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September 24, 2013

The Definition of Graph is Classified

Posted by Tom Leinster

Amid the (to me, highly disturbing) news that the state apparatuses of the US and UK have been secretly and systematically keeping records of our emails, our web browsing, our phone calls, our letters, our financial transactions and our physical location, here’s one half-smile’s-worth of light relief: the definition of graph is classified as “Top Secret”. (Update: or maybe not. See Tod’s comment below.)

The definition of graph, in an NSA slide marked Top Secret

(Click to see the news article this comes from, and to expand the tiny writing along the top and bottom which specifies the precise degree of top-secretness.)

This NSA slide uses the category theorists’ word object for a vertex of a graph. I’m relieved they don’t call the edges morphisms.

This is a deadly serious subject, but this blog isn’t the place for discussing it, and I’m not up for moderating that kind of discussion. So please keep comments light ‘n’ fluffy.

Posted at September 24, 2013 12:52 AM UTC

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Re: The Definition of Graph is Classified

A (U) means that line or sentence is unclassified, whereas the classifications at the top and bottom refer to the whole document.

Posted by: tod on September 24, 2013 2:55 AM | Permalink | Reply to this

Re: The Definition of Graph is Classified

That’s a relief — I was about to use the definition in a paper, and would rather not get arrested.

Posted by: Tom Leinster on September 24, 2013 12:01 PM | Permalink | Reply to this

Re: The Definition of Graph is Classified

Formally that definition of graph is classified. Only with abuse of language can one say it “is unclassified” which stands for it being classified as “unclassified”.

Posted by: RodMcGuire on September 24, 2013 5:19 PM | Permalink | Reply to this

Re: The Definition of Graph is Classified

That isn’t quite true. Properly, the author should have marked that page’s header and footer as UNCLASSIFIED. One can mark with the highest classification the page contains. One defaults to the document’s classification if it’s too hard mark each page individually with the chosen technology.

In this case, the author did not bother to mark each page’s classification individually. He simply resorted to the Slide Master in PowerPoint. There are classification packages for LaTeX on CTAN, but none is very convenient.

Posted by: Eric Jablow on November 24, 2013 12:26 PM | Permalink | Reply to this

Re: The Definition of Graph is Classified

There are so many slightly different definitions of ‘graph’ in mathematics that the definition might as well be classified! But at first I thought you were going to announce a complete classification of all these definitions.

Posted by: John Baez on September 24, 2013 2:59 AM | Permalink | Reply to this

Re: The Definition of Graph is Classified

Lawvere when began to be active against the Vietnam War found that rumours began to circulate that his categorical arrow diagrams were actually plans for attacking the administration building!

Posted by: mozibur ullah on September 26, 2013 4:04 AM | Permalink | Reply to this

Re: The Definition of Graph is Classified

Where did you hear that?

Posted by: Todd Trimble on September 26, 2013 6:00 PM | Permalink | Reply to this

Re: The Definition of Graph is Classified

Here it is straight from the horse’s mouth: page 18 of an interview with Lawvere.

In 1971, official date of the birth of topos theory, unfortunately the dream team at Dalhousie was dispersed. What happened, that made you go to Denmark?

Some members of the team, including myself, became active against the Vietnam war and later against the War Measures Act proclaimed by Trudeau. That Act, similar in many ways to the Patriot Act 35 years later in the US, suspended civil liberties under the pretext of a terrorist danger. (The alleged danger at the time was a Quebec group later revealed to be infiltrated by the RCMP, the Canadian secret police.) Twelve communist bookstores in Quebec (unrelated to the terrorists) were burned down by police; several political activists from various groups across Canada were incarcerated in mental hospitals, etc. etc. I publicly opposed the consolidation of this fascist law, both in the university senate and in public demonstrations. The administration of the university declared me guilty of “disruption of academic activities”. Rumors began to be circulated, for example, that my categorical arrow diagrams were actually plans for attacking the administration building. My contract was not renewed.

Posted by: Tom Leinster on September 26, 2013 6:21 PM | Permalink | Reply to this

Re: The Definition of Graph is Classified

Thanks for finding that, I’d actually checked that my memory hadn’t played me false by digging that interview out online but I didn’t think to link to it.

Reading it again it sounds frightening - I guess it was at the height of the cold war. It was after the MaCarthy era though, it would be interesting to see some historian exploring the parallels and differences between the contemporary situation and then.

This isn’t so light & fluffy, and neither is the following remark by Dr Badash, who is a historian of science in a speech at a conference on Linus Paulings activism - but it is amusing:

In 1954, the White House and the Atomic Energy Commission sought to keep secret from Senator Joseph McCarthy the scheduled security clearance hearing on J. Robert Oppenheimer. A frustrated President Eisenhower said “We’ve got to handle this so that all our scientists are not made out to be Reds.” He feared that “that Goddamn McCarthy is just likely to try such a thing.”

Posted by: mozibur ullah on September 28, 2013 2:49 AM | Permalink | Reply to this

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