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Visualizing Equations

Now we are going to try something with this equation:

x + 2 = 3

Since this equation is so simple, you probably know the answer just by looking at it.^2.2 How easy or hard it is to solve does not matter - we are going to do something else entirely with it.

Imagine that you have written this equation in big letters and numbers on a 3 by 5 card, like this:

Imagine that this card is floating in front of you, where you can see it. It's at a comfortable distance. You can move it around by imagining it. You want be able to see each individual symbol, 'x', '+', '2', '=' and '3', and their position in space relative to each other. Practice this until you can consistently see the equation on the card. It does not matter if you do it with your eyes open or shut. It can help to write the equation on a real 3x5 card, and glance at it as an aid.

By the way, you certainly do NOT need to discern it in great detail. If, in your imagination, you can recognize each of the five symbols, and get the order right, that's all that is necessary. In other words, as long as YOU can tell that the first symbol is an 'x', even if it does not really look anything like it, that's fine - you are the only one who will ever see it anyway!

Now, take the image and move it around. Move it a few inches left, right, up and down. (Your head is motionless. You are getting practice at controlling where you put the image that you see mentally.) Again, practice this until you can consistently do it.

Now make the image of the equation bigger and smaller. You are zooming in and out. Make it twice its original size. Make it half its original size. Practice until you can do it consistently.

Remember, in all of this, you're not doing anything with the equation, mathematically speaking. You are not taking any steps to solve it. You are merely creating a mental image of it, just like you could imagine a car or a banana or anything. You are then moving that image around while keeping the image more or less intact.

Here is a summary of the steps above:

1. Visualize the equation x + 2 = 3 as if it was written on a 3-by-5 card and held in front of you. In your mind's eye, see it in enough detail that you can discern each of the five symbols and their order in the equation.
2. Move the image around - left, right, up, down, towards you (in), away (out) - while keeping it whole and clear.
3. Zoom in and out. Make the image of the equation half its original size, and twice its original size.

If you can do the above, and feel comfortable with it, you can continue to the next section now. If you are having difficulty with it, you have some options. One is to continue forward - it may click into place, especially when you do the chapter exercises. Another option is to stop reading for a day. Tomorrow, practice the above three steps to refresh yourself, and to let you get more comfortable with it. When learning something new like this, giving yourself time to absorb it can be helpful.

Footnotes

...^2.2

If not, you are reading a book that teaches you how, so don't worry.