
What Scientific Term or Concept Ought to be More Widely Known? - booleandilemma
https://www.edge.org/annual-question/what-scientific-term-or%C2%A0concept-ought-to-be-more-widely-known
======
jmount
My pick (I know the article just said "science" and didn't leave the question
open): Noether's Theorem which implies symmetries and conservation laws come
in matched pairs in physics. From this you can derive conservation of momentum
isn't just some empirical relation we have historically observed, but
critically linked to symmetry of translation. Once you learn this you have a
_lot_ less sympathy for reaction-less drive con-artists.

~~~
wfunction
Along those lines (no pun intended), I think every STEM college graduate ought
to be able to prove that the shortest path between 2 points is a line segment
instead of taking it for granted.

~~~
ams6110
That's a high school freshman geometry problem.

~~~
wfunction
> That's a high school freshman geometry problem.

Looks like we found another person who doesn't know how to do it :) look it
up! In pre-college geometry this isn't something you prove, it's something you
postulate and take for granted.

~~~
ams6110
Maybe these days. We definitely proved it in my geometry class in 1980/81.

~~~
wfunction
Share your "proof"?

~~~
ams6110
Well it's been 35 years ... as I recall it's an indirect proof, it starts with
assuming there _is_ some other shorter path, and then showing that to be
impossible by creating a contradiction of other proven theorems and
postulates.

~~~
wfunction
> Well it's been 35 years ... as I recall it's an indirect proof, it starts
> with assuming there is some other shorter path, and then showing that to be
> impossible by creating a contradiction of other proven theorems and
> postulates.

Then I'm gonna call B.S. on this until you can show me the proof somewhere.
Every single time I've searched this the only rigorous proof I've found has
been using calculus (often calculus of variations).

~~~
systoll
I recall doing a proof of the form:

1\. Prove the triangle inequality, & extend via induction to show that [A] a
straight line is the shortest polygonal path, and that [B] adding a point to a
polygonal path can only make it longer.

2\. Arc length is defined as the limit of the length of a polygonal
approximations to a curve. From (B), we know our approximations would approach
the arc length from below.

So if an curve A->B has an arc length, there's a polygon A->B which is at
least as short. And from [A] we know there's no polygon shorter than the
straight line.

This is weaker than proofs you can do with calculus -- it doesn't prove
uniqueness, and it completely ignores non-rectifiable curves, for instance.
But I suspect that's what ams6110 is remembering.

~~~
wfunction
2\. Arc length is defined as the limit of the length of a polygonal
approximations to a curve. From (B), we know our approximations would approach
the arc length from below.

You call this "geometry"? Since when does geometry involve a function limiting
and bounding process? We didn't even know what a limit was until calculus...

------
joshmarlow
Sample bias: I feel that so many subtleties are lost because people don't
generally realize that their observations/anecdotes/experiences are _biased_.

If I see a steak on my plate, I can't conclude that there is no world hunger.
If I see a snowball, I can't conclude that there is no global warming. If I've
never experienced racial bias against me, I can't conclude that it does not
happen to other people.

Edit: for clarity.

~~~
Chronic77
You have to realize that a lot of people understand sample bias. Those people
(myself included) _simply don 't care_ about global warming, global hunger,
racism, etc.

~~~
ulrikrasmussen
Or maybe most people do care, and your extrapolation is an example of sample
bias :)

------
invaliduser
I think we should make it more widely understood how bad we human are at
science. Our brain is full of what we call cognitive biases, that prevent us
from processing data correctly, our sensors are specially bad, even the ones
we mostly rely on (eyes and ears) are very very easily cheated, and we can't
even tell. Our storage unit (memory) is awful, we forget a lot, and time is
our ennemy.

We call a lot of science concepts «not intuitive» because of the limitations
of our brains, and very little people, at the cost of studying a lot, and
being highly stimulated in their first years of life, can actually really get
a grasp of them. Quantum mechanics of course, but just see how people reacted
to the monty hall problem: [https://priceonomics.com/the-time-everyone-
corrected-the-wor...](https://priceonomics.com/the-time-everyone-corrected-
the-worlds-smartest/) Other examples at
[https://en.wikipedia.org/wiki/Counterintuitive#Counterintuit...](https://en.wikipedia.org/wiki/Counterintuitive#Counterintuition_in_science)

Sure, we are better at science than all other species on earth, but in
absolute terms, we human are very badly designed for it. Yet, we try our best.

------
michaelfeathers
Confirmation bias. Once you start looking for confirmation bias you see it
everywhere.

~~~
SudoNhim
> Once you start looking for confirmation bias you see it everywhere.

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

~~~
michaelfeathers
[http://www.catb.org/jargon/html/H/ha-ha-only-
serious.html](http://www.catb.org/jargon/html/H/ha-ha-only-serious.html)

------
hackuser
Scientific method. The great majority don't understand even that fundamental
of science, and thus they cannot utilize it themselves, many do not trust it,
they don't understand the epistemological problems it addresses, and they
don't understand what terms like 'study', 'theory', etc. really mean.

~~~
pdkl95
This is easily the most important topic that needs to be more widely known.
It's hard to progress in any other topic if you don't understand the basic
methods for filtering good information from the many mistakes,
misinterpretations, scams and other bad data. The need for education on the
very basics of the scientific method has even made it into the recent popular
press as concerns about "fake news".

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...
    

Until the public "baloney detection kit"[2] (and uses it regularly), trying to
teach other topic is probably a waste of time[3].

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

[2] [https://www.brainpickings.org/2014/01/03/baloney-
detection-k...](https://www.brainpickings.org/2014/01/03/baloney-detection-
kit-carl-sagan/)

[3] [http://scienceblogs.com/clock/2007/05/31/more-than-just-
resi...](http://scienceblogs.com/clock/2007/05/31/more-than-just-resistance-
of-s/)

~~~
hackuser
Said one smart person:

 _You may fool all the people some of the time; you can even fool some of the
people all the time; but you can’t fool all of the people all the time._

------
teddyh
[https://en.wikipedia.org/wiki/List_of_cognitive_biases](https://en.wikipedia.org/wiki/List_of_cognitive_biases)

“ _The first principle is that you must not fool yourself—and you are the
easiest person to fool. So you have to be very careful about that. After
you’ve not fooled yourself, it’s easy not to fool other scientists. You just
have to be honest in a conventional way after that._ ”

— Richard Feynman

~~~
marviel
Anki deck here: [https://ankiweb.net/shared/](https://ankiweb.net/shared/)

~~~
teddyh
You mean
[https://ankiweb.net/shared/info/970971960](https://ankiweb.net/shared/info/970971960)

~~~
marviel
Thanks!

------
js8
In general, I wish more people understood some elementary facts about global
warming, for example, because we observe more warming at the poles, during the
winter and during the night, and also we observe cooling of the stratosphere,
the cause must be in the Earth's atmosphere, it cannot be the Sun.

In mathematics, I wish more people knew about typed lambda calculus and its
connection to mathematical logic. I think the fact that most mathematicians
use predicate logic, while theorem provers use e.g. calculus of constructions
is one of the big obstacles for more wide usage of automated theorem provers.
But it's just a language barrier.

In economics, I wish more people knew about (I don't know the name,
unfortunately) the approach to calculating of equilibrium prices that is
described in J.M.Blatt's book Dynamic Economic Systems, and is based on input-
output production matrices. It's a much more superior approach to the
classical supply-demand analysis that dominates the textbooks, because it
requires much less free parameters and assumptions.

------
ClayFerguson
"Emergence": Most everything in science (from Chemistry to Consciousness) is
an emergent phenomenon and most people are plain ignorant of the concept and
meaning of that word, although I did see it appear a lot in 2016, in
scientific articles. The only thing (or things) in science that are not
emergent are the laws of Quantum Mechanics and Relativity (as a
simplification), and there are more and more physicists that believe even both
of those "rule sets" probably are emergent from some more fundamental and
simpler set of "rules", that give rise to both QM, Gravity, Spacetime.

~~~
mulcahey
Relevant Less Wrong post:

[http://lesswrong.com/lw/iv/the_futility_of_emergence/](http://lesswrong.com/lw/iv/the_futility_of_emergence/)

~~~
nitrogen
Emergence as a concept only serves to eliminate the need for a designer. It
doesn't actually explain anything to someone who already accepts the
possibility of complexity without design. But that doesn't mean it's a useless
concept, just that it is sometimes misused (if the LW post's premise is true).

~~~
ClayFerguson
Right, Emergence is a general term like Entropy, and I chose that on purpose
because Emergence is more like the negative of or inverse of Entropy.
Emergence is when you get order, complexity, and non-randomness out of pure
randomness plus time plus rules.

------
dispo001
That making enough oxygen for one person, using electrolysis, requires 2000
kwh per day.

That earth's forest area decreases by 13 000 000 hectares per year.

And that we add about 75 000 000 people every year.

~~~
mistermann
Wow, did you read this somewhere in an article that goes into more interesting
depth? 2000 kwh/day is like $200 bucks a day where I live, that's crazy! Now
add in what's needed for the animals I eat. And that's just for the oxygen we
consume?

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.

~~~
mistermann
And if you think about it more, if this number is correct, it shows in a very
understandable way the magnitude of solar energy that the Earth receives - if
this number is true, 100% sustainable energy is not only possible but should
be incredibly easy once we develop the proper technology.

I wonder, could global transmission possibly be an answer to the lack of
storage problem?

------
AndrewOMartin
The No Free Lunch theorem.

Technically put, "any two optimization algorithms are equivalent when their
performance is averaged across all possible problems"

More intuitively paraphrased, "if an algorithm performs well on a certain
class of problems then it necessarily pays for that with degraded performance
on the set of all remaining problems.".

I forget if either or any of these are actually proven, or if they're the
"folkloric" intuitions from more technical papers.

More boldly overstated, there's no such thing as a general optimisation, all
optimisations are relative to a subset of possible inputs.

In extremis, there's exists a situation where Bogosort is preferable to
Quicksort.

~~~
rincebrain
I think this is provably false, probably, since you can compose a pathological
case where you have a no-op that adds an O(n) (or more) step to the runtime
and an optimization step that purely removes that no-op.

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.

~~~
AndrewOMartin
I'm not immediately convinced by your no-op example because I can conceive of
situations that needs a little extra time to be passed between actions, such
as in the case of sorting elements whose value isn't easily determinable and
is best estimated n clock ticks after the previous action.

This is of course a million miles away from the kind of sorting problems you
get in Computer Science 101, but this is my point, the traditional sorting
problems happen in a very well defined context, as soon as that changes, you
might find any algorithm being optimal. Including Bogosort and, for example,
quicksort with some extra no-ops.

I like your point, but for the reason above I still think the No Free Lunch
theorem is valuable, else I wouldn't have had this insight in the first place.
At least, I consider it an insight, YMMV.

~~~
rincebrain
Sure, it's certainly valuable to realize that you rarely get an optimization
in one case that's not pessimal in another, and it is well-removed from the
constrained environments that people work through for demoing algorithms.

I was just thinking in terms of more abstract optimization (e.g. platform-
agnostic ones that just strictly reduce work to be done) versus platform-
specific optimizations/workarounds/bin-packing (like nops to prevent your
pipelines or cache lines from being pathological).

------
artpepper
Bayesian probability. I see a lot of popular reporting that talks very naively
about probability and relative risk.

~~~
wyager
A lot of people on HN consider themselves logical because they know how to
work with Boolean logic and they know how to identify some Boolean fallacies
(slippery slope, correlation does not imply causation, etc.).

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").

------
Gravityloss
Stock and flow or just basic integration.

People have very bad understanding of rate vs level problems.
[http://www.systemdynamics.org/conferences/2004/SDS_2004/PAPE...](http://www.systemdynamics.org/conferences/2004/SDS_2004/PAPERS/197KAPME.pdf)

This doesn't even get to the problem of compounding yet, which is related.

Another pet of mine is Bayesian logic. Doctors and psychologists at least
should definitely be familiar with the idea.

~~~
appleflaxen
> Doctors and psychologists should at least should definitely at least be
> familiar with the idea.

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

[http://www.usmle.org/pdfs/usmlecontentoutline.pdf](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.

------
danharaj
The concept of covariance which describes the way different observers'
measurements of the same phenomenon are related.

More generally the concept that the relationships between observers are a
fundamental aspect of the systems they measure. In special relativity for
example this is the Poincaré group which relates observers in different
inertial reference frames.

Another example is entropy in statistical mechanics (although I'm being weird
by casting it in this light): entropy depends on the knowledge and sensitivity
of the observer to the microstates of the system they are measuring. The
relation to two observers here is considerably more complicated than a group
but it is there and a fundamental aspect of the subject.

I believe this concept is fundamental to every science but the "softer" you
get, the harder it is to model. It is there implicitly whenever we make an
observation.

------
soberhoff
I'd appreciate a more general appreciation of how little can be accurately
predicted. Any time I hear sports commentators predict winners I internally
shake my head. Why do so few people have the ability to admit to themselves
that most things are just unpredictable?

------
quickben
I feel that in this day and age, scientific rigour and reproducibility are
starting to take the back seat in many popular fields.

------
Xcelerate
> Science—that is, reliable methods for obtaining knowledge

I really dislike this definition of science. Science is about making accurate
_predictions_ about the future (even if those future predictions concern the
accuracy of past events). Predictivity is the defining feature of science,
because without it, science may as well be any other subject. The Wikipedia
definition is much better, because it incorporates the _utility_ of knowledge
but emphasizes the key role of prediction:

> Science is a systematic enterprise that builds and organizes knowledge in
> the form of testable explanations and predictions about the universe.

~~~
bagrow
I disagree about the emphasis on prediction. Science involves predictions, but
it does not involve only predictions.

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).

------
spodek
Conservation of energy, not just as an abstract concept, but in that every
time you fly in a plane, drive in a car, turn on the air conditioner, etc, you
are using energy, which pollutes, and, while we use fossil fuels, contributes
to the greenhouse effect.

Most people seem to think their contribution doesn't count or is somehow less
than everyone else's.

Also, curiosity and appreciating the beauty of nature. These were two of my
main motivations to get my PhD in physics. To me they are fundamental to
science.

------
remarkEon
From statistics: Simpson's Paradox. Maybe a little more obscure than what some
others have mentioned, but it is the idea that there can be patterns in data
that appear in separate groups, but then vanish or reverse when those groups
are combined. It can be a useful framework.

[https://en.wikipedia.org/wiki/Simpson's_paradox](https://en.wikipedia.org/wiki/Simpson's_paradox)

------
erik14th
I'd pick Juarez Cirino's book "Radical Criminology". It reeks of ultraidealist
marxism but I think the observations it makes on the workings of the criminal
system in capitalist societies is simply enlightening. He draws from ideas of
Foucault, Marx, Pasukanis and many others to form a concise and understandable
take on modern criminal and penal systems.

~~~
harrumph
Did you read this in English, or Portugese? I'm interested and I can't find an
English translation.

~~~
erik14th
Even in portuguese the book is unfortunately pretty hard to find. I actually
am thinking about translating it myself, I already asked the publisher if I
can make it easily available online(I'm thinking something like a github repo
so people can help translate and fix errors), not sure if they'll answer me
tho.

Send me a mail at erik@14th.info and I'll let you know if I get something
done.

------
witty_username
Comparative advantage (China produces things cheaper) and lump of labor
fallacy (jobs aren't finite; if you work for 0$ a hour you'll get a job).

------
techdragon
The Overton window.

What sometimes looks to be a slippery slope argument is actually just the
first person to see someone constructing the Overton window against them.

I'm not saying slippery slope arguments aren't hideously overused, but it's
deviously hard to explain to many people when their own mind is being used
against them and not knowing what the Overton window is makes that even
harder.

------
vondur
Exponential growth. It's something few people outside of science/engineering
learn.

------
7402
Error bars. Whenever I see a plot without them, I think someone is trying to
pull a fast one. Some scientific fields (or quasi-scientific) fields use them
much more than others.

Quick-and-dirty physicists' method of generating an error bar when dealing
with number of events in an interval is to assume that Poisson counting
statistics apply, and take the square root of the number of events.

Example: Two months ago we sold 400 units. Last month we sold 410 units.
Should we celebrate?

Square root of 400 is 20. The change in sales is within the margin of error.
Celebration would be premature.

------
murkle
Non-transitive dice (ie the idea that it's impossible to rank (almost)
anything/anyone(!) sensibly)

------
convolvatron
sample distribution

processes and measurement aren't ideal. learn to live with it.

------
lightedman
Photon Flux Density.

Lumens is so over-used and so often wrongly used.

------
plg
Affirming the consequent

------
internaut
Did anybody understand where Margaret Levi got this?

"Indeed, the expectation of reciprocity can both reduce and even undermine
altruism."

Surely expectation of reciprocity would make the reciprocal loop stronger, not
weaker.

