[HN Gopher] Simple Mathematical Law Predicts Movement in Cities ...
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Simple Mathematical Law Predicts Movement in Cities Around the
World
Author : iamwil
Score : 37 points
Date : 2021-09-14 16:27 UTC (6 hours ago)
(HTM) web link (www.scientificamerican.com)
(TXT) w3m dump (www.scientificamerican.com)
| Hermitian909 wrote:
| > researchers discovered what is known as an inverse square
| relation between the number of people in a given urban location
| and the distance they traveled to get there
|
| I'm highly skeptical of this result as my lived experience is
| that travel time is so much more important than distance.
|
| There are two parts of my city that I like to visit that are
| roughly equidistant from my home. One can takes 20 minutes to
| arrive at, the other 45. Can you guess which one I visit more
| often?
| Anon84 wrote:
| This is known as a "Gravity Model" in the transportation
| literature and it's very far form being a new discovery. It's
| been around since the 1930s under various guises
| (https://en.wikipedia.org/wiki/Gravity_model_of_trade)
|
| We used the same concept in our 2009 paper
| (https://www.pnas.org/content/106/51/21484) but the exact
| functional form of the distance dependency (1/r, 1/r^2, 1/e^r,
| etc) varies with their exact definition of city due to the
| Modifiable Areal Unit problem
| (https://en.wikipedia.org/wiki/Modifiable_areal_unit_problem).
| In our specific case (cities defined as Voronoi cells centered
| around airports) the dependency was exponential.
| tommymachine wrote:
| From the abstract:
|
| > we reveal a simple and robust scaling law that captures the
| _temporal_ and spatial spectrum of population movement
|
| They throw around the word "temporal", but it's not clear
| exactly how they incorporate the time element without taking
| the plunge on the full study.
| seph-reed wrote:
| The gist is that people bounce around to places with more people.
| Kind of like gravity.
| kazinator wrote:
| > _researchers discovered what is known as an inverse square
| relation between the number of people in a given urban location
| and the distance they traveled to get there_
|
| The found that the frequency of visiting a place, multiplied by
| the distance traveled (rf) forms a stable parameter which can be
| used as a single dependent variable. There is then an
| (approximate, statistically fitted) inverse square law involving
| this combined variable. Or two square laws.
|
| If we hold frequency constant (say "once a month" or whatever),
| then the number of people visiting some place drops off inverse
| square with distance. If 400 people are willing to visit some
| place once a month that is 10 km away, about 100 once-a-month
| visitors will come from 20 km away.
|
| Or if we hold distance constant: if 400 people are visiting some
| place that is 10 km away once a month, about 100 will be visiting
| twice a month.
|
| > _It accurately predicts, for instance, that the number of
| people coming from two kilometers away five times per week will
| be the same as the number coming from five kilometers twice a
| week._
|
| It doesn't predict this; rather this frequency-distance product
| being a stable parameter is a discovery from the data, on which
| the formula is then based. I.e this frequency-distance product
| becomes a model assumption baked into the formula, not a
| prediction.
| beefman wrote:
| https://doi.org/10.1038/s41586-021-03480-9
| Anon84 wrote:
| Full text:
| https://senseable.mit.edu/papers/pdf/20210527_Schlapfer-etal...
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