數字有著真理的光環，因此成為人們操弄的工具＠La Vita è Bella

日前在紐約時報網站上讀到這篇新書介紹的文章，談到一些學術文章報告、政客、專家愈來愈有操弄數字做出自己欲意的結論。真是于心有戚戚焉！事實上，商業廣告也很明顯的有此傾向。

數學是真理，1 + 1 = 2, 2 x 2 = 4但是人世間的事並不是如此簡單的算數，或是統計。長期的觀察，自然界許多現象有一定的規則可循，地球的字轉，歲差，....例如統計上的常態分配。但是除了這些有一訂規則可循的現象外，還有許許多多沒有一定現象，或是關聯的事情。但是人們總是習慣去歸納出一定的規則，並依此規則做出判斷或決定。而數字又因為有著真理的光環，成為人們操弄的工具。

記得前先日子蘋果的愛瘋４上市，就接到有人轉寄一則新聞 iPhone 用戶性伴侶平均逾10人，多於其他手機使用者。這根本是個錯誤的連結，能購買>愛瘋４的人基本上追求流行，而且購買力較強，也較願意花錢在追求新潮的事物，這類人自然較能吸引異性。雖然我沒做過調查，但是我想開當年新款法拉利的30歲車主應該也會有類似的現象－－性伴侶多於其他廠牌汽車30歲的車主。同樣30歲的人，只穿亞曼尼服飾的時尚人士也可能是一樣的。但是雖然牽強，還是相關連不是嗎？那麼儘管我沒有做研究，但是我相信使用核能發電的國家，其人民的平均壽命較沒有使用核能發電國家的人民長壽。或許有某種程度相關，但是這些現象並無因果關係。商業廣告或行銷就操弄這些現象，製造兩者間有因果的假象。

在之前的 blog 中引了 Phys Ed: Can Running Actually Help Your Knees? By Gretchen Reynolds　(August 11, 2009) http://well.blogs.nytimes.com/2009/08/11/phys-ed-can-running-actually-help-your-knees 這篇報導－－在歐洲奧地利一個跨十年的研究，與美國史丹佛大學長達二十多年的追蹤，這兩個研究都發現：「持續跑步的人膝蓋健康狀況優於沒跑步的人，或說是：持續跑步的人罹患膝蓋病變的人的比例小於優於不跑步的人。」但是結語我是這麼寫地：除非實驗組與對照組都是同卵雙胞胎，不然實在不是「真」科學；因為人與人的個體差異很大。所以，對這項的研究結果也可以反過來解釋－天生膝蓋較強壯、不易受傷的人，才可以持續不斷的跑步。膝蓋較易受傷的人，或已經受傷的人都盡量避免跑步。

67頻道播著一部影集「數字搜查線」，我看了幾集後就沒看了，劇中的數學天才犯了一個科學或說是數學萬能的毛病。用數學計算歹徒會往何處？或是炸彈會裝在甚麼地方？如果從歹徒的習慣，執行的難易去判斷還有些道理。但是試著找出行為模式後，用數學加以推算。－－如果個人的行為可經由觀察，然後建立模型，然後用數學準確預測，那這個模型的變數太多了，根本不可能！如果可能的話賓拉登(Osama Bin Laden)老早就被美國人給抓到了！又好比有研究說：穿紅色服裝的運動員能表現較佳！我想最主要是要看那一季 Nike 與 Adidas 等大廠要主打哪個顏色吧！

近來重讀莊子，我覺得齊物論裡的一段話很適合作這個題目的結尾：天地與我並生，而萬物與我為一。既已為一矣，且得有言乎？既已謂之一矣，且得旡言乎？一與言為二，二與一為三。自此以往，巧曆不能得，而況其凡乎？故自旡適有以至於三，而況自有適有乎？無適焉，因是已。

October 29, 2010, 3:35 pm

Will sprinters one day break the sound barrier? Do Olympic athletes win more medals if they wear red? And can a simple formula predict happiness?

While those questions may sound absurd, various studies have found away to prove them true through statistical manipulation of numbers and data. The tendency of academics, politicians and pundits to generate such numerical falsehoods from data — and the tendency of the public to believe the results — is a phenomenon cleverly explored in the new book “Proofiness: The Dark Arts of Mathematical Deception,” by Charles Seife.

Mr. Seife, a writer and professor of journalism at New York University, makes a compelling case that numbers have a unique hold onthe human mind, and that we are routinely bamboozled by phony data, bogus statistics and bad math. I recently spoke with Mr. Seife, whose work has appeared in The New York Times, The Economist and elsewhere, about the role that proofiness plays in health and medical research. Here’s our conversation.

bamboozle to confuse somebody, especially by tricking them 迷惑；（尤指）哄騙，欺騙

What is “proofiness?” [這是這本書的作者自創的字]

It’s the mathematical analog of Stephen Colbert’s “truthiness.”It’s using numbers to prove what you know in your heart is true, even when you know it’s not. Numbers have a particular ability to fool us. It’s using that ability to turn nonsense into something that is believable with numbers.

Was there any particular case or event that inspired you to dedicate an entire book to this phenomenon?

I’ve been gathering thread about the book since my college days. I was always a split personality, studying to be a mathematician but drawn to writing and journalism. One of the things that drove me to journalism was my annoyance at how innumerate the media seemed to be. We just don’t seem to be able to handle numbers. I wound up picking out little stories where people were deceived by numbers. I thoughti nitially it would be a fun little book about the silly ways people’s thinking can go wrong, but it turned into something much more sinister— the idea that mathematical deception is playing a large role in the way our society was run.

You write about the fact that numbers have enormous power over our thinking. Why is that?

From school days, we are trained to treat numbers as platonic, perfect objects. They are the closest we get to absolute truth. Two plus two always equals four. Numbers in the abstract are pure, perfect creatures. The numbers we deal with in the real world are different. They’re created by humans. And we humans are fallible. Our measurements have errors. Our research misses stuff, and we lie sometimes. The numbers we create aren’t perfect platonic ideals. They are mixed with falsehood, but we don’t recognize that.

In the book you make the point that bad math can undermine boththe political and judicial process. How can it affect medicine and health?

One of the things our minds are designed to do is pick up patterns. If you eat a bit of bad shrimp and get sick, your mind makes that association and you get an aversion to that food. We are extraordinary pattern-matchers. Anytime there is something that is happening, we tryto find a cause. But sometimes in medicine, sometimes things are absolutely random. Our minds don’t accept that. We must find a cause for every effect.

A really good example is the autism issue. Whenever a parent has achild who ends up being autistic, the parent more than likely says,“What caused it? How did it happen? Is there anything I could have done differently?” This is part of the reason why people have been so down on the M.M.R. vaccine, because that seems like a proximate cause. It’s something that usually happened shortly before the autism symptoms appeared. So our minds immediately leap to the fact that the vaccine causes autism, when in fact the evidence is strong that there is no link between the M.M.R. vaccine or any other vaccines and autism.

MMR vaccine n. 預防麻疹 (measles)、腮腺炎 (mumps)、德國麻疹 (rubella) 的疫苗。一直以來，人們就接種這種疫苗會不會導致兒童自閉症等疾病產生了爭論。

In the chapter titled “Rorschach’s Demon,” you coin the term “causuistry.” Can you explain the word?

[causuistry 是這本書的作者自創的字，可能是結合cause casuistry 而來]

casuistry n. a way of solving moral or legal problems by using clever arguments that may be false 詭辯（指用似是而非的論點解決倫理或法律問題）

Casuistry is using bogus arguments through seemingly sound principles. Causuistry is my shorthand for wrongly implying causation. The issue is that inmedicine or any other field of study, it’s really easy to show that two things are linked in some manner. Something rises, something else falls. As energy consumption rises, so does life expectancy. However, it’s a fallacy to say without other evidence that one is causing the other. You can’t say building more power plants will cause us to live longer. In fact, what’s going on in this example, there is an underlying cause affecting both. The more technological a society is, the more power plants it has, the longer its people live. It’s very easy for a researcher to mistake a correlation for causation. It’s very hard to show that one thing causes the other.

Can you give me another example of causuistry?

A number of years ago there was a study that showed the higher yourcredit card debt, the worse your health. The conclusion seemed to be“Don’t carry a balance on your credit card, otherwise you’ll get sick.”It’s probably just the opposite. People who are sick are running upmedical bills, missing work or maybe have lost their jobs. It’s notthat credit cards cause bad health. It’s that bad health causes unpaidbills on your credit card.

Another word you use is “randumbness.” Can you explain it?

We’re hard wired to reject the idea that there’s no reason for something happening. This is how Las Vegas makes its money. You’ll have people at the craps table thinking they’re set for a winning streak because they’ve been losing. And you’ll have people who have been winning so they think they’ll keep winning. Neither is true. These events are completely random. The universe doesn’t care if you’ve been winning or losing, but our minds see these pattens we think we can exploit, and this leads us to phony beliefs.

Randumbness is our stupidity about true randomness. We are unable to accept the fact that there’s not a pattern in certain things, so we project our own beliefs and patterns on data, which is pattern-free. In the journal Nature a few years ago, some researcher sanalyzed a number of Olympic sports and saw that people who wore red were winning more than people who wore blue. They concluded that red confers an advantage. This is nonsense. It was a random event. In the 2008 Beijing Olympics, you can analyze the same events in the same way, and you find just the opposite. People who wore blue had a statistically significant advantage over people who wore red.

One of the tools researchers use to find patterns in data is the regression analysis. Why do you call this “regression to the moon?”

A regression analysis is a tool for taking a set of data, a collection of points, and making sense of it with a formula. It’s a powerful technique because it allows you to present data in terms of things you think are relevant.

A good example is in economics. If you think elections are affectedby the inflation rate and G.D.P. and the unemployment rate, you turn all of these things into a regression model, and you come up with a formula that predicts the president based on these variables. The problem is that if your initial assumptions don’t have a basis in reality, then it’s going to come up with an answer that makes it look like there’s a connection when in fact there isn’t. This straight regression analysis assumes everything is linear, that there’s a very simple equation that relates to these variables. But the real world isn’t linear. It’s complex.

How are we harmed by “causuistry,” “randumbness” and “regression to the moon?”

There’s harm in bad research, and there’s harm in biased research. This is a problem the medical research community has been dealing with. We tend to think things work better or work at all when they in fact don’t. It’s undermining not just the information that doctors and consumers use, but also the scientific process in general. As people recognize that scientific studies are often not as objective and scientific as they seem, that they include biases and bad numbers, it undermines the credibility of an evidence-based medicine system.

So should we be skeptical of all scientific research? Can we believe anything we read?

I think the biggest thing to take home is that you have the right to question research, the right to think this number doesn’t make sense. I think the best thing to do is if something doesn’t make sense to you, you’re going to learn something by examining it. Sniff it. Figure out where it’s coming from. A little degree of skepticism is usually warranted, especially when there is a number that doesn’t make sense.

http://well.blogs.nytimes.com/2010/10/29/the-dark-art-of-statistical-deception

iPhone用戶性伴侶平均逾10人
2010年08月12日蘋果日報

[蔡惠如、蔡文英╱綜合報導】蘋果智慧手機iPhone讓人更有性吸引力？美國網路調查指，相較於用其他智慧手機者，拿iPhone者，無論男女，性伴侶人數都比較多，以三十歲iPhone用戶為例，女性平均有十二點三名性伴侶，男性則有十名，高於黑莓機（BlackBerry）和Android平台手機使用戶的性伴侶人數。

「跟陌生人易切入話題」

美國《PC雜誌》前天報導，OKCupid交友網站針對九千七百八十五名十八至四十歲的智慧手機用戶進行的網路調查發現，iPhone用戶性生活最活躍，Android手機用戶男女關係較穩定，性伴侶人數少於iPhone和黑莓機用戶。但由於是網站民調，受訪者不見得絕對誠實。

iPhone 3GS用戶葉玟芳說：「因iPhone有app store平台可下載許多程式，跟陌生人較好切入話題，能交到很多朋友，但增加性伴侶應該跟用iPhone無關，跟人比較有關吧。」也用iPhone的上班族蔡旻融則說：「用iPhone給人感覺較時尚，應可為形象加分。」

使用hTC Android平台手機的民眾陳昭民說：「不覺得使用手機跟性伴侶的多寡有什麼關係。」用黑莓機的民眾陳啟綱說：「現在iPhone太氾濫了，沒什麼特別，不一定為形象加分，受歡迎應是個人特質，跟手機無關。」

http://tw.nextmedia.com/applenews/article/art_id/32731681/IssueID/20100812

Phys Ed: Can Running Actually Help Your Knees?

By Gretchen Reynolds
August 11, 2009, 11:59pm

An article in Skeletal Radiology, a well-respected journal, created something of a sensation in Europe last year. It reported that researchers from Danube Hospital in Austria examined the knees of marathon runners using M.R.I. imaging, before and after the 1997 Vienna marathon. Ten years later, they scanned the same runners’ knees again. The results were striking. “No major new internal damage in the knee joints of marathon runners was found after a 10-year interval,” the researchers reported. Only one of the participants had a knee that was truly a mess, and he’d quit running before the 1997 marathon (but had been included in that study anyway). His 1997 knee M.R.I. revealed cartilage lesions, swelling and other abnormalities. In the years that followed, the knee became worse, showing augmented tissue damage and more serious lesions. His exam prompted the researchers to wonder whether he would have been better off persisting as a runner, because, as they speculate, “continuous exercise is protective, rather than destructive,” to knees.

You can’t be a runner past the age of 40, as I am, without hearing that running will ruin your knees, by which doomsayers usually mean that we’ll develop “degeneration of the cartilage in the kneecap, which reduces its shock-absorbing capacity,” says Ross Tucker, a physiologist in South Africa and co-author of the new book “The Runner’s Body: How the Latest Exercise Science Can Help You Run Stronger, Longer and Faster.” In other words, we’ll be afflicted with arthritis.

It’s not an unreasonable supposition; other sports have been linked with early-onset arthritis in knees. In a British study, almost half of the middle-aged, formerly elite soccer players were found to have crippling, bone-on-bone arthritis in at least one knee. Former weight lifters also have a high incidence of the condition, as do retired N.F.L. players.

But despite entrenched mythology to the contrary, runners don’t seem prone to degenerating knees. An important 2008 study, this one from Stanford University, followed middle-aged, longtime distance runners (not necessarily marathoners) for nearly 20 years, beginning in 1984, when most were in their 50s or 60s. At that time, 6.7 percent of the runners had creaky, mildly arthritic knees, while none of an age-matched control group did. After 20 years, however, the runners’ knees were healthier; only 20 percent showed arthritic changes, versus 32 percent of the control group’s knees. Barely 2 percent of the runners’ knees were severely arthritic, while almost 10 percent of the control group’s were. “We were quite surprised,” says Eliza Chakravarty, an assistant professor at the Stanford University School of Medicine and lead author of the study. “Our hypothesis going in had been that runners, because of the repetitive pounding, would develop more frequent and more severe arthritis.”

Instead, recent evidence suggests that running may actually shield somewhat against arthritis, in part because the knee develops a kind of motion groove. A group of engineers and doctors at Stanford published a study in the February issue of The Journal of Bone and Joint Surgery that showed that by moving and loading your knee joint, as you do when walking or running, you “condition” your cartilage to the load. It grows accustomed to those particular movements. You can run for miles, decades, a lifetime, without harming it. But if this exquisite balance is disturbed, usually by an injury, the loading mechanisms shift, the moving parts of the knee are no longer in their accustomed alignment and a “degenerative pathway” seems to open. The cartilage, like an unbalanced tire, wears away. Pain, tissue disintegration and, eventually, arthritis can follow.

So, the best way to ensure that your knees aren’t hurt by running is not to hurt them in the first place. “The biggest predictor of injury is previous injury,” Tucker says, and one of the best deterrents against a first (or subsequent) knee injury is targeted strength training. “The hip stabilizers, quads, hamstrings and core must all be strong enough. As soon as there is weakness, some other muscle or joint must take over, and that’s when injuries happen.”

If you’ve injured your knee in the past, particularly if you’ve ever torn an A.C.L. (an injury that, in the Stanford gait study, was closely associated with misalignment and cartilage degeneration), talk to your physician before running. But for most runners, the scientific observations of Chakravarty will ring true. “What struck me,” she says, “is that the runners we studied were still running, well into their 70s and 80s.” They weren’t running far, she says. They weren’t running frequently. They averaged perhaps 90 minutes a week. “But they were still running.”

http://well.blogs.nytimes.com/2009/08/11/phys-ed-can-running-actually-help-your-knees

The stories were taken from The New York Times and Apple Daily, which were not involved with nor endorsed the production of this blog. The copyright remains with each article's original owners.