25 Apr 00
So I didn't write an entry on my birthday... I was busy and sick... Had a
lovely Easter Vigil Mass, but I got drafted for altar server duty as per
usual. I believe even last year they conscripted me, even though I was
getting confirmed then.
Shee, now I've been drinking alcohol legally for 5 years (plus a couple
months, if you include my time in Japan). Can't say much for it.
So let's see, what was I up to today... well, I wrote up a student's test
- her hand was disabled (it looked rather messed up, probably due to her
typing out so many notes and attempting to write herself), so she dictated
her Logic Final to me. During those 4 long hours, luckily I picked up a
little light math education reading in the room and realized the
pertinence to the situation I found myself in. To wit, the articles I was
reading were on "New" algebra (to go along with our new calculus I
suppose), and the not-so-astounding discovery that most students looked
upon algebra as simple mechanical manipulations and algorithms, and didn't
associate such structures with actual numbers. All this while a student
is trying to see if she had the answer to a particular test question
already on her sheet of notes that was allowed. Of course math is
confusing if you see it as memorization and manipulation. You've got to
use the basics with facility (I still remember one of my friends who kept
putting down 4*8 = 28, which got her in trouble in Trig during those times
we had to use linear interpolation instead of calculators), but if you are
looking at this as some first-level translation and string manipulation
you're going to have a very difficult time indeed.
In any case, the article brought up that there actually was quite a bit of
controversy in the development of algebra - and I'm talking about good old
9th grade algebra, not linear algebra or abstract algebra. In the 16 and
1700s (I believe), when even coefficients were now represented by letters,
there arose an argument as to what variables actually =were=. When
variables only indicated unknowns to be solved for, such as one finds in
something like 3*x + 4 = 0. But what if one has a*x + c = 0, and one is
asked to solve for x? What on earth can this =mean=? What's interesting
is that once you allow for variables to behave like this, one starts to
create classes of numbers such as complex numbers, and sometimes even
stranger things...
Also today I say a talk by Paul Bressloff concerning geometric
hallucinations, in which he and a few others had concocted a simple,
continuum model of the primary visual cortex, a particular kind of mapping
to actual retinal image, and found conditions under which perturbations
from a homogeneous state gave one persisting geometric patterns. He threw
in: conformal mapping, group theory, and quantum mechanical perturbation
techniques. I love applied math.
But considering the non-math aspects of the talk, I must say that
psychophysics is a very dangerous field to delve into, especially with
regards to pathology induced by drugs or especially with regards to
vision. The temptation to experiment on one's self is very great. Many
of the hallucinations given as examples were reported from people who had
taken LSD (or had the DTs). One does wonder, given the nature of the
pictures, as to when these were drawn - while having the
hallucination? or is it a memory of the hallucination? Anyway, I'm sure
you can see why this is dangerous.
In any case, let me tell you about my favorite visual aberration that has
occurred personally to me. I was on the Duke shuttle bus, and I was
=extremely= tired. I had my head leaned up against the window, and my
nose happened to be at the dividing line between two window panes. Then
all of a sudden, I started to notice that the images from my two eyes were
acting independently; I could shift one in relation to the other, and
position them whereever I wanted. Then I thought "Wait a sec, my brain
shouldn't be doing this" and =sh-thunk=! the images merged to give the
usual binocular result. The only other rather bizarre visual result I've
ever had is looking at one of those stupid Magic Eye pics at 4 in the
morning in Japan (I was up because that's when the sun rose). And I
actually saw the 3D picture! And I had thought for years that it was
simply a hoax....