Up with "UP"...Another reason why English is baffling 5

[CajunCenturion]

==>but found such repeated fractions and irrational numbers obscene.
It is a repeating decimal, not a repeating fraction. By definition, irrational numbers are both non-repeating and non-terminating. Since 0.333... is non-terminating, but repeating, and can be represented by a fraction, it is a rational number. Numbers such as SQRT(2) and PI which are both non-repeating and non-termination are irrational.

==> Think of it this way, the reason such repeated series even exist is because they DON'T reach the fraction.
On the contrary, they do reach the fraction. What cannot be expressed exactly is the decimal equivalent. The limitation is not in the fraction, nor in the value, but in the decimal means of representation.

We could get into what it actually is -- a convergent infinite series with a finite sum -- but that would straying too far off-topic for this thread and forum.

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[CajunCenturion]

==> I was using the finite series to show the fallacy
0.99999... is not a finite series, it is an infinite series.

==> Multiplying .9999[infinite series] by 10 doesn't create 9.999[infinite series]
I disagree. The nines are non-terminating before the multiplication and are just as non-terminating after the multiplication. The act of multiplying by 10 will increase the value my one order of magnitude, but it will not cause a non-terminating number to terminate.

==> It creates 9.9999[infinite series]0.
How can you have a 0 after an infinite series? If the series is infinite, then you never have a place for the 0.

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[ESquared]

In each case, there is a geographic or cultural difference

I agree there is a geographic and cultural difference between the words color and colour. Mind you that these are in fact different words.

But every word has different shades of meaning depending on the geography or the culture where it is found. I rather think that from your perspective, you should argue that not only cannot two words mean exactly the same thing, but the same word cannot mean exactly the same thing! And there goes your objection to Humpty Dumpty's take on the subject. We all have different perspectives, one per customer (or more, I suppose, if one has multiple personality disorder).

Words function because of consensus, because of agreement of intended meaning. If two people agree that two different words or phrases mean exactly the same thing, then, to them, they do! All that is left is to discover the scope to which the agreement belongs: two people, a room, a house, a suburb, a state, a province, a country, a world; English, Swahili, Tagalog; one online forum, 287 online forums.

Maybe it would be fruitful to define word. It is a single spelling? Is it a pronunciation? Is it a dictionary entry? Let's nail it down.

Erik

P.S. I am enjoying the numbers conversation.

 

[tgreer]

You can have infinites within infinities. You an infinty +1, etc. You can have infinity x 2, which is an infinite series followed by another infinite series.

Multiplying by 10 increases by 1 order of magnitude, not 1 order of magnitude plus .000...1.

Can you point me to other links on the subject? I'd like to read up on it. I'm speaking only from my own understanding; I'm certainly not a mathematics authority.

Do mathematicians understand .99999.. to be exactly equal to 10? I'm not convinced. In fact it has a horrifying Orwellian feel to it. The two examples you've given don't "work" as proof for me.



Thomas D. Greer

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[tgreer]

Ok, I found this link:

http://aah.ryan-usa.com/node30.html

Which backs up what CajunCenturion has been trying to teach me.

However! This only shows that .9999... is another notation for "1", just as 5/5 or any other mathematical equation or symbol can be "1". They aren't separate numbers.

Thus I stand by my analogy, that just as no two numbers can be equal, no two words can be equal either. And words are particular more fluid than numbers.

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[SantaMufasa]

...no two numbers can be equal...

By definition, if you have two different numbers, they cannot be equal. But there are infinite expressions which evaluate absolutely equally. Therefore, you can represent one value by an infinite number of expressions.

So, if you accept an algebraic/literary analogy, it does not work in your favour.

Mufasa
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[PaulTEG]

eg. color = colour ;-)
--Paul

cigless ...

 

[BobRodes]

To paraphrase Lao Tzu:

Infinity contains all that is.
Infinity is contained by all that is.
Infinity can be expressed in infinite ways.
All expressions of infinity fall infinitely short of expressing what it is.
All of the logic here, therefore, defines infinity equally well, in that it defines it perfectly (all expressions of infinity express infinity) and just as much does not define it at all. For, the infinity that can be defined is not infinity.

 

[tgreer]

But numbers are not words. Forget the analogy. While it's possible for multiple numeric expressions to represent the same value, it isn't true of words. While I'm not a mathematician and so should never have asserted myself in that exchange with our Cajun friend, I do have a bit of experience with the English language.

color != colour

I could claim that these are alternate spellings of the same word, and give myself an easy out, but I won't even budge that far. When I see words with their "British" spellings, I associate them either with Kipling's pounding, driving Empire poetry, or with British translations of certain French poets. The word "colour" then, has accrued various connotations through usage. It has, to risk another analogy, been to exotic places "color" hasn't, and as a result, to most Americans, "colour" is just a bit more, well, colorful.

Consider advertising slogans or company names that intentially use alternate spellings, and ask yourself why, if they MEANT the same.

"lite" vs. "light" - "lite" looks and feels "lighter". It doesn't have that fat little "g" weighing down the middle.

"Cigar Shoppe" vs. "Cigar Shop" - which spelling conveys the proper mood? What comes to mind with "Shoppe"? Why doesn't it come to mind with "Shop"?

A shopping mall near my home: "Towne East Square".

What are they implying with that extra "e" on "towne"? A bit of elegance, perhaps?



(I still find the fact that .9999infinity equals 1 to be abhorrent. It might just give me nightmares. I could follow most of the mathematical proofs on the link given, and some of them seem tautological, and to my mind seem more like proof that our numbering system is "broken" than anything else. Orwellian, indeed!)


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[PaulTEG]

In the absence of evidence, visa vi a passport for the word colour, I'm going to stick with color === colour, meaning the same thing, unless perhaps there are some shades that are registered over there, to which we on the other side of the pond are being denied access;-)

This is just my opinion on the matter
--Paul

cigless ...

 

[tgreer]

But there isn't an absence of evidence. Every instance where "colour" was used INSTEAD OF "color" is evidence. Each and every instance provides a UNIQUE context which serves to separate the two words.

The "American Heritage Dictionary" (note the "American") doesn't even define "colour", or provide it as an alternate spelling. "Colour" is given in the etymology as ME, or "Middle English".

So, "color" is derived from "colour". Thus they are not equal. "Colour" has an "Englishness" to it that has been subtracted from "color".

Further, each term has unique usages:

"A colour is a name for certain kinds of flags. It usually refers to regimental flags, but the term is used outside military situations - for example, Scout and Girl Guide flags are known as colours. In the British Army, the colours were typically carried by a Colour Sergeant."

And "color" is used to describe the basic characteristic that differentiates the six varieties of quark, in physics.



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[PaulTEG]

When used to describe the visible spectrum as reflected off objects, I propose that color and colour are synonymous, nay identical, in that respect.

Given, other definitions do exist, but in this particluar context, for me at least, they are one and the same.

It's a lot like 0.9999... and 1, being one and the same, as it were ;-)

--Paul

cigless ...

 

[SilentAiche]

The word "colour" then, has accrued various connotations through usage. It has, to risk another analogy, been to exotic places "color" hasn't, and as a result, to most Americans, "colour" is just a bit more, well, colorful.

Outstanding. I genuinely wish I'd written that. Thank you.

Tim, [gray]the lesser poet whenever two of them gather...[/gray]


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[tgreer]

When used to describe the visible spectrum as reflected off objects, I propose that color and colour are synonymous, nay identical, in that respect.

I suppose that's the central disagreement. You think that it's possible to strictly limit the meanings of words to a single context. I submit that that's impossible (except in certain artificial situations) and that I have the entire history of language on my side of the argument.

Now, here's an example where I'd agree with you: programming languages. A programming language strictly and narrowly defines the exact meaning of a word or statement as understood by an interpreter, and in fact, two statements can compile to exactly the same machine instruction.

But please note that in order for this to be true, it was necessary to remove the human observer. Two people could read the exact same source code from the same screen, simultaneously, and one could understand it and the other find it perfectly meaningless. It is only limited to an exact, unchanging meaning by the interpreter.

And even programming languages change, over time. When humans converse, they can never eliminate the alternate meanings, nuances, connotations, and associations of the words they use.







Thomas D. Greer

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[SilentAiche]

-- but that would (be) straying too far off-topic for this thread and forum

ROFLMAO!!! Does this mean I'm not the hijack king anymore? Not that you are - EE started it, after all (see July 8).

Seriously, are we through discussing [blue]UP[/blue]? Anyone even recall the OP about UP? I know, I contributed to the thread's delinquency.

A final thought, from Led Zeppelin (from Stairway to Heaven) listened to this night from a cassette I recorded [red]July 29, 1986[/red] (yeah, the tape really is nearly 20 years old):

"Because, you know, sometimes words have two meanings."

Tim



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[ESquared]

I did not start it! tgreer brought up mathematics as support for his position. I simply responded.

This is really an interesting discussion. tgreer, you're talking as if words have some certain identity, some rich personality which makes them so unique that they cannot function in place of each other.

I'm sure most people have heard someone say something like, "hey, you're wearing the same shirt as I am!" and the person being addressed responds, "I should hope not, I don't think we'd both fit!" It's an amusing joke and I've done it myself, but to give the innocent commenter credit, everyone present knew what was really meant: the two separate shirts, actually completely and absolutely different (when considered at, say, a molecular level) have the same pattern, the same design, the same color and so on, and for all practical purposes, are the same. The shirts might even be two different sizes, but are the same nonetheless.

He was no fool who was actually confused about who was wearing what shirt, nor did he believe that two separate objects could ever be absolutely, perfectly identical.

I picked up a pail and filled it with water.
I picked up a bucket and filled it with water.

Frank: Hey! Those two words mean the same thing.
Bob: Nuh huh-uh! You can kick the bucket but you can't kick the pail. It's obvious they don't mean the same thing.
Frank: I see.

A word is useless and meaningless until instantiated. And, an instantiated word, as distinct from an uninstantiated one rife with all its potential meanings and living only in our heads, may be said to have the same meaning as another instantiated word.

To not allow this is to reject substantial similarity of any kind:

Bob: You're wearing the same shirt as yesterday.
Frank: Ha! I got you! It's not the same shirt. I washed it last night and some of the molecules were removed. This is no longer the same shirt.

If differently-spelled words can't mean the same thing, then neither can samely-spelled words, either.

 

[craigsboyd]

the two separate shirts, actually completely and absolutely different (when considered at, say, a molecular level)...

LMAO! Have a star ESquared for making my night!

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[tsdragon]

The word "colour" then, has accrued various connotations through usage. It has, to risk another analogy, been to exotic places "color" hasn't, and as a result, to most Americans, "colour" is just a bit more, well, colorful.

I agree with Tim. That's wonderful!

A word is useless and meaningless until instantiated. And, an instantiated word, as distinct from an uninstantiated one rife with all its potential meanings and living only in our heads, may be said to have the same meaning as another instantiated word.

Nicely written. The "object-oriented" theory of language.

Tracy Dryden

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[BobRodes]

What are they implying with that extra "e" on "towne"? A bit of elegance, perhaps?

Perhaps, but also more than a bit of pretentiousness.

 

[xlbo]

an extra "e" implies nothing whatsoever - a towne is still a town, it is just that the spelling with the extra e is not used any more as the extra "e" was redundant - kinda proves the point that town and towne do in fact mean exactly the same thing !!

Rgds, Geoff

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