What is a phylum in biology?
For those who are not familiar with a phylum is a taxonomic rank in zoology.
A phylum is typically defined by the similarity of certain cellular traits in the kingdom of life (for more details, see the wikipedia article). The currently accepted phylum containing humans is called Chordata.
A common question for those who want to study biology is what do we mean by study. We here define the following.
Study : A study can be divided into distinct time steps and corresponding objects. For instance, one could conduct a study on the influence of a genetic variant on the level of physical activity in mice. Here one has different time steps, namely weeks, mice, DNA sequence variants, gene expression levels, and physical activity. Each of these represents an object and each object will have its set of properties and measurements. One study might be related to one other study. For instance the study on the effect of a genetic variant on the level of physical activity in mice is related to the study on how this genetic variant regulates the expression of genes involved in metabolism.
The main purpose of this note is to show that the number of objects in a study is infinite. Hence studying a subset of objects is not sufficient to study the universe of all objects. To put this in a mathematical setting, it is mathematically possible to study all the objects by studying all the objects. However, if you wish to study only a small subset of the objects, then it will not be sufficient to only study a subset of the objects.
Why does this matter? Because we generally need to have a finite number of objects to perform a study. This means that if we could reduce the number of objects to study to infinity, then we could easily conduct infinitely many studies. If we could conduct infinitely many studies, then in order to establish any conclusion, we would need to have infinitely many conclusions. This is equivalent to having infinitely many studies. Since this is not possible, we have no reason to believe that any conclusion would be correct.
There is a standard example of why this is not possible. This example also shows why studying the universe of all objects is not possible. The example is based on an experiment on balls.
Suppose that we conduct an experiment where we randomly select a number of balls and place them on a table. Now we assume that our universe consists of two kinds of balls: red balls and blue balls.
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