Different Interpretations for the Number Zero

Zero graduated from a placeholder for absentee digits to its own concept. Here's a few more interpretations of zero:

The void: Utter emptiness, the absence of any activity
The neutral zone: A cancellation between positive and negative influences

Mathematically, we can write:

$\displaystyle{ 0 = 1 - 1}$

And to a calculator, these are the same. Are they? There's a suspicion nothing (0) and complete cancellation (1 - 1) aren't quite identical.

Physics

In physics, there's the notion of a stable and unstable equilibrium. Take two pencils. Lay one on the table, balance the other on its tip.

他们都是“平衡”。零运动。然而，一个是危险的位置，小心地反对重力，而另一个平静地躺着。

在地板上躺10分钟。保持平板支撑姿势10分钟。从物理学的角度来看，没有做功(没有移动)，但你颤抖的手臂讲述了一个不同的故事。

Algebra

In algebra, we constantlyfactor equationsto find roots.

Why? In short, we want to find the "neutral zones" where all forces balance.

Factoring

$\displaystyle{f(x) = x^2 + 2x + 3}$

means "Is there a value where x^2, 2x, and 3 cancel each other out?". We arrange the scenario so the neutral zone is where wewantto be (such as having no error, or having competing goals align).

There is often a "trivial solution", where we can plug in x=0 and all inputs disappear (lying the pencil on the table... or just taking it away!). However, we're more interested in finding a "neutral zone", where multiple, existing forces balance.

Programming

Programming languages distinguish "void/undefined/null" (a value is not set) and "having a value of emptiness".

var i; // i is undefined i = 0; // i is now set to 4 bytes of "nothingness"

If we imagine data storage as a light switch, we have

1: switch is on
0: switch is off
null: there is no switch (or spoon)

By itself,var i只是一个名称或指针，但它还没有指向任何东西(甚至连虚无都没有)。It's not thatGazasdasrbmeans "nonsense", it's thatGazasdasrbhas no meaning at all.

Division By Zero

Many math explanations say you "can't divide by zero". It's not that you can't, it's that it's undefined. What does division by zero mean? What doesGazasdasrbmean?

If we pick a specific value for the result of a division by zero (let's say 3/0 = 15) then we immediately have contradictions (this means 15 * 0 = 3).

为了避免这个麻烦，我们说除以0是“未定义的”，或者“我们还没有抽出时间来选择一个值，nyah". In some games, the only winning move is not to play.

(Sometimes we define a value forstrange expressions(such as $0^0 = 1$), if it's useful and doesn't lead to contradictions.)

Calculus

微积分与零的概念共舞。Beyond the study oflimits and infinitesimals, we are curious about the meaning of "zero change".

当我说一个函数不变(“导数为零”)，这通常是不够的信息。我们改变不就是因为我们处于最小值，最大值，或者不稳定地平衡在山和峡谷之间吗?

这里有一些技巧，比如二阶导数测试，来看看我们拥有哪种类型的“零变化”。

In Society

Society sets many goals for itself. Here's one: reduce littering. Given our "multiple zero" interpretation, we could accomplish this with:

A robot army that picks up thousands of pieces of litter each day (1000 drops - 1000 cleanups)
Teaching people not to litter (0 drops)

It's the same result -- clean streets -- but what strategy do we prefer?

一般来说，任何负面影响(失业、犯罪、污染等)都可以通过预防或治疗的镜头看到，缺席vs.细致的取消。两种情况下的读数都是0，这取决于我们来进行区分。(Sir, unfrozen Caveman Og is asking about Wooly Mammoth attacks again. Should we sell him more repellent?)

Philosophy

In Eastern philosophy there's the notion of non-doing orWu Wei. Our brains think of "non doing" as sitting lazily on the couch. But maybe it's another type of zero. (Again, hold a plank for 10 minutes and tell me nothing happened.)

Exploring Ideas with Math

这篇文章是一个简单的从方程出发的空谈哲学。“无中生有”这句话没有说服力。但如果我写0美元= 1 - 1美元，嘭，一个想法就出现了。5个符号是如何在几秒钟内说服你的?这简直太神奇了不是吗?

计算很好，但不是数学教育的最终目标。直觉意味着你能以数学为路标轻松地思考、做白日梦和探索一个概念。现在想象一下，如果你对形状、变化和偶然性(几何、微积分、统计学)有这样的理解。

让我们和数学一起学唱歌吧，宝贝。