Monday, September 29, 2014

How I Visualize the Number Line

How do you visualize numbers? More specifically, how do you visualize numbers as they progress one to the next? How do you see the "number line"? I've asked a lot of people these questions and I've gotten a lot of strange looks. Most people, I find, don't really think about the number line and certainly don't give any thought to how it lays out in their mind. For the majority of people in the U.S. (my primary source of discussion), they start at zero and go to the right forever. It is just a straight line very much like the number line we used as young children. Numbers were laid out in that fashion never to be thought about again. One or two people have said that numbers go up, but that's about it. At least that's what I've heard from people I have asked. And, let's face it, I haven't asked everyone because there are a lot of people who will just look at me like I am an idiot if I ask something like this.

I see numbers differently. I guess really it is that I see the relationships between numbers differently. For as long as I can remember, this is how numbers appear in my thoughts. I don't know what it means, if anything, but it is intriguing to me that I don't recall anyone else ever giving me numbers in anything other than a straight line.

Are you intrigued? Have you now thought more about number lines than you ever thought you would?

Here is how I see numbers. Starting with zero, right in front of me, one through ten go to the right. So far so good... From there we make a left-hand turn and goes up (or away from me) till we get to the number twenty. At twenty, the line makes a right-hand turn and continues to fifty. Once we get to fifty, the line again turns left (or up) and goes all the way to 100. From 100 to 1,000 goes to the right again. At this point (1,000), there is a sort of dotted-line divider that separates the hundreds from the thousands. I'm not sure what that represents. There is a small voice inside me that says this has significance but I've yet to discover the meaning.

You would think the line would turn left again but it doesn't. The line continues past the 1,000 divider and goes to the right until it reaches 10,000. The line turns left at 10,000 and climbs to 100,000. At 100,000 the line turns right again goes to 1,000,000. Again there is a semi-dotted divider there. Beyond one million it all just sits out there in a cloud.

This is how numbers are laid out for me. When I think of two numbers, their relationship to each other is visually located based on that meandering line. I don't know why and, as I said, I haven't found anyone else who thinks this way.

You would think that negative numbers flow the opposite. They don't negative numbers flow down from zero - down as in "south" to ten and then sort of angle south by southwest to 100. It is all just another cloud of numbers beyond there.