比想象更聪明——会数0的蜜蜂

Honeybees understand that "nothing" can be "something" that has numerical meaning, showing that they have a primitive grasp of the concept of zero.

蜜蜂们能够理解“什么都没有”是有数学含义的事情，这显示它们对0的概念有初步的掌握。

That's according to a newly published study in Science, which shows that bees possess a mathematical ability once thought to exist only in dolphins, primates, birds and humans who are beyond the preschool years.

该结果来自于一篇最近发表于《科学》的研究，该研究显示蜜蜂拥有一种数学能力，而这种能力人们曾经认为只在海豚，灵长类，鸟类和学前班以上的人类中才存在。

"This is quite amazing, in my view, that bees can really do it," says Andreas Nieder, a scientist who studies how animals' process the idea of "nothing" and was not part of the research team.

“这是很令人惊讶的，在我看来，蜜蜂竟然能做到，”安德里亚斯.尼德说，他是一名研究动物能否理解“0”的理念的科学家，并未参与此次研究。

He says zero was discovered relatively recently in human history, and was essential in the development of both mathematics and science.

他说0是在人类历史上相对很晚的时期才发现的，而0在数学和科学的发展上是很基础的。

"It's a hard and very abstract concept," Nieder says. "It is a sort of eccentric uncle in the number family."

“这是一个比较难而又抽象的概念，”尼德说。“属于数字家庭中的怪蜀黍。”

Previous experiments have shown that honeybees have some facility with numbers, because they were able to count landmarks as they foraged around for a sweet reward.

早前实验显示蜜蜂能识别数字，因为它们能在搜寻蜜源补给的时候，数出地标的数目。

But in these tests, the insects couldn't count very high — only to about four.

不过在这样的研究中，这种昆虫没法数到很大的数字——只能数到4.

Still, that made a team of researchers in Australia and France want to explore what else the bees could do with numbers.

不过，这仍然使得一支澳大利亚和法国的研究团队想要探索蜜蜂还能怎样识数。

Scarlett Howard at RMIT University in Melbourne, Australia, lured bees to a wall where they were presented with two square cards.

斯嘉丽.霍华德，来自澳大利亚墨尔本的皇家墨尔本理工大学，她吸引蜜蜂来到一面墙上，墙上它们会看到两张方形卡片。

Each card had a different number of black symbols, such as dots or triangles.

每张卡片上会有不同数目的黑色标记，比如点或者三角形。

Howard trained one group of bees to understand that sugar water would always be located under the card with the least number of symbols.

霍华德训练一组蜜蜂明白了，糖水将总是放在数字标记最少的那张卡片下面。

"They could come and see two circles versus three circles, or four triangles versus one triangle, or something like that," she explains.

“它们来了之后会看见两个或者三个圆圈，或者四个和一个三角形，或者类似的组合，”她解释道。

The bees quickly learned to fly to the card with the fewest symbols, an impressive feat.

蜜蜂们迅速学会了要飞到标记最少的卡片那里，这是个令人震惊的成绩。

But then they got another test: The researchers presented the bees with a card that had a single symbol — and a blank card that had nothing on it.

不过后来它们又面临另一次测试：研究员们给蜜蜂慢展示一张画有单个标记的卡片——还有一张什么都没有的空白卡片。

The bees seemed to understand that "zero" was less than one, because they flew toward the blank card more often than you'd expect if they were choosing at random — although they weren't that good at distinguishing between the two.

蜜蜂们仿佛懂得“0”比1还要小，因为它们如此频繁地飞向空白卡，以至于不能认为这是随机的——尽管它们区分起来不如之前的成绩好。

It got easier for them when they had to compare zero with a larger number.

如果把0和更大的数字作对比，它们区分得更容易些。

"When we showed them zero versus six, they did that at a much higher level than zero versus one," Howard says.

“当我们给它们展示0和6的时候，它们比0和1时选得更好，”霍华德说。

"So what tells us is that they consider zero as an actual quantity along the number line.

“这就告诉我们它们把0作为数轴上的一个实际的量。”

They're actually better at doing zero versus six because those two numbers are further apart."

“它们能更好地区分0和6是因为这两个数隔得更远。”

"We were very surprised and happy, excited, to see that actually the bees were choosing the empty paper," says Aurore Avargues-Weber, a CNRS researcher with the University of Toulouse.

“我们感到又惊又喜，很振奋能看到蜜蜂真的会选空白卡片，”奥罗拉.阿瓦格-韦伯说，她是图卢兹大学联合的法国科学研究中心的一名研究员。

Even very young children, she points out, have trouble understanding that zero is a number.

即使是很小的孩子，她指出，也很难理解0是一个数字。

"It's easy for them to count 'one, two, three, four,' but zero, it's nothing, it's not something to count. So it's not the same category," she explains.

“让他们数'1,2,3,4’比0更简单，0是什么也没有，不能数出来。所以不属于同一类，”她解释道。

She had expected that the bees would see a blank paper as something irrelevant that was completely different than what they had been trained on, because to understand zero, "brains need to represent something out of nothing. It's not trivial."

她本以为蜜蜂会把空白卡片看成不相干的东西，跟它们训练的不一样，因为要理解0“大脑需要明白什么都没有这个概念，这可不简单。”

What's more, the brains of bees are incredibly tiny brains compared with the brains of humans, Nieder notes.

另外，蜜蜂的大脑跟人的大脑比起来是相当微小的，尼德注意到。

"Bees really have a mini-brain with fewer than one million brain cells," he says, "compared to 86 billion nerve cells in our brain."

“蜜蜂微型的大脑只有不到一百万个脑细胞，”他说，“相比之下，我们的大脑有八百六十亿个神经细胞。”

Even so, the bees can understand the abstract concept of an empty set — the precursor or prerequisite to understanding the symbolic number zero — and he says he found that very surprising.

尽管如此，蜜蜂竟能理解空白组的抽象概念—这是理解数字符号0的前提—他说他认为这是非常令人震惊的。