21 June 2013: Harvard Law School and Dijkstra’s Take on Pythagoras!
Edward G. Nilges, “Say Hello to My Grand-Daughters”, pencil and pen, A4 size, May 2013. Copyright 2013 by Edward G. Nilges: (c) 2013: Moral Rights Asserted by the artist.
20 mn first thing: 150 steps alternate left and right foot, walk up just past senior staff quarters, two storey flights up and down. No need for pain killer before, or after so far. Fresh and quiet dawn is good for Soul. Nurses know longer fuss, just chirp how long gone and I say s’allright ees ten meenutes.
Discovered excellent academic videos at Harvard and Harvard Law school (HLS). The HLS law school videos take me back to Princeton where I was accepted as a partner in learning by the wealthy on condition that I restrain my wildness and egalitarianism, and hide my love away, which is why I left…a TIAA/CREF and medical insurance (sob).
I watch these HLS videos when my eyes tire from chemo.
In one made at Harvard Law School’s library, a scion of an old New England family long associated with the Harvard law school, John Palfrey as a young man researches the path of legal information at the library of the school.
The HLS library has one of the most notable collection of law books in the world going back to handwritten manuscripts from the time of Henry II and Bracton (one of the first codifiers of English law). Then to Caxton’s invention of printing and the slow democratization of access to the law…by way of fearful obstacles raised by Palfrey’s physical or spiritual ancestor’s contempt for barrack room and factory floor lawyers.
Then to Lincoln, quietly reading Blackstone by a creek in Illinois from a copy in a barrel of used books bought from a tinker. “I cannot think of Lincoln without great emotion” – Edmund Wilson.
To today…with the transition from overpriced proprietary services like Lexis to unreliable but free copies of decisions, simultaneously fostered by business interests (for this saves firms money) and fought tooth and nail. It’s a dialectic, I would imagine.
Palfrey wants to control “the path of legal information” while in good faith opening it up at Web sites and libraries. He doesn’t realize the mailed fists behind his class who’ll destroy libraries and create a digital divide by eliminating equal Web access.
The spirit is that of Ted Talks. Be like us, and assist us in keeping our privileges and control of society. Well I happen to mostly believe in this model with all due apologies to my former and present radical pals from the 1960s for our Constitution can and should be brought back and reformed to get rid of the thug class that stands between us and people like Palfrey who grew up in a genuine environment of gentle learning. We all want this. My Mom wanted this: nicknamed The Duchess in school, she looked up from feeding chickens on a failing Massachusetts farm to the stars and I don’t blame her, being myself the Duke of Earl.
On p 273 of the Guyer/Wood translation I find this interesting passage: “No image of a triangle would ever be adequate to the concept of it. For it would not attain the generality of the concept, which makes this valid for all triangles, right of acute, etc., but would always be limited to one part the sphere”.
At this site we find a non-visual and symbolic proof, not just of the famous theorem of Pythagoras but also of a MORE GENERAL theorem which applies to all triangles and implies Pythagoras. This dramatic discovery, I believe, was ignored by mathematicians who literally would never know about Dijkstra, predominantly a computer scientist, employed half his career in industry: and given scientific aliteracy (as chronicled by Saul Bellow, who met a U of Chicago math prof who never read anything but journals in his specialty) mathematicians outside of applied math for computer science only tended not to know Dijkstra.
Dijkstra was educated first in the Netherlands whose educational philosophy was in part formed by Kantianism. This of course produced much misunderstanding when Dijkstra worked in industry promoting and advancing the elegant language Algol (ancestor of C, etc.) in the teeth of ugly monsters such as Fortran. But Fortran won. My colleagues at HKUST environmental science use it exclusively, and its designers have long since learned to steal the best ideas from Algol and C including structured programming and its support. Dijkstra is uncredited because successful applied scientists enjoy laboring in obscurity and do not seek fame.
My own hobby-horse as regards geometry is based on my own limited and amateurish experience in computer graphics. It’s not supposed to matter if you measure the distance between two lines AB and CD from inside the space semi bounded by the ones but starting at the inside Euclidean (zero width) line that bounds the rectangle that is actually formed on most displays when we draw a line of one or more pixels in length…but it does, since we cannot be fully Euclidean at least on common computer displays: computer drawn lines at least on such displays must have nonzero thickness!
In my experience you have to take this into account.