Deeper than primes

[zooterkin]

Indeed do some real math, instead of using your mambo jambo reasoning.

What does a Latin-American dancing Hearts fan have to do with anything?

 

[laca]

We all, except you, understand the post perfectly well. It contains no bijection between the null set and its power set.

Nu-uh! Now we have punshhh too. It all makes perfect sense to him. Well, he does believe in fairies too, so it's not all that surprising.

 

[epix]

This is the same point about points, lines, line segments and continuous spaces, that has been made may times before that you still seem to be deliberately ignoring.

The problem is that Doron is self-absorbed on such a level that it prevents him to get inspired by external ideas, such as the Surface-to-Lines test developed by Erasmus Yorkut at Standford:

If there are gaps in the circumference due to the latent discontinuity, then the surface of the semicircle would be leaking straight lines. This idea received wide recognition at the 1953 M.I.P.(Most Ingenious Proof) Conference in Salt Lake City, Utah.

 

[The Man]

Time is not involved here in terms of before\after process.

Evidently for you learning is also “not involved here in terms of before\after process”.

Oh and again….

So by all means please explain to us the difference between changing and unchanging with “no past (before) and no future (after)”?

Your serial-only reasoning can't comprehend the parallel aspect of present continuous state of infinitely many distinct zero dimensional building-blocks that can't completely cover a one dimensional building-block.

So identify a point on a line that can’t be coved by a point, otherwise geometry’s still got you and your line covered with, well, points.

Oh and stop trying to simply posit aspects of your own failed reasoning onto others.

Wrong, no amount of zero dimensional elements completely covers a one dimensional element.

Again identify the point on a “one dimensional element” that can’t be covered by a “zero dimensional element”.

Again your serial-only reasoning rising its limited head.

Again stop trying to simply posit aspects of your own failed reasoning onto others.

No, two points only mark two zero dimensional locations along a line segment. Given any infinite amount of zero dimensional locations along a line segment, it does not completely cover the considered line segment (there is always an uncovered one dimensional element between any arbitrary closer zero dimensional marks, along the considered one dimensional (known as line) segment).

“two zero dimensional locations along a line segment”? Do you mean the end points of that segment or the end points of some smaller segment of that segment?

Please identify this “uncovered one dimensional element” such that there is no point between its end points and thus no smaller line segments.

Wrong reasoning. In the case of infinity sub-line segments, the smallest sub-line segment does not exist exactly because no line segment (a one dimensional building-block) is reducible into a point (a zero dimensional building-block).

Doron you’re the one claiming an “uncovered one dimensional element” and thus a “smallest sub-line segment”. If you think you’re using “Wrong reasoning.” Don’t blame anyone but yourself.

We are explicitly NOT talking about a line segment, which is indeed completely covered by sub-line segments ( as clearly and simply shown in http://www.internationalskeptics.com/forums/showpost.php?p=7030466&postcount=14789 , and you, The Man, can't comprehend it ).

Yes we are, please see your above statements and mine before to disprove your assertion that “We are explicitly NOT talking about a line segment”.

We are explicitly talking about a line segment that is NOT completely covered by any given amount of points.

Talk all you want but what you have continually failed to do is to show any location(s) on a line that can’t be covered by (a) point(s).

Please show me a zero dimensional line, or a one dimensional point, and I'll agree with you.

Why? I have made no such assertions, so you certainly would not be agreeing with me. You seem to be claiming that you would agree if someone were to show you something clearly self-contradictory? Is that why you only agree with yourself because you clearly contradict yourself?

Once again, The Man, there is no before\after here but only present continuous, which is a state that your serial-only reasoning can't comprehend.

It seems reading and learning are both “states” you just don’t want to comprehend. As that is twice now that you have, apparently deliberately, misattributed a reference to time. Also why we go around time and time again repeating the same redresses each time you decide just to change your nonsensical phraseology.

Oh and on the subject of time and repeating things…

So by all means please explain to us the difference between changing and unchanging with “no past (before) and no future (after)”?

 

[The Man]

The problem is that Doron is self-absorbed on such a level that it prevents him to get inspired by external ideas, such as the Surface-to-Lines test developed by Erasmus Yorkut at Standford:

[qimg]http://img812.imageshack.us/img812/3393/surfaceleak.png[/qimg]

If there are gaps in the circumference due to the latent discontinuity, then the surface of the semicircle would be leaking straight lines. This idea received wide recognition at the 1953 M.I.P.(Most Ingenious Proof) Conference in Salt Lake City, Utah.

So that's why my glass drips on my shirt when I drink!!! There must be some cumulative affect as it seems to happen more after I’ve had a few.

 

[epix]

Indeed do some real math, instead of using your mambo jambo reasoning.

You are confused by trying to incorporate your kitchen and bathroom experiences into highly abstract topics like the set theory. Your ideas regarding points and lines lack necessary defining terms and so the whole mix comes to something that Ezekiel would surely marvel over. Sure, there are moments where a curve, for example, is better to be defined as a collection of line segments with length approaching zero unbound. But such definition can be demonstrated visually. Just compute the slopes of the intended curve and draw the tangent lines like you see bellow.

http://www.youtube.com/watch?v=_Y1PWcnOiXw&feature=related

Since your macro-experience with doing the dishes prevents you to grasp lim n → 0, you would never treat a line of length n as a point, as calculus does with no problems whatsoever.

The set theory treats objects that visually support calculus and geometry differently, so the R line is not exactly the same as in other math fields, even though any math topic can be described using the language that the set theory speaks. Cantor's set theory doesn't attempt to locate a single point; it attempts to compare the sizes of different defined collection of points. The modern set theory set its mind on invading the classical fields of mathematics and axiomatize and/or define it according to its image and likeness. It's an activity similar to your OM invasion, but only in its intention to reorganize stuff.

 

[epix]

So that's why my glass drips on my shirt when I drink!!! There must be some cumulative affect as it seems to happen more after I’ve had a few.

I'm not sure what Doron is onto by claiming gaps in a line. Judging from the above, you seem to have enough experience with points B and G to elaborate on Doron's claim. Like the shortest distance between B and G is a straight line. But what happens to the distance when some points in the imaginary straight line are missing? Does that alter the distance between Bottle and Glass? Or does it give you the idea to drink from the bottle to prevent unexpected surprises confused:, I mean just surprises) when you push the bottle toward the glass? Like the bottle falls into some gap and you don't have a rope long enough for the recovery? And what if the bottle breaks upon the impact spilling the Scottish treasure all over the bottom of the pit? Again, there is no straw long enough . . . You know, I hope that Doron is wrong especially with that 2012 around the corner.

 

[jsfisher]

I'm not sure what Doron is onto by claiming gaps in a line.

Actually, he does not claim the line has gaps. He claims the coverage of points has gaps. He sees lines and line segments as atomic things. You can put points on them, much as you mind spread sand over a surface, but they'll never completely cover the line.

 

[zooterkin]

Actually, he does not claim the line has gaps. He claims the coverage of points has gaps. He sees lines and line segments as atomic things. You can put points on them, much as you mind spread sand over a surface, but they'll never completely cover the line.

Indeed, this seems to be how he views things; that when one refers to a point, one is adding a point to a line, not that one is specifying an already existing point. Similarly with sets, he seems to have the need to examine every potential member of a set to see if meets the criteria, so that it's a process which takes time, rather than just accepting something is either a member or not.

 

[punshhh]

I see you are avoiding the issue, punshhh. Why?

I recognise the argument, not mathematically more theoretically.

 

[punshhh]

There is no paradox.

No amount of 0-size elements completely covers a 1-size element.

By this do you mean something with no dimension, can never cover something with 1 dimension, even when in infinite quality?

 

[punshhh]

Geometry isn't constrained by things that exist. You asked for a demonstration

so you got it. There was no stipulation that the object had to have finite dimensions.

I wonder what you been referring to by walking on the surface of a sphere. Doron is into 0-dim objects called points. Now show me something that exists but cannot be measured, as opposed to a sphere whose radius is finite.

A singularity, or are you of the opinion that existence as we know it did not arise from such a thing.

Maths is only notional, it represents things which are considered infinite, but has no true grasp of it, no more than it has any understanding of a singularity.

 

[zooterkin]

By this do you mean something with no dimension, can never cover something with 1 dimension, even when in infinite quality?

He does (though I think you mean quantity not quality). Yet he is unable to identify anywhere on the line where there isn't a point.

 

[punshhh]

He does (though I think you mean quantity not quality). Yet he is unable to identify anywhere on the line where there isn't a point.

This seems paradoxical to me, you can explain how the points can cover the whole surface and he cant explain how there can be somewhere without a point.

 

[epix]

Actually, he does not claim the line has gaps. He claims the coverage of points has gaps. He sees lines and line segments as atomic things. You can put points on them, much as you mind spread sand over a surface, but they'll never completely cover the line.

I thought that Doron's "theorem"

No amount of 0-size elements completely covers a 1-size element.

implied 0 0 0 0 0 0 0 0 0 where 0 is a 0-size object (point) and ______ is a line segment where the gap between two points p and q is a consequence of an irrational number p trying to reach its limit q, which is impossible. This is fun, coz

1) p cannot find q.
2) Therefore q doesn't exist and the point coverage is incomplete.

Since the conclusion smells of the ad ignorantium fallacy, Doron can resort to

1) p cannot reach q
2) Therefore p-q=d where d is a line segment that neither p or q can cover.

The latter argument denies the existence of point r = (p - q)/x with x in R and x≠0. But that only cuts repeatedly a line segment on those "sub-line segments" whose number grows without bound. Doron stumbled upon real example of his speculation in the Koch curve, which he repeatedly exhibited with his own comment. What he saw in the Koch curve filled his heart with joy: ._._._._._. forever and ever. The conclusion was that a curve is a collection of line segments and points -- not just points. That's what I thought went down in his head.

It is interesting stuff, coz there are two numerical formats: exact and approximate, and each format has its own space -- you can't mix the proverbial apples and oranges, otherwise there seems to be a problem.

 

[jsfisher]

This seems paradoxical to me, you can explain how the points can cover the whole surface and he cant explain how there can be somewhere without a point.

It stems from his "process view". Things cannot simple just be, they have to arrive via some process or sequence of operations. Given any two points on a line, there is always a gap between them, and additional steps are required to add more points in the gap. But no amount of adding points (in Doron's mind) ever completely fills the gap.

He also struggles with the whole infinity concept. He desperately wants there to be only one, but since he can't quite reconcile that, he backfills with the contradictory "absolute infinity" concept as an adjunct.

He's even managed to make infinitesimals work by permitting an infinite sequence of decimal places to terminate with room for an additional digit at the end. So, the difference between 1.0 and 0.999... is the paradoxical 0.000...1.

Nothing useful comes out of his fantasies. About all he can do is scream that everyone else is wrong. Doron has no replacement result with any utility, though.

 

[laca]

I recognise the argument, not mathematically more theoretically.

Oh, sorry, I thought mathematics was pure theory...

Just admit it that you have no clue about any of this.

 

[laca]

This seems paradoxical to me, you can explain how the points can cover the whole surface and he cant explain how there can be somewhere without a point.

Nothing paradoxical about that, it's quite logical. Since we can explain how points can cover any finite dimensional space it is quite obvious that he can't show a place on any such space where there is no point. You are just showing that you don't understand what paradoxical means. Again.

 

[epix]

It stems from his "process view". Things cannot simple just be, they have to arrive via some process or sequence of operations. Given any two points on a line, there is always a gap between them, and additional steps are required to add more points in the gap. But no amount of adding points (in Doron's mind) ever completely fills the gap.

Ironically, he rejected as "mambo jumbo" one feature supportive to his claim and that's the Cantor's proof that the set of reals is uncountably infinite. If the real line is fully covered by points, then the diagonal method of detection cannot show that there is an additional point in there whose existence contradicts the assumption of the full coverage. Instead, he unwrapped the diagonal argument, opened his OM toolbox and reshaped the idea into the <0,1> argument, which he used to demonstrate that finite sets by definition are actually infinite. When faced with non-abstract finite set G={male,female}, Doron attempted |G|=3 by sneaking child into the set. He's a pride and joy of every general; he wouldn't stop tossing grenades even from his coffin.

 

[punshhh]

Nothing paradoxical about that, it's quite logical. Since we can explain how points can cover any finite dimensional space it is quite obvious that he can't show a place on any such space where there is no point. You are just showing that you don't understand what paradoxical means. Again.

Sorry I’ve just noticed I missed out a “t” in my message to Zooterkin about the paradox.

Rather than stating that you can show that the points can cover the line, I meant to say that you can’t show it.

This has a similarity with Zeno’s arrow, in theory non (0) dimensional points cannot cover any dimensional space atall, they would always occupy an infinitely small portion of that space, even if in infinite quantity.

However if they had any size (dimension) such as the line segment, this “infinitely small portion of that space” would only ever be an infinitely small portion of it even if the line segment were infinitely short.

We have an infinite regress here, the points can neither cover or not cover a line segment, if the line segment is defined as being between two of the points.

Is this a paradox like Zeno’s arrow?

This reminds me of my question about energy in another thread, energy in itself does not have any dimensional presence, it acts between particles through space.
However on closer inspection it appears that those particles are also energy.

So we have an energy with no dimensional presence, no actual presence in space, acting across space between two points constituted from energies occupying no dimensional space. All happening some how in 3 dimensions, through the agency of time.