Symmetric level-index arithmetic is a way of doing calculations using numbers. It works like this: first, you decide what "level" of numbers you want to use - like counting numbers (1, 2, 3 etc.), or just even numbers (2, 4, 6 etc.). Then, you assign each number in your level a "index", or number. So if your level was just even numbers, 2 would be index 0, 4 would be index 1, and 6 would be index 2. Now, when you do calculations, you can use the indexes instead of the numbers. So for example, if you wanted to add 6 and 4 together, instead of writing 6 + 4 you could write index 2 + index 1, which is much faster and easier!