• Home
• Inner Algebra
• Integrate Your Brain

Windowing

Choose three equations that are big enough that you can remember (meaning you can write them down by memory) but are bigger than you can easily visualize. (If you can visualize all equations you can remember, just choose three of the largest equations you can visualize.) You will get the most out of this exercise if you pick equations that are fairly different from each other. Write down these equations so that you can refer to them. You will also need another blank sheet to write on.

Do the following with each equation.

1. Look at the equation, and study it so that you can remember it. Turn over the sheet or cover it, so you can't see it. On your other sheet, write down that equation from memory. When you are done, check that you remembered it 100% correctly - that's important! If what you wrote down does not match, or you are not able to remember it, study it again and repeat until you are able to do this.
2. Where you wrote down the equation, divide it up into three to five expressions, circling each one. You want to choose expressions that you are able to visualize (since that is what you will be doing with them). When you are done, every quantity in the equation should be in a circled group. For example, if your equation is $\frac{x^{2}+3x+1}{x-1}=4+2\sin\frac{\pi x}{4}$, you might circle the x - 1 on the bottom left, the $x^{2}+3x+1$ on the top left, the 4 on the right, and the $2\sin\frac{\pi x}{4}$, for a total of four circled expressions. (You don't necessarily need to circle all the operators.)
3. Cover the equation so that you can't see it (or close your eyes, etc.) Visualize the structure of the equation, like in the figures on pages to , so that you are able to see its general outline (even if you are not visualizing each and every symbol involved). Include in the image one of the expressions you circled before. You will end up visualizing something that has the general structure of the full equation, with the circled expression visualized and the remaining symbols blurry or just not visualized. Practice if you need to, until you can mentally see this. You can write/draw a diagram (like the figures mentioned above) to help you if needed.
4. Next, allow that circled expression to fade out. Pick one of the other circled expressions, and bring it into the image instead. You are doing something exactly like in the previous step, just with a different circled expression. Practice if needed, until you are able to mentally see this. Repeat this process with each remaining circled expression.