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每个人都能是数学家 – 译学馆
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每个人都能是数学家

Big Think 2017 Top Ten: #4. Po-Shen Loh on How Anyone Can Be a Math Person

《大想法》
我认为世界上每个人
I think that everyone
只要他们想 就能成为一个数学家
in the world could be a math person if they wanted to.
但我想说的是 关键是这是否是他们想要的
The keyword though, I want to say, is if they wanted to.
也就是说 我的确认为每个身处美国的人
That said, I do think that everyone in America
可以合理地运用数学背景来获益
could benefit from having that mathematical background in reasoning
正是因为它可以帮助人们做出非常棒的决定
just to help everyone make very good decisions.
所以在此我已经将人们通常所认为的那种数学
And here I’m distinguishing already between math as people usually conceive of it, and
与实际上我认为帮助人们决策和分析的数学进行了区分
decision making and analysis, which is actually what I think math is.
所以 比如
So, for example,
我不认为成为数学家就意味着你能
I don’t think that being a math person means that you can recite
背诵正弦 余弦 正切的函数公式
the formulas between the sines, cosines,
和转化运用对数和指数
tangents and to use logarithms and exponentials interchangeably.
我认为人们把精力都集中
That’s not necessarily what I think everyone should
在理解这些公式上是不必要的
try to concentrate to understand.
最主要的事情是专注理解
The main things to concentrate to understand are
数学原理的推理
the mathematical principles of reasoning.
但让我们再来说说正弦 余弦和对数函数
But let me go back to these sines, cosines and logarithms.
实际上它们的确有价值
Well actually they do have value.
它们的价值在于向你展示
What they are is that they are ways to
这些基本的推理构建模块是怎样
show you how these basic building blocks of reasoning
被用来推断出令人感到惊喜或困难的问题
can be used to deduce surprising things or difficult things.
在某种程度上它们就像是
In some sense they’re like the historical coverages
对数学领域所获成就的历史性总结
of the triumphs of mathematics,
所以 我们不能只是空洞地谈论
so one can not just talk abstractly
“好 让我们来谈谈数学逻辑”
about “ yes let’s talk about mathematical logic ”,
事实上 学习著名定理的案例和故事
it’s actually quite useful to have case studies or stories,
是相当有用的
which are these famous theorems.
现在 我真的认为所有人都能理解这些定理
Now, I actually think that these are accessibleto everyone.
实际上我想数学真正
I think that actually one reason mathematics
晦涩难懂一个的原因是
is difficult to understand is actually
因为储备知识网
because of that network of prerequisites.
要知道 数学是奇怪的学科之一
You see, math is one of these strange subjects
因为它的概念是按相关性顺序环环相扣的
for which the concepts are chained in sequences of dependencies.
当你形成了一条完整的知识链
When you have long chains
那么需要我记住的东西
there are very few starting points
就很少了
very few things I need to memorize.
比如 我不需要记住
I don’t need to memorize, for example,
历史上所有的事 像是
all these things in history such as
1812年战争是什么时候
“ when was the war of 1812?”
好的 实际上我知道这个 因为这是一个数学事实——是在1812年
Well actually I know that one, because that’s a math fact —it was 1812,
但我不能告诉你
but I can’t tell you a lot of other facts,
许多只是单纯记忆的事实
which are just purely memorized.
数学中 你需要记忆的很少
In mathematics you have very few
而剩下的需要根据你的理解推理出
that you memorize and the rest you deduce as you go through,
实际上 推论的连续性是真正关键所在
and this chain of deductions is actually what’s critical.
现在 让我将它与其他学科比如说历史进行对比
Now, let me contrast that with other subjects like say history.
事实上历史没有这么长的连续性
History doesn’t have this long chain,
如果你真的完全理解了1812年战争
in fact if you fully understand the war of 1812 that’s great
这很好 并且它
and it is true that will influence
也许会影响你对后世女权运动的理解
perhaps your understanding later of the women’s movement,
但是它不会是绝对的前提条件
but it won’t to be as absolutelyprerequisite.
就这而言 如果从概念方面考虑
In the sense that if you think about the concepts I actually think that
我认为历史比数学有更多的概念
history has more concepts than mathematics;
只是历史的概念传播更广而已
it’s just that they’re spread out broader
并且各个概念之间不会有很强的依赖性
and they don’t depend on each other as strongly.
比如 如果你缺席一周
So, for example, if you miss a week,
你将会错过一个单元的知识理解
you will miss the understanding of one unit,
但这不会妨碍你去理解剩下的部分
but that won’t stop you from understanding all of the rest of the components.
所以这就是我认为的数学和其他学科的区别
So that’s actually the difference between math and other subjects in my head.
数学有着很少的概念 但是互相关联很深
Math has fewer concepts but they’re chained deeper.
并且由于我们惯用的学习方法
And because of the way
关联越深 越容易解崩离析
that we usually learn when you had deep chains it’s very fragile
因为只要你错过了任一结点 意思是
because you lose any one link—meaning
如果你遗漏了知识链中的一些概念
if you miss a few concepts along the chain
就会完全无法理解整个知识链
you can actually be completely lost. If,
再比如 你病了一周
for example, you’re sick for a week,
或在那一周你心不在焉
or if your mind is somewhere else for a week,
你也许会在必要知识上有漏洞
you might make a hole in your prerequisites.
而通常的教育方法
And the way that education often works
就像是火车从起点一直开到终点
where it’s almost like riding a train from a beginning to an end,
好 这就像如果你的学习进程中有了漏洞
well it’s such that if you have a hole somewhere in your track
火车将不会通过那个洞
the train is not going to pass that hole.
现在 我认为帮助解决这个漏洞的方法
Now, I think that the way to help to
就是提供让所有人
address this is to provide a way for everyone to learn
能按自己节奏学习的方法并切实可行地
at their own pace and in fact to fill in
填补任何时候发现的漏洞
the holes whenever they are sensed.
实际上我觉得如果每个人都能够
And I actually feel like if everyone was able
学会他们所需的每一部分预备知识
to pick up every one of those prerequisites
并弥补他们自己的不足
as necessary, filling in any gap they have,
数学就会从最困难的学科
mathematics would change from being the hardest
变为最简单的学科
subject to the easiest subject.
我想每个人都是数学家
I think everyone is a math person,
他们需要做的就是经历各个数学知识的环节
and all that one has to do is to go through the chain
并填补所有的空缺
and fill in all the gaps,
这样比起其他学科你将更好地理解数学
and you will understand it better than all the other subjects actually.

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视频概述

每个人都能成为数学家。数学需要的是知识链的连续性,我们在学习数学时不必死记硬背,而要关注推理和思考,及时弥补学习中的漏洞,这样学习数学自然简单轻松了。

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