Hi Mike -- I look at your disk and now see what you mean by the tail of Zipf's distribution dropping off -- see attached for the urban clusters in the US. It seems to fit a log function better than anything else. How and where Zipf's rank-size rule gets violated provides traction for asking questions about the nature of urban networks. Both tails of the distribution provide food for thought. For example, the rapid drop-off of the sizes of urban clusters raises questions about whether small urban places are disappearing in mature systems or whether it is an artifact of our book-keeping (as in the case of your data from England), i.e. will the world become all urban someday? I suppose we could weave in a story about "desakota" processes in Asia as an alternative to Western rural depopulation -- Bangladesh's ruralopolis (1000 people/km2) as it were. I'd be happy to put together some slides for next week's seminar if you and Yichun wish. Tom p.s. I re-ran the US regions as independent entities and found the East and West Coast cities have the highest (lowest?) exponents (-1.26 & -1.27) and the Midwest and South is lowest (-1.07). The Great Plains and Mountains are intermediate at -1.18). Nice range -- what's it mean? -----Original Message----- From: mike batty [mailto:mbatty@geog.ucl.ac.uk] Sent: Wednesday, February 19, 2003 3:34 PM To: tom wagner Subject: Re: Questions on Zipf's Law Tom - in answer to question 3) only for the time being - power laws exist everywhere and in terms of phase transitions, then basically at the edge of chaos then essentially the power law shows how a system connects its bits together - so in a network there are interactions on all scales whereas well below the phase transition they may be an incomplete set of connections while above it there is likely to be too many - the power law explain the scaling at the point of transition from one system to another - like in the self organised criticality sand pile model where the power law shows movements of sand or avalanches on all scales. I dont think that rank size although it is a power law is quite the same - in that we dont have connections within the set of cities although if we did then such a set of connections may ultimately be consistent with a power law. I suppose that what we might be saying in rank size is that the biggest cities have the most connections and that population size is simply an index of their connectivity - number of connections - so if you look at the degree distributions of nodes in a network this is the same as city population Mike At 09:12 AM 2/19/2003 -0500, you wrote: >Mike -- >It's interesting to note that the Census 2000 data shows a total US >urbanized area (densely populated areas of over 50,000) of a bit more >than 71,000 sq. miles (~2% of the US total). This area holds 69% of the >total US population. > >Anticipating possible questions for tomorrow -- >(1) Is there a tautology in Zipf's comparison of population size with >population rank? >(2) In comparing regions (E.Coast, Middle, G.Plains & Mountains, >W.Coast), I kept constant the ranks using the data for the entire US. If >I rerank the urban areas with each region having a no. 1 city, it would >change the exponent somewhat, although not the relative order. Is there >a correct way? >(3) If as Barabasi contends, a power law is nature's signature for a >phase transition, what kind of transition are we talking about with >Zipf's law? >Tom > >-----Original Message----- >From: mike batty [mailto:mbatty@geog.ucl.ac.uk] >Sent: Tuesday, February 18, 2003 4:41 PM >To: Tom Wagner >Subject: Re: Fw: Feb. 20 Seminar on Zipf's Law in Urban Studies > >basically I think the small worlds stuff is suspect too. I dont think >that >networks are clustered at the local level and random at the higher >level. >They may be if one dont understand the higher level but I think there >should be structure on all scales. > >Mike > >At 03:57 PM 2/18/2003 -0500, you wrote: > >Mike: > >Yes, I haven't seen these books either. I guess the Morowitz book came >out > >in November and the Strogatz book is out this month. > >This new Watts book is kind of fun. After devoting a whole chapter to >graph > >theory in "Small Worlds", in "6 Degrees" he declares "as sophisticated >as > >the theory of random graphs is, almost everything we know about real > >networks...suggests they are not random." Clearly, he's upset that >Barabesi > >scooped him with his own data and got his book out earlier. > > > >I'm not a big fan of the "small worlds" concept. During the Great Leap > >Forward in China in 1958-60, it is said that 30-40 million people, >mostly > >young people and old people, died of starvation (1% of the world >population > >at the time) and the world knew nothing about it (still doesn't). What >kind > >of a "small world" is that? I think older Chinese carry a secret >"guilt" > >associated with that tragedy that they don't want to talk about. Tom > >----- Original Message ----- > >From: "mike batty" <mbatty@geog.ucl.ac.uk> > >To: "Tom Wagner" <twagner127363MI@comcast.net> > >Sent: Tuesday, February 18, 2003 11:57 AM > >Subject: Re: Fw: Feb. 20 Seminar on Zipf's Law in Urban Studies > > > > > > > tom can you post the details of the seminars again to dan brown and >the > > > sluce group who were interested > > > > > > Mike > > > > > > also there are a couple of other new books that I havent seen yet on > > > networks and complexity > > > > > > these are > > > > > > > > > Sync: The Emerging Science of Spontaneous Order > > > by Steven Strogatz > > > > > > > ><http://www.amazon.com/exec/obidos/ASIN/0786868449/ref%3Dmk%5Fpb%5Faqa/>103-5>642948-7834215>http://www.amazon.com/exec/obidos/ASIN/0786868449/ ref%3D >mk%5F > >pb%5Faqa/103-5642948-7834215 > > > > > > and > > > > > > The Emergence of Everything: How the World Became Complex > > > by Harold J. Morowitz > > > > > > > ><http://www.amazon.com/exec/obidos/tg/detail/-/019513513X/ref=pd_sim_bo>oks_2>/103-5642948-7834215?v=glance&s=books>http://www.amazon.com/exec/ obidos >/tg/d > >etail/-/019513513X/ref=pd_sim_books_2/103-5642948-7834215?v=glance&s=bo >oks > > > > > > > > > Mike > > > > > > > > > At 11:48 AM 2/18/2003 -0500, you wrote: > > > >Yichun -- > > > >Here's the Announcement for the 1st seminar for Thursday at 4. >This 1st > > > >seminar will provide a background for talking about Zipf's Law: >what is > >it > > > >and how different investigators sought to explain it. > > > >We need to announce the 2nd seminar at EMU a week from Thursday >(27th > >Feb). > > > >John and I talked briefly with Mike and I think we agreed that this > >seminar > > > >should include a discussion of how urban systems network together. >I've > > > >suggested a title of "How do cities talk to each other and what do >they > > > >say?" This seminar could also include a discussion of modeling and >our > > > >propose work with "desakota" in China. > > > >Can you give me the exact room number where we will meet? Does the > >program > > > >fit with your ideas? > > > >Tom > > > > > > > >----- Original Message ----- > > > >From: "Scott J. Swan" <swanner@umich.edu> > > > >To: <gis.discuss@umich.edu> > > > >Sent: Tuesday, February 18, 2003 9:26 AM > > > >Subject: Feb. 20 Seminar on Zipf's Law in Urban Studies > > > > > > > > > > > > > ---------- Forwarded message ---------- > > > > > Date: Mon, 17 Feb 2003 19:01:40 -0500 (EST) > > > > > From: Karl Eric Longstreth <karleric@umich.edu> > > > > > Subject: Feb. 20 Seminar on Zipf's Law in Urban Studies > > > > > > > > > > > > > > > Please share this seminar announcement with colleagues and >students > >who > > > > > may have an interest. Thank you. > > > > > > > > > > Thursday February 20 at 4:00 pm, International Institute, Room >1644 > >School > > > > > of Social Work Building. > > > > > > > > > > "Who was George Kingsley Zipf?". > > > > > > > > > > John Nystuen and Tom Wagner will lead a discussion about one of >the > >most > > > > > remarkable empirical relationships in economic geography, Zipf's >Law, > >and > > > > > its applications in disciplines today. The discussants will >include > > > > > Michael Batty, Director of the Center for Advanced Spatial >Analysis, > > > > > University College London (http://www.casa.ucl.ac.uk) and Yichun >Xie, > > > > > Director of the Institute for Geospatial Research and Education >at EMU > > > > > (http://ceita.emich.edu/). > > > > > > > > > > Zipf's Law (the rank-size rule) - a relationship so exact that > >economist > > > > > Paul Krugman calls it "spooky" - is currently receiving >attention in > > > > > research ranging from demography to urban economics to physics >to the > > > > > Internet, with over 500 references in the last decade alone. > > > > > > > > > > Tom Wagner is a remote sensing researcher and Senior Scientist >at > >EMU's > > > > > IGRE and a Visiting Scientist at UM's China Data Center. John >Nystuen > >is > > > > > UM Prof. Emeritus of Geography and Planning Education and >founded the > >GIS > > > > > Laboratory in the Urban and Environmental Technology Program >(UTEP). > > > > > > > > > > This event is a the first of a joint EMU/UM Seminar Series: "An > >inquiry > > > > > into the reemergence of Zipf's Law and urban network analysis". > > > > > > > > > > > > > > > Karl Longstreth > > > > > Map Library, University Library & > > > > > China Data Center, International Institute > > > > > University of Michigan > > > > > 920 North University Street > > > > > Ann Arbor MI 48109-1205 USA > > > > > > > > > > karleric@umich.edu 734.647.0646 fax 734.763.5080 > > > > > > > > > > -- > > > > > > > > > > UM-GIS Website: http://gis.umich.edu > > > > > > > > > > [To subscribe (or unsubscribe) to the UM SA/GIS email list, >email > > > > > TO: gis.discuss-request@umich.edu, SUBJ: subscribe (or >unsubscribe)] > > > > > > > > > > > ___________________________________________ > > > I am in Ann Arbor Michigan for the next two months > > > at CEITA (EMU) and U Michigan > > > ___________________________________________ > > > Michael Batty > > > Director, CASA, University College London > > > 1-19 Torrington Place, London WC1E 6BT, UK > > > ___________________________________________ > > > See the CASA web site http://www.casa.ucl.ac.uk/ > > > > >___________________________________________ >I am in Ann Arbor Michigan for the next two months >at CEITA (EMU) and U Michigan >___________________________________________ >Michael Batty >Director, CASA, University College London >1-19 Torrington Place, London WC1E 6BT, UK >___________________________________________ >See the CASA web site http://www.casa.ucl.ac.uk/ ___________________________________________ I am in Ann Arbor Michigan for the next two months at CEITA (EMU) and U Michigan ___________________________________________ Michael Batty Director, CASA, University College London 1-19 Torrington Place, London WC1E 6BT, UK ___________________________________________ See the CASA web site http://www.casa.ucl.ac.uk/ UrbanClusters.doc