Line is a Circle

jd · 29-04-2003 12:33am

Originally posted by SOL
My point is not actually any of the above, really I was just waffelling but also that maths is only as accurate as you are

Waffling after how many pints? Mathematical logic and systems as they are abstract (though can be representational of the real world) are independent of the theorist or the observer(for want of a better word.)

jd · 29-04-2003 12:55am

Originally posted by Sev
I hope you get lambasted by stiff arses with no concept of intuitive mathematics but with an obsessive and needless necessity for "rigorous" mathematical convention.

Just being bitter at this hour of the morning. Oh and the "QED" in your signature isn't very appropriate.

Good book I read about an Indian guy called Ramanujan wich is somewhat pertinent

http://www.amazon.com/exec/obidos/tg/detail/-/0671750615/102-6904817-8525749?vi=glance

Talliesin · 29-04-2003 6:07pm

Originally posted by SOL
Okay a [straight] line is a circle of infinite diameter

Okay let's just say that it is. My disproof of SOL works whether it is or isn't.

So it follows that the [straight] line between two points is actually and arc…

Yes, that would follow.

…not a [straight] line

No. You've just said that a straight line is an arc.
If this is so there exists a subset of arcs which are straight lines.
If that is so then being an arc does not preclude being a straight line.
Hence a straight line is a straight line whether it is an arc or not.

Eh?

You're stupid.

SOL · 29-04-2003 9:39pm

Originally posted by bonkey
Alternately, you could just easily prove that two circles of equal radius, where their centres are less than 1 diameter length apart, must intersect.

Yes.. you could quite easily prove such a statement for circle diameters of all values... except infinity.

You are now attempting to use such an incomplete assessment to disprove my supposition which very much involves infinity.

Can you see the flaw in that logic?

Originally posted by bonkey
Now, for a line, the clear and obvious "equivalent" circle would be a parallell line.

Another assumption for which you provide no grounds.

Not a very solid argument you have put forward.

Originally posted by Talliesin
No. You've just said that a straight line is an arc.
If this is so there exists a subset of arcs which are straight lines.
If that is so then being an arc does not preclude being a straight line.
Hence a straight line is a straight line whether it is an arc or not.

I know you think you're right, but let me create an analogy of your argument so that you can now understand what you just said a little easier.

An apple is a fruit.
Therefore there exists a subset of fruit that are apples.
If that is so then being a fruit does not preclude being an apple
Hence an apple is an apple whether it is a fruit or not.

Yes, but an apple is still a fruit. You were supposed to disprove that, not give me an unrelated excercise in self-evident logic.

Think over what you just said.

Horsefumbler · 29-04-2003 9:57pm

A line is a circle? Yeah whatever...

Talliesin · 30-04-2003 11:54am

Originally posted by SOL
I know you think you're right, but let me create an analogy of your argument so that you can now understand what you just said a little easier.

An apple is a fruit.
Therefore there exists a subset of fruit that are apples.
If that is so then being a fruit does not preclude being an apple
Hence an apple is an apple whether it is a fruit or not.

Yes that is completely analogous to what I said, and completely correct.

Yes, but an apple is still a fruit. You were supposed to disprove that,

No, you were supposed to disprove that. Your statement "the line between two points is actually and arc not a line" is analogous to your saying "an apple is actually a fruit and not an apple".

not give me an unrelated excercise in self-evident logic.

I think you should work on exercises in self-evident logic. My point is that the lack of self-evidence in your logic isn't the result of either a blinding flash of genius, nor any sort of paradox, but rather the result of your not being very good at logic.

Think over what you just said.

Yes I did say something incorrect. It is quite likely that you're just a troll and realise your talking bollocks and therefore aren't necessarily stupid. Hence there is a possibility besides your being stupid that I should have included in my original post.

Sev · 30-04-2003 2:45pm

Originally posted by SOL
So it follows that the line between two points is ... not a line

Alarm bells might ring in one's head when one reads such a sentence that clearly defies logic. If they do, then you are clearly reading into his mere supposition far too literally.

Regardless of the fact that he may have accidentally and unconsciously stated illogically that a line is not a line for the sheer effect of emphasising the main concept of such an elementary thought experiment, he has still provided the context and framework for you to construct such an idea, (that as the subject of the thread clearly states) that a line is a circle.

Yes you might have proven that a line is indeed a line, and that it can never not be a line, and it was clearly wrong of him to say then that his argument had made a line no longer a line... but you have not disproven that although a line may be a line, it could also be a circle, an assumption that he has made, founded upon the statement (that you have accepted for the purpose of your rejection), that a circle of infintite radius is a line, regardless of said error. An assumption that you have not yet disproven, as you claim to have.

If anything you have simply corrected a minor technicality in the wording of his origional supposition. I hope you never took what he had said to literally as a formal proof, he's clearly just toying about with an abstract idea. I just cant see why you would want to even bother yourself to try to disprove it. But calling him an idiot? That's hardly called for. Either you have missed the humour in his initial post, or I have missed the humour in your reply.

It would seem, despite the irony of this final comment, that...
Humour Ï Maths.

bonkey · 30-04-2003 7:16pm

Originally posted by SOL
Yes.. you could quite easily prove such a statement for circle diameters of all values... except infinity.

Actually, the proof I'd offer for that will hold regardless of the radius fo the circle. You would need to show why a circle of infinite radius behaves differently to all other circles to invalidate the proof.....which would involve proving that a circle with infinite radius isnt a circle....which would kinda ruin your original argument in the first place because you're arguing that a line isnt a line because its a circle....and would have to qualify that by saying "but the circle it is isnt actually a circle either".

So, you're now saying that a line isnt a circle????

You are now attempting to use such an incomplete assessment to disprove my supposition which very much involves infinity.

Can you see the flaw in that logic?

I can see the flaw you assert exists, but you havent offered a single reason why a circle with radius infinity has properties which differ from all other circles, and why it is still a circle despite all of this.

Another assumption for which you provide no grounds.

I'll quite happily allow you to change that to "non-parallell line" if it makes you feel any better?

It makes no odds to my base argument, which is that intersecting circles must intersect twice.

For your argument to hold, you will still have to prove that two lines (or circles) cross each other at exactly two points, or explain why a circle which isnt behaving like a circle can still be considered one for the sake of proving that a line which doesnt behave like a line isnt a line.

Not a very solid argument you have put forward.

Really? I decided to omit the actual proofs because I hadnt actually seen any of yours here either...just some assertions that you are increasingly falling back on the "I said this is true, so your argument must be false, which means that my argument is still true" line of circular reasoning.

Tell you what...when you put up the formal proof of your initial statement, I'll provide teh "solid" side of my argument as well and we can argue over who's proof is stronger.

Until then, I think I'm the kettle regarding the accusation of non-solid arguments.

jc

jc

Sev · 30-04-2003 7:48pm

So you can prove that two circles of infinite radius, placed less than infinity apart intersect? I would have thought meddling with infinity would plunge you into mathematically absurdity and ambiguity.

What I'm getting at is if you were to construct an inductive proof for circles of all values "to infinity" would that really qualify as a proof "at infinity" too? Or is such a concept too intangible?

Because if you could'nt do that, then I could give a rather cheeky reason why...

Originally posted by bonkey
You would need to show why a circle of infinite radius behaves differently to all other circles to invalidate the proof

Because it's a line.

po0k · 30-04-2003 8:42pm

fucking nerds

There seems to be an awful lot of arse-talking going on here, and alot of people intelligently disproving the arse.
Seems to me that some people are getting their backs up over bollocks and using [quote][/quote] way too often to be healthy.

Just let it die. It's been dealt with.

Go read some papers on string theory or something if you're really that interested...jees :roll:

Gordon · 30-04-2003 8:51pm

lol

Let me guess... Good Will Hunting is somewhere in this thread... 0_o

CuLT · 30-04-2003 9:58pm

Sev · 30-04-2003 10:40pm

Originally posted by bonkey
b) They do intersect, in which case the lines were not parallell, unless we stated we were dealing with a curved space, in which case there is no question - lines are arcs.

Couldn't parallel lines be considered to intersect at infinity?

ecksor · 30-04-2003 10:44pm

Originally posted by Sev
Couldn't parallel lines be considered to intersect at infinity?

No, the definition of parallel lines are lines that do not intersect.

Gordon · 30-04-2003 10:46pm

Originally posted by Sev
Couldn't parallel lines be considered to intersect at infinity?

Sev, I'm no maths genius, I used to be when I was 14 but it all got way over my beer belly after that. But, no parallel lines never intersect, sorry.

Sev · 30-04-2003 10:48pm

Yes, but if you can even conceive initially a circle with infinite radius on the plane, then how can you possibly work with conventional euclidian geometry to counter SOL's little supposition?

ecksor · 30-04-2003 10:57pm

Originally posted by Sev
Yes, but if you can even conceive initially a circle with infinite radius on the plane, then how can you possibly work with conventional euclidian geometry to counter SOL's little supposition?

Is that the first time that anyone has mentioned a specific geometry on this thread? The first post I made on this thread was to try and establish where exactly all this stuff was supposed to be going on. (I tend to think of circles on the plane of R2).

Anyway ....

Parallel lines not meeting doesn't imply euclidean geometry. Check out Gauss's work on trying to disprove the parallel postulate, where he showed that it was a necessary axiom in euclidian geometry, and that parallel lines in one geometry can look quite different to parallel lines in another geometry.

ecksor · 30-04-2003 11:20pm

Originally posted by ecksor
Check out Gauss's work on trying to disprove the parallel postulate

Heh. Of course, he didn't try to disprove it, he tried to show that it was unnecessary in euclidean geometry.

SOL · 30-04-2003 11:32pm

So in conclusion a line is a circle of infinite diameter and this makes maths out by an infinitly small ammount but due to the nature of infinity the harder you look the straighter the line is, so we are argueing about what now?

ecksor · 30-04-2003 11:40pm

Originally posted by SOL
So in conclusion a line is a circle of infinite diameter

You haven't proved this. [edit]or told us what system of geometry the two are supposed to be equivilent in[/edit]

Are you studying geography or geology by any chance?

bonkey · 01-05-2003 9:19am

Originally posted by Sol

So in conclusion a line is a circle of infinite diameter and this makes maths out by an infinitly small ammount

In conclusion???? Sol, you havent put forward a single argument strong enough to draw a conclusion from, and you sure as hell havent gotten concensus.

You have utterly failed to show that a finite-length line is an arc of a circle of infinite diameter, and instead are just insisting that its true....which is really what you've been doing from the start. Whats wrong, did I scare you when I asked for the proof of your assertion? How can you offer a conclusion without your prood?

At the very simplest level, you are assuming that the curvature of a circle with infinite radius is 0. This is fundamentally incorrect. It is an infinitely small non-zero value.

1/infinity <> 0

This is the infinitely small amount that you are out by...not mathematics.

Although at this stage, I think you either dont know mathematics well enough to be able to succintly argue your point, or you do know mathematics well enough and are deliberately trolling.

In either case.....my conclusion is that I have better things to do with my time then continue to answer your posts until you actually offer a solid argument rather than an empty assertion.

jc

Victor · 01-05-2003 1:36pm

Isn't this like the divided by zero / divided by infinity argument? Teh circumfereance of a circle of infinite diameter will tend towards straight, but not actually be straight, i.e. all arcs tend towards being straight (depending on scale).

But to take the correlation that all straight lines are actually arcs is wrong.

Kantankerous · 02-05-2003 9:40am

...to take the correlation that all straight lines are actually arcs is wrong.

Amen to that.

Victor · 02-05-2003 8:53pm

Originally posted by Victor
But to take the correlation that all straight lines are actually arcs is wrong.

Actually if you accept by the nature of infinity, that there are an infinite number of lines and indeed an infinite number of straight lines and alledgely some of those "straight" lines might be arcs, there must still be some of those "Straight" lines that are not arcs.

:rolleyes:

CuLT · 03-05-2003 12:47am

quodlibertarian -
A pedantic person who engages in elaborate arguments about minor things

Nuff said, this is an arguement that can't be solved on boards...

Line is a Circle

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