In this work we describe the distribution of chewing gums around several urban pits. Using this we analyze the aiming capabilities of urban people, which proves to be rather limited.

We divided the space around each pit into circular areas of 18, 30, 60, 90 and 150 cm radius, and counted the number of sticked gums in these 4 regions (the region from 0 to 18 contains the pit, can cannot be counted). From that the gum-density as a function of the distance of the pit can be calculated.

The numbers were counted independently by two persons (the authors) and averaged. This to get a feeling of the accuracy of the decision about when a gum should be counted or not, or to be noticed at all. The results usually differed a few per cent.

Because the number of hits could not be counted directly - these gums did disappear in the sewer system - the central area of the distribution was left out of the measurement. We will be able to extrapolate this number from the rest of the distribution.

The distribution is supposed to be gaussian, dependent on two variables and which we
will find by an optimization based on the measurements. From and then follows the
number of gums in the sewer. This can be expressed by the formula:

was separately measured on a similar location near to the pit, sufficiently far away to assume that no `misses' land there.

The number of gums between and would according to formula (1) be:

Where we define to be the distance to the pit where the gum density takes its average value of the area defined by the two distances and . The number of gums in this area we call , which we want to fit to the counted number . This means that we are minimizing as function of and this expression:

(3) |

For the fitting process this does not matter much, it only means that not only the shape and height
of the gaussian fit-function are changed but, while doing so, also the -values of the fitted data
are varied (but in a *coupled* manner).

So we need an expression for (following from 2):

(4) |

The results fo the gaussian fits are

pit | (total number of gums) | (width of the distribution) (m) |

pit 1 | ||

pit 2 |

We can now calculate how many aimed gums hit the central region (of 18 cm radius) (from eq. 1) :

(5) |

From the figures 1 and 2 it can be seen that 1.5 meters from the pit there are virtually no misses any more, . Therefore the total counted number in the 1.5 meter area (which did not include this central region) plus the calculated number of central hits minus the `background' density should also give approximately the total number of aimed gums at the pit.

For pit 1 the measured number of gums between and distance is: . The number of accidental drops in this region . So the total number of misses outside the central area is , plus the number of hits in the central area = should be equal to , which sounds reasonable.

For pit 2 these numbers are and .

If we are interested only in the relative number of hits then we do not need the number , and we can also take the results of the two measurements together (assuming that the success ratio of the gum aimers is a constant). The weighted average for and is .

The most interesting number if of course the value of , which is the width of the gaussian radial density distribution. This is a measure for the preciseness of aim of the subjects, which are the urban semi-social people, who spit their gums at pits. We found 2 values for for two different targets. These values are very comparable, but probably not the same, since they differ more then twice the estimated standard deviation. This could be caused by the slightly varying demographic circumstances in the neighborhood of the two pits.

When averaged anyway we find that considerably less than of the targeted gums actually hits its goal: disappearance in the sewer system, which is a regrettably low figure. This leads us to conclude that these semi-social aiming individuals can as well not even try, or promote themselves to decent civilians. They can also choose the solution based on swallowing.

- 1
- bbc
- 2
- italy
- 3
- Singapore
- 4
- China
- 5
- Englang
- 6
- http://www.nesta.org.uk/ourawardees/profiles/2932/print.htm
- 7
- http://www.tridentgum.com/consumer/html/x13.htmlxsg
- 8
- http://www.wrigley.com/wrigley/kids/gumstory.pdf
- 9
- Press,
*et al.*- Numerical Recipes in C, second edition - Cambridge University press, 1988. - 10
- Thomas Williams, Colin Kelley,
*et al.*- Version 3.7 patchlevel 3 - Copyright(C) 1986 - 1993, 1998 - 2002.

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