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> physics is just drawing cartoons of reality with math

https://en.wikipedia.org/wiki/Spherical_cow

This is a mean free path computation and everything is spheres (except the skier who is probably a point source).

What you've missed out is that a physicist would need to derive a collision cross section for a typical tree-sphere. That may be as complex or as simple as you like. The simple limit would take into account the trunk diameter and tree density within the forest. But perhaps the skier is particularly agile and can avoid most trees, so the cross section is smaller.

You could add other particles and cross sections, eg the bear in ski free.

>First principles apply very well to our nice toy models, but the sheer vastness of existence usually out-scales our toy models very quickly.

That said, this is how a lot of simulations in astronomy work. You take a bunch of physical laws and apply them at scale on millions of particles.

the bear for anyone curious: https://imgur.com/r/nostalgia/qi8Is1q :)

And to add a bit to how physicists simulate stuff. They build a model. Make it as simple as possible, while still approximating the natural phenomena under investigation. So the mean free path model would have a lot of parameters as the parent commenter noted (collisional cross-section, tree density, trunk diameter, etc.).

And it's also important to keep in mind that there are theory builders in physics (theorists), "applied physicists" (phenomenologists, who try to use the fancy theories, match it with real data) and derive future predictions (like climatologists, cosmologists doing large scale universe evolution simulation from the big bang, and so on), the experiment designers, who basically try to weed out the useless models/theories through very targeted experiments.

All of these are about the same natural world, but different aspects, different levels of details, different concerns. (Eg. experimental physicists place enormous care on quantifying the systemic and particular uncertainties of the experiment, whereas theoretical physicists instead focus on the fundamental workings of the theory - they test it through computation. All of those are math, math, math, just different.)

> Thinking about it reminds me of a quantum mechanics prof who once explained the way a physicist would model a person skiing through the forest. The person would be either a sphere or a box, depending on what's most convenient. The trees in the forest would be cylinders or boxes. The person skiing would then be something like a sphere bouncing around through all these cylinders.

This way of thinking is a bit flawed.

Convenience is an important aspect, but it's not the entire reason. A physicist who wants to study how skiers might cause avalanches by modeling/simulation doesn't care about the details of the people they model because that's just not important. For what they want to study, it doesn't matter if they model the human as a sphere or as a real-life model with limbs and so on. It won't affect the grand picture.

On the other hands, a physicist who wants to study how an avalanche would crush a person? Then yes, modeling the limbs and the person's physical properties become much more important.

In modeling, you choose the model that best fits and represents what you aim to study. You start off with a complex system of equations and then you slowly go through and remove the parts that would be irrelevant. You don't need to account for turbulence if you know that you will never reach the high Reynolds numbers that require it. You don't need to model cellular biology if you're just trying to modeling how a piece of tissue stretches.

All great points.

But yeah it was a joke! And basically I remember his joke having a tangential quip about choosing the shape based on the coordinate system you wanted to stay in.

And the point I got from it was that in modeling we often use crass approximations that are oversimplified in order to get a rough picture of what's going on with respect to certain dynamics, and that one shouldn't assume that the model resembles the full complexities of real life.

By the way, he was a cosmologist, if that helps you understand a little better why he was so flippant with the shapes.

> For what they want to study, it doesn't matter if they model the human as a sphere or as a real-life model with limbs and so on. It won't affect the grand picture.

The exact claim is that such modeling, eg, fails to find avalanche dangers that truly exist in the world of skiers moving their body on physical skies, due to their shifting and localized weight, which is missing in the spherical skier model. Your post does nothing to address this.

The simplifications you call out are all cases of decreased accuracy in exchange for easier computations: that is, for less accurate results that are “good enough”. But the intersection of many such simplified models may fail to accurately model reality.

While it does seem silly trying to model real world physics by approximating everything as basic shapes like spheres/cubes, it turns out that these approximations really are accurate enough for many applications.

You really can get a reasonable estimate of the drag on a cow in crossflow by approximating the cow as a cylinder.

One thing that physics does well is to place upper and lower bounds around what that unpredictable thing that the actual reality can be or do

> And then another time my statistical mechanics prof informed me that "physics is just drawing cartoons of reality with math." That came as a huge existential relief by the way.

One of the most formative and sublimely influential 'aha' remarks I've ever encountered was a line in a Willam Goldman book about screenwriting which simply read, in the manner of a final summation to a chapter: "POETRY IS COMPRESSION." Caps in the original. I had the same sense of instant resolution, like wearing glasses for the first time, that you seem to have had with your prof's insight.