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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: 5, Insightful) by Thexalon on Monday July 06 2020, @08:11PM (2 children)
My experience is that the people who hate math the most passionately are those who focused on developing skills of persuasion rather than developing knowledge, and can't stand the fact that a wrong answer in math is still wrong no matter how persuasively you try to argue that it's right.
Which correlates rather strongly with the people who want to believe that the most fundamental findings of science are, well, just, like, your opinion, man.
Unfortunately, these kinds of people also have a strong tendency to find their way into being in charge of businesses, governments, and other institutions, largely because the people they need to convince to put them in charge are just as ignorant as they are.
The only thing that stops a bad guy with a compiler is a good guy with a compiler.
(Score: 0) by Anonymous Coward on Tuesday July 07 2020, @10:09PM
I disagree on two axes:
1. I had the misfortune - long story - of attending a religious university and had mathematics and computer science professors that were technically brilliant but still devoutly religious. Being unable to understand math is unrelated to being irrational about bearded sky gods, vaccines, or the shape of the earth.
2. Some portion of the population is just plain stupid. I grant that. But many other people who are terrible at math just had a bad educational environment as children. If you spend a long time with someone and decide they're not too bright, that's fine. But if you are only acquainted with someone with poor math skills, you have to find out if their problem is innate stupidity or lack of opportunity. I have two anecdotes. First, one of my neighbors dropped out of high school at 16 to work construction. In his late 20s he decided he wanted a more interesting job so he got his GED, then his bachelor's degree, then a PhD in biochemistry and now he does cancer research. Second, one of my brothers had an elementary school teacher that beat the kids when they got a math problem wrong. (Hooray for religious schools.) He was traumatized by the abuse and barely passed math classes for the rest of his schooling - he could learn the material, but when it was test time he would freeze up. Ten years after high school and a lot of counseling and medication later he bought a book on high school math and worked through it, and took some college preparation standardized tests. He was the the only balding guy with a big beard in the room, and he scored in the top 5%.
(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.