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.... 
 
 
 
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