Research Areas by Size and Countedness
Research Areas by Size and Countedness
[An X-Y scatter plot of research areas, written in gray font, where both axes have arrows in both ends. At the end of each arrow is a label. Above the left part of the X-axis there is a line which goes to a text about the meaning of the X-axis. Similarly there is a line to from the top of the Y-axis to a questions “asked” to those that study the given subject, their answers being somewhere between the two labels on the Y axis.]
[The X-axis from left to right, text first and then labels:] Size of the thing you study Small Big
[The Y-axis from top to bottom, question first and then labels:] "That thing you study - how many of them are there?" "We have a pretty good estimate." "We have no idea"
[The research areas names are listed here below by sorting them into the four quadrants from top left to bottom right. In each quadrant the areas are listed after most left first, and then top to bottom for those at the same x position.]
[Upper left quadrant (Small & count known):] Elementary particle physics Dentistry Shakespeare studies Ornithology Ancient Literature
[Upper right quadrant (Big & count known):] Presidential History Marine Mammology Railway Engineering Geology Cosmology* (*Depends who you ask)
[Lower left quadrant (Small & count unknown):] Pharmacology Microbiology Entymology Mycology
[Upper right quadrant (Big & count unknown):] Botany Paleontology Exobiology Black Hole Astronomy Theology
Sortable table with the coordinates in percent:

This comic is a scatter plot that ranks different research fields according to the precision of the knowledge of the number of the studied object (vertical axis) vs. how large (the size of) the studied object is on the horizontal axis.
For instance, the facts pertaining to the number of United States presidents are well known (although the exact number is disputed in that Grover Cleveland is usually counted twice, because he served non-consecutive terms, so the official count exceeds the number of unique Presidents), so the study of their history is at the top of the Y-axis. This study is placed close to the Y-axis as the size of a president is about midway in size between the two extremes of the X-axis, elementary particles to the left (small) and the entire cosmos (cosmology) to the right (big).
On the X-axis, Presidents are close to the middle. Both presidents and other larger life forms (as a research area) including extinct animals (paleontology) and exobiology are all close to the same central position just right of the Y-axis, with smaller animals like birds and insects just to the left of the Y-axis. But where the number of presidents is well known (aside from the dispute about Cleveland), then the number of exoplanet life forms (exobiology) is completely unknown (and would likely be affected by other disputes, such as whether something the size of Pluto counts as a planet) and thus it will be found at the very bottom of the Y-axis, since we have no idea if there are life elsewhere and if so how many places will it be and how varied.
The 19 research areas are listed and explained in the tables below.
In the title text, mathematicians may give a third answer that the concept of counting the things being studied is not reasonable, because the things are abstract or otherwise not discrete.  There are many different types of math that blend into each other, and many have turned into separate sub-disciplines based on different interpretations of fundamental rules.  As a specific example in geometry, different interpretations of how many lines you may draw parallel to another line through a given point has lead to hyperbolic (infinite parallel lines) and spherical (0 parallel lines) geometric systems that are just as valid (and valuable, in some contexts) as the more commonly known Euclidean (1 parallel line) geometry.  As a specific example of the blending, number theory , set theory , and topology all interrelate and it is difficult to concretely say whether many theorems belong to one branch of math or another.
For a table with the coordinates given in percentage for each research field, see the table in the trivia section
This is the section with the small items with count known.
This is the section with the big items with count known.
This is the section with the small items with count unknown.
This is the section with the big items with count unknown.
[An X-Y scatter plot of research areas, written in gray font, where both axes have arrows in both ends. At the end of each arrow is a label. Above the left part of the X-axis there is a line which goes to a text about the meaning of the X-axis. Similarly there is a line to from the top of the Y-axis to a questions “asked” to those that study the given subject, their answers being somewhere between the two labels on the Y axis.]
[The X-axis from left to right, text first and then labels:] Size of the thing you study Small Big
[The Y-axis from top to bottom, question first and then labels:] "That thing you study - how many of them are there?" "We have a pretty good estimate." "We have no idea"
[The research areas names are listed here below by sorting them into the four quadrants from top left to bottom right. In each quadrant the areas are listed after most left first, and then top to bottom for those at the same x position.]
[Upper left quadrant (Small & count known):] Elementary particle physics Dentistry Shakespeare studies Ornithology Ancient Literature
[Upper right quadrant (Big & count known):] Presidential History Marine Mammology Railway Engineering Geology Cosmology* (*Depends who you ask)
[Lower left quadrant (Small & count unknown):] Pharmacology Microbiology Entymology Mycology
[Upper right quadrant (Big & count unknown):] Botany Paleontology Exobiology Black Hole Astronomy Theology
Sortable table with the coordinates in percent:
