Deeper than primes

[The Man]

Doron is merely pointing out that your reasoning is stuck in a hypothetical abstraction known as mathematics.

"hypothetical"? Is your computer that you are posting such nonsense from, well, hypothetical?

It is time to emerge from this abstraction and realise that in reality/existence size or measurement is entirely relative.

You've heard of this thing called technology right? Do you want to guess what application of 'abstractions' it is based on. Emerge yourself and immerse yourself in applied abstractions.

Oh wait you already have. Perhaps you just need some more emergence to see your own immersion?

Unless you have two or more objects in existence, measurement is meaningless, it is N+or- infinity.

If you have more than two objects you have the existence of relative measurements. Which can then be hypothetically arranged in an abstract thought construct.
That +or-infinity has disappeared, however it is still there, only behind the scenes now.

Imagine a banana in a universe, you know how long it is. Remove that universe so that only the banana remains*. How long is it now?

*for the purposes of this analogy

The length of a banana?

Not to worry, we've had emerged bananas waved around on this thread before.

 

[epix]

Unless you have two or more objects in existence, measurement is meaningless, it is N+or- infinity.

That spells the end to many arguments.

 

[epix]

. He just can't seem to make up his mind. Whether he wants a discrete space with his self-contradictory notation of .00000...1, indicating an infinitesimal and thus a smallest line segment (basically a one dimensional yet infinitely small point). Or a continuous space with no such dimensional limitation on the minimal location. He just wants both in the same context (his own indefinite and self contradictory context that is), which again is why he still remains the staunchest opponent of just his own notions.

I could somewhat follow where that expression 0.000...1 came from. It takes a few lines of code inside an infinite loop to generate a = 0.999... Now Doron knows that a in its approximate form cannot reach 1, unless changes are made to the generating code. And so 1 - 0.999... = 0.000...1. It is possible that Doron extended this value on all irrational numbers, which is wrong, but not that easy to show why. But as a concept, Doron could regard the distance between the limit of an irrational number and the value that is approaching the limit through a convergence as a space where a point need not apply. But I can divide a line segment a unit long by placing a point not at 0.69314... but at Log(2) and perform further algebraic operations, which are exact. When I'm done and the result looks like Log(5) + Cos(2), then I convert the result into the approximate form and chose the desired precision. This is what I think is Doron missing. I also think that he dwells on something really negligible -- something of a little analytic value.

 

[punshhh]

"hypothetical"? Is your computer that you are posting such nonsense from, well, hypothetical?

Perhaps hypothetical is a bit strong, is not all reasoning essentially hypothetical?

"I think therefore I am" cannot be proved, it is hypothetical.

I am not saying that abstracted models cannot be applied, they can, but they are not a substitute for reality.

You've heard of this thing called technology right? Do you want to guess what application of 'abstractions' it is based on. Emerge yourself and immerse yourself in applied abstractions.

I deal in abstractions myself, I have the foresight to accept that they are abstract and only relate to aspects of reality. They do not encompass the whole thing.

Oh wait you already have. Perhaps you just need some more emergence to see your own immersion?

I accept my immersion, you may be stood on the back of a turtle in order to keep your head above the surface of the ocean.

The length of a banana?



Not to worry, we've had emerged bananas waved around on this thread before.

How long where these bananas?

It is indistinguishable wether my banana is infinitely long or infinitely short.

 

[doronshadmi]

You map from/to and it doesn't go the other way around.

Try to define from/to by using a point.

 

[doronshadmi]

In details?
I think I can reply with your own quote:

So you can't share with us your "understanding of the dimensionality of objects", which is derived from "Dragging a point".

Thank you for your honest answer.

 

[doronshadmi]

You will note that he deliberately leaves off the last "AND indivisible" as just a hidden assumption that he just can't hide as it is one major premise of his assertions.

You will note that The Man can't comprehend the irreducibility of a line into a point, and the non-extendability of a point into a line.

Furthermore, you will note that The Man can't comprehend that these inabilities are in co-existence, and as the agents of Unity, they send at the basis of Complexity.

 

[doronshadmi]

Fine, then by all means please define your “succession” without ordering.

It simply the next element of a given collection, where order is insignificant.

Are you perhaps just confusing ordering with some specific ordering?

Do you understand the sentence "order is insignificant" in this case?

As, by your own assertions, your “difference” requires your “interval” and the orderings of your set are different in your example, please tell us what is the “interval” that you require by that difference?

The co-existence of the the irreducibility of a line into a point, and the non-extendability of a point into a line (where a point is the minimal expression of locality and a line is the minimal expression of non-locality).

OH NO!!

Not the ‘get out of your box’ retort!!!

Again…

What a laugh.

This is your box, Doron. That you simply have as much distain (if not more) for your own box as you do for any other, that you would simply like to ascribe to others, is of consequence to no one but you. It is incumbent on no one but you to construct your box in, at the very least, a self consistent manor. Similarly filling your box with some particular meaning of your own choosing befalls no one but you. That you simply can’t be bothered to perform either of those tasks in no way gives anyone else the responsibility to do so for you. Why how deliberately lazy, of just you, Doron.


What Doron is attempting to advocate here, other than simply and deliberately trying to abdicate his own responsibility for his own notions and assertions, is a technique common to cold readers, con artists and other hucksters. By recommending, forcing or even just allowing the audience to provide their own meaning to such assertions the presenter frees themselves of the responsibility of any resulting discrepancies as well as gets the audience invested in such meaning that they choose to ascribe themselves. The problem is that we here on this forum are more than familiar with such antics. Additionally it may not even be intentional on Doron’s part but just a technique that has gotten him what he perceives as preferred results before. So he might have never found the need (nor found it beneficial) to take full responsibility for his own assertions.

As already demonstrated the letters A and B are different (just as the orderings in your set example above are different), but with no interval as a consequence of that difference. Heck, technically an interval doesn’t even require a difference as in the case of [1,1], which results in the set {1}.

Once again, you do not generalize what you read.

By generalization, if there is nothing between A and B, then the different letters A and B are undefined in the first place (there is only one letter).

You still get interval or nothing only in terms of metric-space.

Technically nothing doesn’t even require [1,1] notation, which is actually the set {1} (there is only one member).

http://en.wikipedia.org/wiki/Interval_(mathematics)


http://en.wikipedia.org/wiki/Partially_ordered_set#Interval

OH NO!!

Not again the cut\paste equates from already agreed definitions, instead of re-consider them.

Once again The Man, your responsibility is to use your own mind in order to deal with the considered subjects and not only cut\paste equates from already agreed definitions.

You still do not grasp that this is a Philosophy forum, where new notions are born by active participation and not by using already agreed definitions.

So by all means, please Doron, stop being so dang lazy and do try to at least learn something.

So by all means, please The Man, stop being so dang lazy by only cut\paste equates from already agreed definitions and do try to at least learn something by activate your mind.

Certainly some differences do result in an interval just as some intervals can result from a difference, but neither specifically requires nor is required by the other.

You still do not get that difference is some particular case of interval, where interval is the opposite of nothing between considered things (which is always a one and only one thing, if there is nothing between the asserted things).

The specific fallacy you are engaging in (at least in this particular case), Doron, is called the fallacy of necessity.

This is irrelevant. You simply do not get (yet) the generalization of interval as the opposite of nothing between asserted things.

So your assertion now is that you just want to call your “interval” a “difference” dispite the fact that there is no difference in some intervals? Talk about just being lazy, Doron.

If there is nothing between A and B, then there is one and only one thing, where A and B are asserted letters (there is actually only one thing).

Also the agreed [1,1] notation is actually a one thing (exactly as the member of {1}).

In other words, you still get this fine subject only by using "cut\paste already agreed boxes" thinking style, and as a result you avoid any re-consideration of the discussed.

 

[doronshadmi]

He seems to have a difficulty to understand that in order for h = a/n; n → ∞ to be possible, there exists x such as x in (a, b), to allow the division of the line segment continue ad infinitum. In other words, there is no point such as x not in (a, b).

epix, the division of the line segment continues ad infinitum exactly because a 1-dim is irreducible into a point, try to grasp the result of this irreducibility on a collection of 0-dims along a 1-dim.

All your considered points are between points a and b along a line, but it does not change the fact that there are infinitely many of them exactly because a line is irreducible into a collection of distinct points exactly as the smaller is irreducible into the smallest.

 

[doronshadmi]

He just can't seem to make up his mind.

The Man, thank you for providing a concrete example of your inability to distinguish between smaller and smallest.

Whether he wants a discrete space with his self-contradictory notation of .00000...1, indicating an infinitesimal and thus a smallest line segment (basically a one dimensional yet infinitely small point).

In terms of metric-space, 0.00000...1 is an ever smaller element, which is irreducible to the smallest element 0.

Or a continuous space with no such dimensional limitation on the minimal location.

Nonsense.

0-dim is already a dimensional limitation on the minimal location, and since 0.00000...1 is an ever smaller element it is irreducible into the minimal location (or in other words, it is non-local).

I think this post is a corner stone that clearly exposes your inability to grasp the considered fine subject, as actually can be seen all along this thread.

 

[epix]

The Man, thank you for providing a concrete example of your inability to distinguish between smaller and smallest.

In terms of metric-space, 0.00000...1 is an ever smaller element, which is irreducible to the smallest element 0.

Incredible. Just incredible. It's your inability to come up with symbolism that matches your idea. Your awkward rendition is nothing but

[lim n → ∞] a/n = 0

You don't even bother to indicate the form of the reduction and so you again tail a strong suspicion that you have an immense difficulty of grasping a - a = 0.

 

[epix]

epix, the division of the line segment continues ad infinitum exactly because a 1-dim is irreducible into a point, try to grasp the result of this irreducibility on a collection of 0-dims along a 1-dim.

This property is due to an axiom. In a narrow way to render it, for any positive value a there exists b > 0 such as a/b > 0. Since for any positive a ≥ 0 there exists p and q such as a = |p - q|, it means that p and q can be also the end points of a line segment when p ≠ q.

All your considered points are between points a and b along a line, but it does not change the fact that there are infinitely many of them exactly because a line is irreducible into a collection of distinct points exactly as the smaller is irreducible into the smallest.

It's a rare occassion when you inadvertantly admit that you were wrong in your assertion, but you did exactly that just above.

 

[epix]

So you can't share with us your "understanding of the dimensionality of objects", which is derived from "Dragging a point".

Thank you for your honest answer.

It's a very simple concept which can be explained visually. When you want to measure your . . . Well, when you want to measure the lenght of the kitchen counter, for example, you anchor one end of the tape, which is the point and start to drag . . .

When you stop dragging, an additional point is created. So we have a line segment A, B. Or you can render it as A_______B.

So when you want to create ONE-dimensional object, you drag one point in one direction. If you want to create a TWO-dim. object, you need to drag both connected points simultaneously in another direction.

Pull on the points A______B and you see how the whole line moves

and creates four-sided polygon S, H, I, and T, which has an area.

In the next lesson, you'll learn how to grab all four points of the 2-dimensional object and drag them to create 3-dim object.

 

[doronshadmi]

You don't even bother to indicate the form of the reduction and so you again tail a strong suspicion that you have an immense difficulty of grasping a - a = 0.

a - a = 0 is a phase transition from abs(a>0), which is at least smaller, to 0, which is the smallest .

Again you demonstrate your inability to grasp that smaller can't be smallest, and vice versa.

Incredible. Just incredible. It's your inability to come up with symbolism that matches your idea. Your awkward rendition is nothing but

[lim n → ∞] a/n = 0

No at all epix, you simply can't grasp the notion that is expressed by 0.000...1 symbolism.

 

[doronshadmi]

This property is due to an axiom. In a narrow way to render it, for any positive value a there exists b > 0 such as a/b > 0. Since for any positive a ≥ 0 there exists p and q such as a = |p - q|, it means that p and q can be also the end points of a line segment when p ≠ q.



It's a rare occassion when you inadvertantly admit that you were wrong in your assertion, but you did exactly that just above.

It is a common fact that you show your inability to distinguish between smaller and smallest all along this thread, so?

 

[epix]

a - a = 0 is a phase transition from abs(a>0), which is at least smaller, to 0, which is the smallest .

a-a=0 is called "subtraction" and not "phase transition."

Again you demonstrate your inability to grasp that smaller can't be smallest, and vice versa.

You need to indicate the process of the reduction, but because you still don't understand the meaning of "definition," you keep making biblical-like statements as seen bellow.

No at all epix, you simply can't grasp the notion that is expressed by 0.000...1 symbolism.

0.000...1 = monotheistic system of belief with ever-decreasing faith?

Your symbolism lacks symbolic connection with an expression, which returns 0.000...1.

There is no location on the line segment where a point cannot be placed in order to divide the line segment. If there was, you wouldn't be able to arrive at your 0.000...1 notion. That's why the line segment is said to be "fully covered by points." The term sucks, but anyone but you can recover its meaning.

Remember that a point can be also expressed in the exact form as a solution to an equation. Let's say that a line segment is 5 units long and you want to divide it on two parts a and b, where b > a, such as

b/a = Log(a) + Log(b).

So the position of the dividing point p is a solution to the system of two equations

b/a = Log(a) + Log(b)
a + b = 5

 

[The Man]

Perhaps hypothetical is a bit strong, is not all reasoning essentially hypothetical?

No though certainly some can be.

"I think therefore I am" cannot be proved, it is hypothetical.

I am not saying that abstracted models cannot be applied, they can, but they are not a substitute for reality.

Unfortunately, for some such a substitution is exactly the intent.

I deal in abstractions myself, I have the foresight to accept that they are abstract and only relate to aspects of reality. They do not encompass the whole thing.

Once again the problem is not that “They do not encompass the whole thing” but simply that some just don’t encompass any “aspects of reality”.

I accept my immersion, you may be stood on the back of a turtle in order to keep your head above the surface of the ocean.

Perhaps a testable hypnosis depending on the applied definitions of the terms involved.

How long where these bananas?

Why the lengths of bananas, of course.

It is indistinguishable wether my banana is infinitely long or infinitely short.

Only if your definitions of “banana”, “infinitely long” and “infinitely short” are indistinguishable.

 

[The Man]

You will note that The Man can't comprehend the irreducibility of a line into a point, and the non-extendability of a point into a line.

Furthermore, you will note that The Man can't comprehend that these inabilities are in co-existence, and as the agents of Unity, they send at the basis of Complexity.

You will again note that the fact that a point is not a line by definition has been explained to Doron many times before. So whatever incomprehension he is imagining, asserting and demonstrating above remains simply his.

It simply the next element of a given collection, where order is insignificant.

“the next element” is a direct reference to ordering. So again…

…by all means please define your “succession” without ordering.

Do you understand the sentence "order is insignificant" in this case?

You obviously still don’t understand that a lack of any particular ordering is not a lack of ordering. You have asserted your “succession” as “the next element” a specific reference to ordering. You simply contradicting yourself and claiming “"order is insignificant" in this case” in no way alleviates your own assertion of your “succession”’s dependence on ordering.

The co-existence of the the irreducibility of a line into a point, and the non-extendability of a point into a line (where a point is the minimal expression of locality and a line is the minimal expression of non-locality).

That is not an interval nor does it have anything to do with the differences in the orderings of your example set. Why even quote the questions I asked Doron if you’re not even going to try to write a direct and relevant response.

Once again, you do not generalize what you read.

Once again you attempt simply to take no responsibility for what you write.

By generalization, if there is nothing between A and B, then the different letters A and B are undefined in the first place (there is only one letter).

Nope two letters that are different yet with no interval resulting from that difference. Your “generalization” fails, as usual.

You still get interval or nothing only in terms of metric-space.

I have made no assertion of a “metric-space” concerning the letters A and B. So whatever “terms” you’re thinking and asserting remain still just yours.

Technically nothing doesn’t even require [1,1] notation, which is actually the set {1} (there is only one member).

So your claim is now, that as usual, you’re just saying “Technically”, well, “nothing”?

OH NO!!

Not again the cut\paste equates from already agreed definitions, instead of re-consider them.

Once again The Man, your responsibility is to use your own mind in order to deal with the considered subjects and not only cut\paste equates from already agreed definitions.

Links were given to the articles which themselves have links to other references so this “only cut\paste” nonsense assertion of yours is just a result of you specifically not dealing with “considered subjects”.

You still do not grasp that this is a Philosophy forum, where new notions are born by active participation and not by using already agreed definitions.

Doron you still don’t grasp that just making up your own contradictory nonsense while deliberately misrepresenting and misinterpreting well established concepts and definitions certainly aren’t “new notions”.

So by all means, please The Man, stop being so dang lazy by only cut\paste equates from already agreed definitions and do try to at least learn something by activate your mind.

Stop being so dang lazy Doron and actually read the linked articles and references, heck you might actually learn something like the difference between “only cut\paste”, copy/pasting relevant quotes along with the links.

You still do not get that difference is some particular case of interval, where interval is the opposite of nothing between considered things (which is always a one and only one thing, if there is nothing between the asserted things).

Again show the interval for the difference in the orderings in your pervious set example.

This is irrelevant. You simply do not get (yet) the generalization of interval as the opposite of nothing between asserted things.

I have no doubt that you find the fallacies you engage in to be irrelevant as you simply insist on continuing them.

If there is nothing between A and B, then there is one and only one thing, where A and B are asserted letters (there is actually only one thing).

There is “nothing between A and B” and there are two different letters. So your assertion simply fails by its own self contradiction.

Also the agreed [1,1] notation is actually a one thing (exactly as the member of {1}).

The interval (1,1) results in the empty set so there is no “member” in that case. Your probably should have actually read the article or at the very least the quoted portions.

In other words, you still get this fine subject only by using "cut\paste already agreed boxes" thinking style, and as a result you avoid any re-consideration of the discussed.

Doron you just don’t get “this fine subject” at all, you simply refuse to consider any “thinking” but your own and yours is demonstrably self-contradictory. As a result you simply don’t agree with anyone including yourself.

 

[The Man]

In terms of metric-space, 0.00000...1 is an ever smaller element, which is irreducible to the smallest element 0.

An “ever smaller element” than what? Some other longer line segment? Is it smaller then itself? Do you have a line segment that is “ever smaller” than your “0.00000...1”? If not, then it is your smallest line segment. If so then it is not “ever smaller” than your smaller line segment.

Nonsense.


0-dim is already a dimensional limitation on the minimal location, and since 0.00000...1 is an ever smaller element it is irreducible into the minimal location (or in other words, it is non-local).

“no such dimensional limitation” that you simply choose to read ‘no dimensional limitation’ instead of what was written makes the nonsense, as usual simply and entirely yours.

I think this post is a corner stone that clearly exposes your inability to grasp the considered fine subject, as actually can be seen all along this thread.

Heck, your self-contradictory thinking is just the “corner stone” of everything you assert. So much so that you simply attempt to ascribe your own self-contradictory thinking to others.

 

[doronshadmi]

a-a=0 is called "subtraction" and not "phase transition."

It does not change the fact that a>0 is irreducible to 0.

You need to indicate the process of the reduction, but because you still don't understand the meaning of "definition," you keep making biblical-like statements as seen bellow.

There is no process here, (in terms or metric space) 0-dim element can't be 0-dim element.

Your symbolism lacks symbolic connection with an expression, which returns 0.000...1.

Your used current agreed reasoning can't comprehend the following expression:

1 - 0.999...[base 10] = 0.000...1[base 10]

There is no location on the line segment where a point cannot be placed in order to divide the line segment.

It does not change the fact (in this case, in terms of metric space) of the co-existence of infinitely many sub 1-dims (ever smaller elements that are irreducible into 0-dim elements) AND infinitely many 0-dim (smallest) elements, along some arbitrary line segment.

Remember that a point can be also expressed in the exact form as a solution to an equation. Let's say that a line segment is 5 units long and you want to divide it on two parts a and b, where b > a, such as

b/a = Log(a) + Log(b).

So the position of the dividing point p is a solution to the system of two equations

b/a = Log(a) + Log(b)
a + b = 5

This solution is the result of the co-existence of the smaller AND the smallest as the fundamentals of the researched form.