In order to be precise about the gradient of housing densities, let us agree at once, to analyze the densities by means of three concentric semi-circular rings, of equal radial thickness, around the main center of activity.
[We make them semi-circles, rather than full circles, since it has been shown, empirically, that the catch basin of a given local
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| Rings of equal thickness. |
center is a half-circle, on the side away from the city—see discussion in eccentric nucleus (28) and the references to Brennan and Lee given in that pattern. However, even if you do not accept this finding, and wish to assume that the circles are full circles, the following analysis remains essentially unchanged.] We now define a density gradient, as a set of three densities, one for each of the three rings.
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| A density gradient. |
Imagine that the three rings of some actual neighborhood have densities Dj, D2, D3. And assume, now, that a new person moves into this neighborhood. As we have said, within the given density gradient, he will choose to live in that ring, where his liking for green and quiet just balances his liking for access to shops and public services. This means that each person is essentially faced with a choice among three alternative density-distance combinations:
Ring 1. The density Di, with a distance of about Ri to shops.
Ring 2. The density D2, with a distance of about Ro to shops.
Ring 3. The density D3, with a distance of about R3 to shops.
Now, of course, each person will make a different choice—ac
cording to his own personal preference for the balance of density and distance. Let us imagine, just for the sake of argument, that all the people in the neighborhood are asked to make this choice (forgetting, for a moment, which houses are available). Some will
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choose ring I, some ring 2, and some ring 3. Suppose that Ni choose ring 1, N2 choose ring 2, and N3 choose ring 3. Since the three rings have specific, well-defined areas, the numbers of people who have chosen the three areas, can be turned into hypothetical densities. In other words, if we (in imagination) distribute the people among the three rings according to their choices, we can work out the hypothetical densities which would occur in the three rings as a result.
Nozv zve are suddenly jaced with two fascinating possibilities:
I. These new densities are different from the actual densities.
II. These new densities are the same as the actual densities.
Case I is much more likely to occur. But this is unstable—since
people’s choices will tend to change the densities. Case II, which is less likely to occur, is stable—since it means that people, choosing freely, will together re-create the very same pattern of density within which they have made these choices. This distinction is fundamental.
If we assume that a given neighborhood, with a given total area, must accommodate a certain number of people (given by the average density of people at that point in the region), then there is just one configuration of densities which is stable in this sense. We now describe a computational procedure which can be used to obtain this stable density configuration.
Before we explain the computational procedure, zve must explain how very fundamental and important this kind of stable density configuration is.
In today’s world, where density gradients are usually not stable, in our sense, most people are forced to live under conditions where the balance of quiet and activity does not correspond to their wishes or their needs, because the total number of available houses and apartments at different distances is inappropriate. What happens, then, is that the rich, who can afford to pay for what they want, are able to find houses and apartments with the balance that they want; the not so rich and poor are forced to take the leavings. All this is made legitimate by the middle-class economics of “ground rent”—the idea that land at different distances from centers of activity, commands different prices, because more or less people want to be at those distances. But actually the fact of differential ground rent is an economic
mechanism which springs up, within an unstable density configuration, to compensate for its instability.
We want to point out that in a neighborhood with a stable density configuration (stable in our sense of the word), the land would not need to cost different prices at different distances, because the total available number of houses in each ring would exactly correspond to the number of people who wanted to live at those distances. With demand equal to supply in every ring, the ground rents, or the price of land, could be the same in every ring, and everyone, rich and poor, could be certain of having the balance they require.
We now come to the problem of computing the stable densities for a given neighborhood. The stability depends on very subtle psychological forces; so far as we know these forces cannot be represented in any psychologically accurate way by mathematical equations, and it is therefore, at least for the moment, impossible to give a mathematical model for the stable density. Instead, we have chosen to use the fact that each person can make choices about his required balance of activity and quiet, and to use people’s choices, within a simple game, as the source of the computation. In short, we have constructed a game, which allows one to obtain the stable density configuration within a few minutes. This game essentially simulates the behavior of the real system, and is, we believe, far more reliable than any mathematical computation.
DENSITY GRADIENTS GAME
x. First draw a map of the three concentric half rings. Make it a half-circle—if you accept the arguments of ECCENTRIC nucleus (28)—otherwise a full circle Smooth this half-circle to fit the horseshoe of the highest density—mark its center as the center of that horseshoe.
2. If the overall radius of the half-circle is R, then the mean radii of the three rings are Ri,R2,R3 given by:
Ra = 5R/6
3. Make up a board for the game, which has the three concentric circles shown on it, with the radii marked in blocks, so people can understand them easily, i.e., 1000 feet = 3 blocks.
4. Decide on the total population of this neighborhood. This is
TOWNS
the same as settling on an overall average net density for the area. It will have to be roughly compatible with the overall pattern of density in the region. Let us say that the total population of the community is N families.
5. Find ten people who are roughly similar to the people in the community—vis-a-vis cultural habits, background, and so on. If possible, they should be ten of the people in the actual community itself.
6. Show the players a set of photographs of areas that show typical best examples of different population densities (in families per gross acre), and leave these photographs on display throughout the game so that people can use them when they make their choices.