Way Back Machine

For some utterly unknown reason, I was thinking today about "new math". This was the experiment tried on several of us unsuspecting school kids back in the 60's. The School Mathematics Study Group (SMSG) came up with a curriculum, bound in a yellow paperback textbook, that was supposed to take us all to another level of capability in mathematics excellence. I thought it was stupid and confusing, and they lost me on set theory, which I believe was the first chapter. I was busy still trying to understand how to solve the "a train leaves Seattle, traveling east at 50 miles per hour...." problem, and they wanted me to describe the resulting set that is formed through the confluence of set A and set D. So what? It just leads to academic discussions of junkified weirdness like considering that the set of all sets of unique elements cannot exist. Okay, fine, but that won't solve a quadratic equation (which I never understood the importance of, but we spent almost two years in high school math learning how to solve one).

So, one assumes that 2+2 equals 4, having realized that in kindergarten. However, now we understand that 2 could represent a theoretical set of uniquely relational numbers, in which case 2+2 equals the union of the two sets represented each by the number 2, although in this case, 2 does not necessarily equal 2, since each 2 could represent a discrete set. If each 2 represents the same set, meaning that 2=2, then 2+2=2, since the union of a set with itself is the same set. See, I got it, even though they lost me there. It's difficult to understand how 2+2=4 only in the most elementary and simplistic environments. In more enlightened environments, 2+2 equals an unknown array of potential answers or, if 2=2, then 2+2=2. Wait till we get to subtraction, let alone multiplication and division.

So, as a gullible 4th grader, answer this one: What is the denominator of the fraction that solves the equation 3x-7=8? Well, the simple answer is x=5. But that's not what they asked. 5 is not a fraction, unless you know SMSG. 5/1 is a fraction, equalling the number 5, so the denominator is 1. However, x could equal 10/2, 15/3, 20/4, etc. So the real answer for the denominator is the set of whole positive numbers from 1 to infinity. But wait. What if the numerator is negative? What if it is a non-whole number? The only denominator then that doesn't work is zero. And that's the answer: The set of all numbers not equal to zero. Doesn't have a flippin' thing to do with the reality that you have 3 times as many apples as Billy Bob. You give 7 apples to Emmy Lou, and have 8 left. How many apples does Billy Bob have? Uh, it could be any number other than zero, unless we are constrained to actual whole apples or apples in hand rather than imagined or forecasted, in which case the answer would be all whole numbers greater than zero. Give me a break. Give that answer in class and Billy Bob will meet you on the playground after school, beat you up, throw your SMSG book in a puddle, and take all your apples.

Some Mess Some Garbage, as we called SMSG back then, apparently was a failure and has been abandoned. It left an impact, though. I still feel uncomfortable when I see a yellow paperback book, including the Yellow Pages, at least until I have proven to myself that it really is just a phone book.