【Hacker News搬运】为什么数字线让我抓狂（2016）

[hackernews]

Title: Why the Number Line Freaks Me Out (2016)

为什么数字线让我抓狂（2016）

Text:

hn link

Url: https://mathwithbaddrawings.com/2016/12/28/why-the-number-line-freaks-me-out/

很抱歉，我无法直接访问外部链接来获取内容。不过，我可以根据你提供的链接和描述来猜测内容的大致内容，并提供一个总结。

链接指向的是一篇名为 "Why the Number Line Freaks Me Out" 的文章，作者可能是 Matt Parker，他在个人博客 "Math with Bad Drawings" 上发表。根据标题，这篇文章可能探讨了作者对数轴的某些方面感到困惑或不安的原因。

以下是对这篇文章可能的总结：

文章可能会从数轴的基本概念开始，讨论为什么数轴对于一些人来说可能难以理解或感到困惑。作者可能会解释数轴如何表示实数，以及实数在数轴上的分布。文章可能会探讨以下方面：

1. 数轴上的无穷大和无穷小概念。
2. 数轴上负数和正数的分布。
3. 有理数和无理数在数轴上的表示。
4. 数轴在数学教育和理解数学概念中的作用。

作者可能会通过一些简单的例子或比喻来说明这些概念，并可能分享个人在学习数轴过程中遇到的挑战。文章可能会鼓励读者不要因为对数轴的困惑而气馁，并可能提供一些帮助理解和掌握数轴的方法。

由于我无法访问文章的实际内容，以上总结仅基于标题和可能的主题进行的推测。如果你需要具体的翻译或更详细的内容分析，你可能需要直接阅读原文。

Post by: mananaysiempre

Comments:

ziofill: I find it hard to wrap my head around non computable numbers. How can I even “point to one” of them if I can’t express/describe it? And if I cannot communicate which number I’m referring to, does it really exist? In what way do they exist?

ziofill: 我发现很难理解不可计算的数字。如果我无法表达，我怎么能“指向其中一个”呢；描述一下？如果我不能说出我指的是哪个号码，它真的存在吗？它们以何种方式存在？

routerl: It seems to be an article about all those "harmless" lies we tell students.<p>The vast majority of people think mathematics is about numbers, when it is actually about relations, and numbers are just some of the entities whose relations mathematics studies.<p>Nobody is born with this misconception; we teach it, and test it, and thereby ingrain it in the minds of every student, most of whom will never study mathematics at a level that makes them go "wait, what?". The overwhelming majority of people never get to this level.<p>I suspect this is also why statistics feels so counterintuitive to so many people, including me. The Monty Hall problem is only a problem to those who are naive about probability, which is most people, because most of us don't learn any of this stuff early enough to form long lasting, correct instincts.<p>It's not fair to students to bake "harmless" lies into their early education, as a way to simplify the topic such that it becomes more easily teachable. We've only done this because teaching is hard, and thus expensive. Education is expensive, at every step. It's not fair or productive to build a gate around proper education that makes it available only to those who can afford it at the level where the early misconceptions get corrected. Even those people end up spending a lot of cognitive capital on all those "wait, what?" moments, when their cognitive capital would be better spent elsewhere.

routerl: 这似乎是一篇关于所有这些的文章&quot；无害&quot；我们对学生撒谎<p> 绝大多数人认为数学是关于数字的，但实际上它是关于关系的，而数字只是数学研究关系的一些实体<p> 没有人天生就有这种误解；我们教授数学，并对其进行测试，从而将其深深地铭刻在每个学生的心中，他们中的大多数人将永远无法达到他们所能达到的数学水平；等等，什么&“；。绝大多数人从未达到过这个水平<p> 我怀疑这也是为什么统计数据对包括我在内的许多人来说如此违反直觉的原因。蒙提霍尔问题只对那些对概率天真的人来说是一个问题，这是大多数人的问题，因为我们大多数人都不知道；不要过早地学习这些东西，以形成持久、正确的直觉<p> 它；烘焙对学生来说是不公平的；无害&quot；在于他们的早期教育，作为简化主题的一种方式，使其更容易教授。我们；我这样做只是因为教学很难，所以很贵。教育的每一步都很昂贵。它；围绕适当的教育建立一个大门，只让那些能够负担得起早期误解得到纠正的人接受教育，这是不公平或不富有成效的。即使是这些人最终也在所有这些方面花费了大量的认知资本&quot；等等，什么&“；他们的认知资本最好花在其他地方。

Animats: The underlying problem is that infinity doesn't exist. It's a convenient illusion to make special cases go away. It's possible to have entirely constructive mathematics. In a true constructive model, everything can be constructed in a finite number of steps. There are only integers, no reals.

Animats: 根本问题是无穷大不；不存在。它；让特殊情况消失是一种方便的错觉。它；有可能有完全建设性的数学。在一个真正的构造模型中，一切都可以在有限的步骤中构建。只有整数，没有实数。

BobbyTables2: Even “e” and “pi” would have been noncomputable at one point in time.<p>But the noncomputable numbers make me wonder if our notion of mathematics is too general/powerful.

BobbyTables2: 即使是“e”和“pi”在某个时间点也是不可计算的<p> 但这些不可计算的数字让我怀疑我们的数学概念是否过于笼统；强大。

bawolff: > It should be a timidating<p>Total nitpick, but i think the in in intimidating means "into a state of being timid" and not "in" in the sense of opposite of timidating.

bawolff: &gt；这应该是一个胆怯的<p>全面的挑剔，但我认为这是恐吓的手段&quot；变成胆怯的状态&quot；而不是&quot；在&quot；在与胆怯相反的意义上。