1. Motivation

Last Friday was Donald Trump’s inauguration and, in case you’ve been living under a rock, a lot of people are talking about the size of the crowds. The salient points are that a New York Times story concluded that the crowds sizes of Trump’s inauguration were “about one third” that of Obama’s 2009 inauguration (citing reputed crowd specialist Keith Still); a claim that Trump’s Press Secretary directly and unequivocally disputed. Trump and (and more indirectly) Kellyanne Conway similarly disputed the claims.

Now, there are far better analyses about the claims, but I thought it would be a worthwhile excerciseOk, so maybe I have an "alternative" definition of "worthwhile excercise" to work out a quantification of the crowds in the NYT images in an evening. I mean, Spicer said “no-one has numbers” for the crowds, so let’s get him some.

2. Methodology

We’ll be using the national mall images from the NYT piece to extrapolate the crowd sizes, since we don’t have satelite images of the Trump inauguration yet (or atleast, that I know of). The lack of satelite imagery is a limitation because we now have to assume that the national mall is representative of the crowds outside the ticketed area.

To get an idea of the size of the crowds, I’ll be (1) isolating each section of the national mall (2) project the sections of the national mall on a flat plane and (3) classifying and counting pixels as containing people or not. We’ll be ignoring section H since Trump had tents put up. Lez go!

national mall diagram
crowds overlay

2.1. "That Trump photo was taken before the inauguration!"

It wasn’t. According to Jim Bourg, photographer for Reuters on the US Politics beat who assigned the photo to be taken, the photo was taken at 12:01:18 p.m on the inauguration day. If for some reason you don’t believe that, you can see a timelapse by NPR’s News Hour on the day of which clearly shows the crowds in the photo are representative of the peak.

3. Counting the Hoards

3.1. Isolating and Projecting Sections

Below, we can see each section isolated, and projected on to a flat plane to account for the perspective.

isolated projected

3.2. Classifying Pixels

Pixels were classified as containing people (magenta) or not containing people (blue). Obstructed views (by tents, tress, etc..) will be counted as not containing people in the minimum estimate (Min column, below) and as containing people in the maximum estimate (Max column, below).

pixel classification

3.3. Counting Pixels

To count the pixels, the magenta and blue masked images above were converted to black and white gifs (i.e. the image palletes only had white and black). You can download the dataset if you inexplicably want to follow along.

Below is the python code I used to quantify the black, people-containing pixels.

from PIL import Image

def get_black_px(path):
  im = Image.open(path)

  black = 0

  for pixel in im.getdata():

    if pixel == 0:
      black += 1

  return black

Without further ado:

Table 1. People-containing pixels in NYT National Mall images, by section.
Section # Trump 2017 (Min) Trump 2017 (Max) Obama 2009 (Min) Obama 2009 (Max)

A

35990

35990

47558

47558

B

54766

58703

68927

71243

C

82919

85078

76493

79812

D

48000

48000

52603

54854

E

72122

75391

116704

127388

F

41256

47958

125428

128004

G

1731

17805

125380

128004

3.4. Pixels to People

Before we can know how many people are in people-containing pixels, we need to measure the width and height of each section using the National Mall diagram, where each pixel is 2.96 metres wide, and 2.96 metres heigh. With that, the measurements are:

Table 2. Height and width of sections in National Mall diagram, in pixels and metres.
Section # Height (px) Heigh (m) Width (px) Width (m)

A

20.333

60.185

13.583

40.206

B

14.833

43.906

45.833

135.66

C

15.833

46.866

49.333

146.03

D

15.833

46.866

40.833

120.87

E

28.000

82.880

44.833

132.71

F

28.000

82.880

40.667

120.37

G

28.000

82.880

40.667

120.37

Now we’re going to figure out how much actual area each pixel will map to for each isolated section. We’ll calculate m2/px\text{m}^2/\text{px}:

section width (m)section width (px)=physical px w(mpx w) \dfrac{\text{section width (m)}}{\text{section width (px)}} = \text{physical px w}\left(\dfrac{\text{m}}{\text{px w}}\right) section height (m)section height (px)=physical px h(mpx h) \dfrac{\text{section height (m)}}{\text{section height (px)}} = \text{physical px h} \left(\dfrac{\text{m}}{\text{px h}}\right) physical px w(mpx w)×physical px h(mpx h)=physical px a(m2px) \text{physical px w} \left(\dfrac{\text{m}}{\text{px w}}\right) \times \text{physical px h} \left(\dfrac{\text{m}}{\text{px h}}\right) = \text{physical px a} \left(\dfrac{\text{m}^2}{\text{px}}\right)

This great chart from Prof. Keith Stills himself tells us how many people fit in one metre square before things get unsafe (you can read more on his site). If we assume that the (presumably significant) security team made sure that the crowd didn’t get unsafe, we can say there were about 2 to 3 people per square metre.

stills crowd density
ppl per m2

We can therefore go from m2/px\text{m}^2/\text{px} to people as follow:

physical px a(m2px)×people pixels(px)×2 or 3 people m2=#people \text{physical px a} \left(\dfrac{\text{m}^2}{\text{px}}\right) \times \text{people pixels} (\text{px}) \times \dfrac{2 \text{ or } 3\text{ people }}{\text{m}^2} = \# \text{people}

When we work it all out, we get this table:

Table 3. Calculating Number of People from Pixels
Section # Innauguration Height (m) Width (m) Height (px) Width (px) m2/px People Pixels Min # People Max # People
A (min) Trump 60.185 40.206 59 610 0.0672 35990 4837.056 7255.584
B (min) Trump 43.906 135.66 159 611 0.0613 57466 7045.3316 10567.9974
C (min) Trump 46.866 146.03 174 613 0.0642 82919 10646.7996 15970.1994
D (min) Trump 46.866 120.87 158 612 0.0586 48000 5625.6 8438.4
E (min) Trump 82.880 132.71 179 612 0.1004 72122 14482.0976 21723.1464
F (min) Trump 82.880 120.37 228 608 0.0720 41256 5940.864 8911.296
G (min) Trump 82.880 120.37 221 614 0.0735 1731 254.457 381.6855
A (min) Obama 60.185 40.206 79 602 0.0509 47558 4841.4044 7262.1066
B (min) Obama 43.906 135.66 139 603 0.0711 68927 9801.4194 14702.1291
C (min) Obama 46.866 146.03 149 609 0.0754 76493 11535.1444 17302.7166
D (min) Obama 46.866 120.87 146 616 0.0630 52603 6627.978 9941.967
E (min) Obama 82.880 132.71 215 614 0.0833 116704 19442.8864 29164.3296
F (min) Obama 82.880 120.37 240 623 0.0667 125428 16732.0952 25098.1428
G (min) Obama 82.880 120.37 213 629 0.0745 125380 18681.62 28022.43
A (max) Trump 60.185 40.206 59 610 0.0672 35990 4837.056 7255.584
B (max) Trump 43.906 135.66 159 611 0.0613 58703 7196.9878 10795.4817
C (max) Trump 46.866 146.03 174 613 0.0642 85078 10924.0152 16386.0228
D (max) Trump 46.866 120.87 158 612 0.0586 48000 5625.6 8438.4
E (max) Trump 82.880 132.71 178 612 0.1010 75391 15228.982 22843.473
F (max) Trump 82.880 120.37 228 608 0.0720 47958 6905.952 10358.928
G (max) Trump 82.880 120.37 221 614 0.0735 17805 2617.335 3926.0025
A (max) Obama 60.185 40.206 79 602 0.0509 47558 4841.4044 7262.1066
B (max) Obama 43.906 135.66 139 603 0.0711 71243 10130.7546 15196.1319
C (max) Obama 46.866 146.03 149 609 0.0754 79812 12035.6496 18053.4744
D (max) Obama 46.866 120.87 146 616 0.0630 54854 6911.604 10367.406
E (max) Obama 82.880 132.71 215 614 0.0833 127388 21222.8408 31834.2612
F (max) Obama 82.880 120.37 240 623 0.0667 134215 17904.281 26856.4215
G (max) Obama 82.880 120.37 213 629 0.0745 128004 19072.596 28608.894

Here it is everyone, the chart you’ve been waiting for!

people estimates2

That’s just under twice as many people for Obama’s inauguration.

Well, that took twice as much time as I had hoped, but I’m just glad that Sean Spicer has some numbers he can look at.

I’ll have to write a proper conclusion to this, but briefly: this excercise served the purpose of (1) an interesting dip into crowd estimates and (2) making it clear that you can’t just gaslight the world into believing something that isn’t true. These crowd estimates don’t prove that Trump’s approval is historically low (even though it is), or that he will be a worse president than Obama. They just prove that you can’t provide alternative facts and have people blindly accept them.

4. Changelog

  1. 2017/01/24 00:46 EST

    • Changed the chart from a ./../assets/quantifying-the-trump-and-obama-inauguration-crowds/people-estimates.png[stacked bar] to ./../assets/quantifying-the-trump-and-obama-inauguration-crowds/people-estimates2.png[clustered bar] chart, as the former could be a little misleading.

    • Added §2.1 about claims regarding the Trump photo being taken earlier than claimed, which is patently false.

    • Changed a mistaken instance of m2/px2 inplace of the correct m2/px

    • Fixed some grammatical and typographic errors.

  2. 2017/01/24 20:20 EST

    • Changed the name of some of the variables in the formulas in §3.3 because they were confusing.