I remember sitting there staring at the "linear operators", trying to figure out what the hell they physically did to the eigenvectors—trying to visualize the actual events that were going on in the physical evolution—before it dawned on me that it was just a math trick to extract the average of the eigenvalues. Okay, but... can't you just tell me that up front? Write it down somewhere?
Umm, linear operators rescale the eigenvectors, without changing their direction, seems pretty physical to me. Like those polarizers EY kept talking about, they leave some polarizations unchanged. Another standard example is the rotation matrix, it does not affect the axis of rotation.
Oh, I forgot, the math doesn't mean anything, it just works.
In exactly the same way the Lagrangian and the least action principle "doesn't mean anything, it just works" in classical mechanics.
Honestly, I think the quantum sequence demonstrates that knowing about mental biases isn't enough to avoid falling to them.
I would argue this whole series presents a false dichotomy (many worlds vs. copenhagen). There are many more potential interpretations- there are even no collapse interpretations that rely on a single world. Ensemble/transactional/objective collapse,etc. None are discussed, but all are dismissed.
Further, Yudkowsky confuses the map with the territory in a spectacular fashion. The territory is a series of experiments where scientists can't make specific predictions (and instead can make predictions about classes of experiments). The map is quantum mechanics. Yudkowsky suggests we should believe many worlds, in part, because to do otherwise would require the only non-deterministic rule in physics. Well of course it is- this is the first (seemingly) non-deterministic/probabilistic territory physics has tried to map! Should our instinct, when we find an area where the old map doesn't work, be to assert that territory itself is wrong? Experiments only APPEAR non-deterministic, but really....
Its no surprise that physicists attempting to extend their map would create a deterministic model and graft a non-deterministic component on top- deterministic systems are where they learned cartography (to extend a metaphor). There are active efforts to describe collapse by adding a stochastic term to schroedinger dynamics- why should we take these less seriously than many worlds?
Today's post, Why Quantum? was originally published on 04 June 2008. A summary (taken from the LW wiki):
Why do a series on quantum mechanics? Some of the many morals that are best illustrated by the tale of quantum mechanics and its misinterpretation.
Discuss the post here (rather than in the comments to the original post).
This post is part of the Rerunning the Sequences series, where we'll be going through Eliezer Yudkowsky's old posts in order so that people who are interested can (re-)read and discuss them. The previous post was Timeless Identity, and you can use the sequence_reruns tag or rss feed to follow the rest of the series.
Sequence reruns are a community-driven effort. You can participate by re-reading the sequence post, discussing it here, posting the next day's sequence reruns post, or summarizing forthcoming articles on the wiki. Go here for more details, or to have meta discussions about the Rerunning the Sequences series.