Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
Today is also a single-transposition day, since the each string can be formed by simply transposing the 0 and the 2 in the other string.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
Sheryl Sandberg, the COO of Facebook, recently became one of the world’s youngest female billionaires. The Bloomberg article about this featured a curious quote from David Kirkpatrick, author of The Facebook Effect.
“Did she do a billion dollars-worth of work? I don’t know. She had the good fortune to land in the right place where her talents could really be applauded.” (link)
Critics rightly took issue with the gender-bias inherent in this remark. You’d be hard-pressed to find a high-profile business publication questioning whether a rich man really earned his wealth, I suspect.
But beyond this particular offense, the implication that anyone has done “a billion dollars-worth of work” is rather absurd. That this absurdity isn’t recognized speaks to both a general problem of numeracy and to a specific problem of contextualizing large numbers.
What would a billion-dollars worth of work look like? In some ways it’s an ill-defined question, but we can explore some simple cases to get a sense of the answer.
Consider someone working for the current federal minimum wage of $7.25 an hour. A convenient rule-of-thumb approximation is that one’s hourly wage, doubled, is one’s yearly salary in thousands of dollars. (This assumes someone works 40 hours per week for 50 weeks per year, and so, a total of 2,000 hours per year.)
A full-time minimum wage worker therefore earns about $15,000 per year. At that rate, 7 years of work would be worth around $100,000, and so 70 years of work would be worth around $1 million. Since one billion is equal to 1,000 million, we see that $1 billion is equivalent to around 70,000 years of minimum wage-work.
Would any billionaire claim to have worked an equivalent of 70,000 years at minimum-wage? I doubt it. Not publicly, at least.
Some other benchmarks may help establish further context. For example, the average teacher salary in New York state is around $45,000 per year. Roughly speaking, that’s $100,000 every two years, and so $1 million every 20 years. Thus, $1 billion dollars is worth around 20,000 years of teacher-work.
What about highly-paid professionals? Surgeons typically earn around $250,000 per year. A quick calculation shows that a billion dollars is worth about 4,000 years of surgeon-work.
While the article suggests otherwise, to me, the answer to the question “Has anyone done a billion dolllars-worth of work?” is pretty clearly “No”.
An interesting follow-up question might be, “Has anyone created a billion dollars worth of value?”
Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
Celebrate Permutation Day by mixing things up! Try doing things in a different order today. Just remember, for some operations, order definitely matters!
Today we celebrate a Derangement Day! Usually I call days like today a permutation day because the digits of the day and month can be rearranged to form the year, but there’s something extra special about today’s date:
The numbers of the month and day are a derangement of the year: that is, they are a permutation of the digits of the year in which no digit remains in its original place!
Derangements pop up in some interesting places, and are connected to many rich mathematical ideas. The question “How many derangements of n objects are there?” is a fun and classic application of the principle of inclusion-exclusion. Derangements also figure in to some calculations of e and rook polynomials.
So enjoy Derangement Day! Today, it’s ok to be totally out of order.
Today we celebrate a Permutation Day! I call days like today permutation days because the digits of the day and month can be rearranged to form the year.
Not only is today a permutation day, but it is also a double-transposition day! We can turn the month and day into the year by first transposing the ‘1’ and the ‘2’, and then transposing the ‘1’ and the ‘0’. Permutation days are also nice because, unlike Palindrome days, they can celebrated on both sides of the Atlantic without heated disagreement.
As usual on Permutation Days, I suggest celebrating by mixing things up!