Everday Orthogonality

Another one from Michael, who spotted an article about one of my favorite mathematical words to use in everyday speech (much the chagrin of non-scientists) used in the Supereme Court of the United States:

Supreme Court justices deal in words, and they are always on the lookout for new ones.
University of Michigan law professor Richard D. Friedman discovered that Monday when he answered a question from Justice Anthony M. Kennedy, but added that it was “entirely orthogonal” to the argument he was making in Briscoe v. Virginia.
Friedman attempted to move on, but Chief Justice John G. Roberts Jr. stopped him.
“I’m sorry,” Roberts said. “Entirely what?”
“Orthogonal,” Friedman repeated, and then defined the word: “Right angle. Unrelated. Irrelevant.”
“Oh,” Roberts replied.

“What was that adjective?” Scalia asked Monday. “I liked that.”
“Orthogonal,” Friedman said.
“Orthogonal,” Roberts said.
“Orthogonal,” Scalia said. “Ooh.”
Friedman seemed to start to regret the whole thing, saying the use of the word was “a bit of professorship creeping in, I suppose,” but Scalia was happy.
“I think we should use that in the opinion,” he said.
“Or the dissent,” added Roberts, who in this case was in rare disagreement with Scalia.

Of course last time I commented on using mathematical words outside of their natural habitat it spawned a comment thread with over 2000 comments.
Other favorites that I like to sneak into casual conversation are “canonical”, “dual”, and “asymptotic.” Other good scientific / math words that you like to use in everyday conversation?

19 Replies to “Everday Orthogonality”

  1. Mike: Oh yeah I use the term “does not commute” all the time.
    Gary: “Decidable” is great as well. I guess I have a measurement of test dogs per sq. paw as our dog likes to camp out on top of me despite being 60lbls.

  2. “Does not commute” sounds too much like “does not compute” for it to make sense to use the former in everyday conversation. (Although “does not compute” doesn’t really mean anything!)

  3. The action of turning the steering wheel and pushing the accelerator does not commute: the former misses hitting grandma, while the later runs her over. But yeah often it’s “heh, that’s not commutative, is it beavis!”

  4. All the above. Love ’em. And add:
    a-priori (I guess this one also leaks into legalese, but for me it is part of Predicate Calculus)
    I may be cheating a little – most of my everyday chat is with CS folks.
    But I have to add one last idiosyncracy:
    4 cats / sq. paw
    This describes the feeling of my 22lb cat walking on my chest.

  5. Since there are many pairs of actions in life that don’t commute, I’d like to find a way to work “non-abelian” into daily language. It doesn’t play as naturally as “orthogonal” though.

  6. Dave, I like to use “skew” as in skew lines in geometry. It’s a bit like “orthagonal” in the meaning intended, that the ideas, or whatever, never meet. It is generally understood by the hearer in context.

  7. I’ve been known to use “for some epsilon greater than 0” and “for sufficiently large values of n” in general conversation.

  8. Referring to mere number one as “unity” and to zero as “vanishes” (in effect) sounds cool. Symplectic is a good one. BTW, I don’t think it’s always clear which state in QM is orthogonal to another. Literally perpendicular polarizations are, but two different positions or momenta – no.
    Also, it is said that orthogonal states “don’t interfere.” In a crude, historical sense about amplitude: yes. But all waves “interfere” in the correct sense of their amplitudes adding up, whether the results are clear or stable patterns of light and dark. That could be even if different frequencies combine, or orthogonal polarizations. If we have a source of |x> and a source of |y> that combine at mixed phases, they will form literal “interference” patterns of varying polarization angle and type. That’s why I don’t like the crude sloppy definition of interference. I think this also confuses proponents of decoherence interpretations.
    BTW, anyone else hear this (Facebook quote):
    Symmetry Mag is reading in the Harvard Crimson that scientists have used a quantum computer to calculate the precise energy of a hydrogen molecule, something classical computers have been unable to accomplish.

  9. Neil B: It’s true that the states we can manufacture in the lab will not be perfectly orthogonal, but yes, two different position (or momenta) are defined to be strictly orthogonal in standard quantum theories.

  10. When I was younger and had a dirty mind, I noticed there was a spermicidal gel called ortho-gynol (I’m not making this up). Of course, you used this if you wanted the cross product to be zero.

  11. Most people are not so lucky as the Pontiff to have a canonical choice of breakfast meats! Here are some of my ordinarifications:
    Mod out, modulo
    higher order corrections
    isomorphic/morphisms: form letters, different resumes from the same person, coincidences etc, whenever there is a description to go from one instance to another by a succinctly expressible systematic replacement rule.
    Duality is a pretty broad notion, partly covering the same territory as isomorphism (especially in physics e.g. ising spin models, AdS/CFT). Another notion of dual is “the one who completes / compliments / resolves.” In my opinion this is behind the use of “dual” to refer to linear functionals / co-vectors. In this sense, fire and water are dual, as are rock and paper in Jan-Ken-Pon, or bullets and targets (this last one especially evokes Wheeler’s visualization of dual vectors).
    Compact: in the space of concepts, knowledge, and ideas, some regions are compact while others are not.
    Pullback/Push-Forward: this concept appears in a critique of literature attributed to Edgar Poe, where creativity is present in establishing the general morphism between our world and the fictional world being written, but where much of the effort is just “turning the crank” i.e. uncreatively applying the pullbacks/pushforwards of that morphism to various aspects of reality. IIRC, Poe gives the example of the world of little people, where after choosing that morphism we write that they drink from thimbles, and bathe in upturned flowers, etc.
    One day I would like to use “adjoint”, but I still have not understood the meaning deeply enough.
    Complex: actually this is an anti-example, as I always (strive to) substitute “complicated” wherever I would like to invoke the ordinary meaning of “complex.” In this sense, “Graph” and “Group” are also both anti-examples as I try to always substitute “Plot” or any of the number of words with the same ordinary meaning as “group.” It helps that actual actual graphs are best referred to as “networks” and that groups never arise in an ordinary context (aside from Beavis-type observations). I conclude with a multi-pun that was first formulated in my office:
    Fiber Bundles, a new breakfast cereal from the makers of Mobius Chips!

  12. I left these parts out (and typo-ed my initials) in the post directly above:
    The word “continuous” has an ordinary meaning similar to dense+connected e.g. “I was at work continuously from 9 to 5.” Unfortunately this meaning has reverse-infected the technical domain, wherein, for example, my Group Theory for Physicists course we were told informally that lie groups are “continuous groups.” OK that is fine for playing around, which is all we did, but since any function on a discrete domain is continuous, if “continuous” is taken to refer to the group operation, then this would include finite groups as well 🙁
    Wikipedia: “A very general comment of Martin Hyland is that syntax and semantics are adjoint.”

  13. I’m surprised no one has said “trivial” yet. Trivial and non-trivial are two things physicists say all the time.

  14. Aaron, I’ll accept that you are right at some technical level, but REM that a state can’t be detected by a filter tuned to the orthogonal state. Hence, |x> and |y> pol. are orthogonal because there is (ideally) no chance that a |y> filter will absorb an |x> photon. However, although position can in principle be exact, then momentum is totally uncertain – meaning that realistically I would have a chance of detecting the particle elsewhere than its momentary “exact position” (and what about energy-time uncertainty for that too?) As for momentum, can we really detect only for a specific momentum and not have a chance of getting a hit from something with a different momentum? But yes, in principle a specific position is not composed of other positions, and a specific pure momentum is not composed of other momenta so each is orthogonal in that sense.

  15. Consequently, therefore, thus…
    Another one that many non-mathematical people are guilty of using incorrectly is “exponentially”, when they usually mean “linearly”.

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