前言
Preface
地圖、 手機如拐杖。 我們來看， 能不能不用。
Maps and cellphones are like crutches. Let's see if we can throw them away.
看看我們能做多聰明的方格道路與門牌號碼系統。 民眾用之亦免靠地圖或電子。
Let's see how smart we can make a house addressing system for gridded cities, with maps or electronics needed by the public.
眼睛見到台中市新社區有大片方格路區。 我們開始忙…
Our eyes spot a grid road pattern in Xinshe District, Taichung, Taiwan. Let's get to work…
乍看
First look
二話不說， 先看草案系統吧：
No further ado. Here's what our proposed system looks like:
![[Image: Central Xinshe District, Taichung, Taiwan]](xs1.jpg "Central Xinshe District, Taichung, Taiwan")
圖 1：細部規劃。
Figure 1: Plan detail.
-
號碼巷 / Numbered lanes:
環社路 1000 巷 / Lane 1000 Huanshe Rd.
環社路 6000 巷 / Lane 6000 Huanshe Rd.… -
地址 / Addresses:
環社路 1100 巷 6051 號 / 6051 Lane 1100 Huanshe Rd.
環社路 1100 巷 6158 號 / 6158 Lane 1100 Huanshe Rd.
環社路 6000 巷 1145 號 / 1145 Lane 6000 Huanshe Rd.
環社路 6100 巷 1042 號 / 1042 Lane 6100 Huanshe Rd.
（也看到背景圖裡， 有些現有的 「209…」 門牌， 以及街名， 但都沒有趁方格街網， 做什麼系統化名稱佈置。）
(On the background map we also see some current "209…" addresses and street names. But they all don't take advantage of the street network, to do any logical name arrangement.)
交叉路同制
Cross streets use same system
讀者能發現， 如圖 1 所示， 在我們的系統裡， 環社路 6100 巷 1042 號在於：
The reader will note, as in Figure 1, in our system, the house at 1042 Lane 6100 Huanshe Rd. is located:
-
非在 10 街與 11 街之間.
not between 10th St. and 11th St.
-
又非於 J 街與 K 街之間.
also not between J St. and K St.
而就在：
but instead:
-
1000 巷與 1100 巷之間.
between Lane 1000 and Lane 1100.
亦即 6100 巷之交叉巷之巷號， 與 6100 本巷上之門牌， 採完全一致之系統！
I.e., Lane 6100's cross lanes' lane numbers use the exact same format as Lane 6100's house numbers!
- 推理 1:
- Inference 1:
-
最聰明的系統中， 門牌與路號是一致的。
The smartest system makes no distinction between house numbers and street numbers.
那麼美國有 10.4% 的城市， 不但採號碼街， 又東西、 兼南北， 均為號碼街。 (Rose-Redwood, 2015). 那麼此 10.4% 當中， 只剩下鹽湖城門牌、 路號模式仍能稱我們的競爭對手。
That means that of the 10.4% of United States towns that use numbered streets in both (e.g., north-south, and east-west) directions (Rose-Redwood, 2015), our only competition left is the Salt Lake City numbering model.
我們必須設法超越鹽湖城的系統， 才能奪世界最聰明方格 （或稱網格） 門牌與路號系統冠軍！
We must somehow be even smarter yet than it, if we are to claim the championship of the world's smartest grid road numbering and house addressing system!
又必須超越南美的波哥大系統 （像鹽湖城系統， 只是表達方式略異。）
And we must also beat South America's Bogotá model, which is like Salt Lake City's, just expressed differently.
各系統優缺點
Pros and cons of each system
表1：各系統比對：
Table 1: System comparison:
| 鹽湖城 Salt Lake City |
波哥大 Bogotá |
新社（草案） Xinshe (proposal) |
|
|---|---|---|---|
| 地址舉例 Example address |
6051 North 1100 East | Calle 11 # 60-51 | 環社路 1100 巷 6051 號 |
| 解釋 Explanation |
1100 東街 6051 北號， 或 1100 東街北 6051 號， 等等！ House number "6051 North" on street "1100 East", or house number "6051" on street "North 1100 East" etc.! |
於 11 街上， 過 60 道 51 公尺處 On street 11, 51 meters after the intersection of 60th Avenue |
Number 6051, on Lane 1100, of Huanshe Rd. |
| 無南北東西之別 No N/S/E/W distinction |
X | ✓ | ✓ |
| 無街路道之別 No Street / Avenue distinction |
✓ | X | ✓ |
| 能擴充往幾方向 Can expand in how many directions |
4 | 2 | 1 |
| 一市能容幾方格網 Maximum grids per city |
1 | 1 | 1. 環社路 / Huanshe Rd. 2. 興嶺路 / Xingling Rd. …∞ |
| 若誤成 If mistaken for… |
1100 East 6051 North | Carrera 11 # 60-51 | 環社路 6051 巷 1100 號 |
| …就誤幾街塊註釋
1 / Note 1 then wrong by how many blocks |
0 | √ 2 × ( 60 − 11 ) | 0 |
怎麼贏鹽湖城與波哥大？
How to beat Salt Lake City and Bogotá?
其實， 那較簡單。 看鹽湖城允許四種 6100. 故必加後綴東、南、西、北。
Well that's rather simple in fact. You see Salt Lake City allows four different 6100s, so suffixes N. S. E. W. are needed.
那麼， 我們稍後就會把這些後綴丟掉。 無後綴， 系統變簡單， 我們就贏它了。
Well, we will dispose of those suffixes shortly. No suffixes means a simpler system, so we win compared to them.
又在波哥大， 無法直接說 「10 跟 36 街口見」， 因為 「10 道跟 36 街口」 與 「10 街跟 36 道口」 之間有幾公里距離。 又是後綴惹的禍。
And in Bogotá I can't just say, "Meet me on the corner of 10th and 36th.", because I need to say if I mean "10th Av. and 36th St.", or do I mean "10th St. and 36th Av.", kilometers away! There they are, those nagging suffixes again.
讀者能放心。 在我們的系統這些耽誤救護車之細節， 都要送到歷史的垃圾桶去。
The reader can rest assured that in our system, such rescue-delaying detail is going into the trash pile of history.
是的， 在我們的系統， 能直接說出，
Yes, in our system one can just say,
甲： 「1100 與 6100 巷口見！」
乙： 「您說 6100 與 1100 巷口嗎？」
甲： 「是的。 一樣的。」A: "Meet me on the corner of Lanes 1100 and 6100."
B: "Did you say the corner of Lanes 6100 and 1100?"
A: "That's right! Same thing."
所以只要我們再把我們的橫的巷號， 跟直的巷號， 不重疊， 最聰明方格門牌系統世界冠軍盃就是我們的！
So all we still need to do is make sure our X's never overlap with our Y's, and then the trophy of world's smartest grid addressing system is ours!
- 推理 2:
- Inference 2:
-
最聰明的系統中， 各軸之號碼不重疊。
In the smartest system, each axes' numbers never overlap.
南達科他州非都市地址方格網
South Dakota Rural Addressing Grid
我們停下來， 討論一下南達科他州非都市 〔路號及〕 地址方格網。
Let's digress here and discuss the South Dakota Rural [Road Numbering and House] Addressing Grid.
他們把原點定在該州之西北角， 稱之為 100 道與 100 街路口。 各道、 街號， 往東、 南增加。 一英里增加一道、 街。 一英里預留 100 個門牌 （路各旁 50 個）。 （那樣低密度， 鄉下可以， 都市不行。 但兩者兼具的系統， 就要長一點數字串。 大家地址變長了。 ）
One finds they pin their origin at the northwestern corner of their state, calling that point the corner of 100th Av. and 100th St., and increase to the east and south, one avenue or street per mile. There are 100 house numbers (50 per side of road) reserved per mile. (That thin density is fine in the countryside, but not in cities. But a one-size fits all system would mean more digits.)
注意， 所有路號就三碼， 地址則全五碼， 很有制度！
Notice how all their roads are thus three digits, and all addresses five digits. Very systematic!
那麼， 若是我負責規劃， 同原點我會選擇 100 道與 500 街稱之！ （放心， 南達州寬度未達 400 英里。） （即使保留道街之別， 為什麼他們沒想到這「免費檢查碼」方式？ 我猜只是怕所謂 「號碼太高」。）
Well if I was in charge, I would have instead started with 100th Av. and 500th St.! (Don't worry, South Dakota is less than 400 miles wide.) (Why didn't they think of this bonus checksum digit, even if they kept their St. and Av. distinction. Fear of high numbers I suppose.)
採了 500 之後， 一樣長三碼之路號， 就免 「道」、 「街」 區別之。
Having picked 500, now for the same three digit-long road numbers, the suffixes "Av." and "St." no longer matter.
兩者均稱街， 消防報案時不怕講錯。
In conversation call them both "street". No more worrying about wrong 911 calls.
路牌上， 寫個號碼即可， 後綴免。 省鐵。
On road signs they may now be safely snipped off and sent to the smelter, leaving just the number. Shorter road signs, save metal.
我在充分利用三碼空間， 增進區別南北、 與東西的功能， 又免增加數字， 依然維持三碼。
I am making the most of that three digit space. Adding the ability to distinguish N/S vs. E/W., all without needing additional digits.
總而言之， 怎麼贏過鹽湖城以及波哥大， 秘密揭曉了：
So there you have it. That's the big secret of how we will beat both Salt Lake City and Bogotá and win the crown:
就是拿掉 X 與 Y 座標重疊所有的可能！
Simply remove any possibility of overlap between X and Y!
這沒什麼， 假東、 假北值老早被發明。
It's not like nobody thought about false eastings and false northings before.
只是取消重複， 在街道號碼應用得較少， 或者未曾有。
Well, such a technique isn't seen often with numbered street grids, if at all in fact.
好的， 贏鹽湖城與波哥大容易： 避免重複， 沒什麼了不起。
So fine, now we know how to beat both Salt Lake City and Bogotá. Simply avoid X, Y overlap. Ho hum.
但贏世界冠軍， 那麼必須結合我們已經累積起來的知識， 再以各國路號 ／ 地址表達方式表達之。
But to be the world champion, well we need to express the expertise we have gained via a localized fashion that the population of each country is used to.
偷偷的灌入， 不讓他們知道那山後面的新市鎮， 不起眼的路號、 門牌號碼， 含玄機！
Sort of slip it in under their noses so they don't notice that something smart is going on in with the ho hum innocent looking addresses and street numbers in that new city over there on the back of that hill!
- 推理 3:
- Inference 3:
-
正如傳教士， 最聰明的系統， 須透過當地 「門牌語言」 （表達習慣與格式）， 才有價值， 才會被人民接受。
Just like with missionaries, the smartest system needs to be expressed in the local house addressing "language" (customs and formats of addressing), to have any value, and be accepted by the local population.
再見笛卡兒
Bye bye Descartes
好的， 有兩百多國家的路名、 門牌制度。 於每一個國家， 我們必須將我們的知識當 「砧木」 再將該國當地的制度 「嫁接」 上去。 我們來開始吧。
OK, we've got 200+ countries to work on. In each country, we need to use our knowledge as a "root stock", grafting that country's system(s) on to it. Let's get started.
國家 1: 台灣。 怎麼把我們門牌知識 "DNA" 「栽入」 台灣傳統門牌編訂習俗？
Country 1: Taiwan. How do we "transpose" our addressing "DNA" into Taiwan's traditional addressing systems?
就在這時刻霹靂一閃。 覺悟到笛卡兒坐標系那 X 與 Y 必須丟掉， 送回收場。 換來我們的折疊單軸座標系統。
And it is here where a bolt of lightning came through the clouds. The realization that Rene Descartes' X and Y had to go. Into the dumpster. Replaced by our Folded Single Axis (Co)ordinate System!
是的， 我們把小朋友的數線拿去， 折了 90°， 再返還給他。
That's right. We grabbed little Johnny's number line, bent it 90°, and handed it back to him.
![[Image: Central Xinshe District, Taichung, Taiwan]](xs6.jpg "Central Xinshe District, Taichung, Taiwan")
圖 2：笛卡兒坐標系。
Figure 2: Cartesian coordinate system.
於圖 2 我們見到熟悉的笛卡兒坐標系。 感謝它幾百年之服務。 請好好的看它最後一面， 因遠處我聽到資源回收車來了…
In Figure 2 we see the usual Cartesian coordinates. We thank them for their several hundred years of faithful service. Take a good long last look at them, because in the distance I hear the recycling truck coming…
![[Image: Xinshe District, Taichung, Taiwan]](xs5.jpg "Xinshe District, Taichung, Taiwan")
圖 3：折疊單座標軸 ("⮥" 型， 往東轉北： 0 ↔ 2500 ↔
10000)， 亦即 「虛擬（大）馬路」 ， 全程亦稱 「環社路 2500 巷」。 點標誌
"2500" 為 "--fold" 折疊點。
Figure 3: The Folded Single Axis ("⮥ "-shaped,
eastwards then northwards, 0 ↔ 2500 ↔
10000), also called the "(big) Imaginary Road",
and "Lane 2500 Huanshe Rd.", both for its entire
length. Point marker "2500" is the
"--fold" point.
於圖 3 能見到我們只是採 X 軸之 0 至 2500, Y 軸之 2500 至 10000, 故無重疊。 只有一個 「6100 與 1100 巷口」， 顛倒說成「1100 與 6100 巷口」 也是一樣的巷口。
In Figure 3 we see all we are really doing is using 0 to 2500 of the X axis, and 2500 to 10000 on the Y axis. Thus ensuring that there is no overlap. So there is only one "corner of Lanes 1100 and 6100", no matter how one orders them: "corner of Lanes 6100 and 1100" is the same corner.
另請注意我們的街塊 (city blocks) 是長方形， 不是正方形。
Also note that we are dealing with rectangular, not square, city blocks.
但是在我們的規劃裡， 不管是南北巷， 或東西巷， 均採一街塊配 100 個門牌號碼。 （各側 50 個。）
But in our plan, each block has 100 numbers (50 on each side), no matter if it is a north-south block or east-west block.
所以我們的 X 軸與 Y 軸有不同 「號碼 / 公尺」 比例。
Therefore our X and Y axes have different "house number per meter" scales.
我們也準備帶著此差別， 到下方所談的折疊點之兩邊。
And we will take this differential scaling along with us, on either side of the "fold point", as we will see below.
咱不再提及 X 與 Y 了， 因有單軸能代替之。
But that's the last we will be talking about the X and Y axes, because as it turns out, we can define a new single axis to replace them.
虛擬主道
Imaginary main road
本系統核心為折疊單座標軸， 完全等於台灣號碼巷、 弄制度之「路」， 或 「街」。
At the core of our system is a folded single coordinate axis. In fact it completely can be described as rank "road" or "street" in the Taiwanese numbered lane and alley system.
只需要透過當地號碼巷、 弄、 門牌表達方式就可以了。 亦即由某主道分出來的號碼巷…
Well it turns out all we need to do is express lanes and addresses in the local fashion. I.e., numbered lanes extending from a main road…
我們的虛擬主道或許是一種對 X 與 Y 之抽象化， 來取得所謂 「數學之美」 的當地地址表達方法， 同時努力包裝為本土。
So our imaginary main road is perhaps an abstraction of X and Y allowing a much more elegant way of expressing local addresses. Of course at the same time doing our best to make it look as native as possible.
再看圖 3： 虛擬的主道， 自西南， 沿著南、 西緣， 至東北止。
Have another look at Figure 3: the imaginary big road, starting at the southwest corner, going along the south and then east margins, and ending in the northeast corner.
圖釘 「2500」為 「虛擬路 2500 號」。 其實我們本虛擬路即環社路 2500 巷， 故圖釘 「2500」 為 「環社路 2500 巷 2500 號」。
Marker "2500" is address "2500 Imaginary Rd." And in fact our imaginary road is just Lane 2500 of "Huanshe Rd.". So marker "2500" is address "2500 Lane 2500 Huanshe Road."
若採我們的折疊單座標參數標示法， 這是：
Using our folded single axis parameters, this can be expressed as:
--fold （疊點） 2500 --axis （軸） < e2n (east to north) | 東轉北 | ⮥ >
是的， 您可以說咱單軸只是一種線性參考系統。 好的。 那麼以前的 X 也是， Y 也是…
Yes, you could say our folded axis is merely a form of linear referencing system. Well fine, so was X, and so was Y…
我們只對該大路的雙號側所射出諸號碼巷有興趣。 因為其他就超越我們的單象限…
We are in fact only interested in the lanes extending from the even numbered side of our imaginary big road. That is due to our one quadrant limit…
（我們雖然僅採大路的雙號側所射出來的碼巷， 環社路 { 4128, 4130, 4132, … } 巷， 但該單軸本身的房屋仍採兩側： 環社路 2500 巷 { 4125, 4126, 4127, … } 號。）
(Yes, we use both sided of the street along our folded axis: house numbers { 4125, 4126, 4127, … } Lane 2500 Huanshe Road; but we don't use any lanes extending from the odd side. Thus only Lanes { 4128, 4130, 4132, … } Huanshe Road are possible.)
以說服大眾接受我們這門牌概念， 必建立於其已熟悉之門牌制度上， 如 「新社區環社路 1100 巷 6158 號」。
The key to convincing locals that the new system is nothing to fear is "dressing it up" with the "trappings" of local systems, e.g., "6158 Lane 1100 Huanshe Rd. Xinshe District".
光說 「新社區 1100 巷 6158 號」， 大家會以為您說錯。 反正在台灣門牌 「語言」 裡無前例。
No, one cannot just say "6158 Lane 1100 Xinshe District" because in Taiwan everybody would ask you please say that again, because there has never been such type of address.
未料， 所缺之路名部分， 加上去之後， 「很救命」。 像鹽湖城， 全城只能有一個方格網區域。 我們則才有辦法， 同是新社區， 增加其他， 如下方所談的興嶺路， 方格網區域。
And in fact that missing road name component turns out to be a lifesaver, allowing us to add additional grids (e.g., Xingling, below) for the same District, whereas for e.g., the entire Salt Lake City there can only be one grid.
今天所談的，對 「1100 巷 6158 號」 這段都已經想好。 僅缺個 「環社路」 就完成了。
In our paper here today, we've already fully planned the "6158 Lane 1100" part. We only lack a "Huanshe Road" to tie it all together, making our addresses look complete.
那麼我們需要建構一條虛擬大馬路， 環繞著整個新社平原。 只是現在它已經不在了。
So we need a "big road", that "(at one time) wrapped around the Xinshe plateau", but for some reason "no longer is there."
至於該大馬路為何無人曾見過， 我們可編故事， 見附錄: 大路不見之藉口.
As to why nobody has ever found the big road, we can spin tales: See appendix: Excuses for the missing big road.
環社路
Huanshe Rd.
我們虛擬的路也要取虛擬的名字。 那麼我們就選「環社路」。
Our imaginary road needs an imaginary name. We choose "Huanshe Road".
遠處之大馬路， 雙號（左）側偶爾會分出來些號碼巷。 該大馬路， 東行， 到了門牌 2500 號處大馬路急北轉。 該左側依然偶爾分出號碼巷。 譬如， 1100 巷分出來後， 它自己就往北。 6100 巷分 出來後， 其自己就往西。 （若有個 6101 巷， 它自己就會往東， 但是那就出乎我們的單象限了。 所以， 在我們系統裡， 6101, 6103, … 巷均不允許存在。）
The big road is off in the distance to the south and then (after big turn at address 2500) east of you. And in fact you are on the even numbered side of this big road, and there are lanes, Lane 3600, Lane 7400, etc. extending from the big road. And in fact the big road was named Huanshe Road, and made its big northward turn at address 2500 Huanshe Road, which means e.g., Lane 1100 extends northward from it, and Lane 6100 extends westward from it. (If there were a Lane 6101 it would extend eastward from it, but that would be leaving our single quadrant. So Lanes 6101, 6103, … are not allowed to exist in our system.)
X, Y 時代原來的原點在西南角。 我們將原點移至東南角落， 加上將座標軸 （於環社路 2500 巷 2500 號處； 北美或稱 25 街 2500 號處） 加以曲折 90°。 故所有門牌均落同象限（西北）內。 免加南、北、東、西綴語。
Back in our X, Y era, our origin was in the southwest corner. We now moved our origin to the southeast corner, and even folded our axis (at 2500 Lane 2500 Huanshe Rd.; in North America called "2500 25th St." perhaps) by 90°. Now all our addresses lie in the same quadrant. Hence no need for "North", "South", "East", "West" road name suffixes.
代價是鹽湖城系統能全四向無限延伸， 但是新社的系統受數學的限制， 只能單向延伸。 但沒關係， 新社原來也被山包圍， 不用延伸。 若一定要延伸， 只能往北（更高的號碼）， 且是我們故意選的方向， 萬一某日有人要延伸之。 東西南北中我們選了北。
On the other hand Salt Lake City's system can be extended infinitely in all four directions. Our Xinshe system is mathematically limited: it can only expand in one direction. But Xinshe is surrounded by mountains anyway. The only direction Xinshe's system can be extended is to the north (higher numbers). Which in fact is the direction we chose on purpose, just in case someone wants to extend it someday. Of north, south, east, and west, we chose north.
於鹽湖城僅掛 "300 North". 那是其全名。 後面沒什麼街、 道、 路、 巷等等綴。 或許於某圖庫有， 但人民不知道。 另見其 「300 北」 故知是東西向的路。 毋庸 「街係南北、 路則東西」 等等分法。
In Salt Lake City nobody remembers if a road is a Road or a Street or an Avenue, even if they might actually have such suffixes on some map or in some book somewhere. On signs they are just e.g., "300 North", from which the public thus can tell runs east-west.
若喜歡記得小巧思， 可記得在任何名字含 「環社路」 之十字巷口， 較高號的巷是東西向的， 較低則南北向的。 別擔心 「較一樣的」， 該折疊點（2500 巷 2500 號） 故意設於半山腰， 無方格路之區域。
If one likes remembering tricks, at any "Lane NNNN Huanshe Rd." four-way intersection, the higher numbered lane runs east-west, the lower north-south. Regarding where they are equal, at the fold, 2500 Lane 2500, well we placed that on a mountainside, so it is not in the grid road area in the first place.
更多方格
More grids
其實， 新社台地也有一些其他方格路塊。 只是與主塊有所方位角走向差異。
It turns out the Xinshe plateau has several other areas with roads in a grid pattern, but aligned along different azimuths.
我們也可以替它們做規劃。 最大塊我們稱「興嶺路」塊。
Indeed we can make additional grids for them. The largest such area we'll call the "Xingling Road" area.
興嶺路
Xingling Rd.
中興嶺以東有一大片格子路的平地， 但是它那些道路與北傾斜 45°，向東北、西南、 西北、 東南。
East of Zhongxingling there is a big piece of flat land with grid roads, but at a 45° angle, pointing NE, SW, NW, SE.
故咱採「興嶺路」當該區虛擬主路。
We pick "Xingling Road" as the imaginary road name for this area.
回到圖 3, 可見到我們獨立設系統為該 「興嶺路」的門牌， 就是圖片底部斜著那塊。
Back on Figure 3 you see the independent system we set up for "Xingling Road" addresses. It's that tilted chunk near the bottom of the image.
其 參數 為
Its parameters are
--fold （疊點） 2500 --axis （軸） < w2s (west to south) | 西轉南 | ⮦ >
再則， 需另增加一個步驟， 就是方位角轉移。 致興嶺路方格網
--axis 方位角， 由原正南 180° 轉成
135°, 亦即東南， 才符合地上的路網。
But then a second step is used: we
rotate the Xingling Rd. grid to match the roads on
the ground, so that its --axis points
to azimuth 135° (southeast), instead of its
original 180° (south).
轉移則輕鬆由 OGR/GDAL 的地面控制點法做成。 原始碼。
Our rotation was accomplished simply via GDAL's ground control points method. Source code.
禁用範圍
Prohibited usage
山區不適合方格網
Do not use grids in the mountains
山區不適合方格網式門牌座標。 連直接用到 C, U, Z, S 等字型路也不行。 不但產生雙胞胎門牌， 又路人無法當場理解系統的邏輯。 建議改採線性參考系統。
Do not use grid addressing systems in mountainous areas or even directly on C, U, Z, S, etc. shaped roads. Never mind identical twin addresses, it's just impossible for the person in the street to follow the logic anymore. Stick with linear referencing based systems.
非方格區、 路
Non-gridded areas and roads
本文僅講方格路型區域。 含正方形、 長方形、 甚至斜軸系統如 Highland Park, IL, USA 都在我們能實作範圍內。
This article only discusses house and road numbers on grid roads. Square grids, rectangular grids, even skewed grids like Highland Park, IL, USA are all fair game.
是的，斜的路， 如果大致直直的， 像芝加哥的 Elston Av.,
就可以採當地門牌座標之 X 或 Y 編其門牌。 （亦即 --fold
前段， 或 --fold 後段。）
Yes, for rather straight diagonal
roads like Elston Av. in Chicago, one can just
number its houses based on the local grid's X or Y
(corresponding to pre --fold or post
--fold sections.)
但蛇行的路， 像新社區的中和街， 若硬要採方格門牌， 其一旦折回來， 就會產生雙胞門牌， 所以不能方格網門牌號碼。
But regarding roads that snake back and forth, like Xinshe's Zhonghe St., if forced to use grid addresses, upon bending backwards, they will produce identical twin addresses, so please forget about using grids for them.
三個邊緣應劃於山、 海等中
The three edges should be within mountains,
oceans, etc.
折疊單座標軸形成 "L" 字型。 那麼我們這些以折疊單座標軸為基礎之方格網， 只能生長於該 "L" 之內側， 亦即四象限之一。
Our folded single axis-based grids can only grow on the inside of the "L" formed by the folded axis. I.e., can only grow within one quadrant.
還有， 不能伸張跨越「0 巷」， 因我們不允許負值， 以求簡化。
Furthermore there can be no growth below "Lane 0", as we don't allow negative numbers, in order to keep our system simple.
（其實， 因我們僅採雙號巷號， 又不希望人民遇到陌生之 「0 巷」 ， 所以我們最低採 「2 巷」。）
(In fact as we only use the even numbered lane numbers, and don't want any unfamiliar "0th St." in our system, the lowest lane number we would use is 2, not 0.)
總之， 不能往四向擴充， 只能往一向。
All this means growth can only occur in one direction out of four.
所以務必於 --fold 折疊點外兩側，
與 0 巷外一側， 該三邊， 之外側設有山或海等等阻止都市擴散。
Therefore it is essential that
outside of two edges formed the "L" at the
--fold corner, remaining 3rd edge
formed by the Lane 0 edge, that there are mountain
ranges or oceans beyond.
否則， 遲早， 如加拿大愛德蒙頓市， 跨越 0 街了， 整個系統要套上 "NE NW SE SW" 後綴了。 很可惜。
Else, sure enough, as in Edmonton, Canada, growth eventually went past their version of Lane 0, causing them to burden their whole system with "NE NW SE SW" suffixes.
如圖 2 所示， 我們那三側， 選在山內、 河谷， 離高原方格路區保有安全距離。
As you see in Figure 2 our three edges are in fact embedded in the mountains and river canyon, a safe distance away from the plateau grid area.
亦即於本案， 整條環社路 2500 巷本身， 連巷、 連門牌， 都不存在。
In other words in our implementation there is not even one single address on Lane 2500 Huanshe Rd. And in fact nor does that lane exist.
但是也有些（長）方型城市， 如 Oak Park, IL, USA。 那種地方， 無妨讓折疊軸沿著兩個邊緣， 譬如西和北。
On the other hand, there exists some nicely rectangular towns, like Oak Park, IL, USA, where one might very well have the folded axis run right along the border on two, e.g., north and west, sides.
其實， 我們下次也可以學習南達州之數字位數一致的做法。 若應用在新社， 邏輯是： 既然打算門牌兼巷號欲編到 9999 號， 那麼原規劃門牌兼巷號自 2 至 9999 號編， 改為僅編自 1002 至 9999. 犧牲了 10%, 但所有的號碼， 含巷、 含門牌， 均成為四個數字長， 值得下次考慮吧。 （若某地採三數字長度， 那麼 「自 2 至 999」 改為 「自 102 至 999」， 又僅犧牲 10% 無誤。）
In fact next time we can also take the lesson from South Dakota about always using same length addresses. If applied to Xinshe it would go like this: So we plan to use (house / lane) numbers up to 9999. Well, (next time) let's also keep strings the same length (four digits.) So let's plan to use not 2 through 9999, but instead 1002 through 9999. Therefore we see, any sacrifice to keep numbers the same length is always merely 10% and thus worth it. (Let's double check for a three digit case: from 2 to 999 becomes from 102 to 999: same sacrifice: just 10%.)
（其實， 如美國郵遞區號， 以及美國社會保障號碼， 都也有開頭 0 者。 但門牌不一樣。 一般電腦會把門牌前 0 去掉。）
(Actually US postal Zip Codes, and US Social Security numbers, all can have leading zeros. But for addresses we cannot expect any leading zeros to survive in most computing situations.)
禁弄
No alleys
回到圖 1, 若於 6051 無屋而有路， 是否按照台灣巷弄習慣， 稱之為 「環社路 1100 巷 6051 弄」 呢？
Going back to Figure 1, what if there were a road instead of a house at 6051? Would we would call it "Alley 6051 Lane 1100 Huanshe Rd.", as would be expected in Taiwan's lane/alley numbering conventions?
答案是否定的。 我們必須對所有網狀路， 不管是否貫通到折疊單座標軸與否， 還是以該軸為命名來源。 故該路僅能稱 「… 6148, 6150, 6152 …巷」 。 該間隔應該夠細吧。 順便提， 「6152 巷」 比 「61.52 街」 好看多了。
The answer is no. We must number all our grid roads, continuous or not, as if they connected directly to our folded axis. Thus that road can only be called one of Lane …6148, 6150, 6152…Certainly fine grained enough. By the way, "Lane 6152" looks a whole lot better than "61.52th St." !
所以， 咱方格網內不開放「弄」。
So no alleys are allowed within our grid.
若民眾質疑， 說「某巷只是斷斷續續的， 巷號怎麼可以一致的？」
And if the public says, "Lane NNNN is discontinuous. How can you give all those separate pieces the same lane number?"
我們就答覆： 「必須預備某日一旦貫通…」
We respond: "Got to plan ahead, in case one day they finally get joined…"
紙筆網圖
Pencil and paper grid map
採折疊單座標軸， 快速畫地圖變容易。
With a folded single coordinate axis, making quick maps becomes easy.
假如某住山洞的原始人， 只有紙筆， 無指北針， 其能做出怎樣的基本街道圖？
Let's say a primitive caveperson has a pencil and paper, but no compass. What basic maps can they make of a town's streets?
那麼， 他需要知道：
Well, they need to know:
--fold <value>
譬如 --fold 2500。
e.g., --fold 2500.
他再需要知道 --axis 是順時鐘的：
Then all they also need to know if the --axis is clockwise:
--axis < ⮠ | ⮤ | ⮣ | ⮧ >
--axis < 南轉西 | 西轉北 | 北轉東 | 東轉南 >
--axis < s2w | w2n | n2e | e2s >
還是逆時鐘的：
or counterclockwise:
--axis < ⮡ | ⮥ | ⮢ | ⮦ >
--axis < 西轉東 | 東轉北 | 北轉西 | 西轉南 >
--axis < s2e | e2n | n2w | w2s >
知道之後我們馬上就能畫折疊單座標軸， 自 1
… 2500 ， 再轉 90° 順或逆時鐘， 再由
2500 … ∞.
So then we can immediately make our
folded axis, 1 … 2500 , then
turning 90° clockwise or counterclockwise, and
then continuing on from 2500 …
∞.
接著， 若有需要， 可調準折疊點前、 後段之比例尺， 以配合長方形都市街塊 （正方形則免調。） 該 90° 亦能調， 適應少數街網的斜度。 座標軸處理完畢， 最後填街網。
After which, if needed, we can
differently scale the portions before and after
the --fold point, for rectangular vs.
square city blocks, and occasionally, if needed,
even change that 90° to
skew the two sides, all before finally filling
in all the lanes.
然後某日我們的原始人取得了指北針， 而知道街網方位角， 圖上終於能加羅盤方位圖了。
Then one day when our caveperson acquires a compass and figures out what direction the streets actually point, they can finally get around to adding a compass rose to the map.
結論
Conclusion
不管近年挖土機挖方格路網少些。
Never mind that bulldozers perhaps don't make as many grid roads and streets as they once used to.
但是我們仍成功為它們做了最聰明道路與門牌號碼系統了！
But we managed to make the smartest addressing and road numbering system for them!
世界盃呢？
So did we win the world cup?
嗯… 還有 199+ 國家要做才能確定。
Err, well there are still the remaining 199+ countries before we can be sure.
但我相信讀者只要結合其當地的門牌制度， 與本文討論的門牌知識， 必定也能做出該國冠軍路號兼門牌系統！
However I'm sure all the reader needs to do is graft the addressing knowledge we discussed into their local system. Voila, instant best road / house numbering system winner for that country!
後記
End notes
-
本文僅針對街與門牌之賜號。 未提及街塊 (city blocks) 本身之編號碼。 那是另外一回事。 亦即今僅談及點與線之發號， 不講面。
In this article we are talking about how to number streets and houses, not how to number city blocks themselves, which is a whole other issue. I.e., we are talking about numbering lines and points, not areas.
（給面編號屬於地籍圖問題， 而非民眾較常接觸之門牌與巷號。）
(The numbering of areas would be more of a concern for cadastral mapping (which the public interacts less with than house and lane numbers.))
-
鹽湖城、 波哥大， 門牌怎麼編的， 網路查得到。
How Salt Lake City and Bogotá number their streets and houses can be found out via Internet search.
-
於本文我喜歡寫 "1234 Lane 5678" 而將 "No. 1234 Lane 5678" 之 「號」 譯省略。
In this article I like writing "1234 Lane 5678" instead of "No. 1234 Lane 5678".
-
談南達科他州時， 我說要選 500, 那麼為什麼講環社路時我反而採 --fold 2500 未擇 --fold 5000 呢？
In South Dakota I said choose 500. So why for Huanshe Rd. did I pick --fold 2500 instead of --fold 5000?
那是因為我有信心， 其無法擴充之三邊， 我不會再擴充； 那麼對於北， （這裡北向即無限向） 可以留多些空間， 才開始涉及動到第五碼 （10000 起）。
Well that's because I am confident of no more growth for the three limited sides, so might as well allow more growth on the unlimited side (northwards) before needing a fifth digit! (Starting at 10000.)
-
紐約曼哈頓， 雖然街、 道均採號碼， 但門牌甚至需程式始得計算出來。
Manhattan, New York, despite both streets and avenues being numbered, even needs an algorithm to compute addresses.
註釋
Notes
註釋 1
Note 1
^ 注意此處座標 1100 沒像 6051 那麼精準。 因 1100 代表巷中央， 亦即一個連結點而已。 再必須由單、 雙號原理決定房屋落在那巷哪側。 譬如在這裡我們在講單號那側， 即東側， 因 6051 屬單號…
^ Note that 1100 here is not as exact a coordinate as 6051, as 1100 represents the centerline of the lane, an attachment point, not exactly where in the grid the house is, and is influenced by odd vs. even addresses, which determine which side of the lane the house is on. E.g., here we are talking about the odd side, as 6051 is odd…
還有在波哥大， "+ 51 ÷ 100" 也要加進去…； 我們也忽略了有些 calles （街） 名， 的確加了後綴 Sur （南） …
Also in Bogotá "+ 51 ÷ 100" needs to be added to the equation… Also we ignore that some calles have Sur (south) in their names…
錯置
Mistakes
鹽湖城
Salt Lake City
順便看看， 鹽湖城的地址那麼容易弄錯。
By the way, let's see all the ways we could screw up a Salt Lake City address.
表 1A： 鹽湖城容易搞混單
Table 1A: Salt Lake City confusion
possibilities
| 6051 North 1100 East | A |
| 6051 East 1100 North | B |
| 1100 North 6051 East | B |
| 1100 East 6051 North | A |
A 組與 B 組相遠好幾公里。
Groups A and B are miles apart.
亦即， 雖然我們透過了推理 3, 用當地格式表達我們那最聰明系統了， 又即使僅採東與北， 但這並不代表當地人民繼續永遠用本身有瑕疵之格式是最好的。
Thus, even though (Inference 3) we have expressed our smartest system in terms that the local population is used to, and even only using North and East, that does not necessarily mean the local population is best forever served by an accident prone format.
又僅冰山一角， 全部像：
And that's just the tip of the iceberg, which is something like this:
{1100, 6051} {North, South, East, West} {6051, 1100} {East, West, North, South}
很驕傲能夠說我們的系統都沒有那些問題！
I am proud to say our system puts the fire extinguisher to such problems.
又即使將 1100 巷 6051 號， 誤寫成 6051 巷 1100 號， 位置是差不多一致的！
And even if you write "6051 Lane 1100" instead of "1100 Lane 6051" they are essentially the same place!
波哥大
Bogotá
我們來看看， 拿波哥大格式， 再透過我們的推理 3, 僅用「街」來同時表達街與道。 好像真的達到一個穩定， 「消防安檢通過」的系統了！ （例子見表 1.）
Let's see, if we take the Bogotá model, and via our Inference 3 use calles, for both calles and carreras, it does indeed seem that the public cannot screw it up. And thus such a system meets "fire protection standards". (Example in Table 1.)
但是， 等一下。 譬如什麼都好好的，
But wait. Let's say things are all cheery,
| 新社 Xinshe |
波哥大 Bogotá |
|---|---|
| 7100巷 Lane 7100 |
71 街 Calle 71 |
| 7132巷 Lane 7132 |
71A 街 Calle 71A |
| 7164巷 Lane 7164 |
71B 街 Calle 71B |
接著， 某屋拆了， 來了個新 7148 巷， 波哥大怎麼安插？ 71AA 街嗎？ 難看。 故對波哥大太浪漫前， 我們必須認識它些致命傷。
and a house is torn down and along comes a Lane 7148. What's Bogotá going to call it? Calle 71AA? Thus before we get all dreamy about Bogotá, we must face its fatal flaws.
引用文獻
References
^ Rose-Redwood, R., & Kadonaga, L. (2015). "The Corner of Avenue A and Twenty-Third Street": Geographies of Street Numbering in the United States. The Professional Geographer, 68(1), 39-55. https://doi.org/10.1080/00330124.2015.1007433
使用的軟體
Software used
我們在 Linux 作業系統採 OGR/GDAL 投射點、與線， 再由 Viking 顯示之， 於 OpenStreetMap 及 OpenTopoMap 背景圖上。
On Linux we used OGR/GDAL to project points and lines, and then Viking to display them on OpenStreetMap and OpenTopoMap backgrounds.
我們採那些長方形之街塊， 給予 100 個門牌 （各邊 50 個號碼）。 但是整個過程中我們沒有停下來， 把這些街塊拿去量其長度到底幾公尺長。
We use 100 house number-long rectangular "city blocks". However we never sat down to measure just how many meters long they were. Neither their long nor short edges.
我們只是設很多「控制點」， 交由 OGR/GDAL 處理。
We just simply made lots of ground control points and let OGR/GDAL do the rest.
程式碼
Program code
含本文原檔、 KMZ 圖、 等等：
Includes this document's source file, KMZ maps, etc.:
https://www.jidanni.org/geo/house_numbering/grids/tw/taichung/xinshe/lanes/