When I was younger, my mother always told me that you need maths for everything.
Many things change with time. Differentiation with respect to time measures the rate of change, but this is only at a particular instant in time.
In the short interval of time between the opening and closing of the shutter, one image is captured. Assuming continuity and differentiability, we can think (within bounds) what happened before and after that certain point. Sometimes when we take a photograph, we capture someone blinking - freezing that position and looking at it makes it look, perhaps, rather strange - but it is happening! We are always blinking. When we are eating, people may not look funny, or you may not realise until you take a snapshot in that instant of time, leaving the still image that can be enjoyed.
I let Jess use my camera and I came home to find this!

Thanks Jess! Thanks Cheyenne!
What is Cheyenne doing in the photograph?
10 things she could be doing.
1) Yawning
2) Sneezing
3) Shouting at Jess not to take the photograph
4) Singing
5) The chips might be spicy
6) Caught chewing with her mouth wide open
7) Waiting for Jess to throw a chip in her mouth
8) In shock
9) Breathing through her mouth
10) Posing for the photograph
Based on this instant in time, we could only guess what she is doing. The bag of chips and chip in her hand suggest that she is eating, so we could assume that she is eating, but the facial expression causes doubt, as we do not usually observe this when people eat. A photograph taken before this particular photograph would have aided our prediction about what will happen next - as we learn that the best predictor of the future is often the past. But it will also help build a larger image of what has/will be happening.
Next is my friend ChungYi Chen, when it comes to free stuff - Chung is the champion.
His girlfriend Annie told me that in previous outings, he has made the peoeple serving the food come to him, and he eats, eats and eats! Capturing this wonder in action is amazing!
On Wednesday night, because of Engineering week, we got
free entry into Scitech. On top of that, there was
free food. Of course we wouldn't resist!

Why the long face? The food is free!

Chung on the lookout for the next target before he even finishes what's in his mouth. Alex at the back stuffed his face so much that he needs to use his hand to help him close his mouth.