First, I’m going to present a simple hydraulic system to get the basic idea across. Then I’ll present a simple pneumatic system with a couple of added features. The intention of this model is to explain the results of IQ tests, and why speedsters are generally favored. If my hydraulic explanation doesn’t do it for you, this video might help.
The concept of mental caliber and mental speed is analogous to the behavior of a hydraulic circuit, which has a characteristic pressure and flow rate. Consider a simple circuit with a pressure of 1001 psi, which is driving five identical actuators with piston areas of one inch each. The five cylinders are loaded with 400 lbs, 600 lbs, 1000 lbs, 1400 lbs, and 1800 lbs. Please refer to my incredible CAD drawing, produced using all of the latest technology.
The pressure of the fluid exerts a force on each piston equal to 1001 pounds of force, because force is pressure times piston area. The first three pistons move upward at the same velocity. The latter two do not move at all. This is analogous to a mental test with five problems of increasing difficulty. If a person has adequate mental caliber, they will solve the problem. If not, they will never solve the problem. This is Paul Cooijmans’ model for very high intelligence. I believe he is halfway correct.
Fluid pressure determines how much force is applied, but the speed with which the three cylinders move is not affected by pressure at all. Returning to the hydraulic example, let’s say that the actuators have volumes of 1 gallon. In order to move the pistons, this volume must be gradually filled by pumping hydraulic fluid through the pipework. In order to extend all five actuators, it would be necessary to pump five gallons.
The speed with which the actuators reach their extended position depends on how fast you can pump that five gallons to them. If your pump, pipes, and valves can put out a flow of 1 gallon/minute, it’s going to take 5 minutes to fill up the five cylinders and fully extend them. This is analogous to mental speed. A system with a pressure of 1001 psi and a flow rate of 1 gallon/minute is going to extend the first three cylinders in three minutes, and then stop.
This system is analogous to a person with medium caliber and medium speed taking an IQ test with five problems of increasing difficulty. He solves the first three problems in a minute each, but is stumped by the fourth question and can’t make any progress. If the flow rate in the system were increased to three gallons/minute, then the same three cylinders would be extended in only one minute, but the other two wouldn’t move. This is similar to a person with higher mental speed taking the same IQ test and solving the first three problems in only one minute (much faster than the other testee), and then being stumped by the more difficult questions.
This is the most basic analogy, which I’m using to introduce the idea. In reality, I believe IQ tests are more like a pneumatic system. There are two big differences. The first difference is that pressure has a small, nonlinear effect on flow rate. This is due to the compressibility of air, which is not present in hydraulic systems.
The second difference is “chattering”. This happens when the pressure in the system is just barely high enough for the actuator to move its load. Again, this is due to the compressibility of air. The third actuator in our system is a good example because the force on the piston, 1001 lbs, is very close to the weight sitting on top of it. The piston will not extend smoothly, but rather in little fits and starts. Each time the air pressure overcomes the friction of the piston on the cylinder wall, the piston jumps forward. This increases the volume that the compressed air has to occupy. As a result, the pressure temporarily drops until more air can be pumped in to fill the new volume. Until then, the piston halts due to friction. When the volume is filled with new air, friction is overcome again and the piston jumps forward, and so on.
These two phenomena are analogous to two phenomena that we see in IQ tests.
First, we see that increasing mental caliber does make a testee a bit quicker at the easy problems. But the dependence is nonlinear and not very strong. It looks something like this:
Second, we see that people working to solve problems at the upper limit of their abilities will experience halting progress, as if they are overcoming many small frustrations. If we take both characteristic qualities of the circuit together, we get what’s called “horsepower” in physics. This is a measure of work done per time. I believe that g can be best described as “brainpower”, or the ability to solve difficult problems over time.