I started doing an audio podcast called STUMP – Death and Taxes (and yes, I’m using the old plainchant Dies Irae as my intro/outro on the podcast) this year, up to 25 episodes thus far. It’s just a start, so I’ll pick two as my favorites thus far.

Yes, I know I keep coming back to this one, but I gotta love it:

Interest Rates and Sumo! — interest rates have taken us for a wild ride this year, and so has sumo (I should return to this theme when I get back from my trip, because there’s a new development in the sumo world.)

Because of this episode, I wrote an article: Interest Rates and Sumo for the International Section of the Society of Actuaries. My blog post plugging the article and the last sumo tournament is here: Interest Rates and Sumo, Nagoya 2022 Edition. Watch out for the September 2022 edition… you know it’s coming!

My other favorite episode thus far is Fraudulent Life Insurers — I absolutely love fraud stories, but also, Martin Chuzzlewit is my second favorite Dickens novel. (Our Mutual Friend is my favorite)

Here is my video from a few years back where I’m talking about the Anglo-Bengalee fraudulent life insurance company:

I did turn that one into an article as well for the Society of Actuaries: Dickens and Business Fraud

HOW QUAINT—SO WHAT?

This might seem a cute exercise, looking at the historical frauds and failures related to literature. But who cares? That’s almost 200 years ago! We’ve come so far!

But have we? Think of Bernie Madoff—a man who worked his social connections, who hooked in people who believed that he was doing something legitimate (like Merdle) or those who figured he was corrupt and thought they could also profit (as with Jonas Chuzzlewit hoping to profit from the Anglo-Bengalee). Madoff perpetrated his fraud longer than Montague managed, mainly because he didn’t get murdered by a blackmailed partner.

Think of Enron, where clever people figured that they knew a surefire way to mint money … but then ran into trouble. Think of subprime mortgages, WorldCom, asset bubbles of one sort or another—the essentials of current frauds may differ in the specific details, but many of the human behaviors behind them remain the same.

….

How do we prevent new frauds and asset bubbles? One may take a technical approach, but at the heart is human nature—how people behave, how people have particular goals, and how some will try to get what they want fraudulently. Many of these frauds are successful due to the perpetrator’s own knowledge of human nature. It’s hilarious how often we hear “This time it’s different!”…. and it turns out people’s greed, envy, pride, and pretty much all the mortal sins, come into the mix in the same old way.

Dickens was wise, that man.

Also, he had direct experience in City of London dealings.

When I started my Meep’s Math Matters YouTube channel waaaaaaaaaaaay back in 2007, it was when they restricted you to uploading videos under 10 minutes long. I thought I would do short math lectures at the time. Obviously, the tech was different then.

I’ve added a few videos more recently to the playlist, but it will likely be a while before I built it up. There are loads of other people doing math videos now, after all.

That said, here are a couple videos I hope you find interesting:

One on voting systems:

One on parity:

As I said, there’s a whole playlist, so enjoy!

]]>So, I saw the following via Powerline: Putting the Pi in pies: Twitter user stuns the internet with math that proves one 18-inch pizza has more in it than TWO 12-inch helpings

The theory was posted by U.S.-based Twitter user @fermatslibrary

Supported by a graphic, the theory proves that one 18 inch pizza is better value than two 12 inch pizzas

Since it was posted, the tweet has received almost 1,500 comments and a total of 60,000 likes

It has also been retweeted 25,000 times, as people try to spread the word

Some users are baffled by the theory, claiming that it cannot be true

Last month, an article in the New York Post revealed that it is better value to order individual pizza slices rather than an entire pie

So. This makes the “news”. But not the 80% fundedness myth.

This is what John Hinderaker had to say about this:

I am often baffled as to how so many of our fellow citizens can fail to understand basic facts of politics and economics. It is sobering to be reminded that many of them are stumped by the size of a pizza. I think liberals must understand this better than we do, which is why they generally appeal to emotion rather than reason.

Look, this is not a Democrat vs. Republican issue. I mean not only the pizza but emotion vs. reason. Republican politicians also use emotions, too, but they’re different emotive thrusts.

And that’s not even my point.

**MY POINT: WHAT MATH SHOULD BE KNOWN**

Here is my video take:

**SCHOOL MATH VS LIFE MATH**

I’ve had **calculus** students who claimed not to know the area of a circle. I wrote about this back in 2000:

Some people complain that calculator use in math classes is a crutch. I disagree – they can be very helpful. However, when I see current freshmen in first semester calculus classes, I realize that often calculators are not only crutches given to people who can’t use their legs but crutches given to those who also can’t use their arms. Students come into Calculus, with perfectly fine SAT scores, unable to solve algebraic equations and unable to graph lines. Giving these students graphing calculators which also can do symbolic math helps noone. For when they come to a related rates problem which states “You have a circle whose radius is expanding at the rate of 2 centimeters per second. How fast is its area growing when the radius is a meter?” they will complain to the TA “But we didn’t know what the area of a circle is!” (this happened to me in

the first class I TAed.)These are students, having had Calculus the previous year in high school, classes which went all the way through integrals, who have the slightest idea of a derivative.

Math education hasn’t much improved since then (and my argument is that the main reason it hasn’t improved is that the teachers generally don’t understand the math they are supposed to be teaching)… but don’t feel bad if you don’t know how to compute the area of a circle or don’t know calculus. Heck, I used to help other actuaries with their kids’ calculus homework, because I was the only person who actually remembered it. Actuaries do not directly use calculus very much, though it underlies many of our models.

But actuaries **understand** how the numbers interact. We have some complicated stuff, and it’s okay that non-actuaries don’t understand all the fiddly bits.

A lot of the math you learned in school probably isn’t (directly) useful to you, and that’s even true for numerate folks. I’ve forgotten a lot of not only “school” math (by which, for me, that means grad school math), but also chemistry, literature, etc. That’s okay. It’s even okay that there is some math you didn’t learn (I probably remember a lot of math that many/most of you readers never learned… nor never knew existed. Even if you have a math degree… math is hyuuuge.)

But you **do** need to understand that certain numbers are bigger than other numbers, etc.

That you don’t know that an 18-inch pizza has bigger area than two 12-inch pizzas is no big deal.

If you don’t know that 81 is bigger than 72, then you have a problem.

The math you need to understand to get through life, for most folks, is not really complicated. This stuff is arithmetic + a few other things, and it doesn’t even include algebra.

**THE MATH YOU REALLY NEED TO KNOW**

There is the math you need to know as an individual.

- Taxes

- Interest rates on loans

- How savings compound over time, and what are realistic, and unrealistic, outcomes

- The trade-off between uncertainty in results and paying for insurance against those results

To be able to understand some of these, you mainly need to add, subtract, multiply, and divide, and understand what those mean.

And you really need to understand percentages.

Given what I blog about, I assume most people coming here are numerate on this level. I talk about numbers at that level **a** **lot**. I rarely do anything terribly complicated math-wise here.

But the vast majority of people aren’t reading my blog. And the vast majority of people would rather not think about numbers in the first place. I understand that.

If you know somebody who needs help with math, a great FREE resource is Khan Academy — I highly highly recommend it.

**THE MATH JOURNALISTS NEED TO KNOW**

So, while few people are listening to me, more people are watching, reading, and listening to various news folks.

What math do the journalists really need to understand?

They need to understand:

- how basic statistics work: mean, median, mode, standard deviation, and sample sizes

- the difference between percentage increases and percentage point increases

- The distinction between rates and absolute amounts

- how to read a simple income statement and balance sheet (and what the differences are)

- how units work in general (like miles per hour, etc.)

There is more, but I’m talking about some very basic ideas.

Here is some basic math for journalists

An exhortation from 2010 for journalists to understand numbers more:

CAIRO—I tell my students that in addition to English they should learn two more languages: an in-demand foreign tongue, and statistics.

Studying Chinese or Hindi is a great move for an aspiring reporter, but numbers are the true global language. Journalists who can amass and interpret data can cover more of the world in a short time than reporters who just spill prose based on what they see.

….

And yet this harmful dichotomy persists. It is still common to hear a journalist woefully mumble, or even gleefully declare, that they’re “not a math person.” Plenty of college journalism programs, including the one in which I teach, don’t require students to take a statistics course. Some young people even gravitate toward journalism because they believe there won’t be any math involved.

….

Fortunately for journalists who aren’t “math people,” the latest WikiLeaks bombshell sprayed shards of diplomatic cables, which, if one reads English, can be combed and discussed. But if they don’t have basic knowledge of descriptive and inferential statistics, what will reporters be able to do with even moderately complex datasets dumped on WikiLeaks? Sadly little.

…..

Journalists can’t do everything, and it’s easy for media critics to enumerate all the things that modern reporters must be. I’m not even full of my own medicine: I’ve never taken a macroeconomics course, and I know that my reporting has at times been less substantive as a result.But statistics is too pressing a global language for journalists to neglect. Statistically untrained journalists are watchdogs without olfactory cells; they’ll catch wrongdoing when it’s visible, but they lack the skill to sniff a sour deal.

I **have** talked with some very numerate journalists, and they do tend to gravitate to the business and finance areas. Yes, there are a few journalists covering public finance (such as Mary Williams Walsh), but they are only a few who exist.

There are loads of publicly available data, such as via the Public Plans Database or Open the Books. Local journalists… **if** they understood the numbers, could use these tools to find stories. Do they know what to look for? Is it really news that you have a bunch of people making over $100,000/year in certain positions? (You’d have to compare against comparable positions elsewhere. It doesn’t shock me, for example, that doctors at public university hospitals get paid a lot. What do you think these sorts of specialists get paid at private hospitals?)

A lot of the public finance coverage is driven by both events (annual budgeting) and by press releases (yes, I receive these, so I know what ‘stories driven by some non-profit org pushing out a press release’ looks like.)

But wouldn’t it be nice if an investigative journalist knew how to investigate financials and find the stories on their own?

Now back to silliness.

**PIZZA CRUST: A DIFFERENT TAKE**

I love pizza crust (meaning the edges, without toppings). So I want to maximize my crust take.

Now, I could get complicated and do a “area of pizza crust” comparison (okay, I will do that at the very end, but not quite yet). But let’s keep it simple and measure the crust simply by the circumference of the circles.

While the area of a circle is pi times the radius squared (and the radius is half the diameter), the circumference is simply pi times the diameter.

Circumference of an 18-inch pizza: pi * 18

Circumference of two 12-inch pizzas: 2 * pi * 12 = pi * 24

24 is larger than 18.

MORE CRUST ON TWO 12-INCH PIZZAS! YAAAAS!

**MORE REALISTIC CALCULATION**

Okay, let’s get super fancy. Crust isn’t one-dimensional (which is what circumference measures). It has its own width. Now, I like really crusty pizzas, so let’s say that crust (the part without toppings) is 1 inch thick on pizzas of any size.

So the crust is really the difference of the whole pizza area minus a pizza one inch smaller in radius.

So the crust for an 18 inch pizza -> radius = 9 inch => difference between area of a 9-inch-radius circle and an 8-inch radius circle =

pi * (9^2 – 8^2) = pi * (81 – 64) = 17pi

For the 12 inch pizza -> 6 inch radius -> difference between area of 6-inch-radius pizza and 5-inch radius pizza

pi * (6^2 – 5^2) = pi * (36-25) = 11pi

So two of them is 22pi

MORE CRUST ON TWO 12-INCH PIZZAS WITH ONE INCH WIDE CRUSTS! YAAAAS!

But yes, the 18-inch pizza has more area overall.

]]>As per yesterday’s post, the PNC Christmas Price Index really counts up the cost of all the presents on the 12th day of Christmas and not the cost of the entire song.

Having found the official site of the PNC Christmas Price Index, I was ready to rain down righteous math on their heads….

….and then I read this in their FAQ:

What is the Christmas Price Index®, anyway?

The PNC Christmas Price Index (PNC CPI) shows the current cost for one set of each of the gifts given in the song, “The Twelve Days of Christmas.”

What is the “True Cost of Christmas?”

The True Cost of Christmas is the cumulative cost of all the gifts when you count each repetition in the song, reflecting the cost of 364 gifts. This cost has measured even wider fluctuations over the years.

Well dang.

But just because I haven’t flogged my video enough, here ya go again:

**NOT DOING THE KIDDIES’ HOMEWORK**

On the website, they’ve got some exercises for kids to do to help learn about price indices and inflation. It’s a cute little exercise, and I think if one could extend it to items that the kids know better, that would be cool. (For example, should you have the price of an iPhone in your consumer price index basket? Would you include the latest one? Do you need to take the features & memory into account?) (Separately, I found an error in their exercise sheets… but I leave it up to the reader to find it, too! If you download my spreadsheet, I highlight the error.)

But bah. I’m just going to grab their data for each component (which can be found in the interactive graph on their page) and do a bunch of graphs! WHEE!

**GRAPHING THE CHRISTMAS PRICE INDEX BY COMPONENT**

I’m going to start out with the Christmas Price Index, which is just the 12th day’s cost (as it has each set of gifts once).

Here it is.

It’s difficult to interpret, because there are so many elements…and Excel isn’t that great with its default color palette choices when there are multiple elements. I will just tell you that the swans are the most expensive part of the index… let’s do a break out by percentage and line graphs to see that:

You see that the swans started out at 70% of the index! The second element, by 2017, was the dancing ladies.

Just notice how some elements add essentially 0 to the index, as they’re wiped out by the other costs. But some others are steadily increasing. HMMMM.

**GOODS VS. SERVICES**

If you delve into the underlying data, you’ll see that certain items have really sticky prices. In my last post, I was a bit skeptical, but when I read where they got their info, it became clear that they’re looking at retail prices from somewhere, and many suppliers are loathe to change prices on items when people become used to certain goods being at certain prices…

…but that services have a way of escalating, especially for skilled services.

So I split the 12 days of Christmas into two groups: goods vs. services. The goods come in the first 7 days, what with all the birds, gold, and a tree. The services are the maids, ladies, lords, pipers, and drummers. Let’s do it as an area graph first:

Hmmm, interesting. The goods (in red) seem to go up and down… but it’s not clear what’s happening with services. Let’s turn that into a line graph.

Ah! The goods’ value can drop down and move up drastically… but the services cost has inexorably grown.

**A DIVERSION ABOUT MILKMAIDS**

It is at this point that I mention I think the milking maids are mispriced – they’re just putting it at unskilled labor cost, which they term being worth minimum wage. Ah, but how many jobs really pay minimum wage?

In 2016, 79.9 million workers age 16 and older in the United States were paid at hourly rates, representing 58.7 percent of all wage and salary workers. Among those paid by the hour, 701,000 workers earned exactly the prevailing federal minimum wage of $7.25 per hour. About 1.5 million had wages below the federal minimum. Together, these 2.2 million workers with wages at or below the federal minimum made up 2.7 percent of all hourly paid workers.

Now, of course, not all hourly paid workers are unskilled, but I imagine the grouping of “unskilled” labor is a lot more than 3% of the hourly paid workforce.

In any case, people generally don’t milk cows by hand anymore – that was true when I was a kid (I remember all the milking machine videos from educational TV. Charlotte’s Web was more interesting re: farming than the industrial farm vids I saw. I’d rather see a candy making factory if we’re going to watch machines.)

My point is, they should be calling up some hippie dairy farm that advertises artisanal raw milk, with the cows hand-milked by genuine milkmaids, and find out what those milkmaids are paid.

**TOTAL COST GRAPHS**

Now, of course, that was just the costs from the 12th day. If we include the costs of all 12 days, the weighting of components differs somewhat — those swans weigh a lot heavier on the cost, as they appear on 6 days (the 7th, 8th, 9th, 10th, 11th, and 12th days), whereas all those leaping lords, etc., appear on fewer days.

So here’s the total cost graph:

That area for the swans is a **lot** bigger now.

And here is the goods vs services split:

So we see the goods, appearing on more days (and including the extremely pricey swans), are driving the results more than services when we account for all 12 days of gift-giving.

Spreadsheet is available here.

Watch out for those Swans! They’re pricey!

]]>For those who are interested in how Stu is doing, here is the most recent post. (He is the STU part of STUMP. Obviously, that leaves me the MP part… as I’m Mary Pat.)

**TAXES**

I have let the tax reform thing drop, as mentioned earlier, because I’m supposed to write about it for work… and I keep waiting… and waiting…. I don’t know when they’re actually going to officially pass anything, so we’ll see.

But while we wait, this site purports to calculate the individual tax change for people, approximately.

Now, I supposedly would save about $5K on my federal income taxes according to this calculator (yes, I pay a lot in taxes), even though state & local tax deductions would be gone. As I told many people, if the marginal rates came down (and the exemption/deduction replacing the itemized deductions was reasonable) then probably a lot of people, even in high-tax regimes like NY and CT, would do just fine.

But yes, those in much lower state tax regimes would probably do better. Good for them!

**LOTS AND LOTS OF PRESENTS**

I posted this in the Stu update, but in case you didn’t go there, here is a little Christmas math-related video I made some years ago:

Which reminds me — that cutesy-poo “cost of the 12 Days of Christmas” estimation is wrong every year…because they’re only totalling up the 12th day’s cost.

Let me recalculate:

So, the final cost was actually more like 4.5 times the original, because some fairly pricey items got given on multiple days.

It doesn’t make much of a difference when compared to 2016, mainly because most of the prices didn’t move at all. I’M SKEPTICAL.

**MERRY CHRISTMAS!**

I will likely do some other posts before the end of the year, but it’s a frantic season so I figured I’d do this now….

Enjoy!

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