科学与数学lhup.edu
斐波那契骗局
Fibonacci Flim-Flam.
2010 — 2015，它一次次回到首页
黑点是上首页（≥ 50 分）的那次投稿，空心点是没冲上去的投稿，点越大分数越高。
导读
这篇文章系统批驳了流传甚广的“黄金比例无处不在”神话：从鹦鹉螺、向日葵到人体比例、艺术构图和金融分析，作者逐一检验那些被当作事实教授的斐波那契/黄金比例说法，指出大多是事后牵强附会、测量随意或纯属编造。文章提醒读者警惕在自然和设计中强行寻找神秘数字模式的伪科学倾向。
为什么经久不衰：它戳破了被数学课堂和设计圈反复传播的黄金比例迷思，教人用怀疑精神审视“数字神秘主义”，多年来反复登上首页正说明这种祛魅始终有人需要。
HN 评论精选
作者从小被当作事实教授的黄金比例神话，读到真相时深感震惊
感谢提交这篇文章。之前看到有文章声称 iCloud 图标的设计很了不起，因为包含了黄金比例，我当时就想把这篇文章钉到那位作者的显示器上。每当看到这种毫无根据的斐波那契崇拜，我都有读创世神话或“想当然的故事”的感觉。第一次读到真相时真的很受伤——我意识到小学数学课教给我的许多荒唐说法，正是这位作者所批驳的。
jgershen查看英文原文
Thanks for submitting this. After seeing the article that claimed the design of the iCloud icon was brilliant because it included Fibonacci ratios, I desperately wanted to nail this article to the (other) author's monitor. Whenever I see that kind of unjustifiable Fibonacci-worship, I get the same feeling I do when I read creation myths or just-so stories. It honestly hurt the first time I read the truth, and realized I was taught many of the outlandish claims this author points out as fact in grade school math classes.
构图法则有效是因为促使人认真思考，而非神秘力量
黄金比例、三分法等所谓创造美感的构图公式之所以有效，可能是因为它们促使创作者真正停下来思考构图，就像风水让人比随手摆放更用心地布置家具一样。没有什么神秘力量。至于螺旋，它们只是好看罢了。
5hoom查看英文原文
The golden ratio, rule of thirds and other such formulas for creating aesthetically pleasing images probably work because they cause the artist to actually stop & think about composition, kind of like how feng-shui causes you to think harder about the arrangement of your furniture than if you just put it wherever. No mystical forces involved. As for spirals, well they just look pretty. All swirly & hypnotic...
斐波那契迷信在金融领域已形成完整的骗局产业
这篇文章太有必要写了。有人正靠着金融领域的斐波那契骗局建立整个职业生涯。
jpdoctor查看英文原文
This article soooo needed writing. There are people building entire careers out of financial Fibonacci fakery.
理论上某些尺度不变过程可产生黄金螺旋，但把巧合当事实有损科学
斐波那契数列相邻两项之比确实趋于极限 Phi，这是真的。有趣之处在于：如果一个过程满足尺度不变、旋转不变、且对大结构的作用压过对小结构的作用，理论上就会产生类似黄金螺旋的东西，所以自然界出现某些近似现象并不奇怪。但话说回来，把黄金比例当作事实来讲、实际只是巧合，是对科学的伤害，尤其是由科学老师来做。
EGreg查看英文原文
I don't know about all that, but my math background does nudge me to point out one thing: The fibonacci sequence is such that a[n+2] = a[n+1] + a[n], and as a result, we have a[n+1] / a[n] -> a[n+2] / a[n+1] that is to say, the sequence of ratios a[n+1] / a[n] tends to a limit, and this limit is Phi here is the cool thing: in spirals, there is a certain scale invariance going on when it comes to fibonacci numbers. Consider a rectangle where its larger side is Phi * its smaller side. If whatever process made the rectangle uneven now operates with the larger side, it will make a rectangle whose larger side is Phi * its smaller side (assuming the process is scale invariant). Of course, in reality this would be much more of a continuous process. Put another way, if a process has the following properties: 1) it is scale invariant 2) it is rotation invariant 3) its operation on the larger structure overpowers its operation on the smaller structure then this process would produce something akin to a golden ratio spiral. So I would expect at least some things in nature to be like this, at least theoretically. EDIT: that said, passing the golden ratio thing off as fact when it's just a coincidence is doing a big disservice to science, especially when done by science teachers.
模特照片经修图失真，且艺术家本不严格遵守构图规则
我数学不精，但懂一点艺术和摄影。文章写得不错，但两点：用泳装模特照片做测量方法有严重缺陷，这些图片大量经过 Photoshop 处理，腿长腰身比例早已失真。至于绘画中的三分法或黄金螺旋，艺术家本来就不太遵守“规则”，原则或许适用但没人真的去量。别忘了吉他音箱原本设计为不失真，直到 Link Wray 用铅笔捅穿了喇叭。
slr555查看英文原文
I am not much of a mathematician but I know a little about art and photography. Generally this piece was well written and I don't doubt a lot of it. Two comments though: Using pictures of swimsuit models is a potentially deeply flawed methodology. Photoshop is of course liberally applied to these images and proportions of many aspects (leg length and waist length being perhaps the most germane here) are thus distorted. In regards to painting and the arts in general, people talk about the rule of thirds or the golden spiral but artists are not so good about sticking to "rules". The general principle may apply but no one is measuring. Remember that engineers designed guitar amplifiers originally not to cause distortion. Everything changed when Link Wray put a pencil through the cone of his cabinet. ;)
数字神秘主义古已有之，如 432 Hz 调音迷信
好文。我对鼓吹把音乐调到 432 Hz（而非 440 Hz）的人也有同感。连毕达哥拉斯学派这样在数字中看到有趣规律的人，也未能免于在一切地方寻找数学模式的欲望。
t2015_08_25查看英文原文
Awesome posting. I feel the same way about people advocating tuning music to 432 Hz (as opposed to 440 Hz). Even the Pythagoreans, who saw a few interested patterns in numbers, fell prey to the desire to see mathematical patterns everywhere.
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