happy.

Bottom left: not happy and not sad.

Bottom right: happy and not sad.