James Maxwell's Physical Model

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Re: James Maxwell's Physical Model

Unread post by altonhare » Tue Jun 09, 2009 7:33 am

StefanR wrote:
altonhare wrote:In link 5, what is meant by a "transient aether"? Does this simply mean dynamic, i.e. a "moving aether"?
Can you perhaps give a more specific link?

[url2=http://www.helical-structures.org/new_e ... vision.pdf]This[/url2] one, in speaking of the "steady-state" aether vs. the "transient" aether.

Pet peeve of mine, calling 'it' the "ether". IUPAC and millions of chemists and materials scientists agree that [url2=http://www.helical-structures.org/new_e ... vision.pdf]this is ether[/url2].
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Re: James Maxwell's Physical Model

Unread post by altonhare » Thu Jun 11, 2009 3:20 pm

372. This extension is not mathematically, but only physically, continuous ;
What exactly do you think he meant by this? I don't know what he's getting at.
372.
For these disputants assume that their non-extended points are placed in contact with one another, so as to form a mathematical continuum ; & this
cannot happen, since things that are contiguous as well as non-extended must compenetrate ; but I assume non-extended points that are separated from one another.
Boscovich makes a good point here, and actually hits upon some of the reasoning why I cannot accept 'a' non extended "object".

Contact necessarily requires a surface, which no 2D object has, much less 'a' hypothetical 0D "non extended object". Two non-extended "objects" certainly cannot come in contact, since they occupy only a single "infinitesimal position", as soon as they "touch" they must necessarily occupy the same position.

So good praise for this salient point. His solution is to have non-extended "objects" that are separate. I assume, then, he prescribes action at a distance? I do not see how AAD is discernible from magic. So he'll get no praise from me on this.

Nor indeed have the arguments, which some others use, any validity in opposition to my Theory ; when they say that there is no such extension, since it is founded on non-extended points & empty space, which is absolute nothing. According to my Theory, it is founded, not on points simply, but on points having distance relations with one another ; these relations, in my Theory, are not founded upon an empty intermediate space ; for this space has no actual existence. It is only something that is possible, indefinitely imagined by us ; that is to say, it is the possibility of real local modes of existence, pictured by us after we have mentally excluded every gap, as I explained in the First Part in Art. 142, & more fully in the dissertation on Space & Time, which I give at the end of this work.
Here I think Boscovich is waving his hands here and skirting the issue. We have a bunch of infintesimal points which he says "have distance relations". He insists that distance/separateness "is not founded upon an empty intermediate space", i.e. he means distance/separateness is not nothing.

Not nothing = something (double negative cancels)

So Boscovich insists that there is "something" between his infinitesimal points. However he also asserts that this "something" is 'a' possibility. That 'it' is "indefinitely imagined". These are vague and handwaving. Possibilities are not things, and we certainly cannot discuss that which we cannot even imagine.

I say that they cannot constitute a mathematically extended continuum, but they can a physically extended continuum.
The latter only I admit, & I prove its existence by positive arguments ; none of these arguments being favourable to the other continuum, namely one mathematically extended. This latter, even apart from any arguments of mine, has very many difficulties. The extension, which I admit, is of such a nature that it has some points of matter that lie outside of others, & the points have some distance between them, nor do they all lie on the same straight line, nor all of them in the same plane ; but many of them are so close to one another that the intervals between them are quite beyond the scope of the senses. In that is involved the extension which I admit ; & it is something real, not imaginary, & it will be physically continuous.
I think it sounds like "touch" is outlawed in Boscovich's universe, and that infintesimal dots move around in a way that is a direct result of their location (wrt every other infintesimal dot). Once again, I cannot distinguish this from magic.
142. (A) For instance, I consider that any point of matter has two modes of existence, the one local and the other temporal ; I do not take the trouble to argue the point as to whether these ought to be called things, or merely modes pertaining to a thing, as I consider that this is merely a question of terminology.
I would argue that objects do not have "a temporal existence". An object looks at itself and only "sees" location i.e. presence. Objects exist only in "present mode".An inanimate object does not have the capacity to remember where it was before now or to guess where it will be, and thus deduce velocity. There is no past or future to inanimate things.

I'll be happy to clear this up. If it ain't got shape, it's not a thing. It's a concept.
These modes, or one of them, must of necessity be changed, if the distance, or even if only the position in space is altered. Moreover, for any one mode belonging to any point, taken in conjunction with all the infinite number of possible modes pertaining to any other point, there is in my opinion one which, taken in conjunction with the first mode, leads as far as time is concerned to a relation of coexistence ; so that both cannot have existence unless they have it simultaneously, i.e., they coexist.
Indeed, when an object changes its location it moves, and every other object in the U moves by definition. Time is the conscious identification/observation of relative motion (as opposed to absolute motion). These concepts are indeed inextricably linked (Bosc says "coexistent").

But I have an ill-defined idea of an imaginary space as a possibility of all local modes, which are precisely conceived as existing simultaneously, although they cannot all exist simultaneously. In this space, since there are not modes so near to one another that there cannot be others nearer, or so far separated that there cannot be others more so, there cannot therefore be a distance that is either the greatest or the least of all, amongst those that are possible. So long as we keep the mind free from the idea of actual existence &, in a series of possibles consisting of an indefinite number of finite terms, we mentally exclude the limit both of least & greatest distance, we form for ourselves a conception of continuity & infinity in space. In this, I define the same point of space to be the possibility of all local modes, or what comes to the same thing, of real local points pertaining to all points of matter, which, if they existed, would lead to a relation of compenetration ; just as I define the same instant of time as all temporal modes, which lead to a relation of coexistence. But there is a fuller treatment of both these subjects in the notes referred to ; & in them I investigate further the manifold analogy between space & time.
This strikes somewhat of quantum mechanical wave functions and such.
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Re: James Maxwell's Physical Model

Unread post by StefanR » Fri Jun 12, 2009 6:17 am

Solar wrote:Mileva’s maiden name was Serbian, Boscovich’s Grandfather was Serbian. Somewhere in the mix either, or both, of them would have known about Boscovich’s “relativity” and/or other historical references to it. I say not that this was malicious but that, like the big bang theory, an attempt is made to unite several aspects under one umbrella (UFT). For example, from Christopher Jon Bjerknes:
Those are connections, that might make one wonder indeed. I can make another one, which is totally irrelevant of course, but just let me make it into playfull coincidence, as the first name of the father of Rudjer Boskovich is Nikola, :) ;)
Last edited by StefanR on Fri Jun 12, 2009 6:41 am, edited 1 time in total.
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Re: James Maxwell's Physical Model

Unread post by StefanR » Fri Jun 12, 2009 6:21 am

StevenO wrote:
altonhare wrote:
StevenO wrote:Nah... :idea: everybody knows mass is a 3D scalar inward motion of atoms and gravity is that motion respective to the aether.
I thought inertial mass was resistance to motion.
Resistance to a change in motion indeed...
Here are two sections from Boscovich in which he goes into inertia a bit
Inertia

8. As an attribute of these points I admit an inherent propensity to remain in the same state of rest, or of uniform motion in a straight line, (a) in which they are initially set, if each exists by itself in Nature. But if there are also other points anywhere, there
is an inherent propensity to compound (according to the usual well-known composition of forces & motions by the parallelogram law), the preceding motion with the motion which is determined by the mutual forces that I admit to act between any two of them, depending on the distances & changing, as the distances change, according to a certain law common to them all. This propensity is the origin of what we call the ' force of inertia ' ; whether this is dependent upon an arbitrary law of the Supreme Architect, or on the nature of points itself, or on some attribute of them, whatever it may be, I do not seek to know ; even if I did wish to do so, I see no hope of finding the answer ; and I truly think that this also applies to the law of forces, to which I now pass on.

(a) This indeed holds true for that space in which we, and all bodies that can be observed by our senses, are
contained. Now, if this space is at rest, I do not differ from other philosophers with regard to the matter in question ;
but if perchance space itself moves in some way or other, what motion ought these points of matter to comply with owing
to this kind of propensity ? In that case this force of inertia that I postulate is not absolute, but relative ; as indeed
I explained both in the dissertation De Maris Aestu, and also in the Supplements to Stay's Philosophy, book I, section
13. Here also will be found the conclusions at which I arrived with regard to relative inertia of this sort, and the
arguments by which I think it is proved that it is impossible to show that it is generally abxlute. But these things do
not concern us at present.


382. The inertia of bodies arises from the inertia of their points & their mutual forces, For, in Art. 260, it was proved that, if any points are either at rest, or moving in any directions with any velocities, so long as each of the motions is uniform, then the centre of gravity of the set will either be at rest or move uniformly in a straight line ; & that,whatever mutual forces there may be between the points, these will in no way affect the state of the common centre of gravity, whether it is at rest or whether it is moving uniformly in a straight line. Further the force of inertia is involved in this ; for the force of inertia consists in a propensity for staying in a state of rest or of maintaining a uniform state of motion in a straight line, unless some external force compels a change of this state. Now, since by my Theory it is proved that the centre of gravity of any mass, composed of any number of points disposed in any manner whatever, is bound to have this property, it is clear that the same property can be deduced for all bodies ; by this it can also be understood why bodies can be conceived to be collected & condensed at their centres of gravity.
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Re: James Maxwell's Physical Model

Unread post by StefanR » Fri Jun 12, 2009 6:41 am

altonhare wrote:
StefanR wrote:
altonhare wrote:In link 5, what is meant by a "transient aether"? Does this simply mean dynamic, i.e. a "moving aether"?
Can you perhaps give a more specific link?

[url2=http://www.helical-structures.org/new_e ... vision.pdf]This[/url2] one, in speaking of the "steady-state" aether vs. the "transient" aether.

Pet peeve of mine, calling 'it' the "ether". IUPAC and millions of chemists and materials scientists agree that [url2=http://www.helical-structures.org/new_e ... vision.pdf]this is ether[/url2].
From what I get from that specific article, is that it says
The acceptance of Ether existence automatically leads to the conclusion that it should possess two kinds of features: steady state and transient one. The Maxwel’s belief about the existence of Ether is a riddle for the physicists now. Could it be a Maxwell’s delusion? It becomes apparent now that it is not. His original equations defined for 20 field variables have been formulated in quaternion form (see A. Waser [3]). Later Oliver Heaviside and William Gibbs have transformed them into vector forms that have not been recommended by Maxwell.
Perhaps what is meant by that statement is that on the one hand it should have feature that remains the same in itself, it is not of itself subject to change, and in that sense, steady state, but as it participates, so to say, in objects and certain actions or functions, it has a transient state, perhaps somewhat analogues in some way to a chemical catalyst, which functions in a chemical reaction but is not changed itself
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Re: James Maxwell's Physical Model

Unread post by StefanR » Fri Jun 12, 2009 7:00 am

Solar wrote:Einstein attempted to 'unify' several existing theories, hypothesis, and concepts along with contributing to them while working towards a UFT.
Below is a link to a piece written by Einstein which shows either ignorance of the solution by Boscovich or purposely neglecting him (judging from the writings of TF Torrance above that text, Torrance shows perhaps interest in the subject but has a certain ignorance concerning history, this is also clear when looking at the index page of the below link, when looking at the different propositions made by the different authors, and keeping in mind Boskovich
Maxwell's Influence on the Development of the Conception of Physical Reality
ALBERT EINSTEIN
Written for the centenary of Maxwell's birth [1931]

The greatest change in the axiomatic basis of physics, and correspondingly in our conception of the structure of reality, since the foundation of theoretical physics through Newton, came about through the researches of Faraday and Maxwell on electromagnetic phenomena. In what follows we shall try to present this in a more precise way, while taking the earlier and later development into account.

In accordance with Newton's system, physical reality is characterised by concepts of space, time, the material point and force (interaction between material points). Physical events are to be thought of as movements according to law of material points in space. The material point is the only representative of reality in so far as it is subject to change. The concept of the material point is obviously due to observable bodies; one conceived of the material point on the analogy of movable bodies by omitting characteristics of extension, form, spatial locality, and all their 'inner' qualities, retaining only inertia, translation, and the additional concept of force. The material bodies which had psychologically given rise to the formation of the concept of 'material point' had now for their part to be conceived as a system of material points. It is to be noted that this theoretical system is essentially atomistic and mechanistic.

All happening was to be conceived of as purely mechanical, that is, merely as motions of material points according to Newton's laws of motion.

[ ]

In order to give his system mathematical form at all, Newton had first to invent the concept of the differential quotient, and to draw up the laws of motion in the form of total differential equations - perhaps the greatest intellectual step that it has ever been given to one man to take. Partial differential equations were not needed for this, and Newton did not make any methodical use of them. Partial differential equations were needed, however, for the formulation of the mechanics of deformable bodies; this is bound up with the fact that in such problems the way and the manner in which bodies were thought of as constructed out of material points did not play a significant part to begin with.

Thus the partial differential equation came into theoretical physics as a servant, but little by little it took on the role of master. This began in the nineteenth century, when under the pressure of observational facts the undulatory theory of light asserted itself. Light in empty space was conceived as a vibration of the ether, and it seemed idle to conceive of this in turn as a conglomeration of material points. Here for the first time partial differential equations appeared as the natural expression of the primary realities of physics. In a particular area of theoretical physics the continuous field appeared side by side with the material point as the representative of physical reality. This dualism has to this day not disappeared, disturbing as it must be to any systematic mind.

If the idea of physical reality had ceased to be purely atomistic, it still remained purely mechanistic for the time being. One still sought to interpret all happening as the motion of inert bodies: indeed one could not at all imagine any other way of conceiving of things. Then came the great revolution which will be linked with the names of Faraday, Maxwell, Hertz for all time. Maxwell had the lion s share in this revolution. He showed that the whole of what was known at that time about light and electromagnetic phenomena could be represented by his famous double system of partial differential equations, in which the electric and the magnetic fields made their appearance as dependent variables. To be sure Maxwell did try to find a way of grounding or justifying these equations through mechanical thought-models. However. he employed several models of this kind side by side, and took none of them really seriously, so that only the equations themselves appeared as the essential matter. and the field forces which appeared in them as ultimate entities not reducible to anything else. By the turn of the century the conception of the electromagnetic field as an irreducible entity was already generally established and serious theorists had given up confidence in the justification, or the possibility, of a mechanical foundation for Maxwell's equations. Soon. on the contrary an attempt was made to give a field-theoretical account of material points and their inertia with the help of Maxwell's field theory, but this attempt did not meet with any ultimate success.

If we disregard the important particular results which Maxwell's life work brought about in important areas of physics, and direct attention to the modification which the conception of physical reality experienced through him, we can say: Before Maxwell people thought of physical reality - in so far as it represented events in nature-as material points, whose changes consist only in motions which are subject to total differential equations. After Maxwell they thought of physical reality as represented by continuous fields, not mechanically explicable, which are subject to partial differential equations. This change in the conception of reality is the most profound and the most fruitful that physics has experienced since Newton; but it must also be granted that the complete realisation of the programme implied in this idea has not by any means been carried out yet. The successful systems of physics, which have been set up since then, represent rather compromises between these two programmes, which because of their character as compromises bear the mark of what is provisional and logically incomplete, although in some areas they have made great advances. - Of these the first that must be mentioned is Lorentz's theory of electrons, in which the field and electric corpuscles appear beside one another as equivalent elements in the comprehension of reality. There followed the special and general theory of relativity which - although based entirely on field theory considerations-hitherto could not avoid the independent introduction of material points and total differential equations.
[ ]
http://www.mountainman.com.au/aether_2.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: James Maxwell's Physical Model

Unread post by altonhare » Fri Jun 12, 2009 9:37 am

StefanR wrote:
altonhare wrote:
StefanR wrote:
altonhare wrote:In link 5, what is meant by a "transient aether"? Does this simply mean dynamic, i.e. a "moving aether"?
Can you perhaps give a more specific link?

[url2=http://www.helical-structures.org/new_e ... vision.pdf]This[/url2] one, in speaking of the "steady-state" aether vs. the "transient" aether.

Pet peeve of mine, calling 'it' the "ether". IUPAC and millions of chemists and materials scientists agree that [url2=http://www.helical-structures.org/new_e ... vision.pdf]this is ether[/url2].
From what I get from that specific article, is that it says
The acceptance of Ether existence automatically leads to the conclusion that it should possess two kinds of features: steady state and transient one. The Maxwel’s belief about the existence of Ether is a riddle for the physicists now. Could it be a Maxwell’s delusion? It becomes apparent now that it is not. His original equations defined for 20 field variables have been formulated in quaternion form (see A. Waser [3]). Later Oliver Heaviside and William Gibbs have transformed them into vector forms that have not been recommended by Maxwell.
Perhaps what is meant by that statement is that on the one hand it should have feature that remains the same in itself, it is not of itself subject to change, and in that sense, steady state, but as it participates, so to say, in objects and certain actions or functions, it has a transient state, perhaps somewhat analogues in some way to a chemical catalyst, which functions in a chemical reaction but is not changed itself
The distinction seems cosmetic. If this "aether", whatever 'it' is, is in the so called steady state only transiently before it moves to a so-called transient state, then all the states are transient states.
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Re: James Maxwell's Physical Model

Unread post by junglelord » Fri Jun 12, 2009 2:55 pm

This Aether is a RMF, thats what it is and it has a quantum spin of 2.
Just so thats clear. Until someone can disprove it, or has a better definition, for clarity, it is a RMF.
It can act as a perfect liquid, solid, gas, plasma, all at the same time. It transmitts longitudinal and linear information.
If you couple to the RMF, then you will have evidence of the Aether. Magnets do this all the time.
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Re: James Maxwell's Physical Model

Unread post by Solar » Sat Jun 13, 2009 9:28 am

372. This extension is not mathematically, but only physically, continuous ; & on the matter of the prejudgment, from which we have formed for ourselves the idea of absolutely continuous extension from infancy, enough has been said in the First Part, starting with Art. 158. There, too, we saw that there could not be brought forward against my Theory the arguments which of old were brought against the followers of Zeno, & which now are urged against the disciples of Leibniz, by which it is proved that extension cannot be produced from non-extension. For these disputants assume that their non-extended points are placed in contact with one another, so as to form a mathematical continuum ; & this
cannot happen, since things that are contiguous as well as non-extended must compenetrate ; but I assume non-extended points that are separated from one another. Nor indeed have the arguments, which some others use, any validity in opposition to my Theory ; when they say that there is no such extension, since it is founded on non-extended points & empty space, which is absolute nothing. According to my Theory, it is founded, not on points simply, but on points having distance relations with one another ; these relations, in my Theory, are not founded upon an empty intermediate space ; for this space has no actual existence. It is only something that is possible, indefinitely imagined by us ; that is to say, it is the possibility of real local modes of existence, pictured by us after we have mentally excluded every gap, as I explained in the First Part in Art. 142, & more fully in the dissertation on Space & Time, which I give at the end of this work. The relations are founded on real modes of existence ; & these in every case yield a real relation which is in reality, & not merely in supposition, different for different distances. Further, if anyone should argue that these non-extended points, or non-extended modes of existence, cannot constitute anything extended, the reply is easy. I say that they cannot constitute a mathematically extended continuum, but they can a physically extended continuum.
It appears that Boscovich is saying that the “physically, continuous” reality as observed by the behaviour of discontinuous objects and their ubiquitous motion relative to one another cannot be mathematically represented without currently recognized renormalization of infinite integrals etc (QED). He seems to express the difference between a mathematical continuum as opposed to the reality of something “physically, continuous” apparently having infinite extent as the cause of motion. A state or condition which he left unnamed yet sees evidence for.

So that, the ‘space’ providing ‘distance’ relationships ser is not “empty space” which he recognized as being typically conceptualized as a ‘void’ -” they say that there is no such extension, since it is founded on non-extended points & empty space, which is absolute nothing.” So that, the centre of a group of co-moving objects doesn’t exist within one of the objects alone but sits somewhere in a ‘spatial’ region commensurate with their location. So called “black holes” come to mind as an “object” put forth as being necessary to account for the commoving objects of a galaxy.

But in the theory of Boscovich distance relations “are not founded upon an empty intermediate space”. Instead, his concept of ‘space’ “is only something that is possible” and “the possibility” i.e. “potential”. And this ‘space’ is considered to be a part of the reality necessary for the very establishment of those distance relations. By virtue of the apparently endless and varied distance relations that may be established via relative ‘reference frames’ one automatically establishes the existence of a physical continuum – regardless of the distances involved.

It is interesting that prior to 1923 the universe was considered to consist solely of the Milky Way galaxy. Then, in 1922-23 or so Edwin Hubble suggested that some of the objects vied through the telescope were actually outside of the Milky Way. It took nearly two years before this became accepted as fact making it just over 80 years since this has been recognized.
With that realization one’s perception of the universe exponentially expanded (no pun intended) as ‘space’ functioned to ‘physically’ integrate the newly perceived potential distance relations and automatically subsumes physical continuity. This synthesis, in my opinion, is what Boscovich puts forth by saying:
...if anyone should argue that these non-extended points, or non-extended modes of existence, cannot constitute anything extended, the reply is easy. I say that they cannot constitute a mathematically extended continuum, but they can a physically extended continuum.
Neither is he afraid to entertain the possibility of motion(s) of this substantive intermediate ‘space’:
(a) This indeed holds true for that space in which we, and all bodies that can be observed by our senses, are contained. Now, if this space is at rest, I do not differ from other philosophers with regard to the matter in question ; but if perchance space itself moves in some way or other …
He does seem rather committed on the issue of ‘contact’ and seems to prefer “compentration” which may also make Boscovich one of the earliest to propose what is now known as “superposition” or “superimposition”.

A uniform continuum of electrostaticaly balanced ‘charge’ undergoing asymmetrical superimposition (regions ‘collapsing’ on itself - motion) would result in the formation (phase-shift) of resonantly stable objects that would then exist within that same uniform charge continuum in the form of its own ‘phase space’. For example, all electrons form an electron-plasma. So the relation would be analogous to the compactification (resonant coupling) of electrons bound to atoms in relation to “free electrons”. The former presents itself as an object (the atom); the later does not.

The objects (atoms) formed by the resonant compactification of “bound” electrons do not refute the existence “free electrons”- both ‘states’ of which form the overall continuum of the electron plasma – the ‘phase space’ of which is of unknown extent. Likewise, Boscovich is saying that attention to the variety of objects produced by compound motion does not deny the existence of the motions of something of greater extent.

His perception of ‘space’ as something that undergoes a variety of asymmetrical motions is different than that of ‘space’ as a ‘void’ (literally nothing). He recognized that this is the perception of ‘space’ as opposed to intermediate space being ‘something’ of unknown extent undergoing compound motion(s) as implied in the ubiquitous motion of objects ("points") subsequently formed from those motions.

The “compound motions” (asymmetrical ‘collapse’) of an electrostatically uniform charge continuum would do likewise for the production of electrons via their ‘condensation’ or ‘precipitation’ as a form of energy “shed”. So that, an object in motion; stays in motion because it is the ‘product’ of the compound motions (of the charge continuum) which produce said quantum object.

The permittivity and permeability of “free space” ideally forms just such a dynamical uniform charge continuum of unknown extent; the compound motions of which an object in motion is an integrated phase related product and also kinematically impelled via transduction of the energy so imparted.

Einsteinium Relativity has a true ‘void’ at its center and neo-relativist have championed this form of relativity. Like Boscovich and Maxwell, who used Hamilton’s quaternion ‘spatial rotations’ for a continuum, for someone to then posit that ‘space’ is a ‘something-ness’ is considered somehow even more unusual?? It was a brave attempt he made but I consider him as having realized that he was wrong and thus his subsequent political-like waffling over the issue. Thus Tesla’s Boscovich influenced approach led him to recognize relationships based on relativity of motion but reject ‘space’ as a ‘void’.

Cymatics produces objects via the induction of compound motions in liquids using sound. With the addition of superimposition (Boscovich's "compenetration") resulting in a phase-shift that produces quantum objects constituting their own phase-space the 'something-ness' of "space" does likewise.
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Re: James Maxwell's Physical Model

Unread post by StefanR » Sat Jun 13, 2009 10:33 am

altonhare wrote:
372. This extension is not mathematically, but only physically, continuous ;
What exactly do you think he meant by this? I don't know what he's getting at.
It's part of the continuation of what preceded in section 371 where he starts stating that "From impenetrability there arises extension", and as stated further, in that section 372, he refers to other sections where he has stated the diferences between those types of continuity/continuum
altonhare wrote:
372.
For these disputants assume that their non-extended points are placed in contact with one another, so as to form a mathematical continuum ; & this
cannot happen, since things that are contiguous as well as non-extended must compenetrate ; but I assume non-extended points that are separated from one another.
Boscovich makes a good point here, and actually hits upon some of the reasoning why I cannot accept 'a' non extended "object".

Contact necessarily requires a surface, which no 2D object has, much less 'a' hypothetical 0D "non extended object". Two non-extended "objects" certainly cannot come in contact, since they occupy only a single "infinitesimal position", as soon as they "touch" they must necessarily occupy the same position.

So good praise for this salient point. His solution is to have non-extended "objects" that are separate. I assume, then, he prescribes action at a distance? I do not see how AAD is discernible from magic. So he'll get no praise from me on this.
He has many more of such points wherein he shows the position of somewhat similar ideas, as he is here doing to Leibniz, only from what I see he is taking the consequences of certain reasonings, where the biggest problem lies with understanding Boscovich's model is if one is not able to get rid of distinctions between what an object is and what a physical point is
When one keeps substituting the one for the other only confusion can arise, just have a look at what you did above, you can't just mix up words/things like that, when there meaning is different

As for AAD, as you say assumptions, or did you find something in the text that says so?
And sometimes Clarke's 3rd Law perhaps does apply?? ;)
Any sufficiently advanced technology is indistinguishable from magic.
altonhare wrote:

Nor indeed have the arguments, which some others use, any validity in opposition to my Theory ; when they say that there is no such extension, since it is founded on non-extended points & empty space, which is absolute nothing. According to my Theory, it is founded, not on points simply, but on points having distance relations with one another ; these relations, in my Theory, are not founded upon an empty intermediate space ; for this space has no actual existence. It is only something that is possible, indefinitely imagined by us ; that is to say, it is the possibility of real local modes of existence, pictured by us after we have mentally excluded every gap, as I explained in the First Part in Art. 142, & more fully in the dissertation on Space & Time, which I give at the end of this work.
Here I think Boscovich is waving his hands here and skirting the issue. We have a bunch of infintesimal points which he says "have distance relations". He insists that distance/separateness "is not founded upon an empty intermediate space", i.e. he means distance/separateness is not nothing.

Not nothing = something (double negative cancels)

So Boscovich insists that there is "something" between his infinitesimal points. However he also asserts that this "something" is 'a' possibility. That 'it' is "indefinitely imagined". These are vague and handwaving. Possibilities are not things, and we certainly cannot discuss that which we cannot even imagine.
Well Boskovich never stated that it was easy to understand what he is trying to get across, did you get to read the supplements I and II concerning time and space?
Sometimes to get to a model one has to integrate the whole of the arguments to get to grips with what is proposed, because if taking those propositions on there own and facilitating them with ones own conceptions can lead to not confusion of what is actually meant and consequenses of it being so and not being so and so on
altonhare wrote:

I say that they cannot constitute a mathematically extended continuum, but they can a physically extended continuum.
The latter only I admit, & I prove its existence by positive arguments ; none of these arguments being favourable to the other continuum, namely one mathematically extended. This latter, even apart from any arguments of mine, has very many difficulties. The extension, which I admit, is of such a nature that it has some points of matter that lie outside of others, & the points have some distance between them, nor do they all lie on the same straight line, nor all of them in the same plane ; but many of them are so close to one another that the intervals between them are quite beyond the scope of the senses. In that is involved the extension which I admit ; & it is something real, not imaginary, & it will be physically continuous.
I think it sounds like "touch" is outlawed in Boscovich's universe, and that infintesimal dots move around in a way that is a direct result of their location (wrt every other infintesimal dot). Once again, I cannot distinguish this from magic.
That's something I seem to get from his arguments too, no compenetration, that is perhaps allowed mathematically but not physically with matter points, this is wholly something different with objects, which in his model are compounded from matter points,
And a matter point is not the same as an infinitesimal dot because that is an mathematical term and maths is not physical, but there is a certain analogy between the two that he does seem to acknowledge
As for magic, perhaps again Clarke's 3rd Law applies
altonhare wrote:
142. (A) For instance, I consider that any point of matter has two modes of existence, the one local and the other temporal ; I do not take the trouble to argue the point as to whether these ought to be called things, or merely modes pertaining to a thing, as I consider that this is merely a question of terminology.
I would argue that objects do not have "a temporal existence". An object looks at itself and only "sees" location i.e. presence. Objects exist only in "present mode".An inanimate object does not have the capacity to remember where it was before now or to guess where it will be, and thus deduce velocity. There is no past or future to inanimate things.

I'll be happy to clear this up. If it ain't got shape, it's not a thing. It's a concept.
You are not saying something very different from Boskovich perhaps, but a matter point in his model is just more fundamental and simple than what you concieve of as objects, Boskovich is very clear in that,
altonhare wrote:
These modes, or one of them, must of necessity be changed, if the distance, or even if only the position in space is altered. Moreover, for any one mode belonging to any point, taken in conjunction with all the infinite number of possible modes pertaining to any other point, there is in my opinion one which, taken in conjunction with the first mode, leads as far as time is concerned to a relation of coexistence ; so that both cannot have existence unless they have it simultaneously, i.e., they coexist.
Indeed, when an object changes its location it moves, and every other object in the U moves by definition. Time is the conscious identification/observation of relative motion (as opposed to absolute motion). These concepts are indeed inextricably linked (Bosc says "coexistent").
In the supplements I & II he goes further into this
altonhare wrote:

But I have an ill-defined idea of an imaginary space as a possibility of all local modes, which are precisely conceived as existing simultaneously, although they cannot all exist simultaneously. In this space, since there are not modes so near to one another that there cannot be others nearer, or so far separated that there cannot be others more so, there cannot therefore be a distance that is either the greatest or the least of all, amongst those that are possible. So long as we keep the mind free from the idea of actual existence &, in a series of possibles consisting of an indefinite number of finite terms, we mentally exclude the limit both of least & greatest distance, we form for ourselves a conception of continuity & infinity in space. In this, I define the same point of space to be the possibility of all local modes, or what comes to the same thing, of real local points pertaining to all points of matter, which, if they existed, would lead to a relation of compenetration ; just as I define the same instant of time as all temporal modes, which lead to a relation of coexistence. But there is a fuller treatment of both these subjects in the notes referred to ; & in them I investigate further the manifold analogy between space & time.
This strikes somewhat of quantum mechanical wave functions and such.
Perhaps one of the reasons why Bohr and some of the quantum mechanics had an eye on Boskovich, only just as Einstein in another sense, they were not inclined to see perhaps to what he was saying with respect to that analogy and the reasoning behind matter points

It seems there is something the in which Boskovich handles Time,Space, Motion that has certain consequences that leads to for instance relativity, and just as well the reasoning behind how those three 'things' relate with matter points the way they do in his model that agrees with quantum considerations that seems to solve issues still being struggled with today in combining the 'big' with the 'small'
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: James Maxwell's Physical Model

Unread post by StefanR » Sun Jun 14, 2009 10:11 am

Address to the Mathematical and Physical Sections of the British Association.
James Clerk Maxwell
[From the _British Association Report_, Vol. XL.]
[Liverpool, _September_ 15, 1870.]

The student who wishes to master any particular science must make himself familiar with the various kinds of quantities which belong to that science. When he understands all the relations between these quantities, he regards them as forming a connected system, and he classes the whole system of quantities together as belonging to that particular science. This classification is the most natural from a physical point of view, and it is generally the first in order of time.

But when the student has become acquainted with several different sciences, he finds that the mathematical processes and trains of reasoning in one science resemble those in another so much that his knowledge of the one science may be made a most useful help in the study of the other.

When he examines into the reason of this, he finds that in the two sciences he has been dealing with systems of quantities, in which the mathematical forms of the relations of the quantities are the same in both systems, though the physical nature of the quantities may be utterly different.

He is thus led to recognize a classification of quantities on a new principle, according to which the physical nature of the quantity is subordinated to its mathematical form. This is the point of view which is characteristic of the mathematician; but it stands second to the physical aspect in order of time, because the human mind, in order to conceive of different kinds of quantities, must have them presented to it by nature.

I do not here refer to the fact that all quantities, as such, are subject to the rules of arithmetic and algebra, and are therefore capable of being submitted to those dry calculations which represent, to so many minds, their only idea of mathematics.

The human mind is seldom satisfied, and is certainly never exercising its highest functions, when it is doing the work of a calculating machine. What the man of science, whether he is a mathematician or a physical inquirer, aims at is, to acquire and develope clear ideas of the things he deals with. For this purpose he is willing to enter on long calculations, and to be for a season a calculating machine, if he can only at last make his ideas clearer.

But if he finds that clear ideas are not to be obtained by means of processes the steps of which he is sure to forget before he has reached the conclusion, it is much better that he should turn to another method, and try to understand the subject by means of
well-chosen illustrations derived from subjects with which he is more familiar.

We all know how much more popular the illustrative method of exposition is found, than that in which bare processes of reasoning and calculation form the principal subject of discourse.

Now a truly scientific illustration is a method to enable the mind to grasp some conception or law in one branch of science, by placing before it a conception or a law in a different branch of science, and directing the mind to lay hold of that mathematical form which is common to the corresponding ideas in the two sciences, leaving out of account for the present the difference between the physical nature of the real phenomena.

The correctness of such an illustration depends on whether the two systems of ideas which are compared together are really analogous in form, or whether, in other words, the corresponding physical quantities really belong to the same mathematical class. When this condition is fulfilled, the illustration is not only convenient for teaching science in a pleasant and easy manner, but the recognition of the formal analogy between the two systems of ideas leads to a knowledge of both, more profound than could be obtained by studying each system separately.

There are men who, when any relation or law, however complex, is put before them in a symbolical form, can grasp its full meaning as a relation among abstract quantities. Such men sometimes treat with indifference the further statement that quantities actually exist in nature which fulfil this relation. The mental image of the concrete reality seems rather to disturb than to assist their contemplations. But the great majority of mankind are utterly unable, without long training, to retain in their minds the unembodied symbols of the pure mathematician, so that, if science is ever to become popular, and yet remain scientific, it must be by a profound study and a copious application of those principles of the mathematical classification of quantities which, as we have seen, lie at the root of every truly scientific illustration.

There are, as I have said, some minds which can go on contemplating with satisfaction pure quantities presented to the eye by symbols, and to the mind in a form which none but mathematicians can conceive.

There are others who feel more enjoyment in following geometrical forms, which they draw on paper, or build up in the empty space before them.

Others, again, are not content unless they can project their whole physical energies into the scene which they conjure up. They learn at what a rate the planets rush through space, and they experience a delightful feeling of exhilaration. They calculate the forces with which the heavenly bodies pull at one another, and they feel their own muscles straining with the effort.

To such men momentum, energy, mass are not mere abstract expressions of the results of scientific inquiry. They are words of power, which stir their souls like the memories of childhood.

For the sake of persons of these different types, scientific truth should be presented in different forms, and should be regarded as equally scientific whether it appears in the robust form and the vivid colouring of a physical illustration, or in the tenuity and paleness of a symbolical expression.

Time would fail me if I were to attempt to illustrate by examples the scientific value of the classification of quantities. I shall only mention the name of that important class of magnitudes having direction in space which Hamilton has called vectors, and which form the subject-matter of the Calculus of Quaternions, a branch of mathematics which, when it shall have been thoroughly understood by men of the illustrative type, and clothed by them with physical imagery, will become, perhaps under some new name, a most powerful method of communicating truly scientific knowledge to persons apparently devoid of the calculating spirit.

The mutual action and reaction between the different departments of human thought is so interesting to the student of scientific progress, that, at the risk of still further encroaching on the valuable time of the Section, I shall say a few words on a branch of physics which not very long ago would have been considered rather a branch of metaphysics. I mean the atomic theory, or, as it is now called, the molecular theory of the constitution of bodies.

Not many years ago if we had been asked in what regions of physical science the advance of discovery was least apparent, we should have pointed to the hopelessly distant fixed stars on the one hand, and to the inscrutable delicacy of the texture of material bodies on the other.

Indeed, if we are to regard Comte as in any degree representing the scientific opinion of his time, the research into what takes place beyond our own solar system seemed then to be exceedingly unpromising, if not altogether illusory.

The opinion that the bodies which we see and handle, which we can set in motion or leave at rest, which we can break in pieces and destroy, are composed of smaller bodies which we cannot see or handle, which are always in motion, and which can neither be stopped nor broken in pieces, nor in any way destroyed or deprived of the least of their properties, was known by the name of the Atomic theory. It was associated with the names of Democritus, Epicurus, and Lucretius, and was commonly supposed to admit the existence only of atoms and void, to the exclusion of any other basis of things from the universe.

In many physical reasonings and mathematical calculations we are accustomed to argue as if such substances as air, water, or metal, which appear to our senses uniform and continuous, were strictly and mathematically uniform and continuous.

We know that we can divide a pint of water into many millions of portions, each of which is as fully endowed with all the properties of water as the whole pint was; and it seems only natural to conclude that we might go on subdividing the water for ever, just as we can never come to a limit in subdividing the space in which it is contained. We have heard how Faraday divided a grain of gold into an inconceivable number of separate particles, and we may see Dr Tyndall
produce from a mere suspicion of nitrite of butyle an immense cloud, the minute visible portion of which is still cloud, and therefore must contain many molecules of nitrite of butyle.

But evidence from different and independent sources is now crowding in upon us which compels us to admit that if we could push the process of subdivision still further we should come to a limit, because each portion would then contain only one molecule, an individual body, one and indivisible, unalterable by any power in nature.

Even in our ordinary experiments on very finely divided matter we find that the substance is beginning to lose the properties which it exhibits when in a large mass, and that effects depending on the individual action of molecules are beginning to become prominent.

The study of these phenomena is at present the path which leads to the development of molecular science.

[ ]

Physical research is continually revealing to us new features of natural processes, and we are thus compelled to search for new forms of thought appropriate to these features. Hence the importance of a careful study of those relations between mathematics and Physics which determine the conditions under which the ideas derived from one department of physics may be safely used in forming ideas to be employed in a new department.

The figure of speech or of thought by which we transfer the language and ideas of a familiar science to one with which we are less acquainted may be called Scientific Metaphor.

Thus the words Velocity, Momentum, Force, &c. have acquired certain precise meanings in Elementary Dynamics. They are also employed in the Dynamics of a Connected System in a sense which, though perfectly analogous to the elementary sense, is wider and more general.

These generalized forms of elementary ideas may be called metaphorical terms in the sense in which every abstract term is metaphorical. The characteristic of a truly scientific system of metaphors is that each term in its metaphorical use retains all the formal relations to the other terms of the system which it had in its original use. The method is then truly scientific--that is, not only a legitimate product of science, but capable of generating science in its turn.

There are certain electrical phenomena, again, which are connected together by relations of the same form as those which connect dynamical phenomena. To apply to these the phrases of dynamics with proper distinctions and provisional reservations is an example of a metaphor of a bolder kind; but it is a legitimate metaphor if it conveys a true idea of the electrical relations to those who have been already trained in dynamics.

Suppose, then, that we have successfully introduced certain ideas belonging to an elementary science by applying them metaphorically to some new class of phenomena. It becomes an important philosophical question to determine in what degree the applicability of the old ideas to the new subject may be taken as evidence that the new phenomena are physically similar to the old.

The best instances for the determination of this question are those in which two different explanations have been given of the same thing.

The most celebrated case of this kind is that of the corpuscular and the undulatory theories of light. Up to a certain point the phenomena of light are equally well explained by both; beyond this point, one of them fails.

To understand the true relation of these theories in that part of the field where they seem equally applicable we must look at them in the light which Hamilton has thrown upon them by his discovery that to every brachistochrone problem there corresponds a problem of free motion, involving different velocities and times, but resulting in the same geometrical path. Professor Tait has written a very interesting paper on this subject.

According to a theory of electricity which is making great progress in Germany, two electrical particles act on one another directly at a distance, but with a force which, according to Weber, depends on their relative velocity, and according to a theory hinted at by Gauss, and developed by Riemann, Lorenz, and Neumann, acts not instantaneously, but after a time depending on the distance. The power with which this theory, in the hands of these eminent men, explains every kind of electrical phenomena must be studied in order to be appreciated.

Another theory of electricity, which I prefer, denies action at a distance and attributes electric action to tensions and pressures in an all-pervading medium, these stresses being the same in kind with those familiar to engineers, and the medium being identical with that in which light is supposed to be propagated.

Both these theories are found to explain not only the phenomena by the aid of which they were originally constructed, but other phenomena, which were not thought of or perhaps not known at the time; and both have independently arrived at the same numerical result, which gives the absolute velocity of light in terms of electrical quantities.

That theories apparently so fundamentally opposed should have so large a field of truth common to both is a fact the philosophical importance of which we cannot fully appreciate till we have reached a scientific altitude from which the true relation between hypotheses so different can be seen.

I shall only make one more remark on the relation between Mathematics and Physics. In themselves, one is an operation of the mind, the other is a dance of molecules. The molecules have laws of their own, some of which we select as most intelligible to us and most amenable to our calculation. We form a theory from these partial data, and we ascribe any deviation of the actual phenomena from this theory to disturbing causes. At the same time we confess that what we call disturbing causes are simply those parts of the true circumstances
which we do not know or have neglected, and we endeavour in future to take account of them. We thus acknowledge that the so-called disturbance is a mere figment of the mind, not a fact of nature, and that in natural action there is no disturbance.

But this is not the only way in which the harmony of the material with the mental operation may be disturbed. The mind of the mathematician is subject to many disturbing causes, such as fatigue, loss of memory, and hasty conclusions; and it is found that, from these and other causes, mathematicians make mistakes.

I am not prepared to deny that, to some mind of a higher order than ours, each of these errors might be traced to the regular operation of the laws of actual thinking; in fact we ourselves often do detect, not only errors of calculation, but the causes of these errors. This, however, by no means alters our conviction that they are errors, and that one process of thought is right and another process wrong. I

One of the most profound mathematicians and thinkers of our time, the late George Boole, when reflecting on the precise and almost mathematical character of the laws of right thinking as compared with the exceedingly perplexing though perhaps equally determinate laws of actual and fallible thinking, was led to another of those points of view from which Science seems to look out into a region beyond her own domain.

"We must admit," he says, "that there exist laws" (of thought) "which even the rigour of their mathematical forms does not preserve from violation. We must ascribe to them an authority, the essence of which does not consist in power, a supremacy which the analogy of the inviolable order of the natural world in no way assists us to comprehend."
http://www.archive.org/stream/fiveofmax ... max110.txt
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: James Maxwell's Physical Model

Unread post by StefanR » Sun Jun 14, 2009 10:13 am

The Continuity of Continuity: A Theme in Leibniz, Peirce and Quine
The notion of continuity is of vital importance for an understanding of Peirce's metaphysical ideas and his Leibnizian heritage, and affords an insight into the shortcomings of the specializing scientism of our century. In this paper we aim to trace some of the landmarks in the history of the principle of continuity, not only in its original mathematical formulation, but in its broad metaphysical and epistemological scope as a central component of Leibniz's thought. This perspective contrasts with Quine's contemporary scientist naturalism which, though maintaining that a continuity exists between science and philosophy, ends up by reducing the latter to the former. According to this framework, our discussion is divided into four sections: 1) The history of continuity; 2) Continuity in Leibniz; 3) Continuity in Peirce; and 4) Continuity in Quine*.
1. The history of continuity

The origin of the subject of continuity can be traced back to the problem of the continuum in Greek philosophy. The subject of the continuum is in turn related to that of movement. As Raven wrote "theories of motion depend inevitably on theories of the nature of space and time; and two opposed views of space and time were held in antiquity. Either space and time are infinitely divisible, in which case motion is continuous and smooth-flowing; or else they are made up of indivisible minima, in which case motion is what Lee aptly calls 'cinematographic'"1. From this we can see that the subject of the continuous arose out of the subject of infinity and divisibility, just like that of the one and the many, which "becomes evident at the very heart of continuity"2. Zeno of Elea, Leucippus, Democritus, Anaxagoras and Aristotle devote special attention to analyzing this problem. Zeno of Elea, influenced by Parmenides, considered that unity and divisibility, and therefore continuity, must go together. Zeno's paradoxes try to show that this is so. Leucippus and Democritus hold that reality is made up of infinitely small particles: atoms, which are indivisible. As Aristotle says (De Caelo, 4, 303a 5), they "state that the first magnitudes are infinite in number and indivisible in magnitude, and that plurality does not arise out of unity, nor does unity out of plurality, but that all things are generated by the joining or dispersal of these first magnitudes". The atoms, then, are infinitesimal magnitudes considered from a quantitative point of view.

Anaxagoras conceived of matter as being composed of particles, each of which is irreducible (quality) but not indivisible (quantity). Anaxagoras drew on Zeno's paradoxes, especially the so-called dichotomy, and on the reflections of Leucippus and Democritus concerning matter as being made up of atoms. Anaxagoras found that the infinite is in both the large and the small, and reached the conclusion that everything is in everything "in such a way that even though nothing is the same as anything else, there are infinite degrees of variation between one thing and another"3. Frank compares Anaxagoras' view with that of Leibniz, who also "associated infinitesimal calculus with monadology and, while being fully aware of the scarcely discernible differences between individual beings, asserted the principle of universal continuity with the greatest rigour"4.

The complexity and interest of continuity is obvious. The Gordian knot of the problem lies in whether the existence of continuity should be admitted, or reality should be thought of as an aggregate of points and atoms which are related to each other in some accidental way. According to Aristotle, "the extremes of things can be together without even being one, and can be one without necessarily being together" (Phys V, 3, 227a 22-24). That is, continuity does not simply mean that things are contiguous in space, or even successive in time, but that there may be continuity in all that is real. Our present purpose is to trace the notion of continuity in all its philosophical extension. Continuity is to contiguity as the genus is to the species. From this perspective, we approach the continuity of the sciences, which is a consequence of the continuity of reality understood with all the breadth of Aristotle's definition. Interest in this philosophical issue is heightened by the debate raging between continuism and discontinuism in contemporary scientific theories.
http://www.unav.es/users/Articulo13.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: James Maxwell's Physical Model

Unread post by StefanR » Sun Jun 14, 2009 10:18 am

Boscovich published Theoria philosophiae naturalis reducta ad unicam legem virium in natura existentium in 1758. He criticised Newton's concepts of absolute space and time, absolute motion, action-at-a-distance, and atomism. His own ideas on atomism are described in detail in [36] where the author writes:-

His idea of atoms is opposed against the older Lucretian theory that atom is an extended, hard and elastic body. He intended to explain all natural phenomena by postulating nonextended atom and the law of force between atoms. The influence of Boscovich's theory was wide in the eighteenth and nineteenth centuries especially in Britain. Boscovich assumed point-atoms in opposition to hard, extended atoms. He also postulated the force between atoms to be repulsive at very small distances, attractive and repulsive alternately with increasing distance and attractive, following the law of gravitation, at macroscopic distances. Based on these assumptions he intended to account for the properties of matter. His ideas spread in the eighteenth and nineteenth centuries. His atoms were considered from the different points of view, namely, the point-atoms interacting at a distance and those as singular points in the field of force. The meaning of his ideas in the history of atomism is stated.

In [19] Manara writes about Boscovich's work on continuity and the nature of space:-

In our opinion the great genius, versatile intelligence, and originality of this Dalmatian physicist and mathematician warrant the remembrance and the study of his works and thought. ... In a treatise [held in the Catholic University at Brescia] Boscovich presents his own ideas concerning continuity, which is seen as a property of what is usually called geometric space. Earlier we analysed his treatise from this point of view in an attempt to cast light upon Boscovich's ideas concerning the question, much debated at the time, of what one might call 'the nature and constitution of the geometric continuum', a problem associated with the question of geometric indivisibles, which originated with the works of Bonaventura Cavalieri and was debated at length. Let us briefly summarize what we feel to be the fundamental points of Boscovich's thoughts concerning these topics:

1. Boscovich accepts the Aristotelian definition of continuous quantity; according to that definition, the continuum is characterized by the fact that the parts have a common end.
2. In this conception, the point is considered an 'end' of the line, and is therefore indivisible and of a nature different from that of the segment.
3. The geometric continuum is infinitely divisible; segments, no matter how small or how large, can arise.
4. There do not exist true infinitesimal segments.
5. The law of continuity holds in all cases for geometric curves, which cannot have stopping points or discontinuities.

Boscovich was therefore able to conceive of matter as made up of nonextensive material points acted upon by forces that not only are attractive, as determined by Newton's law of gravitation, but can also become repulsive at short distances; this explains the phenomenon of cohesion no less than that of the impenetrability and solidity of matter.

In a related paper [17] Homann writes:-

Boscovich's implicit, or working, philosophy of mathematics centred on a geometry that was axiomatically Euclidean, abstracted from phenomenal experience, and able to describe, in an approximate manner, phenomena on a macroscopic level. This geometry admitted extension by elements, such as ideal points, with no correspondent in phenomenal experience. In appropriate circumstances, the geometry of the continuum can describe physical reality that, on the microscopic level, is discontinuous and finite.
Finally let us look at Boscovich's scientific methodology. This is discussed in [15] in which Grmek writes:-

In statements pertaining to methodology he insists on the limits and the relativity of all human knowledge; he describes three sources of knowledge; he defines criteria of the scientific soundness of statements; finally, he deals with the problem of induction in a critical manner and sets out a particular heuristic procedure (the 'method of decipherment'). Boscovich describes with clarity the logical procedure by means of which he constructs his 'new world'. Although this procedure is perfectly clear, it corresponds only in part to his actual approach. If Boscovich accepts in his statements on scientific methodology neither pure rationalism, nor Baconian induction, and appears as an adept of the experimental method, he has only slight recourse to this method.
http://www.gap-system.org/~history/Prin ... ovich.html
The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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Re: James Maxwell's Physical Model

Unread post by StefanR » Sun Jun 14, 2009 10:27 am

Maxwell, Mechanism and the Nature of Electricity
Clerk Maxwell sought to explain physical phenomena mechanically, (p. 418).2 In
his view “when a physical phenomenon can be completely described as a change in
the configuration and motion of a material system, the dynamical explanation of that
phenomenon is said to be complete” and he expressed the view, (p. 592),2 that most
of the sciences that deal with systems without life had either been reduced to
mechanics or were in a fair state of preparation for such a reduction.
None of the mechanisms that Maxwell appealed to qualified as mechanical in the
strict sense of seventeenth-century mechanical philosophers such as Boyle. His
electromagnetic ether was elastic as were the colliding molecules in the first version
of his kinetic theory, whilst in later versions of the kinetic theory molecular
collisions were attributed to short-range repulsive forces. Whilst Maxwell was
relaxed about just which primitives were to figure in his mechanical reductions, he
did insist that those primitives be few in number and not subject to ad hoc
adjustment in order to adapt to the variety of observable phenomena. He was
attracted to Kelvin’s theory of the vortex atom because of its non ad hoc character.
In that theory the properties of atoms and of substances composed of them were to
be derived from vortex rings in an ether that possessed the properties of constant
density and zero viscosity only, as compared, for example, to Boscovich’s theory of
point atoms in which one was free to add whatever forces proved appropriate to the
atoms. It is worth quoting Maxwell on this matter in full, (pp. 471-2):2

But the greatest recommendation of this theory, from a philosophical point of view, is that
its success in explaining phenomena does not depend on the ingenuity with which its
contrivers “save appearances”, by introducing first one hypothetical force and then
another. When the vortex atom is once set in motion, all its properties are absolutely fixed
and determined by the laws of motion of the primitive fluid, which are fully expressed in
the fundamental equations. The disciple of Lucretius may cut and carve his solid atoms in
the hope of getting them to combine into worlds; the followers of Boscovich may imagine
new laws of force to meet the requirements of each new phenomenon; but he who dares to
plant his feet in the path opened up by Helmholtz and Thomson has no such resources.
His primitive fluid has no other properties than inertia, invariable density and perfect
mobility, and the method by which the motion of the fluid is to be traced is pure
mathematical analysis. The difficulties of this method are enormous, but the glory of
surmounting them would be unique.


Maxwell sought to explain electromagnetic phenomena mechanically, in terms
of the states of a mechanical ether possessing density and elasticity. Here there is
irony. For it was in electromagnetism that it first became clear that mechanical
explanations could not be universally achieved. The charge on the electron is a nonmechanical
primitive on a par with its mass, whilst the electromagnetic fields are not
the mechanical states of an underlying ether. The energy associated with a magnetic
field is not the kinetic energy of matter in motion. Maxwell’s undoubted successes
in electromagnetism were achieved in spite of his quest for mechanical explanations
in that domain, whilst his approach led to mistakes and dead ends that needed to be
overcome by those taking a different approach. At least, that is what I shall argue. In
the remainder of this paper I document the nature and fate of Maxwell’s attempt to
explain electricity mechanically.
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The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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StefanR
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Re: James Maxwell's Physical Model

Unread post by StefanR » Sun Jun 14, 2009 10:29 am

The illusion from which we are seeking to extricate ourselves is not that constituted by the realm of space and time, but that which comes from failing to know that realm from the standpoint of a higher vision. -L.H.

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