geoffrey west

geoffrey west.png

first vague intro.. Richard had him at www conference..

adding page via this from luke – podcast w Sam Harris – from cells to cities

Geoffrey starts at 6 min

11 min – what got me.. physics science of 19th 20th cent.. bio science of 21st cent.. implicit was.. we know all physics we need to know.. no point going further.. that really got me.. i agreed with first part.. bio significantly important.. nevertheless.. i arrogantly and out of ignorance.. said.. yeah.. but won’t be a real science.. in terms of being quantitative.. predictive..

13 min – so big question.. to what extent can bio be mathematized..

it was that emotional reaction that got me to thinking about this seriously.. how to take tools of physics to bio..

14 min – not just what is mech of aging and why do we die.. where does 100 yrs come from for lifespan… so .. if bio was serious science.. should be able to pick up text and find these things out.. what i found out.. this was not a very well developed area.. no one seems to have asked the question in that form

15 min – so.. how would you show.. that 100 yrs is expected yrs.. so have to think about .. what is going wrong.. what wears out..

16 min – what keeps you alive: metabolism.. so i read about it.. and learned about amazing scaling laws.. ie: metabolic rate needed per/sec/hr to stay alive per size of animal.. i learned this was extremely simple/regular

18 min – city as pseudo org

19 min – phenom of scaling.. how do the characteristics of say mammals.. scale as you change size of mammal.. scaling asks the question.. metabolic rate.. size of heart.. how long live.. that’s just the concept of scaling

20 min – all characteristics scale in a regular/mathematical fashion with growing size of mammal

22 min – underlying this extraordinary complexity (metabolism most complex process).. it scales in this very simple way

so same thing.. cities.. express similar regular/systematic/math scaling.. understanding bio scaling.. details are diff in very important/powerful way.. but quite similar..

23 min – ubiquitous behavior that says despite daunting complexity.. a simplicity that can be expressed graphically/mathematically

24 min – this scaling is non linear.. important..

25 min – 25% savings on every doubling.. energy needed to support individual cell is systematically smaller the bigger you are..

this economy of scale..

27 min – ie: take an elephant.. keep scaling down.. end up with a mouse.. 80-90% level is an elephant..

28 min – rules aren’t like laws of physics.. which we think of as being precise.. not true in bio.. these are laws that we call – cross grain – only true to 80-90% accuracy..

29 min – so can predict from these laws.. the following – how long to live et al.. but only to 80-90% accuracy.. and if asked about prediction of specific mouse/elephant

30 min – get bigger live longer.. because metab slows down..same scaling laws apply to trees/plants.. every time double size of tree. .it uses only 75% more energy

way trunk tree scales is identical to way our aorta scales..

32 min – the analog to the tree inside us is our circulatory system.. analog to aorta is the trunk of the tree..

33 min – the origin of these scaling laws.. what’s common.. they have all evolved to be hierarchical branching network systems..

math/physics are what is being reflected in the scaling laws

34 min – not just the networks.. ie: 1\ space filling (terminal units are capillaries that feed cells.. go everywhere..)

35 min – sam: fractal – piqued in 80s..

36 min – 2\ optimizes system (circulatory system we – all mammals – have minimizes amount of energy to pump blood so that we can max amount of energy devoted to darwinian fitness – having sex and rearing children)

37 min – structure has to be.. so that if we changed it in any way.. that would increase amount of energy your heart has to do..

38 min – idea was.. in order to do this.. need generic principles that transcend and certain assumptions.. one was.. by continuous feedback process.. tend toward minimizing of energy needed.. so can max amount of energy we put into our genes going forward.. that was the hypothesis

40 min – have to remember .. that’s always the case when look at one individual component.. have to remember that is interconnected with everything else.. it’s a systemic problem.. optimization not only taken at individual level.. but at the systemic level..

systemic ness

41 min – all of this is one huge system.. and it’s the systemic optimization rather than the local optimization

42 min – main point – apply underlying generic principles.. learn optimal system is fractal like.. self-similar..

theory is that systems should be fractal in order to optimize.. and fill all of space

43 min – i use the word fractal like.. the things coming out of theory is not precise.. deviates in predictable way

44 min – fractal regularity seems to permeate nature.. relates to.. something is being optimized..

45 min – sam: size of lungs – football.. circulatory – size of tennis court

46 min – spiritual.. inside you is this unbelievable length of tubing.. but that it’s very systematic .. obeying very simple math rules.. power laws

the number 4.. is the number that permeates all these scaling laws.. always 1/4 comes in ..comes out of theory based on math theory of network design..

48 min – 4 comes from – actually 3 + 1.. meaning.. 3: we live in 3 dimensions (up, down, sideways) 1: reflection of fractality of systems.. have peculiar sense of dimensions.. fully fractal system adds extra if we lived in 8 dimensions.. everything would be dominated by 1/9 power

49 min – sam: coch curve – on adding fractal dimension rabbit hole – equilateral triangle divided on each side by smaller 1/3 size.. develop snowflake image.. size of curve is a fully self-contained object.. infinite length of circumference..

50 min – richardson (time of ww1) interested in length of boundaries between countries.. got hold of lots of maps.. discovered.. between spain and portugal.. got completely diff answers from diff maps.. mysterious.. discovered same phenom for many countries.. he knew what was going on but didn’t formalize it

51 min – mandelbort formalized this later – fractal – when people make these measurements have to have ruler with certain scale.. problem is.. if you measure boundary (squiggly line) put ruler on it where resolution is 10 km.. then anything below 10 km you miss.. when line could be squiggly around.. so others could get 25 km

53 min – this followed very regular pattern.. length vs resolution.. that’s where the connection was to fractals.. boundaries are approximately self similar

54 min – sam: mystery why this wasn’t discovered before mandelbrot.. staring all in face

55 min – i think it was the hegemony of euclidian geometry.. so powerful.. the development of physics end of 17th cent.. this .. simple idea of euclidian geometry.. this idea that a length is a length.. the idea that it would depend on the resolution of your ruler.. i don’t think entered anyone’s mind.. until this practical problem of richardson..

56 min – could there be anything else other than euclidian geometry kind of thinking.. richardson’s extraordinary insight/persistence in tracking down and systematizing this problem..

57 min – one of my criticism of benoit.. but he didn’t seem to care about why they were there.. what’s the physics of fractals.. i would like to think my work is explaining why

58 min – goes into the why.. highly mathematical

sam: but math was being forced by physical constraing.. so thinking as a physicist.. what is forcing math to be what they are..

59 min – mandelbrot was interested in generic fractal about the space involved..i was interest in math that gives rise to dynamics..

1:00 – from this.. where does fractal like structure come from.. provides you with a theoretical.. mathematized framework for asking all kinds of questions.. ie: why do we age/die/sleep.. et al

1:01 – sam: life span and diff in dogs (life longer smaller they are)

1:02 – scaling law increasing with this increasing 1/4.. typically between species.. not intra species.. you could ask about dogs..

*they did not evolve by natural selection.. we started training them..

we evolved them to be small and cuddly.. run fast – greyhound.. go down holes.. et al.. that means various things are given up.. so not easy to ask about how things scale w/in dogs

*science of people ness

1:06 – life span x heart rate should be same for everybody.. have same number of heart beats in life.. that number is about 1.5 bn

1:07 – used (mid 19th cent) to be lifespan of 30-40 yrs.. fits that number of 1.5 bn.. since then.. since industrial revolution.. life spans expanding..  now .. over 2.5 bn heartbeats.. reflection of urbanization and extraordinary social/econ dynamics we brought to the planet.. begins with intro of running water and sewer lines.. had profound effect on longevity

1:10 – coupled with that .. cities/govts provide access to health (begin of 19th cent) .. paying much more attention to disease.. leading up to development of antibiotics.. led to this fantastic increase of almost a factor of 2.. from 40 to 80 yrs..

1:11 – sam: what about people like aubrey degrey..

my research suggests the opposite.. you cannot start thinking about extending lifespan w/o understanding why we live to the age we live..  that’s what started me on this whole quest.. to get a mechanistic theory of why we age/die.. why lifespan and what are the parameters..  what this theory can calculate.. the max lifespan

1:13 – very system that’s keeping us alive.. has wear/tear forces.. ie: continual damage by blood flowing thru.. means a scarping.. that damages them.. creates entropy.. caused cellular damage.. so you can calculate that.. determine max lifespan..

1:14 – tells you parameters of lifespan.. has to do with metabolism and the physics of materials.. that do with wear and tear at molecular level.. also .. crucial.. 2ndary.. process of repair.. of damage.. where does that repair come from.. also from metabolism..

1:16 – so can ask.. how to increase lifespan.. 1\reduce damage 2\increase repair.. so one way is to reduce metabolic rate.. by 1\ eat less.. caloric restriction had led to increase in lifespan (w mice – doesn’t work in monkeys)

1:17 – nothing conclusive.. wonderful people like aubrey are working on this

1:18 – i went for several years eating one meal a day.. because i have some mysterious intolerance to most foods.. makes it difficult to work.. to i’d eat evenings so i could work during day..

1:19 – lost so much weight – 30 lbs.. i decided forget this.. i’m going to start enjoying food more.. and feel lousy.. and if i do.. die early or whatever.. learned to work while feeling lousy..


1:20 – the theory does predict this – someone needs to repeat the monkey experiment.. but the other thing it predicts.. another way to decrease metabolic rate: lower its temperature.. all other orgs can do this but us

thinking m wesch and saying how important sweat is as a coolant

1:23 – do we want to live long as couch potatoes..  or live life full (on reducing metabolism/heat)

so the other way to increase.. is to improve repair mechs.. genetic intervention.. many people thinking about

1:24 – other unintended consequences.. may be putting so much toward repair that you are tired all the time.. so issue of lifestyle again..

1:25 – apply these ideas to cancer.. many tumors triggered by damage from metabolism..

cancer ness

roots of healing ness

1:26 – if mice get many more tumors than we do.. and all these experiments we’re doing on mice.. we need to understand that before we extrapolate findings from mice to people..

1:27 – sam: concept of emergence almost always put forward as an embarrassment to reductionism.. i’ve often been skeptical of what is being claimed here.. idea is that we’re urged to acknowledge .. we can’t reduce everything to physics.. ie: if mind is everything brain is doing.. might be no downward ness.. just many states of brain.. so can you think of phenom not reducible..

1:29 – this is of course an ongoing discussion .. esp dealing with mind/brain.. i’ve come more along your lines .. less along lines that something completely new emerges..  let’s take something simpler than brain/mind.. ie: city

1:30 – the idea of emergence where i do like the concept.. city is not sum of all people in it.. something much more than that.. useful as concept to think of it as a collective phenom.. w local/individuality.. it is derivative of all these components.. i would say that the inbetween road i take.. yes.. in principle.. could say city is sum of all variables.. integration of all that.. each could be pinpointed as variable.. so come to this concept .. which is concept inherently of complexity/complex systems.. yes .. made of constituents.. but if start delineating.. infinite.. so can’t come to terms… so not soluble way of deriving a city

1:32 – sam: imagine 2 stones .. one spherical one cubicle.. rolling down hill.. isn’t this just individual atoms with the plane..

1:34 – i would even say.. it’s a useless description.. doesn’t help .. ie: write down every equation for each stone.. no way in finite time to determine motion.. so a moot question.. much more useful to have this concept of the collective.. of the stone..

1:35 – sam: concept of emergence often sold to us as a downward causation issue.. could you dispel that from me..

i do like concept of emergence.. very useful.. part of this is semantic.. depends what you call constituents.. one has to be careful.. true of brain as well.. almost no one talks about fact that all neurons has to be supported by energy system.. has to be metabolized.. integrated with neurosystem.. with system feeding it.. highly integrated in space/time..

1:37 – so .. the brain in our mind is in that sense.. the emergent phenom coming from not just neurons.. white matter.. et al.. but also of support system and whole infrastructure giving rise to this.. 

so one has to be careful about using this language.. i don’t use it in a technical way.. i only use it in descriptive way.. very similar with word complexity.. need to be careful about taking too seriously..

sam: in the spirit of confirmation bias – i like you saying a cop out..

1:39 – sam: so why do cities matter

1:40 – this is where my passion is at the moment.. really pleased you brought up connection between cities and brains.. one thing that distinguishes cities from organisms.. cities integrate both the infrastructure (roads… water lines).. but have this other piece which really isn’t usually a part of an organism.. the social network structure that is implicit in cities.. interacting with each other.. forming groups..  led to socioeconomic system .. standard of living.. privilege.. that is something that doesn’t exist in biology


the structure.. very similar in math.. fractal like.. but also have another part quite diff.. ie: instead of quantity of scale.. opposite.. the bigger you are the more per capita.. we have this sort of positive feed back mech.. that dynamic.. formalize with commerce/business/unis.. that phenom of positive feedback is something we discovered only recently.. esp when evolved from being hunter gatherers to cities.. goes to our huge success.. let do innovation..

? – success..? for who.. ? not all of us.. and that’s messing with us

sam: nonlinearity goes both ways.. also get more crime.. et al

1:44 – cities are what we invented for facilitating that interaction.. all from this positive feedback mech..  but also get access to downside

rather broken feedback

1:45 – everything from wages.. to number of roads.. all scale same.. an extraordinary universality.. mimicking that of organisms..

1:46 – we’re living in an expo expanding socioecon.. ie: china .. building 2-300 new cities.. mn each.. an astonishing rate.. that means creating urban structure of us in next few years.. affect on pressure on rest of us.. to energy/resources/water.. stress on social fabric

1:48 – sam: you make point that cities are greener than small towns

15% savings .. but that’s an econ of scale in terms of infra.. but on socioeconomic side.. 15% increase of everything.. wages/aides/roads/unis..  every time double size of city

1:49 – so increase size less and 15% less infra.. so less carbon.. so ny.. one of greenist cities in us

1:50 – sam: you paint the imperative of innovation.. or catastrophe

1:51 – growth in biology.. in the theory you can understand growth.. predicts growth curve.. grow quickly and then stop growing.. applies to any organism.. so theory tells you how to rescale any organsim..

1:52 – but one of most important things that comes out of this.. reason you stop growing.. related to sub linear nature.. organisms grow to stable.. bigger it is .. slower pace of life.. ultimately dies.. all this comes out of generic network theory

1:53 – in cities.. instead of sub linear.. we have super linear – city can grow indefinitely

1:54 – other thing w super linear.. pace of life increases..

? – science of people.. but is that natural

1:55 – except built into it a fatal flaw.. finite time singularity.. in some finite time.. whatever metric is you’re looking at.. ie: gdp, # of restaurants, # of aides.. will become infinite.. so will collapse.. lead to its death

1:56 – question is how to get out of it and this is where innovation comes in.. because these are all embedded in paradigms.. universal/cultural/socioecon implication.. shift resets clock.. so way avoid stagnation and collapse.. somewhere before singularity.. reach a major innovation.. to reset clock and reinvent yourself

1:58 – so a sort of theorem – if you demand continuous open ending growth.. then have to have continuous innovation cycles.. catch: not only pace of life speeding up.. but time between innovations shorter and shorter.. so need accelerating innovation

like everyday.. 24/7 from 7 bn plus.. a nother way – but on things that matter..

ie: hlb via 2 convos that io dance.. as the day..[aka: not part\ial.. for (blank)’s sake…]..  a nother way

so something quite dramatic has to change for us to avoid this.. the mantra.. economists/others.. all the problems we face.. don’t worry.. because going to innovate way out of them.. those innovations are simply postponing the big problem.. so ..

how do we get out of this..

2:00 – mostly when think of innovation.. think of physical/tech terms.. maybe

we need to rethink what we mean by paradigm shift

and growth.. maybe start introducing real metrics for quality of life.. happiness.. contentment.. maybe we should take that quite seriously .. associate with tradition of innovation as a tech innovation rather than cultural/social innovation..

ie: eudaimoniative surplus

underlying this is dynamic of social network.. continuous positive feedback.. that is part of who we are.. and that we cannot change and don’t want to change.. but

maybe we could have a cultural shift where that gets channeled into a diff way of thinking/dealing with external reality.. maybe that’s a way out.. that’s huge.. truly revolutionary..

ie: a nother way

2:02 – i don’t know if it’s virtual or just a way of being.. with the kinds of desires we have

sam: actually simpler lives

a nother way via 2 convos

yeah because part of the dynamic we have is greed.. we want to have more than we need.. that treadmill affect.. can we channel some of that into social/cultural phenom and still have growth in that .. but a vibrant society.. w/o need for continuous/mindless growth.. that has built in it potentially fatal flaws..

eagle and condor ness..

i haven’t thought thru this carefully.. because it’s got to be a huge shift..

chomsky serious things law

2:04 – trump phenom has made me rethink it.. he implies a paradigm shift.. one i don’t like..

2:06 – so maybe we could do this paradigm shift .. positively.. not only linked to material well-being..

2:07 – sam: don’t think i’ve every seen someone find such a silver lining

is there a way to have our cake and eat it too

sam: sustainable future is some hybrid..

eagle and condor ness..

that’s the challenge.. can we do that

yes please.. let’s try this

ie: hlb via 2 convos that io dance.. as the day..[aka: not part\ial.. for (blank)’s sake…]..  a nother way

sam: i think you and i can.. but i don’t know about 7 bn people

dang.. has to be all of us.. or it won’t work..


2017 book – scale

Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies


tedglobal 2011

2 min – there’s an urgent need for scientific theory of cities

3 min – means.. quantifiable.. relying on underlying generic principles that can be put into a predictive framework..

4 min – why do all companies die.. and cities don’t

5 min – main reason life is so robust.. scalability.. including us..

jo freeman ness

7 min – all diff.. doing own thing.. but fall onto same line.. slope is sublinear.. 75%.. which means if you double size only need 3/4 energy.. bigger you are less energy per capita

8 min – the reason for this.. is because of networks.. all of life is controlled by networks.. if you take this idea of networks and apply universal/mathematizable principles.. all of these scalings/strengths follow..

9 min – systematically.. the pace of life decreases as you get bigger.. heart rates slower, live longer.. the question is.. is any of this true for cities/companies

the most important network of cities is you.. cities are just a physical manifestation of our interactions and the clustering/grouping of individuals..

so let’s facil that

ie: hlb via 2 convos that io dance.. as the day..[aka: not part\ial.. for (blank)’s sake…]..  a nother way

10 min – an integrated system that has evolved despite all the planning and so on

11 min – graphs – wages as a function of supply..  supercreatives..

when throw in economy/money ness.. ie: wages.. opposite of bio growth.. the bigger you are .. the more you have per capita.. creativity/crime/aids/patents/gdp/flu

13 min – the universality is us.. it is our interactions.. unlike biology.. you have economy of scale..bigger you are.. increase pace

14 min – the catch is.. that this system is destined to collapse.. as we approach collapse.. a major innovation takes place..and we start over again.. catch to this.. you have to innovate faster and faster.. not only on treadmill going faster.. have to change treadmill faster

16 min – co’s scale sublinearly like bio.. they all bend over and die.. like you and me


fb share by Dave Gray


The great thing about scaling is that if you observe scaling (that is, how the various characteristics of a system change when you change its size) and if you see regularity over several orders of magnitude, that typically means that there are underlying generic principles, that it is not an accident. If you see that in a system, it is opening a window onto some underlying, let’s use the word, “universal principle”.

And so the question that drove the extension of this work was, “are cities and companies just extensions of biology?” ..They came out of biology. That’s where they came from.

well.. maybe cities.. kind of.. but companies didn’t come out of biology.. anything with measuring transactions.. which.. has me wondering why we need to measure us at scale.. rather than ie: listening deeper to what we need (maybe that’s the same thing.. numbers ness is just very suspect to me when it comes to humans/biology et al)

thinking a bunch here about entropy.. having just read human use of human beings.. et al

All of those results about scaling are derived. A quarter, four, emerges. And what is the four?  It turns out the four isn’t a four. The four is actually a “three plus one”, meaning it’s the dimensionality of the space we live in plus one, which is actually to do, loosely speaking, with the fractal nature of these networks, the fact that there’s a sub-similar property.

x d glasses ness and fractal thinking

organism as fractal

Life in some funny way is actually five dimensional. It’s three space, one time, and one kind of fractal. That’s five. So we’re kind of five dimensional creatures in some curious way, mathematically.

A whole bunch of questions can follow from this. One of the most important is growth. Understanding growth. How do we grow?  And why do we stop growing, for example?  Well, we can answer that. The theory answers that. And it’s quite powerful, and it explains why it is we have this so-called sigmoidal growth where you grow quickly and then you stop. And it explains why that is and it predicts when you stop, and it predicts the shape of that curve for an animal.

Here is this wonderful body of work that explains many things — some fundamental, some to do with very practical problems like understanding sleep, aging. The question is, can we take that over to other kinds of network systems. One of the obvious types of systems is a city. Another obvious one is a company

..we’re all scaled versions of one another…There’s kind of one mammal, and every other mammal, no matter what size it is and where it existed, is actually some well-defined mathematically scaled version of that one master mammal, so to speak. And that is kind of amazing.

Can we understand them as scientists? The prevailing way of investigating them is social sciences and economics  — which have primarily less to do with generic principles and more to do with case studies and narrative (which is of course, very important). But the question is, can we complement them and make a science of cities, so to speak, and a science of corporations?

i think once you bring money/rules in.. you no longer have the authentic people.. ie: via Carol.. like you’re studying a whale in a zoo rather than in the wild.. science of people in schools ness

The first result that we actually got was with my German colleagues, Dirk Helbing, and his then student, Christian Kuhnert, who then worked with me. One of the first results was a very simple one —the number of gas stations as a function of city size in European cities.

not us.. ie: cars.. are destroying us.. taking over spaces.. taking over clean air.. taking us away from community.. (like in Johann’s lost connection – amish ness) .. so if we became wiser and used them less.. how would that show in your scale model.. 1/4..?

The truly remarkable result was when we looked at quantities that I will call “socioeconomic”. That is, quantities that have no analog in biology. These are quantities, phenomena that did not exist until about 10,000 years ago when men and women started talking to one another and working together and forming serious communities leading to what we now call cities, i.e. things like *wages, the number of educational institutions, the number of patents produced, et cetera. Things that have no analog in biology, things we invented.

*things (wages, ed, patents) i’d say that aren’t us.. things that are bad rna copies of cancerous us.. and.. we’re using those things to study us..?

One of the bad things about open-ended growth, growing faster than exponentially, is that open-ended growth eventually leads to collapse. It leads to collapse mathematically because of something called finite times singularity. You hit something that’s called a singularity, which is a technical term, and it turns out as you approach this singularity, the system, if it reaches it, will collapse.

How do you avoid that? Well, how have we avoided it? We’ve avoided it by innovation. By making a major innovation that so to speak, resets the clock and you can kind of start over again with new boundary conditions. We’ve done that by making major discoveries or inventions, like we discover iron, we discover coal. Or we invent computers, or we invent IT. But it has to be something that really changes the cultural and economic paradigm. It kind of resets the clock and we start over again.

i’d suggest those were cycles.. not do overs.. let’s try a real do over..

Theory says, sure, you can get out of collapse by innovating, but you have to innovate faster and faster.

well – faster and slower..  which would happen with the energy from 7 bn alive people.. everyday.. begs we do this first

This leads then to all kinds of questions about global sustainability and how can you construct a conceptual framework that gives rise to having wealth creation, innovation, this kind of quality and standard of life, wealth production, and yet, not grow in such a way that you are probing the singularity and collapsing. That’s the challenge. That’s certainly something that we have to face.

ie: hlb via 2 convos that io dance.. as the day..[aka: not part\ial.. for (blank)’s sake…]..  a nother way

The picture emerges. Companies are more like organisms. They grow and asymptote. Cities are open ended.

i’d say the other way around..

organism as fractal

The great thing about cities, the thing that is amazing about cities is that as they grow, so to speak, their dimensionality increases.


more fb shares via Dave Gray – to Jon Husband – who was talking about reading scale

His ideas were very influential on The Connected Company. His research is available online. I don’t know if you need the book.

with note from Dave Snowden

 I (and others) are not sure that the existence of assemblage type identities in modern society doesn’t change the models


find/follow Geoffrey:

This work, begun at the Institute, has received much attention in both the scientific and popular press, and provides a framework for quantitative understanding of problems ranging from fundamental issues in biology (such as cell size, growth, metabolic rate, DNA nucleotide substitution rates, and the structure and dynamics of ecosystems) to questions at the forefront of medical research (such as aging, sleep, and cancer). Among his current interests is the extension of these ideas to understand quantitatively the structure and dynamics of social organizations, such as cities and corporations, including the relationships between economies of scale, growth, innovation and wealth creation and their implications for long-term survivability and sustainability.

wikipedia small

Geoffrey Brian West (born c. 1940) is a British theoretical physicist, former president and distinguished professor of the Santa Fe Institute. He is one of the leading scientists working on a scientific model of cities. Among other things his work states that with the doubling of a city’s size, services per capita will generally increase by 15%.