# Difference between revisions of "1991: Research Areas by Size and Countedness"

 Research Areas by Size and Countedness Title text: Mathematicians give a third answer on the vertical axis, "That question is poorly defined, but we have a sub-field devoted to every plausible version of it."

## Explanation

 This explanation may be incomplete or incorrect: The tables needs to be filled in. And I think the title text has been explained already... Do NOT delete this tag too soon.If you can address this issue, please edit the page! Thanks.

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 number of presidents is well known, 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 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, then the number of exoplanet life forms (exobiology) is completely unknown 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 Cartesian (1 parallel line) geometry. As a specific example of the blending, number theory and set theory and topology all interrelate and it is difficult to concretely say whether many theorems belong to one branch of math or another.

## Tables of research areas

• 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.
Research field Size of the thing Knowledge of # Explanation
Elementary particle physics The smallest subjects that we have actually detected are the elementary particles. In the Standard Model of particle physics, they are considered point masses (i.e. to have zero width). They may be made of smaller strings but if so these have still not been detected. We have a fairly good estimate of how many elementary particles there are. There could be some uncertainty though, so it is not at the very top. Elementary particle physics is concerned with the study of subatomic particles (the smallest things that can exist), of which there are 17. Most notably, until recently it was uncertain whether the Higgs boson was one of the elementary particles, but scientists have a "pretty good estimate" because the mathematical models don't predict the existence of many other particles
Dentistry Several mm Most teeth are visible to the naked eye, and dentists have x-ray technology to see what's not visible, so counting them is pretty straightforward. Dentistry is the study of teeth (pretty small, both in size as well as in quantity). Humans adults grow 32 teeth, which is a "pretty good estimate" since it is very rare for more than 32 teeth to grow and it is rather common for wisdom teeth to be surgically extracted or in some cases never to develop. Children may only have 20 teeth before they start falling out, but each tooth that falls out is because another tooth is growing underneath, so a child might have as many as 52 teeth, counting the child teeth that haven't fallen out yet plus the adult teeth that are starting to form. So while a dentist will usually have a good idea how many teeth will be in a patient's mouth, they won't know for sure until they look or consult dental records.
Shakespeare studies Shakespeare studies is concerned with the works of William Shakespeare (each book is pretty small). Generally, 36 plays are attributed to him, but between 1 and 3 additional plays are considered "lost" (i.e. at some point between being first published or performed and scholars seriously studying Shakespeare, all known copies, references, and fragments were destroyed, making it impossible to determine whether Shakespeare actually wrote them or whether they actually existed as separate plays), and some 20 more are believed to have been written by him, but not signed. To make matters worse, some plays that were published or performed under Shakespeare's name are believed to have been written as collaborations (not fully by him) or mis-attributed (we don't know who wrote them but, everyone says it was him).
Ornithology Ornithology studies birds (birds tend to be small; even the largest known flying bird, the Condor, stands smaller than the average human, with non-flying avians such as the ostrich being larger, but not that large). As with all animal classifications, we aren't really certain how many species there are, and are constantly revising the figure, but all estimates remain in the low thousands, so we do have a "pretty good estimate"
Ancient literature While it is fairly straightforward to look up how many books are currently in print, or how many books all currently printed information would fit into if bound into equal-length volumes, and then limiting those estimates to those that date before a specific year, counting how many books from the period of interest haven't survived to the present day (books that were "lost" either by deliberate discontinuation, or accidental destruction such as in the Library of Alexandria) is a bit more difficult. However, because we know the work existed (it is mentioned by name in some other text), we have "pretty good estimate" that the number of lost works is "only" in the tens of thousands, as is the number of surviving works.

• This is the section with the big items with count known.
Research field Size Knowledge of # Explanation
Marine Mammology Marine mammals are the largest extant animals. The US Government recognizes 119 marine mammals. However, what constitutes each species is constantly being revised, with new studies indicating either that what used to be considered a subspecies is actually a separate species, or that what used to be considered a separate species is actually a subspecies. As the depths of the ocean are further explored, species that were outright unknown are spotted and need to be classified. However, since marine mammals breathe air, they have to come to the surface where we can see them, so we're pretty sure that we've spotted all species. Note that RAndall has misspelled Mammalogy with o instead of a in the middle.
Presidential History Presidents are generally considered "big" men in history. Therefore, each one is fairly well known and documented. There is, however, some discussion on how many presidents there have been in the history of the United States, since prior to the 25th amendment, it was unspecified whether vice presidents counted as presidents during the President's absence. Most notably, this ambiguity is the reason David Rice Atchison's tombstone is inscribed with the words "President of the United States for one day".
Railway engineering A railway can span anywhere from a few hundred feet, to thousands of miles, so they're pretty big. The type of a railway is generally given by its track gauge, which are defined as "standard" (whatever you're currently using), "narrow" (rails closer together than whatever you're using) and "broad" (rails farther apart than whatever you're using). Since what is standard varies from country to country, and indeed from line to line, how many kinds of "narrow" gauge and "broad" gauge exist depend on who you ask.
Geology Geology is generally considered the study of rocks (small rocks being considered fragments of mountain layers, so what counts as a "rock" for a geologist can be pretty big). There is no universally agreed upon number to how many types of rock there are, but all geologists agree they can be grouped into igneous, metamorphic, and sedimentary rock. Alternatively, geology can be construed as the study of the planet Earth's composition ( *geo*- meaning "Earth" ), and geologists are confident that the planet Earth is big and there is only one of it.
Cosmology As this encompasses (at least) all of the visible parts of the universe we live in, there can be no other "items" to study that would be larger. There is only one visible universe, but there could be multiverses/parallel universes, and also an infinite universe beyond the borders of our own part of this universe's event horizon. So it depends on who you ask if they say there is one of and infinite number of universes to study, thus it is placed close to the middle of the two extremes, Cosmology is the study of the universe. There is an asterisk with the note "Depends on who you ask", relating to the estimate of how many universes there are. While it might seem obvious that there is only one universe, some branches of physics believe that our universe is part of a multiverse, and this remains an open and contested subject in the field.

• This is the section with the small items with count unknown.
Research field Size Knowledge of # Explanation
Mycology Mycology is the study of fungi (since fungi tend to grow flat -- excepting for mushrooms, which are their sexual organs, and do not exceed a foot in height (see World's Largest mushrooms -- mushrooms are generally considered small). It is a lot harder to discern which species a fungus is, and therefore classify it, so we "have no idea" how many kinds of fungi there are. Studies vary wildly between about 70,000 to over 5,000,000. There is a comic named after this study: 1664: Mycology.
Entymology It is unclear whether Randall means entomology or etymology (probably neither; it's likely that this wasn't a mistake and it is possibly a direct reference to 1012: Wrong Superhero). In either case, estimates for insects (entomology) vary from less than 1,000,000 to 30,000,000; and estimates for root words (etymology) reaching hundreds of thousands. Entomology was mentioned in the title text of 1610: Fire Ants.
Microbiology Microbiology studies microscopic (too small to see) organisms, of which some 1,400 are known and "estimates for the total number of microbial species vary wildly, from as low as 120,000 to tens of millions and higher", according to Nature magazine.
Pharmacology The number of drugs (pharmaceuticals) discovered and synthesized is not tallied, according to recent studies, but an estimate can be obtained by seeing how many have passed through the U.S. FDA (1,453). Many home remedies, which might technically qualify as drugs, have not been approved because "everybody knows that", as well as many solely recreational drugs since regulation might result in outlawing. Because of this, "we have no idea" how many drugs truly exist. Since drugs are extremely powerful molecules that are only administered in choice amounts, they are generally perceived as small.

• This is the section with the big items with count unknown.
Research field Size Knowledge of # Explanation
Botany Botany studies plants, which can reach hundreds of feet by any measure. However, plant tend to clump together in forests and jungles, which makes it hard to get to them and document them. Every year, thousands of new plants are discovered, with the best estimate being that there are nearly 400,000 vascular plants and an additional 12,000 non-vascular plants. However, the rate of discovery doesn't appear to be slowing down significantly, so we truly "have no idea."
Paleontology Paleontologists study fossils, which range in size from very small to very large. When most people think of paleontologists though, they tend to think of them as studying large animals such as dinosaurs. Paleontology studies fossils, particularly those of extinct animals, which can reach huge sizes. However, since fossils form under very special circumstances, if the animal did not die under those special circumstances, there will be no record of their existence. Therefore, the number of extinct animals can never truly be known, but we've found around 250,000
Black Hole Astronomy Compared to most astronomical objects, black holes are fairly small. However, most of them (that we are able to detect) are still larger than the Earth, so they would still fall on the "big" end of this chart. Alternatively, Randall may be referring to their mass, which is on the scale of stars. "Most stellar black holes [...] are impossible to detect. Judging from the number of stars large enough to produce such black holes, however, scientists estimate that there are as many as ten million to a billion such black holes in the Milky Way alone." (NASA Black Hole information page)
Exobiology Exobiology refers to the study of life outside Earth, which requires scanning the entire universe for life. Currently, exobiology seeks to find a planet with life (and, to qualify as a planet, it has to be big). The estimate of how many planets with life there are varies from 16 to 40,000,000,000. However, the number of planets apart from Earth confirmed to have life is currently zero. This is known as the Fermi Paradox. For life, of the type we know, to exist outside of the Solar system there need to be planets around other stars. Such planets are called Exoplanets, and they have been a recurrent subject on xkcd.
Theology It is placed at a scale as large as the universe (cosmology) as it should encompass the entire creation. For those not believing in gods it could also be seen as studying something as small as the human brain that has created all the gods in our image. But Randall has chosen to place it in the big section. As no one really can know anything about theology as it is a study covering a wide range of beliefs from a wide range of religions. Theology is concerned with the study of God, which, by definition, is a hypothetical being greater than the universe itself. In particular, theologists study the question of whether a god could exist (there is ≥1 god) or not (there are 0 gods) and, in the former case, whether there could be multiple gods (there are n>1 gods) or just one (there is exactly 1 god) or indeed whether there is one god for each living thing (n≫1 gods). I.e., the very definition of the field is the fact that "we have no idea" how many there are. This quantitative uncertainty is also mentioned in 900: Religions.

## Transcript

[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*
[Lower left quadrant (Small & count unknown):]
Pharmacology
Microbiology
Entymology
Mycology
[Upper right quadrant (Big & count unknown):]
Botany
Paleontology
Exobiology
Black Hole Astronomy
Theology

## Trivia

### Table with coordinates

• Here is a sortable table with the coordinates in percentage given.
• They have been taken from the discussion where "Zetfr" states that
• I have determined the exact position of each science on both axes.
• I computed the center of the smallest rectangle that encloses each name.
• Here they are, expressed as percentages, assuming 0% and 100% correspond to the arrow tips on each axis.
• It could be argued that cosmology size should be at 100% and Theology knowledge 0 %, etc. but that is just semantics.
• The interesting here is what order Randall seems to have put the different fields and object sizes.
• To begin with they are sorted after the size of the ting the research are studies, with the smallest first.
Research area Size (%) Estimate (%)
Elementary Particle Physics 7 72
Pharmacology 12 6
Microbiology 15 13
Dentistry 21 84
Entymology 24 25
Mycology 29 38
Ornithology 34 62
Shakespeare Studies 37 88
Ancient Literature 38 53
Botany 60 40
Presidential History 62 89
Marine Mammology 66 68
Paleontology 68 31
Exobiology 68 5
Railway Engineering 79 81
Geology 90 90
Theology 91 5
Black Hole Astronomy 92 26
Cosmology 94 62

# Discussion

Spelling error? Etymology or Entomology? Randall wrote Entymology. Sebastian --141.101.104.17 15:37, 9 May 2018 (UTC)

My translator at dict.leo.org asks: Did you mean entomology, enzymology, or etymology? --Dgbrt (talk) 16:20, 9 May 2018 (UTC)
I mean, we know about how many words exist; I think he means Entomology.

SilverMagpie (talk) 18:06, 9 May 2018 (UTC)

I'm sorry, we don't know how many words there are in British English, let alone it's off shoots, Chinese has never been fully counted and actually we don't know how many languages there are, but can put a good estimate on it. Nevertheless I agree it's probably entomology.RIIW - Ponder it (talk) 23:00, 9 May 2018 (UTC)
Agree. In context, it's next to several other life science branches, ones which especially deal with species typical in jungle environments where new species are regularly discovered, hence the "we don't know how many" axis. Cgrimes85 (talk) 18:55, 9 May 2018 (UTC)
Wikipedia redirects "Entymology" to "Entomology", fwiw. -boB (talk) 20:46, 9 May 2018 (UTC)
Just a quick note, a previous version said this made reference to 1012: Wrong Superhero, and 1610: Fire Ants (the same revision also shows Mycology might have been a reference to 1664: Mycology), which I appear to have accidentally deleted. Feel free to add them back where they go. --172.69.33.11 23:16, 9 May 2018 (UTC)
Please try to add something you delete by mistake yourself next time. I have re-added the three references you deleted for you. --Kynde (talk) 20:23, 10 May 2018 (UTC)

Dentistry is fairly straightforward, I think. Adults should have 32 teeth, children who have a full set but don't have wisdom teeth yet should have 28. Anyone missing teeth should have that information on their personal record. However, children occasionally lose teeth, and sometimes wisdom teeth need to be removed due to issues with them growing in wrong. It's also possible they could be lost in an accident, or for there to be a new patient with an unknown number of teeth. So a dentist can easily expect to know how many teeth should be in their patient's mouth, but may find they are off in some instances. Hence the mostly towards the top but not quite all the way of its placement. --KingStarscream (talk) 19:06, 9 May 2018 (UTC)

Children have 20 teeth, that will all fall out. But at some point they have all 20 and none other. So saying they have 28 makes no sense. Some adults never get Wisdom teeth. Before the childbegins to loose they original teeth they may start to have some of the permanent though. --Kynde (talk) 21:16, 9 May 2018 (UTC)

As well as some people not developing some / all their wisdom teeth (I have never had any upper ones) some people have "super-numerory" canines (my Dad and sister) RIIW - Ponder it (talk) 23:00, 9 May 2018 (UTC)

Standard gauge is pretty well established as being 1,435 mm. I realize it is tempting to say "standard" is whatever is common and in use in an industry/country, but even India refers to their network as "broad gauge" and the metro/tram lines as "standard gauge". Standard gauge is a commonly accepted technical term among railway engineers, and is used on over 50% of railways and is the primary gauge for North America, Europe, and China. Many countries are slowly converting their lines to standard gauge or only building new lines in standard gauge, such as Japan and Australia. Cgrimes85 (talk) 13:28, 10 May 2018 (UTC)

I have determined the exact position of each science on both axes. I computed the center of the smallest rectangle that encloses each name. Here they are, expressed as percentages, assuming 0% and 100% correspond to the arrow tips on each axis. I can provide raw pixel values if anyone is interested.

Presidential History | 62% | 89%
Geology | 90% | 90%
Shakespeare Studies | 37% | 88%
Dentistry | 21% | 84%
Railway Engineering | 79% | 81%
Elementary Particle Physics | 7% | 72%
Marine Mammology | 66% | 68%
Ornithology | 34% | 62%
Cosmology | 94% | 62%
Ancient Literature | 38% | 53%
Botany | 60% | 40%
Mycology | 29% | 38%
Paleontology | 68% | 31%
Black Hole Astronomy | 92% | 26%
Entymology | 24% | 25%
Microbiology | 15% | 13%
Pharmacology | 12% | 6%
Exobiology | 68% | 5%
Theology | 91% | 5%

Zetfr 23:35, 9 May 2018 (UTC)

Interesting to see which order they are listed in size and knowledge... Maybe an extra table in a trivia section... --Kynde (talk) 20:36, 10 May 2018 (UTC)
I have now added that in a trivia section. --Kynde (talk) 20:53, 10 May 2018 (UTC)

'Microbiology studies microscopic (too small to see) organisms, of which some 1,400 are known and "estimates for the total number of microbial species vary wildly, from as low as 120,000 to tens of millions and higher", according to Nature magazine' What is the 1,400? The other numbers here look reasonable, but this one throws me for a loop. Gene Wirchenko [email protected]@telus.net 108.162.216.220 05:25, 10 May 2018 (UTC)

There is (another) spelling error: mammology instead of mammalogy 172.68.110.76 09:48, 10 May 2018 (UTC)

Regarding the spelling of "mammology" - do you think it was intentional and Randall meant mammo- female breast -logy the study of? mammo- prefix on wiktionary --108.162.216.46 21:18, 14 May 2018 (UTC)

The explanation about railway engineering is incorrect. Whereas every railway has a standard gauge, "standard-gauge rail" has a specific meaning of a track with rails 1435mm (4 ft 8.5 in) apart. Anything narrower than that is described as a narrow-gauge line by rail technicians and enthusiasts, even if it is the standard gauge for a particular rail network. Where I live in New Zealand, for example, the country's standard gauge of 3 ft 6 in means that the country's rail network uses a narrow-gauge track. I've amended the text accordingly. Grutness (talk) 02:58, 18 May 2018 (UTC)

I think the title text is actually a reference to combinatorics, which is a subfield of mathematics. --cajsq0228 20:52, 20 May 2018 (UTC)