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Simple mathematical law predicts movement in cities around the world
- seph-reed 5y agoThe gist is that people bounce around to places with more people. Kind of like gravity.
- TimMurnaghan 5y agoNot very like gravity. They explicitly say "outperforms gravity models". Also the economic concentration laws behind this would often follow power laws - so maybe the inverse square is just a 2nd order approximation rather than a real fundamental principle.
- Hermitian909 5y ago> 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?
- tommymachine 5y agoFrom 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.
- pfortuny 5y agoIn the frequency of visitation, so that sentence seems to be a bit confusing.
- Anon84 5y agoThis 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 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 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 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.
- soVeryTired 5y agoPresumably that just shows that it's easy to fit things with inverse-power functions, rather than revealing some fundamental truth about the behaviour the equation is modelling.
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- shatnersbassoon 5y agoI think that both this and what the paper says can hold true. The paper is saying that from the point of view of the location, the distribution of effective distances traveled is invariant. So if you really like the 45min part of your city, then every one closer really loves it, so visit it much more than you do. Therefore the law holds true, even though on an individual basis you obviously go to the closer parts more frequently. The fact that you might be prepared to go all the way to e.g. Disneyworld means that the people who live closer are massively more likely to go there to the point where people who live 5 miles from it go there all the time.
- yummypaint 5y agoAveraged out over all inhabitants of the city and all areas of the city it wouldn't be surprising if it still held. What is accessible from your dwelling may be less accessible to someone else the same distance away but approaching from a different direction.
- beefman 5y agohttps://doi.org/10.1038/s41586-021-03480-9 https://doi.org/10.1038/s41586-021-03480-9
- kazinator 5y ago> 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.
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- toss1 5y agoGood description — I also thought that the example was off. I'd be very interested to see how this law holds for travel destinations, both from the POV of the destination (national park, ski area, attraction), and from the POV of occasional travelers.
- m0hit 5y agoSome of the specific examples in the article seemed off to me too. However, I did love the book Scale by Geoffrey West who is one of the authors of the paper discussed in the article. At the very least, the book is a great introduction to the many different aspects that scale up with city size.
- yummypaint 5y agoI interpret the inverse square law as being the direct result of the area of a circle scaling as the square of the radius. Imagine dividing a given circle overlaid on a city into fixed sized area units. If you randomly visit a unit, the probability of visiting a particular unit scales as 1/area. Note that this derivation is essentially identical to showing that electric field falls off as 1/(r^2). In that case the area refers to the area of a sphere through which field lines must pass.
- Anon84 5y agoFull text: https://senseable.mit.edu/papers/pdf/20210527_Schlapfer-etal_UniversalVisitation_Nature.pdf https://senseable.mit.edu/papers/pdf/20210527_Schlapfer-etal...
- sneak 5y ago> Studying anonymized cell-phone data, researchers discovered... Anyone else get creeped out by the fact that this is becoming normalized? (Background: it is impossible to anonymize location tracklogs.)
- freemint 5y agoIt's totally possible to to anonymize location data for this study. The idea is that while the mobile IP has location track logs instead a fair sampling of actual travels is provided where a travel is two locations some person visited at some point in time after each other where locations are treated identical if they fall in some grid box of n km coursity. In fact such datasets are available by Telecom providers.
- blitzar 5y ago> Studying health records > Studying spending patters > Studying voting intentions > Studying twitter The only creepy thing is if the data is being collected via dubious means. If they sign up a few 1000 participants, use their data in a transparent manner, I dont have a problem. If however, they buy the data from the lowest bidder on the internet who has a free VPN app that logs location for resale, they yeah that is shitty.
- novok 5y agoAt least twitter is public by default and everyone participating has that expectation, while everything else is not. Big difference studying the language of published books by authors vs. their private conversations in their homes.
- personjerry 5y agoThis is starting to feel like Asimov's psychohistory
- yann2 5y agoCan we get a rule where the adjectives like startling, striking, profound etc get applied after an application has been demonstrated. Speaking as someone who suffers from adjective overload.
- Barrin92 5y agoAnother interesting 'law' of this kind is Zipf's law observing that the largest city is roughly twice as large as the second largest, three times as large as the third largest in any given country, and so on. the same relationship shows up in word-usage frequency in languages.
- _Gyan_ 5y agoExcept for many primate cities: https://en.wikipedia.org/wiki/Primate_city#List https://en.wikipedia.org/wiki/Primate_city#List
- wombatmobile 5y agoWhat countries are consistent with Zipf’s law? Not USA, England, Australia, Thailand, China, England, France.
- dagw 5y agoUS is quite close for the top 10 cities (~1 million 'too many' people in New York, 200k too many in San Diego, Austin and Dallas), but there are FAR too many cities with a population around 250-500k England would be surprisingly close, if London had been half the size it currently is. If you took half the population of London and distributed it proportionally out among the rest of the country then you get quite close to a Zipf law distribution. France doesn't really follow Zipf law for its 5 largest cities, but cities 6-15 follow quite closely. Australia I 'weird' in that it's two largest cities are basically the same size, but if we ignore Melbourne for while the next few cities line up quite nicely before we start seeing a much faster drop off in city population than Zipf's law would predict Thailand is way off, since it has 1 massive city followed by 10 cities of more or less the same size. So yea, no country follows exactly, but it's closer in many cases than you might expect. Plus comparing the actual distribution to Zipf's law is an interesting way of comparing urbanization in different countries
- onlyrealcuzzo 5y agoIn the US, for metros you have NY at 20M, LA at 13M, and Chicago at 9.5M. But if you go by city - NYC is 8.5M, LA is 4M, Chicago is 2.7M.
- reyman 5y agoGeographer works a lot of these questions since 1900's, and there are lot of works/simulation in the domain using Multi Agent Sytem (see journal of artificial societies https://www.jasss.org/JASSS.html https://www.jasss.org/JASSS.html). Mathematican and physician often forget to cite their work :'(
- Atlas667 5y ago>“We tend to think that there are lots of contextual aspects that affect the way we move, such as the transportation system, the morphology of a given place, and socioeconomic aspects. This is true to some extent, but what this shows is that there are some robust laws that apply everywhere.” I'm no computational social scientist, but this analysis doesn't make sense. In fact it would seem to me that if the study took those variables into account the model would become more predictive. It's idealizing the analysis.
- dave333 5y agoWhy does the SciAm web page gobble CPU?