# Equations and Stories

I have ten apples. I eat two apples. I now have 8 apples. I can write that story as 10 – 2 = 8

Let me retell that story. I had ten apples on the table and zero apples in my belly. Now, I have 8 apples on the table and 2 apples in my belly. I can write that story as 10 + 0 = 8 + 2

Let me retell that story. Today I ate two apples. I started with ten apples, but later I only had eight apples. I can tell that story 2 = 10 -8

If someone wanted, they could rewrite either of these expressions to be 10 = 8 – (-2). But just because you can do something, doesn’t mean you should.

For that reason, I don’t like this physics equation,

Ei = Ef – Wnc

It doesn’t tell a very good story.

It makes way more sense (to me) to write it as **Ef = Ei + ΔE. **This simply says the energy you have later is just whatever the energy you started with plus the change, or write it as **Ei¹ + Ei² = Ef¹ + Ef² **This says that what you start with is what you end with, even if you rearrange things to be in different places. I’d even be OK with **ΔE = Ef-Ei = Wnc **because then its clear that the work quantifies that amount of energy coming in or going out.

Any else think that writing KEi + PEi = KEf + PEf – Wnc is a bad story?

I agree, but I’m also curious where you’re seeing that and what the context/derivation is. None of the books I’ve used recently (Cummings/Laws/Redish/Cooney or Knight) use that form, nor does my ancient Halliday and Resnick from 1979. They all seem to use the delta E = Wnc version.

It’s a locally-written online textbook that is used for the course I teach one section of. It’s the equation that’s “bolded” to signify importance… on the pdf version it’s “boxed” to signify importance. They do tell a story with it, but I think it’s awkward and clunky compared to the above stories, and fails to really distinguish energy from mechanism of energy transfer for which we can quantify how much energy transfer.

I have no idea what those equations mean. None at all.

But I do know that you are spot on. Not all facts in a fact family tell the same story equally well. The best formulation of this argument comes from the folks at Cognitively Guided Instruction, about which more here.