# 2. Our Greatest Invention

Model Based Problem Solving

The first blog “Why AI Works” provided the big picture of AI and Understanding Machines. Next we will focus on how to actually implement Understanding in a computer. But before we can attack that core issue we need to simplify the journey a bit by defining four important words and concepts. I’ll define one in this blog, two in the next, and the concept of Reduction after that. We can then discuss the Epistemology-level algorithm for Understanding itself.

If you are already familiar with these concepts, just check the boldfaced headings and definitions below to ensure we are using these words roughly the way you use them.

You may have noticed I write certain (sometimes common) words, such as Model, with an uppercase first letter. This means I am using the word in a technical, well defined, unchanging sense. I will define all such technical terms over time and I will try not to use these terms until I have defined them. We defined 11 such terms in the first chapter, starting with Understanding and Reasoning. A dictionary of defined terms is in the works.

### Models are simplifications of reality

In Epistemology and science, “Models” are simplifications of reality. Our rich mundane reality is too complex to lend itself directly to computation. In old TV science fiction shows, we would sometimes hear “… and then we fed all the information into the computer and this is what came out”. Well, not anymore; audiences now know that’s not how (regular) computers work.

Consider an automobile. It consist of thousands of parts, each with properties like materials, size, color, function, and sometimes complex interactions with other parts. What’s “all the information” here? We can’t just feed all of those properties and measurements and facts into a computer and expect to get “an answer”. We need to ask a question. And we also need to simplify the problem so that we can feed in just the facts or numbers that matter, so that our question can be answered with minimum effort. How do we do that?

We must identify or create, first in our minds, a very simple Model of some sort of a generic automobile, and use that Model for our computation. After we get the answer for the pure and simple Model case, we apply the answer, with some care, back to our complex reality where the real automobile (and the problem) exists.

What kind of Model we choose depends on our goals. As an example of a Model, Newton’s second law states that force equals mass times acceleration: “F = ma”. This equation is a classical scientific Model. If we measure mass and acceleration of a car then we can estimate how many horsepower the engine has. To use this equation, we engineers would model (in our minds) the car as a single small “point mass” with all the mass of the car in that point. Because if we don’t, then we’d have to worry about the car rotating and other problems.

This is how Model based science works. One or more scientists somehow derive a Model for some phenomenon. The Model is published as an equation, a formula, or a computer program. Scientists and engineers anywhere can now use this equation/program/Model, treating it as a quick shortcut that works every time, as long as they have correct input data and are competently applying the formula to a suitable problem in their reality.

### Our Greatest Invention

Model Based Problem Solving (aka Reductionism) is the greatest invention our species has ever made. The general strategy of simplifying problems before solving them must be tens of thousands of years old. In some sense, it is a prerequisite for all other inventions, including the use of fire. If you see a forest fire then you need to first imagine the utility of fire, as a Model, before you can figure out that it might be useful to carry home a burning branch.

We don’t think of this problem solving strategy as an invention because it is already ubiquitous in our lives. We are all taught how to use Model based problem solving in school when we start solving story problems in math class. But most people never learn the names of these strategies and are missing the big Epistemology level picture; this rarely matters… until you start working with AI, where lack of an Epistemological grounding may lead you astray into failing strategies. These blogs are an attempt to remedy that.

Naïve Model based methods were examined and refined into scientific methods over the past 450 years. Science is now a collection of thousands of Models that taken together allow science-competent people to solve problems quickly and efficiently without having to re-do all the work that scientists (like Newton) put into creating these Models in the first place. And the sum total of those Models covers many problems we want to solve scientifically, such as how to build a bridge, or travel to the moon. This reuse is what makes science so effective.

But not all sciences can benefit equally from this Model making; it works well for physics, chemistry, and most of biochemistry. As I’m fond of saying, “Physics is for simple problems”. But as you get to more and more complex sciences — as you get further away from physics and closer to life — it gets harder to make decent Models. The Models used by for instance psychology, ecology, physiology, and medicine are generally more complex but also less powerful than Models in physics. Given some solid data, a physicist can compute the mass of the proton to six decimal places but we would have a harder time predicting the number of muskrats in New England next summer because that outcome depends on millions of parameters. The life sciences base many of their Models on statistics. Statistical Models are among the weakest Models used in science. We use statistical Models when more powerful Models with better predictive capabilities cannot be used for complexity reasons.

Models are

• hypotheses (unverified Models)
• scientific theories (Models verified by peer review)
• equations
• formulas
• complex scientific Models (simulations of climate, weather, etc.)
• naïve models (that we create to simplify our own lives)
• computer programs

And what is Mathematics? It is a system that allows us to manipulate our Models to cover more cases. Mathematics is the purest, most context free of all scientific disciplines. As such, its greatest value to humanity is in its role as a help discipline to all other disciplines. Einstein’s famous E=mc² Model was derived using mathematical manipulation of other Models known to Einstein at the time. But perhaps mathematics isn’t as much a scientific discipline as an Epistemological one; I may explore this aside later.

### Model use requires Understanding

A good Model is context free, since that maximizes the number of contexts it can be applied in. Newton’s second law F=ma works pretty much everywhere we have forces, masses, and accelerations. The tradeoff for this flexibility is that we ourselves need to Understand the problem domain. In rocket science, when maneuvering in space, F=ma will often work perfectly, but when you are applying it to the acceleration of your car you need to account for lots of effects like friction between the road and the wheels, wind resistance, and the like. So F=ma applied naïvely would give you the wrong answer if friction is involved. This demonstrates the main disadvantage with Models. They require that both the Model Maker (scientists like Newton) and the Model users (STEM competent people everywhere) Understand enough about the problem domain to know whether the Model is applicable or not, and how to use it. This Understanding is the expensive part of science, since using science requires first getting a solid science education in order to avoid mistakes when using Models.

And since Models require Understanding, they cannot be used to create Understanding. This is a major problem for AI implementers.