“你是理性的人，还是感性的人？”

这大概是我们最熟悉的性格提问之一。MBTI 里有 T（思考）和 F（情感）；网上流行“左脑型”“右脑型”测试；学校里，理科生被认为冷静，文科生被认为多情。好像理性与感性是一架跷跷板的两端：这头翘起来，那头就得落下去。

可只要往深处看一步，这架跷跷板就摇摇欲坠了。

英国数学家哈代说，数学的第一道检验是美（Beauty is the first test），丑陋的数学在世界上没有永久的位置。诗人济慈却在《希腊古瓮颂》里写：美即是真，真即是美。一个最讲逻辑的学科，把“美”当作门槛；一种最讲感受的艺术，宣称自己通向“真”。

这篇文章想说明一件事：理性与感性不是一条线的两端，而是同一个螺旋上交替的两步。为了说清楚它，我们要请出几位老朋友：柏拉图、休谟、康德；也要走进神经科学实验室；最后回到两个最具体的地方——一间数学教室，一间画室。

把理性和情感对立起来，有很长的历史。

柏拉图在《斐德若篇》里讲过一个比喻：灵魂像一辆双驾马车。车夫是理性，两匹马一匹温驯高贵、一匹桀骜不驯。好的人生，就是车夫勒紧缰绳，驾驭住那匹不听话的马。

这幅图景影响了两千年：理性在上，情感在下；理性是主人，情感是需要管教的牲口。

直到十八世纪，苏格兰哲学家休谟把它整个颠倒过来。他在《人性论》里写下一句著名的话：

休谟的意思是：理性能告诉你“怎样”到达目的地，却不能告诉你“为什么”要去。想要什么、在乎什么，是情感给的。再早一些，法国的帕斯卡已经说过：心灵有它自己的理由，那是理性所不知道的。

你会发现，柏拉图和休谟其实共享了一个前提：理性和情感是两样东西，只是谁当家而已。真正动摇这个前提的，是一位以“冷静”著称的哲学家——康德。

说起康德，很多人想到的是“三大批判”的艰深，还有他每天下午准时散步、邻居拿他对表的传说。但正是这位最“理性”的哲学家，给了感性一个前所未有的地位。

先说一个翻译上的小秘密。中文里的“感性”，在康德那里对应德语 Sinnlichkeit——不是“多愁善感”，而是接受的能力：心灵通过感官被外界“触动”、获得直观的能力。与它并列的是 Verstand，中文译作“知性”，也就是运用概念、做出判断的能力；再往上，才是 Vernunft，“理性”——一种不断追问“为什么”、追求终极整体的能力。

我们日常说的“理性”，会推理、会计算、讲逻辑，其实更接近康德的“知性”。而《纯粹理性批判》里最著名的一句话，恰恰是关于感性与知性的：

概念如果不落到具体的感受材料上，就是空转的齿轮；感受如果没有概念来组织，就是一团看不清的混沌。知识只能从两者的结合中产生。在康德这里，感性和知性不是对手，而是一个人的两条腿。

更让人意外的是康德对数学的看法。按常识，数学是最纯粹的理性产物。可康德认为，数学知识之所以可能，恰恰因为它在纯粹直观中构造自己的对象，也就是在空间和时间这两种感性形式之中。你在纸上画一个三角形来证明内角和，靠的不只是逻辑，还有对空间的“看”。

换句话说，在康德的体系里，数学站在感性的地基上。

到了《判断力批判》（1790），康德把这层关系推得更深。他问：当我们说一朵花“美”的时候，心里发生了什么？

他的回答是：这时，想象力与知性进入了一种自由的游戏。想象力把感受材料组织成形象，知性在其中感到一种秩序，却并不把它套进任何确定的概念。两种能力彼此激发、彼此应和，这份和谐本身被我们感受为愉悦——这就是美感。

所以，美感不是理性的缺席，而是理性与感性的共振。

康德还描述了另一种审美体验：崇高。其中一种，他直接称为“数学的崇高”。面对星空、大海、无穷的数列，想象力试图把它“一眼看全”，却力不从心；而就在想象力力竭的地方，理性升起了“无限”的理念——我们无法想象无穷，却能思考它。那种既渺小又伟大的颤栗，就是崇高感。一个学生第一次弄懂“实数比自然数多”的那一刻，大概就尝过这种滋味。

还有一个容易被忽略的细节。“美学”（Aesthetica）这个学科名，是德国哲学家鲍姆嘉通在 1750 年确立的，他给的定义是“感性认识的科学”。希腊词 aisthēsis 的本义就是“感觉”。所以康德把讨论空间和时间的那部分叫作“先验感性论”（transzendentale Ästhetik）——同一个词，一头连着“感觉”，一头连着“美”。

席勒读完康德，又往前走了一步。他说，人身上有追求感受的“感性冲动”，也有追求秩序的“形式冲动”，两者的和解是“游戏冲动”：只有当人在完整意义上是人的时候，他才游戏；也只有当他游戏的时候，他才是完整的人。

哲学家争论了两千年，神经科学在最近几十年给出了一些相当具体的证据。先拆掉两个流行的神话。

神经科学家达马西奥在《笛卡尔的错误》（1994）里讲过一位病人，书里叫他“艾略特”。他因为切除脑瘤，损伤了前额叶腹内侧的区域。手术后，他的智商、记忆、语言和逻辑测验都正常，甚至能头头是道地分析各种选择的利弊；可在现实生活里，他连最平常的决定都难以做出，事业和家庭一落千丈。

达马西奥的解释叫“躯体标记假说”：过去的经历会在身体上留下情绪的“记号”。面临选择时，这些身体信号会迅速给选项打上“好”或“坏”的权重，帮理性把无穷多的可能性削减到可以计算的范围。情绪不是理性的噪音，而是理性的导航。

他和同事设计了著名的“爱荷华赌博任务”：受试者从四副牌里抽牌，其中两副短期回报高、长期却亏钱。结果发现，普通人在能说清“哪两副牌危险”之前，手就已经开始避开它们；伸手去拿危险的牌时，皮肤电会先出现一个小小的预警反应。而前额叶腹内侧受损的病人既没有这种身体预警，即使后来嘴上知道了哪副牌危险，仍然继续去抽。

身体，比嘴先知道答案。

美国心理学家丽莎·费德曼·巴瑞特走得更远。她的“情绪建构理论”认为，大脑里并没有专门生产恐惧、愤怒的固定回路；情绪是大脑根据身体内部信号和过往经验做出的预测与归类。换句话说，情绪本身，也是一种又快又安静的推理。

2014 年，伦敦大学学院的泽基与数学家阿蒂亚等人做了一个实验：请 15 位数学家给 60 个公式按美丑打分，再让他们在核磁共振仪里看这些公式。结果，数学家觉得越美的公式，越会激活内侧眶额皮层的同一块区域——正是人们欣赏绘画、聆听音乐时被激活的那块区域。被评为最美的，是欧拉恒等式；最不讨喜的，是拉马努金那个求 1/π 的无穷级数。

再看“顿悟”。2004 年，荣格-比曼与库尼奥斯等人发现：人们靠顿悟解出词语谜题时，右侧颞叶前部会在报出答案前约 0.3 秒爆发一阵高频的伽马波；而在它之前，大脑后部先出现一阵阿尔法波，像是暂时关掉外界的视觉输入，把注意力转向内心。

心理学家沃拉斯早在 1926 年就把创造过程分成四步：准备、酝酿、明朗、验证。把它和这些发现放在一起，会看到一幅清楚的图：有意识的推理开路，无意识的酝酿接力，顿悟把结果送上意识的台面，最后再交还给推理去验证。

2018 年，比蒂等人在《美国国家科学院院刊》上报告：创造力更强的人，大脑里有一种特殊的连接模式，把默认网络（负责自由联想）、执行控制网络（负责评估筛选）和显著性网络（负责切换）连在了一起。这几个网络平时往往此消彼长，高创造力的人却能让它们同时在线。

神经科学的结论可以概括成一句话：大脑里没有“理性区”和“感性区”的楚河汉界，只有不同网络之间时刻不停的合作。

把镜头拉回数学课。十九世纪末最伟大的数学家之一庞加莱，留下一句被反复引用的话：

他讲过自己的一次顿悟：为一类函数苦思无果之后，他去参加一次地质考察，旅途中暂时忘了数学；就在踏上公共马车台阶的那一刻，一个念头闪现——他用来定义这类函数的变换，与非欧几何的变换完全相同。他没有停下来验证，回家后才慢慢补上严格的证明。

庞加莱认为，无意识会产生大量的组合，而真正能“浮上来”的，往往是那些让人感到优雅、和谐的组合——是审美的感受力在充当筛子。爱因斯坦在给数学家阿达马的信里也说，他思考时用的主要不是语言，而是一些视觉的、甚至“肌肉性”的意象，词语和逻辑是后来才费力找来的。

更基础的层面，法国认知神经科学家迪昂发现，人类乃至许多动物都天生拥有一种“数感”：不用数，也能大致判断哪一堆东西更多。我们后来学的符号数学，正是建在这块“感”的地基上。

反过来，情绪也能把学习卡死。

2012 年，斯坦福大学梅农团队发现：有数学焦虑的 7 到 9 岁孩子做算术时，负责处理恐惧等负面情绪的杏仁核过度活跃，而负责数学推理的顶叶和背外侧前额叶反而活动不足。同年，芝加哥大学的研究者发现，对高度数学焦虑的人来说，仅仅是预期马上要做数学，大脑中与疼痛有关的区域就会被激活。让人痛苦的不是数学本身，而是对数学的预期。

所以，“学数学只需要理性”是一个误会。一个害怕数学的头脑，连理性的门都进不去。

菲尔兹奖得主陶哲轩在一篇博客里，把数学训练分成三个阶段：

前严谨阶段：靠例子、直觉和比划理解数学，重计算、轻理论。
严谨阶段：学习精确的形式化推理，定义、公理、epsilon-delta，一步也不能错；这时直觉常常要“先放一放”。
后严谨阶段：在牢固的严格基础上，重新回到直觉和大图景，用“感觉”快速抓住问题，再用严格性随时检验。

读到这里，我想起唐代书法家孙过庭在《书谱》里的一段话：

两条路的起点不同：陶哲轩从直觉出发，先“感”后“理”；孙过庭从规矩出发，先“平正”、再“险绝”。可它们的形状一模一样——在两极之间来回，最后在更高的地方会合。最后那个“平正”，已经不是最初那个了；后严谨阶段的直觉，也不是当初那个直觉了。

这张图想表达的是：理与感不是同一根轴的两端，而是两个维度。只会证明、不会“看见”，是右下角的“机械”；感觉很对、却说不清楚，是左上角的“玄想”。真正的成熟，在右上角。

如果说数学是“理性里藏着感性”，那么艺术就是“感性里长着理性”。

想想那些最自由的艺术，往往有最严格的规则：唐诗的平仄格律，巴赫赋格的声部规则；法国“潜在文学工场”的作家佩雷克，写了一整部不用字母 e 的长篇小说。之前写过的双向图，更是戴着镣铐跳舞的极致：每一笔都要同时满足两种读法。

规则没有杀死感性，它给了感性骨架，也给了感性阻力，就像风筝要有线，才飞得起来。

明代的王阳明年轻时，想践行朱熹“格物致知”的教导，对着庭院里的竹子苦思七天，想“格”出竹子的道理，结果什么也没格出来，自己反倒病倒了。

北宋的文与可也和竹子较了半辈子劲。苏轼记他的画法：画竹，必先得成竹于胸中。这就是“胸有成竹”的来历。

一个用纯粹的思辨去“格”竹，七日而病；一个用长年的观看去“养”竹，落笔即成。区别不在于谁更理性，而在于：文与可的理，是长在感受里的。

庄子讲庖丁解牛，是同一个道理。庖丁初学时，眼里是一整头牛；三年之后，“未尝见全牛也”；再往后，“以神遇而不以目视，官知止而神欲行”——感官停下来了，心神却在自行运转。刘勰在《文心雕龙》里形容创作的状态，只用了四个字：神与物游。

神经科学看到的也是这幅图：创作时，负责自由联想的默认网络和负责评估的执行网络此起彼伏，像呼吸。画家克利说：艺术不是复现可见之物，而是使之可见。让不可见者可见，需要感性去捕捉，也需要理性去搭建。

走完这一圈，说说我自己的几点看法。

所以，回到开头那个问题：“你是理性的人，还是感性的人？”更好的问法也许是：你的感性，被理性训练过吗？你的理性，被感性点亮过吗？

康德说：思维无内容是空的，直观无概念是盲的。如果要把它改写成一句可以贴在书桌前的话，我会写：

“感性决定往哪里走，
理性保证每一步都站得住。

“Are you a rational person or an emotional one?”

This is probably one of the personality questions we know best. MBTI has T (Thinking) and F (Feeling); “left-brain or right-brain” quizzes go around online; at school, science students are taken to be cool-headed and humanities students sentimental. It is as if reason and feeling sat at the two ends of a seesaw: when one end goes up, the other has to come down.

But look one step deeper, and the seesaw starts to wobble.

The English mathematician G. H. Hardy wrote: “Beauty is the first test: there is no permanent place in the world for ugly mathematics.” The poet John Keats, for his part, wrote in “Ode on a Grecian Urn”: “Beauty is truth, truth beauty.” The most logical of disciplines makes beauty its gatekeeper; an art made of feeling claims to lead to truth.

This essay sets out to show one thing: reason and feeling are not two ends of a line but two alternating steps on the same spiral. To make the case, we will call on some old friends, Plato, Hume and Kant; we will step into the neuroscience lab; and in the end we will come back to two very concrete places, a math classroom and a painter's studio.

Setting reason against emotion has a long history.

In the “Phaedrus,” Plato offers an image: the soul is like a chariot drawn by two horses. The charioteer is reason; one horse is gentle and noble, the other wild and unruly. A good life means the charioteer pulling the reins tight and mastering the unruly horse.

This picture shaped the next two thousand years: reason above, emotion below; reason the master, emotion a beast to be broken in.

Then, in the eighteenth century, the Scottish philosopher David Hume turned it completely upside down. In “A Treatise of Human Nature” he wrote a famous sentence:

What Hume meant is that reason can tell you “how” to reach a destination, but not “why” you should go there. What you want and what you care about come from emotion. Earlier still, the Frenchman Blaise Pascal had already said: “The heart has its reasons which reason knows nothing of.”

Notice that Plato and Hume actually share a premise: reason and emotion are two separate things, and the only question is who runs the house. The one who really shook that premise was, of all people, a philosopher famous for his cool head: Kant.

Mention Kant and many people think of his forbidding “three Critiques,” or of the legend that he took his afternoon walk so punctually that his neighbors set their clocks by him. Yet it was this most “rational” of philosophers who gave feeling a standing it had never had before.

First, a small secret of translation. The Chinese word for “feeling” in this essay, 感性, is also the standard Chinese rendering of Kant's German Sinnlichkeit, in English “sensibility.” It does not mean being sentimental; it means the capacity to receive: the mind's ability to be “affected” by the outside world through the senses and so to obtain intuitions. Alongside it stands Verstand, “understanding” (知性 in Chinese), the ability to use concepts and make judgments; and above that comes Vernunft, “reason” (理性), a faculty that keeps asking “why” and reaches for the ultimate whole.

What we call “reason” in daily life (reasoning, calculating, following logic) is actually closer to Kant's “understanding.” And the most famous sentence in the “Critique of Pure Reason” is precisely about sensibility and understanding:

Concepts that never land on concrete sensory material are gears spinning idle; sensations with no concepts to organize them are a murky chaos. Knowledge can arise only from the union of the two. For Kant, sensibility and understanding are not rivals but a person's two legs.

Even more surprising is Kant's view of mathematics. Common sense says mathematics is the purest product of reason. Kant, however, held that mathematical knowledge is possible precisely because mathematics constructs its objects in pure intuition, that is, within the two forms of sensibility, space and time. When you draw a triangle on paper to prove what its angles add up to, you rely not only on logic but also on “seeing” space.

In other words, in Kant's system mathematics stands on the ground of sensibility.

In the “Critique of Judgment” (1790), Kant took this relationship further. He asked: when we call a flower “beautiful,” what is going on in our minds?

His answer: imagination and understanding enter into a free play. Imagination organizes sensory material into an image, and understanding senses an order in it, without forcing it under any determinate concept. The two faculties stir and answer each other, and we feel this harmony itself as pleasure. That is the feeling of beauty.

So the sense of beauty is not the absence of reason but a resonance between reason and feeling.

Kant also described another kind of aesthetic experience: the sublime. One variety of it he called simply the “mathematical sublime.” Faced with the starry sky, the ocean, or an endless sequence of numbers, imagination tries to “take it all in at a glance” and cannot; and right where imagination gives out, reason raises the idea of “infinity.” We cannot imagine the infinite, but we can think it. That shiver of feeling at once tiny and great is the feeling of the sublime. A student who first grasps that “there are more real numbers than natural numbers” has probably had a taste of it.

There is another detail that is easy to miss. The name of the discipline of “aesthetics” (Aesthetica) was established in 1750 by the German philosopher Alexander Baumgarten, who defined it as “the science of sensory cognition.” The Greek word aisthēsis originally means “sensation.” That is why Kant called the part of his work dealing with space and time the “Transcendental Aesthetic” (transzendentale Ästhetik): the same word connects to “sensation” at one end and to “beauty” at the other.

Schiller, having read Kant, went one step further. He said that human beings have a “sensuous drive” that seeks sensation and a “form drive” that seeks order, and that the two are reconciled in the “play drive”: man only plays when he is in the fullest sense of the word a human being, and he is only fully a human being when he plays.

Philosophers argued for two thousand years; in the last few decades neuroscience has supplied some fairly concrete evidence. First, let's take down two popular myths.

In “Descartes' Error” (1994), the neuroscientist Antonio Damasio describes a patient he calls “Elliot.” Surgery to remove a brain tumor had damaged his ventromedial prefrontal cortex. After the operation his IQ, memory, language and logic tests were all normal, and he could even analyze the pros and cons of different options quite fluently; yet in real life he could hardly make the most ordinary decisions, and his career and family life fell apart.

Damasio's explanation is called the “somatic marker hypothesis”: past experiences leave emotional “markers” in the body. When we face a choice, these bodily signals quickly weight the options as “good” or “bad,” helping reason cut an endless range of possibilities down to something it can compute. Emotion is not noise in reason; it is reason's navigator.

He and his colleagues designed the famous “Iowa Gambling Task”: participants draw cards from four decks, two of which pay well in the short run but lose money in the long run. Healthy participants' hands began to avoid the bad decks before they could say “which two decks are dangerous”; as they reached for a risky card, their skin conductance showed a small warning response first. Patients with ventromedial prefrontal damage had no such bodily warning, and even after they could say which decks were dangerous, they kept drawing from them.

The body knows the answer before the mouth does.

The American psychologist Lisa Feldman Barrett goes further. Her “theory of constructed emotion” holds that the brain has no dedicated, fixed circuits for producing fear or anger; emotions are predictions and categorizations the brain makes from internal bodily signals and past experience. In other words, emotion itself is a kind of fast, quiet reasoning.

In 2014, Semir Zeki of University College London, together with the mathematician Michael Atiyah and others, ran an experiment: they asked 15 mathematicians to rate 60 formulas for beauty, then had them view the formulas in an MRI scanner. The more beautiful a mathematician found a formula, the more it activated one particular area of the medial orbitofrontal cortex, the very area that is active when people look at paintings or listen to music. The formula rated most beautiful was Euler's identity; the least liked was Ramanujan's infinite series for 1/π.

Now consider insight. In 2004, Mark Jung-Beeman, John Kounios and colleagues found that when people solve word puzzles through sudden insight, the right anterior temporal lobe produces a burst of high-frequency gamma waves about 0.3 seconds before they report the answer; and before that, a burst of alpha waves appears at the back of the brain, as if briefly shutting off visual input from the outside world and turning attention inward.

As early as 1926, the psychologist Graham Wallas divided the creative process into four stages: preparation, incubation, illumination and verification. Put that next to these findings and a clear picture emerges: conscious reasoning clears the way, unconscious incubation takes over, insight brings the result up onto the stage of consciousness, and finally it is handed back to reasoning to be verified.

In 2018, Roger Beaty and colleagues reported in the “Proceedings of the National Academy of Sciences” that more creative people have a distinctive pattern of brain connectivity linking the default network (free association), the executive control network (evaluation and selection) and the salience network (switching). These networks usually rise and fall against each other, yet highly creative people can keep them online at the same time.

The conclusion from neuroscience fits in one sentence: the brain has no dividing line between a “reason zone” and a “feeling zone,” only constant cooperation between different networks.

Let's bring the camera back to the math classroom. Henri Poincaré, one of the greatest mathematicians of the late nineteenth century, left us a line that is quoted again and again:

He described one of his own moments of insight. After struggling in vain with a certain class of functions, he went on a geological excursion and, while traveling, forgot about mathematics for a while. Just as he put his foot on the step of an omnibus, an idea flashed into his mind: the transformations he had used to define these functions were exactly those of non-Euclidean geometry. He did not stop to check it; only after he got home did he work out the rigorous proof at leisure.

Poincaré believed that the unconscious produces a great many combinations, and that the ones that “rise to the surface” tend to be those that strike us as elegant and harmonious: aesthetic sensibility acts as a sieve. Einstein, in a letter to the mathematician Jacques Hadamard, likewise said that when he thinks he uses mainly not words but certain visual and even “muscular” images; words and logic have to be sought for laboriously only afterwards.

At a more basic level, the French cognitive neuroscientist Stanislas Dehaene found that humans, and many animals too, are born with a “number sense”: without counting, we can roughly tell which pile has more. The symbolic mathematics we learn later is built on this foundation of feeling.

Conversely, emotion can also bring learning to a dead stop.

In 2012, Vinod Menon's team at Stanford found that in 7- to 9-year-olds with math anxiety, the amygdala, which processes fear and other negative emotions, was overactive during arithmetic, while the parietal lobe and the dorsolateral prefrontal cortex, which handle mathematical reasoning, were underactive. The same year, researchers at the University of Chicago found that for people with high math anxiety, merely anticipating that they are about to do math activates brain regions associated with pain. What hurts is not the math itself but the anticipation of it.

So “learning math takes nothing but reason” is a misunderstanding. A mind afraid of mathematics cannot even get through reason's front door.

In a blog post, the Fields medalist Terence Tao divides mathematical training into three stages:

The pre-rigorous stage: understanding mathematics through examples, intuition and hand-waving, with the emphasis on computation rather than theory.
The rigorous stage: learning precise, formal reasoning, definitions, axioms, epsilon-delta, where not a single step may go wrong; intuition often has to be “put aside for now.”
The post-rigorous stage: on a firm rigorous foundation, returning to intuition and the big picture, using “feel” to grasp problems quickly and rigor to check them at every turn.

Reading this, I was reminded of a passage from the “Treatise on Calligraphy” by the Tang dynasty calligrapher Sun Guoting:

The two roads start from different places: Tao starts from intuition, feeling first and reason second; Sun Guoting starts from rules, first “balance,” then “daring.” Yet they have exactly the same shape: swinging back and forth between two poles, and finally meeting at a higher place. The final “balance” is no longer the first one, and the intuition of the post-rigorous stage is no longer the intuition you started with.

What this diagram tries to show is that reason and feeling are not two ends of one axis but two dimensions. Being able to prove but not to “see” is “rote,” in the lower right; feeling sure but unable to say why is “mystic,” in the upper left. Real maturity lies in the upper right.

If mathematics is “feeling hidden inside reason,” then art is “reason growing inside feeling.”

Think of how the freest arts often have the strictest rules: the tonal patterns and meters of Tang poetry, the voice-leading rules of a Bach fugue; Georges Perec, of the French group Oulipo (the “Workshop of Potential Literature”), wrote an entire novel without the letter e. The ambigrams I wrote about before are the extreme case of dancing in chains: every stroke has to work for two readings at once.

Rules do not kill feeling. They give it a skeleton and also resistance, just as a kite needs its string in order to fly.

As a young man, the Ming dynasty philosopher Wang Yangming wanted to put into practice Zhu Xi's teaching of “investigating things to extend knowledge.” He sat facing the bamboo in his courtyard and thought hard for seven days, trying to “investigate” his way to the principle of bamboo. He got nothing out of it and fell ill instead.

Wen Yuke of the Northern Song also wrestled with bamboo for half his life. Su Shi recorded his way of painting: to paint bamboo, you must first have the finished bamboo in your chest. This is where the Chinese idiom 胸有成竹, “the finished bamboo in one's chest,” comes from: to have a plan fully formed before you begin.

One tried to “investigate” bamboo by pure speculation and fell ill after seven days; the other “cultivated” bamboo through years of looking, and painted it the moment brush touched paper. The difference is not which was more rational, but this: Wen Yuke's reason had grown inside his feeling.

Zhuangzi's story of Cook Ding carving an ox makes the same point. When Ding was starting out, all he saw was the whole ox; after three years, “I no longer saw the whole ox”; later still, “I go at it by spirit and don't look with my eyes. Perception and understanding have come to a stop and spirit moves where it wants.” The senses have come to rest, while the spirit runs on its own. Liu Xie, in “The Literary Mind and the Carving of Dragons,” captured the state of creation in just four characters: 神与物游, “the spirit roams with things.”

Neuroscience sees the same picture: during creative work, the default network for free association and the executive network for evaluation rise and fall by turns, like breathing. The painter Paul Klee said: “Art does not reproduce the visible; rather, it makes visible.” Making the invisible visible takes feeling to catch it and reason to build it.

Having come full circle, let me offer a few views of my own.

So, back to the question we started with: “Are you a rational person or an emotional one?” A better question might be: Has your feeling been trained by reason? Has your reason been lit up by feeling?

Kant said: thoughts without content are empty, intuitions without concepts are blind. If I had to rewrite that as a line to pin above my desk, I would write:

“Feeling decides where to go;
reason makes sure every step holds.