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Thread: How Big Is a City?

  1. #1

    Default How Big Is a City?

    Quote Originally Posted by Turboff View Post
    Well, Rome and Madrid have nearly the same population. According to wikipedia.org, Rome has 5.48 million, Madrid 5.56. But yes, Copenhagen, Brussels, Vienna, and Amsterdam may be a bit too small among the other candidates with only about 2 million each (metro).
    Your post brings up a point of interest to anyone wanting to compare cities by size.



    HOW BIG IS A CITY?


    When I was a kid with an hour to kill, I’d sometimes memorize city population figures. Those figures are all obsolete now, and they weren’t so much use then either because --as many have remarked-- it’s misleading to compare sizes of cities by just one of the readily-available measures of a city’s relative size. Actually, it can even be misleading to look at two. Though they’re both flawed, the two figures often employed to compare city size scientifically are city-limit population and metropolitan population.

    If you look at Boston’s latest city-limit population estimates, you’ll conclude it’s smaller than Charlotte, El Paso or Austin and a third the size of Philadelphia, while its metropolitan population shows it to be nearly the same size as Philadelphia and bigger than Dallas/Fort Worth. Yet Charlotteans visiting Boston think they’re in the big city; clearly city-limit figures don’t convey the reality.

    It does, however, have the undeniable benefit of being hard and verifiable fact, not much subject to controversy over definition. What it shows, however, mostly interests politicians; every mayor likes to know how many votes he needs to get elected. The political limits of such cities as Boston or San Francisco contain only a fraction of the metropolitan population, while in the case of Hong Kong or Budapest or Rome almost everyone lives within the limits.

    City-limit population was a useful basis of relative city-size comparisons before suburbs grew widespread. In 1900 this figure meant more than it does today. If you look at1900’s city-limit lineup of the top five, it differs more from today’s city-limit roster than from today’s metropolitan lineup of the top five. The exception --Los Angeles-- illustrates the suburban nature of 20th Century growth.

    Metropolitan population is less cut and dry and generally includes the population of the entire region of which a city is the center according to such criteria as commuting patterns and adjoining density. New York City’s metropolitan area includes parts of three states by some yardsticks, and four by others.


    * * *

    There could be a third measure of a city’s size that’s not yet widely used, though it’s at least as valid as the other two if you want to know a city’s size. This is the population of the more-or-less contiguous central urban area –that is, the territory where folks might say they live an urban life.

    This usually means being able to conduct the day’s business without driving; you can conveniently take public transport to work, to major shopping trips or to evening amusement, and you can get your daily necessities within walking distance. All of Manhattan meets these criteria, and large swathes of Brooklyn and the Bronx, as well as some places (like Astoria) in Queens.

    Physically, such places are most often recognizable by the fact that most buildings touch, and thus form a street wall-- whether it’s row houses in Brooklyn or apartment buildings on the Grand Concourse. It’s also true of a double house in London or Charleston; each half touches the other.

    Occasionally, urban densities are approached almost entirely with free-standing buildings, though such instances are fairly rare. Examples are Cambridge, Miami Beach and three-decker portions of Boston’s Dorchester, as well as city-absorbed towers-in-the-park developments such as Stuyvesant Town, the Barbican or Boston’s West End.

    Urban places are invariably well-served by public transport --almost always rail-based-- or like Miami Beach and Charleston, they’re small enough that you can walk from one end of the urban area to the other.


    * * *

    Any method of measurement is useless if it doesn’t deliver a usable truth. If you want to establish the relative size of a mature tapeworm and an anaconda, for example, it’s pointless to compare just their length; the tapeworm is likely to win that match-up.

    To get a meaningful handle on the relative size of cities by using population statistics, I think you need all three measures --metropolitan population, city-limit population and contiguous urban population-- and you have to assign each a relative weight.


    * * *

    Statistics show Chicago and Paris each have about the same metropolitan and city-limit populations. Yet anyone who has lived for a while in Paris and Chicago knows that Paris feels like much more of a big city, regardless of what the two commonly-used statistics may show.

    “Feels”: hardly a scientific term --unless you can devise a scientific (i.e. numerical) method of measuring the concept.

    The feeling itself, however, is real enough; everyone is able to discern it, even if they can’t numerically describe it. Though Chicago is certainly a great city, Paris is more cosmopolitan; has more variety, density, destinations, cultural impact, a larger area of interest Paris gives birth to more international trends, offers greater availabilities, a semblance of infinitude, more for the tourist, more prestige and more gravitational pull on the rest of the cosmos.

    When you compare Paris and Chicago by the third measure, the truth comes into focus: Paris’ contiguous urban population is actually greater than its city limit population, while Chicago’s is much smaller. This is because much territory within Chicago’s city limits is actually suburban, while in Paris even the “suburbs” (banlieue) are mostly urban.

    Suburbia near the city’s center dilutes its urbanity, while further out it contributes population mass that’s a supply of commuters, occasional theatregoers and warm bodies to comprise a regional culture or mass of public opinion. Though Washington is certainly enhanced by residents of suburban Fairfax, their contribution to DC’s big city ethos pales beside Georgetowners’.

    If you regard only contiguous urban area, however, you’ll wrongly conclude that Hong Kong is a bigger city than New York because more folks live in Hong Kong’s dense urban area, while it has only few and sparsely-settled suburbs within its limits or its metropolitan area.

    So you need a balance; all three numbers count for something: metropolitan, city-limit and urban area. They play different roles in different cities; if you take account of them all, you can get a much less distorted picture of cities’ relative size. Paris’ large metropolitan population helps recalibrate perceptions that might form in your mind by overemphasizing the smallish city-limit population.


    * * *

    Now most of us have a pretty good feeling for the size of a place if we’ve spent some time there; a week is usually enough to take the measure of a city. We know that Washington’s about the size of Vienna regardless of what commonly available statistics may tell us to the contrary.

    You need all three population figures –metropolitan, city-limit and urban area—to make a fairly accurate estimate of a city’s size without actually visiting. And the three measures need to be weighted; the unweighted statistics won’t yield the truth any more than knowing the length of a tapeworm would give you much useful information about its actual size. You have to also know its weight and width and then you have to find a consistent way to assess the relative importance of these characteristics. Obviously in the case of the above example, you’d attach more importance to weight.

    So to see how this might be accomplished, I started with reality as I was able to perceive it –that is, I started with the conclusion.

    In other words, to find the methodology that would lead mathematically to an approximate truth, I had to start with my perception of the truth itself, plus access to the statistics; and then I had to find a simple and near-universally applicable formula that would yield the rankings I was looking for. That is, I already knew the anaconda was bigger than the tapeworm.

    This methodology is often used [surreptitiously ] by car magazines to rank autos in comparison tests and travel magazines to rank destinations. Of course, the method’s validity can be disputed –especially when applied to subjective questions such as “what is a good place for a vacation?”


    * * *

    So I wrote down some larger cities in which I had spent more than seven consecutive days, and then I arranged them according to my perception of their relative “size.”

    I think I’m well-traveled, but the list was fairly short, and turned out to contain mostly cities in which I had actually lived, i.e. not in a hotel; travelers rarely spend a whole week in one place.

    The list looked like this, with cities arranged in descending order and in clumps according to my subjective (and therefore --by my rules-- accurate) assessment of their true size:

    New York
    London
    Hong Kong
    Paris

    Chicago

    Milan
    Rome
    Philadelphia
    Washington
    San Francisco
    Boston
    Budapest
    Vienna
    Munich
    Amsterdam

    Copenhagen
    Florence
    Nice


    I’ve been to Tokyo, Montreal, San Juan, Toronto and Los Angeles, though never for a whole week at a time, so they’re omitted. I’m certain Tokyo exceeds New York’s population by all three measures, while Los Angeles might not even qualify for the list, since I’m not sure it actually contains any urban areas to measure by the third criterion.

    Next I looked up the easily-available city-limit and metropolitan populations of each city. The list then looked as follows, with numbers in millions. (The third column of numbers indicates city limit density in persons per square mile. A low density figure turns out to be a useful indicator of a city whose city limits reflect annexation of extensive suburbia; look at the figure for Rome. Conversely, a very high figure indicates that the city limit area [and even beyond] is entirely urban. Look at the figure for Paris for an example; Paris' city-limit density is more than ten times Rome's):

    New York ...... 8.2 ..18.7 ..26,720
    London ......... 7.7 ..13.5 ..12,300
    Hong Kong...... 6.9 ...7.0 ..16,500
    Paris............. 2.2 ..11.5 ..63,400

    Chicago......... 2.9 ....9.4 ..12,600

    Milan............. 1.3 ....7.4 ..17,900
    Rome............. 2.8 ....5.3 ...5,600
    Philadelphia..... 1.5 ...5.8 ..10,900
    Washington..... 0.6 ...5.8 ....9,000
    San Francisco.. 0.7 ...4.2 ..15,800
    Boston............ 0.6 ...4.4 ..11,600
    Budapest........ 1.7 ...3.2 ....8,300
    Vienna............ 1.7 ...2.2 ..10,100
    Munich........... 1.3 ...2.7 ..10,900

    Amsterdam....... 0.7 ..2.5 ..11,500
    Copenhagen..... 0.5 ..1.4 ..14,600

    Florence........... 0.4 ..1.0 ...9,200
    Nice................ 0.3 ..0.9 ..12,400

    Plugging in the contiguous urban population is the hardest, because the statistics aren’t widely available --nor are they scientifically acquirable unless you’re willing to invest a few weeks on Google aerials and census tracts info-- but you can make an educated guess.

    In the case of New York, you can start with Manhattan’s 100% urban population of about 1.6 million and add to it Brooklyn’s Williamsburg, Brooklyn Heights, Dumbo, Downtown, Fort Greene, Red Hook, Park Slope, Bedford Stuyvesant, et al., large parts of the Bronx and a bit of Queens. Combined, this amounts to about 4 million people. That’s about the same as the urban population of Paris, which includes numerous completely urban inner-city “suburbs” like St. Denis, Neuilly, St. Cloud and Vincennes.

    In Boston, you’d include downtown districts such as the North and West Ends, Beacon Hill, Back Bay, the South End and much of badly-damaged Roxbury –as well as districts contiguous across bodies of water, such as Charlestown and East Boston. Boston’s municipal boundaries are so old and chopped up that they don’t include high-density urban parts of Cambridge, Somerville, Chelsea and even stretches of Brookline along the streetcar routes. I’ve included these outside-city-limits areas in Boston’s contiguous urban population estimate.

    Google’s satellite photos clearly reveal such high-density urban districts, which can then be coordinated with census tracts. I’ve done an approximation of that by means of informed guesses based on personal familiarity with these places to come up with rough figures to suggest a methodology.

    Adding contiguous urban populations (column #1) completes the three ways of measuring city size. Column #2 is city-limit population and column #3 is metropolitan population. Note that Paris has a smaller city-limit population than Rome, but perhaps five times the contiguous urban population; Rome pretty quickly dissolves into commie blocks and villas in the outskirts. The table looks like this:

    New York......... 4.0 ...8.2 ..18.7
    London............ 3.5 ...7.7 ..13.5
    Hong Kong....... 4.5 ...6.9 ....7.0
    Paris............... 4.5 ...2.2 ..11.5

    Chicago........... 1.0 ...2.9 ...9.4

    Milan............... 1.1 ....1.3 ...7.4
    Rome............... 0.9 ...2.8 ...5.3
    Philadelphia....... 0.7 ...1.5 ...5.8
    Washington....... 0.4 ...0.6 ...5.8
    San Francisco.... 0.5 ...0.7 ...4.2
    Boston.............. 0.4 ...0.6 ...4.4
    Budapest........... 0.9 ...1.7 ...3.2
    Vienna.............. 0.8 ...1.7 ...2.2
    Munich.............. 0.8 ...1.3 ...2.7

    Amsterdam........ 0.6 ...0.7 ...2.5
    Copenhagen....... 0.4 ...0.5 ...1.4

    Florence............ 0.3 ...0.4 ...1.0
    Nice.................. 0.3 ...0.3 ...0.9
    Venice............... 0.1 ...0.3 ...1.6

    What’s left is to assign a weight factor to each population criterion. (Remember this is working backwards from the predetermined conclusion to a method of guaranteeing that
    conclusion.)

    Observation reveals that city-limit population (the most hard-edged category) averages a bit less than twice the contiguous urban population (though not in the case of Paris!!), while it seems to have less actual bearing on actual big-city feel than the amount of contiguous central urban fabric (who thinks Hyde Park contributes much to Boston’s big-city feel?). So I chose a weight factor of two (2) for contiguous urban population.

    City-limit population tends to about a half or more of the metropolitan population in foreign cities and in New York, which resembles a foreign city-- while it’s about a sixth of the metropolitan population for American cities with their parasitic suburbs (compare that with Hong Kong!!). I chose a half (1/2) as the weight factor for metropolitan population.

    City-limit population (a hard-edged, objective measure) gets a weight factor of 1.

    This way the first three columns mostly resemble each other when weighted (boldface numbers), while the fourth boldface number is the one that tells the cities' relative size by *ahem* feel. Wherever there’s a big deviation in the first three numbers (red), it’s meaningful. Here are the first four cities:

    New York...... 2(4.0) = 8.0 ...1(8.2) = 8.2 ...18.7/2 = 9.4 ...Average score: (25.6)/3 = 8.5
    London......... 2(3.5) = 7.0 ...1(7.7) = 7.7 ...13.5/2 = 6.3 ...Average score: (21.2)/3 = 7.0
    Hong Kong.... 2(4.5) = 9.0 ...1(6.9) = 6.9 .....7.0/2 = 3.5 ...Average score: (19.4)/3 = 6.5
    Paris............ 2(4.5) = 9.0 ...1(2.2) = 2.2 ...11.5/2 = 5.8 ...Average score: (17.0)/3 = 5.7

    The others:

    Chicago......... 2(1.0) = 2.0 ...1(2.9) = 2.9 ....9.4/2 = 4.7 ....Average score: (9.6)/3 = 3.2

    Milan............. 2(1.2) = 2.4 ...1(1.3) = 1.3 ....7.4/2 = 3.7 ....Average score: (7.4)/3 = 2.5
    Rome............. 2(0.9) = 1.8 ...1(2.8] = 2.8 ....5.3/2 = 2.7 ...Average score: (7.3)/3 = 2.4
    Philadelphia.... 2(0.7) = 1.4 ...1(1.5) = 1.5 ....5.8/2 = 2.9 ....Average score: (5.8)/3 = 1.9
    Budapest....... 2(0.9) = 1.8 ...1(1.7) = 1.7 ....3.2/2 = 1.6 ....Average score: (5.1)/3 = 1.7
    Vienna.......... 2(0.8] = 1.6 ...1(1.7) = 1.7 ....2.2/2 = 1.1 ....Average score: (4.4)/3 = 1.5
    Washington.... 2(0.4) = 0.8 ...1(0.6) = 0.6 ....5.8/2 = 2.9 ....Average score: (4.3)/3 = 1.4
    Munich.......... 2(0.7) = 1.4 ...1(1.3) = 1.3 ....2.7/2 = 1.4 ....Average score: (4.1)/3 = 1.4
    San Francisco.. 2(0.5) = 1.0 ..1(0.7) = 0.7 ....4.2/2 = 2.1 ....Average score: (3.8)/3 = 1.3
    Boston........... 2(0.4) = 0.8 ...1(0.6) = 0.6 ....4.4/2 = 2.2 ....Average score: (3.6)/3 = 1.2
    Amsterdam..... 2(0.6) = 1.2 ...1(0.7) = 0.7 ....2.5/2 = 1.3 ....Average score: (3.2)/3 = 1.1

    Copenhagen... 2(0.3) = 0.6 ...1(0.5) = 0.5 ....1.4/2 = 0.7 ....Average score: (1.8)/3 = 0.6
    Florence......... 2(0.3) = 0.6 ...1(0.4) = 0.4 ....1.0/2 = 0.5 ...Average score: (1.5)/3 = 0.5
    Nice.............. 2(0.3) = 0.6 ...1(0.3) = 0.3 ....0.9/2 = 0.5 ....Average score: (1.4)/3 = 0.5
    Venice............ 2(0.1) = 0.2 ...1(0.3) = 0.3 ....1.6/2 = 0.8 ...Average score: (1.3)/3 = 0.4


    * * *

    I look at the above chart and I say, “Works for me.” The cities are arranged in the size order that squares with my perceptions.

    Seems that metropolitan population’s absolute numbers count about half as much in assessing the feel of a city’s size than city-limit population figures, while contiguous urban numbers count about twice as much.

    After testing the methodology on the city specimens I already knew well, I felt I could later apply it to examples that I didn’t know as intimately and get accurate readings from application of the formula.

    Some forumers live in cities not on the above list. I’ve never had the pleasure of a Glasgow visit, but I can put together its figures:

    Glasgow.......... 2(0.5) = 1.0 ...1(0.6) = 0.6 ...(2.3)/2 = 1.2 ...Average score: (2.8)/3 = 0.9

    The figures would lead me to believe that Glasgow’s “true size” is about that of Amsterdam and bigger than Copenhagen. AlonzoNY, does that seem about right?

    .
    Last edited by ablarc; June 23rd, 2007 at 05:59 PM. Reason: typo

  2. #2

    Question

    Is the question really:
    "How does one measure the size of a city?"

  3. #3

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    That would make the title as boring as the text.

  4. #4

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    I skipped the text- went straight to the numbers. <insert egghead emoticon>

  5. #5

    Default

    Quote Originally Posted by Rapunzel View Post
    I skipped the text- went straight to the numbers.
    Yeah, me too.

  6. #6

    Default

    Woah! That must have taken you hours to write. It's great, though. I admit that I myself have never really cared too much for "official" population figures, because they never match up with my own perceptions.

    It's really tricky to get a correct balance, especially when comparing European cities with American cities (except for NYC). Of the cities that I've been to, Chicago seems to be the most tricky. To me, it doesn't "feel" very large at first glance, especially if you only stay around the skyscrapers. You don't start realizing how large it is until you drive outwards and it goes on and on. My own "feeling" is that Munich is larger, but I can't explain it.

    Once again, great post.

  7. #7

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    Well thought out and methodical. Nicely done...and I read it all.

  8. #8

    Default

    The suggested formula for calculating size of a city:

    P = (2U + C + M/2)/3

    where:

    U = contiguous urban population in millions

    C = city-limit population in millions

    M = metropolitan population in millions

    P = adjusted population.


    Note that often P resembles C, especially in European cities. It also often resembles 2U and M/2. Where this is not the case, it's meaningful, and obvious conclusions can usually be drawn.

  9. #9
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    Quote Originally Posted by ablarc View Post
    So to see how this might be accomplished, I started with reality as I was able to perceive it –that is, I started with the conclusion.

    In other words, to find the methodology that would lead mathematically to an approximate truth, I had to start with my perception of the truth itself, plus access to the statistics; and then I had to find a simple and near-universally applicable formula that would yield the rankings I was looking for. That is, I already knew the anaconda was bigger than the tapeworm.
    You picked a tough question, ablarc, and a rather simple solution. I must say, I admire your honesty in explaining your methodology and your expectations, because we all know there are experts who publish similar studies and will never be as straightforward and humble in their justification.

    In my view, there must be a more accurate way to ascertain what you've told us in this thread, with less bias. But I wonder: would I even want to read the findings of someone who has not nearly the experience - no, appreciation - for the topic?

    I look at the above chart and I say, “Works for me.” The cities are arranged in the size order that squares with my perceptions.
    As you expected, right? Thing is, statistics aren't used nearly as much to verify the known, as opposed to trying to predict the unknown. We can argue back and forth about which goal is more reasonable, but I think it's safe to say the discipline, if it were used predominantly as you used it, would rather quickly become unattractive.

    Seems that metropolitan population’s absolute numbers count about half as much in assessing the feel of a city’s size than city-limit population figures, while contiguous urban numbers count about twice as much.
    "Feel" is, as I'm sure you know, a poorly suited coefficient to include in statistics, and something most statisticians seek to root out. In my experience reading about it, though, it seems most, if not every statistician, inadvertently includes his "feeling" about the subject into his analysis, skewing the end results. A feel could be anything as significant as a predetermined conclusion, which serves to guide the testing in a biased, confirming direction, or something as insignificant as an overly strict adherence to empirical skepticism. That is, after all, what they all strive for; but ultimately, it's within the person's own control and way of thinking that he chooses a certain path toward an answer.

    In your case, I think the choice for methodology was efficient, and you may very well be on to something. Not sure about those weights, though.

  10. #10

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    Quote Originally Posted by ablarc View Post

    The figures would lead me to believe that Glasgow’s “true size” is about that of Amsterdam and bigger than Copenhagen. AlonzoNY, does that seem about right?

    .
    Your numbers sound perfect although by some peoples accounts as many as 2.25mil are in this area of west scotland, this takes into account 'new towns' such as cumbernauld which arent contained in the urban area but are dependant upon Glasgow. You could also look at the central belt of glasgow-edinburgh as one big metro area. This 'dual-city' is soon to be linked by reopened rail link and there are talks of a maglev service between the cities.

    My preference is to quote metro pop numbers as i think this shows the true size of cities as the suburbs of cities wouldnt exist without the city itself.

  11. #11

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    Quote Originally Posted by pianoman11686 View Post
    In your case, I think the choice for methodology was efficient, and you may very well be on to something.
    No doubt in my mind that the three figures weighted give you better rankings than the two commonly-used measures, either weighted or used alone. So it's a step closer to truth than we've been used to. We all know that existing methods are inadequate, and so is this --though it is a little less inadequate.

    A baby step (but in the right direction).

    Not sure about those weights, though.
    Standard deviation obviates greater precision until someone comes up with an advance over this method, which probably won't come from tinkering with the ratios --at least not from adding a false precision to them. Greater precision would introduce unintended aberrations but not greater accuracy. Ratios of say, 2.25 and 35/64 would promote only an illusion of the scientific.

    I'm satisfied that the formula gives you closer approximation of relative size than any technique in use that I'm aware of.

    .
    Last edited by ablarc; June 25th, 2007 at 07:32 AM. Reason: added a word for clarity

  12. #12

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    If you want to look at a city's true size Canadians cities are underrated, just look at the areas the US gives its cities under the heading consolidated metro areas which today they have just shortened to metro area.

    Chicago is almost 30 thousand square kilometers in area. Metro Toronto is 7 thousand square km in area. How is that fair ? If you gave Toronto another 23 thousand km squared you would get it at least another 2-3 million people considering one third of Canada's 33 million people live in the small area in southern Ontario between Toronto and Canada's border with the US.

    So if you want to put Chicago up there with over 9 million people you have to put Toronto there somewhere. I'm not sure of the size Europe gives its cities but I'm guessing cities like Berlin and Milan are very underrated.
    Metro Chicago in area is almost one tenth the size of Germany which has 82 million people. I'm guessing if you gave that much area to Berlin it would have over 10 million people.
    and why is metro Boston allowed to cover an area twice the size of Toronto's GTA ?
    Last edited by canguy23m; June 25th, 2007 at 08:10 AM. Reason: i want to

  13. #13

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    Quote Originally Posted by ablarc View Post
    Your post brings up a point of interest to anyone wanting to compare cities by size.



    HOW BIG IS A CITY?




    .
    http://en.wikipedia.org/wiki/Chicago

    according to that website metro Chicago covers an area of 28,163 km squared.
    I think the best way to compare cities is just to give them each 7000 km squared and compare what they have within those limits.
    Last edited by canguy23m; June 25th, 2007 at 08:17 AM. Reason: to add something

  14. #14

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    another thing that I find misleading is when atlas's rank the world economies based on PPP Gdp rather than Nominal Gdp. Doesn't it make more sense to measure a country's economy based on current exchange rates rather than what their currency was worth a decade ago ?

  15. #15
    Forum Veteran MidtownGuy's Avatar
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    Yeah, that would sure make America come down a few notches, wouldn't it.
    Planning my vacation to Europe, I'm definitely experiencing sticker shock when I do the euro-dollar conversion. The American empire is so over. We're experiencing the last, desperate, dying attempts of an Empire to hold onto what it is losing. Like a cornered beast, it won't go down willingly but in the end it's inevitable.
    Within our lifetime the dollar will be an international joke, valued somewhere near the Brazilian Real!

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