On the utility of applied mathematics

From one of my favorite novels, which has the great Soviet mathematician and economics Nobelist Leonid Kantorovich as one of the lead characters.

It was a pleasure to put the lucid order in his [Kantorovich’s] head to use. More than a pleasure, a relief almost, because every time the pure pattern of mathematics turned out to have a purchase on the way the world worked, turned out to provide the secret thread controlling something loud and various and apparently arbitrary, it provided one more quantum of confirmation for what Leonid Vitalevich wanted to believe, needed to believe, did believe when he was happy: that all of this, this swirl of phenomena lurching on through time, this mess of interlocked systems, some filigree-fine, some huge and simple, this tram full of strangers and smoky air, this city of Peter built on human bones, all ultimately made sense, were all intricately generated by some intelligeble principle or set of principles working themselves out on many levels at once, even if the expressions didn’t exist yet which could capture much of the process.

Francis Spufford, “Red Plenty”

Methodology note for India-US defence trade article

General/Data Sources

  1. Foreign Military Sales (FMS) data taken from the US Defense Security Cooperation Agency’s (DSCA) “Foreign Military Sales, Foreign Military Construction Sales and Military Assistance Facts” reports. The latest publicly-available edition is that of 2017. For 2003-2009 data, I have used the 2009 report. For 2010-2017 data, I have used the 2017 report. Note that across individual yearly reports, certain data entries may have minor discrepancies; I have resolved this issue by using two reports (2009 and 2017) dividing the 15-year time period (2003-2017) into two non-overlapping bins.
  2. Direct Commercial Sales (DCS) data taken for the US State Department’s Section 655 Reports to the US Congress. I have used 16 individual year reports to collate the 2003-2018 data set. Note that DCS shipment data for 2009 is missing. I have “filled” this missing entry by replacing it with the median of the 2008-2018 data. The SIPRI database of Section 655 Reports do not have country data for 2011 which was obtained from the Federation of American Scientists.
  3. Indian military modernisation data is from successive Union Budget Revised Expenditure numbers. For definitions used, see an earlier methodology note.


  1. Foreign Military Sales Agreements, 2003 – 2017: tabulation of FMS Agreements between 2003 and 2017 with data from 2009 and 2017 reports (see no. 1 above).
  2. Comparison of Foreign Military Sales, 1950-1999 and 2000-2005: Historical data for 1950-1999 taken from the 2009 DSCA report. (In 2000 and 2001, there were no FMS agreements between India and the US on account of sanctions from the 1998 nuclear tests).
  3. Direct Commercial Sales Authorized, Including Agreements (million USD): do note that this includes agreements signed in individual years (reported separately in the Section 655 Reports as Defence Services Authorized till 2013).
  4. Comparison of Agreements & Authorizations with Military Modernisation Budgets, 2006-2014:
    1. ‘Commercial and Government Agreements & Authorizations Total’ is the sum of FMS and DCS for each year between 2006 and 2014.
    2. ‘Foreign Component of Indian Military Modernisation Budgets Total’ was estimated by recording the modernization budgets for each year, and taking a fraction of that using the import content of the modernisation budget. (See points 1 and 2 in page 5 of an earlier methodology note for data sources.) Conversion to USD using each year’s reference exchange (USD/INR) rate, with data from the RBI.
    3. ‘Indian Military Modernisation Budgets Total’ was estimated by summing over the modernisation budgets of each year. (For definition of modernisation budget, see point 1 in page 7 of this note.)
  5. Deliveries and Shipment, 2003-2017: data from State Department Section 655 and DSCA reports. For 2009, the missing DCS shipment data was inferred from other observations (see no. 2 in the previous section).