2013.04.24一个 "人类计算机 "

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一个 "人类计算机 "的惊人讣告中的6个惊人事实
当面对沙昆塔拉-德维的故事时，每个人都会问一个问题。"她是怎么做到的？"

作者：丽贝卡-J-罗森
2013年4月24日


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路透社
纽约时报》刊登了一篇珍贵的讣告，500字的讣告充满了关于其主题的精彩片段，一位名叫沙昆塔拉-德维的数学家于周日在班加罗尔去世，享年83岁。


德维的数学能力为她赢得了 "人类计算机 "的美誉。她的功绩非同一般，而《泰晤士报》提供的关于她生活的非数学细节只是为其一生的成就增添色彩。下面是一些最好的细节。

"1977年，在达拉斯的南卫理公会大学，她在50秒内提取了一个201位数的第23个根，超过了Univac计算机，后者需要62秒。
三年后，她为自己赢得了吉尼斯世界纪录的一席之地，她将两个13位数（7,686,369,774,870和2,465,099,745,779）相乘，*并在短短28秒内阐明了解决方案（26位数：18,947,668,177,995,426,462,773,730）。
1976年一篇关于她的文章这样描述她的能力。"她可以在问问题的时间内给你188,132,517的立方根--或者几乎任何其他数字。如果你给她上个世纪的任何日期，她会告诉你那一天是星期几。"
在欧洲巡演时，不是一次而是两次--一次是在英国广播公司，第二次是在罗马大学--她的问答者宣布她错了，然后被迫承认自己工作中的计算错误。
"她的父亲是马戏团的空中飞人和驯兽师"。
据《泰晤士报》报道，她 "也是一位成功的占星家、烹饪书作者和小说家"。

1990年《情报》杂志的一篇文章探讨了 "每个人都问的问题"。"她是如何做到的？"

他继续说，她自己的答案 "相当不一致"，而且，我想补充一点，不令人满意：，包括。包括："上帝的礼物"、"与生俱来的天赋"、"我想任何人都可以做到，如果他们像我一样热爱数字"，以及 "也许任何人都可以做到，如果他们从幼年开始每天都玩几个小时的数字"。

作者，加州大学伯克利分校的阿瑟-R-詹森推测，德维的能力不是来自 "任何不寻常的基本能力"，而是来自她长期记忆中一个完全不同的 "编码和检索 "过程。他写道。

虽然严格来说，德维不是记忆学家，但从她解决问题的速度可以推断出，记忆在她的技能中一定起着重要作用。显然，最特殊的不是 "工作记忆"，而是长期记忆（LTM），它必须极好地储存着高度过度学习的、有效组织的数字信息和各种计算算法。简而言之，对德维来说，正常工作记忆能力的基本信息处理限制，在数字领域已被LTM中异常高效的数字信息编码和检索所克服。德维利用这些大量积累的数字信息和算法来解决问题，这清楚地表明了他是希夫林和施耐德（1977）所描述的 "自动处理 "的一个极端例子，与信息的 "控制处理 "形成了对比。

詹森继续描述德维的过程，指出她似乎以一种对我们其他人来说很陌生的方式 "感知 "大数字。"当她接受一个大数字时（她必须通过视觉来完成），它几乎瞬间就发生了某种转变--通常是对数字进行某种简化。但这并不是将数字简单地'分块'成更小的集合，"詹森写道。她讨厌逗号，发现它们拖慢了她的速度。但是，他继续说："这并不是说德维不把大数字分解或分析成某种数字成分，而只是说她没有对每个数字使用任何统一类型的'分块'。"

不管这种能力是什么，也不管是什么驱使她去磨练它、完善它，都是值得惊叹、钦佩的，也许，现在还在怀念。

丽贝卡-J-罗森（Rebecca J. Rosen）是《大西洋》杂志的高级编辑，她负责监督《宪法之战》系列中美国宪法法律和政府的报道。



6 Amazing Facts From an Amazing Obituary of a 'Human Computer'
When confronted with the story of Shakuntala Devi there's one question everyone asks: "How does she do it?"

By Rebecca J. Rosen
APRIL 24, 2013
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Reuters
The New York Times has up a gem of an obituary, 500 words chock-full of wonderful bits about its subject, a mathematician by the name of Shakuntala Devi, who passed away in Bangalore on Sunday at the age of 83.


Devi's mathematical prowess earned her the moniker "human computer." Her feats were extraordinary, and the non-math details of her life that the Times provides only add color to a life of accomplishments. Here's a rundown of some of the best factlets:

"In 1977, at Southern Methodist University in Dallas, she extracted the 23rd root of a 201-digit number in 50 seconds, beating a Univac computer, which took 62 seconds."
Three years later, she earned herself a spot in the Guinness Book of World Records when she multiplied two 13-digit numbers (7,686,369,774,870 and 2,465,099,745,779) *and* articulated the solution (26-digits: 18,947,668,177,995,426,462,773,730) in just 28 seconds.
A 1976 article about her described her abilities thusly: "She could give you the cube root of 188,132,517 -- or almost any other number -- in the time it took to ask the question. If you gave her any date in the last century, she would tell you what day of the week it fell on."
Not once but twice while on tour in Europe -- one time on the BBC, the second at the University of Rome -- her quizzers pronounced her wrong, and then were forced to admit to calculation errors in their own work.
"Her father was a trapeze artist and lion tamer in a circus."
And, according to the Times, she "was also a successful astrologer, cookbook author and novelist."

A 1990 article from the journal Intelligence explored "the question everyone asks": "How does she do it?"

Her own answers, he continued, were "rather inconsistent" and, I'd add, unsatisfactory:, including: "a gift from God," "an inborn gift," "I think anyone could do it if they loved numbers the way I do,"and "Perhaps anyone could do it if they had played with numbers for hours every day since early childhood."

The author, Arthur R. Jensen of the University of California, Berkeley, speculated that Devi's abilities stemmed not from "any unusual basic capacities" but from a totally different "encoding and retrieval" process in her long-term memory. He wrote:

Although Devi is not, strictly speaking, a mnemonist, one may infer from the speed of her solutions that memory must play an important part in her skill. It is apparently not the "working memory" that is most exceptional, but the long-term memory (LTM), which must be extremely well stocked with highly over-learned and efficiently organized numerical information and various calculating algorithms. In short, for Devi the basic information processing limitations of normal working memory capacity have been largely overcome in the numerical domain by unusually efficient encoding and retrieval of numerical information in LTM. Devi's use of this vast accumulation of numerical information and algorithms for solving problems clearly evinces all the signs of being an extreme example of what Shiffrin and Schneider (1977) have described as "automatic processing," as contrasted with "controlled processing" of information.

Jensen went on to describe Devi's process, noting that she seems to "perceive" large numbers in a way that would be foreign to the rest of us. "When she takes in a large number (and she must do this visually), it undergoes some transformation, almost instantly--usually some kind of simplification of the number. But this is not a simple 'chunking' of the number into smaller sets," Jensen wrote. She hated commas, finding that they slowed her down. But, he continued, "This is not to say that Devi does not break up or analyze large numbers into some kind of numerical components, but only that she does not use any uniform type of 'chunking' on every number."

Whatever that ability was, and whatever it was that drove her to hone it and perfect it, is something to marvel at, admire, and, perhaps, now miss.

Rebecca J. Rosen is a senior editor at The Atlantic, where she oversees coverage of American constitutional law and government in the Battle for the Constitution series.