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I was interested to see how much higher Austin is than Columbus, but I think that is driven by the fact that UT is about 1-2 miles closer to downtown Austin than OSU is to downtown Columbus. Depending on where you define "the center of downtown", you can include the entire UT campus within the 2 mile radius for Austin, whereas in Columbus the southern tip of campus is about 2.5 miles from the intersection of Broad & High. 

 

The same could be said for how Akron ends up ahead of Columbus in the 1-mile radius metric. 

 

When you are looking at such a small area of land, these numbers can be greatly affected by many different factors, such as waterways, highways, public spaces, and even where you define the center of downtown to be. 

 

@DEPACincy are you able to see where the pin is dropped for the "center of downtown"? I would be interested to see that for the Ohio cities as well as for a place like NYC. In NYC, defining lower Manhattan as the "center of downtown" is going greatly reduce the population compared to dropping the pin in midtown Manhattan. 

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I wouldn't say the location of the lake affects Cleveland, per se.  Look at Milwaukee and Buffalo for impressive numbers for also having a giant lake (inland sea) next to their downtown.  Hell, Milwaukee beats EVERY Midwest city except Chicago.

"You don't just walk into a bar and mix it up by calling a girl fat" - buildingcincinnati speaking about new forumers

If it's the Statehouse that's going to hurt Columbus in the 1-mile.

24 minutes ago, ColDayMan said:

I wouldn't say the location of the lake affects Cleveland, per se.  Look at Milwaukee and Buffalo for impressive numbers for also having a giant lake (inland sea) next to their downtown.  Hell, Milwaukee beats EVERY Midwest city except Chicago.

 

This is definitely true.

21 minutes ago, ColDayMan said:

I wouldn't say the location of the lake affects Cleveland, per se.  Look at Milwaukee and Buffalo for impressive numbers for also having a giant lake (inland sea) next to their downtown.  Hell, Milwaukee beats EVERY Midwest city except Chicago.

Yep. Buffalo up there, too in midsize lakeside metros. I've never bought the lake decreases density argument. If anything it's the opposite.

31 minutes ago, cbussoccer said:

I was interested to see how much higher Austin is than Columbus, but I think that is driven by the fact that UT is about 1-2 miles closer to downtown Austin than OSU is to downtown Columbus. Depending on where you define "the center of downtown", you can include the entire UT campus within the 2 mile radius for Austin, whereas in Columbus the southern tip of campus is about 2.5 miles from the intersection of Broad & High. 

 

The same could be said for how Akron ends up ahead of Columbus in the 1-mile radius metric. 

 

When you are looking at such a small area of land, these numbers can be greatly affected by many different factors, such as waterways, highways, public spaces, and even where you define the center of downtown to be. 

 

@DEPACincy are you able to see where the pin is dropped for the "center of downtown"? I would be interested to see that for the Ohio cities as well as for a place like NYC. In NYC, defining lower Manhattan as the "center of downtown" is going greatly reduce the population compared to dropping the pin in midtown Manhattan. 

 

Cbus = Statehouse. 

Cincy = Contemporary Arts Center. 

Cleveland = Public Square

Akron = Bowery and S. Main

Austin = 5th and Congress

NYC = City Hall (1 and 2 mile radius pop jumps to 177k and 591k if you use center of Midtown)

 

 

And just for fun, since I went to OU, if you do Athens, OH here are the numbers:

 

1-mile: 19,190 (Would be 14th on the list)

2-mile: 23,270 (Would be 40th on the list, but still ahead of Youngstown)

8 minutes ago, aderwent said:

Yep. Buffalo up there, too in midsize lakeside metros. I've never bought the lake decreases density argument. If anything it's the opposite.

 

Obviously half the circle is in the lake so no one can live there. But it is possible that the land area is more densely populated because of the lake as well. So it is hard to tell what the net effect is and it may differ by city.

38 minutes ago, ColDayMan said:

I wouldn't say the location of the lake affects Cleveland, per se.  Look at Milwaukee and Buffalo for impressive numbers for also having a giant lake (inland sea) next to their downtown.  Hell, Milwaukee beats EVERY Midwest city except Chicago.

Lake and nearly a mile to the west for the river valley. 

Why do people care about this?  

1 minute ago, jmecklenborg said:

Why do people care about this?  

 

Population density is important for a city to thrive. If I was the mayor of Cincinnati I'd post this list up on the wall and say "ok, now how do we move up?" For the 1-mile radius there is obviously a huge drop-off between Baltimore and Houston. It would take a looonnnggg time for Cincy to get 40k in the basin, but 22k is within reach in a few years. I'd make it clear that it is a goal for the city to do everything to make it happen.

 

As for why we care on here? For the same reason we care about the development threads. People are here because they like talking about cities. 

There are too many variables for anyone to draw any sort of meaningful conclusion from the radius game.  Plus, a dropping density is likely caused by new construction.  An influx of childless yuppies occupy much more space than the welfare set.  

 

There was an old woman who lived in a shoe.

She had so many children, she didn't know what to do.

She gave them some broth without any bread;

And whipped them all soundly and put them to bed.

 

12 minutes ago, DEPACincy said:

And just for fun, since I went to OU, if you do Athens, OH here are the numbers:

 

1-mile: 19,190 (Would be 14th on the list)

2-mile: 23,270 (Would be 40th on the list, but still ahead of Youngstown)

 

 

If you did this for any large university, they would rank pretty high up the list. OU makes up the majority of Athens and has an enrollment of 25-30k so it's not surprising it would be so high. Heck, if you dropped the pin on the Oval or at 15th & High at OSU, it would shoot way up the list. 

21 minutes ago, cbussoccer said:

 

 

 

If you did this for any large university, they would rank pretty high up the list. OU makes up the majority of Athens and has an enrollment of 25-30k so it's not surprising it would be so high. Heck, if you dropped the pin on the Oval or at 15th & High at OSU, it would shoot way up the list. 

 

Yep! That is absolutely true.

22 minutes ago, jmecklenborg said:

Plus, a dropping density is likely caused by new construction.  An influx of childless yuppies occupy much more space than the welfare set.  

 

This is certainly true to an extent. But eventually the number of new housing units offsets the smaller household sizes. Look at the growth in Center City Philly this decade as an example. 

37 minutes ago, DEPACincy said:

 

Obviously half the circle is in the lake so no one can live there. But it is possible that the land area is more densely populated because of the lake as well. So it is hard to tell what the net effect is and it may differ by city.

Do you ever wonder why Cleveland has the most dense built environment in Ohio? It's very likely because it had to. The same number of people had to fit in less area. It may have pushed density out further, but until fairly recently distance from the CBD was a very real limitation. Therefore, the lake caused more density, and when looking at land area instead of radii that include water, it's why Cleveland is the most dense city in Ohio. It wasn't because Cleveland was just in tune with urbanity or some strange coincidence.

7 minutes ago, aderwent said:

Do you ever wonder why Cleveland has the most dense built environment in Ohio? It's very likely because it had to. The same number of people had to fit in less area. It may have pushed density out further, but until fairly recently distance from the CBD was a very real limitation. Therefore, the lake caused more density, and when looking at land area instead of radii that include water, it's why Cleveland is the most dense city in Ohio. It wasn't because Cleveland was just in tune with urbanity or some strange coincidence.

 

No, Cincinnati's basin was at its peak the densest area of the United States outside of New York City.  Apartments were built to the rear lot lines for several square miles.  There was no equivalent in Cleveland outside of the immediate downtown.  There are regular detached single-family homes pretty close to Cleveland's downtown.  

1 minute ago, jmecklenborg said:

 

No, Cincinnati's basin was at its peak the densest area of the United States outside of New York City.  Apartments were built to the rear lot lines for several square miles.  There was no equivalent in Cleveland outside of the immediate downtown.  There are regular detached single-family homes pretty close to Cleveland's downtown.  

 

Cincinnati was affected much more by its geography when it was at it's prime than Cleveland ever was. The basin is hemmed in by a large river one side and very steep hills on the other sides. In the late 1800s and early 1900s, when the majority of the economy was centered around the river, it would not have been easy to travel up and down those hills regularly using horses or very early cars. This meant that Cincinnati actually had much less usable area than Cleveland.  

 

Cincinnati didn't just decide to build extremely dense at that time, they had to because of their geography. 

The point everyone seems to be making is that geography affects density. Which is absolutely true. And the dominant transportation technology when a city boomed is also important. I think we all get this.

Let's look at the 5-mile ring. 

 

  • Boston climbs to 3rd. 
  • Chicago drops to 7th, below DC. 
  • Vegas is a big surprise here at 9th. 
  • By this measure Milwaukee is bigger than Houston. 
  • Cbus now overtakes Cincy. 
  • Cleveland moves up from 36th at the 2-mile radius to 25th at the 5-mile. 
  • Akron still looks bigger than a lot of bigger cities, including Charlotte, Nashville, Raleigh, Kansas City, and Detroit (In fairness, this doesn't count any of the Canadian residents across from Detroit). 
  • Dayton is higher than Raleigh, Kansas City, Detroit, and Jacksonville. Toledo is higher than all of those as well, with the exception of Raleigh. 

 

EDIT TO ADD: For numbers over 1 million I rounded to the nearest thousand. 

5-mile.JPG

Edited by DEPACincy

2 hours ago, ColDayMan said:

I wouldn't say the location of the lake affects Cleveland, per se.  Look at Milwaukee and Buffalo for impressive numbers for also having a giant lake (inland sea) next to their downtown.  Hell, Milwaukee beats EVERY Midwest city except Chicago.

 

 

not so fast, you would have to cut cleveland's waterfront area in half to match those waterfronts.

 

that is, they have waterfronts, but they are not built along the waterfront as cle mostly is.

 

anyway, that's why a radial measure always kills the clev.

2 hours ago, DEPACincy said:

 

Cbus = Statehouse. 

Cincy = Contemporary Arts Center. 

Cleveland = Public Square

Akron = Bowery and S. Main

Austin = 5th and Congress

NYC = City Hall (1 and 2 mile radius pop jumps to 177k and 591k if you use center of Midtown)

 

 

And just for fun, since I went to OU, if you do Athens, OH here are the numbers:

 

1-mile: 19,190 (Would be 14th on the list)

2-mile: 23,270 (Would be 40th on the list, but still ahead of Youngstown)

 

Re Cleveland, Public Square may be the symbolic "center" of the city and of Downtown, but its not the physical center of either.  Regarding Downtown, Public Square is fairly west of center. Do a goole aerial view of Downtown CLE and you'll see that the center would be to the east of Public Square.

4 minutes ago, Pugu said:

 

Re Cleveland, Public Square may be the symbolic "center" of the city and of Downtown, but its not the physical center of either.  Regarding Downtown, Public Square is fairly west of center. Do a goole aerial view of Downtown CLE and you'll see that the center would be to the east of Public Square.

 

This is true. But I didn't pick Public Square. The tool did. And I didn't mess with any of the defaults because I didn't want to introduce my own biases. In fairness to the tool though, using Public Square probably actually helps CLE at the 2-mile radius because it captures part of Detroit Shoreway instead of the western part of Hough.

33 minutes ago, mrnyc said:

 

 

not so fast, you would have to cut cleveland's waterfront area in half to match those waterfronts.

 

that is, they have waterfronts, but they are not built along the waterfront as cle mostly is.

 

anyway, that's why a radial measure always kills the clev.

 

?

 

Milwaukee looks eerily similar to Cleveland with a central industrial valley, the port, hills, a Gold Coast, and a warehouse district.  They are just more "intact" overall, which shows in these numbers pulled.

"You don't just walk into a bar and mix it up by calling a girl fat" - buildingcincinnati speaking about new forumers

What's crazy about Cleveland is how much of the metro area's pre-war construction is outside of the 5 mile radius. Five miles doesn't even get you to Shaker Square or Coventry. Cleveland's been sprawling forever. 

9 minutes ago, StapHanger said:

What's crazy about Cleveland is how much of the metro area's pre-war construction is outside of the 5 mile radius. Five miles doesn't even get you to Shaker Square or Coventry. Cleveland's been sprawling forever. 

 

I don't know how many places this applies to but it does also apply to places in Cincinnati like Oakley Square and Mariemont. Mt. Lookout Square is barely inside the 5 mile radius.

Let's take it out even farther. Here is the 10-mile radius. In my opinion, this might be the best measure of a city's true size. 

 

  • NYC is at 7 mil, getting closer to the 8.4 mil in its actual boundaries.
  • Chicago jumps from 7th at the 5-mile radius, to 3rd at the 10-mile radius. At 2.5 mil, it is also very close to its actual 2.7 mil
  • Philly is at 2.2 mil, up from its actual population of 1.6 mil. Density!
  • Las Vegas still surprisingly large, with 1.4 mil. 
  • Baltimore is almost as big as Houston by this measure.
  • Columbus jumps up to 17th at 960k. Again very close to its actual pop of 893k. Just above Atlanta.
  • Cleveland takes a big jump from 248k at 5-mile radius to 816k at 10-mile radius. Surpasses Cincy. 
  • Cincy falls to 25th, settling in at 790k. More than 2.5 times its actual city-proper population.
  • Dayton is still bigger than Nashville. 
  • The other Ohio cities settle in at the bottom of the list. Notably Akron comes in more than twice its actual population. Canton comes in about 4 times its actual population.

 

Overall, I think this radius is most indicative of how much of a "big" city each city actually is. Ohio cities are "bigger" than their actual populations indicate due to small geographic boundaries. Philly, Boston, Las Vegas, San Fran, and Baltimore are bigger than their actual populations, while Houston, Phoenix, and Dallas are smaller. 

 

 

10-mile.JPG

Milwaukee still is quite impressive on that 10-mile list.  Western metropolitan areas aren't a surprise; Charlotte over KC and Louisville is a bit surprising.

"You don't just walk into a bar and mix it up by calling a girl fat" - buildingcincinnati speaking about new forumers

12 minutes ago, DEPACincy said:

Overall, I think this radius is most indicative of how much of a "big" city each city actually is. Ohio cities are "bigger" than their actual populations indicate due to small geographic boundaries. Philly, Boston, Las Vegas, San Fran, and Baltimore are bigger than their actual populations, while Houston, Phoenix, and Dallas are smaller. 

 

 

 

 

This.  Thanks for putting together the spreadsheets.  It's really interesting to see Dayton compete with Nashville and Jacksonville with both cities having massive boundaries.  This just doesn't happen in Ohio with established inner ring (even outer ring) suburbs, but the density numbers are there to prove they pack a punch.

7 minutes ago, ColDayMan said:

Milwaukee still is quite impressive on that 10-mile list.  Western metropolitan areas aren't a surprise; Charlotte over KC and Louisville is a bit surprising.

 

 

Charlotte's river is way off to the side.

Edited by GCrites80s

We get it.  Everything in San Francisco is a house except Golden Gate Park.  That city barely even has a railroad yard, let alone cemeteries, golf courses, and all of the other crap that breaks up every other city.  

 

 

1 hour ago, ColDayMan said:

 

?

 

Milwaukee looks eerily similar to Cleveland with a central industrial valley, the port, hills, a Gold Coast, and a warehouse district.  They are just more "intact" overall, which shows in these numbers pulled.

 

 

the majority of the cityscapes of mil and buf are further away from the waterfront than cle, thus radial measurements hurt more.

 

you could throw a rock into lake erie from standing around much of cle, it runs along the waterfront more.

 

more similar to the cle waterfront would be places like seattle and miami.

 

mil is much more intact though by any measure. also bigger area-wise and more people these days than cle. and more importantly slight growth, not slight shrinkage.

^If everyone wanted something similar / across the board for say Cleveland and Cincinnati, couldn't you just measure the 5 mile in Cincinnati then measure the 10 mile in Cleveland and say that's a wrap because it cuts off half off the population because of the lake?

 

Or put the dot right on the river in Cincinnati, the dot right on the lake in Cleveland, then cut it in half?

No, because of pi.  

27 minutes ago, IAGuy39 said:

^If everyone wanted something similar / across the board for say Cleveland and Cincinnati, couldn't you just measure the 5 mile in Cincinnati then measure the 10 mile in Cleveland and say that's a wrap because it cuts off half off the population because of the lake?

 

Or put the dot right on the river in Cincinnati, the dot right on the lake in Cleveland, then cut it in half?

 

A circle with a 5 mile radius has 78 square miles. 

 

A circle with a 10 mile radius has 314 square miles.

46 minutes ago, DEPACincy said:

 

A circle with a 5 mile radius has 78 square miles. 

 

A circle with a 10 mile radius has 314 square miles.

 

I was only just checking to make sure you all were staying sharp on your math.

 

In that case, take the Cleveland one at 7.05 mile radius than divide in half?

 

A = pi R^2

 

A = 156 square miles (twice as needed)

 

Square Root (156/pi) = R

 

R = 7.05

 

Then take that number for Cleveland to equal other 5 mile radius?

23 minutes ago, IAGuy39 said:

 

I was only just checking to make sure you all were staying sharp on your math.

 

In that case, take the Cleveland one at 7.05 mile radius than divide in half?

 

A = pi R^2

 

A = 156 square miles (twice as needed)

 

Square Root (156/pi) = R

 

R = 7.05

 

Then take that number for Cleveland to equal other 5 mile radius?

 

giphy.gif

"In the souls of the people the grapes of wrath are filling and growing heavy, growing heavy for the vintage." -- John Steinbeck

14 hours ago, IAGuy39 said:

 

I was only just checking to make sure you all were staying sharp on your math.

 

In that case, take the Cleveland one at 7.05 mile radius than divide in half?

 

A = pi R^2

 

A = 156 square miles (twice as needed)

 

Square Root (156/pi) = R

 

R = 7.05

 

Then take that number for Cleveland to equal other 5 mile radius?

 

You can do stuff like this, but it doesn't exactly create an equivalent scenario. You'll have people in the Cleveland boundary that live ~7 miles from Downtown. which is different than only having people living 5 miles from another Downtown from an accessibility perspective (or infrastructure perspective, etc.); we're talking 40% more distance. Plus, to the extent that development might be more concentrated specifically because of the natural boundary, it could be "cheating."

16 hours ago, IAGuy39 said:

 

I was only just checking to make sure you all were staying sharp on your math.

 

In that case, take the Cleveland one at 7.05 mile radius than divide in half?

 

A = pi R^2

 

A = 156 square miles (twice as needed)

 

Square Root (156/pi) = R

 

R = 7.05

 

Then take that number for Cleveland to equal other 5 mile radius?

 

Yea, I'm not sure it solves the problem. You could start throwing in all kinds geographic obstacles to account for. What about the Ohio River? What about topography? What about the effect of being split between two states? Cincy development spreads farther north than it does south. I think we just have to accept that there is no perfect way to compare. 

 

One of the reasons I'm collecting this data is because I've been developing a "sprawl index." It's not ready yet, but I think it'll be a pretty good measure of how sprawling a metro area is.

1 minute ago, DEPACincy said:

 

Yea, I'm not sure it solves the problem. You could start throwing in all kinds geographic obstacles to account for. What about the Ohio River? What about topography? What about the effect of being split between two states? Cincy development spreads farther north than it does south. I think we just have to accept that there is no perfect way to compare. 

 

One of the reasons I'm collecting this data is because I've been developing a "sprawl index." It's not ready yet, but I think it'll be a pretty good measure of how sprawling a metro area is.

 

Exactly. This radial population comparison can be useful, but you need to compare comparable cities, if that makes sense. For example, Columbus and Indianapolis are laid out almost identically. As a result, this statistic is very useful. The statistic is not very useful at all for comparing Columbus to Cleveland because the lake skews things drastically.

 

We have many different ways to slice and dice things, and all can be useful if they are utilized properly. Unfortunately, there is no perfect manner for comparing populations in a "fair" way. 

I'll take half as much density if it's paired with thriving businesses and minimal couchlock.

I never really got the lake argument with these type of measurements.  Like with all geographical barriers, it should only serve to concentrate population into a smaller area, meaning that even though half of the circle is the lake, the other half should theoretically include all the population that would've been there anyway.  Cleveland isn't the only city with geographical barriers.  NYC, Chicago, etc. all seem to do fine on this type of metric.

And that's why this kind of talk ends up being wankery

 

"but what about the quarry" "that park is huge" "the hills are really steep" "huge abandoned industrial site" "flood plain"

7 minutes ago, jonoh81 said:

I never really got the lake argument with these type of measurements.  Like with all geographical barriers, it should only serve to concentrate population into a smaller area, meaning that even though half of the circle is the lake, the other half should theoretically include all the population that would've been there anyway.  Cleveland isn't the only city with geographical barriers.  NYC, Chicago, etc. all seem to do fine on this type of metric.

 

^I agree with that logic.  But what  I don't agree with--and this is true for probably all cities--is that Downtowns are not necessarily circular in shape. NY is more oblong (north south), Cleveland is more oblong (east-west---say E. 18 to W. 9). Cinci may be more E-W as well--since the river flows that way. Not sure about Columbus. Chicago is more N-S than a circle. So a circle around a Downtown these doesn't really capture an even "buffer" of x miles around a Downtown.  It'd be more accurate if you outlined the downtowns and THEN drew a shape--of the same shape--around the downtown at various miles out.

21 minutes ago, GCrites80s said:

And that's why this kind of talk ends up being wankery

 

"but what about the quarry" "that park is huge" "the hills are really steep" "huge abandoned industrial site" "flood plain"

 

Yep, every city has empty space, geographical barriers, industrial areas, etc. There is never going to be a perfect metric to exactly compare every single city, and radius population isn't perfect either.  But some of the arguments why so and so city doesn't perform as well on it are paper thin.

Edited by jonoh81

15 minutes ago, Pugu said:

 

^I agree with that logic.  But what  I don't agree with--and this is true for probably all cities--is that Downtowns are not necessarily circular in shape. NY is more oblong (north south), Cleveland is more oblong (east-west---say E. 18 to W. 9). Cinci may be more E-W as well--since the river flows that way. Not sure about Columbus. Chicago is more N-S than a circle. So a circle around a Downtown these doesn't really capture an even "buffer" of x miles around a Downtown.  It'd be more accurate if you outlined the downtowns and THEN drew a shape--of the same shape--around the downtown at various miles out.

Right, Cleveland has the lake to the north, the industrial valley to the south, and the light manufacturing area that advances into the east 30s. The residential population may be lower in those areas, but there are also simply less residential use neighborhoods within that circumference because of the factors I described.

2 minutes ago, jonoh81 said:

 

Yep, every city has empty space, geographical barriers, industrial areas, etc. There is never going to be a perfect metric to exactly compare every single city, and radius population isn't perfect either.  But some of the arguments why so and so city doesn't perform as well on it are paper thin.

 

By your logic, the argument for why a city performs well is also paper thin.

20 minutes ago, Pugu said:

 

^I agree with that logic.  But what  I don't agree with--and this is true for probably all cities--is that Downtowns are not necessarily circular in shape. NY is more oblong (north south), Cleveland is more oblong (east-west---say E. 18 to W. 9). Cinci may be more E-W as well--since the river flows that way. Not sure about Columbus. Chicago is more N-S than a circle. So a circle around a Downtown these doesn't really capture an even "buffer" of x miles around a Downtown.  It'd be more accurate if you outlined the downtowns and THEN drew a shape--of the same shape--around the downtown at various miles out.

 

True, every city is different, so radius measurements work better for some than others.  I would also argue that the most populated areas of a city aren't always their downtowns.   Columbus is certainly one of those cases- I would argue the center of population if further north toward Campus.  The reality is that we're never going to have a single metric that accurately takes into account all the differences from city to city, but also that every argument against a metric doesn't necessarily hold up either.

Edited by jonoh81

7 minutes ago, Clefan98 said:

 

By your logic, the argument for why a city performs well is also paper thin.

 

Not really.  I'm just saying that geographical barriers alone don't always explain the performance with this particular comparison.  A geographical barrier, by itself, is not necessarily detrimental, so using the lake as the reason why Cleveland might not perform as well is pretty thin without doing any detailed analysis on its effects to population.  

 

For example, if this comparison was done in 1950 when Cleveland's population was heavily concentrated in and near Downtown, its ranking would be much higher on this list, despite the lake.  This means that it's not just the lake.  It's where people have concentrated.

Edited by jonoh81

^ Unless all city's geographical barriers are the same, your comparisons are pointless, as others have noted. Comparing Cleveland of today vs 1950 makes more sense because of the like data points.

I guess I don’t understand what there is to argue about. We are looking at the population within a certain radius from downtown. This population affects many things about our cities. Dead zones, regardless of the type, impact the vitality of the core. In Cleveland the lake does eat up a ton of space that would have otherwise been residential. It’s clear to see the actual impacts of that when visiting downtown. Cities without large dead zones are at a natural advantage but that doesn’t make the comparison unfair. Cleveland has to overcome the lake with greater density, something that it hasn’t done. In addition, like mentioned before,  downtown is surrounded by many man made dead zones as well, from light industry to the east, interchanges to the south, and the river and industry to the west. 

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