Introduction
The Tipping Point is the biography of how little things had big effects.
From 1992 to 1997, murder rates dropped 64.3% to 770 and total crimes fell by \(\approx\) 50% to 355,893.
Geometric progressions are non-intuitive, e.g. if given a large paper and asked to fold it 50x, the stack’s height will be \(\approx\) the distance to the sun.
When the # of incoming African Americans reached \(\approx\) 20%, most of the remaining whites would leave almost immediately.
When a neighborhood had \(<\) 5% high status workers, school dropouts and teen pregnancy rates doubled.
References
- Dynamic models of segregation. Schelling, Thomas C. Journal of Mathematical Sociology, Vol. 1, No. 2. www.uzh.ch . 1971.
- The Epidemic Theory of Ghettos and Neighborhood Effects on Dropping Out and Childbearing. Jonathan Crane. American Journal of Sociology, Vol. 96, No. 5. www.uvm.edu . 1991.
- Exponential Growth. en.wikipedia.org .
- Exponential Growth. Raju Varghese. raju.varghese.org . Nov 20, 2007.
This is a popular illustration. The standard paper’s thickness, \(h_0\), is \(0.1\) milllimeters, and the distance to the sun, \(d_{sun}\), is \(149.6\) million kilometers. Solving for \(n\) in \( h_{0} \cdot 2^n = d_{sun} \) gives \(n = 50.41 \).
However, how long does the paper need to be, i.e. \(l_0\)? Assuming that we don’t even fold it over but instead cut it each time into two and stack, then \(\frac{l_0}{2^{50}} = l_{f} \). If we want a stack that is 1cm wide, then \(l_0 = 11.26\) billion km, i.e. \(75.26\) times the distance to the sun.
Ergo, if you had a piece of paper whose length is \(75 \times \) the distance to the sun, and you folded it \(50 \times \), then the final stack would be as high as the distance to the sun, and 1cm wide.
Doesn’t pack the same punch. The illustrations that use grains of rice to show how quick exponential growth is are more apt.