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?

3 thoughts on “Equations and Stories

Add yours

  1. 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.

  2. 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.

  3. 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.

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