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Some Points Concerning Dialectical Materialism

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Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 27 Jun 2012, 05:54
FW:

Quote:
You don't get the contradiction between x and dx and that elementary weakness leads you further to ridiculous ruminations such as the one about adolescent John struggling with other men.


1. You haven't yet explained it, so no wonder I 'don't get it'.

2. The things I say about John follow from the confused things theorists like Engels, Plekhanov, Lenin and Mao say about those obscure 'unity of opposites' you keep mentioning. Of course, if I have gone wrong, then a towering intellect like you should be able to put me straight, and show me where my argument goes astray. If so, why haven't you?

Quote:
One can always say funny things like that about said John, and the rest of your examples for that matter, but this conversation calls not for this kind of entertainment.


As I have said several times, show me and the comrades here why the odd things Engels, Plekhanov, Lenin and Mao say about change -- how it is produced by a struggle between opposites, how these opposites all change into one another, and how every object and process changes into that with which they struggle, their opposites -- do not imply the things I have pointed out.

If so, and John-the-boy changes in to John-the-man, he must struggle with John-the-man. But, to do that, John-the-man must already exist (or no struggle can take place). But, John-the-boy can't change into John-the-man since John-the-man already exists!

My argument just generalises this obvious flaw in the dialectical 'theory' of change -- which implies that if this it were true, change would be impossible.

where does this proof go wrong?

[It's no good saying that I 'don't understand'. It should be easy to explain this to me and show me where I go wrong. The fact that you keep dodging this no matter how many times I ask for clarification suggests that you just do not know the answer, and are just playing for time -- or both.]

Aha, at last, an 'attempt' to put me right:

Quote:
Although I don't need to explain this, I am doing it just for you -- x signifies that the body occupies a single position in space, while dx signifies that the body does not occupy a single position in space. Occupying and not occupying a single position in space is a contradiction.


it's not a contradiction if this is takes place at different times, or in a time interval, which you have already conceded is the case with dt. That is why Engels added this comment (in Anti-Dühring):

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Motion itself is a contradiction; even simple mechanical change of place can only come about through a body being both in one place and in another place at one and the same moment of time, being in one and the same place and also not in it.


Hegel agreed:

Quote:
Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here', it at once is and is not.
[Science of Logic, pp.439-41, §955-§960.]

Bold added to help you get the point.

Notice "at one and the same moment it is here and not here..."

This is something you keep forgetting about, which makes your version of this 'theory' a revisionist version.

Now, a sort of case could be made for Engels's version being a sort of contradiction (but I show at my site that even this isn't so), but not yours, since you omit the vital clause: "at one and the same moment of time". Your dt is an interval, and so no contradiction can ensue, for the object could be at the first of your two places at the beginning of this interval, and at the second place at the end of that interval. You need your dt to be zero, just like Engels.

He even tells us this later on in the same book (and I have quoted this at you already, but you ignored it):

Quote:
How are these forms of calculus used? In a given problem, for example, I have two variables, x and y, neither of which can vary without the other also varying in a ratio determined by the facts of the case. I differentiate x and y, i.e., I take x and y as so infinitely small that in comparison with any real quantity, however small, they disappear, that nothing is left of x and y but their reciprocal relation without any, so to speak, material basis, a quantitative ratio in which there is no quantity. Therefore, dy/dx, the ratio between the differentials of x and y, is dx equal to 0/0 but 0/0 taken as the expression of y/x. I only mention in passing that this ratio between two quantities which have disappeared, caught at the moment of their disappearance, is a contradiction; however, it cannot disturb us any more than it has disturbed the whole of mathematics for almost two hundred years. And now, what have I done but negate x and y, though not in such a way that I need not bother about them any more, not in the way that metaphysics negates, but in the way that corresponds with the facts of the case? In place of x and y, therefore, I have their negation, dx and dy, in the formulas or equations before me. I continue then to operate with these formulas, treating dx and dy as quantities which are real, though subject to certain exceptional laws, and at a certain point I negate the negation, i.e., I integrate the differential formula, and in place of dx and dy again get the real quantities x and y, and am then not where I was at the beginning, but by using this method I have solved the problem on which ordinary geometry and algebra might perhaps have broken their jaws in vain.


You can find the link on page one of this thread.

So, yours isn't a contradiction, whereas Engels's version might be.

Quote:
The first thing for you to understand, prior to understanding whether or not x and dx can coexist, let alone prior to trying to understand Hegel and his followers, is to come to terms with the elementary fact that x and dx are opposites are in contradiction and


1. But, you have yet to explain why x and dx are opposites, and what the 'contradiction' here is. Sure, you certainly assert it is, and repeatedly, but, alas, with no explanation. I'm beginning to think that you can't explain it, just like every other Hegel-fan who has put pen to misuse over this.

2. If they are opposites, then according to the dialectical classics, quoted in my earlier threads, they should 'struggle' with one another. Do they really? Is this 'struggle' to be found in standard 'math' texts you keep banging on about.

Worse, still, they should turn into one another too. Do they do that, too?

But, you have an 'answer':

Quote:
that exact contradiction is what we're discussing here, not barley/sprout, adolescence/adulthood, war and peace. The latter are only concrete expressions of contradictions which we discuss in an abstract form through x and dx, to avoid the ambush of language.


1. Then you disagree with the dialectical classics and Hegel (quoted at length in a previous thread), all of whom argue that these opposites change into one another, and with the former arguing that they also struggle with each other.

2. This comment of yours is rather puzzling: "to avoid the ambush of language". What do you propose we use, then? Semaphore, Aldis Lamp, smoke signals?

You perhaps need to take Marx's advice, here:

Quote:
The philosophers have only to dissolve their language into the ordinary language, from which it is abstracted, in order to recognise it, as the distorted language of the actual world, and to realise that neither thoughts nor language in themselves form a realm of their own, that they are only manifestations of actual life. [The German Ideology.]


Which I think might help account for the fact that you seem not to be able to explain yourself no matter how many times you are asked to do so -- the distorted language you half-inherited from Hegel has crippled your thought processes -- "half-inherited", since your account of motion contradicts his (rather fittingly!).

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Therefore, first understand that x and dx are in contradiction and then go to your citations.


I'll be only too happy to 'understand' this just as soon as you explain how they can be in contradiction with one another, as opposed to merely asserting they are.

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Otherwise you'll remain in the intellectual mess you're now, befuddled by the meaning of words and what not.


You mean just like you are befuddled, since you seem not to be able to explain yourself.

Quote:
Stay simple if you want to understand anything.


That reminds me of a passage from the New Testament:

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And he said: "I tell you the truth, unless you change and become like little children, you will never enter the kingdom of heaven.


http://bible.cc/matthew/18-3.htm

So, only those with a simple faith will be able to see the truth, and it will set them free...

Alas for you, nature is complex, and our attempt to understand it can't fail to be either.

But, let us suppose you are right; even then we still lack a simple explanation why this is a contradiction. Just asserting it is one is no help at all.

By the way, have you been able to locate a standard physics or mathematics text that tells us that a moving body can occupy dx?

FW:

Quote:
That dx has nothing to do with time is obvious. Maybe it isn't for you, so first show us where do we see time in dx? Do this first before we even get to discussing whether dx is a quantity or not or whether it is some kind of container or a bucket.


Ah, I see you have returned to type and are beginning tell fibs again.

Where did I say we see time in dx?

I said this:

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As I have already pointed out, you seem to be super-glued to the old, pre-19th century view of 'dx'. 'dx' isn't a quantity, or a location, but expresses a functional relation between time and displacement. Anyway, how can a moving body be in 'dx'? Is 'dx' a container of some sort?


Bold added.

Even you linked these variables on page two of this thread:

Quote:
You can now plot dy/dt as a function of t and it will not be true that each point of that new dy/dt = F(t) function corresponds to only one t and only one y of the y = f(t) function. Every point on the dy/dt = F(t) will, undoubtedly, correspond to two t’s and two y’s of the y = f(t) function. This is an inherent property of the dy/dt = F(t), derived from y = f(t). That’s also an undeniable mathematical fact.

Now, you can talk all you want that each one single point on the y = f(t) function corresponds to only one single t but in talking that way you cannot make the fact disappear that there is also an inevitable dy/dt = F(t), each point of which corresponds to two t’s and two y’s of the y = f(t) function.

The coexistence of y = f(x) and dy/dt = F(t) is an undeniable mathematical fact (which in this particular case has a clear physical content). This fact of inevitable coexistence you’re trying to swipe under the rug and are foisting a discussion only about y = f(x), as if dy/dt = F(t) doesn’t exist. This is your mistake expressed now in mathematical terms. You have to correct that mistake in order to understand further what the resolution of the above inherent contradiction is.


Let, y = f(x) and dy/dt = F(t) -- but, by the chain rule, dy/dt = dy/dx.dx/dt.

Now, dy/dx = f'(x), so dy/dt= f'(x).dx/dt = F(t). QED!

Hence, even your revisionist theory has a functional relationship between time and displacement.

Ok, so now as promised, you can proceed to explain this:

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Do this first before we even get to discussing whether dx is a quantity or not or whether it is some kind of container or a bucket


[Don't forget to cite a standard text that tells us a moving body can be in dx.]

Finally, I am still waiting for an explanation of this:

Quote:
If the body in question is not in x, then it can't be the case that it is both in x and not in it. Unless, of course, you mean something different by 'not'. If so, what?


Rosa, this is the last time I clean your posts of sarcastic remarks. I'm very sure you can have a healthy debate without demeaning whomever disagrees with you.

First World, the same goes for you.
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 27 Jun 2012, 06:37
Again, you have the trajectory x = f(t) and dx/dt = F(t) and you claim that dx is a function of t because dx = F(t)dt, is that it? How is dx a single point (to not contradict the single point x, which is also a function of t) and not an interval?
Soviet cogitations: 10005
Defected to the U.S.S.R.: 14 Jul 2008, 20:01
Ideology: Trotskyism
Philosophized
Post 27 Jun 2012, 07:28
Quote:
Something moves, not because at one moment it is here and at another there, but because at one and the same moment it is here and not here, because in this 'here', it at once is and is not.


Slightly off topic, but this makes so much more sense if you say it in Spanish because "estar" (the word you'd use for "to be" in this instance. Spanish has two copulae which is awesome) etymologically means to stand. To "stand" (or otherwise, to be located) at one point and another simultaneously is motion, and a clear contradiction.

Just sayin. Amirite, prax?
"Don't know why i'm still surprised with this shit anyway." - Loz
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 04:43
FW -- still ducking the difficult questions I see. That's cool..., we all know why?


Quote:
Again, you have the trajectory x = f(t) and dx/dt = F(t) and you claim that dx is a function of t because dx = F(t)dt, is that it?


Well it follows from the formulae you posted; if you don't like it, may I respectfully suggest you pick a fight with yourself, not me.

Quote:
How is dx a single point (to not contradict the single point x, which is also a function of t) and not an interval?


It's no use asking me what your quirky use of 'dx' implies. All I have to go on are the inconsistent (and odd) things you say about it. I am just as much at a loss about what you mean you seem to be. Goodness knows I have tried my level best to get you to come straight about this, but all that happens is you either ignore my sincere attempts in this direction, or you continue to post baseless assertions about motion (that no one seems to be able to find in standard texts) and these obscure 'dialectical contradictions' (which you have yet to explain to us), all the while blaming me for not being able to follow a single thing you say!


One final point:

Any luck yet finding a single standard text that tells us that a moving object is in dx, as you claimed?

Or, do we just have to accept your word for this?

----------------------

Mabool:

Quote:
Slightly off topic, but this makes so much more sense if you say it in Spanish because "estar" (the word you'd use for "to be" in this instance. Spanish has two copulae which is awesome) etymologically means to stand. To "stand" (or otherwise, to be located) at one point and another simultaneously is motion, and a clear contradiction.


I'm sorry, but why is this a 'contradcition'?

If what you say is correct, then objects do not so much move as expand!

Anyway, I covered this sort of reply earlier:

Quote:
Here's a nice conundrum for you (and if we stick to your abstract one dimensional world) -- this has been adapted from my site, hence the odd line-numbering:

L35: Motion implies that a body is in one place and not in; that it is in one place and in another at once.

L36: Let B be in motion and at X1.

L37: L35 implies that B is also at some other point -- say, X2.

L38: But, L35 also implies that B is at X2 and at another place; hence it is also at X3.

L39: Again, L35 implies that B is at X3, and at another place; hence it is also at X4.

L40: Once more, L35 implies that B is at X4, and at another place; hence it is also at X5.

By n successive applications of L35 it is possible to show that, as a result of the 'contradictory' nature of motion, B must be everywhere in its trajectory if it is anywhere, all at once.

The only way to avoid such an outlandish conclusion would be to maintain that L35 implies that a moving body is in no more than two places at once. But even this won't help, for if a body is moving and in the second of those two places, it would not now be in motion at this second location, unless it were in a third place at once (by L15 and L35). Once again, just as soon as a body is located in any one place it is at rest there, given this odd way of viewing things.

[L15: If an object is located at a point it must be at rest at that point.]

Without L15 (and hence L35), Engels's conclusions won't follow; so on this view, if a body is moving, it has to occupy at least two points at once, or it will be at rest. But, that is just what creates the problem.

This follows from L17 (now encapsulated in L17b):

L17: A moving body must both occupy and not occupy a point at once.

L17b: A moving object must occupy at least two places at once.

Of course, it could be argued that L17b is in fact true of the scenario depicted in L35-L40 -- the said body does occupy at least two places at once namely X1 and X2. In that case, the above argument is misconceived.

The above argument would indeed be misconceived if Engels had managed to show that a body can only be in at most two (but not in at least two) places at once, which he not only failed to do, he could not do:

L17c: A moving object must occupy at most two places at once.

That is because, between any two points there is a third point, and if the body is in X1 and X2 at once then it must also be in any point between X1 and X2 at once --, say Xk. Once that is admitted, there seems to be no way to forestall the conclusion drawn above that if a moving body is anywhere it is everywhere, at once.

[The same applies to the motion of the abstract 'centre of mass' of B.]

On the other hand, the combination here of an "at least two places at once" with and an "at most two places at once" would be equivalent to an "exactly two places at once".

L17d: A moving object must occupy exactly two places at once.

L15: If an object is located at a point it must be at rest at that point.

But, any attempt made by dialecticians to restrict a moving body to the occupancy of exactly two places at once would work only if that body came to rest at the second of those two points! L15 says quite clearly that if a body is located at a point (even if this is the second of these two points), it must be at rest at that point. In that case, the above escape route will only work if dialecticians reject their own characterisation of motion, which was partially captured by L15.

[This option also falls foul of the intermediate points objection, above.]

In that case, if L15 still stands, then at the second of these two proposed points (say, X2), a moving body must still be moving, and hence in and not in that second point, at once, too.

It's worth underling this conclusion: if a body is located at a second point (say, X2), it will be at rest there, contrary to the assumption that it is moving. Conversely, if it is still in motion, it must be elsewhere also at once, and so on. Otherwise, the condition that a moving body must be both in a place and not in will have to be abandoned. So, dialecticians cannot afford to accept L17d.

Consequently, the unacceptable outcome --, which holds that as a result of the 'contradictory' nature of motion, a moving body must be everywhere along its trajectory, if it is anywhere, all at once -- still follows.

Again, it could be objected that when body B is in the second place, a new moment in time could begin.

To be sure, this amendment avoids the disastrous implications recorded above. However, it only succeeds in doing so by introducing several new difficulties of its own, for this would mean that B would be in X2 at two moments, which would plainly entail that B was stationary!

So, dialectical objects either do not move, or if they move, they not do not so much move as expand and fill their entire trajectory.

Another, perhaps less well appreciated consequence of this view of motion and change -- which, if anything, is even more absurd than the one outline above --, is the following:

If Engels were correct (in his characterisation of motion and change), we would have no right to say that a moving body was in the first of these Engelsian locations before it was in the second.

L3: Motion involves a body being in one place and in another place at once, and being in one and the same place and not in it.

This is because such a body, according to Engels, is in both places at once. Now, if the conclusions in the previous argument are valid (that is, if dialectical objects are anywhere in their trajectories, they are everywhere in them all at once), then it follows that no moving body can be said to be anywhere before it is anywhere else in its entire journey! That is because such bodies are everywhere all at once. If so they can't be anywhere first and then later somewhere else.

In the dialectical universe, therefore, there is no before and no after!

In that case, along the entire trajectory of a body's motion it would be impossible to say that that object was at the beginning of its journey before it was at the end! So, while you might foolishly think, for example, that you have to board an aeroplane (in order to go on your holidays) before you disembark at your destination, this 'path-breaking' theory tells us you are mistaken, and that you must board the plane at the very same moment as you disembark at the 'end' of your journey!

And the same applies to the 'Big Bang'. While we might think that this event took place billions of years ago, we are surely mistaken if this 'super-scientific' theory is correct. That is because any two events in the entire history of the universe must have taken place at once, by the above argument. Naturally, this means that while you are reading this, the 'Big Bang' is in fact still taking place!

To be sure, this is absurd, but that's Diabolical Logic for you!

You can read other similar conundrums, and more besides, here:

Essay Five: http://anti-dialectics.co.uk/page%2005.htm
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 05:09
So, indeed, a body being in one point x contradicts that same body is in the interval dx. You could say nothing against that. Thus, don't blame dialectics, don't even try to understand unity of opposites, let alone struggle of opposites and how this causes change, prior to understanding that contradiction. At this point you shouldn't even attempt to begin understanding what the classics in the subject have said (posting citations doesn't mean you understand what is said there). Blame only yourself for not being able to understand the most elementary notion of contradiction in the position of a body. Like I said, first and foremost, understand that when a body is in a single position x that situation is in contradiction with the situation when that same body is in the interval dx. This has nothing to do with the fact that both x and dx are functions of t but has everything to do with the fact that both x and dx pertain to the position of the body -- x is a single position, while dx is not. This is the first thing to understand before we go any further.

EDIT: I saw you have again added your incorrect explanation which stems from failing to understand the contradiction between x and dx. Motion is not described the way you imagine but has strictly defined equations to describe it: x = f(t) and dx/dt = F(t). Try to understand what these equations express and don't invent things which fit your incorrect view of motion.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 06:25
FW:

Quote:
So, indeed, a body being in one point x contradicts that same body is in the interval dx.


1. Why is this a contradiction? You keep saying it is, but have yet to explain why -- despite being asked to do so many times.

2. And, you have yet to explain how an object can move in dx. Nor have you quoted or cited a single standard text that argues this way.

Quote:
You could say nothing against that.


It's far too vague and confused for me to do this. You might just as well have posted this for all the good it did:

Quote:
So, indeed, a body being in one point x shmontradicts that same body is in the interval dx.


FW:

Quote:
Thus, don't blame dialectics, don't even try to understand unity of opposites, let alone struggle of opposites and how this causes change, prior to understanding that contradiction.


In fact, I blame you for being terminally unclear. Your maverick 'theory' doesn't even agree with Hegel and Engels on this!

Quote:
At this point you shouldn't even attempt to begin understanding what the classics in the subject have said (posting citations doesn't mean you understand what is said there).


So you keep saying, but I have asked you several times to show me where I go wrong. In response, all we get from you is deafening silence. So, the suspicion remains that you don't understand your own theory -- and so it will remain until you manage to explain it.

[And, 'explain' is not the same as 'assert'.]

Quote:
Blame only yourself for not being able to understand the most elementary notion of contradiction in the position of a body.


There's a very easy solution: explain it to me.

But, we already know that if you could do this, you'd have done it by now.

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Like I said, first and foremost, understand that when a body is in a single position x that situation is in contradiction with the situation when that same body is in the interval dx.


Yet another repetition without an explanation why this is a contradiction, when it doesn't even look like one.

Quote:
This has nothing to do with the fact that both x and dx are functions of t


But this shows that dx isn't a quantity, or even an interval. You are plainly stuck in a pre-19th century understanding of the derivative.

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but has everything to do with the fact that both x and dx pertain to the position of the body -- x is a single position, while dx is not. This is the first thing to understand before we go any further.


Yet another assertion with no explanation!

Quote:
I saw you have again added your incorrect explanation which stems from failing to understand the contradiction between x and dx.


And yet another!

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Motion is not described the way you imagine but has strictly defined equations to describe it: x = f(t) and dx/dy = F(t). Try to understand what these equations express and don't invent things which fit your incorrect view of motion.


It would help if you explained this. As things stand, there is no contradiction here.

But I am sure you'll just repeat that assertion again (with no explanation why this is a contradiction). It's all you do.

And we both know why.

[Hint for neutral observers: FW hasn't a clue why this is a 'contradiction'. Hence his prevarication and avoiding tactics.]
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 06:34
The fact that x is a function of t doesn't mean it isn't a quantity. The fact that dx is a function of t doesn't mean that dx isn't a quantity. This you should understand first before even touching on why x and dx are in contradiction. So, your problems are rooted in the very first introductory steps of scientific analysis while you're trying to tackle the advanced matters. No wonder there's such a mess in your texts. So, first things first -- prior to continuing we have to establish that you understand that both x and dx are quantities.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 06:46
FW:

Quote:
The fact that dx is a function of t doesn't mean that dx isn't a quantity


I think you are confusing a functional symbol with that it maps.

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This you should understand first before even touching on why x and dx are in contradiction.


Well, perhaps you can quote or cite a standard text that tells us that dx is a quantity, or even an interval, and that objects can move about in it. [But you'd have done that by now if you could.]

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So, your problems are rooted in the very first introductory steps of scientific analysis while you're trying to tackle the advanced matters. No wonder there's such a mess in your texts.


As predicted, you have ducked this one, yet again.

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So, first things first.


It would be even better if you learnt to be clear, and accurate, first.

And, it would help if you managed to get your own theory right!

We have already seen your quirky version disagrees with Hegel and Engels.
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 06:58
Well, now it's clear where your problem lies. You don't consider the quantity x to be a quantity and you don't consider the quantity dx to be a quantity. Like I said, don't blame it on anybody else, this is your own problem and nobody else's, least of which it is dialectic's problem. How can you ever understand anything pertaining to motion let alone its dialectical aspect if you aren't comfortable with the simple fact that x and dx are quantities? I mentioned standard texts such as the one by Planck which you may consult but I'm afraid you have to read something even more introductory than that text. For now, take it from me, both x and dx are quantities and they can be defined for every t through the equations I wrote couple of times which I won't repeat. This you have to understand, otherwise your trying to make anything of what anybody says about motion will be a futile effort on your part.

EDIT: I guess, because of your having trouble in tackling infinitesimal math, it would be easier for you to understand this matter if deltax is used instead of dx. It is especially convenient when the trajectory is a parabola.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 07:32
FW:

Quote:
Well, now it's clear where your problem lies. You don't consider the quantity x to be a quantity and you don't consider the quantity dx to be a quantity.


Where have I said x isn't a quantity?

More problematically, you continue to assert that dx is a quantity (and it seems it's a contained of some sort, too -- so that objects can move about in it!), without citing or quoting a single standard text that depicts it this way -- despite being asked repeatedly to do so.

Quote:
Like I said, don't blame it on anybody else, this is your own problem and nobody else's, least of which it is dialectic's problem.


In fact, it's tour problem, since you refuse to quote or cite a single standard text that talks this way.

Quote:
How can you ever understand anything pertaining to motion let alone its dialectical aspect if you aren't comfortable with the simple fact that x and dx are quantities?


Even more pertinent is this question: Why do you keep asserting dx is a quantity when you can't cite a single standard text that talks this way.

Quote:
I mentioned standard texts such as the one by Planck which you may consult but I'm afraid you have to read something even more introductory than that text.


Indeed, you did, and I then asked you on which page he said such things, and you went very quiet -- as you usually do when you are confronted with questions you can't answer.

But, you have failed even to cite an elementary text that says dx is a quantity or an interval.

Quote:
For now, take it from me, both x and dx are quantities and they can be defined for every t through the equations I wrote couple of times which I won't repeat. This you have to understand, otherwise your trying to make anything of what anybody says about motion will be a futile effort on your part.


I'd like to take it from you, but since you can't even get Hegel and Engels right, I think it wise to retain a healthy scepticism.

-------------------

FW:

Quote:
I guess, because of your having trouble in tackling infinitesimal math, it would be easier for you to understand this matter if deltax is used instead of dx. It is especially convenient when the trajectory is a parabola.


Once more, which standard text (page references please!) talks the way you do?
"The emancipation of the working class will be an act of the workers themselves."
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Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 07:43
Together with the rest of the problems you have regarding scientific analysis you are unaware, as I already said, that even if there are standard texts, they cannot be used as arguments in a discussion such as this one. Arguments and counter-arguments are exchanged, based on the claims at hand, excluding arguments from authority. It is especially easy in this case, because it is trivial. Like I said, dx is a quantity because it is defined through the equation dx = F(t)dt. The two letters, dx, symbolize a differential which is the main part of the change of F(t). Thus, the differential dx has a value; that is, it is a quantity. I shouldn't even have to explain that because it goes without saying. I'm doing it especially for you because, as evident, you're struggling with the infinitesimal math. I suggested that, because of the trouble you have with infinitesimal math, to consider deltax instead of dx. In this way you will clearly see the difference of two x's making up the deltax, which will also help you to comprehend it as a quantity.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
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Pioneer
Post 28 Jun 2012, 08:06
FW:

Quote:
Together with the rest of the problems you have regarding scientific analysis you are unaware, as I already said, that even if there are standard texts, they cannot be used as arguments in a discussion such as this one


They can (and must) if you keep claiming non-standard interpretations of dx (and one that I certainly didn't come across in my mathematics degree, and haven't seen since, even though I have taught mathematics for over 20 years). If your view of, say, dx is just standard 'math' as you claim, then you'd be able to cite or quote (with page references) a standard text that treats dx in the same way as you.

The fact that you have serially refused to do this tells us all we need to know: you have simply made this up.

Quote:
Arguments and counter-arguments are exchanged, based on the claims at hand, excluding arguments from authority. It is especially easy in this case, because it is trivial. Like I said, dx is a quantity because it is defined through the equation dx = F(t)dt. The two letters, dx, symbolize a differential which is the main part of the change of F(t). Thus, the differential dx has a value; that is, it is a quantity. I shouldn't even have to explain that because it goes without saying. I'm doing it especially for you because, as evident, you're struggling with the infinitesimal math. I suggested that, because of the trouble you have with infinitesimal math, to consider deltax instead of dx. In this way you will clearly see the difference of two x's making up the deltax, which will also help you to comprehend it as a quantity.


Once more you confuse repetition with proof: if you are right in what you say, and this is all standardly accepted theory, then there'd be literally hundreds of texts that say what you say about dx, that it is a quantity, and an interval, and objects can move about in it!

You need to stop prevaricating.
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 08:13
I am right in what I say because it is obviously trivial. There's nothing more to it than noticing trivially that dx being equal to F(t)dt does have a value at a given t; that is, dx is a quantity. No need to cite anything with regard to trivialities such as this one. Your or anybody else's degree doesn't matter in this case so don't give it as an argument.
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Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 13:49
Ok, I have downloaded a copy of Max Planck's book (in djvu format). However, I can't see in it any reference to dx being a quantity, or an interval, and that objects can move about in it, or that there is a contradiction in there somewhere.

Perhaps you dreamt it?

Or, serial fibber that you are, you just made this up.


Unless, of course, you can give me a page reference...

[Ha! Some hope!]

Quote:
I am right in what I say because it is obviously trivial. There's nothing more to it than noticing trivially that dx being equal to F(t)dt does have a value at a given t; that is, dx is a quantity. No need to cite anything with regard to trivialities such as this one. Your or anybody else's degree doesn't matter in this case so don't give it as an argument.


So, we only have your word for it that dx is a quantity, or an interval, and that objects can move about in it.

Now, why didn't you say so at the beginning, instead of pretending that this is standard 'math'?
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 14:06
No, it is not only my word that dx is a quantity but this is standard math. That's the basis of calculus. As I said more than once, you should stop asking me for references on that matter because they are plentiful and you can find them in any calculus book. Of course, authors such as Planck take that elementary fact for granted and will not spend time on defining elementary things. I gave Planck's text as a reference to show you how motion is described by observing the motion of a material point, which you spent a lot of time denying. Also we can do without the uncalled for snide remarks.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
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Pioneer
Post 28 Jun 2012, 15:11
FW:

Quote:
No, it is not only my word that dx is a quantity but this is standard math. As I said more than once, you should stop asking me for references on that matter because they are plentiful and you can find them in any calculus book.


Well, until you provide the missing citations from standard texts (not even Max Planck calls dx an interval, nor does he tell us that bodies can move about in it), this repeated claim of yours can be seen for what it is: pure invention.

It would be very easy to shut me up: provide a quotation from or a citation to a standard text (in physics or mathematics) -- and provide page references (since we know by know how slippery you are) -- that speaks of the calculus in the way you do.

I can't find such a reference in any of the many books on the calculus I have in my library (both Introductory and Advanced texts).

Ah, now we come to the give-away:

Quote:
Of course, authors such as Planck take that elementary fact for granted and will not spend time on defining elementary things. I gave Planck's text as a reference to show you how motion is described by observing the motion of a material point, which you spent a lot of time denying. Also we can do without the uncalled for snide remarks.


But, not even elementary books on the calculus argue the way you do -- or if they do, you will surely be able to cite one that does. None of the ones I have used (which I have employed to teach 16-18 year olds basic Differentiation -- printed by Cambridge University Press, too) tell us that dx is a quantity, or that it is an interval, or that objects can move about in it.

Sure, Max Planck describes the motion of a point (but he does not call it a 'mathematical point', so we still require a standard text that tells us mathematical points can move -- when I have shown they can't) in Chapter One: 'Motion Along A Straight Line', but he nowhere tells us that dx is a quantity, or that it is an interval and that bodies can move about in it.

So, no advanced or elementary text can be cited that supports your odd claims about dx -- or if they can, you have yet to offer one in your defence -- in which case it looks like you have just made this up.

Or, which is much more likely, you are still stuck in a pre-19th century view of the calculus, where theorists did used to talk this way (but even they didn't talk about dx being an interval in which bodies could move!).

Check out these standard texts:

Baron, M. (1969), The Origins Of The Infinitesimal Calculus (Pergamon Press).

Edwards, C. (1979), The Historical Development Of The Calculus (Springer-Verlag).

Boyer, C. (1959), The History Of The Calculus And Its Conceptual Development (Dover).

Or, this philosophically/mathematically illuminating study:

Kitcher, P. (1984), The Nature Of Mathematical Knowledge (Oxford University Press).

So, and once more, stop prevaricating: if this is indeed standard mathematics, as you claim, then you will be able to cite or quote a standard text (elementary or otherwise) -- giving page references -- that argues the way you do.
"The emancipation of the working class will be an act of the workers themselves."
Soviet cogitations: 79
Defected to the U.S.S.R.: 30 May 2012, 00:59
Unperson
Post 28 Jun 2012, 15:28
Like I said, a discussion need not get into elementary notions such as what dx is in mathematics. Nevertheless, and probably this should be the last time to get into such freshman type trivialities, here's the first link of many that pops-up when typing 'dx in mathematics': http://www4.ncsu.edu/unity/lockers/user ... rs/dx.html. Read it and somehow try to understand it to avoid sidetracking the discussion. Now, as for 'material point', you can consult, for instance, most of the standard physical chemistry textbooks such as Atkins, Moore etc. This is a non-issue and we should not waste any more time on it.
Soviet cogitations: 231
Defected to the U.S.S.R.: 08 Nov 2010, 22:13
Ideology: Trotskyism
Pioneer
Post 28 Jun 2012, 17:32
FW:

Quote:
Like I said, a discussion need not get into elementary notions such as what dx is in mathematics.


So, you can't point even to an elementary text that speaks of dx in the way you do.

Fine, at least we now know you made this all up -- as suspected.

So, what do you do instead? You do a hurried Google search -- which means that you can't cite a standard text in support of your quirky view of mathematics, since citing just one such text would have taken you far less time to do -- or, what is far more likely, you actually tried to find a standard text that talks the way you do, and found that none of them do:

Quote:
Nevertheless, and probably this should be the last time to get into such freshman type trivialities, here's the first link of many that pops-up when typing 'dx in mathematics': http://www4.ncsu.edu/unity/lockers/user ... rs/dx.html. Read it and somehow try to understand it to avoid sidetracking the discussion.


Unfortunately, the above is not a standard text -- or if it is, perhaps you can tell me when and where it was published, so I can obtain a copy and check it for myself.

Indeed, for all we know, this could be a page you wrote! It certainly hasn't been peer reviewed. Or if it has, can we have the details?

But, what does this non-standard page actually say:

Quote:
You remember talking about Dx in a precalculus course. It represents a distance along the x-axis; or, to put it another way, the difference between any two values of x. Well, dx means exactly the same thing, with one key difference: it is a differential distance, which is a fancy way of saying very, very, very small. In technical terms, dx is what happens to Dx in the limit when Dx approaches zero.

Now, when you have a quantity whose value is virtually zero, there's not much you can do with it. 2+dx is pretty much, well, 2. Or to take another example, 2/dx blows up to infinity. Not much fun there, right?

But there are two circumstances under which terms involving dx can yield a finite number. One is when you divide two differentials; for instance, 2dx/dx=2, and dy/dx can be just about anything. Since the top and the bottom are both close to zero, the quotient can be some reasonable number. The other case is when you add up an almost infinite number of differentials: which is kind of like an almost infinite number of atoms, each of which has an almost zero size, adding up to a basketball. In both of these cases, differentials can wind up giving you a number greater than zero and less than infinity: an actually interesting number. As you may have guessed, those two cases describe the derivative and the integral, respectively. So let's talk a bit more about those, one at a time.


But, this is precisely the pre-19th century view of the calculus (with the word 'limit' thrown in for good measure) I mentioned earlier.

Even so, we have established that you are physically capable of citing a text that seems to support your view (except even the above does not say a moving object is capable of moving about in dx), so what it stopping you citing a published standard text that does this?

By citing this non-standard source, you have conceded the point that it is important to substantiate your odd claims about dx, so why not do this properly: cite a standard, or even an elementary (standard) published text that does this?

[Well, we both know why -- there aren't any -- or, at least, none that were published after Cauchy and Weierstrass's work in this area.]

FW:

Quote:
Now, as for 'material point', you can consult, for instance, most of the standard physical chemistry textbooks such as Atkins, Moore etc. This is a non-issue and we should not waste any more time on it.


So, now you switch to a few vague allusions to physical chemistry books (with no page references -- no surprise there!).

Fortunately, I have a copy of Atkins (2006 edition) and it nowhere tells us that material points are mathematical points. Or, if you think it does, can you tell me which page to turn to? [Ha! Some hope!]

Quote:
This is a non-issue and we should not waste any more time on it.


It can't be a non-issue since it is central to your quirky view of physics, mathematics and now physical chemistry.

I have the books in front of me, so this is an ideal opportunity for you to shut me up -- give me an exact citation.

[Prediction: expect yet more prevarication...]
"The emancipation of the working class will be an act of the workers themselves."
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Post 28 Jun 2012, 18:11
Rosa, Belligerent behavior will not win you an argument or and friends here. Remember our forum rule about being CIVIL at all times


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