Spanish subtitles

← Fractals08 02EmpiricalScaling01

Get Embed Code
4 Languages

Showing Revision 2 created 03/24/2017 by SIMON CASTILLO.

  1. Not Synced
    El punto de partida para el escalamiento urbano es similar
  2. Not Synced
    al punto de partida para el escalamiento metabólico.
  3. Not Synced
    En ambos casos preguntamos acerca de cómo las propiedades
  4. Not Synced
    de algo dependen de su tamaño.
  5. Not Synced
    En el caso del escalamiento urbano
  6. Not Synced
    el tamaño de interés es su población
  7. Not Synced
    y veremos distintas propiedades.
  8. Not Synced
    salarios, PIB, longitud de los caminos,
  9. Not Synced
    cantidad de electricidad utilizada, entre otros.
  10. Not Synced
    En este video, sólo quiero tomar una visión empírica de esto
  11. Not Synced
    es decir, lo que los datos sugieren en relación a esta pregunta.
  12. Not Synced
    Esto lo haré enseñándoles varios gráficos
  13. Not Synced
    Y como es usual, los gráficos irán acompañados de sus referencias acá abajo.
  14. Not Synced
    Este es es primero,
  15. Not Synced
    Este está mostrando la población en este eje inferior,
  16. Not Synced
    Y este eje es el salario total, esto es para ciudades en EEUU
  17. Not Synced
    Y en este contexto, la ciudad es considerada
  18. Not Synced
    como un área estadística metropolitana.
  19. Not Synced
    Por lo que puede que no sea exactamente igual que los límites formales de una ciudad,
  20. Not Synced
    a menudo puede incluir suburbios.
  21. Not Synced
    Si tienes dos ciudades colindantes
  22. Not Synced
    estás serán consideradas como parte de la misma área metropolitana.
  23. Not Synced
    Por lo tanto, para cada evento, estos son los datos.
  24. Not Synced
    Creo que tenemos alrededor de 300 puntos en este caso.
  25. Not Synced
    Y esto está en escala logarítmica (log(e)) en ambos ejes.
  26. Not Synced
    Y podemos ver que hay claramente una tendencia lineal entre ambas variables.
  27. Not Synced
    Podmeos calcular la pendiente,
  28. Not Synced
    que es lo que conocemos como el exponente de una regla de poder (power-law).
  29. Not Synced
    Y esto nos da un valor de Beta igual a 1.12
  30. Not Synced
    Si se dan cuenta, esto es mayor que 1
  31. Not Synced
    Entonces, ¿Cuál es el significado de esto?
  32. Not Synced
    si tenemos una ciudad pequeña
  33. Not Synced
    y la comparamos con una ciudad que la dobla en tamaño
  34. Not Synced
    nos pdemos preguntar, bueno ¿cómo serían los salarios?
  35. Not Synced
    los salarios totales, la cantidad total de dinero,
  36. Not Synced
    en las ciudades comparadas.
  37. Not Synced
    Y podrías estar pensando, bueno
  38. Not Synced
    la ciudad que tiene el doble de tamaño poblacional
  39. Not Synced
    debería tener como máximo el doble de salario total.
  40. Not Synced
    Lo que dicen los datos, es de hecho más que esto,
  41. Not Synced
    esto es más rápido que lineal, es super lineal.
  42. Not Synced
    Por lo tanto, si tenemos el doble de población en una ciudad,
  43. Not Synced
    en promedio de acuerdo a esta tendencia,
  44. Not Synced
    podrías esperar más del doble del salario total.
  45. Not Synced
    It would go by to do though the 1.12 not to do the 1
  46. Not Synced
    Alright so, that’s sort of interesting I think
  47. Not Synced
    and others have thought.
  48. Not Synced
    Because we might expect that it would be linear
  49. Not Synced
    doubling population with double wages,
  50. Not Synced
    but that’s definitely now what we see
  51. Not Synced
    of course that can’t help but notice that
  52. Not Synced
    there is an awful a lot fuzz around this line.
  53. Not Synced
    so there’s a very clear trend
  54. Not Synced
    that’s pretty hard to deny
  55. Not Synced
    but it’s not an exact relationship like a physical law might be
  56. Not Synced
    there is even more scattered I think
  57. Not Synced
    than for most of the metabolic scaling plots.
  58. Not Synced
    So there’s a lot of variation among cities as well.
  59. Not Synced
    And there is a clear trend.
  60. Not Synced
    And as we talked about in metabolic scaling
  61. Not Synced
    the trend can be interesting
  62. Not Synced
    and the deviations from the trend can be interesting
  63. Not Synced
    and those two statements don’t need
  64. Not Synced
    to be in competition to each other.
  65. Not Synced
    Both can be interesting.
  66. Not Synced
    In this case I think both are interesting.
  67. Not Synced
    Ok, let’s look at a few other results.
  68. Not Synced
    And there are lots of lots of data sets like this
  69. Not Synced
    But I’ll show you a few more.
  70. Not Synced
    Alright, again we have population on the horizontal axis.
  71. Not Synced
    A log-log scale
  72. Not Synced
    This is log not a wages but it’s GDP, gross domestic product
  73. Not Synced
    And these are for Chinese cities
  74. Not Synced
    so this is measured in million Yuan.
  75. Not Synced
    And again we can see there is a very clear trend.
  76. Not Synced
    It’s certainly not a flat line. Beta is 1.12
  77. Not Synced
    But for this data set there is even more
  78. Not Synced
    variation about that trend.
  79. Not Synced
    But again there definitely is a trend line.
  80. Not Synced
    This plot here is for Germany, German cities
  81. Not Synced
    Again this is a log of GDP,
  82. Not Synced
    gross domestic product measured in Euros,
  83. Not Synced
    very clearly trend here. Beta in this case is 1.10
  84. Not Synced
    and some variations about the trend
  85. Not Synced
    but not as much as for China.
  86. Not Synced
    In both cases though this exponent is larger than 1
  87. Not Synced
    This is statistically significantly so indicating that
  88. Not Synced
    log of GDP or GDP grows faster than linearly with population.
  89. Not Synced
    So again in both these cases if you double population,
  90. Not Synced
    you more than double the GDP of the city
  91. Not Synced
    Alright, let’s look a one more this sort of plots
  92. Not Synced
    So here this is now the total road miles in the city
  93. Not Synced
    How many roads are there measured in miles
  94. Not Synced
    And again this is a log-log plot, population here
  95. Not Synced
    and in this case the exponent is 0.85
  96. Not Synced
    So that means the growth is slower than linear.
  97. Not Synced
    If you double the size of a population on average,
  98. Not Synced
    you don’t double the length the roads
  99. Not Synced
    It’s actually less than double it, through to the 0.85
  100. Not Synced
    So let me also explain what these lines are
  101. Not Synced
    This line here, this is the darkest line is a line with a slope of 1
  102. Not Synced
    And what this is showing is that
  103. Not Synced
    this data themselves are clearly
  104. Not Synced
    there is trend clearly less than 1
  105. Not Synced
    These two here, one of these lines is a fit line with that data.
  106. Not Synced
    The other is a line from the theory.
  107. Not Synced
    So it’s sort of theoretical fit
  108. Not Synced
    that I’ll explain in a subsequent video.
  109. Not Synced
    So note again here we see a quantity road miles
  110. Not Synced
    that’s not scaling linearly.
  111. Not Synced
    But in this case the exponent is less than 1
  112. Not Synced
    And here’s one more GDP plot
  113. Not Synced
    This is for US cities
  114. Not Synced
    again we’re seeing faster than linear growth.
  115. Not Synced
    This black line would indicate linear growth that’s a slope of 1
  116. Not Synced
    The measured data, the measured exponent is 1.13
  117. Not Synced
    That’s faster than linear.
  118. Not Synced
    And there are actually two lines here.
  119. Not Synced
    One is the measured exponent.
  120. Not Synced
    The other is that predicted by theory.
  121. Not Synced
    So there’s an urban scaling group at the Santa Fe Institute
  122. Not Synced
    lead by Luis Bettencourt, Geoffrey West and many others.
  123. Not Synced
    They produced a series of papers and are continuing to do so
  124. Not Synced
    with a lots of lots of plots like this.
  125. Not Synced
    So there are many, a lot more data we can look at
  126. Not Synced
    but for this video the main observation is that
  127. Not Synced
    there is evidence of scaling,
  128. Not Synced
    some sort of linear relationship on a log-log plot.
  129. Not Synced
    In some cases less than linear.
  130. Not Synced
    In some cases more than linear.
  131. Not Synced
    And there is a fair amount of fuzz around this,
  132. Not Synced
    It’s not an exact relationship, it’s a trend.
  133. Not Synced
    But there is still a fair amount of variation around this trend.