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Two orders of magnitude in The Social Network

Counting down to the Oscars to be awarded this Sunday, February 27, two favourites for best picture have emerged: The Social Network and The King's Speech. I must admit that I don't usually follow motion picture awards, but these two films, both based on true stories, took me by surprise.

I'll start off with The King's Speech. It first caught my attention when I saw a quote from TIME magazine proclaiming that "The oscar race is over" in a promo clip. With a plot that could be summarized in one sentence (King George VI works to overcome his stammering with speech therapist Lionel Logue), I was puzzled by how it received such critical acclaim. I decided to see the film to try to understand TIME's raving review. Against my initial reservations, the film managed to take an arguably minor detail, which may not even have been featured in some British history textbooks, and turned it into two rather entertaining hours. The attention to detail was also remarkable. For example, it seemed strange to me that the Logue family was dressed in formals in the scene where they were listening to the radio news broadcast announcing the declaration of war on the morning of September 3. After looking up the 1939 calendar, I realized that September 3 was a Sunday. This film certainly has what it takes to win best film at the Oscars. The royal profanity was icing on the cake.

If you're wondering where I'm going with this and what two orders of magnitude has to do with The Social Network, read on...

I was a little skeptical when The Social Network was dubbed "a film that defines a generation." I suspected that it was an opportunistic film riding on the popularity of Facebook. After The Social Network beat The King's Speech for best motion picture (drama) at the Golden Globes, I went to see this film in order to understand why.

I was impressed by the film's attention to detail. In one of the first scenes, Mark Zuckerberg is shown using a laptop running an unidentified linux distribution (I suspect Debian because of the Iceweasel logo) with a KDE (K Desktop Environment) 3.1 graphical user interface, which is accurate for 2003 (if they could only get wget to say 2003 instead of 2009). KDE 3.4 was featured in the last scene, which is accurate for 2005.

The same, however, cannot be said for their math. In the scene where lawyers were explaining the distribution of shares in the newly reincorporated Facebook, the ownership percentages summed to just over 105%. It resembled a case of round-off error at first, but the two decimal-place precision quoted by the lawyers suggests instead a violation of sig figs. I suppose it could be forgiven if we simply assume a 5% uncertainty on the lawyers' mathematical abilities.

The figure that struck me the hardest was the 0.03%. To set up the problem:

  • Before reincorporation, Zuckerberg held a 65% interest, Eduardo Saverin (co-founder who provided the initial financial investment) held a 30% interest, and Dustin Moskovitz (programmer) held a 5% interest.
  • After reincorporation, Eduardo now held 1,328,334 shares (34.4%).
  • 24 million new shares were introduced, diluting Eduardo's ownership to an alleged 0.03%, according to the film.

The interesting thing here is that the film provides all the numbers that we would need to calculate what Eduardo's new ownership interest should be. Let's do some high school math:

  • If 1,328,334 (1.33 million) shares constitute 34.4%, then there were originally 3,861,436 shares (3.86 million), check: 3.86 × 0.344 = 1.33.
  • Adding 24 million new shares, there are now 27.86 million shares in total.
  • 1.33 million / 27.86 million = 0.048 ≈ 5%

The 0.03% quoted in the film is two orders of magnitude too low!

While it may be true that Facebook partially defines our generation (along with Google, Wikipedia, Twitter, ...), it leaves me thinking about what lasting impact the film The Social Network will have on our generation. Perhaps its biggest contribution may be in advocating and promoting the need to strengthen our elementary and secondary school mathematics curriculum?

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