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Geek Culture / Math Question

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Osiris
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Posted: 17th Oct 2007 20:01
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Well sort of, does anyone know the origin of X and Y in algebra?

Your signature has been erased by a mod because it's larger than 600x120....
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Zombie 20
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Posted: 17th Oct 2007 20:13
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Can't really say that I do, I mean they could have easily made it H and P.

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PowerSoft
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Posted: 17th Oct 2007 20:20
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What do you mean...is that even a question?

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BiggAdd
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Posted: 17th Oct 2007 20:23 Edited at: 17th Oct 2007 20:25
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Yeh its x=0 y=0.

But seriously, I don't know how those letters came about. Just look up Cartesian coordinates. I think thats what they are called.

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Lost in Thought
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Posted: 17th Oct 2007 21:19
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They come fron "x" marks the spot and "y" does x mark the spot.

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Chris K
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Posted: 17th Oct 2007 21:28
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http://en.wikipedia.org/wiki/Algebra

Unknown Quantity is a good book about the history of Algebra.

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mamaji4
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Posted: 19th Oct 2007 13:33
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I think it all started with the X-Files where x was the unknown.
The logical thing then was to make y a function of x and there you have the mystery of the X-files solved
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Ric
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Posted: 19th Oct 2007 14:06 Edited at: 19th Oct 2007 14:07
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One theory is that x could be derived from the Arabic 'shei', meaning 'thing' which, when translated into Greek becomes 'xei', shortened to 'x'. Another theory is that x and y were the easiest letters to write with a feather. Or, it could simply be that a cross is used to mark a point on a graph.

Whatever the origin of 'x', the choices of y and z would naturally follow for a 3d coordinate system.

<beware - completely irrelevant ramble follows>

Next interesting thng that just popped into my empty head: I think the alphabet is missing at least one letter - the letter that should be at the start of the word 'hiccup'. When you hiccup, the first sound is not an 'h', like the noise you make when you breath out through your mouth, it is a different noise made by breathing IN through your mouth. Therefore I think the correct letter should be a backwards h. In fact, I think we could have some other backwards letters - like a backwards 's' for the beginning of the word 'slurp', where the air is also moving in the opposite direction to a normal s.

Any other words which don't have existing letters for them?

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mamaji4
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Posted: 19th Oct 2007 14:44
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You know how people are always going, "explain this to me" and "explain that to me"
If you want something 'explained' you would have to get to the 'ex' first. But nobody wanted two letters for an unexplained literal, so they dropped the 'e' and we are left with the unknown 'x' which has to still be explained. I hope that explains it
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Green Gandalf
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Posted: 19th Oct 2007 15:08
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And why do shaders use xyzw (in that order) as the coordinates of a float4?
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mamaji4
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Posted: 19th Oct 2007 15:17
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Because its a logical grouping of letters. xyz and w
It follows the convention of using m,n,o as a group
u,v,w as a group etc.
It would seem a bit unconventional if you were to use xyza unless it was a word wrap app.
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Chris K
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Posted: 19th Oct 2007 15:48
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Normally it's grouped l,m,n and p,q,r - o looks too much like 0.

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Peter H
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Posted: 19th Oct 2007 16:54
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Quote: "And why do shaders use xyzw (in that order) as the coordinates of a float4?"

because z is the last letter in the alpha bet... and you need a fourth... so you go to the letter before x.

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mamaji4
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Posted: 19th Oct 2007 17:16
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So if you need to use unknowns for n-dimensional spaace
where n -> infinity
what do you do when you run out of variables. That does seem to me to be a very pertinent obstruction to mathematical research in n dimensions.
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demons breath
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Posted: 19th Oct 2007 18:38
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uhhh... pictograms? heiroglyphics?

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Chris K
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Posted: 19th Oct 2007 19:49
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Quote: "So if you need to use unknowns for n-dimensional spaace
where n -> infinity
what do you do when you run out of variables. That does seem to me to be a very pertinent obstruction to mathematical research in n dimensions."


Look up Suffix Notation and the Summation Convention.

Essentially you would use x1, x2, x3 etc. (where the number is subscript) but you would just write xi, the "for i = 1, 2, 3" is assumed.

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Libervurto
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Posted: 19th Oct 2007 20:00
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XYZ are nowhere near each other in the Greek Alphabet.


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Suicidal Sledder
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Posted: 19th Oct 2007 22:26
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Probably since X has always been the letter used least in the engish language, therefore it represents much more of the unknown. A bit like mamaji said we have xfiles, project x planet x(the original title of pluto), mr x. etc... X is a very rarely used letter so I think its psycologicaly closer to being a mathmatical unkown.

Then when they needed a second letter they just jumped up to Y sinec it was handy and x and y sound nice together. Imagine something stupid like L and F? lol

Thats my thoughts.

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Insert Name Here
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Posted: 19th Oct 2007 23:35
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Now, a random rant about that grrek alphabet up there.
Interesting that Y and E are so simmilarly pronounced, and both are like the greman 'oopsilon' for Y.
Also interesting is the way that n=pi. How very apt.
I=iota, a very small amount.
That e-type one is 'sigma'. Sigma was the name of the technology in impossible creatures.
The r looking one is 'gamma', also interesting.
X is 'Chi', the strange power we apparently all have inside us. (Apart from Seppuku Arts)
Psi is 'sigh'. How fun. I wonder how then inflectuate when they say that.
And finnaly Omega is pronounced similarly to Oh my God.

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Suicidal Sledder
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Posted: 20th Oct 2007 01:49
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I dont get the point of your last post....

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LD52
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Posted: 20th Oct 2007 01:56
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Quote: "Also interesting is the way that n=pi. How very apt."


The way i look at it is that symbol that looks like a "n" looks more like the symbol for pie in math and its pronounced pi ? weird.
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Suicidal Sledder
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Posted: 20th Oct 2007 01:58
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Ummmmm.... its because the mathmatical symbol for Pi is the greek letter Pi........

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LD52
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Posted: 20th Oct 2007 02:10
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Lol yup
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Jess T
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Posted: 20th Oct 2007 03:50
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Quote: "XYZ are nowhere near each other in the Greek Alphabet."


XYZ in English has nothing to do with the 'almost-the-same-looking' letters in Greek.

It's like saying that A is the same as the hyroghlyph for a pyramid just because they have the same general shape!

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mamaji4
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Posted: 20th Oct 2007 20:59 Edited at: 20th Oct 2007 21:12
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Quote: "Essentially you would use x1, x2, x3 etc. (where the number is subscript) but you would just write xi, the "for i = 1, 2, 3" is assumed.
"


xi for i = 1,2,3...
If I want to solved an equation of the millionth degree in x how long would it take me to write the equation? Would I finish it during my lifetime? Can I write x with a subscript of 1 million and get away with it on a single piece of A4 paper. I hope you comprehend now what I mean by "pertinent obstruction to math research"
We are talking pragmatics here. Not theoretics.
Assuming I solve the equation, how do you propose I write out 1 million roots of the equation
x1,x2,x3...
And if i -> infinity what should I do?

Quote: "Normally it's grouped l,m,n and p,q,r - o looks too much like 0."

Algebraic variables would take values l,m,n conventionally
Analytical Geometry generally uses O as the vertex or any important primary co-ordinate with the arms of the angle extending from O generally being M,N, as in, one arm of the angle MON is OM and the other arm is ON
So depending on which field of math you are working on at present would dictate the naming convention you use.
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Chris K
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Posted: 21st Oct 2007 01:34
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You = pseudomathematician.

Go and look up the Summation Convention and Suffix Notation.

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mamaji4
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Posted: 21st Oct 2007 22:34 Edited at: 21st Oct 2007 23:28
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Yeah. I'm the pseudomathematician
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Insert Name Here
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Posted: 21st Oct 2007 22:56
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0/0= 8 on it's side.
Sin, Cos and Tan are calculated by calculations.
And the nine thing is because so is life.

the rabi, Nancy DrewG and Sudoku Arts.

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mamaji4
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Posted: 21st Oct 2007 23:12 Edited at: 21st Oct 2007 23:26
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Yeah.


INH
Geeze, I nearly ruined my TFT monitor when I swatted the bug. Can I borrow your gif.
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Insert Name Here
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Posted: 21st Oct 2007 23:45
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T'ain't mine, but sure.
And yeah, your about the seventh who though it was real.

the rabi, Nancy DrewG and Sudoku Arts.

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mamaji4
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Posted: 21st Oct 2007 23:55
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Every time you post another bug appears on my screen.
How do you debug a screen bug.
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Insert Name Here
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Posted: 22nd Oct 2007 12:45
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Block all images from the net, but then you get weird boxy x things.

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mamaji4
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Posted: 23rd Oct 2007 20:22
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I don't like wierd boxy x things. I'll stick with the bugs.
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Peter H
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Posted: 23rd Oct 2007 20:49
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Quote: "xi for i = 1,2,3...
If I want to solved an equation of the millionth degree in x how long would it take me to write the equation? Would I finish it during my lifetime? Can I write x with a subscript of 1 million and get away with it on a single piece of A4 paper. I hope you comprehend now what I mean by "pertinent obstruction to math research"
We are talking pragmatics here. Not theoretics.
Assuming I solve the equation, how do you propose I write out 1 million roots of the equation
x1,x2,x3...
And if i -> infinity what should I do?
"

dude... no offense but you obviously haven't taken much math.

mathematicians aren't going to write out x 1 million times... they have summations for that.

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PowerSoft
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Posted: 23rd Oct 2007 21:19
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Writing 'xi' would/could be plain confusing..... sqrt(-1) lots of x....nah


Insert Name Here,

0/0 != Infinity,

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Insert Name Here
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Posted: 23rd Oct 2007 21:31
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... yes it does.

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mamaji4
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Posted: 23rd Oct 2007 23:01 Edited at: 23rd Oct 2007 23:11
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x/0 -> infinity for x > 0, x belonging to the set of positive Complex numbers.

My take on 0/0

Let 0/0 = x
Therefore, 0 = x*0 - equn.(1)
equn. (1) holds true for any value of x in the Complex plane
i.e. 0/0 has an infinite number of solutions.
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mamaji4
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Posted: 23rd Oct 2007 23:05
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Quote: "dude... no offense but you obviously haven't taken much math"


@Peter H
Yup. I'm the pseudomathematician as Chris rightfully named me
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Chris K
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Posted: 24th Oct 2007 04:11
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Quote: "Writing 'xi' would/could be plain confusing..... sqrt(-1) lots of x....nah"


The i is subscript, but also, if it ever did get confusing you would just change the subscript to m or whatever.

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Peter H
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Posted: 24th Oct 2007 04:35
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Quote: "x/0"

undefined.

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mamaji4
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Posted: 24th Oct 2007 12:36 Edited at: 24th Oct 2007 15:40
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I hereby propose a new mathematical naming convention using the ASCII character set:

All subscripts to be contained in curly brackets with no space between the variable and its associated subscript
e.g. x{i} would denote the variable x with subscript i

Since the exponent noatation is already represented by the ASCII set, it shall continue to remain as is
e.g. x^n would denote the variable x raised to the power n

The summation symbol sigma to be represented by the uppercase letter E as it has the closest resemblance to the summation symbol sigma.

"0/0" to denote the symbol for infinity as it does resemble it a lot.

I think that should take care of the Summation Convention and the Suffix notation, unless there is something I left out, in which case please feel free to add to the list above.

Note: We still have the square brackets available for use, probably in the superscript notation if anyone can suggest how.

At the end of the post we shall have a meeting of the Apollo Math Community, comprising of the best mathematical minds in the world, to create a draft of the final notation as an Apollo Math Standard, to avoid any future confusion when trying to discuss posts of a mathematical nature, where the use of symbols becomes imperative to get the meaning across.
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demons breath
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Posted: 24th Oct 2007 13:55
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what do you use superscript for apart from indicies though? and you already included exponent notation

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mamaji4
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Posted: 24th Oct 2007 14:01 Edited at: 24th Oct 2007 14:03
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@DB
I stand corrected. Thanks for pointing it out. The use for superscript would be in Chemistry, etc. So that leaves us with a couple of square brackets for which we have to figure out some use.
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PowerSoft
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Posted: 24th Oct 2007 14:02
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Exactly PeterH. As you can't divide by 0 you cannot achieve a value for the calculation. If something is undefined then it doesn't necessarily mean it's infinite.

Chris, I know its subscript but I wouldn't personally use i at all, I mean we have r (yet that could get mixed up with product moment and spearmans) and 22 other letters we could possibly use whats the point of using i? (That said if we wrote it by hand it would appear smaller and sub-scripted anyway so no real worry...

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Peter H
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Posted: 24th Oct 2007 14:41
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Quote: "All subscripts to be contained in curly brackets with no space between the variable and its associated subscript
e.g. x{i} would denote the variable x with subscript i"

there is no need for this and any mathematician would shoot you for suggesting it...

there doesn't need to be a space in-between x and i because it is a subscript

http://en.wikipedia.org/wiki/Subscript

i am not going to bother with the rest of your suggestions

Quote: "(That said if we wrote it by hand it would appear smaller and sub-scripted anyway so no real worry..."

^indeed^

Quote: "whats the point of using i?"

I don't know but my best guess is that the word index starts with i.

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mamaji4
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Posted: 24th Oct 2007 15:21 Edited at: 24th Oct 2007 15:29
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Quote: "Abstract algebra
Any number system which forms a commutative ring, as do the integers, the real numbers, and the complex numbers, for instance, can be extended to a wheel in which division by zero is always possible, but division has then a slightly different meaning.
"


From the link
http://en.wikipedia.org/wiki/Division_by_zero#_note-0

Although division by zero is taken to mean different things in different contexts, it can be evaluated under certain contexts and cannot be said to be "undefined" for all contexts.
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Peter H
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Posted: 24th Oct 2007 15:31
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well sure, but you can make anything equal anything else if you set up your number system the way you want it... (think discrete mathematics *shudder*)

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Insert Name Here
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Posted: 24th Oct 2007 15:33
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x-1/100<x/((x/x)*100)

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mamaji4
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Posted: 24th Oct 2007 15:38
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Quote: "there is no need for this and any mathematician would shoot you for suggesting it...
there doesn't need to be a space in-between x and i because it is a subscript"


Boy, I'd hate to be at the wrong end of a mathematician's gun
If there is no space between x and i , you would have to specify that
a)It is not an implicit multiplication of two variables x and i
b)When using the {} notation it is necessary to specify the exact spacing because it would be assumed that a variable x without an immediately following brace is not a subscripted variable. And no other meaning has been assigned to standalone curly braces other than their use as holders of subscripted variables.
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mamaji4
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Posted: 24th Oct 2007 15:49 Edited at: 24th Oct 2007 15:51
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Quote: "British computer scientist's new "nullity" idea provokes reaction from mathematicians"


From link
http://en.wikinews.org/wiki/British_computer_scientist%27s_new_%22nullity%22_idea_provokes_reaction_from_mathematicians

I had no idea I was trying to solve an age old non-problem.
I deserve to be lambasted by one and all for my ridiculous solution to the 0/0 problem. I rest my case.
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