蜜蜂也能理解数字零

即使对于人类，0也不是一个容易理解的概念。儿童学会0往往比其他数字晚，而且他们经常弄不清楚0是大于1还是小于1。0这个数学符号的发明，在历史上也比其他数字晚。

除了人类，还有其他一些动物也掌握了0的概念。例如，黑猩猩和猴子经过训练之后，能把0视为一个数量。

由于蜜蜂的大脑太小，它们似乎不太可能加入这个“识0俱乐部”。但先前有研究已经发现，蜜蜂拥有惊人的数数本领，可以数到4。于是有人想看看，它们经过训练之后是否也能理解0。

首先，训练蜜蜂在两个数之间作区分。研究小组建了两个平台，每个平台上都放有1到4个方块。如果蜜蜂停留在方块数少的平台上，蜜蜂将得到甜蔗糖饮料作奖励；否则等待它们将是一种苦味的奎宁溶液。通过反复训练，它们在80%的时间里都能做出正确的选择。

接下来，把平台上甜和苦的饮料都撤去。在一个平台上摆上2或3个方块，另一个平台上的方块数则为0。有意思的是，蜜蜂大部分时间都停留在方块数为0的平台。由此可见，蜜蜂已经知道，“没有（即0）”是一个比2或3更小的数。

如果让一个平台上的方块数始终保持0，而另一个平台上的方块数从1到6逐次增加。蜜蜂一般都会选择0，但在0和1之间做选择，比起在0和6之间做选择，蜜蜂犹豫的时间更长些，出错的概率也要高些。这说明：一、一个数和0的差距似乎也能影响蜜蜂的选择；二、蜜蜂把0视作与1接近的数，正如人类的儿童一样，有时候搞不清0大还是1大。

这些实验表明，蜜蜂对0的理解与人类和某些灵长类动物对0的理解是相似的，比如我们也把“没有（0）”看作是一个比其他自然数更小的数。只是我们目前还不清楚为什么它们会拥有这种能力。

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.05);--weui-ACTIVE-MASK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-REDORANGE: #ff6146;--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}body,.wx-root{--weui-BG-0: #ededed;--weui-BG-1: #f7f7f7;--weui-BG-2: #fff;--weui-BG-3: #f7f7f7;--weui-BG-4: #4c4c4c;--weui-BG-5: #fff;--weui-FG-0: rgba(0, 0, 0, .9);--weui-FG-HALF: rgba(0, 0, 0, .9);--weui-FG-1: rgba(0, 0, 0, .55);--weui-FG-2: rgba(0, 0, 0, .3);--weui-FG-3: rgba(0, 0, 0, .1);--weui-FG-4: rgba(0, 0, 0, .15);--weui-FG-5: rgba(0, 0, 0, .05);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #fa9d3b;--weui-YELLOW: #ffc300;--weui-GREEN: #91d300;--weui-LIGHTGREEN: #95ec69;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1485ee;--weui-PURPLE: #6467f0;--weui-WHITE: #fff;--weui-LINK: #576b95;--weui-TEXTGREEN: #06ae56;--weui-FG: #000;--weui-BG: #fff;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: #fa9d3b;--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: #06ae56;--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: #10aeff;--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(0, 0, 0, .5);--weui-TAG-BACKGROUND-BLACK: rgba(0, 0, 0, .05)}.wx-root,body{--weui-BTN-ACTIVE-MASK: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BTN-DEFAULT-ACTIVE-BG: #e6e6e6}.wx-root,body{--weui-DIALOG-LINE-COLOR: rgba(0, 0, 0, .1)}.wx-root,body{--weui-BG-COLOR-ACTIVE: #ececec}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BTN-DEFAULT-ACTIVE-BG: rgba(255, 255, 255, .126)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-DIALOG-LINE-COLOR: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-BG: #1E1E1E}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--APPMSGCARD-LINE-BG: rgba(255, 255, 255, .07)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-COLOR-ACTIVE: #373737}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-6: rgba(255, 255, 255, .1);--weui-ACTIVE-MASK: rgba(255, 255, 255, .1)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-REDORANGE: #ff6146;--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--discussInput-BG: rgba(255, 255, 255, .03)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--nickName-FG: #959595}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--weui-BG-0: #111;--weui-BG-1: #1e1e1e;--weui-BG-2: #191919;--weui-BG-3: #202020;--weui-BG-4: #404040;--weui-BG-5: #2c2c2c;--weui-FG-0: rgba(255, 255, 255, .8);--weui-FG-HALF: rgba(255, 255, 255, .6);--weui-FG-1: rgba(255, 255, 255, .5);--weui-FG-2: rgba(255, 255, 255, .3);--weui-FG-3: rgba(255, 255, 255, .1);--weui-FG-4: rgba(255, 255, 255, .15);--weui-FG-5: rgba(255, 255, 255, .1);--weui-RED: #fa5151;--weui-ORANGERED: #ff6146;--weui-ORANGE: #c87d2f;--weui-YELLOW: #cc9c00;--weui-GREEN: #74a800;--weui-LIGHTGREEN: #3eb575;--weui-BRAND: #07c160;--weui-BLUE: #10aeff;--weui-INDIGO: #1196ff;--weui-PURPLE: #8183ff;--weui-WHITE: rgba(255, 255, 255, .8);--weui-LINK: #7d90a9;--weui-TEXTGREEN: #259c5c;--weui-FG: #fff;--weui-BG: #000;--weui-TAG-TEXT-RED: rgba(250, 81, 81, .6);--weui-TAG-BACKGROUND-RED: rgba(250, 81, 81, .1);--weui-TAG-TEXT-ORANGE: rgba(250, 157, 59, .6);--weui-TAG-BACKGROUND-ORANGE: rgba(250, 157, 59, .1);--weui-TAG-TEXT-GREEN: rgba(6, 174, 86, .6);--weui-TAG-BACKGROUND-GREEN: rgba(6, 174, 86, .1);--weui-TAG-TEXT-BLUE: rgba(16, 174, 255, .6);--weui-TAG-BACKGROUND-BLUE: rgba(16, 174, 255, .1);--weui-TAG-TEXT-BLACK: rgba(255, 255, 255, .5);--weui-TAG-BACKGROUND-BLACK: rgba(255, 255, 255, .05)}}@media(prefers-color-scheme:dark){.wx-root:not([data-weui-theme=light]),body:not([data-weui-theme=light]){--appmsgExtra-BG: #121212}}.rich_media_content p{clear:both;min-height:1em}td p{margin:0;padding:0}

div.autoTypeSetting24psection > p,div.autoTypeSetting24psection > section{margin-bottom: 24px;}