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数学天才:有如电影般的人生际遇

The violent attack that turned a man into a maths genius
数学天才:有如电影般的人生际遇

Jason Padgett sees maths everywhere. Even something as ordinary as brushing his teeth is governed by mathematics – he turns the tap on and dips his toothbrush into the water 16 times.

帕吉特(Jason Padgett)在他的生活周遭到处都看得到数学。即使是像刷牙这样普通的事情,也会受到数学的支配——他拧开水龙头,牙刷要在水里浸16下。

“I don’t know why I like perfect squares,” he says. “It’s not just a perfect square, it’s two to the power of four or four squared but I just like perfect squares… I automatically do that stuff with everything.”

他说:“我不知道为什么自己喜欢完全平方数。这不仅是一个完全平方数,它是2的4次方或者4的平方,但我就是喜欢完全平方数……我做所有事情都会不由自主地做到完全平方数。”

Padgett is so obsessed with maths and understands such complex concepts, he's been called a genius. He certainly has a rare talent for drawing repeating geometric patterns – known as fractals – by hand.

由于帕吉特痴迷于数学,能理解复杂的概念,他被称为天才。在他身上,确实有一种罕见的天赋,可以手绘重复的几何图形,即所谓的分形图。

But the former futon salesman from Alaska hasn’t always had a way with numbers. Just under 17 years ago he was living a very different life in Tacoma, Washington.

但这位来自阿拉斯加的前床垫推销员并非一直这样擅长数字。17年前,他在华盛顿州的塔科马过着混乱不堪的生活。

“I was very shallow,” he laughs. “Life rotated around girls, partying, drinking, waking up with a hangover and then going out and chasing girls and going out to bars again.”

他笑着说:“我以前放荡不羁。生活就是围绕着女孩们转,派对、喝酒、宿醉醒来,然后又到外面追女孩,再去酒吧。”

Maths wasn’t on his radar whatsoever.

数学跟他八杆子也打不着。

“I used to say ‘math is stupid, how can you use that in the real world’? And I thought that was like a smart statement. I really believed it.”

他说:“我过去常说,‘数学无聊死,在现实生活中有什么用呢?’我觉得这话说得很对。我真的是这么想的。”
 

帕吉特以前对数学根本不关心,只想着找乐子,直到那次攻击改变了他的大脑

But on the night of Friday 13 September 2002 everything changed.

但在2002年9月13日那个星期五的晚上,一切都改变了。

While out with friends, Padgett was attacked and robbed by two men outside a karaoke bar. They took his already torn leather jacket.

帕吉特和朋友们出去玩的时候,在一家卡拉OK吧外面遭到两名男子的袭击和抢劫。劫匪拿走了已经扯破的皮夹克。

“I heard as much as felt this deep, low-pitched thud as the first guy ran up behind me and smashed me in the back of the head,” he recalls. “And I saw this puff of white light just like someone took a picture. The next thing I knew I was on my knees and everything was spinning and I didn’t know where I was or how I got there.”

他回忆道:“当第一个人跑到我身后,砸中我后脑勺时,我听到了低沉的声音并感受到了猛烈的撞击。然后眼前闪过一道白光,就像有人用闪光灯拍了一张照片一样。接着,我意识到自己跪倒在地,一切都在旋转,我不知道自己在哪里,也不知道是怎么来到医院的。”

Padgett staggered to a hospital across the street where he was told he had concussion and a bleeding kidney thanks to a punch to the gut. “They gave me a shot of pain medication and sent me home,” he remembers.

帕吉特跌跌撞撞地来到马路对面的医院,医生说,有脑震荡,并且因肚子受了一击,导致肾脏出血。“他们给我打了一针止痛,然后就把我送回家了。”

But once home, Padgett’s behaviour changed quickly and dramatically. He had sustained a traumatic brain injury, which can bring on obsessive compulsive disorder - OCD. In Jason's case, he became increasingly afraid of the outside world and would only leave his house to stock up on food.

回到家后,帕吉特的行为很快就发生了戏剧性的变化。他患有创伤性脑损伤,这可能会导致强迫症。帕吉特越来越害怕外面的世界,除了出去补充粮食,平日不会出门。

“I just remember nailing blankets and towels over all the windows in the house… I remember actually using this spray foam and gluing the front door shut.”

他说:“我只记得自己把房间的窗户都用毯子和毛巾钉上……我记得真的是用喷雾泡沫把大门给封上了。”

The OCD had made Padgett irrationally afraid of germs, which had a knock-on effect on his daughter who would come to stay with him amidst custody negotiations with his ex-partner.

强迫症让帕吉特对细菌产生了非理性的恐惧,他的女儿也因此事遭受连累——在与之前的伴侣就监护权谈判期间,她会过来跟他住。

“When she would come over I would obsessively wash my hands and clean,” he says. “The very first thing I would want to do is get her shoes off, get her into clean clothes, wash her hands.”

他说:“她过来住的时候,我会控制不住地反复洗手、打扫卫生。我让她把鞋子脱了,换上干净的衣服,还要洗手。”

But while Padgett was experiencing all these negative consequences from his attack, something incredible was happening too. The way Jason was seeing things changed.

但正当帕吉特经历着袭击所带来的负面影响时,不可思议的事情也发生了。他看待事物的方式发生了改变。

“Everything that was curved looked like it was slightly pixelated,” he explains. “Water coming down the drain didn’t look like it was a smooth, flowing thing anymore, it looked like these little tangent lines.”

他解释说:“所有弯曲的东西边缘都开始像素化。水龙头流出来的水不再是连续流动的,看起来有许多小切线。”

The same thing happened with clouds, sunlight streaming between trees and puddles. To Padgett, the world essentially looked like a retro video game. Seeing such a radically different view of his surroundings evoked conflicting emotions in Padgett. “I was surprised…confused. It was beautiful but it was also scary at the same time.”

云朵、阳光、树木、水坑也都看起来完全不一样了。在帕吉特看来,这个世界本质上就像一款复古的电动游戏。想到自己对周围环境产生了如此截然不同的看法,帕吉特心里为此矛盾重重。他说:“我很惊讶……也很困惑。它很漂亮,但同时也很可怕。”

Because of these visions, Padgett began to think about huge questions in relation to mathematics and physics. Given his hermit-like existence at that time, the internet became a valuable source of information to him as he read extensively about mathematics online.

由于这些幻象,帕吉特开始思考与数学和物理有关的一些问题。当时他过着隐居般的生活,互联网成了他珍贵的信息来源,他在网上阅读了大量与数学相关的文章。

He stumbled across a webpage about fractals which struck a chord with him. It’s a difficult mathematical concept which, put at its most basic, can be likened to a snowflake. When you zoom in, you will see it’s made up of smaller snowflakes connected together, zoom in again and those snowflakes are made of smaller snowflakes, and so on until infinity.

他偶然发现了一个关于分形的网页,引起了他的共鸣。这是一个难度很高的数学概念,从最基本的意义上讲,可以将它比作雪花。当你放大的时候,会看到它是由更小的雪花连接在一起组成的,再放大,这些雪花又是由更小的雪花组成,依此类推,直至无穷无尽。

Padgett was fascinated by this concept but didn’t yet have the words to describe it until one day his daughter asked him how the TV worked.

帕吉特被这个概念迷住了,直到有一天女儿问电视画面是如何出现的时候,他才知道怎么用语言来描述它。

“When you’re looking at a TV screen and you see a circle it’s really not a circle,” he says. “It’s made with rectangles or squares and, if you look close, the edge of the circle is really a zig zag. You can take those pixels and cut them in half and cut them in half and you get closer and closer to a perfect circle but you never actually reach one because you can keep cutting the pixels in half forever, so the resolution gets better but you never have a perfect circle.”

他说:“当你看电视屏幕时,看到的是一个圆圈,它真的不是一个圆圈。它是由矩形或者正方形组成的,如果你仔细观察,会发现圆圈的边缘真的是锯齿形。你可以把这些像素切成两半,再切两半,你会越来越接近一个完美的圆,但你可能永远达不到,因为你可以永远把像素切成两半,所以分辨率会越来越好,但你永远无法得到一个完美的圆。”

Padgett felt compelled to explore this intriguing concept further. So, he began to draw. And he kept drawing.

帕吉特觉得有必要进一步探索这个有趣的概念。于是,他开始画画。不停地画。

“I had literally a thousand or more drawings of circles, fractals, every shape that I could manage to draw. It was the only way I could manage to communicate effectively what I was seeing.”

他说:“我有圆圈图、分形图,我能画出来的每一个形状的图,上千张都不止。这是就我所看到的东西进行有效沟通的唯一方法。”

Padgett believed his drawings “held the key to the universe” and were so important that he needed to take them everywhere with him.

帕吉特认为,他的画“掌握了宇宙的钥匙”,而且它们太重要了,得随身携带。

While on a rare trip out one day, he was approached by a man who had noticed Padgett with his drawings and told him they looked mathematical.

有一天,在一次难得的外出期间,有一男子走近他,这个人注意到帕吉特的那些绘画,并告诉他,这些画看起来很像数学画。

“I’m trying to describe the discrete structure of space time based on Planck length (a tiny unit of measurement developed by physicist Max Planck) and quantum black holes,” Padgett told him. It turned out the man was a physicist and recognised the high-level mathematics Padgett was drawing. He urged him to take a maths class, which led Padgett to enrol in a community college, where he began to learn the language he needed to describe his obsession.

帕吉特告诉他:“我尝试在普朗克长度(物理学家普朗克提出的一种极小的测量单位)和量子黑洞基础上来描述时空离散结构。”偶遇的男子是一名物理学家,他认出帕吉特画的是高级数学。他敦促帕吉特去上数学课。这让帕吉特进入了一所社区大学,在那里开始学习描述令他痴迷的事物时所需要的语言。

After three and a half years of living like a virtual hermit, going to school changed everything for Padgett. He started to get psychological help for his OCD and even met the woman who would become his wife.

在过了三年半隐士般的生活后,学习改变了帕吉特的一切。他开始为自己的强迫症寻求心理帮助,以至遇到了后来成为他妻子的那个女人。

But why was he seeing things in such a strange and different way? Why was his world now comprised of geometric shapes and graphs?

但为什么帕吉特看事物的方式如此奇怪、如此与众不同?为什么他的世界是由几何形状和图形组成的呢?

Poetically, it was television that again provided him with a clue. Padgett saw a man, a so-called savant, who had extraordinary numerical abilities and talked about what numbers looked like to him.

富有诗意的是,电视为帕吉特提供了线索。帕吉特在电视上看到一个人,一个具有非凡数字能力的学者,在谈论他眼里的数字是什么样子的。

“I would always describe that math was shapes not numbers and that was the first time I’d heard anybody but me talk about what numbers looked like,” says Padgett.

帕吉特说:“我总是把数学描述成形状,而不是数字,这是我第一次听到除了我以外的人谈论数学的样子。”

He scoured the internet for more information and came across Berit Brogaard, a cognitive neuroscientist now at the University of Miami. The pair spent hours talking on the phone and from these conversations, Brogaard hypothesised that Padgett had synaesthesia – essentially a cross-wiring of the brain in which the senses get mixed up.

他在网上搜寻更多信息,偶然认识了迈阿密大学(University of Miami)的认知神经学家布罗加德(Berit Brogaard)。两人在电话里聊了好几个小时,通过这些交谈,布罗加德推测帕吉特有联觉——感觉混淆了大脑的交叉连接。

It is estimated to effect only around 4% of the population. Some synesthetes might see certain colours when they hear music or smell something that’s not there when feeling a particular emotion.

据估计,大约4%的人具有联觉。有联觉者可能会在听到音乐的时候看到特定的颜色,或者在感受到某种特定情绪时闻到对应东西的味道。

The condition is caused by connections between parts of the brain that are not there in other people. You can be born this way or some type of trauma, an injury, a stroke, an allergic reaction, can change the brain.

这种情况是由大脑各部分之间的连接引发,这种连接在一般人身上并不存在。极少数人可能是生来如此,也可能是因为某种创伤、外伤、中风、过敏反应而引发了大脑的改变。

Brogaard believes the brain injury Padgett sustained caused him to develop a form of synaesthesia where certain things triggered visions of mathematical formulas or geometric shapes, either in his mind or projected in front of him. She also hypothesised that synaesthesia made Padgett an acquired savant.

布罗加德认为,帕吉特所受的脑损伤使他形成了一种联觉,在这种联觉中,某些东西触发了数学公式或者几何形状的视觉,也许是在他的脑海里,也许是投射到他面前。布罗加德还假设联觉使帕吉特通过学习成为了一名专家。

“Most of us don’t have that kind of insight because we don’t visualise mathematical formulas,” says Brogaard.

布罗加德说:“我们大多数人没有这样的洞察力,因为我们没有能力把数学公式形象化。”

To test these ideas, Brogaard brought Padgett to the Brain Research Unit of Aalto University in Helsinki, where he underwent a series of brain scans.

为了验证这些想法,布罗加德把帕吉特带到赫尔辛基阿尔托大学(Aalto University)的大脑研究部门,在那里帕吉特接受了一系列的脑部扫描。

While in the MRI scanner, hundreds of equations, including fake ones, flashed on a screen in front of Padgett’s eyes. The researchers then watched which parts of his brain lit up in response.

在做核磁共振扫描时,帕吉特眼前的屏幕上闪现着数百个方程式,其中包括一些假的方程式。然后,研究人员观察他大脑里有哪些部位被激活。

“They found that I had access to parts of the brain that we don’t have conscious access to and also the visual cortex was working in conjunction with the part of the brain that does mathematics, which obviously makes sense,” says Padgett.

帕吉特说:“扫描发现,我可以进入大脑中人们无法有意识访问到的部分,而且视觉皮层与大脑中负责数学的部分协同工作,这显然是有意义的。”

Brogaard’s hypotheses turned out to be true. Padgett was formally diagnosed with acquired savant syndrome and a form of synaesthesia. Finally, he had answers.

布罗加德的假设被证明是正确的。帕吉特被正式诊断为:获得性学者综合征和某种形式的联觉。帕吉特终于得到了答案。

Since his diagnosis, Padgett has published a book about his experience called Struck by Genius, he’s toured the world telling people his story and educating them about maths. He is aiming to help others who have had unique or rare/interesting lives by getting their stories published or made into movies. He even sells his drawings of fractals.

自确诊后,帕吉特出版了一本关于自身经历的书,名为《一夕之间变天才》(Struck by Genius)。他在世界各地向人们讲述自己的故事,并向人们传授数学知识。他还希望能帮助其他拥有独特或罕见人生的人将经历拍摄成电影。他甚至出售他画的分形图。

The two men who attacked him that fateful September night were never convicted despite Padgett identifying them and pressing charges.

至于那个灾难性的9月夜晚袭击他的两名男子,虽然帕吉特已指认出并提出指控,但他们最终没有被定罪。

Years later, however, one of the men, Brady Simmons, wrote to Padgett to apologise while he was undergoing treatment for prescription drug addiction following a suicide attempt. In a sense, two lives were changed in the years that followed the attack.

然而,数年后,其中一名男子西蒙斯(Brady Simmons)给帕吉特写信道歉,当时帕吉特正在接受自杀未遂后的处方药成瘾治疗。从某种意义上说,在袭击之后的几年里,有两个人的生活发生了改变。

“I’m a completely different person,” says Simmons. “When I look back the abysmal person that I was in the past, I just don’t see how I existed on that level.”

西蒙斯说:“我现在成了一个与以前完全不同的人。当回头看过去那个糟糕透顶的我时,我根本不知道自己怎么会是那样一个人。”

Padgett too feels like he is a different person than he was before.

帕吉特也觉得自己和以前不一样了。

“I see it [beauty] everywhere,” he says. He is mesmerised by simple things that most people don’t even notice such as raindrops falling on a puddle.

帕吉特说:“我现在到处都能发现它(美)。”他痴迷于一些多数人甚至没有注意到的小事,比如雨滴落进水坑。

Through Padgett’s eyes, the puddle is transformed into complex rippling patterns, overlapping and forming shapes like stars or snowflakes. And he wants everyone else to see what he sees.

在帕吉特的眼睛里,水坑变成了复杂的波纹图案,重叠形成了星星或雪花的形状。他想让其他人也看到他所看到的。

“You should be walking around in absolute amazement at all times that reality even exists,” he says. “I’m having this mathematical awakening and all around us is absolute magic or about as close as you can get to magic.”

他说:“在任何时候,都应该对现实的存在感到惊奇。我正在经历数学上的觉醒,我们周围的一切都是绝对的魔幻,或者你要尽可能地去接近魔幻。”
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