Why do we use expressions such as "math and science?" Etymologically, I think they mean the same. Set me straight if I'm wrong.

Math is about symbol manipulation games; science is about understanding how the universe works. What does etymology have to do with it?

I don't know how the two terms diverged, and why Latin didn't pick up the Greek term, as so often it did.

You taught me something I didn't know, Asa--that the Greek word for mathematics, mathema, means "science." So saying "math and science," "science" being from the Latin word for "science," is, literally, saying "science and science!"

Good question. Of course, mathematics is a branch of science dealing with numbers. People who earn degrees in math(s) earn bachelors, masters and doctorates in science.

Perhaps everybody just forgot.

Wordmatic

I don't think "science" came into common use until the 19th century -- it was natural philosophy before that. And "scientist" was coined as something of a joke, as an analogy with "artist".

Well, scientia (< scio, scire 'to know') means 'knowledge' in Latin, the word for which is επιστημη (epistēmē) (< επισταμαι (epistamai) 'to know'), as well as μαθημα (mathēma), in Greek. The word epistamai also meant 'skill' or, by extension, 'profession' in Greek, and, in English, we have the word epistemology 'the study of knowledge, knowing'. Natural science in Latin was physica < the Greek term. Greek τεχνη (tekhnē) and Latin ars both meant, cunning, skill, craft'; we get technology and art from these two words. Greek φιλοσοφια (philosophia), literally 'love of wisdom', gives us philosophy.

[Edited incorrect markup.]

This message has been edited. Last edited by: zmježd,

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Math is about symbol manipulation games; science is about understanding how the universe works.

Math is about understanding how the universe works, too. Most sciences (particularly in my field) are intricately related to mathematics.

That's applied math. Pure math is universe-independent.

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Originally posted by zmježd:
Well, scientia[i] (< [i]scio, scire 'to know') means 'knowledge' in Latin, the word for which is επιστημη (epistēmē) (< επισταμαι (epistamai) 'to know'), as well as μαθημα (mathēma), in Greek. The word epistamai also meant 'skill' or, by extension, 'profession' in Greek, and, in English, we have the word epistemology

So why is someone who is learned in many fields a polymath instead of a polyepistomologist? From Latin we have omniscient,, but not multiniscient.

So why is someone who is learned in many fields a polymath instead of a polyepistomologist? From Latin we have omniscient,, but not multiniscient.

The short answer is, because that's how language works. The relationship between a sign and its meaning is arbitrary at best. English polymath 'a person of much or varied learning', and its rarer, synonym, polyhistor, came into English as learned borrowings from Greek. I indicated that Greek επιστημη (epistēmē) was a synonym, not a replacement or the correct word, for Greek μαθημα (mathēma). Epistemologist is an English word, coined in the mid-19th century, from Greek roots. It has the meaning of 'the study of knowledge'. I'm not sure what a polyepistemologist would be, but I doubt that she or he would be a polymath. Though Latin multisciens does not exist, I think it would be different in meaning (more along the lines of 'much-learned') from omnisciens 'all-knowing'. Your multiscient is an English word, judging by its form. Latin is not Greek, nor is it English. To ask that words keep their original meaning is to fall prey to the etymological fallacy. To ask that language be consistent and logical in its deployment of words, meanings, and forms is another kind of fallacy. I'm not saying you oughtn't to wrestle with language, but I just don't think much will come of it. Language outlives its users, and moves moves all ever-changing like Heraclytus' river.

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That's applied math. Pure math is universe-independent.

Well, I am not speaking from as much experience as you are, neveu, but I would disagree. I don't think you can have "applied math" without "pure math." Besides, the original question didn't specifically ask about pure math...just math.

My point was just that science and math really are separate things, and that math shouldn't be thought of as a science -- it's a game. You can do it without ever looking up from your paper and pencil. Science uses a few of these games to model the universe (after having gone into the field and taken lots of measurements). And the only reason they use these games is simply because they are objective: everyone who follows the rules of the game gets the same answer. Some of these games are nearly perfect at predicting how the universe will behave, others not so much.

science is from Latin scio "to know" (<"to separate one thing from another") from Proto-Indo-European *skei- "to cut". In Germanic this became *skītan "to separate, defecate" - ie "separate from the body", and English shit.

Not scat?

OED defines mathematics as a science:

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mathematics

• plural noun usu. treated as sing. the branch of science concerned with number, quantity, and space, either as abstract ideas (pure mathematics) or as applied to physics, engineering, and other subjects (applied mathematics).

— ORIGIN from Greek mathema ‘science’, from manthanein ‘learn’.

WM

I confess that I don't know if neveu is kidding or not. Math is a game? Either I am being hysterically laughed at...or "game" has a definition that I am unaware of. I guess it's the former.

Either I am being hysterically laughed at...or "game" has a definition that I am unaware of. I guess it's the former.

Neither. You just have not read up on the philosophy of mathematics. As neveu said, math is pretty much about manipulating symbols, and it is pretty much based on first premises which are arbitrary and unprovable. Think of Euclid's axioms in Euclidian geometry. If you choose different premises, you get a different kind of math. Think of non-Euclidian geometry (link). Science is usually about observing the world and trying to come up with explanations of how things work, how they got that way, etc. Think biology, physics, etc. In the 20th century, mathematicians and philosophers like Church, Turing, Gödel explored and revealed some amazing stuff about mathematics. Ask a physicist about math, she'll usually say that it's a useful tool to get her job done. Ask a mathematician what physics is and he'll state that it's applied math. (There's your joke, K.) Going back to philosophy for a minute. Bertrand Russell, who co-wrote the Principia Mathematica with Alfred North Whitehead, nonce stated that he very nearly gave up mathematics when his good friend and colleague Ludwig Wittgenstein had nearly convinced him that math was nothing but tautologies. Wittgenstein very famously analyzed language as a game (link). This thread does prove that people all have very different ideas about what words mean, and yet we can speak and write to another, and some kind of communication can occur. I feel neveu's frustration at something that seems patently obvious to him, but not to any of his interlocutors. I feel the same when people start discussing "grammar" on these words boards. For linguists grammar has a very precise meaning. For others, language enthusiasts or not, it can mean anything from rhetoric, style, punctuation, writing and spelling systems, etc.

Personally, I like to think of math as a foreign language. That concept helped me to conquer my math-aversion to a certain extent as an adult student determined not to be math-ignorant after having read Innumeracy.

It seems to me that besides being about the manipulation of symbols, mathematics is also about observation of the behaviors of quantities of things, whether or not they are manipulated, things that can be represented by those symbols. Likewise, in science, there is both observation and manipulation of the things being observed (e.g., the biologist dissecting the lab rat after the experiment is over, to examine its heart.)And in science, the things being observed are often reduced to symbols (e.g. in chemistry, AU=gold; NA=sodium.) Why does the fact that mathematicians manipulate one kind of symbol, and chemists, another, make mathematics any less a science than chemistry or physics or biology?

Wordmatic

Yes, scientists do tend to manipulate symbols, too, but those symbols stand in a relationship to real objects in the world. Only some kinds of math do that. Mathematicians tend to manipulate symbols qua symbols. And because both are human and use language, there is another kind of symbol manipulation game being played.

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I don't know if neveu is kidding or not

Kidding? Moi?!

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Ask a physicist about math, she'll usually say that it's a useful tool to get her job done. Ask a mathematician what physics is and he'll state that it's applied math. (There's your joke, K.)

And the punchline is that they are both right.

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Wittgenstein had nearly convinced him that math was nothing but tautologies

The great British engineer Oliver Heaviside once described the study of geometry as proving the obvious in terms of the equally obvious.

So, zmj and neveu, are you both saying that math is not a branch of science (although dictionaries define it as such) merely because the manipulation of some of its symbols has to do with abstract concepts rather than a bearing direct relationship to objects in the real world? It seems to me that other branches of science use mathematical models to to explore the likelihood of the existence of objects which may or may not exist in the real world, objects which have not yet been, and may never be observed. And some branches of mathematics, such as chaos theory and game theory, help to predict actual occurences in the world of real objects in situations where everything seems perfectly random. It seems to me that "math" and "science" are not separate entities, but part of the same whole.

Wordmatic

As a foundation to this discussion, here is the OED's first definition for mathematics. I do realize that what you're talking about is more a metaphor than anything, but it might help:

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1. Originally: (a collective term for) geometry, arithmetic, and certain physical sciences involving geometrical reasoning, such as astronomy and optics; spec. the disciplines of the quadrivium collectively. In later use: the science of space, number, quantity, and arrangement, whose methods involve logical reasoning and usually the use of symbolic notation, and which includes geometry, arithmetic, algebra, and analysis; mathematical operations or calculations. Colloq. abbreviated maths, (N. Amer.) math.

As for game, there are 17 definitions in the OED, with multiple sections under each, including a "draft addition," as of March 2007, for the slang, "he got game." None of them mentions mathematics.

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You just have not read up on the philosophy of mathematics.

You are correct, though perhaps I'll ask Shu for one of his books on the subject. Shu has been sick, but I will alert him to this thread. He was a mathematics and philosophy major, and has read up on it. For what it's worth, I have formally studied the philosophy of science and in fact I've taught it to graduate students.

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I feel neveu's frustration at something that seems patently obvious to him, but not to any of his interlocutors. I feel the same when people start discussing "grammar" on these words boards. For linguists grammar has a very precise meaning. For others, language enthusiasts or not, it can mean anything from rhetoric, style, punctuation, writing and spelling systems, etc.

Ah, isn't it the truth? I feel the same way when someone pontificates about health care. I am sure that is true of all our fields.

Related to linguists being frustrated about the use of grammar, I have been thinking of this for awhile. Many people, I agree, use the word grammar wrong. Sometimes I revert to old bad habits. But here's my point. Since many use the word grammar not as specifically as linguists would like, is that how the word grammar has evolved? While linguists describe themselves, generally speaking, as descriptivists, are they being descriptivists with the word grammar?

I am definitely thinking too much tonight! This has been an interesting discussion

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While linguists describe themselves, generally speaking, as descriptivists, are they being descriptivists with the word grammar?

Sure, there are multiple meanings of the word grammar, science, and mathematics. It's just that when I talk about grammar or neveu talks about science or math, we use the words in a very special sense. If we disagree about what words mean in the course and context of our discussion, then communication cannot really take place. Ask shu about that. Lawyers spend a lot of time defining terms in a particular context of a law or a contract. They have to, because if they don't somebody can interpret the words differently as is their wont and right. The thing is all words are polysemous.

Okay. Point well taken. I will call the head of the department of mathematics at a world class university (U. of Chicago) and ask him if he considers math a game. I'll be back...

[Note how I assume the head of the department is a man. How disgusting, but it's a fact of life. Note the experts in this thread who are being cited. Oh well.]

Well, we'll see if he answers. I sent an email to the chair of the department of math at U of C, a Dr. Peter Constantin. He probably won't answer, but we'll see. I'd like a fresh perspective on this interesting question of math being considered a game.

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I'd like a fresh perspective on this interesting question of math being considered a game

Here's one. It's concerned with math education but it explains the formalist point of view in the second section.

a game

There's also an assumption that if something is a game it is less useful than if it is something else, like a science perhaps. I remember years ago, I found myself in a discussion with a physics major who had dropped out of school and become a fundamentalist Christian. I did not know him well, but he was the friend of a good friend of mine. Anyway, he was going on about the bible, and somehow paused in medias rant and asked me what I thought about the book. I said there were some parts that lovely poems, but on the whole I had been unimpressed with it. He flew into a rage. He screamed these were no poems in the Bible. It was the word of God! I suggested he take a look at some Christian commentary on the book of Job, or perhaps, ask his pastor. He did just that, by calling the man that instant at his home. When he hung up, he was quite dejected, his pastor agreed with me. Oh, well. The discussion stopped at that point, neither of us really satisfied, but sort of sad.

The document neveu linked to was interesting.

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in medias rant

I am so stealing that.

I am so stealing that.

Honored.

Yeah, it's great!

In the opening question I asked to be set straight regarding the use of math and science. Boy have I ever been set straight! That link reminded me of Richard Feynman's rant about math textbooks he was asked to review for the Los Angeles school board, as presented in the book, Surely You're Joking, Mr. Feynman.

Asa, I, for one, would like to thank you for starting one of the more interesting threads in a long time. Keep up the socratic questioning.

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He screamed these were no poems in the Bible.

Wow. You'd think Song of Solomon would have been a hint. This reminds me of the thread about Willis Barnstone's project to translate the Bible into English verse, which, in my opinion, is just as kooky, as most of the Old Testament and none of the New are actually poetry.

Song of Solomon

Or the Psalms.

Yes, quite uncharacteristically, I'd agree with z ( ), Asa, that this has been a great thread.

neveu, I did enjoy the link. I didn't agree with all of it (now I recall that you home school your children, which somewhat explains your perspective), but it surely made me understand your use of "games" for your definition. Our kids were very lucky and attended schools (elementary and middle particularly, which I consider to be the most important part of education) where math was engaging, and they all still love math. I realize, though, that it isn't the norm.

I did, however, think this wasn't correct:

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English teachers know that spelling and pronunciation are best learned in a context of reading
and writing. History teachers know that names and dates are uninteresting when removed from
the unfolding backstory of events.

That's not the norm. Spelling tests, learning dates of history, correcting grammar, etc. are the norm and completely turn off children to reading, writing, language and history. Creative teachers surely teach like that, but not all teachers. I'd submit that English, history, social studies, and science are all taught along the lines of math. Math is no different in that, though this author seems to think it is.

I also disagreed that you can't teach teachers to teach, but I do see where he's coming from there. Some people naturally can engage students more than others.

[P.S. No word from the math department at the U of C, so I am not optimistic that he will answer. He probably thinks I am some kook.]

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I did, however, think this wasn't correct:

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English teachers know that spelling and pronunciation are best learned in a context of reading and writing. History teachers know that names and dates are uninteresting when removed from the unfolding backstory of events.

That's not the norm. Spelling tests, learning dates of history, correcting grammar, etc. are the norm and completely turn off children to reading, writing, language and history. ...

I also disagreed that you can't teach teachers to teach, but I do see where he's coming from there. Some people naturally can engage students more than others.

I can only speak for the UK but over here most teachers do feel this way. As a teacher I rarely do spelling tests, though I will throw one in occasionally because the students often feel that they are necessary. When I was at school it certainly was common to teach history with lists of names and dates, it was common to use spelling and grammar tests but not any more. There has recently been a news story here about schools no longer teaching physics, biology and chemistry as individual subjects but as an integrated subject called "science". The methodologies commonly in use here now are to use projects and more student involvement rather than simple "fact learning".
Whether this approach is better or not is a matter of opinion. Personally I think it's much better as long as we avoid the danger of throwing out all the content in the interests of making it fun. The facts still need to be there no matter how jazzy the presentation is. By and large I think that teachers in the UK are getting it about right nowadays.

As for teaching people to teach. Not only can you, you must. Before I became an English teacher I had previously done a single day as a computer science teacher. A single day because I handed in my notice five minutes after leaving the classroom. It had become obvious to me in that seven hours that I had absolutely no idea what I was doing. I knew my subject but I simply couldn't teach. I couldn't organise the knowledge, plan the lessons, deliver the material, control the class: all skills that a teacher MUST have. And, crucially, all skills that a teacher can learn.
I can do them now because I've been taught how to do them.
Some elements of being a good teacher can't be taught. You need to have the right kind of personality and the right kind of outlook for a start but all those other things, the mechanics of teaching, can, should and must be learned before you walk into a classroom.

Perhaps Edison's "1% inspiration, 99% perspiration" fits here. The trouble is, nearly all the teachers (or were they wardens?) I had lacked the ability to provide even 1% inspiration to the students. An aeronautical engineer friend often quotes Isaac Asimov's statement, "The most exciting phrase to hear in science, the one that heralds new discoveries, is not 'Eureka!' but 'That's funny'". It's inciting curiosity that gets the job done, IMHO.

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I can only speak for the UK but over here most teachers do feel this way. As a teacher I rarely do spelling tests, though I will throw one in occasionally because the students often feel that they are necessary.

I don't know what ages you teach, but I was referring to elementary and middle school students (ages 6-12 about). While I surely agree that language, reading, and writing are best taught by reading, often one doesn't see it here. I remember when I was visiting schools (kindergarten) to decide where to send our kids, the teacher had every kid lined up at a long table with a boring textbook in front of them. They were all on the same page doing the same thing, not having fun at all. One little kid decided to go about his own business, and he actually snuck out the door and started playing with his truck outside. The teacher was so intent on making sure they were all on the same word that she didn't even see him. I told the teacher what had happened, and obviously she was embarrassed, so she brought the boy in, made him sit by himself, and told the rest of the class not to talk to him for the rest of the day. This was in an affluent suburb which is known to have excellent schools. It made me wonder what occurs at the Chicago public schools, which have a terrible reputation. Needless to say, we did not choose that school.

I find that quite shocking, both in what happened and in the teacher's response to it. However my experience (admitedly, in the case of teaching kids, limited to talking to other teachers and reading the journals) is that modern schools us a much more communicative and activities based approach than was ever the case when I was at school. An approach, in fact, that is quite similar to the way that we are supposed to teach adults, with short, varied activities and lots of fun.

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Originally posted by Asa Lovejoy:
Not scat?

Probably not. scat is from *sker- "excrement".

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scat is from *sker-

Who made that decision?

Louis Armstrong? http://en.wikipedia.org/wiki/Louis_Armstrong

I thought this Mr. Boffo comic belonged here (put 6/21/09 in).

We don't get that strip around here, but isn't Joe Martin one of the Mad Magazine guys?

I am not sure, but if you recall, we were just talking about Mad Magazine on the chat. Perhaps someone else knows?

No, Don Martin wrote for MAD.