高考|考研阅读风向预测 · 外刊精读 13:Can Bees Count?|蜜蜂真的会＂数数＂吗?科学家发现,问题可能出在我们怎么看它们

Can bees really judge numbers, or are they simply reacting to visual patterns? Image credit: Dr Scarlett Howard / Monash University

Humans often think of numbers as a highly advanced form of thought. Yet research over the past several decades has suggested that numerical abilities may not be limited to humans. Birds, fish and even insects have shown an ability to distinguish between different quantities.

Honeybees are a particularly surprising example. In previous experiments, researchers trained bees to choose between images containing different numbers of objects. Some bees learned rules such as "choose the smaller number" or "choose the larger number." They were then able to apply these rules to new combinations that they had not seen during training. In one well-known experiment, bees trained to choose the smaller quantity even selected an empty image — representing zero — when it was presented against images containing objects. Such findings seemed to suggest that bees were processing numerical information.

But not everyone agreed. Some scientists argued that the bees might have been responding to simpler visual features rather than number itself. For example, a picture containing five objects may differ from a picture containing two objects not only in number but also in total area, edge length, density or visual complexity. One possible cue is spatial frequency, which describes how often patterns or changes in light and dark appear across a visual scene. If pictures with larger numbers also tend to contain different spatial frequencies, bees might learn to use this visual property instead of counting the objects.

This criticism raised an important question: Were the bees really responding to number, or were humans mistaking a simple visual strategy for numerical thought?

A team of researchers from several universities has now re-examined the debate. Their argument begins with a basic principle: before deciding what visual information an animal is using, scientists must first know what that animal is actually capable of seeing.

A bee does not see the world the way a human does. Honeybee eyes have much lower spatial resolution than human eyes. Fine visual patterns that are obvious to us may appear blurred or may not be detectable by a bee at all. Previous research has measured these limits. Honeybees are mainly able to distinguish relatively low spatial frequencies — broad patterns rather than very fine details. Their ability to tell patterns apart falls sharply as spatial frequency increases.

The researchers noticed a problem with an earlier criticism of the numerical experiments. That analysis had removed the lowest spatial frequencies when calculating the visual properties of the images. Yet those low frequencies are precisely the range that honeybees are best able to see. As a result, the analysis may have given strong importance to visual information that was clear to a human or a computer calculation but much less useful to a bee.

The new team therefore recalculated the properties of the experimental images while including the full range of spatial frequencies relevant to honeybee vision. The result changed the picture. Once the analysis was adjusted to match what bees can actually perceive, the previously reported close relationship between spatial frequency and number disappeared. The visual cue alone could no longer explain the bees' earlier performance.

Another piece of evidence came from the "zero" test. Imagine a bee that has been trained to choose the smaller number. It has learned from images containing several objects. Then it is given a choice between an image with objects and a completely empty image. If the animal relies only on familiar patterns or visual complexity, an empty image should present a serious problem. It does not resemble the training images in the same way. Yet bees in previous experiments successfully chose the empty set as the smaller quantity. For the researchers, this behavior is difficult to explain using spatial frequency alone. It strengthens the case that the bees were responding, at least partly, to numerical information.

The scientists are careful not to claim that bees understand numbers exactly as humans do. Nor do they argue that visual features such as spatial frequency are irrelevant. Bees certainly use many visual cues when navigating, finding flowers and making decisions. Instead, the study makes a more specific point: a proposed alternative explanation must itself be biologically possible. If an analysis depends mainly on visual details that an animal cannot actually resolve, it may tell us more about human assumptions than about the animal's strategy.

This lesson extends beyond bees. Scientists studying animal intelligence often design tasks from a human point of view. But different species experience very different sensory worlds. Some animals see ultraviolet light. Others depend heavily on smell, sound or vibration. A task that seems simple to a human may be nearly impossible for another species — or difficult for reasons unrelated to the ability researchers intended to test.

Understanding animal cognition therefore requires more than asking whether an animal succeeds or fails. Scientists must also ask: What information was actually available to the animal when it made the decision?

这篇真正高级的地方不是 Bees are smart，而是研究者在质疑一个 alternative explanation。旧实验：Bees choose according to number。后来有人说：Maybe they use spatial frequency instead——这当然是一个合理质疑。但新论文继续追问：Can bees actually perceive the particular spatial information used in that explanation? 如果理论上的 cue 动物实际上根本看不清，那么这个 alternative explanation 就会明显变弱。全文真正的逻辑是：

这就是非常标准的高考 D 篇研究逻辑。

这个词看起来很专业，其实不需要学物理定义。你只需要知道：它和图像中 light / dark patterns 以及 visual detail 的重复频率有关。简单理解：low spatial frequency——比较大的、粗略的图案；high spatial frequency——更多细小变化和精细纹理。而蜜蜂的视觉系统更适合处理 relatively coarse visual information，对特别精细的高频视觉细节辨别能力有限。

旧分析做了一件事情：计算实验图片里的 spatial frequency，但是它去掉了一部分 low-frequency information。问题来了：偏偏蜜蜂主要能利用的，就是 low spatial frequencies。也就是说，分析人员认为重要的信息，和蜜蜂真正能看到的信息，可能根本不是一套东西。新研究于是 recalculated the visual properties using the frequency range biologically relevant to bees，然后原来所谓"spatial frequency closely tracks number"的关系明显变弱。

我们看到一张图片觉得"这个图案明显更密啊"，但"明显"对谁？对人类明显，并不意味着蜜蜂看到的也是同样的信息。动物认知研究有一个非常重要的原则：The relevant world is the animal's perceptual world. 研究者在论文中强调，实验刺激和数据分析应该符合被研究动物的 sensory and psychophysical constraints。

假设蜜蜂学习的是 choose the smaller number：训练的时候 ● ● ● ● vs. ● ●，然后突然测试：空白 vs. ● ●，蜜蜂选择空白。为什么这个结果重要？因为"零个东西"在视觉上和之前那些有多个黑色形状的图片差别非常大。如果蜜蜂只是在机械匹配某种图案密度，这个测试会变得很难解释。而此前实验中，蜜蜂依然能够把 empty set 放到"less than"这一边。新论文认为，这个 control test 是支持数量加工的重要证据之一。

媒体标题当然可以说 Bees pass the maths test——这是传播标题。但科学结论更加谨慎：研究支持 honeybees can process numerical information，不等于 honeybees understand mathematics like humans，更不等于 bees can calculate equations。这是非常典型的 scientific claim vs. media headline。

论文讨论 spurious correlations。前面的背景是：有人发现"number 增加"和"某种视觉指标增加"看起来高度相关。但新研究认为，这种相关关系部分来自分析方式本身。所以 spurious 最接近：appearing to be real or meaningful, but actually misleading——表面存在、但可能具有误导性的。

Animal cognition experiments must take into account what the animal itself can actually perceive. Image: UC Davis / experimental bumblebee setup.

蜜蜂数量实验经常使用 Y-maze，结构非常简单：蜜蜂从中间进入，前面分左路和右路，两边各放一张图（比如左边 ● ●，右边 ● ● ● ●）。如果蜜蜂选择符合训练规则的一侧，就获得 sugar water reward。长期训练以后，再给它从没见过的新图片——这时候才真正有意思：如果它只是背图片，新图片应该让它失败；如果仍然能够 apply the rule to novel stimuli，就说明它可能学到了比"记住一幅图"更抽象的东西。原论文回顾了这类数量判断和规则迁移实验，并特别强调实验刺激必须符合蜂类视觉分辨能力。

全文其实在提醒：如果一个动物实验失败，不一定说明 The animal lacks the ability，可能还有另一种解释：The task was poorly matched to the animal's sensory system. 举个最极端的例子：如果你用红色和绿色测试一种根本分不清这两种颜色的动物，最后它做错了，你不能立刻说 This animal cannot learn categories——也许只是你给它的信息，它根本看不见。

这一篇只需要三个步骤：