Moo!

A farmer asked a physicist to help him figure out how to increase milk production. After gathering data and studying the problem, the physicist came to the farmer and said: “I have a solution, but it only works for spherical cows in a vacuum.”

There are several variations on the spherical cow story and its application to physics (if you make allowances for horses and chickens), but there are even more if you include economics. #TIL about the can opener, which mocks economists in a similar way, when an economist on a desert island solves the problem of opening a can of food by simply assuming a can opener.

I’ve commented before on how complicated physics is, and on how vastly more complicated human interactions are, and I think this explains why we need assumptions. Taking the example of falling objects, what are some factors affecting the velocity of the object?

These include (but are by no means limited to) the mass of the object...

Wait! What if the object is radioactive – what about the change in mass due to radioactive decay?

Erm, well, the change in mass due to radioactive decay is likely to be so small that we can’t even measure it, so let’s assume the mass doesn’t change. Ok?

Moving on, another factor is the gravitational force, which is 9.8 metres per second squared -

Wait! Won’t that actually vary based on your exact distance from the centre of the Earth? And the way the Earth’s mass is distributed? How about the effect of the moon’s gravity? Or the sun? Or the other planets? And what about nearby mountains and buildings?

Well, in practice, the Earth’s gravitational force utterly overwhelms the affects of these other factors, so it’s easiest to assume that both the Earth and our falling object are point-sources and not affected by the mass of any other objects.

Then we get into things like the shape of the object, wind resistance, atmospheric pressure, the aerodynamics of the object, and a bunch of other factors.

How about magnetism? What if the object is being pulled by magnetic fields? And how about solar radiation? What about the temperature of the object, and how it might vary by altitude? How about friction?

Sigh.

To simplify all of this, let’s assume a solid dense sphere of non-ferromagnetic, non-radioactive material which is not affected by temperature changes. Let’s then assume that the gravitational force is based on both the object and the falling object being gravitational point sources? Let’s then assume a constant temperature, no wind, and a constant atmospheric pressure?

Is that enough?

Probably not, but it’s pretty close. And, more importantly, it’s an extremely close approximation, as most of the other factors are negligible in their effect. That’s why we didn’t need to “change all the text books” when relativity came along, as relativistic effects are negligible unless you are moving at a significant percentage of the speed of light.

Of course, this is a trivial example. In practice, though, most of the assumptions made for most purposes have negligible impact, and generate results which are valid for most practical purposes... at least when you’re talking about physics. Where necessary, physicists will simply refine the assumptions to ensure that they keep the ones which are likely to be relevant.

Economics, on the other hand, is affected by humans, which makes it vastly more complicated, vastly more in need of assumptions to simplify, and vastly more likely to be “wrong” when you compare theory to practice. A cursory look at economics will find many “silly” assumptions, such as the idea of a human as a “rational” and “self-interested” agent, though the idea is much less “silly” if you understand the technical definitions of those words in the context of economics. The idea, of course, is to try to control variables in an analysis so that you can understand the effect of a particular variable, and the biggest problem is that people (non-experts, or sometimes those arguing in bad faith) will often combine ideas from multiple models with different assumptions, leading to (sometimes entertainingly) ridiculous conclusions.

But does this actually matter in most situations? Do assumptions help us, or hurt us?

In my experience, they help us if they are documented in order to clarify something, and hurt us in most other cases. Assumptions can help us understand (or define) the scope of a project, or hurt us and waste time.

Let’s say that Alice asks Bob to create an app to help people catalogue their favourite cat videos.

Scenario 1:

Bob spends weeks to design a mobile app for iOS and Android, which allows people to list the cat videos they have marked as favourites, and organize them by keywords that have been assigned to them as tags.

Alice reviews the design, is not happy with it, and clarifies that the intent is to have an application which can be used either online or on a mobile device. It should also be generic enough to include not only existing cat videos, but other videos as well, even from other services. It should also be flexible enough to allow the user to define their own keywords and tags for indexing.

Scenario 2:

Bob takes a day to define a set of assumptions, then sketches out a few ideas for a user-interface and sends them to Alice for a first review. These assumptions include:

• Tool is a mobile application for iOS and Android, and not supported on other platforms

• Tool will catalogue only cat videos from their services, with predefined keywords

• Tool will use a “freemium” model, with certain services available only to subscribers

Alice reviews the list of assumptions, and quickly realizes that the original idea was not sufficiently clear, but Bob’s assumptions helped them catch it before it became a problem. Alice then clarifies that the intent is for a tool which is available either online or using a mobile app, and confirms that the intent is for something flexible enough to include videos from other sites – it turns out that this might end up being a joint-venture with a ferret video site. Alice had not though much about the pricing model, but liked the idea of a freemium model with basics for anyone and additional features for subscribers. In the end, Alice is quite pleased, and asks Bob to keep going with the design work.

In scenario 1, Bob made assumptions and ended up wasting a few weeks on something Alice didn’t want. In scenario 2, Bob made the same assumptions, but documented them and very quickly confirmed important features of the scope of the project, while also raising an idea which hadn’t previously been considered.

Sadly, documenting assumptions is not a silver bullet for addressing all problems, but it’s better than nothing, and at least provides an opportunity to catch some of the big issues which cause problems for many projects. I find Wile E. Coyote to be a great illustration of this sort of thing...

Cheers!