Part One: NUMBERS
Chapter 3. The Enemy of My Enemy
The disturbing concept of subtraction, and how we deal with the fact that negative numbers seem so…negative
This chapter goes into the problem of subtraction in the real world. The problem arises because we can only think of negatives and conceive them in our mind, because there’s no such thing as negative apples in the real world. Although, there are examples that negatives are helpful such as financial balances and temperature. It also talks about the “nature” of subtraction in the real world, and gives the example of balanced and unbalanced triangles taken as the relationships between people or countries, and that’s where the title of this chapter comes from.
Chapter 4. Commuting
When you buy jeans on sale, do you save more money if the clerk applies the discount after the tax, or before?
This chapter talks about the commutative law. First, he explains the difference of commuting verbally (which gives a very different meaning to the operation) and visually (which is barely different, but it’s only visually different). Then, he explains how in our daily life we get confused by the application of this law and almost intentionally forget it, but no matter if we are buying jeans on sale of a retirement plan, this law can be applied (ceteris paribus). Finally, he explains why some things in the world are not subject to this law and explains that they require certain sequencing, thus they are non-commutable. One example is Heisenberg principle in quantum mechanics.
Chapter 5. Division and Its Discontents
Helping Verizon grasp the difference between .002 dollars and .002 cents.
In this chapter, he explains the divisibility of numbers, going through decimals and fractions. He also explains some of the problems we encounter when thinking of this and how we can sometimes not conceive why some numbers are divisible or how fractions are to be interpreted. He also explains a little about periodic (0.333…) and irrational numbers (0.12122…; 3.1416…).
Chapter 6. Location, Location, Location
How the place-value system for writing numbers brought arithmetic to the masses.
This chapter is about number systems and how the location of the digits in a number system has allowed us to expand arithmetic to many uses. He explains how we started using our fingers as a way to count or digitalize this counting by putting strokes, and later they evolved to our current Hindu-Arabic system. One of the main points is the creation of the ten digits in this system and specially the zero. He also explains other systems such as the base-60 of the Babylonians or the binary system, which has the base-2.