A break in combat means downtime blah blah blah

Is it Friday yet? Caleb and Kara have teamed up for the double-whammy on Lynn-nore and I recently. He won't sleep while she plays, and then, when he finally begins to drift off, she rushes in and wakes him back up. It is a perfect scheme, and they both get something out of it. She gets playtime without adult interference and he gets plenty of parental holding coupled with obsessive amounts of attention to his every bodily need. Flatulence becomes the topic of conversation. Debate centers around his schedules for bathing and feeding.

Now I confess that this assault has not been easy on me. I just don't do well with sleep deprivation. My inner jerk (and c'mon guys, we all have one) forges a get-out-of-mouth-free card, and morality is just too tired to care. Lynn-nore has to put up with the whole lot of us!

The life of the mind isn't hurting too much, though. I have been reading one of the books whose review was due weeks ago (the inner jerk doesn't care.) It is a collection of essays clustered about the theological assertion, and practical contextualization, of eschatological hope. Here's an excerpt:

History does not "belong to us," he [Gadamer] explains; "we belong to it. Long before we understand ourselves through the process of self-examination, we understand ourselves in a self-evident way in thie family, society, and state in which we live." Traditions constitute our identities and make reason possible. Subjectivity may be a "distorting mirror," Gadamer acknowledges. But "[the] self-awareness of the individual is only a flickering presence in the closed circuits of historical life. That is why the prejudices of the individual, far more than his judgments, constitute the historical reality of his being. [In other words, our] 'being-in-the-world,' our finitude, sets formidable limits around our knowledge and truth claims but also makes meaning possible for us.

Second, I have also begun studying beginning algebra in preparation for the GRE. Here's a bit that I wrote to John G. about it last week:

It really doesn't take that long to advance in the study of mathematics. Most of our time in secondary school was spent doing pages of problems and review; the actual swallowing of concepts was pretty light. Add a drop of adult study skills and the drive to know this for your own sake and I don't think it will be too difficult to plow in to Algebra a good distance before slowing up. The trick, too, is to always keep in view the "mathematical cosmology" you are working in.

I got this trick from a quip I heard from a mathematician on NPR who was also a bit of a classicist. He said that Greek mathematicians never presented their ideas without representing them both mathematically (xy+ab=P) AND graphically. In other words, Geometry sits behind arithmetic, and the progression of mathematical paedegogy is from the most abstract kind of geometry to the most exact mathematical descriptions of the dimensional world that we actually inhabit (from 2, to 3, and finally to multi-dimensionality in higher mathematics.) You can see that our own abilities at mathematical description never advance beyond 2-dimensions in secondary school.

Now, all of pre-algebra and a good bit of algebra, for example, is simply manipulating one's position upon the number line., whether forward or backward. The figure of the Number Line is straight out of Euclid, where a line is "breadthless length" until it begins to be defined in larger or smaller elements by points.

As soon as possible, a second line is added, so that the student can begin manipulating lines upon a plane (x, y). And from there, one can jump off into the computation of diameter, volume and angle within triangles, circles and other figures to one's heart's content. The addition of a third variable (x,y,z) makes the leap into 3 dimension and such things as volume, and there you go, you've pretty much done everything. What I just did in two paragraphs took several years in school. Why is that....?