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==Explanation==
 
==Explanation==
{{w|Mathematics}} is the abstract study of topics encompassing quantity, structure, space, change, and others. {{w|Physics}} is a natural science that involves the study of matter-energy and its motion through space and time, along with related concepts such as forces. Physics is described using mathematics. {{w|Chemistry}} is the science of matter, especially its chemical reactions, but also its composition, structure, and properties. As chemical reactions are governed by physical laws (electromagnetism being particularly important), one could say that chemists are studying a subset of physics. {{w|Biology}} is the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. As biological life is the result of a large number of complex chemical reactions, one could say that it is studying a subset of chemistry. {{w|Psychology}} is the study of mental functions and behaviors, why thinking beings do what they do.  As thought is (currently) a capability exclusive to living things, one could say that it is [https://www.youtube.com/watch?v=umN7YOsmGl4 a subset of biology]. {{w|Sociology}} is the study of society, or the study of groups of people and their interactions.  Since a group of people is composed of many individuals, one could say that it is an application of psychology.  Of course, one could also say that the fields are all independent, as deriving one from another would require not only good, but perfect understanding of the more fundamental field.
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{{w|Mathematics}} is the abstract study of topics encompassing quantity, structure, space, change, and others. {{w|Physics}} is a natural science that involves the study of matter and its motion through space and time, along with related concepts such as energy and force. They do this using mathematics. {{w|Chemistry}} is the science of matter, especially its chemical reactions, but also its composition, structure and properties. That is, they study a subset of physics, using a subset of physics. {{w|Biology}} is the subset of chemistry that is concerned with the study of life and living organisms, including their structure, function, growth, origin, evolution, distribution, and taxonomy. {{w|Psychology}} is the study of mental functions and behaviors, why living things do what they do individually, which makes it a subset of Biology. {{w|Sociology}} is the study of society, or, the study of groups of people and their interactions, which sounds an awful lot like taking the skills of psychology and applying them to a large group of people.
  
Mathematics has two classifications: {{w|pure mathematics}} (mathematics for its own sake, without any real-world interpretation) and {{w|applied mathematics}} (mathematics intended to solve real-world problems). It is not uncommon for scientists to formulate a problem that can be reduced to a problem already solved by pure mathematicians. Taking this to its logical extreme, the comic arranges the six scientific fields according to the {{w|Hierarchy of the sciences}}, represented by a person on a chart of purity, saying that a field is 'more pure' than the fields depending on it. This is a topic often used in jokes between scientists of various fields as to who is more important. The physicist, [[Cueball]], feels that he is at the top, that all other fields are based upon his... but is ultimately upstaged by the mathematician, [[Blondie]], whose field is so pure that its relationship to more applied fields can be distant or nonexistent. Unlike the others, however, the mathematician notably does not claim that physics is merely applied mathematics, because that claim would be categorically untrue. While physics makes extensive use of applied mathematical methods, physics (and, by extension, all the other sciences) are based on the analysis of experimental data collected about the universe—data which mathematics does not and cannot on its own provide. Later a similar setup was used in [[2057: Internal Monologues]], although here the different science fields are not ranked against each other, and only the physicist is represented in both comics (although as Cueball in both).
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Now, mathematics has the classifications {{w|Pure mathematics}} (the maths you learned in school, and the subject of the field of maths,) and {{w|Applied mathematics}} (physics, chem, and so on.) Taking this to its logical extreme, the comic arranges the six scientific fields according to the {{w|Hierarchy of science}}, represented by a person on a chart of purity, saying that a field is 'more pure', than the fields depending on it. This is a topic often used in jokes between scientists of various fields as to who is more important. The physicist, [[Cueball]], of which everyone else's work is based upon, feels that he is at the top... but is ultimately upstaged by the mathematician, [[Blondie]], whose field is so pure that ultimately everything else could be seen as derived from it. After all, physics could not exist without math, thus ultimately everything can be expressed as a mathematical equation. Thus, the mathematician snobbishly says that she didn't even see any of the other fields standing so far over to the left on the graph. Alternatively she is not snobby - she is just so far detached from the real world - that she doesn't even understand that there could be a comparison between her field and other fields. That is if she even knows about these other fields (''what are you doing over there''...)
  
Philosophy is presumably not pictured as it would be so far off to the right end of the image it would require a scroll bar, not that Randall has shied away from large format strips. {{citation needed}}
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The title text points out that math all by itself is not connected to the real world and is only done for your own pleasure. Physics involves interactions with other objects and can create a result, but only by applying mathematics to the real world. This leads to a comparison between sex (physics) and masturbation (mathematics), implying that physics is applying mathematics, just like people having sex likely rely on experiences they have had while masturbating, i.e. sex as applied masturbation. (See also the title text of [[1158: Rubber Sheet]].) This also gives a new meaning to the physicist comment that it is nice to be on top! It is also a reference to a quote by Richard Feynman, a famous physicist, who is attributed with having said “Physics is to math what sex is to masturbation.
  
The title text indicates that physicists like to repeat the following quote attributed to Richard Feynman: "Physics is to math what sex is to masturbation.". This ties the title of the comic, "Purity," to tie between various fields, to the topic of sex, as measured by the {{w|Purity Test}}.
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In the main comic [[Randall]] clearly ranked mathematicians higher than physicist, but in the title text he turns this around, and notices that the physicist would then notices that mathematics is very pure, but believes that it is not very interesting without something real to apply it to.
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Blondie appearing as the mathematician could mean she is supposed to represent [[Miss Lenhart]], but since Lenhart is defined as a teacher, which she can not clearly be said to be here, it is uncertain.
  
 
==Transcript==
 
==Transcript==
 
<!--Remember this is not the transcript from xkcd http://xkcd.com/435/info.0.json, but a description of what is actually shown in the comic! -->
 
<!--Remember this is not the transcript from xkcd http://xkcd.com/435/info.0.json, but a description of what is actually shown in the comic! -->
:[Six characters are standing on a line with small ticks under each person. Above the two persons most central in the comic is an arrow pointing right. There are labels both above and below the arrow. Beneath each tick is a label. All the labels are listed here in order.]
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:[Six characters are standing on a line with small ticks under each person. Above the two persons most central in the comic is an arrow pointing right. There are labels both above and below the arrow. Beneath each tick is a label. All the labels are listed here in order]
 
:<big>Fields</big> arranged by <big>purity</big>  
 
:<big>Fields</big> arranged by <big>purity</big>  
 
:::More pure
 
:::More pure
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:Mathematicians
 
:Mathematicians
  
:[Above each of the six ticks, there is a person. The last person to the right is the mathematician. She stands at the far right edge of the comic, with much farther distance between her and the second to last person going right. The first four spaces between the first five people are of equal distance. Except for the least pure sociologist, they all say something addressed to the less pure person(s) on their left. The first mute person above the Sociologists tick is Megan. The second person above the Psychologists tick is a bald man with glasses and a goatee beard holding a book under one arm. The third person above the Biologists tick is a Cueball-like guy with a squirming octopus in his hand. The fourth person above the Chemists tick is Ponytail holding up a test tube with bubbles coming out of the top. The fifth person above the Physicists tick is Cueball standing with his hands in his sides. Farthest out, the sixth and final person above the Mathematicians tick is Blondie. She waves to the other five.]
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:[Above each of the six tick there is a person. The last person to the right is the mathematician, she stands at the far right edge of the comic, with much further distance between her and the second last person going right. The first four spaces between the first five persons are of equal distance. Except for the least pure sociologist they all say something addressed to the less pure person(s) on their left. The first mute person above the Sociologists tick is Megan. The second person above the Psychologists tick is a bald man with glasses and goatee beard holding a book under one arm. The third person above the Biologists tick is a Cueball-like guy with a squirming octopus in his hand. The fourth person above the Chemists tick is Ponytail holding up a test tube with bubbles coming out of the top. The fifth person above the Physicists tick is Cueball standing with his hands in his sides. Farthest out the final and sixth person above the Mathematicians tick is Blondie. She waves to the other five.]
  
 
:Psychologist: Sociology is just applied psychology.
 
:Psychologist: Sociology is just applied psychology.
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:Mathematician: Oh, hey, I didn't see you guys all the way over there.
 
:Mathematician: Oh, hey, I didn't see you guys all the way over there.
 
==Trivia==
 
This comic used to be [https://web.archive.org/web/20220125023401/https://store.xkcd.com/products/signed-prints available as a signed print] in the xkcd store before it was [[Store|shut down]].
 
  
 
{{comic discussion}}
 
{{comic discussion}}
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[[Category:Comics featuring Ponytail]]
 
[[Category:Comics featuring Ponytail]]
 
[[Category:Comics featuring Blondie]]
 
[[Category:Comics featuring Blondie]]
[[Category:Comics featuring Psychology guy]] <!-- Currently will be a red-link, but in anticipation of the change from the wrong name... -->
 
 
[[Category:Multiple Cueballs]]
 
[[Category:Multiple Cueballs]]
 
[[Category:Science]]
 
[[Category:Science]]
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[[Category:Rankings]]
 
[[Category:Rankings]]
 
[[Category:Animals]]
 
[[Category:Animals]]
[[Category:Comics with xkcd store products]]
 

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