catastrophic cancellation
Okay kiddo, let me explain what catastrophic cancellation is. Imagine you have two big numbers, like 10,000 and 9,999. We want to subtract these two numbers to find the difference between them.
But sometimes, when we subtract two similar big numbers, problems can happen. When doing the subtraction, we first subtract the digits in the rightmost column, which are both 0. Then we move to the next column, where we want to subtract 9 from 0. But uh oh, we can't do that, because 0 is smaller than 9.
So what happens next is what we call catastrophic cancellation. The 9 is so much bigger than the number to the left of it that it cancels out the smaller number, rather than being subtracted from it. So instead of getting a difference of 1 between the two numbers, we get a result of 1 and some tiny bit left over, almost nothing at all.
This can be a big problem in some situations, especially when we're dealing with really tiny numbers or very large ones, like in science or engineering. We have to be very careful when subtracting numbers to avoid this kind of error.
But sometimes, when we subtract two similar big numbers, problems can happen. When doing the subtraction, we first subtract the digits in the rightmost column, which are both 0. Then we move to the next column, where we want to subtract 9 from 0. But uh oh, we can't do that, because 0 is smaller than 9.
So what happens next is what we call catastrophic cancellation. The 9 is so much bigger than the number to the left of it that it cancels out the smaller number, rather than being subtracted from it. So instead of getting a difference of 1 between the two numbers, we get a result of 1 and some tiny bit left over, almost nothing at all.
This can be a big problem in some situations, especially when we're dealing with really tiny numbers or very large ones, like in science or engineering. We have to be very careful when subtracting numbers to avoid this kind of error.