Dunning with Kruger, Socrates and circles of knowledge

I have long been interested in the topic of knowledge. So I was faced with the dictum of Socrates - “I know that I know nothing,” with the effect of Dunning-Kruger. He was convinced of the truth of these concepts. Saw their relationship. And besides, I became confident that you can mathematically substantiate the presence of the Dunning-Kruger effect.

Dunning-Kruger effect

The Danning-Krueger effect is a metacognitive distortion, which is that people with a low level of qualification make erroneous conclusions, make bad decisions and are unable to realize their mistakes due to the low level of their qualifications.

Below is a simplified graph with a demonstration of the Dunning-Kruger effect.

The graph with a demonstration of the effect of Dunning - Kruger does not give us any explanation of what is happening. But gives us only hope that you can get out of the Valley of despair. The schedule is very smooth and reflects the reality relatively well. For use in the psychology of such a schedule is almost enough. Sometimes he is misleading. For example, judging by the schedule, once you get out of the Valley of Despair, you will never return to it. In practice, it turns out that you come back more than once. However, such a schedule is a good starting point for further research.

The graph of functions is a mathematical tool and perhaps there is some function that will help us mathematically justify the manifestation of the effect itself.

Socrates

The effect of Danning - Krueger in some way echoes the dictum of Socrates - "I know that I know nothing."

Similar ideas can be traced in the writings of other thinkers who can read independently.

The meaning of the expression can be visualized as follows: let us imagine that all our knowledge is the inside of the ball, and ignorance is the exterior of the ball. The more our knowledge becomes, the more becomes the surface area of ​​the ball, and therefore our “contact” with ignorance.

Knowledge Circles

It seems to me the correct argument about the ball of knowledge. But the term Ball of Knowledge sounds unscientific somehow. Replace the ball of knowledge on the circle of knowledge. Or rather the circles of knowledge. There are four such circles:

1. I know.
2. I know that I do not know. Conscious unknown.
3. I don't know, I don't know. This is all the knowledge of humanity.
4. Absolute knowledge.

Each of the outer circles fully includes the inner circle.

3 and 4 circles are the same for all mankind. 1 and 2 circles for each person are individual.

Usually the expansion of the first circle contributes to the expansion and the second circle. Each expansion of the second circle brings us closer to the border of the third circle. If the growth rate of the second circle is much faster than the growth rate of the first circle, the person will inevitably fall into the Valley of Despair on the graph of the Dunning-Kruger effect.

Dunning-Kruger effect

Let's look at what happens to a person in the process of cognition and how this is related to the Dunning-Kruger effect.

Legend

• K1 = I know.
• K2 = I know that I do not know. Conscious unknown.
• K3 = I do not know that I do not know. This is all the knowledge of humanity.
• K4 = Absolute knowledge.

Newbie

K1 is very small. K2 is slightly larger than K1.

In the process of learning, K1 grows faster than K2.

Peak of Stupidity

K1 is catching up with K2. K2 is very far from K3.

Valley of Despair

K2 grows very much. This happens after switching to large projects from very small, attending conferences or starting listening to podcasts.

K1 does not keep up with the increase in K2.

Immediately it becomes clear what to do to get out of the Valley of Despair. It is necessary to pump the existing knowledge (K1). You can limit the growth of K2. This should be done consciously if you are absolutely uncomfortable in the Valley of Despair. Personally, I feel comfortable referring to Socrates and remain in the Valley of Despair.

It must be understood that even in this valley there is no stagnation. The volume of your knowledge is still growing. But the conscious unknown also grows (K2). Feels like you're staying in this valley. However, continue your development. And then K1 will start to catch up with K2 and get out on the Slope of Enlightenment.

The slope of enlightenment

K1 is growing faster than K2.

Here is what you need to do to increase the growth of K1 K2:

1. Start exploring your field more intensively.
2. Choose a narrower specialization.
3. Limit K2 growth
   
   • stop listening to podcasts;
   • stop attending conferences;
   • downshifting.

Ways 1-2 are good. Method 3 should be applied in the presence of psychological problems.

Plateau of Stability

K1 is catching up with K2. This has already been with us at the Peak of Foolishness.

The Plateau of Stability differs from the Peak of Foolishness only in the ratio of K2 and K3. On the Stability Plateau, K2 should be very close to K3. However, it is not easy to recognize. Indeed, at the previous stage, our K2 growth was very limited. Look carefully around.

The correct schedule of confidence in their knowledge

This graph shows the dependence of confidence on your own knowledge. It looks like a graph from the Dunning-Kruger effect, but there will be differences.

Suppose that confidence in knowledge is equal to the ratio of the volume of own knowledge to the volume of knowledge of the second circle (K1 / K2). Both parameters change with time.

Lines on the chart:

• The blue line shows confidence in your own knowledge.
• The red line shows the size of the second circle of knowledge.
• The green line shows the difference between the volume of knowledge of the second circle and the volume of own knowledge (K2-K1).
  You can look at the table with data and graph here .

Conclusion

The function of confidence in their knowledge is as follows:

Confidence in knowledge = K1 / K2.
Where K1 own knowledge, and K2 conscious unknown.

You can get out of the Valley of Despair. But you can go back and back with a greater amount of knowledge than the first time.

People who actually move science forward are permanently in the Valley of Despair, because they have ...