The Agony and the Apostasy

The Creation of Adam, Michelangelo Buonaroti

The construction of the Sistine Chapel (Capella Sistina) was completed in 1481. Its construction was commissioned by Pope Sixtus IV for whom it was named. One hundred thirty four feet long and 44 feet wide, the huge chapel is a towering 68 feet high. The ceiling, originally painted in a field of blue with gold stars, was covered in beautiful frescoes by Michelangelo at the behest of Pope Julius II.

Michelangelo labored for four years, from 1508 to 1512. He painted over 5,000 square feet of frescoes containing over 300 figures. Some of the most beautiful art ever created, such as The Creation of Adam, embellish the chapel’s ceiling. In addition to being one of the world’s most talented sculptors and painters, Michelangelo proved to be a highly competent engineer, designing a clever scaffolding system that allowed services to be held in the chapel below as he painted above. Four years of talent, genius, and backbreaking labor resulted in one of the world’s most breathtaking works of art.

And at the end of these four year, Michelangelo approached Pope Julius and, on bended knee, kissed his ring and asked for payment. “No,” the Pope responded, “you did not do that. The chapel was funded by the Church. The paints were purchased by the Church. The laborers who erected your scaffolding were paid by the Church. You did not do that.”

A small fiction, of course, but of a spirit with the narrative presented by the Democratic left. Elizabeth Warren, Barack Obama, and, most recently, Hillary Clinton assert that entrepreneurs do not create businesses and corporations do not create jobs.

Those to the political right, Senator Cruz and friends, are aghast at such apostasy, believing that no one but entrepreneurs and corporations create businesses and jobs.

How to explain this chasm?

First, let’s try to understand what each side is actually saying. The Warren camp means to say that public spending, public infrastructures, public services, are all essential to the entrepreneur and corporations. That businesses and jobs couldn’t be created without reliance on government.

Those on the right recognize that government creates a public infrastructure. And, more importantly, it creates a system of laws that protects each citizen’s liberty and property rights. But they are just as adamant that, government or no, businesses and jobs wouldn’t exist without those who create them.

Both positions are a bit more sympathetic when viewed in a larger context. But which is right? This seems a bit of a standoff, a chicken or the egg puzzle. What came first, the jobs or the highways?

To answer this, we must delve into the tangle of Aristotelian logic and the concept of necessity and sufficiency. While logic can be quite complex (after all, it underlies all computers, the internet, Facebook, and silly cat videos), in this case it is quite straightforward.

This is something you already know. Think of the components of a grilled cheese sandwich: bread and cheese. Is it necessary to have cheese to make a grilled cheese sandwich? Obviously, yes. But is it sufficient to make a grilled cheese sandwich with only cheese? Equally obviously, no.

The cheese is necessary but not sufficient. The bread is also necessary but not sufficient. One needs both cheese and bread to prepare the grilled cheese sandwich. But to make simple toast, the bread is both necessary and sufficient.

Apply to the Sistine Chapel. The Pope is correct, Michelangelo could not have painted the ceiling if the Church had not built the chapel. But the ceiling would not have been painted so beautifully without Michelangelo (or someone of equal talent). Both conditions are necessary for the result. 

Fast forward 1,500 years. Senator Warren is correct that jobs and businesses could not (easily) be created without the infrastructure provided by government. But Senator Cruz is equally correct that jobs and businesses would not exist without entrepreneurs and corporations to create them. Just like a grilled cheese sandwich, we need both government and business. One cannot thrive without the other.

One way to view it is that government creates a canvas upon which the creative, risk-taking entrepreneur paints her vision, creating businesses and jobs as a result.

Which is a tale of caution, for those who would strangle government in the extreme risk the ability of entrepreneurs to create. But those who would smother business risk government as well. It is, after all, the taxes and fees paid by businesses and corporations and taxes paid by wage employees that support government. Without a healthy, bustling economy, from where will government funding be obtained?

Food for thought next time you see corporations and businesses taking it on the chin.  

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!