{"id":134,"date":"2008-10-01T23:41:38","date_gmt":"2008-10-02T03:41:38","guid":{"rendered":"http:\/\/metcaffeination.net\/weblog\/?p=134"},"modified":"2008-10-01T23:41:38","modified_gmt":"2008-10-02T03:41:38","slug":"bailout-and-mathematica","status":"publish","type":"post","link":"https:\/\/metcaffeination.net\/weblog\/2008\/10\/01\/bailout-and-mathematica\/","title":{"rendered":"Bailout and Mathematica"},"content":{"rendered":"

A friend of mine (and regular commenter here) has pointed out that, even if the $700,000,000,000 bailout passes, and adds to our National Debt, we’d still have a Debt-to-GDP ratio<\/a> that was less than Germany’s.1<\/a><\/sup> Wikipedia says that the US National Debt is 60.8% of our GDP, that Germany’s is 63.1%, and that our GDP is $13.8 trillion. Well, add $700 billion to 60.8% of $13.8 trillion and the new figure is 65.8%–pretty close; there are different ways of measuring both GDP and the Debt.<\/p>\n

But I realized that this sort of comparison is something that Mathematica 6<\/a> is supposed to be good at. Mathematica is an amazingly powerful system for doing mathematics on a computer. Its strength, traditionally, has been symbolic manipulation–I most often use it for the Integrate<\/a> command, which can do most of the integrals that in grad school I’d look up in Gradshteyn and Ryzhik<\/a>. Version 6 has added, amongst other things<\/a>, a huge library of curated data<\/a>, loaded over the Internet, that’s relatively straightforward to use.<\/p>\n

The command CountryData<\/a> gives access to all sorts of country-by-country information, including “GDP” and “GovernmentDebt”. So following one of the examples in the documentation, I produced this graph, plotting the Debt-to-GDP ratio versus GDP for (nearly) all the countries for which Mathematica has data. (Note that the x-axis is a logarithmic scale.) The United States, before and after a $700 billion bailout, are shown in green and red, respectively. <\/p>\n

If the xhtml export actually works the way it’s supposed to, you should be able to hover your mouse cursor over each point and have a little ToolTip pop up telling you which country the data are for.<\/p>\n\n\n\n
\"debtgdp.xhtml_1.gif\"<\/p>\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n<\/map>\n

<\/span><\/td>\n<\/tr>\n

GDP [$US]<\/span><\/span><\/span><\/span><\/td>\n<\/tr>\n<\/table>\n

Mathematica has a syntax that strikes many as arcane. Since I learned about computers with procedural programming<\/a>, and haven’t really done any functional programming<\/a>, I too struggle to get Mathematica to do what I want it to do. But one can often do complicated things, such as the above graph, with a very compact command. To make the main graph–the red and green dots are relatively trivial additions–the command I used is:
\n
\n
\ngdpplot =
\n ListLogLinearPlot[
\n Tooltip[{CountryData[#, \"GDP\"],
\n CountryData[#, \"GovernmentDebt\"]\/CountryData[#, \"GDP\"]},
\n CountryData[#, \"Name\"]] & \/@ CountryData[\"Countries\"],
\n PlotRange -> {{10^9, 2 10^13}, {0, 2}}]
\n<\/code><\/p>\n

There are a couple things one needs to understand for this to make sense: First is Mathematica’s syntax for pure functions<\/a>, using all the stuff with the #s and up through the &. Second, the \/@ is shorthand for the Map<\/a> command, which means apply the function on the left to each element of the list on the right. Finally, the command CountryData[\"Countries\"]<\/code> produces a list of all the countries for which Mathematica has data. <\/p>\n

  1. He is, nevertheless, against the bailout. [↩<\/a>]<\/li><\/ol>","protected":false},"excerpt":{"rendered":"

    A friend of mine (and regular commenter here) has pointed out that, even if the $700,000,000,000 bailout passes, and adds to our National Debt, we’d still have a Debt-to-GDP ratio that was less than Germany’s.1 Wikipedia says that the US National Debt is 60.8% of our GDP, that Germany’s is 63.1%, and that our GDP […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[15,12,26],"tags":[],"class_list":["post-134","post","type-post","status-publish","format-standard","hentry","category-consumer-society","category-doing-the-math","category-politics"],"_links":{"self":[{"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/posts\/134","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/comments?post=134"}],"version-history":[{"count":2,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/posts\/134\/revisions"}],"predecessor-version":[{"id":137,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/posts\/134\/revisions\/137"}],"wp:attachment":[{"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/media?parent=134"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/categories?post=134"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/metcaffeination.net\/weblog\/wp-json\/wp\/v2\/tags?post=134"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}