What Scientific Term or Concept Ought to be More Widely Known?

It changes conservation of momentum from an empirical relation we have historically observed to something that is derivable from a different empirical relation (translation symmetry) that we have historically observed. It's still ultimately an observed empirical relation.

This one is so odd to me. There's plenty of logical errors and shortcuts the brain takes that I had to learn to consciously think around, but the idea that my experience isn't necessarily representative of the entire world was something that was blindingly obvious when I was literally a child. I'm still taken aback for a second when I see people say things like "most of the people I know do X" or even "everyone in my family has Y", without giving any thought to whether their sample even approaches representativeness.

Hah. I can't tell if you are joking, because it's true.

Democracy and modern civilization itself requires at last some understanding of the scientific method. Sagan's warning in "The Demon-Haunted World"[1] was frighteningly prescient:

    I have a foreboding of an America in my children's or grandchildren's time --
    when the United States is a service and information economy; when nearly all
    the manufacturing industries have slipped away to other countries; when awesome
    technological powers are in the hands of a very few, and no one representing
    the public interest can even grasp the issues; when the people have lost the
    ability to set their own agendas or knowledgeably question those in authority;
    when, clutching our crystals and nervously consulting our horoscopes, our
    critical faculties in decline, unable to distinguish between what feels good
    and what's true, we slide, almost without noticing, back into superstition
    and darkness...

[1] https://en.wikipedia.org/wiki/The_Demon-Haunted_World

[2] https://www.brainpickings.org/2014/01/03/baloney-detection-k...

[3] http://scienceblogs.com/clock/2007/05/31/more-than-just-resi...

To explain, emergence as stated in the parent is a name for how a bunch of molecules could interact to make something you might call a football. This is a phenomenon at the "higher" everyday physical level emerging from the phenomena of the "lower" chemical level.

What I think this story misses is the importance of the "even higher" phenomena which resulted in a football being created, those of the human cultural level which caused the football to be manufactured and, for example, placed on some grass, or a desk, to be studied.

This isn't a purely sociological or philosophical point either, when you're looking at brain macro-activity for example, it's only partially explicable by referencing the micro-activity of, say, individual neurons, to get a better understanding you need to refer to activity outside of the brain that caused certain individual neurons to be acting like that. These higher level phenomena can be simple things like the movement in the neck that caused a change in stimulation, and also more wooly concepts like cultures which provide certain aesthetics or behaviours.

Emergence is important, but I feel its too often considered as a standalone phenomenon, rather than as one side of an irreducible causal cycle.

http://lesswrong.com/lw/iv/the_futility_of_emergence/

By "relativity" I'm assuming you're referring to SR or GR here. I always thought of relativity as an emergent phenomenon due to the large scales we are working with. What makes you say it is not?

One of the more interesting things I've learned in quite some time.

EDIT: You know, this is something that is so relate-able to the layman, it should be a widely used propaganda talking point.

First, the raw amount of oxygen in the atmosphere is large enough that fluctuations can go unnoticed. To decrease the percentage of oxygen by 5% would result in many orders of magnitude more CO2 (proportionally) being released, such that the oxygen would be negligible.

There's also the geology of it: rocks absorb and release oxygen over millions of years and add hysteresis to atmospheric composition. The amount of atmospheric gases trapped in the Earth's crust is significant and resists long-term changes.

There's optimizations which are tradeoffs against reducing the valid input space (or optimization for the common input cases), and then there's optimizations that eliminate unnecessary operations or combine things cleverly without degrading the worst-case scenario.

It has been proven, but only for the useless statement that an algorithm that does better on some case does worse on some other case (that you may not care about). Originally it was for search using that if you happen to look the right place first you win. This almost made sense, but then it get extended to general optimization, algorithms, and machine learning.

There are in fact algorithms that do better than others with respect to realistic distributions. And that contradicts the strong interpretations of the no-free lunch theorem bandied about in search, algorithms, and machine learning.

Of course, this is absolutely insufficient for almost any real-world scenario; Boolean logic does not equip one to make probabilistic inferences about the state of the world, which is the best we can do for the vast majority of everyday propositions.

The reality is that "slippery slope" is a very powerful heuristic, correlation correlates with causation, etc. People here often mistakenly think probabilistic arguments are Boolean (e.g. thinking Occam's razor tells you to believe only the most a priori likely hypothesis) or mistakenly think that Boolean arguments can be interpreted probabilistically (e.g. "Correlation doesn't imply causation, so I'm not going to treat this demonstrated correlation as evidence for causation").

this is covered in all medical schools because it's part of the licensing exam:

http://www.usmle.org/pdfs/usmlecontentoutline.pdf

It's about 1/4 of the way down on page 28.

Not sure about psychologists, but I'm guessing they are exposed to it to.

The big difference IMO is learning it vs. understanding/internalizing/recognizing it when it is applicable.

Chaos theory, for example, shows that physical, deterministic systems can be rigorously understood while prediction is (approximately) impossible. Likewise, you can make predictions without understanding, with sufficiently advanced machine learning (interpretability vs. flexibility).