Transitive Optimization Considered—Interesting

Published on July 10, 2024, filed under (RSS feed for all categories).

Transitive optimization is optimizing Y by virtue of optimizing X.

The idea borrows from mathematics and economics* To explain, I prefer the economics definition:

Consider three bundles of goods, A, B, and C. If a consumer prefers A to B (denoted as 𝐴≻𝐵) and B to C (𝐵≻𝐶), transitivity implies that the consumer will prefer A to C (𝐴≻𝐶).

Accordingly, transitive optimization means that if we improve A to optimize B, and optimizations of B also optimize C, then improving A should also lead to an optimization of C.

For example, if we do something (A) that optimizes website performance (B), and website performance benefits the user experience (C), then A, optimizing B, should also optimize C. Transitive optimization.

Here is where things get tricky—and hopefully  interesting:

  1. Optimizations are not always checked on transitivity.
  2. Optimizations may or may not be transitive.
  3. One-dimensional optimizations have their own problems.

1. The Curious Case of Neither Checking Nor Mentioning That an Optimization Is Transitive

The first observation we can make is that transitive optimizations aren’t always called out as such. That’s not a terminology thing—it’s instead both a bug and a feature.

Take performance optimization again. It doesn’t seem common that user experience (which performance optimization optimizes transitively) is being called out as the optimization target. (Scanning headlines, that checks out.)

This appears to be a feature: That performance benefits the user experience seems clear, and therefore repeatedly mentioning UX would be spelling out the obvious.

But it also looks like a bug: Anything that optimizes transitively seems to be an optimization for the reason of optimizing whatever it optimizes transitively. That is, if we optimize performance in order to improve UX, then that doesn’t look like something never to be mentioned—it looks so substantial perhaps always to be mentioned.

That makes for the somewhat curious case, of not mentioning (and maybe not even checking) that an optimization is transitive. Interesting 🙂

2. The Non-Trivial Question of Whether an Optimization Is Transitive

Not every optimization can be transitive, because then there would be no “final” optimization. Some optimization must be the target optimization.

That means that an optimization needs checking whether it is transitive.

Performance optimization seems to be on the easier side—if better performance is better for a user, then performance optimization leads to user experience optimization. Cool!

But take accessibility, and accessibility improvements, and therefore accessibility optimization. That seems transitive, too—it seems to likewise transitively optimize the user experience.

But, again, is this as true, or true as often, as with the more trivial case of performance optimization? If we improve TTFB, FID, LCP, INP, some other three- or four-letter abbreviation, it seems to benefit most every user.

But, once more,—and this isn’t a case against accessibility, which would be a serious error in thinking and logic—the adding of alternative content, the simplifying of language, or the improving of contrast do not have the same reach. They improve the experience for various groups of people, of various sizes. And, something we get to in the next point, they may have consequences for other areas.

Make it easier—or different—, and now take SEO (an optimization that’s even called an optimization!). Is SEO transitive? Google, originally putting the user first, might say so (i.e., SEO means UXO). Many people observing SEO over the last 20 years might disagree—yet they may say SEO optimizes site owner bottom line or search engine bottom line, or perhaps nothing at all anymore.

We could pick other areas in which we optimize something, and look into whether or to what degree the optimization is transitive. In the end, that seems non-trivial to determine. Interesting 🙃

3. The General Issue of One-Dimensional Optimization

About this, I’ve written an entire article: One-Dimensional Website Optimization Considered Interesting Harmful.

The gist is, we also have the following problem: It’s not economical, even harmful, to push hard and exclusively on a single optimization. That gets really expensive, and can lead to highly impressive garbage.

Transitive optimization may suggest that in certain cases, we couldn’t only do one type of optimization, which would seem like transitive optimization was at least two-dimensional.

But that doesn’t follow logically, and it misses the first two points—we first need to (be able to) determine whether an optimization is transitive, and then we may benefit from labeling it as such… which kind of exposes the one-dimensionality of the optimization, if whatever optimization we’re talking about is all we’re optimizing all day. Interesting!

Are you still there? 🫰

What Does This All Mean, and Why Does It Matter

This whole essay isn’t going to change the world.

However, I hope to have shown that the case is, indeed, interesting. (At least a little bit. Don’t you agree?)

Yet it means this:

And that’s enough “interesting” for today. Next time, I’ll be back with something dry again.

* Given few mentions, that’s at least where I borrow from. But I may always miss something, obvious or not, so perhaps this is all clear, or all known, or goes under a different name, or something else.

I’ve meant to have this post reviewed, and then opted to publish even though I’ve felt like I may be missing something obvious. Did I? Please teach me!

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About Me

Jens Oliver Meiert, on September 30, 2021.

I’m Jens (long: Jens Oliver Meiert), and I’m a frontend engineering leader and tech author/publisher. I’ve worked as a technical lead for companies like Google and as an engineering manager for companies like Miro, I’m close to W3C and WHATWG, and I write and review books for O’Reilly and Frontend Dogma.

I love trying things, not only in web development (and engineering management), but also in other areas like philosophy. Here on meiert.com I share some of my views and experiences.

If you want to do me a favor, interpret charitably (I speak three languages, and they can collide), yet be critical and give feedback for me to learn and improve. Thank you!