Table of Contents
1 The Limit of Knowledge
1.1 The Physical Limit
There various kinds of information in the Nature. In order to clarify the point, let us take an example of human observers. Well, that's us! We have in general the five senses that catch the incoming information. They are sight, smell, hearing, touching, tasting. For now, let us take a close look at the sight.
We see objects around us. Scientifically this signifies that the visible light has been traveled from the objects in question by reflection to the eyes, which play the role of censors. Here it is important to notice that the visible light is the only information that we, human observers, can actually catch. We have already acknowledged that there are many kinds of light (photons), which is more technically called electromagnetic waves (from now on, E&M waves). The names of the E&M waves change depending on their frequencies, and a small range of the frequencies would become visible to human observers. Well, we can detect the other E&M waves with the help of a sophisticated apparatus but let's not get into it. The point here is that we, human observers, can only gain such small portion of the E&M information by nature. In other words,
Observers cannot receive all possible information.
or
There is the limit of knowledge.
1.2 The Conscious Limit
The physical limit of obtainable knowledge is intrinsic to the Nature, and this aspect seems to influence the conscious level of human observers. Although this part needs to be developed (or will be developed naturally in the future) further, I have added it for the sake of argument. Probably the model of observers (in this case, human observers) needs to be replaced.
In our languages, the name, "apple", indicates the type of fruits that is in general red, if it is ripe, and is sweet and sour. Its size is about a little bigger than a baseball. An apple-tree produces many those "apples" and the productions contain many seeds for reproductions. Well, the point here is that even though we call them all "apple", there is no identical twin of them. All apples are distinct from each other in terms of the color, size, and taste. But we ignore such differences.
This is the conscious level of the limit of knowledge.
1.3 The conscious level of the limit may have a purpose
Why do we have such tendency to ignore the details of objects in question?
Well, the answer is probably because the observers (information receivers) must minimize the incoming information in order to grasp the world of Nature. If we name each individual apple uniquely, the list of names is too large, which is out of our hands. Moreover, the importance of the differences is subtle, and of course, most of us never do pay attention to such differences purposely.
We, human observers, have been developed that way.
But this idea may be generalized to any observer (or in more general term, information receiver).
2 The Asymmetric Information Influences the State of Knowledge
The asymmetric information occurs quite often in our lives, although most of us hardly recognize it. The following example is an extreme case, but it will helpful to clarify the point.
The existence of black swans was discovered not too long ago. It defied our concept of this particular bird, swans. In Japanese, the swan is called "hakucho" which literally means a white bird. The name is coined to describe the appearance of the bird.
The black swan looks very different from white ones. We may claim that there is a DNA malformation in the process of reproduction. Well, even so, it comes down to the question of why we consider white swans to be normal rather than black. The answer is quite simple; we see white swans more often than black ones because it is still statistically true that most swans are white.

As shown above, we, human observers, intrinsically possess the well-developed foundation of knowledge about swans that they are normally white. We have learned it through the process of growing up in school or family. The Nature does not, however, intend such outcome, though.
From the perspective of Nature, the difference between a white swan and a black one is extremely subtle. Only a small portion of DNA functionality is responsible for actually coloring the outer skin of swans. In other words,
the information that human observers gain from the appearance of swans is incomparable with the information that the Nature produces.
The asymmetric information is the intrinsic nature in the natural world.
3 The Tautology Establishes the Shared (Social) Knowledge
Let us raise a question.
Why did we believe that swans are white, even though each individual human observer may not be able to see them statistically?
The answer is simple. The knowledge of swans is shared among other people (human observers) and

The figure above shows the image of how people share the knowledge. Of course, in reality, there are more people who share the knowledge and that is why the knowledge becomes more solid. And furthermore,
The more people share the knowledge, the stronger the reaction is when it is defied.
Let us imagine a society consisting of only a few people. Some of the people have seen white swans and he told other people about it. Now all the member of the small society shared the same knowledge. One day, they saw a black swan. They may be surprised but they reformed the knowledge among them relatively easily.
The discovery of black swans surprised many people in the world because the knowledge that swans are white was shared among people across the countries. The level of shared (social) knowledge corresponds to the population of the observers which share the knowledge.
4 The Diversity of the Nature
Now let us consider a more general case. The ideas are
- Knowledge has the limit
- Information can be asymmetric
- Knowledge is shared among others
Let us consider three cases.

The figure above shows that the subject 1 passes its own information to the observers A and B, but not C. The observer A and B share the knowledge of the subject 1; hence, they have the common recognition. However, the observer C gains the information by sharing, although it does not obtain directly from the subject 1. There is the asymmetric information: the difference in intention between the subject and the observer. The subject 1 may appear to the observer C differently than it does to other observers.

The second case is that all observers gain the information of subject 2 but the observers do not share the information among them at all. That means that there is no way to confirm that the observers actually see the same subject. This is also a possibility of the asymmetric information.

The third case is that only observer A cannot gain the information of the subject 3. This means that the subject 3 does not exist for the observer A.
The subjects appear and disappear depending on how the observers gain the information. And also the subjects look differently depending on how the observers gain the information. Even the same subject may not look the same to all observers. Sometimes it is impossible to confirm the sameness. If they do not recognize the existence of certain subjects, the interaction between them cannot be achieved. Even a simple model can show the diversity of subjects in question. If they repeat reproductions, the diversity of the Nature gets more and more complex.
The diversity of the Nature can be described by the transmission of information.
















