0435: "Purity"

[MysticTerminator]

I think the old joke was along the lines of "biologists all aspire to be chemists. chemists all aspire to be physicists. and physicists all aspire to be god. ... and god aspires to be a mathematician."

[crp]

Lol is this applied physics or applied philosophy?
http://www.youtube.com/watch?v=wvRzWYCZ2e0

[scarletmanuka]

retaliate with certainty!

Or Tesla Coil.

[Grego]

And imply that the man's "cute when he gets into something"?

[MysticTerminator]

a thought -- mathematics is certainly derived from some parts of philosophy at some level. but the foundations of math - proof theory, model theory, and so forth - are equally part of theoretical computer science. looks like inserting computer science into the purity ordering might be tricky after all ?

[westsurfer]

The first computer scientists, such as Ada, were mathematicians, which disproves the computer science notion. Math has been around far longer than computers so it's no use to even compare them.

I love this comic. You could have easily added Political Science is just applied Sociology, but anyone can understand why you kept it as concise as possible.

[King of Frogs]

Ok, this is my first post here so hey guys - great comic by the way Mr Munroe *salutes for no apparent reason*.

This thread is so large I couldn't be assed reading through it all so I don't know if this has been said already or not, but as soon as I saw that comic I just wanted to draw a big circle around the scale and label it "philosophy". But then again, I'm a philosophy student, so I may be biased...

[King of Frogs]

Oh god, I killed the thread! What have I done!

[scarletmanuka]

Given that prior to your first post there were only two other posts in four weeks, I'd say it was pretty well dead already...

[annabelle_the_brave]

I have something to add that isn't important at all. But I want to say it anyway.

I was feeling sort of miffed as to why there was no geologist in this comic. Then I realized:

If there were a geologist in this comic, he would be way off the page (above on a mountain, or perhaps below in a cave) and saying, "Hey guys! What are you doing, all standing in a line? You look pretty stupid! Come look at this sweet thing I found!"

That's all, really.

yours,
annie bell

[kelvinc]

Oh, and if you want to hate on econ more just remember this, we still get a nobel prize... bitches!

No, you don't! You don't have the Nobel Prize, you have The Sveriges Riksbank Prize in Economic Sciences in Memory of Alfred Nobel. Common misunderstanding

As Professor Farnsworth said: "I don't care: they all pay the same!"

Generally this is how microeconomics works:
We sit around and think up models.
Someone gets a grant to do some experiments, usually in the psychology building 'cuz us economists don't actually touch this stuff.
Experiment comes back and says our model doesn't actually work in certain situations.
We reply that models are approximations and what we've got predicts things pretty well already, and go back to making more models.

In most other economics fields, we generally preface everything with the statement that we can't do controlled experiments and get results that we take with varying amounts of salt.

On the other hand, that's the thing about social sciences: for the most part, we don't actually claim that our models explain perfectly what happens. When chemists talk about atoms, they can get some cloudy solutions, look at the Brownian motion, and say that these things actually agree with observations, and act as if atoms exist. No economist actually thinks that choosing between difference apple and orange consumption levels involve plugging in the amounts into a utility function and see what number comes out. It just seems like, on average, that this approach works pretty well.

[Cooley]

My physics teacher mentioned that physics was the most fundamental science today...

Everyone staring at me laughing in my first class at uni... great. But it was worth it.

[koesherbacon]

Where does Cognitive Neuroscience fit in there?

[imMAW]

I'm going to put this on my door. I'm living with a bunch of non-math scientists
hitler

[lbutler]

When I sent this comic to a friend of mine, he replied:

"I got your amusing little comic, but it seems to have been cut off on the right. Naturally, far to the right of Maths is Philosophy."

[King of Frogs]

Like I said, glad someone agrees!

[qinwamascot]

The first computer scientists, such as Ada, were mathematicians, which disproves the computer science notion. Math has been around far longer than computers so it's no use to even compare them.

I love this comic. You could have easily added Political Science is just applied Sociology, but anyone can understand why you kept it as concise as possible.

According to E. W. Dijkstra, "Computer Science is no more about computers than astronomy is about telescopes." Not that I'm a CS major, but CS really is just a subgenre of math that is applied to computer programming, much like how physical math is a subgenre of math that is useful for physics. I put CS like a level below math, because it uses a single set of axioms and studies the consequences, whereas true math uses many sets of axioms and studies the consequences. Or in the case of logic, it uses an arbitrary set of axioms and studies the consequences.

[Tolchok]

I realize that this post is more or less dead, but I just registered now, so sorry I didn't post sooner...

So, saying that "math is applied philosophy" strikes me as utter nonsense. If I have one <thing> and then another <thing>, now I have two <thing>s. That's math. 1+1=2. You can argue "Oh, what if one <thing> breaks into two" or something, but then you're missing the point. I don't derive math from philosophy. Some people derive math from set theory, but I've never heard that proof and I can use math anyway, so math doesn't have to be derived from that. This is what we mean by applied/pure.

And arguing about Descartes-esque questions like: Is this universe the real universe? Maybe it's constructed for us? seems like it doesn't matter. It's not "If this is the real universe, 1+1=2, and every time I add, I'm actually using the philosophical idea that this is the real universe." It's more like "Regardless of whether this universe is the universe or not, 1+1 in this universe =2." That's how I see it, anyway.

And about this whole physics/math thing, I think there was something about that in Cryptonomicon. (As much as xkcd does, that book describes my life. Except much cooler.) It was something along the lines of: If math can be proven by using actual <thing>s, then you're treating math like applied physics. But if math can't be proven by using actual <thing>s, aren't you wasting your time with something so abstract?

[King of Frogs]

I realize that this post is more or less dead, but I just registered now, so sorry I didn't post sooner...

So, saying that "math is applied philosophy" strikes me as utter nonsense. If I have one <thing> and then another <thing>, now I have two <thing>s. That's math. 1+1=2. You can argue "Oh, what if one <thing> breaks into two" or something, but then you're missing the point. I don't derive math from philosophy. Some people derive math from set theory, but I've never heard that proof and I can use math anyway, so math doesn't have to be derived from that. This is what we mean by applied/pure.

And arguing about Descartes-esque questions like: Is this universe the real universe? Maybe it's constructed for us? seems like it doesn't matter. It's not "If this is the real universe, 1+1=2, and every time I add, I'm actually using the philosophical idea that this is the real universe." It's more like "Regardless of whether this universe is the universe or not, 1+1 in this universe =2." That's how I see it, anyway.

I completely disagree, mathematics only has validity thanks to philosophers such as Russell and those who came after him who acertained that mathematics can be a system one can use to derive truth about the universe, as there was a school of thought that lasted for several hundred years which stated that mathematics, whilst intetresting, was just an academic exercise and did not really reperesent objects in the real.

Also, ontology is important here. You mention set theory; even though the questions that it poses don't bother you, they are still important in the application of mathematics. If you say you have one <thing> then you need to have a good conception of what a <thing> is. What properties must something have in order to be considered a sperate object in and of itself? You need to resolve this issue in order for mathematics to be in any way representative of reality.

And what about the numbers themselves? Should we think of the number 2 as a metaphysical or mathematical object, as it is treated in mathematics, or should we think of it as a general term of represention; any two objects?

Philosophy has a lot to say about mathematics and a lot to add to it's application and most mathematicians I have spoken to have said as much, especially in the more advanced levels of mathematics where it begins to move outside the realm of human rationality.

[kjsharke]

I completely disagree, mathematics only has validity thanks to philosophers such as Russell and those who came after him who acertained that mathematics can be a system one can use to derive truth about the universe, as there was a school of thought that lasted for several hundred years which stated that mathematics, whilst intetresting, was just an academic exercise and did not really reperesent objects in the real.

I'd disagree that Russell (or anyone) proved anything to that effect. Russell (Gödel) only proved things about math as mathematicians, though they may have been philosophers as well... They are related, I would accept that they both are "Applied Reasoning"

If there were a geologist in this comic, he would be way off the page

I'd say geology is another application of chemistry. Or physics depending on what you're doing, but for the seminars I have gone to, chemistry. (OTOH, I am a chemist, so perhaps my sampling method is imperfect).

(though geologists <strong>do</strong> seem to have an enviable tendency to be off somewhere cool..)

Anyhow, it reminds me of arguing whose programming language is closer to the essence of things.
(prolog < java < C++ < C < C-- < Assembly < bitcode < flip-flops < erector set < prolog)

[Tolchok]

Also, ontology is important here. You mention set theory; even though the questions that it poses don't bother you, they are still important in the application of mathematics. If you say you have one <thing> then you need to have a good conception of what a <thing> is. What properties must something have in order to be considered a sperate object in and of itself? You need to resolve this issue in order for mathematics to be in any way representative of reality.

This is exactly what I meant when I said that you could argue that an object breaks in half and 1=2 because both halves count or something, but you'd be missing the point.

OK, don't think of it as individual objects. Think of it as a sliding-scale sort of units thing. Hypothetically, I have a perfect scale. On each side, I put stuff that weighs one gram. The scale balances. One = one. No philosophy necessary.

What does this have to do with ontology? I forget what that is.

And what about the numbers themselves? Should we think of the number 2 as a metaphysical or mathematical object, as it is treated in mathematics, or should we think of it as a general term of represention; any two objects?

It's not an object at all (not that I'm sure what you mean by object). It's an amount. Anyone who's had a science class knows that you have to put your units in. Syntactically, it makes no sense to run around saying "I have three!" unless people know what you have three of.

Philosophy has a lot to say about mathematics and a lot to add to it's application and most mathematicians I have spoken to have said as much, especially in the more advanced levels of mathematics where it begins to move outside the realm of human rationality.

I don't know much about advanced math (the extent of my knowledge is up to about a month into AP Calc), so I'm not going to argue with this here.

[Matthias]

You know what I liked about this one? The puffly-chested outrage I can picture the respective scientists having.

"Applied? You want to apply physics? This is science, you buffoons! Science!"

[TheKrikkitWars]

And what about the numbers themselves? Should we think of the number 2 as a metaphysical or mathematical object, as it is treated in mathematics, or should we think of it as a general term of represention; any two objects?

It's not an object at all (not that I'm sure what you mean by object). It's an amount. Anyone who's had a science class knows that you have to put your units in. Syntactically, it makes no sense to run around saying "I have three!" unless people know what you have three of.

Sure it is:

3

that was three, he's an object, he represents three of something in the arabic numeral system, he's also the magic number, nice guy

(the point is, that it represents an amount doesn't remove the fact that the word or numeral is a lexical object to represent the concept of a particular multiple of single items or units.)

[skatcat31]

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

Hah, my science teachers always say their science is the central science etc. But math rules!

A+B=C? What? Half angle identities and unit circles? Algebra?!?!?!? OH SNAP! MATH DOES RULE SCIENCE!!! MOBIUS STRIP FTW! wow, congratulations internets, you have for once one(won).

[LISStryfe]

And somewhere to the right of the Mathematician, the Information Scientist is checking the stacks, nods to everyone else and says "Right... and you'll be by Tuesday, 11 AM for your research session, right?"

[Onehitwonder]

Sorry to metaphysically beat a dead existential horse, but I spent 10,000 hours in Paint to make my contribution. Of course, that was before I read the thread. Now I wish I had my 10,000 hours back


I was amused, at least.

[Cheshire]

As someone with no part in the sciences I must say; My respect for each of these goes down the purer and purer they get.

[littlebuddy]

after mathematicians there would be logicians followed by philosophers and then sociologists...

[marukabu]

life!
the ultimate science

[Felstaff]

I'm looking for xkcd the comic where all scientific disciplines are derived from math. Last night I went through all the xkcd comics and must have missed it. Does anyone have an idea which one it is?

TIA,
- Alex

[Moo]

http://xkcd.com/435/

That took me about 2 minutes in Google, dude.

[zav]

Your powers are strong; far beyond my meagre abilities.

Granted, going through all the xkcd comics was fun.

Thanks.

[Moo]

As good an excuse as any I suppose, young grasshopper

[zav]

Oh, hey. Just saw that you were from South EHfrika. If you dig Namibia, you might get a kick out of this little trip I took earlier this year.

http://www.youtube.com/watch?v=N9iKhLYQYh4

Be patient. The youtube video loads slowly.

Thanks again.

[Akinera]

I love this comic. I showed it to a couple people at work over the summer (I was a science mentor for middle school students), and they just got a kick out of it.

Well done, Munroe.

[userxp]

Unidimensional classification is not enough!

s.png (13.21 KiB) Viewed 5663 times

[HighwoodFool]

I really like this particular comic. The alt-text accurately describes why I picked physics over math as a major, in addition to the fact that I would be studying the math, anyways.

I believe that the relationship between mathematics and physics differs from the relationship between physics and other sciences. The laws that physicists seek to discern determine the behavior of the particles in a chemical reaction, which, in turn, direct biological processes. These biological processes include neurological events, which are manifested as psychological events (assuming monism, which seems to best match experience, given the consistent, observable effects of brain surgery and psychoactive drugs). Society can be thought of as a network of minds. Thus, the other sciences can, theoretically, be reduced to physics, and can, therefore, be thought of as approximations of physics – hence, less pure - arising out of practicality. The analogy does not seem to of the mathematics-physics relationship. Physics cannot be reduced as pure mathematics, unless it can be proven that there is only one law or set of laws that can be mathematically consistent.

Where would other fields lie on this line? Other social sciences (e.g. poli-sci) could be thought as applied sociology, whereas logic and philosophy would be purer than mathematics. However, in an anti-Platonic view, reason’s existence would be limited to a product of human cognition and could, therefore, be analyzed in terms of psychology, suggesting a loop. Logic could also be thought of as a social construct, as an agreed-upon set of rules. Furthermore, to include other fields, adding branches may be necessary, although it is unclear where they would originate. For example, is music an application of number, a set of vibrations, a product of the psyche, or an aspect of society?

Nevertheless, Munroe’s concise comic seems best without all this excessive nitpicking. Thanks for the thought-provocation, Randall.

[Pfhorrest]

Physics cannot be reduced as pure mathematics

logic and philosophy would be purer than mathematics

I like to treat the root elements of the various disciplines as a two-branch system based off of physics on the one hand (with a chain of abstracted disciplines similar to that depicted in the comic) and, loosely speaking, "economics" on the other hand. More closely, I'd say the other branch is grounded in game theory, that being an application of mathematical models to strategic, goal-seeking purposes, akin to physics as an application of mathematical models to theoretic or explanatory purposes; though the title "game theory" alone doesn't carry any ethical connotations with it the way "physics" carries certain metaphysical and epistemological connotations of naturalism. (I'm tempted for aesthetic and etymological purposes to call the second branch the "ethical sciences", in reflection of the "physical sciences", but that would be confusing given the modern connotations of "ethics").

More to the point of this thread, both of these branches are grounded, as already obvious from the above, in mathematics, so the comic's depiction of it as "most pure" is still accurate in my book; but as HighwoodFool here points out, physics is not entirely reducible to mathematics, and logic and philosophy have their own claim as the "purest" as well.

My answer to that is that both physics and the root of the "ethical sciences" (whatever we are to call it) are grounded not only in mathematics but equally in philosophy. Mathematics provides the tools for building theoretic and strategic models, but philosophy provides the guides for how to judge one model as superior to another. We've got general consensus in the case of physical models that that criterion is consistency with empirical observation, but... well, the ethical side of things is still contentious, though we seem to be coming slowly closer over the centuries to agreement that it's some kind of altruistic hedonism (i.e. the happiness/well-being of everybody in this world, rather than any transcendent/otherworldly [on the one hand] or egotistic [on the other hand] standard).

I'd say that there is also a third "purest" root, along with mathematics and philosophy: art, encompassing writing and music as well. Whereas mathematics is purely analytic, breaking ideas apart into their more base structures, the arts are synthetic, as in creative, putting things together into new combinations. When you throw this into the mix, you get another branch of disciplines parallel to the sciences: engineering. Engineering is, very loosely speaking, taking the "parts" sorted and identified by the sciences, and combining them together into new things. On the physical side of things these fields are well-known as engineering fields - mechanical engineering, genetic engineering, etc - but I see faint parallels on the other side in fields such as political economics, and I hope that some day, when the ethical side of philosophy has settled down as much as the physical side has, we might see similar levels of mathematical rigor applied to fields in that domain as well.

[AlexanderRM]

Math is just applied language arts.

Using our powers of semantic representation to add stuff together.

And language arts is just applied English, and English is just applied psychology...


(or, really, what made me say that is that at least in my schooling system, after 6th grade language arts and reading are combined into English. On top of this, my 6th grade reading and lang. arts teachers were the same person, so I've generally gotten the impression that language arts was just a subset of English or whatever. I think the claim that it's "applied" English is still sorta reasonable, though...)

[Fixblor]

Re: alt text => Go screw yourself, Randall. I'm sure you can count to one.