Study shows: Fish can calculate
Cichlids and stingrays can perform simple addition and subtraction in the number range of one to five. This has been shown in a recent study by the University of Bonn, which has now been published in the journal Scientific Reports. It is not known what the animals need their mathematical abilities for.
Suppose there are some coins on the table in front of you. If the number is small, you can tell right away exactly how many there are. You don't even have to count them -- a single glance is enough. Cichlids and stingrays are astonishingly similar to us in this respect: they can detect small quantities precisely -- and presumably without counting. For example, they can be trained to reliably distinguish quantities of three from quantities of four.
This fact has been known for some time. However, the research group led by Prof. Dr. Vera Schluessel from the Institute of Zoology at the University of Bonn has now shown that both species can even calculate. "We trained the animals to perform simple additions and subtractions," Schluessel explains. "In doing so, they had to increase or decrease an initial value by one."
Blue means "add one," yellow means "subtract one"
But how do you ask a cichlid for the result of "2+1" or "5-1"? The researchers used a method that other research groups had already successfully used to test the mathematical abilities of bees: They showed the fish a collection of geometric shapes -- for example, four squares. If these objects were colored blue, this meant "add one" for the following discrimination. Yellow, on the other hand, meant "subtract one."
After showing the original stimulus (e.g. four squares), the animals were shown two new pictures -- one with five and one with three squares. If they swam to the correct picture (i.e. to the five squares in the "blue" arithmetic task), they were rewarded with food. If they gave the wrong answer, they went away empty-handed. Over time, they learned to associate the blue color with an increase of one in the amount shown at the beginning, and the yellow number with a decrease.
But can the fish apply this knowledge to new tasks? Had they actually internalized the mathematical rule behind the colors? "To check this, we deliberately omitted some calculations during training," Schluessel explains. "Namely, 3+1 and 3-1. After the learning phase, the animals got to see these two tasks for the first time. But even in those tests, they significantly often chose the correct answer." This was true even when they had to decide between choosing four or five objects after being shown a blue 3 -- that is, two outcomes that were both greater than the initial value. In this case, the fish chose four over five, indicating they had not learned the rule 'chose the largest (or smallest) amount presented' but the rule 'always add or subtract one'.
Computing without a cerebral cortex
This achievement surprised the researchers themselves -- especially since the tasks were even more difficult in reality than just described. The fish were not shown objects of the same shape (e.g. four squares), but a combination of different shapes. A "four," for example, could be represented by a small and a larger circle, a square and a triangle, whereas in another calculation it could be represented by three triangles of different sizes and a square.
"So the animals had to recognize the number of objects depicted and at the same time infer the calculation rule from their color," Schluessel says. "They had to keep both in working memory when the original picture was exchanged for the two result pictures. And they had to decide on the correct result afterwards. Overall, it's a feat that requires complex thinking skills."
To some it may be surprising because fish don't have a neocortex -- the part of the brain also known as the "cerebral cortex" that's responsible for complex cognitive tasks in mammals. Moreover, neither species of fish is known to require particularly good numerical abilities in the wild. Other species might pay attention to the strip count of their sexual partners or the amount of eggs in their clutches. "However, this is not known from stingrays and cichlids," emphasizes the zoology professor at the University of Bonn.
She also sees the result of the experiments as confirmation that humans tend to underestimate other species -- especially those that do not belong to our immediate family or mammals in general. Moreover, fish are not particularly cute and do not have cuddly fur or plumage.
难点注释：
Stingray, n
表示“黄貂鱼，刺魟（一种鱼，体型大而扁圆，尾长具毒刺）”，means“a large, flat, round fish with a long tail that has poisonous points on it”.如：An elderly Florida man is in critical condition after a stingray jumped onto his boat and stung him in the chest. 一位年长的佛罗里达州男子在一条黄貂鱼跳上他的船并刺穿了他的胸腔后生命垂危。
subtraction, n
表示“减法”，means“the process of removing one number from another”.如：Subtraction is the inverse operation of addition.减法是加法的逆运算。
Glance， n; v
1) 表示“一瞥，看一眼”，means“to quickly look at someone or something”.如：
He gave her an admiring glance. 他向她投以敬慕的一瞥。（n）
She glanced round the room before she left. 她略微环视了一下房间才离开。(v)
2) The man glanced nervously at his watch.那人紧张地看了一眼手表。表示“闪耀”， means” hit at an angle", 如：Their bayonets glanced in the sunlight.他们的刺刀在阳光下闪耀。
3) 表示“掠过”， means” blow which slips to the side“，如：The bullet glanced off his helmet. 那颗子弹掠过他的头盔。
Presumably, adv
表示“据推测，大概，可能”，means“used to say what you think is the likely situation”.如：He will presumably resign in view of the complete failure of his policy. 由于他所推行的政策彻底失败了,他很可能辞职。
Distinguish, v
1) 表示“辨别；区分”，means“If you can distinguish one thing from another or distinguish between two things, you can see or understand how they are different.”.如：Speeches distinguish human beings from animals. 人类和动物的区别在于人会说话。
2) 表示“使杰出，使出众,显扬自己,使自己扬名”，means" behave so as to bring credit to oneself".如：She distinguished herself by her coolness and bravery. 她因头脑冷静、敢作敢为而为人称道。
Geometric, adj
表示“几何图形的，几何的”，means“A geometric pattern or arrangement is made up of shapes such as squares, triangles, or rectangles.”
Stimulus, n
表示“刺激（物），激励（物）；促进因素”，means“something that causes growth or activity”.如：The nutrient in the soil acts as a stimulus to growth. 土壤中的养分能促进植物生长。Her words of praise were a stimulus for people to work harder.她赞扬的话鼓舞人们工作更努力。
Arithmetic, n
表示“算术运算；演算；计算”，means“calculations involving adding and multiplying, etc. numbers”.如：He got the answer by mental arithmetic. 他用心算得出了答案。
internalise/internalize, v
表示“将（情感）藏在心底；使（想法、态度、信仰等）成为性格的一部分，使内化”，means“If you internalize your emotions or feelings, you do not allow them to show although you think about them. To accept or absorb an idea, opinion, belief, etc. so that it becomes part of your character”.如：The innovation process is to accept, activate, internalize and construct knowledge. 创新学习过程是接受、活化、内化和建构知识的过程. Many people tend to internalize their anxiety and distress. 许多人常常将所有的焦虑和苦恼都深藏心底。
Omit, v
表示“疏忽，遗漏；删节，排除”，means“to fail to include or do something”.如：I could omit the overseas section at this point. 我可以暂时把海外部分省略掉。
Don't omit locking the door.别忘了锁门。
Cerebral, adj
1）表示“脑的，大脑的”，means“relating to the brain or the cerebrum”。如：This bibliography provides references to studies that attempt to correlate cerebral functions to cerebral structures in individuals with abnormalities.
在研究变态个体时企图使大脑皮层官能与大脑的结构相关提供参考。
2）表示“理智的”“冷静的”，means” involving intelligence rather than emotions or instinct”.如：Bryant still puts up the numbers, but he is a more cerebral player now. 科比还是能打出不错的数据，但他现在更是一个更理智的球员。
Cortex, n
表示“（尤指大脑或其他器官的）皮层，皮质”，means“the outer layer, especially of the brain and other organs”如：the cerebral cortex 大脑皮层。
However, the cortex is not without purpose in pain processing.然而，皮层在疼痛处理过程中并非无目的性。
Depict, v
表示“描写，描述，描绘；描绘，绘画”，means“to describe something or someone in writing or speech, or to show them in a painting, picture etc”，.如：The fellow depicted the beggar ordinary as a dog. 这家伙把那乞丐描述成一只狗。
Feat, n
feat表示“功绩；技艺；武艺；功绩；英勇事迹”，means“If you refer to an action, or the result of an action, as a feat, you admire it because it is an impressive and difficult achievement.”如：Apparently impossible feats are now accomplished by science. 许多看起来不可能的伟大业绩现在已经由科学实现了。
An acrobatic feat that made a terrific hit with the audience was the somersaulting. 大受观众欢迎的杂技表演是翻筋斗。
be no easy feat 不容易，非易事。类似的还有be no small feat/ be no mean feat可以理解为“是了不起的成就，绝非易事”，means：to be a great achievement，.如：
But getting a guy to bare his soul is no easy feat. 但是，让一个男人对你毫无保留可不是一件容易的事情。
电影《惊天魔盗团2》（Now You See Me 2）中的台词：by performing what he calls an impossible feat. 在这里上演他所谓不可能的奇迹。
Neocortex, n
表示“（大脑）新皮质”，means“part of the brain that controls sight and hearing”
Cognitive, adj
表示“认知的；感知的；认识的”，means“Cognitive means relating to the mental process involved in knowing, learning, and understanding things.”.如：
Thinking in terms of dualisms is common in our cognitive culture. 我们的认识文化通常具有两重性思考。
Mammal, adj
表示“哺乳动物”，means“any animal of which the female feeds her young on milk from her own body. Most mammals give birth to live young, not eggs.”.如：The bat is the only mammal that can fly. 蝙蝠是唯一会飞的哺乳动物。
in the wild
表示“在野外，野生的；在自然环境下；在野生环境中”，means“in natural conditions, independent of humans”.如：I don't know exactly where he lives, except that it's somewhere out in the wilds.他住在哪里我不很清楚，只知道他住得离城市很偏远。
Animals would produce more young in the wild than they do in the zoo.动物在野生环境中的产崽数量要比在动物园里多。
Clutch, n；v
1）表示“群，窝，（尤指鸟巢里的）一窝蛋”，means“a small group of eggs produced by the same bird, especially in a nest”。如：He fell into the clutches of the criminal gang.他落到了犯罪集团的魔爪中。
2）表示“ 抓住; 紧紧抓住; 抱住”，means" seize; take hold of tightly with the hands".如：It is useless to clutch at a straw. 抓救命稻草是无济于事的。
The eagle flew away with a rabbit in the clutch of its claws. 鹰用爪子紧紧抓住一只野兔，飞走了。
Underestimate, v
表示“低估；（对…）估计不足”，means“to fail to guess or understand the real cost, size, difficulty, etc. of something”.如：It seems to have been due to his consistent underestimate of her political weight. 看来是由于希思一贯低估她的政治能量。
Never underestimate the power of a woman. 绝不要低估妇女的力量。
Cuddly, adv
表示“可爱的；令人想抱的”，means“liking to cuddle, or making you want to cuddle”如：Mr Packham is known for favouring less cuddly animals. 众所周知，派克汉姆不喜欢可爱型动物。
Plumage, n
表示“（鸟的）全身羽毛”，means“a bird's covering of feathers”.如：The parrot has got bright plumage.鹦鹉有一身漂亮的羽毛。