# The Gelato Model

“Eddie, this ginger gelato’s delicious — not too sweet and just the right amount of ginger bite.”

On the way down here, Sy was telling me about how so many things in the Universe run on the same mathematics if you look at them with the right coordinate system. Sy, how do you pick ‘the right coordinate system?”

“The same way you pick the right property to serve as a momentum in Newton’s Equation of Motion — physical intuition. You look for things that fit the system. Sometimes that puts you on the road to understanding, sometimes not. Eddie, you keep track of your gelato sales by flavor. How are they doing?”

“Pistachio’s always a good seller, Sy, but ginger has been coming on strong this year.”

“In motion terns, pistachio’s momentum is constant but ginger is gaining momentum, right?”

“S’what I said.”

“Measured in dollars or trayfuls?”

“In batches. I make it all in-house. I’m proud of that. Dollars, too, of course, but that’s just total for all flavors.”

“Batches all the same size?”

“Some are, some not, depending. If I had a bigger machine I could make more but I do what I can.”

“There you go, Anne, each gelato flavor is like a separate degree of freedom. Eddie’s tracked sales since he started so we can take that date as the origin. Measuring change along any degree in either batches or dollars we have perfectly respectable coordinates although the money view of the system is fuzzier. Velocity is batches per unit time, there’s even a speed limit, and ginger has accelerated. Sound familiar?”

“Sounds like you’re setting up a Physics model.”

“Call it gelato trend physics, but I don’t think I can push the analogy much further. The next step would be to define a useful momentum like Newton did with his Law of Motion.”

F=ma? That’s about acceleration, isn’t it?”

“Probably not in Newton’s mind. Back in his day they were arguing about which was conserved, energy or momentum. It was a sloppy argument because no‑one agreed on crisp definitions. People could use words like ‘quantity of motion‘ to refer to energy or momentum or even something else. Finally Newton defined momentum as ‘mass times velocity‘, but first he had to define ‘mass‘ as ‘quantity of matter‘ to distinguish it from weight which he showed is a force that’s indirectly related to mass.”

“So is it energy or momentum that’s conserved?”

“Both, once you’ve got good definitions of them. But my point is, our car culture has trained us to emphasize acceleration. Newton’s thinking centered on momentum and its changes. In modern terms he defined force as momentum change per unit time. I’m trying to think of a force‑momentum pair for Eddie’s gelato. That’s a problem because I can’t identify an analog for inertia.”

“Inertia? What’s that got to do with my gelato?”

“Not much, and that’s the problem. Inertia is resistance to force. Who can resist gelato? If it weren’t for inertia, the smallest touch would be enough to send an object at high speed off to forever. The Universe would be filled with dust because stars and planets would never get the chance to form. But here we are, which I consider a good thing. Where does inertia come from? Newton changed his mind a couple of times. To this day we only have maybe‑answers to that question.”

“You know we want to know, Sy.”

“Einstein’s favorite guess was Mach’s Principle. There’s about a dozen different versions of the basic idea but they boil down to matter interacting with the combined gravitational and electromagnetic fields generated by the entire rest of the Universe.”

“Wow. Wait, the stars are far away and the galaxies are much, much further away. Their fields would be so faint, how can they have any effect at all?”

“You’re right, Anne, field intensity per star does drop with distance squared. But the number of stars goes up with distance cubed. The two trends multiply together so the force trends grow linearly. It’s a big Universe and size matters.”