The field as continuum -Split from How does a higg's field

PeterJ · March 20, 2013

Sorry.not quiet what I was getting at.what is the graininess,the distance between each point of space-time,if every point is considered as zero dimension then all of space-time would occupy zero dimension?

Ah. Not just me then. This naive question has bothered me for a long time. It's not particularly associated with the Higgs field, Any theory that has space as a collection of points seems to run into this problem. Logically, it seems to me, spacetime must be a continuum, but a continuum would be a unity, and as Leibnitz points out a unity cannot have parts and so cannot be extended,.

Maybe this seems like idle hair-splitting or useless philosophising in this context, but I feel it may tell us something very profound about spacetime.

**imatfaal** · March 20, 2013

Depends on how and what you define as a continuum - most modern definitions of a continuum directly contradict your statement "but a continuum would be a unity". It is clear that space time is not a group of continua but is one single undivided continuum - yet the nature of a continuum is that whilst it is undivided it must also be capable of being divided in to smaller and smaller parts without ever reaching a termination in a smallest possible divisible part (the basis of leibniz saying "natura non facit saltus". )

PeterJ · March 20, 2013

I see what you're saying. I appreciate that we can define a continuum in ways that would not make it a Leibnitzean unity. But how can we call something a continuum and then say it is infinitely divisible? How can say that an infinitely extended spacetime is made out an infinite quantity of unextended parts?

For me a continuum would be the very opposite of a collection of parts, and an infinte quantity of 'ghosts of departed quantities' would not be big enough to measure. When we assume otherwise we end up wtih a paradoxical spacetime. Your answer explains how we can deal with this paradox in physics but it does not make it go away.

I believe that this paradox arises because we are reifying a spacetime that is not really there, and that spacetime appears paradoxical to us because its existence as anything more than a conceptual imputation would contradict our reason. That is to say, it would be our concept of spacetime that is paradoxical and not the phenomenon itself. This would explain why, in metaphysics, it can be demonstrated that the existence of an extended spacetime would contradict our reason. This is the central problem of metaphysics, that our usual idea of 'existence' is paradoxical. In this case our notion of spacetime is bound to be paradoxical.

It seems inevitable to me that spacetime will remain a paradoxical idea in physics until the problem is solved in metaphysics. It is not that physics cannot solve it, but it is such a deep problem that any solution would have to take the form of a fundamental theory and thus a metaphysical one. In metaphysics no exclusively physical theory works. If it did then metaphysics would be unnecessary.

So there seem to be two solutions for spacetime, Either we say that it is a mystery, for how it can be both a series of points and a continuum at the same time? Or we say that it is neither, and that it is our concept of spacetime that is paradoxical, not the phenomenon itself. ,

Some physicists have expressed doubts about the reality of spacetime, and I think they;re on the right track.

At any rate, this would be my approach to answering the question about why all Higg's bosons aren't always in the same time and place. For a fundamental theory there would be no time and place for them to be, just as metaphysics would suggest.

I believe that this is what Zeno was trying to show us all that time ago. There is something very odd about our folk-psychological notions of space, time, motion, change,and so forth, which is that we cannot make sense of them.

. .

.

,

ajb · March 21, 2013

Depends on how and what you define as a continuum - most modern definitions of a continuum directly contradict your statement "but a continuum would be a unity".

In relation to space-time we mean nonempty, compact, connected Hausdorff space. More usually this has this space as the structure of a smooth manifold. I think there are weaker versions of continuum in use, just ask your friendly neighborhood topologist. Edited March 21, 2013 by ajb

PeterJ · March 21, 2013

Hmm. From a dictionary...

"a continuous sequence in which adjacent elements are not perceptibly different from each other, but the extremes are quite distinct"

and

"a series of events. changes, features etc that all have a particular quality to different degrees"

By these defintions my use of 'continuum' is plain wrong. .

But to me these defintions describe an imperfect continuum, where some property is continuus but not all. I was using the word to mean a perfect contimuum, where no properties differ, Seems I need another word for this. . . ,

Edited March 21, 2013 by PeterJ

kristalris · March 21, 2013

IMO it depends what you take to be true a priori. That will determine the outcome of your question.

I.e. if you take that the prime suspect of mass murdering Mother Nature to be Illona Illusionist or another suspect? (I.e. suspect: to difficult for man to comprehend, suspect: extremely difficult yet unlikely but true; suspect God? et cetera).

You have to choose before you can answer your question. (BTW having as suspect doesn't mean it's the culprit. It means you should put effort in eliminating the suspect of the suspect list. Prime suspects first. You work that via taking it that the suspect is the culprit as a hypothesis.)

If you choose as a prime suspect MN as an illusionist (i.e. the basic truth can be found relatively quick, given rigorously only looking at observed facts AND answering all questions) then you may assume space as basically infinite and absolutely void per definition. Yet filled with stuff that is un-split-able (i.e. the actual yet as yet unobserved atom or atoms). These atoms then create the observed illusion of curved space. (You may then immediately assume these atoms to have volume and mass yet themselves not have gravity (thus then per definition be matter-less) yet cause gravity.

You may then also assume that MN is and has always been on the move. If so, then the concept of time is then per definition a convention. I.e. if you just run around you don't need the concept of time in order to do that. You do need a concept of time when you want to describe what you observe. If the easiest way is to have time as being relative in curved space than so be it. That doesn't mean then that time actually slows down, you then only observe the clock slow down.

I think most physicists would agree that time is - per definition - what the clock reads.

Given this a priori that would then answer your question as a concept.

If you on the other hand take MN as prime suspect that it is extremely difficult and an extremely improbable scenario to be true then as a dogma only working from what you observe gives: nothing moves > c and time is always at the deepest level relative, then you will end up having to believe that something comes from nothing and it all being a one off. And you ending up in an as yet - even as concept - unsolvable conundrum.

So if you ask questions like these then you must a priori answer all questions (as a guess or what ever). So there are several answers possible, only very few of which will provide you with a testable concept. Being the latter the practical reason for the mental exercise.

edit: BTW it is Occams razor that provides an answer to who is the prime suspect. I.e. what is the easiest way to solve the problem at a concept level at least? Illona illusionist wins that hands down, per definition even.

Edited March 21, 2013 by kristalris

**imatfaal** · March 21, 2013

Hmm. From a dictionary...

"a continuous sequence in which adjacent elements are not perceptibly different from each other, but the extremes are quite distinct"

and

"a series of events. changes, features etc that all have a particular quality to different degrees"

By these defintions my use of 'continuum' is plain wrong. .

But to me these defintions describe an imperfect continuum, where some property is continuus but not all. I was using the word to mean a perfect contimuum, where no properties differ, Seems I need another word for this. . . ,

Peter, I know you read and write a lot in these areas - and so much these days is setting your ground rules and definitions! As soon as one strays into an area that is, to any extent, new then all bets are off and terminiology seems to change by more or less arbitrary amounts. I think of continuum as amorphous - boring, unchanging, and the sort of thing that causes one to lose perspective (literally not metaphorically). The continuum is that which, although you know that distances are large, scale is lost; length and extension can be judged only in the presence of foreign objects. I think one can encompass and visualize a unity - and I would say that is definitionally impossible for a continuum

You might want to read some Weyl - in "das kontinuum" he investigated different forms of continuum, from the clear distinct discrete entities that make up the real number line but which also form a prototypical continuum, via space, time and space time, to the more "perfect continuum" (in your terms) which verges on the infinitely extended unity.

IMO it depends what you take to be true a priori. That will determine the outcome of your question.

I.e. if you take that the prime suspect of mass murdering Mother Nature to be Illona Illusionist or another suspect? (I.e. suspect: to difficult for man to comprehend, suspect: extremely difficult yet unlikely but true; suspect God? et cetera).

OK - so we were talking about the ontology of continuum, not sure how this relates at all.

You have to choose before you can answer your question. (BTW having as suspect doesn't mean it's the culprit. It means you should put effort in eliminating the suspect of the suspect list. Prime suspects first. You work that via taking it that the suspect is the culprit as a hypothesis.)

Right - or actually no.

If you choose as a prime suspect MN as an illusionist (i.e. the basic truth can be found relatively quick, given rigorously only looking at observed facts AND answering all questions) then you may assume space as basically infinite and absolutely void per definition. Yet filled with stuff that is un-split-able (i.e. the actual yet as yet unobserved atom or atoms). These atoms then create the observed illusion of curved space. (You may then immediately assume these atoms to have volume and mass yet themselves not have gravity (thus then per definition be matter-less) yet cause gravity.

If there are atoms then the point is moot. We are talking about the gap - the nothingness - that may or may not exist in that state; but be that as it may, the question was about the void.

You may then also assume that MN is and has always been on the move. If so, then the concept of time is then per definition a convention. I.e. if you just run around you don't need the concept of time in order to do that. You do need a concept of time when you want to describe what you observe. If the easiest way is to have time as being relative in curved space than so be it. That doesn't mean then that time actually slows down, you then only observe the clock slow down.

I think most physicists would agree that time is - per definition - what the clock reads.

Time is what you measure with a clock might be slightly more apposite; time is, more often than not, not what the clock reads

Given this a priori that would then answer your question as a concept.

If you on the other hand take MN as prime suspect that it is extremely difficult and an extremely improbable scenario to be true then as a dogma only working from what you observe gives: nothing moves > c and time is always at the deepest level relative, then you will end up having to believe that something comes from nothing and it all being a one off. And you ending up in an as yet - even as concept - unsolvable conundrum.

Again, are you sure this is the thread you meant to post in?

So if you ask questions like these then you must a priori answer all questions (as a guess or what ever). So there are several answers possible, only very few of which will provide you with a testable concept. Being the latter the practical reason for the mental exercise.

If the answer to all questions is an a priori necessity why would you want to ask any more questions?

edit: BTW it is Occams razor that provides an answer to who is the prime suspect. I.e. what is the easiest way to solve the problem at a concept level at least? Illona illusionist wins that hands down, per definition even.

I may regret asking this - but WhoTF is Illona the Illusionist?

PeterJ · March 21, 2013

Peter, I know you read and write a lot in these areas - and so much these days is setting your ground rules and definitions! As soon as one strays into an area that is, to any extent, new then all bets are off and terminiology seems to change by more or less arbitrary amounts. I think of continuum as amorphous - boring, unchanging, and the sort of thing that causes one to lose perspective (literally not metaphorically). The continuum is that which, although you know that distances are large, scale is lost; length and extension can be judged only in the presence of foreign objects. I think one can encompass and visualize a unity - and I would say that is definitionally impossible for a continuum

Yes, the words are such a problem. One reason I post here is to practice getting my words to line up with the way they are used in physics. It's quite easy to say something that makes perfect sense in metaphysics but which is pure goobledygook in physics and makes one look a right idiot. I need to understand more about the various uses of 'continuum' and 'unity' in physics,

I think we do not disagree about continuums and unities. For me it would be definitionally impossible to conceive of either a unity or a continuum, for in their most minimal state they would be the same thing. So we agree on this, but are defining 'unity' differently.

Thanks for the mention of Weyl's "das kontinuum". I will definitely be having a look at it, I'll be amazed if I can understand the mathematics.

I would question the use of 'continuum' to describe... 'the clear distinct discrete entities that make up the real number line but which also form a prototypical continuum'. This seems to be the very opposite of a continuum, just a collection of discrete entities. If we want to call it a continuum, would we not have to assume that there is a continuous medium underlying or joining up all these discrete entitites - real numbers, Higg's bosons or whatever - an empty number line prior to the numbers, or in physics something like an aether? To call the discrete entitites that populate the real number line a 'continuum' seems to be misuse of the word. To call the Higg's field a continuum would seem dodgy to me, and this may be what prompts the OP's question. If it isn't, then what is?

Because I take 'unity' to mean the same as 'continuum' you'll see why for me an 'infinitely extended unity' would be an impossble object. By 'perfect continuum' I would mean a phenomenon which has no parts and is thus a unity.

Is there a better term for what I mean by 'pefect continuum'?

It seems to me that what you would call an 'ideal condensate' is about as close to a 'perfect' unity or continuum as one can get, either conceptually or observationally, before it becomes unextended and inconceivable. Do you see what I mean? Or is that more goobledygook?

kristalris · March 21, 2013

OK - so we were talking about the ontology of continuum, not sure how this relates at all

http://en.wikipedia.org/wiki/Continuum_mechanics#Concept_of_a_continuu

this is what I'm talking about. If the thread is on an other topic then I'm mistaken.

Problem with disappearing quote box:

Right - or actually no.

end quote

Clarify why you think not then.

If there are atoms then the point is moot. We are talking about the gap - the nothingness - that may or may not exist in that state; but be that as it may, the question was about the void.

I'm talking about atoms in their historic philosophical context and not current atoms. I.e. un-split-table stuff that might or might not exist as the stuff that is not void in a void. If we are talking about a void sec then we are talking about per definition nothing. Only "solvable" if you believe in the contradiction of Krauss et all with his something from nothing. So that is why you first have to answer prior questions. I.e. relevant questions.

If we are talking about a pure mathematical problem then I misread the topic, due to the mentioning of the Higgs field et cetera.

Time is what you measure with a clock might be slightly more apposite; time is, more often than not, not what the clock reads

Well according to Wikipedia this definition is uncontroversial: maybe you should oppose that Wikipedia page then .http://en.wikipedia.org/wiki/Time

Quote:

Some simple, relatively uncontroversial definitions of time include "time is what clocks measure"^[7]^[15]

^{End quote.}

Again, are you sure this is the thread you meant to post in?

No

If the answer to all questions is an a priori necessity why would you want to ask any more questions?

I meant of course all relevant prior questions. Are we talking an infinite absolute void? A void as an "aether" of nothingness that fills up space between two theoretical points, i.e. a pure mathematical problem? If so, then I'm in the wrong thread. As soon as you start talking Higgsfield et cetera however much more relevant questions have to be answered before the question at hand can be answered.Questions such as: infinite space / void? Stuff with a volume as an actual un-split-able atom? If the answer is "yes" you immediately answer the question at hand. All empty space as an absolute void exists then at any moment in time and not as a sort of singularity of nothing as I understand the OP.

I may regret asking this - but WhoTF is Illona the Illusionist?

You clearly don't know what a metaphor is then, because I explained what it stands for.

PeterJ · March 22, 2013

Well, I expect he did regret asking,

I have trouble following you, kristalris, but I do not see any disagreement here, just different perspectives on the problem.

Wikepedia says:

"Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of etc.etc. "

This seems to sum up one issue. We can think of a series of points as a continuum, but this does not make it one. We can do the mathematics of spacetime by modelling it as a sea of points and calling this a continuum, but this is to create the paradox.that leads to OPs question.

By the definition I prefer, a true continuum would be indivisible and unextended. Also inconceivable, for reasons given by Imatfaal.

kristalris · March 22, 2013

Well, I expect he did regret asking,

I wouldn't, because as you in the OP stated it IMO provides the possibility of profound insights into space time.

I have trouble following you, kristalris, but I do not see any disagreement here, just different perspectives on the problem.

I don't see any disagreement either. Indeed different perspectives. The question is which one is your topic?

Wikepedia says:

"Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of etc.etc. "

Bear in mind I'm talking of atoms in an historic philosophical context: http://en.wikipedia.org/wiki/Atom#Atomism

This seems to sum up one issue. We can think of a series of points as a continuum, but this does not make it one. We can do the mathematics of spacetime by modelling it as a sea of points and calling this a continuum, but this is to create the paradox.that leads to OPs question.

By the definition I prefer, a true continuum would be indivisible and unextended. Also inconceivable, for reasons given by Imatfaal.

That is exactly the reason for me to point out to you the necessity to choose. This is dependent on your prior choices / answers on the relevant prior questions.

You want unification yet make implicit choices that prevent unification, hence the problem.

To narrow it down for you: you have five choices:

a. a pure mathematical problem (excludes Higgs et cetera for the time being, that you included in your OP);

b. something from nothing (i.e, what Krauss et all are on about) (Being IMO neigh absolutely dis-proven, because a contradiction)

c. having one or more sorts of (historical) atoms on the move being in one point of time (thus then stationary) a near void space and in a short time frame creating an illusion of a static solid in space (your table for instance) yet being a dynamic solid (historical atom or atoms) of sorts. (IMO extremely probably correct, and completely consistent with current science.) In fact then thus proving hidden variables to the standard model.

d. something else: God, Magic et cetera: all extremely improbable (and thus disproven IMO, and practically no one in science holds this position as far as I know as a scientific explanation. Except Krauss et all because choice "b" constitutes magic: belief in a contradiction.)

e. Ignoring the problem (per definition unscientific) Mostly held and personally safe position: you regret asking the question:

Edited March 22, 2013 by kristalris

PeterJ · March 22, 2013

(This is not what I meant by 'regretting asking the question'. I was referring to your seemingly rude reply to imatfaal. No matter)

Your list seems a good one, but there's another possibility.

There is a dilemma here but we are not forced to choose between the horns of it. You may be forgetting compatabilism, the idea that spacetime is not a continuum or a series of points. Remember, it is our concept of spacetime that we are discussing, not the thing itself. Our usual concept is paradoxical, this is clear, but it would not follow that spacetime is paradoxical. Usually where a concept is paradoxical we abandon it.

I agree with what you say mostly, but not when you say that 'there is a necessity to choose'. I'm suggesting that there is a solution and it would require that we do not choose. This would be a general solution for metaphysical problems, which all take the form of a dilemma and seem to present us with a necessity to choose, but which can be solved by not choosing and opting for compatabilism.

By this view spacetime would be a series of points and a continuum, depending on how we wish to conceive of it for our practical purposes, but which for an ultimate view, or by reduction, would be neither. It would seem paradoxical only because of the way we think about it, not because it is a true contradiction.

I daren't delve too deep into this because it would be innapropriate here, but in brief I would suggest that spacetime is a metaphysical problem, so must be solved in the same way as all metaphysical questions. Or to put it another way, the current view in physics, by which spacetime is paradoxical, would be nonreductive. The solution would be to reduce the continuum and the series of points to a phenomenon that has these two properties as aspects, and not to attempt to make a continuum and a series of points the same thing by using very loose definitions, or to choose one view over the other.

Otherwise we are forced to suppose that there are true contradictions, as does Melhuish, Priest, Routley and, or so it seems from what you say. Krauss et al.

kristalris · March 22, 2013

(This is not what I meant by 'regretting asking the question'. I was referring to your seemingly rude reply to imatfaal. No matter)

I didn't mean to be rude to anyone, and haven't been so either I gather.

Your list seems a good one, but there's another possibility.

Very good, thanks, now let's see on this other possibility:

There is a dilemma here but we are not forced to choose between the horns of it. You may be forgetting compatabilism, the idea that spacetime is not a continuum or a series of points. Remember, it is our concept of spacetime that we are discussing, not the thing itself. Our usual concept is paradoxical, this is clear, but it would not follow that spacetime is paradoxical. Usually where a concept is paradoxical we abandon it.

Ah, the problem here I've now come across several times: that is that physicists like to euphemistically call a contradiction a paradox. And subsequently quite a few of them get the two mixed up. A paradox is seemingly a contradiction, thus not a contradiction at all: yet an illusion for instance. A contradiction can't be in science, because that would entail believing in magic.

Now I'm a bit at a loss. Your OP starts off with a given continuum yet now you leave that be and thus become off topic it seems.Yet it is your thread so I guess you may state on this topic the possibility of there not being a continuum at all. Which you then continue doing under the heading compatibilism. Well given the strong probability of the Higgs field by current science and that having to be an omnipresent field in our entire visible universe everywhere where normal atoms can be presumed to exist, a continuum for our visible universe has at least to be probable as well in current science.

I agree with what you say mostly, but not when you say that 'there is a necessity to choose'. I'm suggesting that there is a solution and it would require that we do not choose. This would be a general solution for metaphysical problems, which all take the form of a dilemma and seem to present us with a necessity to choose, but which can be solved by not choosing and opting for compatabilism.

By this view spacetime would be a series of points and a continuum, depending on how we wish to conceive of it for our practical purposes, but which for an ultimate view, or by reduction, would be neither. It would seem paradoxical only because of the way we think about it, not because it is a true contradiction.

The choice of not choosing is a true contradiction and isn't compatible with anything IMO. At least at a deepest level. I.e. the fact that GR and QM aren't fully compatible (yet) doesn't mean you can't practically use either. You can, they are IMO even the best laws of physics we ever had. Yet on the topic of unification, they don't meet. Given the need for unification - your topic - you then can't leave it at that.

I daren't delve too deep into this because it would be innapropriate here, but in brief I would suggest that spacetime is a metaphysical problem, so must be solved in the same way as all metaphysical questions. Or to put it another way, the current view in physics, by which spacetime is paradoxical, would be nonreductive. The solution would be to reduce the continuum and the series of points to a phenomenon that has these two properties as aspects, and not to attempt to make a continuum and a series of points the same thing by using very loose definitions, or to choose one view over the other.

I only accept meta physics (I'd prefer to call it philosophy) i.e. asking and answering questions that can't be observed such as: "is the universe infinite or not?" as a practical means to an end to find out where to start looking for testable positions.

Otherwise we are forced to suppose that there are true contradictions, as does Melhuish, Priest, Routley and, or so it seems from what you say. Krauss et al.

Not true: position c doesn't pose any such problem, is testable and thus falsifiable and based on pure evidence based logical deduction.

Edited March 22, 2013 by kristalris

PeterJ · March 22, 2013

I didn't mean to be rude to anyone, and haven't been so either I gather.

Sorry. I must have misread the comment.

Can't get the hang of the quotes system. I'll do a dialogue.

:

R - Ah, the problem here I've now come across several times: that is that physicists like to euphemistically call a contradiction a paradox. And subsequently quite a few of them get the two mixed up. A paradox is seemingly a contradiction, thus not a contradiction at all: yet an illusion for instance. A contradiction can't be in science, because that would entail believing in magic.

P - Not quite. Check out 'Dialethism', For dialethism there would be true contradictions but no magic. A true contradiction is a true paradox, I would say, while many so-called contradictions and paradoxes are in the eye of the beholder.

.

R - Now I'm a bit at a loss. Your OP starts off with a given continuum yet now you leave that be and thus become off topic it seems.Yet it is your thread so I guess you may state on this topic the possibility of there not being a continuum at all. Which you then continue doing under the heading compatibilism. Well given the strong probability of the Higgs field by current science and that having to be an omnipresent field in our entire visible universe everywhere where normal atoms can be presumed to exist, a continuum for our visible universe has at least to be probable as well in current science.

P - . Ah, A misunderstanding. No, I am not the thread starter. You are assuming here that a continuum can be extended. This is exactly what I am arguing against. I'm suggesting that this is a logical contradiction.

R - The choice of not choosing is a true contradiction and isn't compatible with anything IMO.

P - It is not a contradiction. It is the reduction of two categories, and thus the solution to a contradiction. It may seem 'illogical', but it is not a contradiction according to Aristotle's rules.

R - I only accept meta physics (I'd prefer to call it philosophy) i.e. asking and answering questions that can't be observed such as: "is the universe infinite or not?" as a practical means to an end to find out where to start looking for testable positions.

P - There are no testable positions,. This is why they are metaphysical problems. You have to make up your mind on the basis of human reason.

kristalris · March 22, 2013

Sorry. I must have misread the comment.

Can't get the hang of the quotes system. I'll do a dialogue.

Put the marker at the end of the quote you want to take and double click. Then a white bit appears and place your remark in there. That said I also have problems with quote-boxes suddenly seemingly ad random disappearing. Anyway still learning.

:

R - Ah, the problem here I've now come across several times: that is that physicists like to euphemistically call a contradiction a paradox. And subsequently quite a few of them get the two mixed up. A paradox is seemingly a contradiction, thus not a contradiction at all: yet an illusion for instance. A contradiction can't be in science, because that would entail believing in magic.

P - Not quite. Check out 'Dialethism', For dialethism there would be true contradictions but no magic. A true contradiction is a true paradox, I would say, while many so-called contradictions and paradoxes are in the eye of the beholder.

Well I disagree with dialethism. It's IMO a form of defeatism or appeasement. I.e. you then for instance accept that we humans are say to stupid to comprehend Mother Nature. Now that might be true, yet we can't accept that until we've truly run out of options. And we haven't IMO.

But I now, thanks to you have seen that in Dutch a paradox only means a true paradox and in English it can mean both a fallacy and a seeming fallacy. Thus becoming quite meaningless in English without succinct context or an adjective.

.

R - Now I'm a bit at a loss. Your OP starts off with a given continuum yet now you leave that be and thus become off topic it seems.Yet it is your thread so I guess you may state on this topic the possibility of there not being a continuum at all. Which you then continue doing under the heading compatibilism. Well given the strong probability of the Higgs field by current science and that having to be an omnipresent field in our entire visible universe everywhere where normal atoms can be presumed to exist, a continuum for our visible universe has at least to be probable as well in current science.

P - . Ah, A misunderstanding. No, I am not the thread starter. You are assuming here that a continuum can be extended. This is exactly what I am arguing against. I'm suggesting that this is a logical contradiction.

Are there two PeterJ's? A continuum can be limited or unlimited whatever you like IMO. I.e. you fill up the holes in a limited or unlimited space. I don't see any logical contradiction either way, or I don't know what you mean by an extended continuum.

R - The choice of not choosing is a true contradiction and isn't compatible with anything IMO.

P - It is not a contradiction. It is the reduction of two categories, and thus the solution to a contradiction. It may seem 'illogical', but it is not a contradiction according to Aristotle's rules.

At the same time choosing and not choosing something given the same choice is a contradiction IMO according to Aristotle's rules.

R - I only accept meta physics (I'd prefer to call it philosophy) i.e. asking and answering questions that can't be observed such as: "is the universe infinite or not?" as a practical means to an end to find out where to start looking for testable positions.

P - There are no testable positions,. This is why they are metaphysical problems. You have to make up your mind on the basis of human reason.

Well yes and no. Indeed the question whether the universe is infinite or not is inherently un-testable. Yet if you take (choose) it to be infinite for instance and you fill in a lot of other questions in so doing answering all relevant questions, in a logical way, then that can lead to testable predictions. Leading for instance to an idea how to simulate certain ways in which particles can go to order instead of disorder. If it shows that it goes to order you've achieved a major breakthrough.

You can play the same game in which you take the universe to be finite and answer all the relevant questions that way.

If the one way provides you with an elegant testable concept, then you should subsequently test that.

Edited March 22, 2013 by kristalris

**imatfaal** · March 22, 2013

http://en.wikipedia.org/wiki/Continuum_mechanics#Concept_of_a_continuu

this is what I'm talking about. If the thread is on an other topic then I'm mistaken.

Problem with disappearing quote box:

Right - or actually no.

end quote

Clarify why you think not then.

I'm talking about atoms in their historic philosophical context and not current atoms. I.e. un-split-table stuff that might or might not exist as the stuff that is not void in a void. If we are talking about a void sec then we are talking about per definition nothing. Only "solvable" if you believe in the contradiction of Krauss et all with his something from nothing. So that is why you first have to answer prior questions. I.e. relevant questions.

Doesn't matter what sort of atoms you are talking about - if you can split it up into indivisible and discrete units then it fails most definitions of a continuum . For PeterJ - cos you will probably ask this - I presume the real number line does not fail on this measure as between any two points you care to choose is an infinity of real number in between.

If we are talking about a pure mathematical problem then I misread the topic, due to the mentioning of the Higgs field et cetera.

No - but physics cares little about absolute definitions along this lines of this one, whereas maths and philosophy do. Physics relies on observations and experiment - logical progressions are beautiful but just as likely to be wrong as right so scientists tend (but not always) to ignore them and concentrate on the emprical data.

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Well according to Wikipedia this definition is uncontroversial: maybe you should oppose that Wikipedia page then .http://en.wikipedia.org/wiki/Time

Quote:

Some simple, relatively uncontroversial definitions of time include "time is what clocks measure"^[7]^[15]

^{End quote.}

It's pernickity - but this a thread about definitions - you wrote "I think most physicists would agree that time is - per definition - what the clock reads." - I corrected it to almost the same as wiki - it is measured by a clock; but its absolute extent (ie the time that the clock reads) is a purely human construct and varies between countries and cultures.

No

I meant of course all relevant prior questions. Are we talking an infinite absolute void? A void as an "aether" of nothingness that fills up space between two theoretical points, i.e. a pure mathematical problem? If so, then I'm in the wrong thread. As soon as you start talking Higgsfield et cetera however much more relevant questions have to be answered before the question at hand can be answered.Questions such as: infinite space / void? Stuff with a volume as an actual un-split-able atom? If the answer is "yes" you immediately answer the question at hand. All empty space as an absolute void exists then at any moment in time and not as a sort of singularity of nothing as I understand the OP.

The question was is it correct to treat a continuum as a unity - introducing details about the higgs's, about speed of light, metaphors about unknown people, personifications, occam's razor etc are all complications and confusions.

You clearly don't know what a metaphor is then, because I explained what it stands for.

Thanks for explaining what a metaphor is.

Yes, the words are such a problem. One reason I post here is to practice getting my words to line up with the way they are used in physics. It's quite easy to say something that makes perfect sense in metaphysics but which is pure goobledygook in physics and makes one look a right idiot. I need to understand more about the various uses of 'continuum' and 'unity' in physics,

Continuum would have the simple mathematical definition I mentioned above - unity is not a term I have had heard physicists using in any way approaching the way you use it. Physicists would use it to mean one - real number +1 - eg the sum of all probabilities is unity, the f(X) approaches infinity as x approaches unity

.I think we do not disagree about continuums and unities. For me it would be definitionally impossible to conceive of either a unity or a continuum, for in their most minimal state they would be the same thing. So we agree on this, but are defining 'unity' differently.

No - I think we are still defining continuum differently. Can I not conceive of a point (1,0) on the cartesian plane, self-contained, unextended, indivisible. Can I not also conceive of the line y=x ?

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Thanks for the mention of Weyl's "das kontinuum". I will definitely be having a look at it, I'll be amazed if I can understand the mathematics.

I have a feeling I have a non-mathematicians crib somewhere - might be buried tho.

I would question the use of 'continuum' to describe... 'the clear distinct discrete entities that make up the real number line but which also form a prototypical continuum'. This seems to be the very opposite of a continuum, just a collection of discrete entities. If we want to call it a continuum, would we not have to assume that there is a continuous medium underlying or joining up all these discrete entitites - real numbers, Higg's bosons or whatever - an empty number line prior to the numbers, or in physics something like an aether? To call the discrete entitites that populate the real number line a 'continuum' seems to be misuse of the word. To call the Higg's field a continuum would seem dodgy to me, and this may be what prompts the OP's question. If it isn't, then what is?

But the real numbers are continuous. THey are mind-blowingly continuous - what ever scale you choose, look as the closest two numbers you can find and there is an infinity of numbers in between. I would say that the higg's field and the electromagnetic field are continuous - I am not convinced they are a continuum. The only thing I hear described physically as a continuum is space-time, and that is more poetic than philosophical in its origin. However I do think it fits the bill totally.

.Because I take 'unity' to mean the same as 'continuum' you'll see why for me an 'infinitely extended unity' would be an impossble object. By 'perfect continuum' I would mean a phenomenon which has no parts and is thus a unity.

I am not sure continuous necessarily means no parts - more that parts cannot be discerned. The line y=x is the collection of points f(x) for all x - each point can be enumerated - yet it is continuous and fulfills many of the ideas of continuum

Is there a better term for what I mean by 'pefect continuum'?

What you mean by perfect continuum - is a unity. But I think you are wrong

It seems to me that what you would call an 'ideal condensate' is about as close to a 'perfect' unity or continuum as one can get, either conceptually or observationally, before it becomes unextended and inconceivable. Do you see what I mean? Or is that more goobledygook?

I would disagree - as at some scales it would clearly still be lumpy, and you do not get lumpy disjointed continua (I think we agree on that). Fields and nothingness are the only physical (how physical is nothingness? - ed.) things that I can paint as a continuum.

.

Wikepedia says:

"Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms, and so is not continuous; however, on length scales much greater than that of etc.etc. "

We can ignore that I think.

This seems to sum up one issue. We can think of a series of points as a continuum, but this does not make it one. We can do the mathematics of spacetime by modelling it as a sea of points and calling this a continuum, but this is to create the paradox.that leads to OPs question.

By the definition I prefer, a true continuum would be indivisible and unextended. Also inconceivable, for reasons given by Imatfaal.

I think you have to explain therefore: what is the difference between a continuum and a unity? Your definitions conflate the two - and render one of the terms otiose; my usage, and I believe the accepted usage, at least preserves a difference between the two.

Actaully Peter I have in my notes about Heraclitus - "not strict monist - viewed reality as multiplicity and a unity at the same instant" . This was in my stuff about unity of opposites that he banged on about. And the followers of Heraclitus (but not he himself) felt that the void was filled with flux - which is about as close to the fields EMF and Higgs as you are likely to get from 2500 years ago

I wouldn't, because as you in the OP stated it IMO provides the possibility of profound insights into space time.

I don't see any disagreement either. Indeed different perspectives. The question is which one is your topic?

Bear in mind I'm talking of atoms in an historic philosophical context: http://en.wikipedia.org/wiki/Atom#Atomism

I really do not think the division between the atoms of leuccipus & democritus and those of rutherford & bohr this context. I maintain that as soon as an entity has discernable and unbreakable graininess - whether bits in it (rutherford) or instrinsic bits (democritus) then it fails the test of continua.

That is exactly the reason for me to point out to you the necessity to choose. This is dependent on your prior choices / answers on the relevant prior questions.

You want unification yet make implicit choices that prevent unification, hence the problem.

To narrow it down for you: you have five choices:

a. a pure mathematical problem (excludes Higgs et cetera for the time being, that you included in your OP);

b. something from nothing (i.e, what Krauss et all are on about) (Being IMO neigh absolutely dis-proven, because a contradiction)

c. having one or more sorts of (historical) atoms on the move being in one point of time (thus then stationary) a near void space and in a short time frame creating an illusion of a static solid in space (your table for instance) yet being a dynamic solid (historical atom or atoms) of sorts. (IMO extremely probably correct, and completely consistent with current science.) In fact then thus proving hidden variables to the standard model.

d. something else: God, Magic et cetera: all extremely improbable (and thus disproven IMO, and practically no one in science holds this position as far as I know as a scientific explanation. Except Krauss et all because choice "b" constitutes magic: belief in a contradiction.)

e. Ignoring the problem (per definition unscientific) Mostly held and personally safe position: you regret asking the question:

I like your list in some ways but not in others - I feel you are right to try and constrain the problem and thus make it more handleable and manageable; quite right that stating your terms is a prerequisite.

I though Peter was more asking about the ontology of the continuum - in an abstract form (ie removed from the vagaries of actual physics) so that then he could move on to answer the question of the OP which is clearly regarding the space-time continuum in modern physics. How you can extend this to Krauss, hidden variables in the standard model (of particle physics? surely not) I am not sure. Ignoring the question is often very very relevant and completely scientific - when you are considering the spacetime continuum you tend to ignore the eightfold path (both the original and murray gell-mann's rip off) because otherwise you end up unable to proceed. Scientists have to compartmentalise, aggregate, and approximate. Every problem in physics has at its ultimate and infinitesimal root a need for a theory of quantum gravity - which we do not have - and which we can safely ignore in almost every problem (cept black holes and the big bang). An agreed theory on the origin of spacetime would help us immeasureably - but we do not have one, and there is little prospect of getting one in the not too distant future, so we move on and work on what we have.

(This is not what I meant by 'regretting asking the question'. I was referring to your seemingly rude reply to imatfaal. No matter)

Your list seems a good one, but there's another possibility.

There is a dilemma here but we are not forced to choose between the horns of it. You may be forgetting compatabilism, the idea that spacetime is not a continuum or a series of points. Remember, it is our concept of spacetime that we are discussing, not the thing itself. Our usual concept is paradoxical, this is clear, but it would not follow that spacetime is paradoxical. Usually where a concept is paradoxical we abandon it.

Yes yes yes.

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I agree with what you say mostly, but not when you say that 'there is a necessity to choose'. I'm suggesting that there is a solution and it would require that we do not choose. This would be a general solution for metaphysical problems, which all take the form of a dilemma and seem to present us with a necessity to choose, but which can be solved by not choosing and opting for compatabilism.

By this view spacetime would be a series of points and a continuum, depending on how we wish to conceive of it for our practical purposes, but which for an ultimate view, or by reduction, would be neither. It would seem paradoxical only because of the way we think about it, not because it is a true contradiction.

Agree almost entirely - but not sure I even think of it as paradoxical.

I daren't delve too deep into this because it would be innapropriate here, but in brief I would suggest that spacetime is a metaphysical problem, so must be solved in the same way as all metaphysical questions. Or to put it another way, the current view in physics, by which spacetime is paradoxical, would be nonreductive. The solution would be to reduce the continuum and the series of points to a phenomenon that has these two properties as aspects, and not to attempt to make a continuum and a series of points the same thing by using very loose definitions, or to choose one view over the other.

Otherwise we are forced to suppose that there are true contradictions, as does Melhuish, Priest, Routley and, or so it seems from what you say. Krauss et al.

Our conceptualization of spacetime is metaphysical problem ...

And I still think it is more your particular reading of terms that renders the current view paradoxical rather than it being paradoxical per se - this of course adds even more weight to your argument that it is merely our philosophizing which is creating the paradox rather than discovering the inate paradox.

oh delve away.

I didn't mean to be rude to anyone, and haven't been so either I gather.

Very good, thanks, now let's see on this other possibility:

Ah, the problem here I've now come across several times: that is that physicists like to euphemistically call a contradiction a paradox. And subsequently quite a few of them get the two mixed up. A paradox is seemingly a contradiction, thus not a contradiction at all: yet an illusion for instance. A contradiction can't be in science, because that would entail believing in magic.

Until Bell's Inequalities I would have entirely agreed. And paradox is used far too much.

On the definitions and without checking - paradox surely comes from talking along beyond alongside different + opinion being glory

whereas contradiction is against + speaking. Paradox seems much weaker from the etymological view but is much stronger in the modern view. just sayin' - was curious

To defend physicists - most call very few things paradoxes; however, many things get called paradoxes despite the physicists best intents (the twin paradox - which any 1st year physics student is merely confusing and difficult but is logically sound as a bell).

Now I'm a bit at a loss. Your OP starts off with a given continuum yet now you leave that be and thus become off topic it seems.Yet it is your thread so I guess you may state on this topic the possibility of there not being a continuum at all. Which you then continue doing under the heading compatibilism. Well given the strong probability of the Higgs field by current science and that having to be an omnipresent field in our entire visible universe everywhere where normal atoms can be presumed to exist, a continuum for our visible universe has at least to be probable as well in current science.

Agree there.

...The choice of not choosing is a true contradiction and isn't compatible with anything IMO. At least at a deepest level. I.e. the fact that GR and QM aren't fully compatible (yet) doesn't mean you can't practically use either. You can, they are IMO even the best laws of physics we ever had. Yet on the topic of unification, they don't meet. Given the need for unification - your topic - you then can't leave it at that.

I am in a position of agreeing with both of you in part - yet you are adopting almost opposite positions. "Not choosing" is a valid way forward as I mentioned above. QM GR - yes agree. But the topic is not about unification, it is about leveraging one discipline to gain insight in the other.

I only accept meta physics (I'd prefer to call it philosophy) i.e. asking and answering questions that can't be observed such as: "is the universe infinite or not?" as a practical means to an end to find out where to start looking for testable positions.

Not true: position c doesn't pose any such problem, is testable and thus falsifiable and based on pure evidence based logical deduction.

I would define metaphysics as a subset of philosophy that deals with the nature of reality - ethics is philosophy but not metaphysics. If you are lookin to move to testable positions I think you are out of philosophy and into hypothetical physics; philosophy rests on logic, science rests on empiricism.

c. having one or more sorts of (historical) atoms on the move being in one point of time (thus then stationary) a near void space and in a short time frame creating an illusion of a static solid in space (your table for instance) yet being a dynamic solid (historical atom or atoms) of sorts. (IMO extremely probably correct, and completely consistent with current science.) In fact then thus proving hidden variables to the standard model.

"pure evidence based logical deduction" - this sounds like an oxymoron to me. However, this is speculative physics and not really at home here in the philosophy forum - we like to stick to philosophy and if science pokes it's nose in we prefer it is mainstream

Put the marker at the end of the quote you want to take and double click. Then a white bit appears and place your remark in there. That said I also have problems with quote-boxes suddenly seemingly ad random disappearing. Anyway still learning.

The new software has a mind of its own and sometimes thinks it knows best. Apologies. In addition to this above advice.

1. Click where you want break

2. Double return (if this doesnt work)

3. Double back cursor

4. Return again

5. Do not highlight the gap you just created and delete - it will fritz the hidden code that holds the quote. You can however (completely illogically) highlight the gap and replace with a point or a space.

Well I disagree with dialethism. It's IMO a form of defeatism or appeasement. I.e. you then for instance accept that we humans are say to stupid to comprehend Mother Nature. Now that might be true, yet we can't accept that until we've truly run out of options. And we haven't IMO.

Not at all - we hang on Aristotle's every word and enshrine his law of non-contradiction - and we don't need to. The pre-socratics were at home with paraconsistency - and the modern term springs from wittgenstein . Recursive self-contradictions are the basis of much of godels work which is some of the most beautiful and insightful in all mathematics and logic.

But I now, thanks to you have seen that in Dutch a paradox only means a true paradox and in English it can mean both a fallacy and a seeming fallacy. Thus becoming quite meaningless in English without succinct context or an adjective.

So in dutch a paradox is by definition only a state of logical self contradiction? I would say that in English this is the technical usage - but the common usage is much much wider. English - unbeknownst to many of its practitioners - is a highly contextual language; it is by no means as precise and non-arbitrary as german (i do not know enough about dutch to comment but from your paragraph I feel it may be similar to german in this respect)

Are there two PeterJ's? A continuum can be limited or unlimited whatever you like IMO. I.e. you fill up the holes in a limited or unlimited space. I don't see any logical contradiction either way, or I don't know what you mean by an extended continuum.

At the same time choosing and not choosing something given the same choice is a contradiction IMO according to Aristotle's rules.

Well yes and no. Indeed the question whether the universe is infinite or not is inherently un-testable.

Not untestable at all . If the WMAP had come back with a definied positive curvature we would have known a couple of years ago. The planck telescope is doing the same thing more precisely - and it might come back result that show positive curvature; and suddenly the universe will be unfeasibly big, but not infinite. you can never prove an infinite nature - but you can show finitude and disprove the claim of infinitude.

.Yet if you take (choose) it to be infinite for instance and you fill in a lot of other questions in so doing answering all relevant questions, in a logical way, then that can lead to testable predictions. Leading for instance to an idea how to simulate certain ways in which particles can go to order instead of disorder. If it shows that it goes to order you've achieved a major breakthrough.

Not sure how the second law applies here

.You can play the same game in which you take the universe to be finite and answer all the relevant questions that way.

If the one way provides you with an elegant testable concept, then you should subsequently test that.

PeterJ · March 22, 2013

Put the marker at the end of the quote you want to take and double click. Then a white bit appears and place your remark in there. That said I also have problems with quote-boxes suddenly seemingly ad random disappearing. Anyway still learning.

Thanks. I'm getting it.

.

Well I disagree with dialethism. It's IMO a form of defeatism or appeasement. I.e. you then for instance accept that we humans are say to stupid to comprehend Mother Nature. Now that might be true, yet we can't accept that until we've truly run out of options. And we haven't IMO.

I couldn't agree more. But it is a possible position, or some people think it is. .

But I now, thanks to you have seen that in Dutch a paradox only means a true paradox and in English it can mean both a fallacy and a seeming fallacy. Thus becoming quite meaningless in English without succinct context or an adjective.

These details cause endless problems. It's good that we're noting them and not letting them cause unnecessary arguments.

Are there two PeterJ's?

Ah. I forgot that Imfataal used my post to start this breakaway discussion. The original question about Higgs fields was not me.

A continuum can be limited or unlimited whatever you like IMO. I.e. you fill up the holes in a limited or unlimited space. I don't see any logical contradiction either way, or I don't know what you mean by an extended continuum.

This is the issue. I would say that an extended continuum is a contradiction. But I'm using a strict definition of continuum, ie an ideal continuum. A partial continuum (spacetime, the reals etc) is not one in a full sense. Imfataall sent me to read Weyl on this, and it seems that he came around to the idea that a continuum cannot be a series of points. It would be a contradiction, and if we say that spacetime is such continuum this causes insoluble problems.

At the same time choosing and not choosing something given the same choice is a contradiction IMO according to Aristotle's rules.

Don't get this one. My point was that the contradiction is between the two extreme views. If do not choose either then there is no contradiction. There is still a problem, but it is no longer a logical problem. (of course, this is still a choice). ,

Well yes and no. Indeed the question whether the universe is infinite or not is inherently un-testable.

In physics yes. But we have other means to test ideas.

Oh hell, the box disappeared.

K - Yet if you take (choose) it to be infinite for instance and you fill in a lot of other questions in so doing answering all relevant questions, in a logical way, then that can lead to testable predictions.

Me - I think this is just simply wrong. If you take it to be infinite you create a paradox and a lot of philosophical problems. This is in addition to the fatal problem that it would cause for Big Bang theory. It is not possible for physics to test the size of the universe. I agree that if we say it is one mile across this idea is testable, but such theories are obviously not worth testing. .

.

K - You can play the same game in which you take the universe to be finite and answer all the relevant questions that way.

Me - Exactly, and with same result, which is that the idea is paradoxical and causes problems. The two extreme views do not work. Luckily we do not have to choose between them, there is another option. . .

K - If the one way provides you with an elegant testable concept, then you should subsequently test that.

Me - Yes, but this is a big 'if'.,Physics cannot test metaphysical ideas, elegant or not. This is not to say they cannot be tested, but I think you mean testable in physics. Specifically, the idea that spacetime is a series of points or an ideal continuum is not testable in physics, It is treated as one or the other depending on the requirements of the situation. But for a fundamental view it cannot be both. I think I may have Weyl on my side here, but I need to read more.

Interesting discussion. I still think we agree on the main issue, but are seeing things differently.

Doesn't matter what sort of atoms you are talking about - if you can split it up into indivisible and discrete units then it fails most definitions of a continuum . For PeterJ - cos you will probably ask this - I presume the real number line does not fail on this measure as between any two points you care to choose is an infinity of real number in between.

I'm not sure I'm understanding you correctly but no. it would fail if there are two discrete points. A (perfect/ideal) continuum by my defintion could not be divided. .

No - but physics cares little about absolute definitions along this lines of this one, whereas maths and philosophy do. Physics relies on observations and experiment - logical progressions are beautiful but just as likely to be wrong as right so scientists tend (but not always) to ignore them and concentrate on the emprical data.

Yes, For such a physics we must ignore the results of human reasoning. I would not agree that this is a scientific approach to the problem but, rather, a sweeping of it under the carpet, to the detriment of scientific progress.

Continuum would have the simple mathematical definition I mentioned above - unity is not a term I have had heard physicists using in any way approaching the way you use it. Physicists would use it to mean one - real number +1 - eg the sum of all probabilities is unity, the f(X) approaches infinity as x approaches unity

Sorry but I can't follow this. It does not seem to be a defintion that would be useful beyond mathematics. (I would also call a unity a perfect symmetry, another term that will cause trouble for us). .

Oops. Deleted the box again.

Imatfaal - I think we are still defining continuum differently. Can I not conceive of a point (1,0) on the cartesian plane, self-contained, unextended, indivisible. Can I not also conceive of the line y=x ?

P - Well, we can think of what we like. The question is whether our concept is paradoxical or plausible.as a description of something 'out there' in the world. If it is paradoxical then I would call it implausible. Well. just plain wrong actually. I don't believe in real paradoxes.

Btw, I see the need to use all these words in a certain way in physics and have no complaints. It's just that this useage of the words, where they are ringed around with provisos, is very unhelpful when trying to get to the bottom of things.

Imatfaal - But the real numbers are continuous. THey are mind-blowingly continuous - what ever scale you choose, look as the closest two numbers you can find and there is an infinity of numbers in between.

PJ - Yes, in our imagination. But not in reality. A collection of numbers is clearly not continuous, since there must be something separating them. .

Imatfaal - I would say that the higg's field and the electromagnetic field are continuous - I am not convinced they are a continuum.

PJ - Now this I would find weird. For me the two words would mean the same thing. This really does seem a more sensible view to me.

Imatfaal - The only thing I hear described physically as a continuum is space-time, and that is more poetic than philosophical in its origin. However I do think it fits the bill totally.

PJ - But how can a continuum be extended? What would stop everything happening in the same place at the same time?

Imatfaal - I am not sure continuous necessarily means no parts - more that parts cannot be discerned. The line y=x is the collection of points f(x) for all x - each point can be enumerated - yet it is continuous and fulfills many of the ideas of continuum.

PJ - I have no problem with this just as long as we say that this is a definition of how we intend to use the words, and not a claim about spacetime. The line cannot be a continuum if it has discrete locations at which can be placed discrete numbers.

Perhaps we could focus on the idea that a continuum cannot have parts, since we seem to disagree directly on this. This is both a question of defintions and of philophical absolutes. By defintion a continuum can have as many parts as we like, and as many legs and arms, but the question is whether this would have anything to do with spacetime, It may be just this assumption, built into our definitions, that makes it paradoxical. This is what I'm suggesting at any rate.

Imatfaal What you mean by perfect continuum - is a unity. But I think you are wrong

PJ - Yes, this seems to be the problem. Let's focus on it. .

Imatfaal - I would disagree - as at some scales it would clearly still be lumpy, and you do not get lumpy disjointed continua (I think we agree on that). Fields and nothingness are the only physical (how physical is nothingness? - ed.) things that I can paint as a continuum.

PJ - Yes!! Well, not fields, but nothingness certainly. The question now would be what we mean by 'nothingness'.

Imatfaal - I think you have to explain therefore: what is the difference between a continuum and a unity? Your definitions conflate the two - and render one of the terms otiose; my usage, and I believe the accepted usage, at least preserves a difference between the two.

PJ - I would not want to preserve a difference. But I would be fine with the term 'incomplete continuum' or maybe 'notional continuum' and saying that this is not a unity. You said earlier, I think, that a true continuum would be inconceivable. So would a unity, and for the same reason. It is only incomplete continuums (those that have parts along some dimension) that we can conceive. .

Imatfaal - Actually Peter I have in my notes about Heraclitus - "not strict monist - viewed reality as multiplicity and a unity at the same instant" . This was in my stuff about unity of opposites that he banged on about. And the followers of Heraclitus (but not he himself) felt that the void was filled with flux - which is about as close to the fields EMF and Higgs as you are likely to get from 2500 years ago

Pj - Yes, yes, yes. This is where I'm trying to get to, an analysis of what Hercaclitus' dcorine would mean for physics. .

Imatfaal - I really do not think the division between the atoms of leuccipus & democritus and those of rutherford & bohr this context. I maintain that as soon as an entity has discernable and unbreakable graininess - whether bits in it (rutherford) or instrinsic bits (democritus) then it fails the test of continua.

Pj - Agreed. Totally.

(Losing tracfk of who said what here) .

Imatfaal? - I though Peter was more asking about the ontology of the continuum - in an abstract form (ie removed from the vagaries of actual physics) so that then he could move on to answer the question of the OP which is clearly regarding the space-time continuum in modern physics.

Kris? - Our conceptualization of spacetime is metaphysical problem ...

Spot on imho. The phenomenon itself is another matter.

Retired exhaused...

Edited March 22, 2013 by PeterJ

kristalris · March 24, 2013

Doesn't matter what sort of atoms you are talking about - if you can split it up into indivisible and discrete units then it fails most definitions of a continuum . For PeterJ - cos you will probably ask this - I presume the real number line does not fail on this measure as between any two points you care to choose is an infinity of real number in between.

A pure continuum is pure mathematics thus off topic then. IMO the line between pure mathematics and other uses of mathematics or logic is / should be a strict one.

Taking position c as the choice in a stationary view you get a void as a continuum with some lumps in it making it impure. If you take it in a shortest time-frame where these lumps have been everywhere in space you have a pure continuum if the stuff the lumps are made of is identical. You could however have aeries of higher density if stuff has been in one part more times than other parts in that shortest time-frame. Also then not a pure continuum, but something that in both cases could be defined as a continuum, and studied with the mathematics in that sense. (Very much statistical in nature then, as we already know BTW.)

No - but physics cares little about absolute definitions along this lines of this one, whereas maths and philosophy do. Physics relies on observations and experiment - logical progressions are beautiful but just as likely to be wrong as right so scientists tend (but not always) to ignore them and concentrate on the emprical data.

Pure definitions should IMO bring discussions into the realm of pure mathematics. Otherwise you run into paradoxes (now what does "paradox" mean in this context? It's meaningless IMO I'll come back to this below.)

The division between philosophy (meta-physics) and physics should not be a strict one IMO. I.e. physicists should do more philosophy when working on certain issues, such as the nature of the Higgs-field. And vice versa. It can IMO be seen as a continuum of sorts, but then you need to deal with several philosophical issues i.e. issues that are inherently un-observable and thus un-falsifiable other than via probabilistic reasoning. You can only link up the two if you have sufficient leeway within either area to discus the issues.

It's pernickity - but this a thread about definitions - you wrote "I think most physicists would agree that time is - per definition - what the clock reads." - I corrected it to almost the same as wiki - it is measured by a clock; but its absolute extent (ie the time that the clock reads) is a purely human construct and varies between countries and cultures.

Oh it's far more profound then that, within this context of Higgs fields etc. being a continuum. In this context time is to be taken with the most accurate clock available i.e. an atom clock. taking position "c" the continuum is to be viewed in a time-frame. Given this definition of time we immediately can deduce that MN doesn't need time, yet we do in order to describe what we observe. Further more that speeding up the clock doesn't slow down time but slows down the clock (the waves change in an accurate way as a function of the change in speed) Direct consequence is that there is no inconsistency with current science with speeds > c in the continuum and no problem with time then being seen as absolute, So it readily opens up more possibilities to gain profound insights.

The question was is it correct to treat a continuum as a unity - introducing details about the higgs's, about speed of light, metaphors about unknown people, personifications, occam's razor etc are all complications and confusions.

Disagree. If you want it your way you should be talking pure mathematics. You can not have it both way's. As soon as you leave the pure mathematics which you do when placing the continuum in a context of a Higgs field or any other reality of space time concept, it becomes un-pure by nature. Demanding purity is then a fallacy.

Thanks for explaining what a metaphor is.

No bother.

Continuum would have the simple mathematical definition I mentioned above - unity is not a term I have had heard physicists using in any way approaching the way you use it. Physicists would use it to mean one - real number +1 - eg the sum of all probabilities is unity, the f(X) approaches infinity as x approaches unity

GUT and TOE are inherently unifying goals of physics. Profound insights for these goals to be got IMO via studying Higgs fields etc. as a continuum of sorts.

No - I think we are still defining continuum differently. Can I not conceive of a point (1,0) on the cartesian plane, self-contained, unextended, indivisible. Can I not also conceive of the line y=x ?

I have a feeling I have a non-mathematicians crib somewhere - might be buried tho.

Of course you can. Yet then in a pure mathematical way please.

But the real numbers are continuous. THey are mind-blowingly continuous - what ever scale you choose, look as the closest two numbers you can find and there is an infinity of numbers in between. I would say that the higg's field and the electromagnetic field are continuous - I am not convinced they are a continuum. The only thing I hear described physically as a continuum is space-time, and that is more poetic than philosophical in its origin. However I do think it fits the bill totally.

I am not sure continuous necessarily means no parts - more that parts cannot be discerned. The line y=x is the collection of points f(x) for all x - each point can be enumerated - yet it is continuous and fulfills many of the ideas of continuum

Applied mathematics is a tool that is essential and extremely successful in describing MN. Yet you seem to demand to keep it as pure as in pure mathematics. That can't be done. I.e. you can IMO use the mathematical insights concerning a continuum to describe the Higgs field. That doesn't make the Higgs field a continuum without problems. Yet I think we are quite in agreement that space time / Higgs field indeed can be also / to a very great degree can best be seen as a continuum.

What you mean by perfect continuum - is a unity. But I think you are wrong

I would disagree - as at some scales it would clearly still be lumpy, and you do not get lumpy disjointed continua (I think we agree on that). Fields and nothingness are the only physical (how physical is nothingness? - ed.) things that I can paint as a continuum.

agree

We can ignore that I think.

I think you have to explain therefore: what is the difference between a continuum and a unity? Your definitions conflate the two - and render one of the terms otiose; my usage, and I believe the accepted usage, at least preserves a difference between the two.

A pure continuum is unity and a continuum isn't pure. No difference then.

Actaully Peter I have in my notes about Heraclitus - "not strict monist - viewed reality as multiplicity and a unity at the same instant" . This was in my stuff about unity of opposites that he banged on about. And the followers of Heraclitus (but not he himself) felt that the void was filled with flux - which is about as close to the fields EMF and Higgs as you are likely to get from 2500 years ago

I really do not think the division between the atoms of leuccipus & democritus and those of rutherford & bohr this context. I maintain that as soon as an entity has discernable and unbreakable graininess - whether bits in it (rutherford) or instrinsic bits (democritus) then it fails the test of continua.

You should see it as a useful tool for applied mathematics and not as an attempt to describe the absolute truth of MN IMO.

I like your list in some ways but not in others - I feel you are right to try and constrain the problem and thus make it more handleable and manageable; quite right that stating your terms is a prerequisite.

Thanks. I'm not quite clear what bit you don't like.

I though Peter was more asking about the ontology of the continuum - in an abstract form (ie removed from the vagaries of actual physics) so that then he could move on to answer the question of the OP which is clearly regarding the space-time continuum in modern physics. How you can extend this to Krauss, hidden variables in the standard model (of particle physics? surely not) I am not sure. Ignoring the question is often very very relevant and completely scientific - when you are considering the spacetime continuum you tend to ignore the eightfold path (both the original and murray gell-mann's rip off) because otherwise you end up unable to proceed. Scientists have to compartmentalise, aggregate, and approximate. Every problem in physics has at its ultimate and infinitesimal root a need for a theory of quantum gravity - which we do not have - and which we can safely ignore in almost every problem (cept black holes and the big bang). An agreed theory on the origin of spacetime would help us immeasureably - but we do not have one, and there is little prospect of getting one in the not too distant future, so we move on and work on what we have.

It is not as difficult as you think, the other method. It is exactly the same method of reasoning and investigation you use to successfully solve a crime scene.

Given that MN is most probably an mass murdering illusionist, that gives that most probably the answer at a deepest level is a simple set of moving stuff following a simple set of rules, creating an extremely complex observed phenomena.

As in a crime scene we simply rigorously look at all the evidence via correct definitions and as a scenario fill in all the remaining questions by educated guesswork, i.e probabilistic reasoning. Using words because these are pliable yet concise enough to get close enough to the truth in order to find where to start looking. And thus testing. This works extremely faster than mathematics. The practical reason for the mental exercise.

If you then end up with a logically consistent idea / concept that deals with all problems of physics in a elegant simple way and is testable: you should test it. Al the more so when all parts of the puzzle and subsequent parts of the puzzle neatly fall into place. The probability of then being correct rises.

That historically speaking this seemingly hasn't worked (it has BTW) doesn't say that much if no one has actually tried it in the correct way. Why would a present day Einstein as a professor of physics want to run the risk of loss of face and future funding for being deemed a crackpot in a funded failed attempt on TOE when he has a 9/10 probability of failure? He won't try.

Now let's look at our Higgs field as a continuum of space time to see if we can get a profound and testable insight. This is a mainstream way to analyse problems of any nature. What do we think the Higgs field does? Slow down matter by providing mass in a continuous field. If the field slows stuff down and is neigh omnipresent it can be assumed to slow down the observed SM particles < c. But also by adding mass ad momentum in order to accelerate: law of Hubble. Also if it adds stuff it also takes stuff away out of the field so you can assume an under-pressure in the field i.e. gravity. If we accept black holes then we can see matter as little black holes in order to let the stuff disappear. If you take MN to be cyclic via moving un-splitable stuff then you have no beginning or end of time but permanent motion. You can then assume the observed spin to be energy stored in a repeated big bang becoming extremely slowly un-spun. Keeping say a photon at c accelerating but paying the price via red-shifting and curving in like a car accelerating in a cure at twice the Newton value in a gravitational field.

Now what analogy do we have in nature that could cause the order and the waves? And how many fundamental particles do we need in order to get the observed yin and yang of order and disorder, and make the theoretically needed infinite Euclidian space to be observed as non-Euclidian?

If you subsequently take this scenario to be true it must render relative easy ways to start testing whether it is correct or not.

Same way as solving a crime scene. A way current science on solving crime scenes is proven to work.

Part of current science has mixed up it's definitions, norms and goals. Incorrectly demanding neigh absolute proof before starting to test. It is also current mainstream science not to make such errors in reasoning.

Yes yes yes.

Agree almost entirely - but not sure I even think of it as paradoxical.

Our conceptualization of spacetime is metaphysical problem ...

And I still think it is more your particular reading of terms that renders the current view paradoxical rather than it being paradoxical per se - this of course adds even more weight to your argument that it is merely our philosophizing which is creating the paradox rather than discovering the inate paradox.

oh delve away.

Until Bell's Inequalities I would have entirely agreed. And paradox is used far too much.

On the definitions and without checking - paradox surely comes from talking along beyond alongside different + opinion being glory

whereas contradiction is against + speaking. Paradox seems much weaker from the etymological view but is much stronger in the modern view. just sayin' - was curious

To defend physicists - most call very few things paradoxes; however, many things get called paradoxes despite the physicists best intents (the twin paradox - which any 1st year physics student is merely confusing and difficult but is logically sound as a bell).

Agree there.

I am in a position of agreeing with both of you in part - yet you are adopting almost opposite positions. "Not choosing" is a valid way forward as I mentioned above. QM GR - yes agree. But the topic is not about unification, it is about leveraging one discipline to gain insight in the other.

I would define metaphysics as a subset of philosophy that deals with the nature of reality - ethics is philosophy but not metaphysics. If you are lookin to move to testable positions I think you are out of philosophy and into hypothetical physics; philosophy rests on logic, science rests on empiricism.

Like a said earlier on you shouldn't IMO make a strict division between physics and philosophy. You need overlap.

"pure evidence based logical deduction" - this sounds like an oxymoron to me. However, this is speculative physics and not really at home here in the philosophy forum - we like to stick to philosophy and if science pokes it's nose in we prefer it is mainstream

Slight fight with the quote boxes, seem to have come out on top.

Philosophy proper is never mainstream.

Not at all - we hang on Aristotle's every word and enshrine his law of non-contradiction - and we don't need to. The pre-socratics were at home with paraconsistency - and the modern term springs from wittgenstein . Recursive self-contradictions are the basis of much of godels work which is some of the most beautiful and insightful in all mathematics and logic.

So in dutch a paradox is by definition only a state of logical self contradiction? I would say that in English this is the technical usage - but the common usage is much much wider. English - unbeknownst to many of its practitioners - is a highly contextual language; it is by no means as precise and non-arbitrary as german (i do not know enough about dutch to comment but from your paragraph I feel it may be similar to german in this respect)

I looked up the German Wikipedia on paradox and that is - typically German - extremely thorough and seems to put it more as "ambiguous".

So

English paradox: contradiction or seeming contradiction;

Dutch paradox: seeming contradiction;

German paradox: unsolved possible contradiction;

So not just for chauvinistic reasons the Dutch way is IMO most succinct and thus scientifically systematically correct for international scientific use. You seem to agree.

All languages are contextual. If you look at the users manual on any technical device when written correctly in these three different languages English seems to me to always be the shortest and German the longest. Dutch is a Germanic language.

Not untestable at all . If the WMAP had come back with a definied positive curvature we would have known a couple of years ago. The planck telescope is doing the same thing more precisely - and it might come back result that show positive curvature; and suddenly the universe will be unfeasibly big, but not infinite. you can never prove an infinite nature - but you can show finitude and disprove the claim of infinitude.

Not sure how the second law applies here

Agree

PeterJ · March 24, 2013

Kritalris - Sorry to respond before Imatfaal, but you make some intersting points. ,

I see what you mean when you say that a real continuum (as opposed to an idealised mathematical one) cannot be 'pure',

It is possible, I think, that this is exactly what Imatfaal and I are suggesting when we say that a pure continuum would be inconceivable. It's existence would be paradoxical, It would not be an instance of a category, thus innaccessible to the intellect. This would be Kant and Hegel's fundamental phenomemon, and the reason why one mathematician can conclude that universe may be more simple than we can think.

A 'pure' continuum could not exist, for otherwise there would be a difference between existence and non-existence. This would be an extension along a dimension, thus an 'impurity'. It would also require that an extreme metaphysical position is true, which would make the universe paradoxical in philosophy. A pure continuum would be an ideal mathematical object, not an existing phenomenon.

So maybe we three agree about the impossibility of a pure continuum as an existing object.

Thus we get to the Tao, a continuum that cannot be said to exist or not-exist, and an explanation for Heraclitus' odd remarks about existence. .

Then we can say that spacetime seems paradoxical because we are reifying a paradoxical concept.of it We are assuming that a pure continuum can be extended, same as we do for the number line. But this idea simply does not fly. .

kristalris · March 25, 2013

Kritalris - Sorry to respond before Imatfaal, but you make some intersting points. ,

Wel likewise sorry I haven't reacted to your earlier post I run out of time.

I see what you mean when you say that a real continuum (as opposed to an idealised mathematical one) cannot be 'pure',

It is possible, I think, that this is exactly what Imatfaal and I are suggesting when we say that a pure continuum would be inconceivable. It's existence would be paradoxical, It would not be an instance of a category, thus innaccessible to the intellect. This would be Kant and Hegel's fundamental phenomemon, and the reason why one mathematician can conclude that universe may be more simple than we can think.

A 'pure' continuum could not exist, for otherwise there would be a difference between existence and non-existence. This would be an extension along a dimension, thus an 'impurity'. It would also require that an extreme metaphysical position is true, which would make the universe paradoxical in philosophy. A pure continuum would be an ideal mathematical object, not an existing phenomenon.

So maybe we three agree about the impossibility of a pure continuum as an existing object.

Thus we get to the Tao, a continuum that cannot be said to exist or not-exist, and an explanation for Heraclitus' odd remarks about existence. .

Then we can say that spacetime seems paradoxical because we are reifying a paradoxical concept.of it We are assuming that a pure continuum can be extended, same as we do for the number line. But this idea simply does not fly. .

Now you use "paradoxical" again.

Anyway I've been thinking about what qualm Imatfaal had with my list. I guess it is point "e"(ignoring the problem) being unscientific.What I mean to say is that ignoring or worse still opposing the line of reasoning in "c" is unscientific. Not unscientific is supporting it, yet ignoring it further because you yourself don't believe it correct. I.e. the stance: "I think it is incorrect yet it should indeed be investigated via funding, but I'm going to ignore it further." is choice c and not e.

What I'd also like to point out is that more than one choice is correct scientifically. I.e. choice a (pure mathematics), c (and e in the context c) are scientifically correct IMO. Choices b, d and e (the latter outside context c) are unscientific.

Choice "a" in the context of this thread of a continuum would entail practically speaking (given that the Higss field is probably a fact probably a continuum of sorts) that further effort and funding should go into fundamental/ pure mathematics on continua if mathematicians think there is anything further to gain in that area. (I don't know.) Then you are in the business of making tools that might come in handy later on. I.e. there is all the more reason to concentrate in this area.

What I further more would like to point out is that mainstream science holds that on any issue of any nature you must look at all relevant observations and answer all relevant questions (by at least guessing) on a given probandum. You can always work the issue via probabilistic reasoning. Of course if at all possible you use empirical statistics or deterministic mathematics. Choice "c" does this. I claim it to be a verifiable scientific fact that what I state is the most probable scenario in this context of this thread.

Correct probabilistic reasoning via words is interchangeable with Bayesian probabilistic mathematics.The first works quicker. Philosophers and lawyers alike have the natural tendency to try and overdo it with being succinct in the use of words. If you want to be extremely succinct use mathematics.If you a priori know that you have insufficient data to be extremely succinct use words. But again don't overdo it. Close is close enough to warrant testing.

On the other hand you must be succinct enough. The use of key definitions must be sufficiently correct to play the game on "c "properly. The problem is they aren't in order all across the board. GR & QM should be defined as laws of physics. The best we ever had. Otherwise you will have difficulty spotting that these laws have their limits. Yet they are not defined as such. Certain key issues are defined as paradoxes. Where it is unclear what is meant, unless paradox means seeming contradiction. Yet a lot of so called paradoxes in physics are blatent contradictions. Doing science means you don't believe in magic i.e. let contradictions be as explanation. Time is seen as a physical something thinking that when you go > c that we will travel back in it. This error in reasoning stems from incorrect definitions and not rigorously looking at the observations. Photons should be defined as matter-less and not as mass-less particles. The simplest way to look at choice "c"is that the continuum is built up out of moving mass, that itself doesn't exert gravity yet causes it. The observation that something seems to come from nothing most probably means that it is all the same stuff (i.e. mass on the move) of which some is in spin and the rest isn't in a cyclic event.

The fact that the greek Dio... what his name came up with the idea of an atom in a time when we didn't have a slide ruler but only a straight stick, a string on a sandy beach and the use of the apparatus between our ears proves that working "c" works. +++ if you do it properly! ++++

So words in the idea and concept fase: not to strict yet not to sloppy either. It's a bandwidth of accuracy you should try to stay within and subsequently try and get that ever more succinct. You pass it on to pure mathematics if possible to describe it absolutely exact. Yet we will probably never get there. We will be working with very successful estimations of models. Like GR and QM. Yet then covering more ground.

Edit: further more keep in mind that the probandum defines what becomes the relevant questions. You can of course always in science state a less broad question and work that. However, once you ask the question, science dictates you look at all relevant data and answer all relevant questions in order to proceed. NO EXCEPTION! That is a conditio sine qua non on scientific method for the furtherance of science.

Edit 2: and although science is sometimes furthered by errors in reasoning, mistakes and whatnot, it doesn't mean you should try to make mistakes, it means you should accept errors and take risks and support that in stead of opposing it. It has become far to bureaucratic at the moment. To few dare to take sufficient risks.

Edited March 25, 2013 by kristalris

PeterJ · March 25, 2013

Hmm. Not sure what your getting at here. I'm a bit confused.

Is the point numbered 'c'. the idea of atoms in the void? If so I cannot agree that this is a sensible idea. Are you advocating ex nihilo creation?

kristalris · March 25, 2013

Hmm. Not sure what your getting at here. I'm a bit confused.

Is the point numbered 'c'. the idea of atoms in the void? If so I cannot agree that this is a sensible idea. Are you advocating ex nihilo creation?

No not ex nihilo creation that is what Krauss et all are on about. I oppose that.

I say that at the deepest level it is most probable seeing all observations, that the Higgs field is built up of un-splitable lumps of mass (historical atoms) on the move in an absolute void. Mass that doesn't exert gravity but moves in such a way that it causes it in a way that more mass gives more gravity. (Then it is all simply Newton at the deepest level and MN is then indeed an illusionist. Which I believe her most probably to be.)

Also we observe a Yin and Yang of order and disorder. We observe more order than we at the moment can account for. The easiest way to look at this is to assume that one sort of of atoms want to go to order in a field causing disorder in another sort of atoms in another field occupying the same space, wanting to go to order that likewise causes disorder in the other field. Together forming the Higgs field of un-spun particles that in part are brought into spin when a particle of the SM (that are all in spin (edit "spin" in this sense like a toy gyro. i.e. in the sense that it is turning more or less around its own center. )) comes along through the Higgs field. What we observe is built up of this. It is obvious that we need to look at the mathematics how things can at all go to order in stead of disorder. As a pure mathematical problem or via computer simulation. That must be inherently testable now you know where to start looking.

Then we observe spin: what would be another way to store energy instead of movement through the field. If there are to many of these different lumps to have complete order than a continuous cycle of order and disorder should ensue. Forcing some lumps into spin spiraling through the orderly field of un-spun lumps of the same mass. Yet having a measurable effect on each other. That would then be a very simple and elegant way to look at it all.

So it is a true paradox then of seemingly ex nihilo creation. We can't directly observe the mass at this deepest level yet observe its effects.

If these lumps of mass are > c it would then be consistent with QM & GR and the rest of science and provide an immediate way to explain say entanglement. Because GR & QM apply to the SM and we are then talking hidden variables outside that model. Taking fields that can create an influence above c makes entanglement for instance in principle easy to explain.

Of course given that MN is an illusionist. I.e. that the basic rules are simple. If not (given that we humans are to stupid) then this line of reasoning will of course be proven to be a dead end. It isn't as yet a proven dead end because I can prove that choice "c" hasn't been properly investigated as the prime suspect. And I can elaborate further on this. It's most probably just an illusion of an expanding universe. Easily explainable as a cyclic affair in which all possible scenario's are being played out all the time for ever. No beginning no end. (The impossible scenarios are thus not played out.)

Edit: The most fundamental philosophical question to be asked at this moment on a continuum like the Higgs field is thus: what dynamic perpetual movement of lumps of un-spun mass without gravity could cause the surplus of order and also the observed waves? You could try to solve this by looking for analogies in nature where you see matter go to order in a way that has a link with waves. Now what would that be I Kristalris ask myself? Care to guess?

Edited March 25, 2013 by kristalris

PeterJ · March 25, 2013

I can't comment on the physics of this and can't always see what you mean, but it seems to be rather metaphysically questionnable. It does not seem to get to the bottom of the issues. It seem to take for granted the reality of mass, time, space, etc. But if our concepts of these things are contradictions then I don;t think we can assume they are correct and would prefer the opposite assumption. MN mat be an illusionist, but an illusion of a contradiciton is not a real contradiction.

But I'm aware that I may be missing your point here.

kristalris · March 25, 2013

I can't comment on the physics of this and can't always see what you mean, but it seems to be rather metaphysically questionnable. It does not seem to get to the bottom of the issues. It seem to take for granted the reality of mass, time, space, etc. But if our concepts of these things are contradictions then I don;t think we can assume they are correct and would prefer the opposite assumption. MN mat be an illusionist, but an illusion of a contradiciton is not a real contradiction.

But I'm aware that I may be missing your point here.

Yes you are missing the point. I don't see any contradictions at all. I see true paradoxes i.e. seeming contradictions. It can all be explained by pure logical deduction based on all known data and further assumptions based on probabilistic reasoning. you simply inspect the most probable first. Even what is or is not most probable can be ascertained in a falsifiable way. So there is no speculation either if you want to crowd source the issue, even that becomes measurable.

In fact doing the same the old Greek philosophers did so successful in the past. You can't get more to the bottom of the issue then this i.e. when you in effect only need an infinite space filled with an infinite amount of two different sorts of atoms moving in a mathematical order explaining it all. These forming the continuum. The mathematics of which is yet to be found, but MN points us in the right direction where to start looking for that and how to test that IMO.

The physics of this is so easy that it can be explained to any high school kid, because it is then all simply Newton.

Mind you GIVEN that MN is an illusionist, i.e. that indeed the fundamental rules are simple. But this position is the first issue that has to be scientifically investigated in order to falsify that position that MN is indeed or not an illusionist..

Edited March 25, 2013 by kristalris

PeterJ · March 25, 2013

But this is just the view that is contradictory and paradoxical. It is not solving the problem but ignoring it. An infinite space filled with atoms takes us back to Democritus and this is not progress. It cannot be a fundamental view. It does not answer any questions but is just our usual folk-psychological and paradoxical view of spacetime. The only person I know who argues for Democritus (Victor Stenger) finds, as a consequence, that he has to argue for ex nihilo creation. This is a contradiction and a paradox. It is the abandonment of reason for untestable and incomprehensible speculation. This doesn't mean it is wrong, of course, but if is right then the universe is a true contradiction.

I do not see how atoms can 'form a continuum'. If we assume they can,then we'd have to ask what keeps the atoms apart, and then we are back to the OPs question.

You may be right that a paradox is not always a contradiction and vice versa, but I'm struggling to think of a case where they are not the same thing. In philosophy, as a far as I'm aware, they would always be the same thing. A true paradox would be a true contradiction.

I believe that it is possible to get 'more to the bottom of the issues than this'. But probablistic reasoning won't do it. You'd have to reason deterministically all the way to the answer, since it would be untestable in physics.

Edited March 25, 2013 by PeterJ

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