Copying by hand

A couple weeks ago, I noticed in a BoingBoing post the following quote:

Before literacy, we were mere listeners. We heard stories read to us as a group. After the printing press, we were elevating to individuals, each with our own, acknowledged perspective on what we read.

I made a comment (as "hilbertastronaut"), and I feel like expanding on
it a bit more.

The writer argues that the printing press elevated us (Westerners,
perhaps?) from mere listeners to individuals with opinions. If
anything, the opposite might be true. Back when the only way to
propagate information was to copy it by hand, it was standard practice
to add commentary to the margins of the document. This could include
clarifications or even personal reflections. One sees this in Western
monastic manuscripts as well as Chinese brush paintings (where
standard practice was to indicate receipt of the painting by marking
it with one's personal stamp, and then perhaps write one's thoughts on
the piece in the margin). In contrast, the printing press (and the
Reformation in some sense) gave people the idea of a book as an
official, received text. Written comments have a lesser status than
the printed text. For example, if one buys a used textbook at a
college bookstore, one generally hopes that it hasn't been written on
much. Before the printing press, the commentary could often be equally
or more valuable than the main text itself.

Copying other kinds of information by hand besides text also has
the same effect. For example, when J. S. Bach copied Italian
concerti, he added inner voices and ornamentation, making the concerti
into pieces universally recognized as his own compositions (and
arguably more interesting than the originals!). Bach treated copying
both as an end (to get his hands on other people's music), and as a
means (to improve his compositional skills). Even today, mathematics
teachers consider copying out and working through proofs an important
part of learning mathematics. This is because mathematics, like music
composition, is not about memorization of facts but about developing
one's creative problem-solving ability according to a combination of
rules and aesthetic principles. Copying a proof and understanding
each step is a guided re-creation of the original author's work.
Furthermore, creative mathematical thinkers in this process of
re-creation usually have new things to say, like clarifications or
generalizations, which they "write in the margins" and use in their
research -- just like Bach wrote inner voices and ornamentations "in
the margins" to produce new compositions.

My sophomore high school English teacher handed out red pens on
the first day of class, and exhorted us, even required us to
write in our books with them. At the time, it seemed ridiculous to
ruin books which could be reused for the next class. Pencil
annotations could at least be erased. Now I understand that using a
red pen elevates the status of the handwritten text, to be more
visible and more permanent even than the printed text. It makes the
reader's commentary just as valuable, if not more so, than the
original document. Whether my commentary really was more valuable
than what I read at the time is doubtful, but at least the long-term
lesson of the value of "manual" commentary stuck in my head.

ImageMagick crops your white space!

ImageMagick is a fabulous command-line tool for image processing. I use it a lot for converting between different image formats, which it does with no fuss whatsoever -- as the following PNG to PDF example illustrates:

$ convert in.png out.pdf

ImageMagick can do much, much more than conversions. Today I learned the following trick from an
e-mail list discussion:

$ convert -trim img.pdf

which trims all the white space from around an image. It's a great trick for inserting Matlab plots into papers! I used to do this by hand with an image editing program like the GIMP; it's great to know that I don't have to fire up such a massive tool in order to accomplish this simple task. (The GIMP is a wonderful program, incidentally, but starting it up just to crop some white space is a task beneath its mighty powers.)

New version of ECL is out

A new version of Embeddable Common Lisp (ECL) is out!!! I use ECL in my projects to support Lisp as an embedded scripting language in large C-based projects. ECL's chief developer (Juan Jose Garcia Ripoll) is amazingly responsive, which makes the library a pleasure to use. Yay ECL!!!

(Pseudo)random numbers matter

The newly released LAPACK Working Note #206 gives yet another reason why generating good pseudorandom numbers matters:

In May 2007, a large high performance computer manufacturer ran a twenty-hour long High Performance Linpack benchmark. The run fails with the following output:

|| A x - b ||_oo / ( eps * ||A||_1 * N ) = 9.22e+94 ...... FAILED


What happened was that the benchmark's matrix generator uses a lame linear congruential pseudorandom number generator, which causes generated matrices to have repeated columns for certain unfortunate choices of matrix dimension. This of course makes one wonder why the generator doesn't just make a matrix which is known to be invertible, say, by generating a sufficiently nonzero diagonal matrix and hitting it on both sides with orthogonal transforms until the zeros are filled in. Regardless, the bug meant 20 hours of very expensive, intensely power-consuming supercomputer time were wasted on computing the wrong answer to a problem which at such sizes very few people need to solve. So, random numbers do matter ;-)

Contemplation leads to messes

I like to make espresso using one of these gadgets. When you press out all the water, it leaves a "puck" of compressed grounds, which you can pop out straight into the garbage or compost just by pushing on the handle. I was looking at the puck this morning and saw some lovely patterns made by different layers of grounds. One thin layer in the puck appeared more compressed than the other layers, but this more compact layer wasn't a straightforward horizontal cross section -- it had a ridged topography like one sees in the sedimentary rock hills around here. It made me wonder about the bulk properties of solid particles, about which I had seen an interesting presentation a few months before, on simulating such materials.

As I was holding the puck in my hand and examining this layer from all angles, the puck suddenly broke into its constituent coffee grounds and made a huge mess all over the floor. I realized then that I had fallen into the nerd's usual trap of neglecting practical matters for the sake of contemplating lovely abstractions ;-)

Verifying identity: Existence and uniqueness

Some friends of mine have been playing an online diplomacy and military simulation game, in which each player represents an independent country. One of the biggest problems in the game is "multis" -- multiple accounts created by one person. The one person uses the multiple nations to magnify his/her power in the game. The rules prohibit this practice, but it can be hard to detect. Restricting each player to use only one IP address is annoying (as it prevents multiple people from using the same computer), but a start. The underlying problem is how to establish uniqueness of identity: Are you the only person who claims to be you?

Another identity problem is that of verification: Are you the person whom you claim to be? This was a problem faced by Daniel Plainview, the protagonist of the 2008 movie There Will Be Blood. Was the man claiming to be his brother Henry actually that person? Daniel is understandably mistrustful. Ultimately the question is resolved accidentally, by the exchange of a bit of personal information -- an oblique reference to an inside joke. When verifying identity, one has to take care not to give away information when asking for it: for example, if you give a bank your social security number, the bank could then use it to masquerade as you. Some recent security research has addressed the question of how to verify identity without giving away a secret. Daniel Plainview's homegrown solution is just as effective: inside jokes rely not only on objective information, but on a particular emotional response which would be very hard for either a machine or an unrelated human to mimic. In that sense, they are even better than CAPTCHAs: They give away very little information and are very difficult for unauthorized agents to solve.

Uniqueness is an easy problem to solve in person, aside from comedy sketches involving twins. This is because human "duplicates" (genetically identical multiple births) are difficult to "make." In contrast, it's very hard to solve remotely and electronically. If you can fake a verification test, then you can break a uniqueness test. So verification and uniqueness go hand-in-hand.

Oftentimes in math, there's a fruitful tension between existence and uniqueness. When one wishes to prove that "there exists a unique object," one generally proves existence and uniqueness separately. (In this context, "uniqueness" means that if such a thing does exist, it must be unique. So uniqueness by itself doesn't necessarily imply existence, nor does existence by itself necessarily imply uniqueness.) I'm curious whether this tension could be helpful in the field of verifying identity. Answering the question "Am I Jane Doe?" is relatively easy, but the question "If I am really Jane Doe as I claim to be, then there is only one such person" doesn't even seem to be the right question to answer. Furthermore, it shouldn't be necessary to reveal your true identity in order to play an online game. Can uniqueness be solved without verification?

Two new LAPACK Working Notes have been published!

"LAPACK Working Note 199: Regular Full Packed Format for Cholesky's Algorithm: Factorization, Solution and Inversion."

by Fred G. Gustavson, Jerzy Wasniewski, and Jack J. Dongarra

UT-CS-08-614, April 28, 2008.

"LAPACK Working Note 200: Some Issues in Dense Linear Algebra for Multicore and Special Purpose Architectures."

by Marc Baboulin, Jack Dongarra and Stanimire Tomov

UT-CS-08-615, May 6, 2008.

You can download them at the above link.