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2020/06/02 第464期 訂閱/退訂看歷史報份直接訂閱

The Shortest Distance between Two Points Is Not Necessarily a Straight Line! 繞彎路比較近?飛機路線大揭密
by Bruce E. Bagnell


  The shortest distance between two points is a straight line, right? Not necessarily! That depends on the scale of what we are talking about. True, the most direct path from one side of a room to the opposite side is a straight line. We can measure the span to prove this. However, when we use a much larger scope—a global scale, perhaps—a straight line as measured on a map is not necessarily the fastest way to move between two points. How can that be?
  Most maps are printed on flat pieces of paper. The most commonly used is called the Mercator projection, which projects the spherical world onto a flat, two-dimensional surface, exaggerating the size of the northern and southern polar areas. Pull up a map. As you can clearly see, the island of Greenland—located up by the North Pole—is depicted as a huge landmass. As a matter of fact, it is merely two-thirds the size of India, which appears smaller as it lies much closer to the equator. This distortion of space on flat maps warps our impression of straight lines and of relative distances.
  As an example, suppose you want to journey from New York to Taipei. Using a typical Mercator projection map, you would assume that the best flight route would be by heading west via the continental US and over the Pacific Ocean. In reality, that itinerary would be a considerable waste of both time and money. To show why, prepare a piece of string and get hold of a globe. With one end affixed to New York and the other to Taipei, pull the strand taut. Surprise! Now, you’ll have to concede that the shortest distance is going north over Alaska and Russia, then southward towards Taipei.


scale n. 尺度,範圍,規模
Mercator projection  麥卡托投影法(一種等角的圓柱形地圖投影法,在以此投影法繪製的地圖上,經緯線於任何位置皆垂直相交,使世界地圖可以繪製在一個長方形上)
spherical a. 球形/體的
dimensional a. 空間維度的,次元的
polar a. 極區的
landmass n. 地塊,陸塊
equator n. 赤道
warp vt. 扭曲;使有偏見
journey vi. & n. 旅行(尤指長途旅行)
route n. 路線
continental a. 大陸的
affix vt. 附/貼上(常用被動)
taut a. 拉緊的
southward adv. 向南

1. opposite a. 對面的;相反的 & prep. 在……對面
• To be honest, I think the picture would look better on the opposite wall.
• The library is next to the bank, opposite the post office.

2. span n.(從一端到另一端)全長
• That bird has huge wings with a span of over a meter.

3. scope n. 範圍;空間;機會
beyond the scope of...  超出……的範圍
• These questions are beyond the scope of my research.

4. project vt. 投射;規劃
• This lamp is used to project light onto the stage.

5. exaggerate vt. 誇大
• The young child exaggerated the extent of his injury in order to gain sympathy.

6. distortion n. 扭曲
• What the reporter wrote about the event was a complete distortion of the facts.

7. relative a. 相對的;比較的
• They weighed the relative advantages and disadvantages of buying a house and renting an apartment.

8. suppose vt. 假定;想,認為
be supposed to V  理應……
• Suppose you are walking on a hot and dusty road.
• You are not supposed to wear jeans to such a formal meeting.

9. assume vt. 認為;假定,假設
• Elaine didn’t see Daniel’s wedding ring, so she assumed that he was single.

10. itinerary n.(旅行的)行程,路線
• A travel agent said she would plan my itinerary.

11. considerable a. 相當大的
• The sports car costs a considerable amount of money.

12. strand n.(繩子)一根;(頭髮)一撮
• Peter brushed a strand of hair from his forehead, cleared his throat, and began to speak.

13. concede vt.(常指不情願地)承認
concede + that 子句  承認……
• The mayor conceded that he had made the wrong decision on that issue.

1. depend on / upon...  視……而定;依賴……
• Which channel I watch depends on what’s on at that time.
• To Julie, her husband is the only one in the world she can depend on.

2. pull up...  拿出……
• Wayne pulled up a map and pointed out the US to his kid.

3. be depicted as...  被描述成/形容為……
• In that magazine article, the pop singer is depicted as the next Madonna.

4. get hold of...  拿來/找來……
• Daisy managed to get hold of a first edition of the classic novel.

distance n. 距離
• Can you run the entire distance without stopping?
以下介紹 distance 的搭配詞與其他意思的用法:
a. in the distance  在遙遠處(但依稀可見)
• I could see a wisp of smoke in the distance.
b. at / from a distance  從遠方,從遠處
• The huge neon sign was visible from a distance.
c. be within walking distance  在走路能到的範圍內
• I want to live in a place where the MRT station is within walking distance.
d. a safe distance  安全距離
• The car bumped into the one in front of it because the driver didn’t keep a safe distance.
e. keep sb at a distance  與某人保持距離
= keep a distance from sb
• Sal tends to lie, so keep him at a distance.
f. go the (full) distance  堅持下去
• Though exhausted, Ken still went the full distance and finished the marathon.
g. distance 亦可表「(關係的)疏遠」。
• There has been a distance between Jay and May since they split up.


  兩點之間最短的距離是直線,對嗎?不見得!要視我們正在談論的尺度而定。確實,要從房間的一邊到對面的話,最直接的路徑是直線。我們可以測量空間兩點的長度來證明這點。不過,當我們說的是更大的範圍 ── 或許是全球尺度 ── 那麼要在兩點之間移動,地圖上測量到的直線就不見得是最快的路徑了。怎麼會這樣呢?
  大多數的地圖都印在平面的紙上。最常使用的方法是麥卡托投影法,這種方法是將球狀的世界投射到二維平面上,加大了南北極區域的大小。拿出一張地圖。正如你可以清楚見到的,格陵蘭島 ── 位於北極上方 ── 被描繪成一大塊土地。實際上,它僅有印度的三分之二大,而印度卻因為離赤道近得多而變得較小。在平面地圖上扭曲的空間曲解了我們對直線和相對距離的印象。


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