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Tuesday, September 2, 2025

some more math education rambling

-"one size fits all" does not work

In the US, students are required to take algebra. If they don't pass it the first time, they usually take it 3 more times. Even in the so-called advanced classes are full of dullards who squeak by due to lax standards. I remember once being in Algebra 2 with a high school senior when I was a sophomore. It was amusing that he still tried to lord over me. What a putz.

-being a disciplinarian is unpleasant and tiresome

In many times and places, most students don't like school, don't benefit from being there, and in some cases, shouldn't be there. Yet there they are, and it falls to the teachers to keep them in line somehow. Now that corporal punishment has fallen out of fashion, the standard tactic is to tire them out with busywork. 

-it's fun to teach students who want to learn

And it's even more fun when they actually learn. There's also the satisfaction of helping students get scholarships, etc. That was my motivation to keep teaching besides money. High school math does not stimulate my intellect much. 

-there will always be jobs for those good at math

And they pay well. Students with any interest on ability in it should be encouraged to develop.

-whatever you choose to do in life (college, trade school, military), at some point you will have to take a standardized math test

And the better you do on it, the more options you will have.

-it's silly to get good at math just to teach math or pass a test

It's a case of a self-licking ice cream cone. I don't regret my time in school, and I like teaching. It's just that high school math education should be about preparing students to be scientists, engineers, mathematicians, etc. 




 

What if there were no hard currencies?

If the US dollar, Euro, and other hard currencies all plummeted in value at the same time, there'd be no point in trying to acquire them. Those who could afford gold or silver would buy and hold those. Everyday business and trade would be done with inflated currencies and barter. 

It's basically the case of generalizing hyperinflation to a global scale. 

My daily grind at NSA & related ramblings

I was an Army Arabic linguist assigned to them from 2018 to 2021. For most of it, I was on the night shift from 1500 (3 pm) to 0100 (1 am) 4 nights per week. It was good schedule as it got me out of a lot of Army bullwinkle like group PT. I'd come in, check my email, what the previous shift did, and any instructions they left for us. Then I'd spend the rest of time listening to intercepted audio clips called cuts. I'd usually listen to at least 100 per night. Many of my peers of similar rank and experience might listen to 10. If a cut had intel value, someone would transcribe it, and that transcription would get checked by someone else. Then it would go into a report which 50 people might read. Those people would be various higher ups in the military and government. Less 1% of the intercepted audio got checked and about 1% of that had any intel value. To help pass the time, I read the news, classified reports, NSA archives, and Wikipedia while I listened. I wasn't much of a transcriber, so I figured scanning as many cuts as possible was the best use of my time. It turns out I had the right idea. The odds of any cut being important were about the same, so the logical action was to just listen to as many as possible after some filtering. My approach was criticized a few times before I was vindicated. 

It was a low stress job for the most part. No one was shooting at us, and we could pretend to be civilians in our free time. When I got off shift, I'd exercise on my own usually with a long walk around Barton Field on Fort Gordon. Then I'd go back to my barracks room, have a beer and a shot, and read the news or listen to music before going to be around 0400 and waking up around 1100. Excessive online training paperwork, and pointless classes were basically my only hassles. Even those get unbearable after a while. At NSA, I had to digitally sign umpteen digital agreements for access. Each one was many pages of legalese. My thinking was: I have to sign it to do this job, which trained hard for and am stuck in, and since there is no chance of modifying the agreement if I refuse any part of it, it doesn't matter if I read it or not. All these bureaucratic absurdities can drive people crazy and routinely do. 

When I got there in 2018, I had to sit through about 100 hours of PowerPoint before I actually got to do the job I'd already spent 3,000 hours training for. This was around the time that I got completely burned out on speeches, lectures, sermons, etc. I never liked them to begin with, but now, they're intolerable.

The pandemic really messed up my schedule. My hours kept getting changed, and there were several multiweek stretches where I barely left my room. The gyms were closed for months, and a curfew prevented my nightly walks. For my details on how I flamed out, see my autobiography, which is also posted on this site.


The ending was painful, but I'm glad I made the journey. In high school, I wanted to be a military linguist, and I was able to do that just before the window of opportunity closed. Some people join the Army and get an early grave. I left with all the body parts I came in with and most of my sanity. The Army was not going to work out for me long-term for various reasons. The struggle to keep my weight down was tiresome enough. 

If I was still with NSA or one of their contractors, I'd be sitting, reading, listening, and typing in front of a screen for 40 hours per week. The pay and working conditions are good, at least compared to most other jobs I've had, but I don't think I'd be happy doing it for decades. Basically, my job would be a minor role in helping America meddle in the Middle East. That's been going on my entire adult life with disastrous results. It was great to get paid to learn another language because that's something I do for fun anyway. 

My code breaker application with them has been open for 4 years. Not sure how I did on the online tests, but I suppose it was good enough not to be rejected immediately. In the unlikely event they offered me that job or any other, I'd take it despite not wanting to move again or live in the DC metro area. When I ponder trends in US education, especially math, I wonder how NSA is going to fill its ranks. My guess is they will lower their standards since that's what the military and other large bureaucracies do. 


The situation with AI reminds me of the way the Soviets lagged because their system depended on copying and stealing technology from the West rather than innovating. But at least they were stealing from educated, intelligent people. All the students today using AI to cheat aren't even doing that. AI can't come up with original ideas, only sloppy remixes. 

My libertarian side is somewhat happy the dumbing down of everything will cause governments to fade into irrelevance. 

deriving the formula for the area of a circle without knowing pi and by using calculus

Say we have a square inscribed in a circle. The diagonal of the square will equal the diameter (twice the radius or 2*r) of the circle. For any square, the length of the diagonal is the length of a side times the squared root of two. Thus, if we let x be the side length, x*sqrt(2) = 2*r and so x = r*sqrt(2). Thus, the area of the square is :

(r*sqrt(2))^2 = 2*r^2 

That's close to the actual area of a circle. If we repeat this process with regular polygons with more sides, the answer should converge on the correct formula.

OK, let's repeat with a pentagon. It can be cut up into 5 isosceles triangles which each have 2 sides of length r. Using the formula for the sum of interior angles (n-2)*180, we get each angle of the pentagon has 108 degrees ((5-2)*180/5 = 108). That means that 2 of the angles in each triangle are 108/2 = 54 degrees. If we draw the altitude of each triangle, we get right triangles where the hypotenuse is r and the two acute angles are 54 and 36 degrees. The cosine of 36 degrees equals the altitude divided by r and the sine of 36 equals half the pentagon side length divided by r. So r*cos(36) is the altitude or height and 2*r*sin(36) is the base of each isosceles triangle. Thus the area of the pentagon is 5 times the area of each isosceles triangle or 5*(1/2)*(2*r*sin(36))(r*cos(36)). This is about 2.37*r^2, so a bit closer to the true formula.

We can generalize this process for polygons with n sides. The area of such a polygon is 

n*1/2*2*r*sin(x)*r*cos(x) = n*sin(x)*cos(x)*r^2

where x = 90-(n-2)*180/(2*n)

As n increases, x decreases. For n = 10, we get x = 18 degrees and an area of about 2.94*r^2

For n = 100, we get x = 1.8 and an area of about 3.14*r^2. 

For n = 1000, we x = 0.18 and an area of about 3.1415*r^2

This is similar to the idea of realizing that the base of each triangle approaches 2*pi*r/n and the height approaches r as n in increases. The area formula then becomes the limit as n increases of n*1/2*base*height = n*1/2*(2*pi*r/n)*r = pi*r^2

It's a bit easier with calculus. Take a circle of radius R and cut it into many thin rings. Each ring can be cut and unrolled to make rectangles of length 2*pi*r and thickness of dr. Integrate from 2*pi*r dr from 0 to R and you get pi*R^2 as the area of the circle. 

There are often many paths to the top of a mountain. 

Pemmy Majodina - silly hat world champion

As someone who also enjoys wearing silly hats, I feel it is proper to recognize her.


If you like the pic below, you'll like this article:




Monday, September 1, 2025

Soviet Scooby Doo - Investigation Held by Kolobki

Since it took me forever to track down this cartoon, I decided to make a post about it.  


***
A foreign smuggler named Karbophos (an allusion to Karabas Barabas, though also a Soviet term for Malathion insecticide), under the guise of a tourist, steals a rare striped elephant—named Baldakhin—from a city zoo in Berdychiv. Previously, Karbophos had been the owner of Baldakhin, but due to his abuse of the elephant, it fled from him. The renowned Kolobki brothers—a detective duo—take up the investigation.
***




Soviet cartoons of Ray Bradbury stories

Здесь могут водиться тигры. Мультфильм по мотивам фантастического рассказа Рэя Брэдбери (1989)