Complex Epistemology
As nearly anyone looking at this website will know, "epistemology" is the area of philosophy concerned with knowledge and how knowledge is gained. As usual, I will assert that gaining and having knowledge is a complex process and state of being, respectively. Of course, most epistemic theories propose that they can be explained in some "simple" way. By "simple," I mean theories like "all true knowledge" is obtained by pure reason, or only by experience, etc., instead of a complex admixture of ways,
I'll begin this section by graphically illustrating the common epistemic aphorism: "The more you know, the more you know you don't know." As another aphorism states, "a picture speaks a thousand words," and sometimes a graphical representation opens up new insights that might be missed by pure sentential explanations. And besides, I often ponder about things and try to visualize their representation or solution :)
The More You Know, the More You Know You Don't Know!
We can depict the amount of knowledge that we have in our "head" as the interior volume of a sphere, and the unknown as that which is outside the sphere as shown in figure 1 below. Given this "sphere of knowledge," our awareness of the unknown is represented by the surface of the sphere because it is the boundary between what we think we know and what we do not know. This drawing also suggests that the volume of what we do not know is much, much larger than what we know. Consider - do you know how many blades of grass are in your yard? What species of bacteria are on your skin or in your gut? What is the surface of the planet like that revolves around the star Sirius A (if it has a planet) . . . and so on ad finitum.
Figure 1
If knowledge is represented as the volume of a sphere, then it would increase by a rate of a cube or 3rd power, while the surface area increase by a square or a 2nd power. This increase in our awareness of our ignorance is consistent with the "letter" of the saying, but not perhaps with its spirit . . . It seems that the awareness of our ignorance should increase at a faster rate than our knowledge base. If graph our knowledge content more carefully, we can see that this greater increase in the awareness of our ignorance is actually the case. Importantly, our knowledge of the "world" is not monolithic. Instead, we have knowledge about different aspects of the world as depicted in figure 2. In this drawing, you will note that I have a "core" of common knowledge, that includes things like, "water quenches thirst," or "the sun comes up in the east. I also have knowledge in various fields like medicine and history, but I know very little about other fields like the works of Shakespeare, which I haven't included in my sphere of knowledge below.
Figure 2
Although figure 2 is a more accurate representation of our sphere of knowledge, it still doesn't necessarily mean that the surface area of ignorance awareness increases as fast as it should with a gain in knowledge. Figure 3 below is not "pretty" because it looks like a warty bubble if you will. The little odd shaped warts with labels are meant to represent that my knowledge of "Jump Rope," for example, is much greater than the average person because I excelled at it to the point that I was a national champion, wrote several instructional books on it, and was one of the founders of the sport to name a few of the things I did in the activity. The same goes for the field of medicine, history, and so forth. The "warts" of knowledge are irregular because I know more about emergency medicine, in which I practiced, than I do about other areas of medicine. I also do not know much about cooking, so I don't even have a bump for it on my general sphere of knowledge.
In the end, the surface area on this bumpy or warty sphere of knowledge increases faster than the volume does, just as the gyri of the human brain or the villi of the small intestine help to increase those structures surface area to a great degree. Hence, the more I know (volume of warty sphere) the more I don't know I don't know (surface area of warty sphere). Also, Gordon Ramsey, the famously temperamental TV chef, would become infuriated with my degree of ignorance in cooking!
Figure 3
One final note. Be careful of what you think that you know. It was not that long ago that people KNEW that there were witches and burned 10,000's of innocent women at the stake; or they KNEW that the rain god was angry and caused a drought which could only be lifted if more people were sacrificed. We still carry heavy burdens of unrealized ignorance which only seems to get worse with the concomitant rise in misinformation. I won't illustrate it further than figure 4, but false "knowledge" (supposedly an oxymoron in epistemology) is accompanied by a belief in their ignorance of a greater false reality, e.g., "I know that witches can float or swim, but I don't know how the devil taught them how or where!"
Figure 4.
