Even the most abstract theorem may have unexpected practical applications, even the most mundane engineering challenge may reveal marvelous mathematical depths, even the most commonplace-seeming medical case may in fact be a rare-and-curable medical condition.

Thus (as my wife says) “Attitude is everything!” đź™‚

]]>Scott, this strategy works well in mathematics, and yet it is an utter disaster in medicine … where we have to treat the (often confusing and incurable) diseases that patients *actually* present with, not the (rare, fascinating, and curable) diseases we *wish* we were seeing.

Engineering is IMHO a happy middle ground, in which creativity and responsibility mix in (roughly) equal proportion.

Like rhyming poetry, or tennis *with* a net.

Scott, in your capacity as an professor of engineering, it would be interesting to know what *engineering* aspects of QM interest you most.

Is it the practical engineering aspects? Or are your interests more aligned with the post-modern, theorem-proving, academic variety of engineering?

In these difficult economic times, deans are becoming very fond of theorem-proving faculty … for the pragmatic reason that they require substantially less (expensive) infrastructure than any other variety.

Does this mean that young engineers who have academic aspirations should focus mainly on theorem-proving?

]]>Staying with your squirrel-behind-bushes analogy, when I read about it I first thought of physical TM’s (paper & pencil or silicon) where bushes stand for tape positions. In an abstract TM we don’t have this limitation, but could a physical machine (including paper & pencil) be more limited?

]]>Koray: I’ve blogged about quantum logic in the past. There are interesting things to say about it mathematically, but

(1) I don’t think it “challenges the laws of logic,” nor do I think there’s any empirical discovery that could. The fact that one can *define and study* formal systems that break (say) the distributive law, doesn’t make the slightest difference to the truth of the distributive law as conventionally understood.

(2) Judging it as a way of reasoning about quantum mechanics, I find that quantum logic leaves an enormous part out: **probabilities!** Quantum logic is basically what you get by throwing away the probabilistic part of quantum mechanics (i.e., the Born rule), and considering only the lattice of subspaces of Hilbert space. Then, to make the problems more interesting, you tend to go immediately to infinite-dimensional Hilbert spaces, which takes you even further from the conceptual aspects of QM that interest me the most. Thus, I think that quantum information and computing, where you generally care only about achieving some goal with probability 1-ε, and not about whether a given state *is* or *is not* in a given subspace, does a better job of capturing what QM is really about.