Numerals are the names we give to numbers. Twelve, 12, Dozen, XII, Двенадцать, Twaalf, and Doce all refer to the same number. The number is the collection of objects, so the numeral is an adjective describing the collection. In the sentence “Bob has twelve blue eggs” the words “twelve” and “blue” describe the eggs Bob has. If he gives away an egg, the collection has changed as much as if he had bleached one white.
Just wanted to get that out of the way. The word “number” is in some ways similar to the word “anesthesia”, something that makes you numb. Maybe not you, but many people.
Most people do not understand numbers or their relationship to each other. As the data is translated into numerals, the level of understanding does not increase. Part of this is rooted in language, almost everyone understands the difference between addition and geometry, without realizing the difference between million and trillion is geometrical rather than linear. Moving a decimal point is not a function of counting, the simple addition or subtraction of a single unit, it is the multiplication (or division) of a number by a factor of the base. We use base ten, one hundred is ten times ten, or ten squared, one thousand is ten times ten times ten, or ten cubed. One is ten divided by ten, zero point one (0.1) is ten divided by ten divided by ten. 0.1 is related to 10 the same way 10 is related to 1,000. Decimals are easy, fractions drive people insane.
Really big events are often expressed using numerals, but if numerals and the numbers they represents are not understood, the event isn’t understood either. It is often said “Numbers don’t lie”. Words don’t lie either. Both can be used to tell lies.
I give you this as a preface to some numbers I’ll be referring to in the coming weeks. I’m going to be exploring some common myths in our culture, and I want to get your minds in a place where they can analyze the data without taking my word for the meaning of the numbers. For today, I’m just going to go over a couple of ways numbers have been used to lie, or at least mislead.
I have nothing against H&R Block, I’m using their ad as an illustration.
There is a commercial for H&R Block in which they state one billion dollars in tax deductions are missed by people who complete their own returns. We’re going to accept this as a fact without any verification, one billion dollars in deductions. As anyone who has prepared a tax return is aware, one dollar of deductions does not equal one dollar of taxes, but this is an ad for people who haven’t done their own tax returns, so why not go ahead and accept that one billion dollars in taxes have been overpaid. I won’t go into the representations of one billion dollars used in the commercials other than to say there would be different results if the money was in one dollar bills, hundred dollar bills, or pennies.
The population of the United Sates is estimated to be just over 316 million people in 2013. That means the one billion dollars is about $3.16 per person. Using the logic presented by H&R Block, your family of four is due an extra $12.65. Knowing that, are you ready to spend thirty dollars to have them prepare your taxes?
Of course, my numbers are wrong. Although each person should be represented on a tax return, each person does not file a tax return. Of actual tax returns, less than half are individuals (people rather than businesses). A small number (relatively speaking) are filed on paper rather than digitally. That small number is estimated as less than ten percent of the total number of returns, or a little over twenty four million returns for 2013. What, you didn’t think twenty four million was a small number?
So who knows what H&R Block is referring to in its commercials? All that is important is you should get your share of one billion dollars. If that share is a three hundred sixteen millionth, it isn’t much of a share, but you’re not supposed to think about anything other than the pile of bills shown in the commercial.
Next we’ll talk about graphs, visual representations of numbers.