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Math Genius Has Come Up With a Wildly Simple New Way to Solve Quadratic Equations:
If you studied algebra in high school (or you're learning it right now), there's a good chance you're familiar with the quadratic formula. If not, it's possible you repressed it.
By this point, billions of us have had to learn, memorise, and implement this unwieldy algorithm in order to solve quadratic equations, but according to mathematician Po-Shen Loh from Carnegie Mellon University, there's actually been an easier and better way all along, although it's remained almost entirely hidden for thousands of years.
In a 2019 research paper, Loh celebrates the quadratic formula as a "remarkable triumph of early mathematicians" dating back to the beginnings of the Old Babylonian Period around 2000 BCE, but also freely acknowledges some of its ancient shortcomings.
"It is unfortunate that for billions of people worldwide, the quadratic formula is also their first (and perhaps only) experience of a rather complicated formula which they must memorise," Loh writes.
[...] We still don't know how this escaped wider notice for millennia, but if Loh's instincts are right, maths textbooks could be on the verge of a historic rewriting - and we don't take textbook-changing discoveries lightly.
"I wanted to share it as widely as possible with the world," Loh says, "because it can demystify a complicated part of maths that makes many people feel that maybe maths is not for them."
The research paper is available at pre-print website arXiv.org, and you can read Po-Shen Loh's generalised explanation of the simple proof here.
(Score: 1, Interesting) by Anonymous Coward on Thursday July 09 2020, @08:59AM
The vaccine for this effect would be to also teach kids the content of Chris Voss' book 'Never Split the Difference'.
This will give them the tools they need so they are able to defend themselves against the self-styled 'winners' who are really just luckily born rich + aggressive.
These are the same people who *think* they have developed said "skills of persuasion": anyone who resorts to force/coercion. You know, that same set who seem to find their way into being in charge. Because aggressiveness and self-ignorance-of-failure are enough to give a mistaken self-impression of being 'good' at persuasion.
A truly impressive negotiator can 'get their way' from a position of *weakness*.
But, why would one trust a 'winner' once you discover this is all they're doing? Winning from a position of strength... using strength. Any dangerous animal can do that, it doesn't even require the ability to speak, necessarily. Let the Wookie win.
Why do we all still bother listening to such people, and even letting them take charge of us? Because we're programmed to.
Humans are social animals. We are predisposed to 'be good' and minimise conflict. (so says all the science).
Even our ultimate beliefs are controlled more by peer pressure than you would at first imagine. But it is true: Surround yourself in people who believe your bullshit, and you'll believe it too. It's automatic. Want to change some believe about yourself? Convince your friends and families that it is true -- even by faking it -- and you'll come to believe it too. Such as is the power of 'confidence'.
It's just social positive-feedback, and it's also why the problem people can learn to be really good at just not hearing or seeing anything that might prove them otherwise.
We are also not in fact 'fundamentally evil' - the process about how one can become personally mistaken about this is also well-known. Recently scientist have been forced to conclude that many religions saying otherwise are in fact mistaken, following a common and very early mechanism due to individual intelligence conflicting with tradition.
The greatest of evils might come from those with the best of intentions... who also happen to be aggressive, and 'heroically willing' to do what others will not.
It seems that due to structural racism they're probably also old, white, and somewhat demented men who were born to rich parents.
One of the lessons of Voss' work is this: Whenever someone seems to be making crazy decisions -- someone (either you, or them) is missing some critical information.
If one's mind is starting to go, such that basic facts aren't held too tightly, then it's probably one self - but one also wouldn't know - for exactly the same reason.
If you see someone else acting crazy -- either they know something that you don't, or you know something they don't.
People can also become addicted to ritual (with which each practise comes with a burst of anxiety-reliving biochemicals). Those people have 'OCD', and they know they're 'crazy'. It's the ones that don't know they're crazy, that you have to watch out for.
Given that we are social beings who believe in things that 'everyone knows' this also means we all behave to limit the damage that would be caused by the hypothetical 'bad actor' -- or give into the temptation to do others bad for our own benefit because it would be expected that 'someone else will anyway'. So most of that bad behaviour probably just happens because its what we expect to happen.
Based on an inaccurate understanding of exactly what we are.