Trump lawyer John Lauro requested a date of 2026 for his (Mr. Trump’s) trial in Washington, D.C., so that the team could go through the 11.5 million pages of information that might be useful to them. He also supplied a graph (shown above), trying to show why this is completely unreasonable. However, there is a basic problem with the graph, which is what this post/diary/story is about.
Warning: I’m going to geek out here, but hopefully not too much. It’s about math, but not anything beyond high school. (Well, maybe not for the Statue of Liberty, but I’m getting ahead of myself.)
Mr. Lauro said
If we were to print and stack 11.5 million pages of documents, with no gap between pages, at 200 pages per inch, the result would be a tower of paper stretching nearly 5,000 feet into the sky. That is taller than the Washington Monument, stacked on top of itself eight times, with nearly a million pages to spare [...]
There are a couple of things wrong here. This article is about the fact that the cross-section of the Statue of Liberty, and of the Washington Monument, is more than the area of a sheet of paper.
So my mathematical brain asked the question: What are the volumes of the three things? (the Statue of Liberty, Washington Monument, and the documents, which I am facetiously going to call “Trump Tower”).
Luckily for me, two of these have been calculated already by other people.
What is the volume of “Trump Tower”? Well, it’s a rectangular box of height 4822 feet, and length and width of the text on a sheet of paper. Accounting for one-inch margins of an 8.5’’ x 11’’ sheet of paper, the area of the text is (6.5 / 12) * (9 / 12) = 0.406 square feet, making the volume equal to 4822 * 0.406 = 1,959 cubic feet.
The graph paints a different picture, doesn’t it?
Okay, let’s do some more math, in the spirit of Randall Munroe’s What If? books. (This is the guy who draws the XKCD comic.) If you want to, you can skip ahead to the “Now, let’s plug in the numbers” paragraph.
If we slice “Trump Tower” into sheets with 200 pages per inch, we get 11.5 million pages of text. If we slice the Statue of Liberty and the Washington Monument into slices this thick, how many pages of text would the cross-sections represent?
This isn’t actually that difficult, because we can set up ratios with a couple of constants. The first constant (“A”) is the conversion factor between number of pages and the area of the cross section:
11.5 * 106 = A * 1959
A = 11.5 * 106 / 1959 = 5870.53
in the appropriate units (pages per square feet). We also need to account for the fact that the cross-sections of the two real buildings will have margins put around them. For that, we need the fraction of the area of a sheet of paper that is covered, when you put the margins in. This is also a straightforward calculation:
B = (6.5 * 9) / (8.5 * 11) = 0.6257
And we now have an equation that relates number of pages to volume in cubic feet, for our two buildings. (Note that the B factor is not part of the “Trump Tower” calculation, because we’ve already accounted for the margins.)
[number of pages] = A / B * [volume in cubic feet]
Now, let’s plug in the numbers.
88,286.67 * A / B = 828335536 = 8.28 * 108 = 828 million pages of reading
1,241,455.875 * A / B = 11647760840 = 1.16 * 1010 = 11.6 billion pages
The upshot, in either version of the calculation, is that Lauro’s chart is highly misleading.