Conjunction Junction

So the other night while I was recovering from class, I wound up on YouTube watching the "Conjunction Junction" video, from the Schoolhouse Rock series that was broadcast after Saturday-morning shows on ABC all through the 1970's and 1980's. I was kind of surprised by how irritated it made me in one small detail.

I've grown accustomed to teaching the standard logical operators in all of my classes -- whether they be fundamentals of math, introduction to computers, statistics and probability, etc. So when the song starts and says, "I got three favorite cars/ That get most of my job done", well, of course I expected to see "And/ Or/ Not" -- but then what actually appears (as you can see in the top picture) is "And/ But/ Or". So, I was surprised at how jarred I was by that.

As the song explains each connecting word, it first says, "And: That's an additive, like 'this and that'". Okay, makes sense. Then the next bit is: "But: That's sort of the opposite, 'Not this but that'". (See picture below.)

Wait a minute, that's not right! The truth is, the word "But" has the exact same logical meaning as "And" (both clauses are true); all it does is put an interpretive spin on the latter clause, as if to say "this second part may be somewhat surprising to you". And in fact, in order to make the argument that "that's sort of the opposite", they had to go and use the missing logical operator than actually does make things "opposite", namely "Not".

So stick that in your smokestack, Schoolhouse Rock! (But -- I still have the danged thing stuck in my head...)
Watch video here. Or: Read lyrics here.

New Blog Tagline

You may notice up above I've got a new tag-line ("blog description") under the title of my blog above. This is something one of my better students said at the end of class tonight (making up a lost day of statistics from snow days here in NYC).

"It's like you took a bat and clubbed us with math"; which I think is entirely delightful to think about.

Naming Large Numbers

A very small observation I'll throw out: Sometimes I want to name a large number that pops up on my calculator in scientific notation (like while lecturing in class, for example). A fast way to do that is to take the exponent and:

• Divide by 3
• Subtract 1
• Say that in Latin (with "-illion").

Now, obviously this requires you to do a few elementary operations in your head and to also know Latin (or at least how to count therein). And: I'm doing this in the "short scale", of course.

Example #1: 1.01238 x 10^18.
Do 18/3-1 = 6-1 = 5. So this is about "one quintillion".

Example #2: 2.13129 x 10^48
Do 48/3-1 = 16-1 = 15. So this is about "two quindecillion".

Example #3: 6.38733 x 10^95
Do 95/3-1 = 31-1 = 30. Since we had a remainder of 2 at the division step, I'll say this is about "six hundred trigintillion".

Grants & Remediation

A FAQ on New York State TAP (Tuition Assistance Program) grants says this:

Can I get TAP for remedial courses? Remedial courses may be counted towards either full-time or part time enrollment for TAP purposes. However, to qualify for TAP, you must always be registered for a certain number of degree credit courses. [http://www.cuny.edu/admissions/financial-aid/grants-scholarships/nys-grants.html]

Now, why would you want to incentivize taking degree-credit courses when someone hasn't yet completed necessary remedial courses (i.e., prerequisites thereof)? In fact -- require full-time registration for credit courses prior to paying for remedial courses? Especially so when we know half or more of such students won't graduate from the program? (Link.)

That seems quite backwards. Complete the basics first (remediation), then qualify for funding for credit courses afterward.

Stuff I'm Reading

"Preferred numbers" in engineering and product design; standardized near-logarithm increments to make both interchanging parts and mental arithmetic as easy as possible. (I've liked 1-2-5 for some time, myself.)

The "19-equal temperament" scale in music, a proposal to divide the octave (doubling of frequency) into 19 near-logarithmic parts. Argued in composer Joel Mandelbaum's PhD thesis that it's the only viable system with a number of divisions on this order of magnitude. Coincidentally matches the Hebrew calendar system and its pattern of leap years.

One-Day Calculus Lecture

Dan's brief one-day calculus lecture (1-page PDF): link.

Morse Code

Visited the USS Intrepid aircraft carrier museum yesterday (here in New York City). Among the numerous exhibits in the hangar deck is this one on Morse Code. The scrolling digital blue lines are supposed to be translations of each other. What's rather glaringly wrong with this?