Monday, January 16, 2017

Save your pennies, I mean Nickels, wait, wha....?

There are a lot of people out there who want to get rid of the penny, including myself. But why stop there?

I'm not sure if I ever posted this, but I'll give you a few reasons why base ten is stupid, and getting rid of the penny would be a step in the right direction, but more importantly, getting rid of decimal would be the ultimate goal in mind, but we'll start with the penny.

The common argument goes that the penny is far too expensive to produce anymore. The reasons for this are kind of interesting, but more like a red herring. I don't like that argument, though.

Did you know that in strict inflation terms, a penny was worth todays quarter in 1895? It's true. You can look it up in the CPI. Of course, the CPI for specific goods was much different back then, but the average was about a quarter. If you go all the way back to earlier in our nations history, the value actually wasn't that much. Apparently from 1800 to 1900 there had been a gradual deflation of about 49%. Regardless, the penny was worth more back then, meaning that it would have been completely unfair to the general public regardless of the cost of their production, but the cost of production was lower back then anyway, so it all worked out for the Bureau of Engraving and Printing.

So the question begs to be asked: if the people in the eighteen hundreds only had what today we would call a dime or a quarter, why can't we deal with just having a dime or a quarter?

Well, the argument for the penny goes something along the lines of it not being fair to the people who have lower incomes to force them to pay a rounded up sales tax. Perhaps this is a straw man, but we already round up our sales to the nearest penny. Right now in Minnesota, the sales tax is 7.125%, so if you buy one something at dollar tree, you have to pay $1.07, because it's a bit of a trick to pay .125 of a penny. I don't know how exactly the people who made up the sales tax figured out that the .125% extra was important, but apparently it is.

The reason why that's probably a straw man is because I'm equivocating a round of ± $.005 to a round of ± $.025. Regardless, you will notice the ± sign that I use. I don't know if this is universal, but I think it should be rounded to the nearest and not automatically rounded up.

But here's the thing, hearkening back to what I was talking about before: What's the point of using the nickel as our lowest denomination?  I've got a better idea.

Let's make a list of all the denominations that are legal tender here in the US

$100.00, $50.00, $20.00, $10.00, $5.00, $2.00, $1.00, $.50, $.25, $.10, $.050, $.01.

Maybe some of you are looking at that list and saying $2 & $.5? Yes, they do still exist, and they're really cool. If you ever walk into a bank, ask for a roll of half dollars, and a wad of two dollar bills, then get a free lunch at McDonald's because the cashier hasn't ever seen them, and makes an issue about you trying to use counterfeit money, and the manager gets mad at him and gives you a free lunch.

Anyway, what do you notice about our currency? I notice that out of the twelve denominations, three of them end in something other than zero. This says to me that it would greatly simplify accounting if we just got rid of all the denominations that end in something other than zero, and suffered through what those of the 19th century had to deal with. What could be so wrong with that?

Notice that I'm not asking for us to get rid of the penny, I'm asking for us to get rid of the cent!

Why would I suggest such a thing? Well, I just said: it would make everything easier. We would just remove all .00 and replace them with .0. Doesn't that just look and sound so much more elegant? We've had it with the cent! Give us the dec! We'll still call them dimes, but that would be as low as we could go.

"But Ed," you say, "that would mean we would have to get rid of the nickel and the quarter too!"

Yes! Exactly! That's exactly what I want. That would make me so happy. Sure, nickels are fun, because they're so fat and heavy, but really, they're just next after pennies, so why don't we get rid of them too. And then quarters. Let's just get rid of those too. We can replace them with something that we already have: the half dollar.

"But Ed," you say, "Half dollars are huge, and nobody uses them anymore."

Okay, then if you really want, you can have a $.20 piece. How does that sound? Or, we could just make half dollars smaller. That would be nice too.

Now the opposition I can see is greedy retailers wanting to keep the $4.99 thing. Apparently that actually does help in tricking people into buying something even though effectively it's $5.00. I don't care. They can use $4.9 as the new standard for retail psychological trickery. So there.

Another great thing about this would be piggy banks. You see, you think you have a huge container of money, but about ten percent turn out to be pennies and another ten percent turn out to be nickels, so if we got rid of those, that would mean that a full piggybank would be about 30% more valuable! Sure, it would take longer to fill, but it would be so much more rewarding at the end.

And yet another thing would be at the checkout line, paying for your stuff with cash, and the person hands you a bunch of coins because your change turned out to be $.94. Three quarters, a dime, a nickel, and four pennies. That's a pile of nine coins. Now, let's say that your change had to be $.9. That would be so much easier. Either five coins, a half doll and four dimes, or a half dollar and two $.20 coins.

Alright, now here's the even more controversial argument: should we even be using the decimal system? Wait, what?

What's wrong with the decimal system, Ed? It's easy to understand, and makes adding and subtracting on paper easy, and makes comparing things also easier. Plus, we can count on our fingers.

Well, the entire premise of that argument relies on the assumption that our decimal system is the equivalent of a placement system of numerical notation. Did you know that Base ten was not the first numerical system to use a placement system? No, the Mayas, some of the greatest ancient mathematicians used a base twenty system, and the babylonians used a base sixty system. Of course, these are technically hybrid systems, because the digits were split into blocks that combined individual symbols that stood for five and one in Mayan math, which formed blocks that added up to a maximum of twenty, which were multiplied by that factor with each place moved.

Twenty doesn't make much more sense to me than ten, because it only adds two new factors: 20, and 4. It would be great if we could switch to a base sixty system, because that would mean we would have loads of factors: 1, 2, 3, 4, 5, 6, 10, 12, 15, 20, 30, and 60.

Why do factors matter? Because the number of factors determines how many fractions you can evenly divide the number into. Sixty can be evenly divided into 2, 3, 4, 5, 6, 10, 12, 15, 30, and of course, 60. But sixty is impractical, because we don't want to have big blocks of symbols that add up to sixty, we want a row of symbols, with each symbol standing for one of sixty values. That would pretty much take up our entire keyboard, and would be impossible to teach to elementary school kids. Factors matter because we can represent more numbers without a repeating decimal. The more factors, the more common repeating decimals we can avoid.

Twenty isn't a very good idea, because it only adds four as a factor. How about twelve? It adds three, four, and six, so now even halves, thirds, fourths, sixths, and even sevenths without a repeating decimal.

But what does this have to do with money?

Well, in serious mathematics, algebra, trig, calculus, and so on, it makes about zero difference. It's just a different way of writing numbers. But in everyday life, it makes a lot more sense. We can have a half dollar coin, a third dollar coin, a quarter dollar coin, a sixth dollar coin and a twelfth dollar coin that all have representations using just one decimal point. What about a fifth dollar coin? We don't really need a fifth dollar coin, since really we only use a third and a quarter when doing everyday measurements. (We already have a quarter dollar, for crying out loud!) Have you ever seen a recipe that called for 1/5 cups of flour? Didn't think so. 1/5 seems to me as being the useless only fraction that we can represent with one decimal place in base ten.

Last semester I came across a girl who liked decimals more than fractions. I couldn't believe my ears. Why on God's good Earth would anyone like decimals more than fractions? I dislike decimals for the exact reason I just stated: They're pretty useless in expressing common fractions. I like fractions because they can precisely express almost any number imaginable. No, they can't express pi and √2, but we have other symbols to do that, and pi shouldn't even count because it's transcendental, and as such its very definition states that it can never be expressed without using some pretty wacky notation, so I'm fine with it being expressed with decimals.

This is just a quick tangent: Never write pi = 3.14159. You may write π ≈ 3.14159, but you are lying. If you don't have those fancy keys on your computer, either get a Mac, or write pi = 3.14159... The ellipsis is important.

Anyway, to review,

1) Get rid of the penny.
2) Get rid of the nickel.
3) Get rid of the quarter and maybe replace it with a 20¢ coin.
4) Get rid of the decimal system altogether and replace it with the dozenal system.
5) Enjoy a simpler life without nearly as much change.

Inflation rate sources:

http://www.westegg.com/inflation/

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