435: Purity

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On the other hand, physicists like to say physics is to math as sex is to masturbation.
Title text: On the other hand, physicists like to say physics is to math as sex is to masturbation.


Mathematics is the abstract study of topics encompassing quantity, structure, space, change, and others. 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. 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. 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. 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 a subset of biology. 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.

Mathematics has two classifications: pure mathematics (mathematics for its own sake, without any real-world interpretation) and 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 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).

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]

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 Purity Test.


[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.]
Fields arranged by purity
More pure
[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.]
Psychologist: Sociology is just applied psychology.
Biologist: Psychology is just applied biology.
Chemist: Biology is just applied chemistry
Physicist: Which is just applied physics. It's nice to be on top.
Mathematician: Oh, hey, I didn't see you guys all the way over there.


This comic used to be available as a signed print in the xkcd store before it was shut down.

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See Comte's hierarchy of the sciences from his law of three stages: Mathematics; Astronomy; Physics; Chemistry; Biology; Psychology; Sociology. -- 07:20, 3 December 2012 (UTC)

Which is on top? Quantum Physics or Mathematics? (talk) 17:57, 9 April 2024 (please sign your comments with ~~~~)

Quantum Physics is probably top, bottom, up, down, strange and charmed... 21:44, 9 April 2024 (UTC)

In addition to Comte, Randall's tweaking P.W. Anderson's 1972 article "More Is Different." Anderson gives a similar list and then says "But this hierarchy does not imply that science X is "just applied Y*" 22:47, 2 January 2014 (UTC)

Shame it leaves out Engineering running parellel to all of them - maybe Engineering is just too busy getting shit done? -- (talk) (please sign your comments with ~~~~)

- What can we learn from this? - Actually as an Engineer I have a different view point to We are implementers of original ideas and a few of us are lucky to be original idea generators. As a successful full time Engineer I still find time to be a philosopher and aspiring teacher (who simply didn't want to be poor, which is hard to do when specializing in the other two professions). How ever I do keep asking myself often who wrote the laws that mathematicians and theoretical scientists keep re-discovering for us... - E-inspired (talk) 17:04, 28 February 2013 (UTC)

"More is Different", written by Nobel laureate P.W. Anderson, is an insightful critique of constructivism. Quote:

But this hierarchy does not imply that science X is "just applied Y." At each stage entirely new laws, concepts, and generalizations are necessary, requiring inspiration and creativity to just as great a degree as in the previous one.

Allenz (talk) 02:20, 7 August 2013 (UTC)

This one resonated around the Internet quite a bit more than average, and deservedly so. I'd think it'd be almost as far-reaching as the grownups one. I did wonder, after I saw this, how one would take into account things like linguistics, logic, and philosophy. Then I read Gödel, Escher, Bach and returned to normal. --Quicksilver (talk) 03:58, 21 August 2013 (UTC)

Could one argue that Mathematics is applied Philosophy? NikoNarf (talk) 15:27, 14 November 2013 (UTC)

Physics and mathematics

Physics, chemistry, biology, earth science,... are science on how things work. Mathematics and philosophy are science on how things can be predicted to work. 10:08, 22 November 2013 (UTC)

A friend of mine compared the math-physics relationship to linguist-regular person. A linguist researches all the little details in a language that a normal person merely uses in his everyday life without giving the language itself much thought. 08:09, 24 January 2014 (UTC)

Before we get into an edit war here, I'd just like to say that "physics is the real joy in the world" would make absolutely no sense to me if I was not a native English speaker or I simply wasn't getting the comic's point in the first place. Not only does it have shades of grammatical incorrectness, it does absolutely nothing to actually explain how mathematics and physics can be compared to sex and masturbation. Thus I've changed the title text around to a compromise between my edit and what it was before. I hope this is more acceptable. Jetman123 (talk) 13:06, 10 March 2014 (UTC)

I'm still not happy with the title text explain:
  • The explain implies that masturbation "is all just in your head" and not "involves interactions with real objects". Isn't a vagina/penis also a real object?
My last edit on this wasn't perfect as well, so it still needs an enhancement. The joke is more like this: Math/maturbation gives only satisfaction to the subject acting on this — Physics/sex are related to the real world (applied science/babies). And this is surely exaggerated by Randall because physics couldn't exist without mathematics — those faculties just joking about each other. --Dgbrt (talk) 20:13, 10 March 2014 (UTC)

Some experts say the universe is a computer. Some other experts say all computers can be hacked. If both groups are right, then it follows that physics is one stack-overflow exploit away from being reduced to applied computer science. Promethean (talk) 23:48, 14 April 2014 (UTC) Logicians: hi.

From: The psychology of the pure mathematician

  • "On the other hand, physicists like to say physics is to math as sex is to masturbation."
  • Are physicists born with particles- or are they implanted because they are born without balls?
  • Would a mathematician have much better analogies than orgasms?

I wouldn't know.

  • Math is to physics as,
  • drugs are to prostitutes,
  • green eggs are to ham,
  • quod erat demonstrandum is to cogito ergo sum,
  • masterbating is to shakespearing,
  • coffee is to sugar,
  • Spock is to House,
  • category theory is to Kama Sutra,
  • Cicero is to Caesar.

Sorry physics, but it seems to me that your particle accelerators are gluttonously huge scientifically unnecessary and totally useless particle-crunchers, functionally comparable to fastest-known super-computer designs for discovering new large prime numbers. I wonder if physicists are actually the heaviest consumers of funding that would otherwise be available to support mathematicians, who are obviously the lightest consumers of research funding and also the most productive of new discoveries. Mathematicians can actually tell the difference between an arbitrary mathematical information computational process, and an orgy of man-boy physicists playing with their tiny balls in a spaceship-submarine with a warp-core that could give anyone an involuntary geek-gasm easily shrinking physics to the size of sex. QED.

Thanks for the joke, any offense taken it was not my intention to return. I just felt the need to point out that, although I agree that physics is a respectable second-best, sexy is a long way from first.

Nafindix 06:02, 20 May 2014 (UTC)

Random side note: One could argue that mathematics is applied philosophy (if we take philosophy as a way to create an understanding of the world), and that philosophy (as a product of human societies) is applied sociology. It's a weak argument, but the circular-ness is appealing. 15:41, 14 March 2016 (UTC)

Equivocation!--Troy0 (talk) 06:54, 24 July 2016 (UTC)

Last night, I passed around my phone in a discussion group, and it showed the philosopher both on the left, and again WAY OVER on the right, with a "Whoa!" This morning, it is back to how it is presented above. Randall, are you messing with me? Knechod (talk) 17:28, 31 August 2017 (UTC)

First, the terminology: cold science is an observation described with math, that can give stable objective (meaning they could be potentially disproved by an experiment) predictions in a certain range of conditions. Philosophy is an interpretation of science. Math is purely artificial and doesn't require translation, it is pretty much the only abstract symbol system we have now that follows the principle of objectivity, and any solid generalization model requires abstraction by definition. A natural language can't do that because it's subjective, and it's philosophy that is about subjective terms, what do they mean and how do they relate to objectivity and perceived reality. Gather 5 quantum physicists and show them an equation - they will nod agreeably, but ask them to explain it - and they will fight eventually. Despite that, mobile phones work the same way in hands of any person, because that's an applied science, which is roughly equivalent to engineering + inventing. So in that terms the relationship between sciences can be seen as an example of what's called emergence [1], and this concept quite well exists inside any particular science, i.e. in physics thermodynamics is just a generalization of Newtonian mechanics for certain kind of systems (a temperature is a mean kinetic energy of comprising particles, and so on), and mechanics itself is one of generalizations of electrodynamics (things like friction and collision are electromagnetic by nature). The same applies to all other sciences - they just describe different systems of different scales, and most borders become very smeared nowadays, with things like molecular biology, quantum electrodynamics (which is essentially a whole new branch of math), chemical kinetics, ethology and many other continuously evolving cross-disciplinary branches of science. So there's no contradiction here, sciences are different in many aspects but yet they all are reflections of a global pattern, and thus should operate on the same conceptual field. And in this case the contextual field is maths itself. In the end even our subjective descriptions of reality could (and probably would) be represented as a set of math equations, because our brains are nothing more than big calculators, and our language is nothing more than a system of symbols, represented with geometrical shapes and sound waves, and the same mathematical patterns are repeated all over the different aspects of those. All is one, just like our universe itself. octaharon @ 09:00, 1 September 2018 (UTC)

Sincerely, Summer Glau 42.book.addict (talk) 18:16, 3 February 2024 (UTC)

Media:Example.oggWhen you think about it, math is just applied language, and language is is just applied sociology.--ExistentialGrasshopper34 (talk) 05:08, 4 November 2018 (UTC) Logicians: hi.Scci0927 (talk) 02:29, 14 February 2022 (UTC)

Math vs. Logic[edit]

It should be mentioned that Hofstadter's Gödel, Escher, Bach sets logic as being even more pure than mathematics. All mathematical systems can be derived given basic logical precepts. That is how many mathematical/geometrical proofs are structured.

I totally agree. Mathematics is just applied Logic. (Perhaps we can go one more step, to say that Logic is just applied Philosophy?) -- 15:59, 9 May 2024 (UTC)