The factory analogy for the two-factor intelligence model, part 2

The “brainpower” model of IQ
The factory analogy for the two-factor intelligence model
Traits related to mental speed and caliber

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.

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19 Responses to The factory analogy for the two-factor intelligence model, part 2

  1. Santoculto says:

    My concept of g is much more referential than applicational in most instances seems. First everything have a factor g, something that is totally underlying, conceptually omniscient to the given thing. Cooijmans said something that help me, I believe, to understand the essential nature of factor g, at least of intelligence. Pattern recognition is at the same time as usually happen the most basic and the most decisive thing that express all types of smart behavior or action/reaction. Everything that express intelligence is based on diversely correct pattern recognition. Diversely, specially in personal inter-actions. Factor g is analogous to the nuclei of cell. G is the fundamental shape that result in diversely smarter behavior. IQ tests express g of intelligence because all tests that was designed to measure or to intercept this construct also express its g: Pattern recognition, by obvious reasons. IQ tests measure very what I call auxiliary or secondary human capacities: Verbal, spatial, memory and arithmetic. But IQ don’t measure primary human capacities or decisive ones that are intimately related with pure g or pattern recognition. It’s not what you can do with your verbal skills in recreational or in technical ways but what your capacity to recognize facts in other words to understand the reality and seems there non linear and bigger un-correlation between higher scores in IQ tests and rationality and factual understanding. By nebulous reasons psychology, embodied by nihilism and subjectivities seems never created a concept that express capacity of people to understand reality. I coined this very simple concept but also extremely important exactly to avoid this black hole of nihilism and subjectivities where many if not most of post modern bobos believe facts don’t exist or be subjectively influenced or be a western construct to oppress third world people of color.

  2. Ophiuchus says:

    Some rambling thoughts.

    -Pneumatic (as opposed to hydraulic) is definitely the more appropriate analogy for how people overcome long-form problem solving (and your conception of brainpower/g as a whole). “Chattering” is a good piece of terminology, I can sometimes feel myself doing it

    -James Sidis-tier psychological burnout = high caliber + high speed pump failing suddenly (e.g. packing suddenly blowing out or lovejoy/rotor disconnecting). Water hammer. Bad times.

    -This mechanical analogy for brainpower works really well when compared to the two main types of positive displacement pumps used in hydraulic fracturing (fracing). For tighter/higher-pressure hydrocarbon-bearing formations, a higher total number of pumps with fewer pistons and higher gear ratios/torque is what’s called for. For lower-pressure/sluttier formations a lower number of pumps with more pistons and lower gear ratios/better cruising velocity is the better rig-up. Both types of pumps (analogous to natural modes of cognition) are appropriate in different situations and are different functional configurations of horsepower, which again works very nicely as an analogy to your “brainpower” model. So I like this model for g you’ve got going here. Regards, former oil and gas nigger

    @Santoculto what you call “auxillary human capacities” is analogous to a model of intelligence that Koanic(?) had that divided general intelligence (I think) into three fundamental categories: verbal, logical/deductive, and visuospatial. Or something to that effect.

    • Santoculto says:

      ”what you call “auxillary human capacities” is analogous to a model of intelligence that Koanic(?) had that divided general intelligence (I think) into three fundamental categories: verbal, logical/deductive, and visuospatial. Or something to that effect.”

      We need verbal skills to help us to organize our thoughts. Verbal, math or spatial are auxiliary or secondary in importance, what is in the first is the thinking or reasoning skills. It’s just like a recipe: verb, math etc are ingredients, the recipe itself is the reasoning-result.

      He put verbal and arithmetic in the same boat*

      I don’t see ”logical/deductive”, maybe the reasoning/thinking skills i’m talking, in the same category to verbal, arythmetic and spatial.

      IQ tests measure in certain degree of atomization the ingredients that forge our real general intellectual skills.

      • Ophiuchus says:

        He/they put logic in the same boat, deciding that math is basically a nested subtype of logic. More here:

        And yes, I agree that the fundamental “reasoning” skills you’re describing are functionally the same thing as the “logical ability” they’re talking about in that thread.

        As for IQ tests measuring a certain degree of atomized “ingredients” of general intelligence, I think that’s pretty widely agreed upon in this intellectual neck of the woods; Aeoli talks about it here:

        “Beyond a baseline healthfulness and capacity for growth of new neurons, axons, synapses, etc., IQ is not a very useful measure for general ability (as in Spearman’s g). After that, IQ scores grow according to the healthy production of special modules that happen to be useful for answering problems on IQ tests, like having a large working memory, high spatial manipulation ability, etc.”

        ^Well said, Neanderboon.

        • Santoculto says:

          I think logic is a broader term that not only encompass mathematics. It’s not just ”think in logic way to solve math problems” but general problems, whatever the type. And i also believe logic is a low-vibration expression of rationality, in the same spectrum, as extroversion is to introversion in sensibility. Logic is more a instinctive way to solve problems while rationality is a deliberated way to do the same. Instead we trust in our gut we try to ratio-nalize realities or balance sides/perspectives.

          So logic is located in ”fundamental or primary mental capacities” while math is auxiliary or secondary.

          insanity/chaos, sub-logic, logic, rationality, wisdom/order.

      • rusty fife says:

        I suspect the naming convention is what has understanding of non-g IQ hosed up.
        Verbal => symbolic relationships (who and why? Not strong in this area myself)
        Spatial relationships => what and where
        Mathmatics => temporal/ process relationships (frequency and when)

        The stuttering might be caused by the weak part of the brain catching up. Frequently I know the answer, it just takes me a long time to figure out how to express it.

        • Santoculto says:

          I as myself if stutter people lived in places with more musical or swing-ish language they still stutter.

          Stuttering is the incapacity to be fluent without emotion. Seems all stutters can speak better when they are:

          – singing
          – speaking or reading with emotional emphasis
          – speaking in ”foreign” accents.

          ”Verbal => symbolic relationships (who and why? Not strong in this area myself)
          Spatial relationships => what and where
          Mathmatics => temporal/ process relationships (frequency and when)”

          Verbal is the most symbolical because we need words and its meanings to solve math and geometric/spatial problems.

          Intelligence itself would be how we can integrate all this parts of ”ingredients” to produce a recipe and not exactly how we operates in separated/divided ways in each ”ingredients”, what IQ measures. IQ is based on a lot of logical statements [and growing partially empirical ones], but not in decisively factual ones.

          This integration among this ”ingredients” that usually result in creativity and in rationality.

          • rusty fife says:

            “Verbal is the most symbolical because we need words and its meanings to solve math and geometric/spatial problems.”

            Aparently you’ve never been introduced to graphical methods for problem solving. They are nicely analog and require little symbolic manipulation.

            • Santoculto says:

              I don’t understand your critical observation…

            • Santoculto says:

              Maybe i was not understandable. I want to say verbal is the first because it embody math and geometry/spatial. I mean, to interpret a mathematical/spatial problem/task we need first have little knowledge about words. Even numbers is already verbally shaped, the quantitative symbol 1 and the verbal symbol one.

            • Santoculto says:

              ”verbal symbol” or combination of verbal symbols/words.

            • rusty fife says:


              Can’t seem to reply to you directly….

              My verbal scores are relatively low; therefore symbols and laguage lack “meaming” to me. To create a symbol that allows me to communicate to you, I first have to solve the problem; then turn it into symbols.

              Within mathematics and engineering there are alternative ways to solve problems from equation type manipulation of symbols. Graphical calculations is one. They rearely teach these methods any more because of the errors introduced by mismeasurement. They used to be very popular for drafting on paper and field calculations. They are extremely fast. Check out the Smith Chart as an example.

            • Santoculto says:

              Sorry Rusty Fife, i still don’t understand your replies, your points.

              Even i may have/score higher in verbal tests, namely in my mother tongue, in english, at least by now, i also have lower verbal IQ as you.

              ”My verbal scores are relatively low; therefore symbols and laguage lack “meaming” to me. To create a symbol that allows me to communicate to you, I first have to solve the problem; then turn it into symbols.”

              Are you sure about it** How you can communicate with other people*

              Seems a type of profound dyslexia.

  3. Boneflour says:

    I like this analogy. The Brain Juice Model of Intelligence.

    Gonna have to get that MM guy to use this for the ThalForce. “Increase your brain juice speed and power with ThalForce today! Knock out hard problems at work like firehoses on protestors!”

  4. Santoculto says:


    • Santoculto says:

      This alpha mythology is real*

      I think many if not most alphas, specially ”pure breed” alphas, this days, don’t care about this things. We are, via logical ways, transferring a common narrative in nature, i mean, among less selfconscious creatures, to humans.

      Yes, alphas in natural world will be likely to act in several ways, namely in social contexts, the alpha lion for example, the leader of group, but human alphas in unatural world don’t necessarily will act in the same way and even, it doesn’t mean ”alpha leaders” in natural world are always beneficial to the group.

      What amaze me is how Sweden become so white-guiltying without even a single colony of exploitation in new world’s.

  5. MM says:

    Oh that’s right I’m supposed to post music.

    The whole album is great

  6. Pingback: Revisiting the brainpower and competence models | Aeoli Pera

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