Recently in world events Category

Rad Intro to Calculus

| | TrackBacks (0)

Today is the 40th anniversary of the first manned lunar landing (1969) .. a historic event for techies .. cuz it was techies who put us there. And techies used » calculus to put a man on the moon (some 240,000 miles away).

MoonAt the heart of calculus lies the notion of » limits (a concept I'm quite familiar with, unfortunately).

Calculus was invented to solve (among other things) the problem associated with finding the instantaneous rate-of-change .. as visualized by the slope of a line tangential to any given point on a curve (of a graph).

To calculate a slope, you might recall (dust off them algebraic brain cells) we pick two representative points, find their difference and divide the » "rise by the run" .. the change-in-Y / change-in-X (.. commonly referred to as "delta-Y over delta-X").

As the change in the X coordinates (recall from basic Algebra) gets smaller and smaller, we get closer and closer to determining the slope (rate-of-change) at a particular point.

The problem however .. is that a point has no size, so the "change" or 'difference' (in the X coordinates) becomes zero. And dividing anything by zero is a major mathematical no-no. (Defined as "undefined" .. a mathematical black hole that will crash your computer.)

See t=13:00 here, and especiaaly t=13:30.


The concept of » limits was introduced to address this problem. Imagine standing in your living room, and walking half the distance to the furthest wall. Then walk half the distance again. And again & again.

Each time, you keep getting closer & closer. But .. you'll never actually reach the wall (cuz you keep going only half the distance). A hundred years from now, you'll be very, very close (to the wall), but still not quite there.

Getting closer & closer to the wall is analogous to decreasing the size of the difference between the two X coordinates along a curve plotted on a standard graph (which contains an X & Y axis). But the limit (drum-roll, please .. here it comes) is » the wall! .. even tho, in reality, you never actually get there.

That's why the notion of a limit represents a mathemetical "concept" (not reality). If you think about it, you can't really have an instantaneous rate-of-change (.. cuz nothing can change in an instant, cuz an instant contains no time). And the word 'rate' implies "per-unit-something." That 'something can be (and often is) » time.

That's also why the result is called/termed a 'derivative' .. cuz you can't get there with conventional mathematical manipulations. It's kinda like what that old farmer told me down South when I asked for directions » "Son, you can't get there from here." =)

Frontline is my favorite TV show. I like the way they take the viewer inside places we'd normally never be permitted. (Deep inside.) And I like their understated narrator » Will Lyman.

Hank Paulson: Secretary of the Treasury who presided over the economic meltdown of 2008

Yesterday they released a documentary titled » Inside the Meltdown. One of the most hair-raising programs I've seen.

Many smart people (and very highly-paid, too) were so enchanted by the glitter that they apparently failed to notice they were undermining the foundations of our economy. (Or maybe they did notice, but didn't care.)

Sad. Tragic. Disturbing.

Speaks volumes about certain parts of our culture and its priorities .. where profit-n-loss usurp right-n-wrong .. and even common sense gets shoved aside .. when there's money to be made. These people give capitalism a bad name.

It wasn't like nobody saw this coming, or didn't try to stop it. The Chairman of the FDIC, Sheila Bair, was one of those waving a red flag far back as 2001 regarding a potential crisis in the subprime market. (That had to be a frustrating experience.)

If you play the video-excerpt posted on THIS page, you'll hear Sheila say (in her own words):

"For years there were bills in congress to try to address 'predatory lending'. They just couldn't get the political momentum to get anything done. And I think that's because everybody was making money. It's very difficult to get the political will in Washington to move when everybody is making a profit."

On THIS page, we read reports of Bernanke telling members of Congress things like, "After today, we won't even discuss the Great Depression, because this is much worse. Nothing like this has ever happened before."

The new term we learn is » moral hazard (or lack thereof) .. tho I don't see how 'morals' has anything to do with it.

The big day came on Monday September 29, 2008, when the Dow plunged 777 points, its biggest-ever single-day drop .. shortly after the government (suffering from bail-out fatigue) let Lehman Bros fail.

Watch the remarkable hour-long special » HERE. What a picture it paints of how close to the edge we live, and the condition of our (fracturing) economic foundations.

Today is Martin Luther King day. I find it interesting (and coincidental) that the very next day we swear-in our first black president. What are the odds these two (seemingly unrelated) days/events would occur consecutively?

Martin Luther King Jr.

I've always been good in math. I got the highest grade, for example, in my (first) Calculus class .. even after I opted to skip pre-Calculus, and hadn't had a math class in/for 10 years. (Pre-Calc is now a mandatory prerequisite, I hear.)

I also got the highest grade in my Statistics class (taken the same semester as Calculus). The professor who taught my 'Stats' class taught two classes that semester. He told me I got the highest grade in *both* classes.

Depending on how you categorize the variables, the odds of these two days/events occurring consecutively..

.. would be between 1-in-365 (the number of days in a year) and 1-in-133,225 (which = 365x365, since each event could theoretically fall on any given day).

I could spend today's entire entry discussing the nuances associated with probability & statistics, but my point is » the odds are miniscule .. no matter how you dice the math.

My brain, for some reason, seems predisposed to identify the statistical curios associated with seemingly unrelated events ('coincidences'). It's not something I try to do, mind you. Just seems to occur on its own.

We know that the inauguration date would've been the same whether Obama or McCain was elected. And (we know that) MLK could've been born on any day. Moreover, his birth (which we celebrate with today's holiday) obviously had nothing to do with our presidential inauguration.

So the proximity of these two events seem totally unrelated (from a design standpoint). Yet in reality, and certainly in influence, they are obviously very much related. So much so that many feel the accomplishments of one man could not exist without the efforts of the other. (See my point?)

I'm not drawing any conclusions .. merely identifying a curious coincidence. And it's obvious the work MLK did back in the 60's preceded Obama's rise to the presidency (chronologically). So even the ordering of the consecutive days aligns correctly with historical events.

Statistics suggest 2008 was the worst year most Americans can recall .. with stocks posting their biggest annual drop since the Great Depression. (Only 1907 and 1931 posted bigger negatives.)

Family of the Great Depression, liberated from a sense of futility

People who work with such statistics seem to agree things will likely worsen before they improve. Exactly how much worse is, of course, the source of much speculation. (Because nobody knows for sure.)

From what I've gathered (in talking and listening), most people are hoping for the best, but "preparing for the worst," which means they're buying nothing but essentials (.. further depressing the economy).

Might be worth noting that the worst year most Americans will ever see would still represent the best year for people living in many other parts of the world. So the terms 'worst' and 'best' are relative. (Important we maintain perspective.)

Interesting that (as someone recently noted) bin Laden's aim in targeting the World Trade Center towers was to criple the US economy .. (cuz that's how they defeated the mighty Soviet Red Army in Afganistan).

Another thing I find interesting is that everybody now claims to have seen it coming. Even at the coffee shop, I hear people saying things like, "Everybody knew this was coming. No big surprise."

Winter solstice today (here in the Northern hemisphere, anyway) .. at 3:04 AM Pacific Daylight Time (if my calculations are correct), heralding the first day of winter. Interesting how they're able to pinpoint the exact moment .. to within one second.

Winter SolsticeThe seasons are caused by the earth tilting on its axis (23.5 degrees). Today, the sun reaches its furthest-most point of travel in the southern direction, and begins heading back north (or so it appears).

Today is also the shortest day with the longest night. Beginning today, the days get longer .. until the summer solstice, on (or about) June 21st.

Went to Tom's last night for a house-warming party. He recently sold his townhome and moved into an apartment.

President-elect Obama & family

I said, "Dude, turn on the elections." He hadn't yet set up his cable TV service, so he dug out an old set of rabbit ears from a storage box, and spent 20 minutes trying to get a signal.

We watched the election returns on his (new) plasma TV .. connected to a (old) set of rabbit ears.

The signal periodically faded, then returned. Interesting how we watched history being made via the old (rabbit ears) and new (plasma TV). Kinda symbolic.

Everybody was wiping tears. (Tho for different reasons.) Some felt history books a hundred years from now will point back to this night as a major milestone (.. for better or worse, which remains to be seen).

Frontline airs the first of a 2-part special tonight, titled » Bush's War (the war which will define the Bush presidency) .. to mark the 5th anniversary of the Iraq invasion. (Part II airs tomorrow night.)

If you miss it, you can catch this (and other Frontline specials) online. See here » Watch Frontline Online.

Bush's WarFrontline is my favorite TV show. Besides no commercials (PBS), and a decidedly understated approach, they manage to uncover facts you simply can't find anywhere else (based on more than 400 interviews) ...

.. which helps us become better-informed citizens.

I also like the way they present their findings .. as objectively as possible, focusing more on the facts than trying to sway the audience .. allowing us to draw our own conclusions. And I like their narrator, too » Will Lyman.

About this Archive

This page is a archive of recent entries in the world events category.

WiredTree is the previous category.

xhtml/css is the next category.

Find recent content on the main index or look in the archives to find all content.