The Theory and Geometry of Gears and the Transmission of Torque in Space

It is quite exciting to be reviving the Newtonian paradigm at a time when others are generally abandoning it.

It is always very satisfying to be able to reinterpret it in terms of a rotational motion field in which the motion is relative. I also expect to find a full and workable mathematical treatment of one aspect of transmission in space which is based on the interaction of gears, levers and pistons, springs and other such paradigms.

The watchmaker analogy has served science well in explaining the mechanical aspects of the cosmos, and this is precisely due to Eudoxian proportion and Pythagorean harmonics. The watchmaker analogy was very much a mechanical working out of the Pythagorean notions of "musical" relationships underlying the fundamental structure of the cosmos. No learned man was unaware of that harmonic relationship and the inspiring anaLogical connection. Modern views tend to dismiss the views of the past as inferior, rather than paying close attention to cultural arrogance, and false pride.

However it cuts both ways. The religious system the thought police of the recent past and in some countries the present, restricted a mature and smooth reworking of these essential ideas , forcing a more contentious and belligerent contestation of the interpretation. It was not so much that the ideas were being uprooted, more an interpretation of the notions being changed. The more rational and reasonable mind allowed for this, but the religious bigot forced a sharp divide claiming God as the source of authority and creating a situation that even today barely remains civil.

The empirical nature of the Pythagorean discoveries testify to the obvious code of conduct :empiricism. The pythagoreans were not immune to religious bigotry and neither is any scientist today. We often wish to hold our subjective view as being the overlord of all others, rather than the subjective perception that it is. Curiously this arises due to the basic biological driver of symbiosis and quorum sense, which has a biologically necessary attachment called antibiosis.. At the level of complexity, or rather convolution complexity that we enjoy we have many deterministic choices. Whereas we can never achieve an " ideal" world because the "idea" part is subjective, we can achieve a compromise and generally comfortable alternative. But we cannot remove the antibiosis that comes with that system of relationships we seek to establish for the common good..

Nowadays we are more aware that the propositions and propaganda are meaningless. The demonstrable empirical action is what defines a meaning. Thus the truth is the biggest lie that we have commonly accepted. Pragmatic empiricism is perhaps the nearest ideology that I can recommend to you as a way of life, study and wisdom development.. Is not the same thing, but to be skeptical and to trust no one or no thing , not even oneself is entirely possible, feasible and not at all disagreeable or disingenuous. In fact it is liberating and reveals much about the interplay of power relationships established within the general symbiotic " good".

As an individual I have acknowledged my inter and intra dependency on the collective communities which constitute my experiential continuum, which shapes my understanding of my independent action amongst so many dependent ones.

Consequently, the description of space and cosmos is not devoid of "chaos" , but some have wanted it to be so. Therefore they have resolutely refused to accept that a watchmakers product could produce "chaos" nor yet indeed arise out of " chaos" without some divine agency. Setting these things in these religious terms clouded the empirical mind for millennia, and I mean for most of recorded history. I have no axe to grind about any word, but the referent of the word is the communication, and the misdirected referents I do take issue with.

Pragmatically however I cannot determine what referents another individual attaches to a culturally accepted norm, and therefore a willing and observant student who communicates is the best vehicle for receiving any subjective insight I might develop. By such means the fortunes of families nations and tribes have been developed and played out, in all animate spheres of influence. We generally call this social evolution, but it has a biological counterpart.

the close packing of spheroids from the point of view of fractal packing. Provides the geometry and structure for mechanical transmissions of pressure and rotating pressure or torque. This transmission is sufficient to explain all four "forces", and all radiative behaviours in terms of rotating regions gearing relationships to those surrounding it, and those within. The fact that this is based in a field and not on solid gears should not be forgotten. The relative rotational motions therefore are dynamically changeable in relation to region attributes, like size shape, speed,
Of rotation and translation and meshable surface attributes such as regularity of pattern.

When i was first researching 3d trochoids I did not understand the relationship to gears, and so was puzzled and delighted by the frequent references to gears. Now I see a glimpse of a unifying notion whack may take me forward to where I want to go.

http://www.zakgear.com/Art1.html
http://books.google.com/books?id=I2NnbsyJsvAC&printsec=frontcover#v=onepage&q&f=false

http://books.google.com/books?id=XUSHSYwdiV8C&pg=PA330&lpg=PA330&dq=Geometrical+gear+theory&source=bl&ots=-2DEWFc89d&sig=gQYWuBP_SEPEHXws2N7M6s3JfzE&hl=en&ei=obM7Ts_FE4uxhAesxtSFAg&sa=X&oi=book_result&ct=result&resnum=5&ved=0CDMQ6AEwBA#v=onepage&q=Geometrical%20gear%20theory&f=false

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