Use AI like you'd use a calculator for matrix multiplication

For a while I’ve been thinking about how I want to view my relationship to GenAI as a tool, and I think I’ve settled on a metaphor: I use GenAI in the same way as I use a calculator to do matrix multiplication.

I’m busy relearning maths from the ground up, and I hate doing matrix multiplication by hand. I mostly use a calculator. But is that okay?

Multiplying matrices by hand is a pain in the butt. You multiply the elements of the row of the first matrix with the elements of the column of the second matrix and sum.

The problem here is twofold.

Mechanically there are a lot of moving parts. The “recipe” is easy enough to remember, but one small slipup will invalidate all of the work (frustrating). This is why just punching this into a calculator is way easier.

The second problem is the bigger problem: it’s wildly unintuitive. Sure, it’s easy enough to mechanically follow that little recipe, but what does it actually mean?

I’ve sat with not understanding this in the past (and still sometimes do) and then I force myself to write it out until I get it again.

Every time I use the calculator, I ask myself if I understand what it means. If I don’t, I take out pen and paper and go back to basics.