El punto de partida para el escalamiento urbano es similar

al punto de partida para el escalamiento metabólico.

En ambos casos preguntamos acerca de cómo las propiedades

de algo dependen de su tamaño.

En el caso del escalamiento urbano

el tamaño de interés es su población

y veremos distintas propiedades.

salarios, PIB, longitud de los caminos,

cantidad de electricidad utilizada, entre otros.

En este video, sólo quiero tomar una visión empírica de esto

es decir, lo que los datos sugieren en relación a esta pregunta.

Esto lo haré enseñándoles varios gráficos

Y como es usual, los gráficos irán acompañados de sus referencias acá abajo.

Este es es primero,

Este está mostrando la población en este eje inferior,

Y este eje es el salario total, esto es para ciudades en EEUU

Y en este contexto, la ciudad es considerada

como un área estadística metropolitana.

Por lo que puede que no sea exactamente igual que los límites formales de una ciudad,

a menudo puede incluir suburbios.

Si tienes dos ciudades colindantes

estás serán consideradas como parte de la misma área metropolitana.

Por lo tanto, para cada evento, estos son los datos.

Creo que tenemos alrededor de 300 puntos en este caso.

Y esto está en escala logarítmica (log(e)) en ambos ejes.

Y podemos ver que hay claramente una tendencia lineal entre ambas variables.

Podmeos calcular la pendiente,

que es lo que conocemos como el exponente de una regla de poder (power-law).

Y esto nos da un valor de Beta igual a 1.12

Si se dan cuenta, esto es mayor que 1

Entonces, ¿Cuál es el significado de esto?

si tenemos una ciudad pequeña

y la comparamos con una ciudad que la dobla en tamaño

nos pdemos preguntar, bueno ¿cómo serían los salarios?

los salarios totales, la cantidad total de dinero,

en las ciudades comparadas.

Y podrías estar pensando, bueno

la ciudad que tiene el doble de tamaño poblacional

debería tener como máximo el doble de salario total.

Lo que dicen los datos, es de hecho más que esto,

esto es más rápido que lineal, es super lineal.

Por lo tanto, si tenemos el doble de población en una ciudad,

en promedio de acuerdo a esta tendencia,

podrías esperar más del doble del salario total.

It would go by to do though the 1.12 not to do the 1

Alright so, that’s sort of interesting I think

and others have thought.

Because we might expect that it would be linear

doubling population with double wages,

but that’s definitely now what we see

of course that can’t help but notice that

there is an awful a lot fuzz around this line.

so there’s a very clear trend

that’s pretty hard to deny

but it’s not an exact relationship like a physical law might be

there is even more scattered I think

than for most of the metabolic scaling plots.

So there’s a lot of variation among cities as well.

And there is a clear trend.

And as we talked about in metabolic scaling

the trend can be interesting

and the deviations from the trend can be interesting

and those two statements don’t need

to be in competition to each other.

Both can be interesting.

In this case I think both are interesting.

Ok, let’s look at a few other results.

And there are lots of lots of data sets like this

But I’ll show you a few more.

Alright, again we have population on the horizontal axis.

A log-log scale

This is log not a wages but it’s GDP, gross domestic product

And these are for Chinese cities

so this is measured in million Yuan.

And again we can see there is a very clear trend.

It’s certainly not a flat line. Beta is 1.12

But for this data set there is even more

variation about that trend.

But again there definitely is a trend line.

This plot here is for Germany, German cities

Again this is a log of GDP,

gross domestic product measured in Euros,

very clearly trend here. Beta in this case is 1.10

and some variations about the trend

but not as much as for China.

In both cases though this exponent is larger than 1

This is statistically significantly so indicating that

log of GDP or GDP grows faster than linearly with population.

So again in both these cases if you double population,

you more than double the GDP of the city

Alright, let’s look a one more this sort of plots

So here this is now the total road miles in the city

How many roads are there measured in miles

And again this is a log-log plot, population here

and in this case the exponent is 0.85

So that means the growth is slower than linear.

If you double the size of a population on average,

you don’t double the length the roads

It’s actually less than double it, through to the 0.85

So let me also explain what these lines are

This line here, this is the darkest line is a line with a slope of 1

And what this is showing is that

this data themselves are clearly

there is trend clearly less than 1

These two here, one of these lines is a fit line with that data.

The other is a line from the theory.

So it’s sort of theoretical fit

that I’ll explain in a subsequent video.

So note again here we see a quantity road miles

that’s not scaling linearly.

But in this case the exponent is less than 1

And here’s one more GDP plot

This is for US cities

again we’re seeing faster than linear growth.

This black line would indicate linear growth that’s a slope of 1

The measured data, the measured exponent is 1.13

That’s faster than linear.

And there are actually two lines here.

One is the measured exponent.

The other is that predicted by theory.

So there’s an urban scaling group at the Santa Fe Institute

lead by Luis Bettencourt, Geoffrey West and many others.

They produced a series of papers and are continuing to do so

with a lots of lots of plots like this.

So there are many, a lot more data we can look at

but for this video the main observation is that

there is evidence of scaling,

some sort of linear relationship on a log-log plot.

In some cases less than linear.

In some cases more than linear.

And there is a fair amount of fuzz around this,

It’s not an exact relationship, it’s a trend.

But there is still a fair amount of variation around this trend.