The Hitchhiker's Guide to Mathematical Balderdash

By the time you read this, the midterm elections of 2014 will have passed. You will be either ecstatic with the peoples’ decision or deeply disappointed. In either case, it’s time to take a breather and think of more ethereal things.

The internet is fascinating. The topics which ebb and flow on social media are a revealing window on the subject of human thought, susceptibility, and superstition. Perhaps a lesson or two to learn here.

For instance, a recent post making the rounds is typical, piquing our interest and suggesting some magical properties. It proposes that our shoe size can predict our age.

One of a class of such postings, this one posits that your shoe size can predict your age as follows:

1.       Take your shoe size (whole number, round up if necessary)

2.       Multiply it by 5

3.       Add 50

4.       Multiply by 20

5.       Add 1014

6.       Subtract the year you were born

And voila, the result is your shoe size as the leftmost digits and your age as the rightmost. “It’s magic!” proclaims the post. Balderdash.

Let’s take this apart, understand it, and identify its limitations.

Our first task is to express this as a simple expression:

(SHOE x 5 + 50) x 20 + 1014 – BIRTHYEAR

Let’s try it assuming a shoe size of 9 and birth year of 1971.

(9 x 5 + 50) x 20 + 1014 - 1971

The result is 943. Shoe magic, indeed! This person’s shoe size is 9 and age 43!

Dang – how did it know?

Rest assured, there is no mystery here. Let’s apply a little math. Starting with the first expression, we can reduce and represent it as follows:

((SHOE x 5) + 50) x 20 + 1014 – BIRTHYEAR

SHOE x 100 + 1000 + 1014 – BIRTHYEAR

SHOE x 100 + 2014 – BIRTHYEAR   

                                                                             

Now it begins to make a bit more sense. SHOE x 100 shifts the shoe size to the left and 2014-BIRTHYEAR yields the person’s age. Adding them together gives us the result:  943 in this case.

A few things might become obvious to you at this point. The use of shoe size is completely arbitrary. We could use hat size or the number of cups of oatmeal in your breakfast or any other number. Shoe size, per se, has nothing at all to do with it.

If you play around, you will also find that if the birth year is over 100 years ago, the calculation breaks down. Also, once we get to next year (2015), the age calculation is no longer valid: it only works for 2014 because of the constant “1014” in the original expression.

No magic at all, this is a cheap algebraic parlor trick.

Another recent math problem making the rounds of social media raised more acrimonious debate than that of the supporters of Senator Elizabeth Warren vs. those of Senator Ted Cruz. My goodness, math has only one right answer, what is the grounds of debate?

This one is based on mistaken assumptions, perhaps a cautionary note in all of our dealings.

Take a look at this expression:

36 / 6 x 3 + 2

In other words, 36, divided by 6, times 3, plus 2. But in which order do we apply these operations?

One option is to divide 36 by six first, then multiply by 3 , finally adding 2. The answer would be 20.

18 + 2 = 20

Another alternative is to multiply 6 by 3 first, the divide into 36, finally adding 2 yielding 4.

36 / 18 + 2 = 4

Two distinct answers, 20 and 4. Which is correct? The wrong answer could blow up the next resupply mission to the International Space Station (math applied to the real world can be really important).

There is a guide known by the acronym of PEMDAS which describes the order in which operations are to be performed:

1.       Parenthesis

2.       Exponents

3.       Multiplication

4.       Division

5.       Addition

6.       Subtraction

This guide is a gentleman’s agreement meant to remove ambiguity. But the prescription leaves itself open to misinterpretation.

A common (incorrect) assumption is that multiplication comes first relative to division but, in fact, multiplication and division are of equal weight  (as are addition and subtraction). When operations are of equal weight, they are processed left to right as encountered. The correct way to interpret PEMDAS is PE(MD)(AS), meaning;

1.       Parenthesis

2.       Exponents

3.       Multiplication and division, equal weight, left to right

4.       Addition and subtraction, equal weight, left to right

So the proper way to evaluate the above expression is as follows:

36 / 6 x 3 + 2

6 x 3 + 2

18 + 2

20

If you guessed 20, you win the prize!

Enough of the numbers. Revel (or commiserate) the recent election results, and embrace a bold new confidence in debunking the Internet’s mathematical puzzles. You can do it!