北美洲的中心在哪里?地理学家的新方法发现了一个新答案

2017-01-06 11:20:45 来源: 中国科技网 作者: 张微编译

一个州、一个国家或一个大陆的地理中心在哪里?

这是一个充满不确定性的问题。你的计算中包括水域吗?那么岛屿呢?如果海岸线迁移那又该怎么办?

1964年美国地质调查局一份有关州中心的报告中,提到了这个复杂问题,报告中说,“地理中心并没有令人普遍接受的定义,而且也没有令人完全满意的方法来确定它。”最近很多学术机构的代表也在报纸上发表了相同言论。

但是,对于布法罗大学的地质学家皮特 罗杰森博士来说,找到地理中心虽然有难度,但这并不意味着你不去努力。

“所有听到这个问题的人都会说,‘没有什么好办法’” 布法罗大学艺术与科学学院的罗杰森说,他也是纽约州立大学地理学特聘教授。他坚决不同意这一说法:“作为一个地理学家,我的感觉是,如果我想要提出一个定义地理中心的好方法,那么我们可以做到,而且应该去做。”

2015年发表在学术期刊《专业地理学家》(The Professional Geographer)上的论文中,罗杰森提出了一个定义空间实体中心的新方法。这种方法改进了过去的技术,他说,将地球的曲率考虑进去,利用定义(合理的数学方法)来识别地理中心。

2016年末,他用这种方法找到了北美洲的中心。结果是偶然发现的:根据他的计算,北美大陆的中心是在一个名叫森特(center:英文名字中心的意思)的地方,这是北达科他州一个570人的小镇。

对地理中心的痴迷

在他2015年的研究中,罗杰森讲述了美洲人对地理中心持续的兴趣,无论这是否实用,但是他们就是想知道。

他写道,在19世纪初期和中期,美国的县政府所在地的选择惯例,是根据它们距县中心的临近性,这个实践方法提升了地理位置的重要性。今天,一些社区已经设立了纪念牌匾或纪念碑来证明它们作为州中心的地位。

被认可为地理中心可以带来旅游收入,让当地的居民感到骄傲,罗杰森在《专业地理学家》的论文中写道:“地理中心附带的相关收益相当高,以至于不同社区的人都在争夺这一称谓,记者们乐于进行报道,公众也对他们所在地区的地理中心到底在哪里很感兴趣。”

他不知道为什么地理中心会如此吸引大众的关注。就像一个地区的最高峰或最低点一样,地理中心,虽然很难找到,但似乎大家都对它感兴趣。

“这是有点古怪。我想有些人对事物的细节和事实感兴趣,”罗杰森说。“对某些人来说,痴迷的是体育统计,还有些人对某些地方感兴趣。”

优于传统的方法

寻找地理中心的一个早期方法是,在一个地区纸板剪贴图上找到平衡点,剪贴图上有针状点。从那以后,技术不断进行革新,研究人员已经开发出了更精确的技术。

罗杰森说,有一个数学定义能够确定地理中心:物理学中物体的重心就是它的几何中心,其位置就是该区域内到所有其它点平方和最小的点。

确定地理中心的方法在不断变化,但是有一个因素会影响结果的准确性,就是根据地图的分析,没有考虑到地球的曲率问题,这个特性会影响两个地点的真实距离。

罗杰森使用了一种地理学家称为等距方位投影的技术,当把地球的一个圆形三维部分投影成二维平面时,该技术使图上面积和相应的实际地面面积相等。

使用该投影,辅助计算机程序和一个著名的、求解二维多边形中心的数学公式,他能够缩小地理中心的范围,而且符合中心应该是哪里的数学定义。

在罗杰森2015年的论文中提到的北美洲地理中心,它的计算方法包括陆地和内陆水域(像湖泊),以及岛屿。对于北达科他州的森特,它的计算利用了北美洲的本土,而不包括离岛。(过去的计算将北美洲的中心确定在北达科他州东北部以远的地方,距离森特车程100英里以外的城镇附近)

当然,罗杰森对自己的工作还有一点不满意:他使用的方位投影方法,假设地球是圆的,但实际上,地球是椭圆形球体。“它还可以做到更精确,”他说。(张微编译)

以下为英文原文:

Where's the center of North America? Geographer's new method finds a new answer

Where is the geographic center of a state, country or a continent?

It's a question fraught with uncertainty. Do you include water in your calculation? What about islands? What happens when the shoreline shifts?

The U.S. Geological Survey alluded to these complexities in a 1964 report on the centers of states, which opened by stating, "There is no generally accepted definition of geographic center, and no completely satisfactory method for determining it." More recently, various representatives of the agency have given quotes to newspapers saying much the same, hedging.

But to University at Buffalo geologist Peter Rogerson, PhD, the challenge of finding a middle doesn't mean you shouldn't try.

"There are all these people out there saying, 'There's no real good way to do this,'" says Rogerson, a SUNY Distinguished Professor of geography in UB's College of Arts and Sciences. He respectfully disagrees: "As a geographer, my feeling is that if we want to come up with a good way of defining a center, we can and we should."

In a 2015 paper in The Professional Geographer, an academic journal, Rogerson describes a new method for pinpointing the heart of a spatial entity. The approach improves on past techniques, he says, by taking the curvature of the Earth into account appropriately and by identifying geographic centers using a definition that's mathematically sound.

In late 2016, he employed his method to find the heart of North America. The result was serendipitous: According to his calculations, the center of the continent is in a place called Center, a town of 570 people in North Dakota.

An odd fascination with geographic centers

In his 2015 study, Rogerson recounts Americans' enduring interest in geographic centers, whether practical or not.

He writes that in the early and mid-19th century, county seats in the U.S. were routinely chosen based on their proximity to the county's center, a practice geared toward promoting accessibility. Today, some communities have erected plaques or other monuments attesting to their (sometimes questionable) status as the center of their states.

Recognition as a geographic center can generate tourist dollars and civic pride, as Rogerson writes in The Professional Geographer: "The associated attachments often run surprisingly deep—deep enough for communities to do (usually good-natured) battle with each other and for journalists to run feel-good, public interest stories on what lies at the core of their region."

He's not sure why the idea of a geographic center is so intriguing to so many. But like a region's highest mountain or lowest point, the center is a landmark, however elusive, that seems to resonate.

"It's quirky. I think some people are just really interested in facts and the details of things," Rogerson says. "For some people, the obsession is sports statistics, and for some people, it's places."

Better than a cardboard cutout balanced on a point

One early method for finding geographic centers was balancing a cardboard cutout of a region atop a needle-like point, Rogerson says. Technology has come a long way since then, of course, and researchers have developed more precise techniques.

Rogerson says there is actually a solid, mathematical definition for what a geographic center is: It's the spatial equivalent of the center of gravity in physics, and its location minimizes the sum of the squared distances to all other points in a region.

Recent approaches to identifying geographic centers have varied, but one factor that has skewed some results is basing analyses on maps that fail to account appropriately for the curvature of the Earth—a property that affects the true distance between two locations.

Rogerson's technique uses what geographers call an azimuthal equidistant map projection, which preserves important qualities related to distance when a rounded 3-D portion of the Earth is projected as a flat, 2-D surface.

Using this projection, paired with a computer program and a known mathematical formula for finding the centroids of 2-D polygons, he is able to narrow down a geographic center that meets the mathematical definition of what a center should be.

For geographic centers of states, which Rogerson reported in his 2015 paper, his calculations included both land and interior waters (like lakes), as well as islands. For Center, North Dakota, his calculations used the main land mass of North America, and not outlying islands. (Past calculations have placed the middle of North America further to the northeast, near towns more than 100 miles away by car in North Dakota.)

Of course, Rogerson has a small criticism of his own work: The azimuthal projection he's using assumes the Earth is a sphere, but really, the planet is slightly ellipsoidal. "It could always be more exact," he says.

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