What physics is, and how to look

A dropped mug falls. A heavy box resists your shove. A rolling ball slows and stops. A hot drink goes cold. Four unrelated little dramas, or four clues to the same hidden rules?

You already run experiments every day without calling them that. Nudge a glass toward the table edge and you flinch, because you can predict what happens next. That flinch is physics in miniature: a tiny model in your head that takes a situation and returns a prediction. This whole course is about making those models explicit, checkable, and, because you are a programmer, runnable. We start from nothing. No formula from school is assumed, and every idea earns its name only after you have already felt it.

So begin with the everyday scenes above. It is tempting to file them as four separate facts. The physicist's bet, the one that has paid off for four centuries, is that they are not separate: a small number of simple rules sit underneath all of them. The job is to find those rules and, just as important, to find where each rule stops working.

Play first: how big is the thing you are modeling?

Before any rule, get a feel for the arena. The same word, "small," covers an atom and a virus and a grain of sand, but they are worlds apart. Drag the ladder from an atom up to a galaxy and read how fast size explodes. There is no need to memorize a single number here. The point is the sweep.

From an atom to the Milky Way is more than thirty jumps of ten, each jump a multiplication, not an addition.^[1] That range is why there is no single equation for everything. The rules that describe a jiggling atom are not the rules that describe a galaxy, and part of being a physicist is knowing which model the scale in front of you calls for. Choosing the model starts with knowing the scale.

What a model actually is

A model is a deliberately simplified picture that trades some accuracy for the power to predict. "Treat the mug as a single point with all its weight at the center" ignores its handle and its paint, and in exchange it lets you predict where it lands. Every model states, out loud or not, the situations it covers and the ones it does not. A map of your city is a model: perfect for walking to the shop, useless for predicting the weather. Physics is a drawer full of such maps.^[2]

Why we measure, and why units matter

A prediction you cannot check is just a story. To check one you have to measure, and to measure you need a shared unit. "The room is three long" means nothing until we agree on three of what. Two quantities can only be compared when they are measured in the same unit, which is why the metre, the second, and the kilogram exist: not as trivia to memorize, but as the common language that lets your measurement and mine be the same measurement.

Closely related is the order of magnitude, the rough size of a thing to the nearest power of ten. You do not need to know the Earth is 6,371 km in radius to reason about it; knowing it is roughly $10^7$ metres is often enough to catch a wrong answer. Estimating to the nearest power of ten is a real engineering skill, and it is the first one this course leans on.

The same ideas, in code you already trust

Three of these ideas map cleanly onto things you build every day. A model is a function: a situation goes in, a prediction comes out. A unit is a type: adding metres to seconds is a type error the same way adding a string to a list is, and catching that mismatch saves you before you ever run the numbers. And reasoning to the nearest power of ten is exactly Big-O thinking, aimed at the physical world instead of an algorithm: you throw away the constant factors and ask only how big.

# situation in, prediction out - the shape of every physical model
def will_it_overflow(users, mb_per_user, ram_mb):
    needed_mb = users * mb_per_user      # units must line up: MB with MB
    return needed_mb > ram_mb            # a checkable prediction, not a story

# order-of-magnitude first: 10^6 users, ~10 MB each -> ~10^7 MB needed.
# no exact digits required to see it will not fit in 10^4 MB of RAM.

Check yourself