一个虚数下的狂想

九月 27, 2012

昨天中午,你给坐你身旁的女生抛出了这问题:为什么人们需要虚数(complex number)这概念?

对于知识、概念和文艺,你总是持有一种进化论式的观点。简单来说,从进化的角度来看,所有存于任何物种的遗传表现,它们之所以还被保留,是因为它们还启着与生存相关的作用和利益。它们鲜少是种毫无意义和目的的存在。

举例眼睛。人类眼球里含有三种不同的视锥细胞,各别分辨三种相异的基色,可并非所有哺乳动物皆如此。事实上只有人和灵长动物有此性征。根据考究,这"三相"视锥细胞的形成,来自于一段基因的多一次复制,使得在同一染色体上,该段基因出现两次。而这意外的基因变化,给相关个体一个很好的生存优势:若个体有多一能分辨不同基色的视锥细胞,那它将更易于分辨食物(比如说,水果)和敌人。与仅拥有两种视锥细胞的物种相比,它的生存机率显然更高,这遗传表现也就因此留了下来。假定,另一种基因变化导致癌症,或对生存无益甚至有害,可以想像带有那遗传表现的个体甚至群体,长期下来绝大多数会给淘汰(简单来说,就是在它还没来得及繁衍时就已先死了)。

在文艺作品上也有相似的情况。那时你还在念大一,你总是想象人类的所有文艺作品,收集在一个容积有限的图书馆。随着时间推移,有越来越多的作品要往这馆子藏,但因为位子有限,于是自然的,某种逐步淘汰的程序就会发生。比如说,作品平平无奇,或与一般作品在意蕴和手法雷同的,会被移走,腾出空间来容纳下来较有价值的作品。

换句话说,无论在物种、文艺作品甚至概念,它们鲜少毫无理由地流传至今。

那虚数呢?拿近的来说,关键就在一元多次方程式。自巴比伦以来,人们就在寻找一元二次、三次、四次方程的解,尽管偶有斩获,但不尽令人满意。比如说,象这么个方程"3x^2-x+3=0"在十六世纪之前多被认为无解。为何(对我们来说,任何一元二次方程都有解)?因为b^2-4ac小于零。那时他们没有虚数的概念,不知道要如何去安插"根号负一"这怪物。也因为缺了虚数这概念,那时的人们不如我们当代人命好,有一个漂亮的式子给出通解。所以,如今人们在十五岁以前就掌握的这基本代数,实在是人们自巴比伦文明至十六世纪近两三千年探索之下的结晶。

而这旅程的尾末几站,有一处名叫虚数。

是喜是悲

九月 27, 2012

记得在你被确诊患上Crohn’s disease的前几个晚上,你和父亲通了电话。话筒另一端的他向你保证,他给你的遗传因子,绝对是好的,所以你不可能患上这类的遗传疾病。你心里当下对此嗤之以鼻。

但,或许,他说的真的没错。

基因学家Matteo Fumagalli和Manuela Sironi于2009年发布了一篇学术文章,他们发现,六个与Inflammatory bowel disease(Inflammatory bowel disease共有两种,一是ulcerative colitis,另一是Crohn’s disease)相关的基因变种,更多存在于那些过去生长在环境有较多病毒、细菌和寄生虫的族群里。这些基因变种并不随机发生,相反的,那是一种演化下所带来的优势——拥有这些变种让个体更好地对抗那些外来入侵者。

换句话说,如果你现今生活在一个落后,或病毒、细菌、寄生虫布满的社区里,与当地其他人们相比,你将更健康,生活得更好,或许脑部会更加发达(因为身体不需要花费太多能量去抵抗不速之客,这让脑部更好的发育)。只是如今你处在二十一世纪、卫生环境良好的马来西亚和新加坡,你那优势不但英雄无用武之地,相反的,它还带给你不小的问题,攻击你自身组织。

相同的问题也发生在拥有STAT6的变种基因的哮喘病患身上。拥有这变种的人,他们身体更能抑制血吸虫(Schistosoma haematobium)的生长繁衍,这对过去生活在荒蛮之境的人们来说,绝对是个优势。可这优势来到了近代,血吸虫已少见,这好处倒成了哮喘的根源。

因此,你或许可以感到一些欣慰——是的,你这病的发生不是一种纯粹的倒霉,只是时不与你。

July 7, 2009
By SANDEEP JAUHAR, M.D.

To meet the expenses of my growing family, I recently started moonlighting at a private medical practice in Queens. On Saturday mornings, I drive past Chinese takeout places and storefronts advertising cheap divorces to a white-shingled office building in a middle-class neighborhood.

I often reflect on how different this job is from my regular one, at an academic medical center on Long Island. For it forces me, again and again, to think about how much money my practice is generating.

A patient comes in with chest pains. It is hard not to order a heart-stress test when the nuclear camera is in the next room. Palpitations? Get a Holter monitor — and throw in an echocardiogram for good measure. It is not easy to ignore reimbursement when prescribing tests, especially in a practice where nearly half the revenue goes to paying overhead.

Few people believed the recent pledge by leaders of the hospital, insurance and drug and device industries to cut billions of dollars in wasteful spending. We’ve heard it before. Without fundamental changes in health financing, this promise, like the ones before it, will be impossible to fulfill. What one person calls waste, another calls income.

It is doubtful that doctors and other medical professionals would voluntarily cut their own income (even if some of it is generated by profligate spending). Most doctors I know say they are not paid enough. Their practices are like cars on a hill with the parking brake on. Looking on, you don’t realize how much force is being applied just to maintain stasis.

I recently spoke with a friend who dropped out of medical school 20 years ago to pursue investment banking. Whenever we meet, he finds a way to congratulate me on what he considers my professional calling. He often wonders whether he should have stuck with medicine. Like many expatriates, he has idealistic notions of the world he left.

At our most recent meeting, we talked about the tumult on Wall Street. Like many bankers, he was worried about the future. “It is a good time to be a doctor,” he said yet again, as I recall. “I’d love a job where I didn’t have to constantly think about money.”

I didn’t bother to disillusion him, but the reality is that most doctors today, whether in academic or private practice, constantly have to think about money. Last January, Dr. Pamela Hartzband and Dr. Jerome Groopman, physicians at Beth Israel Deaconess Medical Center in Boston, wrote in The New England Journal of Medicine that “price tags are being applied to every aspect of a doctor’s day, creating an acute awareness of costs and reimbursement.” And they added, “Today’s medical students are being inducted into a culture in which their profession is seen increasingly in financial terms.”

The rising commercialism, driven in part by increasing expenses and decreasing reimbursement, has obvious consequences for the public: ballooning costs, fraying of the traditional doctor-patient relationship. What is not so obvious is the harmful effects on doctors themselves. We were trained to think like caregivers, not businesspeople. The constant intrusion of the marketplace is creating serious and deepening anxiety in the profession.

Not long ago, a cardiology fellow who had been interviewing for jobs came to my office, clearly disillusioned. “I was naïve,” he said. “I never thought of medicine as a business. I thought we were in it to take care of patients. But I guess it is.”

I asked him how he felt about going into private practice. “I’ll be too busy vomiting for the first six months — I won’t have much time to think about it,” he replied.

Of course, there has always been a profit motive in medicine. Doctors who own their own imaging machines order more imaging tests; to take an example from my moonlighting work, a doctor who owns a scanner is seven times as likely as other doctors to refer a patient for a scan. In regions where there are more doctors, there is more per capita use of doctors’ services and testing. Supply often dictates demand.

But financial considerations have never been as prominent as they are today, probably because so many hospitals and doctors, especially in large metropolitan areas, are in financial trouble. More and more doctors are trying to sell their practices, or are negotiating with hospitals for jobs, equipment or financial aid.

At hospitals, uncompensated care is increasing as patients suffering from the economic downturn lose health insurance. Admissions and elective procedures — big moneymakers — are declining. Hospitals are cutting administrative costs, staff and services.

“More and more you’ll see people in medicine get M.B.A.’s,” a doctor told me at a seminar, in a prediction borne out in my experience. “We are in a total crisis, and I don’t know the answer.”

I must admit that part of me wants to see doctors master the business side of our profession. When I hear about executives at health companies getting tens of millions of dollars in bonuses, I am nauseated by the blatant profiteering. As a loyal member of my guild, I want to see doctors exert more control over our financial house.

And yet the consequences of this commercial consciousness are troubling. Among my colleagues I sense an emotional emptiness created by the relentless consideration of money. Most doctors went into medicine for intellectual stimulation or the desire to develop relationships with patients, not to maximize income. There is a palpable sense of grieving. We strove for so long, made so many sacrifices, and for what? In the end, for many, the job has become only that — a job.

Until I went into practice, I never had an interest in the business side of medicine. I sometimes yearn to be a resident or fellow again, discussing the intricacies of a case rather than worrying about the bottom line. “You need to learn a little of the private-practice mind-set,” a doctor friend recently advised me. “You can’t survive with your head in the clouds.”

But something fundamental is lost when doctors start thinking of medicine as a business. In their essay, Dr. Hartzband and Dr. Groopman talk about the erosion of collegiality, cooperation and teamwork when a marketplace environment takes hold in the hospital. “The balance has tipped toward market exchanges at the expense of medicine’s communal or social dimension,” they write.

How this battle plays out will determine to a great extent what medicine will look like in 20 years. This is about much more than dollars and cents. It is a battle for the soul of medicine.

Sandeep Jauhar is a cardiologist on Long Island and the author of the recent memoir “Intern: A Doctor’s Initiation.”

地震与蛋白质检测

十一月 11, 2008

马来西亚几乎没经历大波幅地震,或许是上苍的眷顾,她并不处在地震带。但不见得所有非地震带地区都能免去激烈摇晃之苦,像是密苏里州的新马德里。1811年12月11日当地居民就经历了颇为激烈的地震。这类非典型地震给科学家带来了难题,特别是对过往(以及史前)地震爆发时间的追朔,还有未来地震发生的预测。不过透过邻近洞穴里石笋的年龄,科学家似乎找到了办法。

福尔摩斯曾说过,推理专家仅透过一粒潜在海底的沙子就能一窥海洋的全貌,虽然这说法挺夸张,但也有些道理。溶有二氧化碳的雨水,流过洞穴顶处的裂缝溶解了少量的石灰岩,滴至洞底,经年累月不断重复地发生,逐渐形成了石笋。科学家发现,每当有新一次地震发生,洞穴顶处会有新裂缝,许多年之后新石笋也就伴随而生。通过检验洞里石笋的年龄——审核石笋里特定元素同位素的数量——科学家能推算过去数千年特定地区有多少地震发生,大略在何时。这推理虽不及福尔摩斯所言般神奇,但也不算差。

就密苏里州的新马德里来说,相关人员在当地邻近洞穴首先发现起始于1917年与1811年的石笋形成——这与历史纪录中地震发生的时间相吻合。接着,科研人员得出在过往的一万八千年该地共发生了七次地震,平均间隔是两千五百年。这消息想必让新马德里现下居民甚感放心:下轮地震还有些时日才会来。

把石笋年龄与地震发生时间相联结,这无疑是个相当美妙的科学方法。向来,科学家大多通过严谨的理论推理,旁敲侧击,大胆假设与小心求证,来另辟蹊径去了解这世界。天体物理学家不曾接近过太阳,但却知晓太阳的组成。甚至那遥不可及的星系,里头的恒星,仅凭它们送至地球的星光,透过光谱的分析,科学家就能大略知晓它们情况还有它们的组成。还有不必通过具体去计算溶液里蛋白质的数量,就能大略知道里头蛋白质的成分含量。

溶液里蛋白质的检测向来都不是易事,含量的确定更困难。主要问题落在蛋白质的种类太繁多,即便是计算溶液里蛋白质的基本组成单位——氨基酸的数量也相当不容易。人体所能消化吸收及利用的氨基酸就有22种,若要确定溶液里氨基酸的总含量,也就得对溶液里各个氨基酸种类的数量去进行计算,这太不经济也太费时。

好在氨基酸都含氮,而且这元素鲜少出现在非蛋白类的有机化合物当中。所以只要检测溶液里的氮,就能大略知晓里头蛋白质的含量,不必去鉴定氨基酸或是蛋白质的数量,简单又方便。如今食品工业皆用此套原则来检定他们的原料和产品。

这真是个美妙的方法——至少在人们滥用三聚氰胺去凑数前,它提供了人类巨大的方便。无论是运用石笋的年龄来追朔地震发生,还是通过氮来鉴定蛋白质含量,人们企图藉着其他途径,特别是科学的方法,来达致生产与认识的目的。但科学都立足于理论,理论的推导必然存有些许的假设来方便思索,而假设的存在则反过来划出理论有效的范围,过了那范围那理论便不适用,结论会错误。就那蛋白质的检测法来说,那方法至少隐含着这么个假设:人类不会用非有机化合物三聚氰胺充替氨基酸,来逃过蛋白质含量的检测。

越过这假设,那方法和理论便失效,所以我们有了乳制品的信心危机。

刊登于2008年11月11日东马《联合日报》

By Juan Carlos Perez, IDG News Service
Published: July 25, 2008

In a discovery that would probably send the Dr. Evil character of the “Austin Powers” movies into cardiac arrest, Google recently detected more than a trillion unique URLs on the Web.

This milestone awed Google search engineers, who are seeing the Web growing by several billion individual pages every day, company officials wrote in a blog post Friday.

In addition to announcing this finding, Google took the opportunity to promote the scope and magnitude of its index.

“We don’t index every one of those trillion pages — many of them are similar to each other, or represent auto-generated content … that isn’t very useful to searchers. But we’re proud to have the most comprehensive index of any search engine, and our goal always has been to index all the world’s data,” wrote Jesse Alpert and Nissan Hajaj, software engineers in Google’s Web Search Infrastructure Team.

It had been a while since Google had made public pronouncements about the size of its index, a topic that routinely generated controversy and counterclaims among the major search engine players years ago.

Those days of index-size envy ended when it became clear that most people rarely scan more than two pages of Web results. In other words, what matters is delivering 10 or 20 really relevant Web links, or, even better, a direct factual answer, because few people will wade through 5,000 results to find the desired information.

It will be interesting to see if this announcement from Google, posted on its main official blog, will trigger a round of reactions from rivals like Yahoo, Microsoft and Ask.com.

In the meantime, Google also disclosed interesting information about how and with what frequency it analyzes these links.

“Today, Google downloads the web continuously, collecting updated page information and re-processing the entire web-link graph several times per day. This graph of one trillion URLs is similar to a map made up of one trillion intersections. So multiple times every day, we do the computational equivalent of fully exploring every intersection of every road in the United States. Except it’d be a map about 50,000 times as big as the U.S., with 50,000 times as many roads and intersections,” the officials wrote.

Yahoo和aaS

五月 5, 2008

Microsoft并购Yahoo一案在美国闹得沸沸扬扬,微软这般动作显是冲着Google而来。未来毫无疑问将是网络的天下,但这曾雄霸一方的软体巨擎 即便是吞并了Yahoo,它在搜索市场也只有不到20%的市场占有率,Google则已有了62%。不仅是为着一口气,这场硬仗还紧关乎Microsoft未来的生存空间。

科技这玩意儿总是很吊诡。在过去,人们看好电子邮件是个能赚钱的好门路,结果这愿景从未曾实现,接连还沦落至大量免钱供应的境地。倒是搜索服务成了新商机,但这匹千里马还真要遇伯乐:当年杨致远拒绝了Page和Brin的搜索技术,微软对此也漠视不理。谁知,由paged files所形成的database能把广告送至较有相关需求的人手上,大大提升网络广告的经济效益,花花绿绿的钞票也就随着滚至Google的口袋。这点Yahoo和Microsoft做梦都没想到。

现在又有所谓“Software as a service”(SaaS)的东西,逐步威胁微软的老窝。这项技术让人直接在web browser里头进行许多软体的作业,像是写邮件、打文件或是spreadsheet的处理。或许日后我们再也不用买软体,只要贱价购买网络服务机提供的处理服务,就像我们不曾买过发电机,但却买电流。

盗版软体使用者终于盼到了春天,finally,可以卸下肩上多年盗版的包袱,光明正大使用不要钱的东西了。因为在所有电脑相关的事物都在走向“as a service”(aaS)的当儿,其中许多要收钱,更多是免费。连黑客们也顺应了这点潮流转移他们目光的焦点,开始通过网络出售他们hacking的服务。

是否有哪个网站让你不痛快?你不必是个机灵的黑客,开个价,自然有人把那网站给淹死。至于这新一轮的安全问题——The Economist把它叫做“pain in the aaS”(不是pain in the ass)——则不是我们普通老百姓所能解决的。