The universe?

Hello Canute
You raise something that was put to JR way back.

Even if his reasoning meant that his line was longer than his definition of finite length, it could still be a finite length by a new definition.

The only possibility was not that the line was of infinite length.

Regards

leeaus
 
Originally posted by Canute
I think what leeaus is trying to argue, in his irrational and infuriatingly annoying fashion, is a metaphysical point that has little to do with mathematics.

However isn't his conclusion (when argued rationally) very close to Brouwer's 'intuitionism'. In this view proofs by contradiction fail because the law of the excluded middle is rejected, and the existence of a thing cannot be proved by proving its non-existence to be impossible. Intuitionism is also a semi-metaphysical position since it slightly redefines existence.

I don't know the technicalities but I remembered this from Penrose's 'Emperor's New Mind'. Is intuitionism a way of actually arming the troll with a reasonable argument?
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That's interesting...I haven't heard of that. If there's any parallels between it and leeaus' argument, they must surely be coincidental, at least from what I gather from your description. It seems to me his disagreement is based mostly on a misunderstanding of the proof, not a problem with the method. Then again, maybe I just can't see past the absurdities in his argument.
 
Originally posted by malkiri
That's interesting...I haven't heard of that. If there's any parallels between it and leeaus' argument, they must surely be coincidental, at least from what I gather from your description. It seems to me his disagreement is based mostly on a misunderstanding of the proof, not a problem with the method. Then again, maybe I just can't see past the absurdities in his argument.
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Yeah, I certainly didn't mean to suggest that his argument wasn't completely absurd. But I wondered if his conclusion might accidently be reasonable, if you see what I mean.
 
Originally posted by leeaus
Hello Canute
You raise something that was put to JR way back.

Even if his reasoning meant that his line was longer than his definition of finite length, it could still be a finite length by a new definition.

The only possibility was not that the line was of infinite length.

Regards

leeaus
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That's nothing like what I said.
 
Originally posted by Canute
Yeah, I certainly didn't mean to suggest that his argument wasn't completely absurd. But I wondered if his conclusion might accidently be reasonable, if you see what I mean.
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If I understand intuitionism correctly, wouldn't it say that by relying on James' proof (which would be considered faulty), the existence of infinity is not proven, rather than saying it does or doesn't exist? Leeaus is firm in his belief that infinity doesn't exist.
 
I think at this stage that this thread has pretty much run its course. Clearly, leeaus has much to learn. Enough said.
 
Originally posted by malkiri
If I understand intuitionism correctly, wouldn't it say that by relying on James' proof (which would be considered faulty), the existence of infinity is not proven, rather than saying it does or doesn't exist? Leeaus is firm in his belief that infinity doesn't exist.
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Probably you're right. I wondered what JR would think, but I'm not surprised he's had enough.
 
Hello JR
Agreed, this thread has run far enough and who hasn’t something to learn.
Your problem is what you have learnt at school is wrong or at best unproven.
Infinity remains an absurdity to use the term of recent contributor Kaduseus. Infinite length likewise.

You have learnt things about infinity, e.g. infinity + 1 = infinity, accepted them and now have a feeling of necessity to represent what you have learnt in your later life. This feeling that you have does not make what you have learnt right.

When it comes to the fact that a closed shaped can not be infinite, Leeaus has nothing to learn. You, and most others it would seem, need much tuition in this area.


If you believe that some part of this proof is wrong, please point out exactly which step is flawed. JR

Your proof of the existence of infinite length was flawed on these levels.

1/ It did not encompass all distance. Your infinite length began at zero length.

2/ It used a system of numbers to represent distance. (e was a real number in the proof and distance upon recent questioning of JR). This made your proof meaningless or at least nothing more than the mathematical concept of 1,2,3....infinity. It was not about length, a geometric entity.

True the thread has gone further than need be when it is centred on such obvious nonrepresentational mistakes. Allowing that the world is not ideal, ideally this is the last Leeaus post.

Regards
Leeaus
 
RE leeaus

True the thread has gone further than need be when it is centred on such obvious nonrepresentational mistakes. Allowing that the world is not ideal, ideally this is the last Leeaus post.
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I was very much impressed by the concept you presented, leeaus. You have an admirable thinking power. But, possibly, the way you put it forward could be done differently. E.g. Pirsig in "The Art of Motorcycle Maintenace" put his "alternative" view in a novel and it have reached and influenced many people. In such way a rigorous scientific scrutiny is (wisely) avoided. Even though some new concepts are coherent in their inner logic (as yours is) they go far away from the formed picture of the world.

Anyway, I hope you will go on, and Iwish you good luck in it.
 
Procop:

<i>I was very much impressed by the concept you presented, leeaus. You have an admirable thinking power</i>

I take it this is tongue-in-cheek.
 
1/ It did not encompass all distance. Your infinite length began at zero length.

2/ It used a system of numbers to represent distance. (e was a real number in the proof and distance upon recent questioning of JR). This made your proof meaningless or at least nothing more than the mathematical concept of 1,2,3....infinity. It was not about length, a geometric entity.
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Leeaus:

If a line has only one end, you claim it is not infinite. What is it then? It cannot be finite, as that would mean that it had two ends.

I think the time has come either for you to give some proof of what you claim, or just shut up. No progress is being made while you sit there with your fingers in your ears, telling yourself 'I am right'. JR and I have both at least attempted a proof, and I at least have proved that a sequence with only one end is infinite.

Where you move into a circumference being cut by a radius, wrong by your own argument. The ratio of a circumference to a radius is irrational. Thus where can they be said to intersect.
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Again, I don't understand what you are trying to say. Are you saying that because the ratios of the lengths are not rational, the lines never meet? Clarity is the key to sucessful communication, rather than the whole third person narrative thing of yours.
 
RE JR

I take it this is tongue-in-cheek.
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What we know about infinity isn too little to conclusively refute the model of the 3d's cutting through one space causing non-infinity of such space even if the model is itself non-conclusive at some parts (eg. semi infinite line). Concepts can have scientific value (even if they are finally proven conclusively untrue) eg. <a href=http://www.english.upenn.edu/~jlynch/Frank/Contexts/phlog.html>Phlogiston Theory</a>
 
Hello Procop

Appreciate your comments, thinking power and general scientific disposition towards life.

All the best
Regards
Leeaus
 
Hello Geodesic.

A line that has a beginning can be longer. It can start from a point prior to its existing beginning. If it is not the longest line, it is not an infinite line.

You make the same rash mistakes as JR in allowing for a myriad of infinite lengths, all different in length. Infinite length, if there is such a thing, can only be the longest length. Otherwise you are engaging a contradiction of terms. JR admitted during the thread that his proof related to a ray, not infinite length, anyway. And rays are specified as being half infinite as they do not encompass all length.
Once again for you. See if it helps.

A dimension of infinite length is a dimension that encompasses all length. (as JR says on page 2 of this thread with respect of distance but had a mind change later on for reasons never made clear.)

Each dimension exists in sections as it is intersected by the other two dimensions.

One section of each dimension does not encompass all the length of a dimension.

Thus each section of each dimension is of finite length.

Finite length + finite length = finite length.

Thus each of the three dimensions is finite.

Proof by contradiction that three dimensions are finite and also that space is finite, space being the occupier of the three dimensions.

In the words of JR, can anyone see a flaw in one of these steps.

With respect of what you wanted clarified, your line of reasoning about a circle was the fact of a radius gives a circle a beginning and an end. That would be O’K if the radius was part of the structure of the circle.

Regards
leeaus
 
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RE leeaus

Mathematicians zero, Logical truth 1.
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Not really my idea. But it was proposed to me by a poster here, Gudham Wing (a mathematician): He said that one must support concepts with maths otherwise they are worthless scientifically (regardless their having logical coherence). Himself he had some similair ideas as I proposed in my DvD theory but had to drop them because he couldn't back them up mathematically. A concept which doesn't comply with maths is hard to defend (as you experinced). Don't know any way around it at the moment. Maybe you might find one - but it won't be easy.
 
Originally posted by leeaus
One section of each dimension does not encompass all the length of a dimension.

Thus each section of each dimension is of finite length.

Finite length + finite length = finite length.

Thus each of the three dimensions is finite.
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That italic section is where "logical truth" falls apart.
 
Hello Whiteknight
Neither section encompasses the length of a dimension. Thus each section is finite.

That follows from A dimension of infinite length is a dimension that encompasses all length.

There is no break down where you indicate.

Regards
leeaus
 
leeaus,

I think the claim of breakdown comes from the purely mathematical assumption that infinity/2 = infinity.

I understand the terminology in the definition of infinity appears to defy the accepted practice of allowing infinity to be bounded at one end.

But none the less it is the general practice.
 
Hello Macm

The infinity of infinity/2 = infinity would refer to an unbounded quantity greater than every real number.

Whether such an infinity exists and whether such an infinity could be divided if it did exist is a separate consideration to infinite length.

But it should be suffice is to state anything that can be or is divided up was not infinite in the first place.

Mathematics as it is known carries a few logical flaws in the zero/infinity area.

Both area and volume must always be finite as each is bounded. There is no break down in what is presented from that point of view.

Regards
leeaus
 
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