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Solfe
2010-Aug-24, 01:16 AM
If the x axis is called the abscissa and the y axis is the ordinate, is there a term for the z axis?

Just wondering.

Solfe

caveman1917
2010-Aug-24, 01:28 AM
Wikipedia says this here (http://en.wikipedia.org/wiki/Cartesian_coordinate_system#Notations_and_conventi ons)


In three dimensions, the names "abscissa" and "ordinate" are rarely used for x and y, respectively. When they are, the z-coordinate is sometimes called the applicate.

Ken G
2010-Aug-24, 01:39 AM
Who makes up these crazy terms, and why do we follow them? I'm going to make up a word for that last little bit of peanut butter stuck to the bottom of the jar that you can never get. The "remnut." Let's see if it catches on.

grant hutchison
2010-Aug-24, 02:04 AM
Who makes up these crazy terms, and why do we follow them?Geometers made them up, and they meant something in their day. An ordinate was a line drawn from a point, parallel to one line, and intersecting another line. Hence co-ordinates, which are generated (geometrically) by a pair of ordinates. An abscissa is the part of a line between some point on its length and its intersection with another line. So each ordinate parallel to one axis generates an abscissa on the other axis. An applicate is just another ordinate.
If you had the elaborate background in geometry that was around when Cartesian coordinates were invented, it all made perfect sense: these were just old words pressed into new duties.

Grant Hutchison

George
2010-Aug-24, 04:12 AM
Who makes up these crazy terms, and why do we follow them? I'm going to make up a word for that last little bit of peanut butter stuck to the bottom of the jar that you can never get. The "remnut." Let's see if it catches on. What about the similar circumstance for jelly or jam - remjam?

Now that you've given it a name, I wonder how long it will take before some quickly invents the Remnut Remover? Without a name, it is unidentfied, thus too inconsequential to deserve a device to address it. :)

Ken G
2010-Aug-24, 02:03 PM
So each ordinate parallel to one axis generates an abscissa on the other axis. An applicate is just another ordinate.
If you had the elaborate background in geometry that was around when Cartesian coordinates were invented, it all made perfect sense: these were just old words pressed into new duties.That's well explained, but that means the x co-ordinate is an abscissa of a y ordinate, and the y co-ordinate is an abscissa of an x ordinate. What we call coordinates are really coabscissas. So like many things, there's a history to why the words came out like that, but they really don't make any logical sense. Dinosaurs of tradition, that survive because we need some word for these things. Personally, I'd say "x-coordinate" and "y-coordinate" are no more arbitrary conventions, and make more logical sense, so I see no need to replace those terms with their arcane fore-bears! Using "x" and "y" is downright more honest about the purely conventional character of these quantities, and what I object to is the attitude that "we can't just call them x and y, that's too arbitrary, we should call them what they 'really are'-- abscissa and ordinate." But the latter are equally purely convention, and cannot be used to reconstruct the original meanings of an abscissa and an ordinate. Thus, use of them smacks of just trying to make things sound more difficult than they really are-- the poor student is having enough trouble, and has to hear something that translates to "this is Bob, whom we call James, and this is Mary, whom we call Sue."

mike alexander
2010-Aug-24, 02:12 PM
I never had a problem with ordinate and abscissa, but I could not remember which was which. Still can't on a dare, for that matter.

Grant's explanation is concise, elegant and made my eyes glaze over. It's in that necessary subset of language that hurts to read.

Nick Theodorakis
2010-Aug-24, 02:25 PM
I never had a problem with ordinate and abscissa, but I could not remember which was which. Still can't on a dare, for that matter.
...

When I was in school, the mnemonic I used is that "abscissa" had some of the same letters as "scissors" and the "x" resembles an open pair of scissors.

Nick

grant hutchison
2010-Aug-24, 03:08 PM
That's well explained, but that means the x co-ordinate is an abscissa of a y ordinate, and the y co-ordinate is an abscissa of an x ordinate. What we call coordinates are really coabscissas. So like many things, there's a history to why the words came out like that, but they really don't make any logical sense.They did make logical sense, when the x and y axes were not equal partners. In graphing terms, one always dropped an ordinate on to an abscissa, never drew it horizontally. Co-ordinates came later, and with them the inability to differentiate sensibly between ordinate and abscissa.
Old words are little bits of linguistic archaeology, hinting at how people used to think about stuff. That's a separate area of endeavour from teaching and understanding current practice. I offered my little dissertation only as a curiosity, not a defence of using old expressions for modern teaching. (I'm not aware of any campaign to replace the current axis labels with the old words. They lingered into my early childhood, but seemed to vanish in the UK with the teaching of "New Maths" in the early 70s.)

Grant Hutchison

grant hutchison
2010-Aug-24, 03:09 PM
Grant's explanation is concise, elegant and made my eyes glaze over. It's in that necessary subset of language that hurts to read.Um. Thank you.

Grant Hutchison

grant hutchison
2010-Aug-24, 03:13 PM
When I was in school, the mnemonic I used is that "abscissa" had some of the same letters as "scissors" and the "x" resembles an open pair of scissors.In fact, the etymology of abscissa and scissor is the same, since both words imply the action of "cutting".
I had the same association with scissors, but to me the letter "X" conjured up the same "ks" sound as a set of scissor blades closing.

Grant Hutchison

mike alexander
2010-Aug-24, 04:52 PM
Um. Thank you.

Grant Hutchison

It was meant as an unadulterated complement.

My mind starts to read things of that nature and immediately decides to go on a walkabout. I'm not happy about it, but there you are.

I'm sure it explains my grades in geometry.

Ken G
2010-Aug-24, 05:17 PM
They did make logical sense, when the x and y axes were not equal partners. In graphing terms, one always dropped an ordinate on to an abscissa, never drew it horizontally. Co-ordinates came later, and with them the inability to differentiate sensibly between ordinate and abscissa.OK, then it sounds like you are saying an "ordinate" is a line segment starting from a given point and concluding in a pre-existing line, and an abscissa is a line segment that exists in a pre-existing ray when a new line intersects it. Then the terms are also applied to the lengths of those line segments. In other words, they are both perpendicular distances between a point and a line, and the difference is whether the line is an axis or an ordinate, and whether the point is a data point or an origin. Then when you add the convention of always using vertical ordinates and a horizontal axis, you get the associations you mention. OK, I can grant that there's a logical basis there, but should have been tossed when the "co-ordinate" concept took over, as that should have unified the ordinates and the abscissas.
I offered my little dissertation only as a curiosity, not a defence of using old expressions for modern teaching.I didn't suggest you had favored the old terms-- my objection to them is purely my own. I feel there is a tendency for many educators to mix what is a true finding about how things work, with what is purely an arbitrary convention for talking about those things, as if they were one and the same. This causes confusion about what students are really supposed to understand, and what they are not supposed to understand, and it supports a dogmatic approach. When one label is already a necessary evil, resuscitating a second one is overkill.

HenrikOlsen
2010-Aug-25, 11:10 PM
I feel there is a tendency for many educators to mix what is a true finding about how things work, with what is purely an arbitrary convention for talking about those things, as if they were one and the same. This causes confusion about what students are really supposed to understand, and what they are not supposed to understand, and it supports a dogmatic approach. When one label is already a necessary evil, resuscitating a second one is overkill.
I suspect it's a result of the politically mandated drive towards more unified testing of education efficiency, which tends strongly to favor role learning over understanding because that's easier to write specific tests for.

"If we 'teach' them all these labels, then by showing they remember them we can show that they learn something from us."

To me, the name/label of something is its least interesting feature, though I'll freely admit that labels have a reason to exist.

novaderrik
2010-Aug-26, 12:47 AM
maybe tomorrow i'll use these fancy terms when i'm adjusting the offsets on the cnc milling machine i run at work..

Ken G
2010-Aug-26, 03:21 AM
I suspect it's a result of the politically mandated drive towards more unified testing of education efficiency, which tends strongly to favor role learning over understanding because that's easier to write specific tests for.
Yes, that would be particularly awful. I really don't mind if someone wants to throw in the archaic names as a kind of cultural dressing of some kind, in which case they may as well say where they came from. But just inventing something to teach because it's easy to ask on a test, giving the impression thereby that the educational process has been a success, comes under the heading of "teaching as imparting an illusion of mastery." It's less frustrating than finding out what students have really learned how to do, but that's about all you can say for it.

To me, the name/label of something is its least interesting feature, though I'll freely admit that labels have a reason to exist.It reminds me of something Feynman said-- his dad would take him on walks and tell him all about the reasons that various plants and animals functioned the way they did, but he wouldn't bother with the labels for anything. Then when Feynman would interact with people who knew all the labels but none of the reasons, there would be a kind of illusion as to which party really had learned something about those plants and animals.

grapes
2010-Aug-26, 05:40 PM
It reminds me of something Feynman said-- his dad would take him on walks and tell him all about the reasons that various plants and animals functioned the way they did, but he wouldn't bother with the labels for anything. Then when Feynman would interact with people who knew all the labels but none of the reasons, there would be a kind of illusion as to which party really had learned something about those plants and animals.Learning is illusory :)

That story is from The Making of a Scientist, the first chapter of the book "What Do You Care What Other People Think?" Feynman says his dad would tell him the names of the bird in English, Italian, Portuguese, Chinese, and Japanese--but it was different from the name that the other kid knew. Feynman says, about his dad, "I knew he didn't know the real name."

Apparently, the dad knew that it was important to name the bird, he just didn't know the name. That's a step removed from Louis Alvarez who deprecated such naming/classification science as stamp collecting1. Of course, such classification effort is necessary to the subsequent analysis: if you see a brown-throated thrush preening itself after eating but don't see a spencer's warbler, you could say "some birds do, some birds don't" or you could ask "why does the brown-throated thrush preen then, but the spencer's warbler not." And how could you even generate such a question without knowing the names, or something akin to a "name"?

But I use "mantissa" all the time. Wait, that was "abscissa"? isn't that a kind of sore?

1 "I don't like to say bad things about paleontologists, but they are not very good scientists. They're more like stamp collectors." Said in response to criticism of his idea of a meteor-caused extinction event. (http://ncse.com/cej/8/3/obituary-luis-alvarez)

Ken G
2010-Aug-26, 06:39 PM
Learning is illusory :)Or worse-- let me put it this way, the only thing you can really learn is how much you don't know. But that's not as bad as it sounds-- consider the oft-quoted words of Newton:
"I do not know what I may appear to the world, but to myself I seem to have been only like a boy playing on the sea-shore, and diverting myself in now and then finding a smoother pebble or a prettier shell than ordinary, whilst the great ocean of truth lay all undiscovered before me."
I'll take Newton at his word, but most of us would be pleased with those shells all the same.


Of course, such classification effort is necessary to the subsequent analysis: if you see a brown-throated thrush preening itself after eating but don't see a spencer's warbler, you could say "some birds do, some birds don't" or you could ask "why does the brown-throated thrush preen then, but the spencer's warbler not." And how could you even generate such a question without knowing the names, or something akin to a "name"?Right, I certainly agree it is necessary-- one name is necessary. Two is culture, not mathematics.

grapes
2010-Aug-26, 07:25 PM
Right, I certainly agree it is necessary-- one name is necessary. Two is culture, not mathematics.Is that "x axis/y axis" instead of "abscissa/ordinate"? There's a push for "independent variable/dependent variable" in some quarters, not necessarily mathematical.

But even two names can be mathematics--that's the whole idea behind duality, or it could be. :)

HenrikOlsen
2010-Aug-26, 07:43 PM
That story is from The Making of a Scientist, the first chapter of the book "What Do You Care What Other People Think?" Feynman says his dad would tell him the names of the bird in English, Italian, Portuguese, Chinese, and Japanese--but it was different from the name that the other kid knew. Feynman says, about his dad, "I knew he didn't know the real name."
I was reminded of that story as well, but got it from The pleasure of finding things out on Horizon. Here (http://www.youtube.com/watch?v=0XgmrMZ0h54) or, higher bandwidth, here (http://www.youtube.com/watch?v=AAmH3nkBtgQ).
The bit from about 6:00.

In that version what his father said was "Do you know what that bird is? It's a [likely invented names in lots of languages]. Now then you know, in all the languages you wanna know, what that bird is, and when you're finished with all that," he says, "you'll know absolutely nothing whatever about the bird. You only know about humans and different places and what they call the bird."

Hearing the context makes it clear that the point was that he considered labels to be practical but not as meaning anything in themselves.

He also tells the story in Take the world from another point of view (YouTubed here (http://www.youtube.com/watch?v=PsgBtOVzHKI&feature=related) starting around 3:50), with the laughing addition that he later realized that names are nice to know when you want to talk to other people about things.

Ken G
2010-Aug-26, 08:56 PM
Is that "x axis/y axis" instead of "abscissa/ordinate"? Yes, if they are going to label the axes x,y, then they should call them that too. Saying "we find the abscissa on the x-axis and the ordinate on the y-axis" is like saying "my name is Ken but when I refer to my clothes I'll call them Bob's clothes."

There's a push for "independent variable/dependent variable" in some quarters, not necessarily mathematical.
That at least has some meaning, it's more than just a label. But it's only true in applications where you really do have a dependent variable.

But even two names can be mathematics--that's the whole idea behind duality, or it could be. Two names is the opposite of duality. Two names is taking what is clearly the same thing and treating it like it is two things. Duality is taking two seemingly different things and noticing that in some sense they are the same.

grapes
2010-Aug-26, 10:10 PM
Yes, if they are going to label the axes x,y, then they should call them that too. Saying "we find the abscissa on the x-axis and the ordinate on the y-axis" is like saying "my name is Ken but when I refer to my clothes I'll call them Bob's clothes."But why is that different than "We're going to plot GNP on the y-axis, and Febrile Tendency on the x-axis." Shouldn't the terms "x-axis" and "y-axis" really be treated the same as "abscissa" and "ordinant"? Both would be improved by "vertical" and "horizontal" no?

That at least has some meaning, it's more than just a label. But it's only true in applications where you really do have a dependent variable.Weird, I was going to mention that. I must've lost it. That's something that trips up students: x=y, which one is which, and why? :)
Two names is the opposite of duality. Two names is taking what is clearly the same thing and treating it like it is two things. Duality is taking two seemingly different things and noticing that in some sense they are the same.A point and a line? No, under duality they are always two different things, but it doesn't matter whether you call them points and lines, or lines and points.

caveman1917
2010-Aug-26, 11:21 PM
How about just not giving it any a priori name?
Just saying "this thing is an axis".
And when you're plotting y to x, it's the y-axis and x-axis.
When you're plotting GNP and FT(Febrile Tendency), it's the GNP-axis and FT-axis.

The only thing that can be said in general about it is that it's an axis.
Any other name-giving is application specific.

grapes
2010-Aug-27, 02:03 AM
How about just not giving it any a priori name?
Just saying "this thing is an axis".
And when you're plotting y to x, it's the y-axis and x-axis.
When you're plotting GNP and FT(Febrile Tendency), it's the GNP-axis and FT-axis.

The only thing that can be said in general about it is that it's an axis.
Any other name-giving is application specific.I already mentioned "vertical" and "horizontal"--don't you need at least something? Otherwise, how do you answer the question "which axis shall I graph FT on?" without, you know, touching it?

Ken G
2010-Aug-27, 04:27 AM
But why is that different than "We're going to plot GNP on the y-axis, and Febrile Tendency on the x-axis." Shouldn't the terms "x-axis" and "y-axis" really be treated the same as "abscissa" and "ordinant"? I'm just saying we should pick one-- and since everyone always uses x and y, there's no need for abscissa and ordinate. More, calling them x and y makes it perfectly clear they are arbitrary labels-- calling them abscissa and ordinate creates the illusion that there is "something more there to understand." This is one reason why many people have a hard time with elementary math-- they are given the impression there is something terribly difficult to understand there, when in fact there's nothing to understand at all in the labels of an axis. It's kind of the way lawyers use language-- to insure that you have to hire one of them to understand what the others are talking about (partially kidding, we all use jargon).


That's something that trips up students: x=y, which one is which, and why?Right, it's a classic case of thinking there is more to understand than there is. I remember asking my Dad what f(x) = x2 meant-- I told him I knew what x2 means, but what does f(x) mean? He said it means you can plug in an x and get out a f(x). I said isn't that what x2 does? What do you need f(x) for? He said I'd understand eventually why that question is not something to get tripped up over. It took me a while to get that pure labels aren't supposed to mean anything. Later my grandmother told me she didn't get algebra because people kept telling her x was a number when in fact it is a letter. She was asking the same question about numbers that I was asking about functions.

A point and a line? No, under duality they are always two different things, but it doesn't matter whether you call them points and lines, or lines and points.
I don't see the relevance-- if they are not the same thing, then those are not two different labels for the same thing, they are two labels for two different things, and we can then look for some dualities that connect them. Nothing like that holds for x and abscissa.

caveman1917
2010-Aug-28, 12:17 AM
I already mentioned "vertical" and "horizontal"--don't you need at least something? Otherwise, how do you answer the question "which axis shall I graph FT on?" without, you know, touching it?

The way i see it the question would be more like "where will i put the FT-axis?", and then one could for example say "let's put the FT-axis horizontal, and the GNP-axis vertical".
Although nobody would, you could just as well say "let's put the FT-axis diagonal and the GNP-axis at a 12 angle to that". It seems to me that an axis is just an abstract visualisation tool used in many contexts, there is no a priori difference between a horizontal and vertical (or x and y) axis except for their labelling. So why not just keep the labelling to the application?

caveman1917
2010-Aug-28, 12:24 AM
I'm just saying we should pick one-- and since everyone always uses x and y, there's no need for abscissa and ordinate.

What reason is there for the need to pick one at all?
I think it also has many uses where it is not used for x and y, but for some economic or biological, or anything really, parameters.
One might say 'x' and 'y' are just placeholders for any values so basically saying "not labelled yet", but why would anything need to be labelled with "not labelled yet"?

kleindoofy
2010-Aug-28, 12:28 AM
Funny. The words abscissa and ordinate seem to be problems, but the word axis obviously doesn't.

Why not go the whole way and say x-line and y-line?

Disinfo Agent
2010-Sep-02, 04:00 PM
I'm just saying we should pick one-- and since everyone always uses x and y, there's no need for abscissa and ordinate.Sometimes we use other letters. Occasionally it's useful to plot x versus y instead of y versus x. "Abscissa" and "ordinate" is just another way to say "horizontal co-ordinate" and "vertical co-ordinate" without assuming any letters for the variables. They're not much more abstruse terms than "longitude and latitude" or "elevation and azimuth", IMO.


I remember asking my Dad what f(x) = x2 meant-- I told him I knew what x2 means, but what does f(x) mean? He said it means you can plug in an x and get out a f(x). I said isn't that what x2 does? What do you need f(x) for?A simple answer is that it's a shorthand for the same thing. When we write f(x) = x2 it means we're making the convention of meaning the latter by the former.

A deeper answer is that x2 could be just the square of an unspecified number (a constant, or an unknown), while the notation f(x) = x2 implies that we're talking about a function, a more abstract notion. Even in mathematics, language doesn't just carry meaning, but sometimes also implies a context.

Ken G
2010-Sep-02, 04:53 PM
Why not go the whole way and say x-line and y-line?Because an axis is something different from just a line, it is a line equipped with a demarcation of lengths, i.e., a line with distance labels that we are going to use to place things. Note I am not advocating stripping language down such that all connotations are lost, that could be a tradeoff, I'm simply advocating not have two words that are intended to mean exactly the same thing, especially when one sounds like a simple label and the other sounds like a jargony reference to a history that is not being invoked-- there's no tradeoff there.

Ken G
2010-Sep-02, 05:03 PM
Sometimes we use other letters. Occasionally it's useful to plot x versus y instead of y versus x. "Abscissa" and "ordinate" is just another way to say "horizontal co-ordinate" and "vertical co-ordinate" without assuming any letters for the variables. Except there's no more truth in saying the abscissa is the horizontal axis than there is in saying the x-axis is the horizontal axis. Either assumes a convention, and if the convention is not being used, there's still no difference between the terms.

A simple answer is that it's a shorthand for the same thing. When we write f(x) = x2 it means we're making the convention of meaning the latter by the former.
Exactly-- f(x) is just a label. That's what was tripping me up-- it looked like it was trying to actually say something. That's also my problem with "abscissa" and "ordinate"-- they look like they have some complicated meaning we are supposed to be getting from them, but they don't-- any such meaning is lost to history, now they're just words that label the axes, typically the independent and dependent variables. That's exactly what x and y are, just much more clear that they are just labels.

A deeper answer is that x2 could be just the square of an unspecified number (a constant, or an unknown), while the notation f(x) = x2 implies that we're talking about a function, a more abstract notion.x2 already says that, that's its meaning, when x is the convention for a variable. It's just a kind of fixation on complete sentences, I can't just say "I", I have to say "I am Ken." As if that said anything about me at all.

Disinfo Agent
2010-Sep-03, 01:31 PM
Except there's no more truth in saying the abscissa is the horizontal axis than there is in saying the x-axis is the horizontal axis. Either assumes a convention, and if the convention is not being used, there's still no difference between the terms.The standard convention is:


abscissa = horizontal, ordinate = vertical

The convention


x = horizontal, y = vertical

while common, is not universal.


Exactly-- f(x) is just a label. That's what was tripping me up-- it looked like it was trying to actually say something. That's also my problem with "abscissa" and "ordinate"-- they look like they have some complicated meaning we are supposed to be getting from them, but they don't-- any such meaning is lost to history, now they're just words that label the axes, typically the independent and dependent variables. That's exactly what x and y are, just much more clear that they are just labels.While the most common by far is for x to denote the abscissa and y the ordinate, occasionally we do the reverse. And frequently we use different letters altogether. The letters are indeed just labels; but the words "abscissa" and "ordinate" have a more restricted meaning.


x2 already says that, that's its meaning, when x is the convention for a variable.That's not correct. When x stands for a variable, 'x2' is ambiguous. Granted that more often than not we're thinking of the general expression of a function, but it can also stand for a purely formal expression (a polynomial). Furthermore, 'x' need not stand for a variable (it's just a label, remember?); there's nothing wrong with denoting a constant by 'x'; indeed, it is quite common to use 'x' for an unknown in an equation or inequation. The very notion of 'variable' is ambivalent: sometimes 'x' is a function of some other 'variable'.

Ken G
2010-Sep-03, 03:38 PM
The standard convention is:


abscissa = horizontal, ordinate = vertical

The convention


x = horizontal, y = vertical

while common, is not universal.We are not talking about how conventions are used in practice, we are asking how they should be used. I'm saying that we should simply make x,y convention replace the abscissa, ordinate convention in every way, expressly because it is not trying to be anything but a labeling convention, is less jargony, and is already in wider usage. Seen from a different perspective, any axes will appear rotated-- including axes called abscissa and ordinate.

The letters are indeed just labels; but the words "abscissa" and "ordinate" have a more restricted meaning.Sometimes we don't use letters, sometimes we use words. So why is OK to replace the words abscissa and ordinate, but for some reason it's not OK to replace the letters x and y? There's just no distinction there-- a label is a label. The convention calls for using x and y like you are advocating using abscissa and ordinate, so the letters x and y should not be used to mean something different, any more that your words abscissa and ordinate should.


That's not correct. When x stands for a variable, 'x2' is ambiguous. Granted that more often than not we're thinking of the general expression of a function, but it can also stand for a purely formal expression (a polynomial).If you look at the Principia Mathematica, for example, the attempt to place objects like polynomials on a firm foundation, you will find they are all considered functions. The formal manipulation of polynomials is the same as the manipulation of functions.


Furthermore, 'x' need not stand for a variable (it's just a label, remember?);It's a label for a variable, so x2 is always a function. Mentioning that it is a function is always redundant, it is just that complete sentence thing ("I am me"). There is never any point to writing f(x) = x2 unless you are going to write f(x) instead of x2 from then on, which is actually not what is done. If the book had said "instead of writing x2, we will write f(x) to mean x2", then I would have understood why they wrote f(x) = x2. But they didn't, so I didn't. Another way it could be useful is in an expression like f(x) = ax2, to make it clear that a is being treated as a constant and x as a variable. Again, that is not how the expression that confused me was used-- instead, it is as though people feel they cannot just talk about the meaning of the expression x2 without first labeling it f(x), and that's what confused me. Later, we fall into the same habit, and forget there was ever the option to require that a label actually have some purpose before we leap to applying it. It's just like Feynman's birds.

The very notion of 'variable' is ambivalent: sometimes 'x' is a function of some other 'variable'.Yes, when it is being used as a coordinate. But even when it is being used as a coordinate, x2 is still a function, without the label of same. Using x to mean a constant is highly nonstandard, and is an ill-advised convention. You may as well use the convention x(f) to mean a function of x, if you are going to fly in the face of fashion.