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So somebody start with what empiricism is and how we can revise it to reflect fractal notions, please.

Joseph Locke may be a good start, i dunno.

Maybe Benoit may be a better start.

Of course i have some ideas, but this ain' t my blog!  :dink:

This is a fundamental breakthrough (http://www.eurekalert.org/pub_releases/2011-01/eu-nmt011911.php), and the sort of thing i think of when meditating on fractal empiricism.

Any thought s or comments (http://esciencecommons.blogspot.com/2011/01/new-dimension-to-adding-and-counting.html) on it?

Fractal woman said something fractal about Buddhist philosophy and world view here (http://www.fractalforums.com/meet-and-greet/fractalcosmology/msg17153/#msg17153). Any comments on that?

Ok, then.

Is there any scientific basis to Astrology, given the collapse of the Newtonian view of God in the machine?

I think recent thinking is heading that way despite a desperate steer away from such thinking!

Al righty!

Do we now have an empirical and fractal basis for autogenesis, or do we have empirical fractal proof of the existence of a supreme God?

Come on! somebody take a bite! :laugh:

an ontology for geometry > http://www.astro.umd.edu/~eshaya/astro-onto/ontologies/geometry.html

Since this is for everyone, can you give a rough idea of what empiricism is, what ontology is and how they relate to our everyday concerns?

Why would we want an ontology of geometry as empiricists?

As fractal empiricists is this ontology adequate to the fractal view?

Hi, just a quick answer..
I'm not an ontologist myself..it was just an idea.
Ontology is something used in philosophy and computer-science..could be more or less formal..it's just a simple (?) way to give shape to knowledge using a system of axioms..
from google>(computer science) a rigorous and exhaustive organization of some knowledge domain that is usually hierarchical and contains all the relevant entities and their relations.
Is it useful? can't tell..not so much maybe..would be adequate? it's possible.
Is there a problem with empiricism? don't think so
..
empiricism:the application of empirical methods in any art or science..
from wiki:
A pursuit of knowledge purely through experience, especially by means of observation and sometimes by experimentation; A doctrine which holds that the only or, at least, the most reliable source of human knowledge is experience, especially perception by means of the physical senses. ...

Thank you so much visual for starting the thread off on the right track! Respect!

I was going to write, as a provoker:

Science is commonly stated to be empirical and not related to or in need of a god. But how can this be, when it relies on the agencies of gods and godesses the chief ones being Natura, the goddess of nature and Logos the god of reason. How can prof Dawkins maintain his position as an atheist in the light of that observation?

I was then going to remind that I hope that we could move toward a fractal concept of empiricism, whatever that means, rather than a defence for and against prof Dawkins!

I believe without hyprbole that we have the greatest practitioners of "fractal magic" in the world, right here in this forum. So who better to opine on fractal empiricism?

I hope now that we might take some time to really understand, compare contrast and define what empiricism and ontology means in simple everyday language and ways of speech.

The reason I am not taking a leading role in defining is I habitually tend to confuse with my language!

So, over to you whoever you are who wants to contribute. I value everyones insight, particularly those who have not been spoilt by too much " education" !

So do ghosts happen? Do the dead speak to us through Sally Morgan?
Is Dark energy a cop out?

Yes, No, and Maybe.

In that order.   :gum:

Pythagoras once said or wrote ; God is the devine math artist.

The Latin term; Deus Ex Machina (the god out of the machine) already existed way before Newton was born.

Why searching for the proof of the creators existence ?
                                                                           Better use that time to enjoy it`s creation.

 

Is that an empirical yes? If so would you care to elaborate on that?

Similarly is that an empirical no? How can you negate the assertion empirically?

Hmmm , maybe. i will reserve question until you comment further.

My mum told me god exists and jesus saved her. Why should i believe Pythagoras and not my dear old mum( now deceased)?

Which latin wit coined "Deus Ex Machina (the god out of the machine)", and why should i accept his/her description over Newton's? Newton by the way believed in God but accepted in part a philosophy due to Descartes. Why should i accept Descartes description?

OK, I'll bite - but first I state that I am only an armchair philosopher and only vaguely aware of terms such as ontology, empiricism etc.

My own beliefs that differ from what appears to be the standard "norms" (scientific and theological both) are:

1. "God" is not an observer, external to existence, nor Creator of said existence but rather the totality of Existence.
2. Existence is Fractal.
3. Based on 1&2 God is everywhere and both within and without everything.
4. Time is not the 4th dimension, in fact it's not a dimension at all, it's merely a consequence of change of state.
5. I believe mass should be considered as the *real* 4th dimension - but if (for instance) there were only 4 (as in say quaternions) then mass would be the *first* dimension (i.e. the *real* axis in quaternions).
6. A reason for 5: Clearly spatial energy and mass are interchangeable therefore mass *has* to be a dimension i.e. nuclear reaction is simply rotation of mass into space.
7. Question - is "Mass" relative position or relative "speed" along the mass dimension ? I'd say relative speed.

Plus an alternative to the big bang (needs a little visualisation):

Rather than a big bang resulting initially in expanding "plasma" consider an infinite of "plasma" that then coalesces into clumps, said clumps continue to coalesce *and* shrink, in such a way that some become linked (by gravitational forces) (galaxies) but overall they continue to coalesce (shrink) so that the relative distances between them *based on their own shrinking scale* become larger and larger *though the whole remains infinite*.

Possibilities if Existence is fractal - Astrology could be valid, zero-content homeopathy could be valid, zero-point energy would certainly be valid....

I should add that I sincerely believe the only undeniable "true fact" is "I think therefore I am", beyond that everything is speculation.

Thanks Dave.

The vagueness of the terms are what i think need clarifying. However when they are clarified it is important that it is agreed by consensus that they are clear! So i feel that some discussion or analogy on this aspect alone is worthwhile.

Your set of propositions and beliefs are fascinating, and only go to show that there is more wisdom in the "unlearned " than the scholars give credit. Why shouldn't you be right and bang on the money?

Your ideas and opinions are as valid as Einstein's or Newton's or Feynman' s . How do we test which views are useful and which are not? Do we need to know which are true and which are not?
Can we ever justify just believing?

Recently i surveyed the empirical evidence we have amassed for a finite universe and concluded that the only paradigm that makes sense of it all is the Principles of Fractal Geometry. That is not to say that Benoit's Fractal Geometry is the bible, far from it. It is to say that like relativity in its time, Fractal has become a powerful paradigm of its own that founds all aspects of our knowledge making, and our belief systems.

This topic is old because no one wants to deal with the everyday notion of empiricism, because your daily life is not fractal enough?

Come on, make a cup of coffee and put your fractal "experiences" to good use in a discussion of how we "sense" this crazy world we live in.

Seeing as we, myself included , have no appetite to do the basic work i envisaged in this thread, i thought that i might refer to my recent biog post as a possible agent provocateur.
http://my.opera.com/jehovajah/blog/2012/07/02/the-conception-of-magnitude-language.

I want to make this thread accessible, so i changed its name.

Empiricism is defined in Visuals contribution, but can you give us an anecdote or a story that makes sense of that definition?

Ontology is nicely defined by visual as well, but can you give a more accessible example?

Heres one that affects me, on ontology. I regularly get mail, which i leave unopened, after a quick decision about its relative importance. I end up with a pile of mail i have to sort one day, but a pile of low grade information mostly in terms of impact on my behaviours.

Occasionally i miss something really to my advantage, but only occasionally. I have to balance this disadvantage with the huge advantage of extra time to pursue what i find interesting and important, and a less cluttered mind.

My "ontology" is a simple one, let us say i divide my mail into 3 categories: bill; family,everything else.

How have i arrived at this ontology? By experiencing the consequents of a few others and selecting by trial and error the one that suits me most, weighing the advantages against the disadvantages. This is what i mean by an empirical method.

Any body got any examples like that or your own anecdotes?

Come on, make a cup of coffee and put your fractal "experiences" to good use in a discussion of how we "sense" this crazy world we live in.
[/quote]
Ah, the quotidian world- it's empirically everywhere..standing in a queue for tickets, groceries..whatever. How one might stand while waiting, the nature of thoughts passing thru one's mind....Certainly we all develop reflexive body patterns ( external & internal) that  might be glimpsed in things like which box of cereal chosen to how much of an impulse buyer one might be. The latter possibly a mini example of someone who hasn't worked out an empirical ideal to, say, save money, or only get what they really need.

Getting what one really needs. Call me a semi -pessimist re the state of the larger human spirit-mind (please, please let me link them),but
altho' everyone must have worked out a personal roster of ways & means  for themselves I worry there's some kind of hollowing out of real self scrutiny/understanding. Am not one to generalize- would fail as a statistician. Do we drown out a critical inner refrain with our ipods, cell phones, incessant contact-mode, background noise at -all-costs thingamajiggy...? Is that inner chord involved with some fractal aspect ?
Frak me. Yes , a Battlestar Galactica fan. No, the new one.

How much is too much self-scrutiny ? How aware should one 'try' to become- I wonder if the simplest way is to see the moments, inhabit them ( as in being in the now) & then feel/live one of the many off-shoots of this which would be a more whole-cloth mind and body awareness. And think of the sweet spot of EACH iterative moment. A daisy chain of moments. OMG.

There's a wonderful little dialog in the ( highly recommend) movie "Get Low" with Robert Duvall. He's asked how he is and he answers " I am". This is someone contemplating having a pre- death funeral. Speaking of death, think of all the biological fractal cascades that must occur during decomposition. Anyway, the above quote got me ruminating on the concept of a brain dead person. They still 'are' but are not 'am'?  Could there be some sub thinking manifestation that all our astonishing machinery just cannot plumb ?  This of course is part of the enormous ethical dilemmas inherent in keeping people alive. Think on the weird empirical dances that have developed over letting somebody 'go' who's in this twilight land- mix up of a fandango & a waltz. The heart trying to guide what theory cannot.

Maybe there exists an exquisite inter-dimensional/between the numbers level of energy existance where a life- force can dally while the body is in arrears. A lay-away for the filament of consciousness that might return if circumstances allow. Wishful thinking ? Sally Morgan?

Not to be savage- but a thinking animal waiting in line to be stun bolted, or any of the issues connected enduringly to it , well, what's the supporting empirical evidence to support this. Off topic.

Although I see that 'just believing' is outrageously popular in our mainsteam life ( ie: visualisation, vibratonal intent/aka "The Secret", even
(most respctfully) prayer) I don't think it could be rigorously justified. Although, since part of this line of questions requests anecdotal evidence , I can see this raining down on me just for saying that. I commented in fractal cpu that I am personally comfortable with the mysteries inherent in living/ growing/ changing one's mind.....comfortable leaving an open ended, music still being written, line of sight .
Am reminded of how you can sometimes return years later to a book that just fretted your mind the first time you tried it- made no sense. Then you pick it up again at the RIGHT (whatever that may mean) time and it feels like a door opening, a personal manifesto into some new level of insight. Hey is insight a fractal animal ? Can it be measured in an equational sense ?definition: capacity of understanding hidden truths, etc. Fractals sometimes seem hidden, like brownian motion, but never-the-less, remain stunningly omnipresent.

 :star: Gosh- did Mr K. add more emoticons to the menu ?

Thanks filagree. Great contribution.

One cannot separate as we are taught to do these internal and external connections, we can only agree to ignore or downplay some. Does that consensus distort the fractal experience?
What is the fractal experience?

I just finished a speculative piece on quanta, which begins to make sense of quantum physics to me, in terms of fractal processes.
http://my.opera.com/jehovajah/blog/2012/07/16/quantity-of-twistorque.

I s this my fractal experience?

Just realised that my latest empirical meanderings are taking me to NASA. I have already seen fractal sand patterns on Mars, and the explanation of the heliosphere is too fractal to miss!

The more I look outside at the growing data sets we may now comfortably call knowledge bases, the more fundamentally important an empirical fractal philosophy becomes.

Similarly, but less intuitively, the quantum data sets are starting to reveal the fractal structures beneath the atom. Some experiments are even attempting to tackle the Planck limit. Whichever way you go it's fractals all the way, at least empirically.

When I started this thread it was to fulfill a responsibility I felt that the fractal paradigm should be developed on the philosophising of those engaged in the work of this forum.

Dotted about in various threads responses have been posted that show the depth of wisdom available to this task. I think particularly of the thread started by Lar2 with regard to the fractal CPU.
http://www.youtube.com/watch?v=v1MnNO4I9aU
Today I watched a BBC  documentary on the secret life of the cell. Much of it I already had researched as part of the empirical data required to support the fractal paradigm. The cgi and the collected information makes it a recommend from me, although I do not endorse the narrow militaristic paradigm it uses to portray viruses. Nevertheless, it packs a powerful punch!

For a wider view, you are welcome to see/ read my blog on Bacteriphages.
Just google jehovajah!

Sorry for getting back to you so late.
Just a few links, regarding ontologies, that may be of interest.
Dichotomous Thinking IS related to ontology.
For the ontologists a complex systems is nothing else than the sum of its parts; like complex patterns are the result of simple interactions (see http://en.wikipedia.org/wiki/Emergence).
When we are talking about 'representing parts-whole relations', we talk about mereology: it could be seen as a logic language/system similar to the one used in set theory, but made in a way to avoid antinomies (see http://plato.stanford.edu/entries/mereology/ and http://deed.ryerson.ca/~fil/I/Papers/iced99.html).

This is a small example to see the difference in taxonomy and ontology (from http://www.ontologyweb.com/2009/10/difference-between-an-ontology-and-a-taxonomy/):

TAXONOMY:

Cats
    Related term: Housepets
    Narrower term: tabby cat, black cat, kitten
    Broader term: Housepets

ONTOLOGY:

Cats
    LivesIn: House
    Chases: Mouses
    CrapsOn: Carpeting

And here is an attempt to describe the formation of Cantor set, made following the mereology of Lesenieski.
See http://air.unimi.it/bitstream/2434/126674/2/Valore%202006a%20Topics%20on%20General%20and%20Formal%20Ontology.pdf pag.53
(http://s7.postimage.org/jl8g1jty3/o15322.png) <- http://www.stanford.edu/~boas/science/ftext/  :dink:

 ;D Yay visual, thanks for that. Can't stop smiling at the cat crapson attribute!

A lot to digest and discuss in just this one post! I for one hold my hand up and say I do not get the fine distinction.

Ontology has a long history so I am not dissing that. My friend Vasil gave a talk in Bulgaria on it, and in Bulgarian! So I still do not know what he was on about! Lol!

The way I like to approach these things is to suck it and see if I think it is useful, so a discussion can ensue.

Also I have to say I am a bit dubious about taxonomy in its finer distinctions. However, in a computer database world, a taxonomy Ontology distinction might just be what is needed to pass the Turin test!

Certainly your humorous example makes a very valid point! Imagine a computer that could come up with that. It would almost be human!

It is impossible to have empirical proof of G-d. That is totaly nonsence exept when you wiev G-d as some kind of miracle machine as Vatican beliews. You do this and that, and then miracle machine do what you wanted.

But King David clearly hadn't been the greatest king ever, Chingiskhan (Gengishan in english) were much greater. As were hittites. But now there are more Davids than Chingiskhans and hittites taken together.

In Russia in early 30ies there were 10 commandments of communism builders, but they kind of not sucseeded. All the world lives by 7 day week with hollydays at the end, but it is secular like 10 commandements of communism builders or western values of "thou shall not kill". And it is kind of working even if there are disputes does it extends to eutanasia and abortions.

Charles Darwin could be a one of the gratest genius ever lived, but nationalistic exUSSR eastern european states built upon principle "survival of fittest" with first enterprises run by crime lords tops the world in suicide rates (in Latvia largest external cause of death is suicide). From here population are running including to Russia. Papua New Guine (were lots of missionaries were eaten) soon will outperform Moldova, but GDP per capita of Trinidad of Tobago (Tobago once was colony of  Dutchy of Courland) allredy are higher than GDP per capita of Latvia (with Courland being integral part of it), and in Trinidad & Tobago they don't need to warm their homes.

But Haiti with its premodern woodoo mindset are complete disaster. Earthquake spared Dominican Republic, probably becouse they had normal homes built according to laws and regulations.

If you want, I can put prooflinks:

http://en.wikipedia.org/wiki/Trinidad_and_Tobago (http://en.wikipedia.org/wiki/Trinidad_and_Tobago)
Trinidad and Tobago
Per capita $17,158

http://en.wikipedia.org/wiki/Latvia (http://en.wikipedia.org/wiki/Latvia)
Latvia
Per capita $13,316

http://en.wikipedia.org/wiki/Angola (http://en.wikipedia.org/wiki/Angola)
Angola
Per capita $5,144

http://en.wikipedia.org/wiki/Georgia_(country) (http://en.wikipedia.org/wiki/Georgia_(country))
Georgia
Per capita $3,210

http://en.wikipedia.org/wiki/Moldova (http://en.wikipedia.org/wiki/Moldova)
Moldova
Per capita $1,968

http://en.wikipedia.org/wiki/Papua_New_Guinea (http://en.wikipedia.org/wiki/Papua_New_Guinea)
Papua New Guinea
Per capita $1,900


http://en.wikipedia.org/wiki/List_of_countries_by_suicide_rate (http://en.wikipedia.org/wiki/List_of_countries_by_suicide_rate)
List of countries by suicide rate. Lithuania seems to be least happy, however data is somewhat old.



Whatever about G-d, but if you take 3D plane and iterate some whatever bulb, iterations looks like 4th dimension, the time. Iteration number and time allways goes just in one direction, to the increasing enthropy. You can not go back in time as you can not go back to previous iterations, but you allways can go further. There are casual dinamic triangulation I kind of not understand, but it sound simmilar to iterations.. Iteration number consists of discrete units, but well, there are plank unit of time too. Maybe this can lead to new formula, maybe where 4th part of quaternion is iteration number.

Although I believe evolutionary theory can be applied to many things other than genetic evolution I don't think you can mix separate subjects like genetics, race (as in Nationhood not genetics), social policies, economic policies, religion, traditions etc. and apply a single combined evolutionary path to all.
Inherited traits are purely down to the genes, which genes get mixed is very independent of *all* the others - for instance the overall population change throughout the world over a period varies only a little and usually it's the less economically successful that have too many births - admittedly they also have too many deaths :(
Economic policy is almost completely independent of genetics, as is fiscal policy though as I say an evolutionary system could probably be applied individually to both individually - I'm not saying that these different things don't affect each other, just that the way they do so cannot be boiled down to something as simple as an evolutionary model *for the whole* and most certainly not in a short-term way, perhaps considering whole millennia but then the older data would be a little sparse ;)

We do not often speak as we find. We mythologise, and do so to make sense of the "raw" data. When you put your data together, what sense do you make of it? How do you communicate this to your fellow man assuming you want to?

The gods of mythology have always been a standard device for communicating these abstract relationships. The principles of evolution have become another standard device. The idea is to take "non sense" data and make sense of it. But to do so means we have to come to some consensus on terminology and definitions, and we have to agree on process.
In this forum the process paradigm is more fractal more iterative and recursive than in common sensibility in the west. In certain eastern cultures the cyclical nature of time is a standard paradigm. The usual question is combative, adversarial, antagonistic: "which paradigm is right?!"
The question here in this thread  is: "which is empirical?"

There is always a third "way" , in my opinion

http://www.bbc.co.uk/programmes/b01mwx64
Ontological Argument, existence or experiential continuum

http://www.thunderbolts.info/wp/mm/
Our philosophy and our insights as fractalists are more crucial than ever. Recently I have begun to experiment with Marko Rodin vortex 9 group. This I have determined will be mapped out under the vortex18 group or rather both are rings in current mathematical terminology.

These rings have to do with everyday life and everyday reality so can we spot patterns of 9 in our experiences. For  example, do things happen in 3's?

I forget what i have posted sometimes!

The Electric Universe/ Plasma Universe is a fundamental movement in science to redefine the scientific understanding of Astronomy, and this pans down to every technology we use today eventually, and into biology.

The fractal foundation of mathematics is not immune to its impact, as my recent blogs show.(google: jehovajah shunya)

What this means to me is that humanly speaking, before religion, before even Mythology empirical observations were a significant human response to space and spatial awareness. This has to reflect the fundamental fractalisation of our experiences that we iteratively and sequentially arrive at through our processing reactions.

The mythologising of these empirical fractals is a mnemonic device for storing the experience in human collective memory for transmission through the generations.
My point is that we can create these original fractals and initiate the mythologies that are passed down

As an example of this, the Mandelbrot set in its iconic form is such a fractal. Long after the mathematical details of the set may be forgotten the dynamic detailed image will not.

Jos Leys!
http://www.youtube.com/watch?v=x4aJvNA-2ZU&list=PLw2BeOjATqruoac7tS6Clnn-mpxlRkXfV

This is part of a new series of instructional videos by Jos. Fantastic presentation. Worth studying.

But i have a problem with it. It is not radical enough because it does not acknowledge the Fractal paradigm from the outset. He starts from the Chaos paradigm. This chaos paradigm is now not so radical as it once appeared to be, and yet it is only now that it is being put in its rightful position in mathematical modeling.

As usual the rabbit hole goes deeper, and the source is fractal not differential!

Empirical observation encodes this fractal interaction in several representational systems so one cannot give preeminence to the visual as many "mathematicians " do. The combinatorial sequencing of these modeling  attributions resolve simply to the combination of fractal metrons/metrics in recursive or iterative identities. We can do this now because we have the cybernetic systems to compute theses complex interactions. The fractal generators that we use is some serious modeling software for what our biological processing networks do in creating our experiential continuum.

I want you to always remember that no matter how smart a "mathematical" description looks or is it is dumber than what your natural cybernetic systems deliver to you every moment of your conscious experience, and the experience is fractal!

one question i would like to ask is:

the ball on the wooden plane is rolling without friction ... ok, but, hey, there is friction between the board and the ball created through gravity, because the gravity comes into place after the plane has removed ... isnt the statement wrong that the ball would roll along its way all the time ?! isnt pressing the gravity the ball on the plane CREATING COME KIND OF FRICTION !?!?
this really bugged me in the video, but nice video after all...

I think he meant frictional drag. Balls roll through friction at the point of contact!

Have you ever thought that the several levels of "you" are a fractal? That your constructed "self" is an iterated pattern? That your "mysterious" consciousness is a recursive formulation of your everyday experiences? That habit is a many layered fractal product? That personality is a wondrous colouring algorithm?

Is your heart beat the pulse of your fundamental iterative clock cycle?

I can recommend Fractals to any young and enquiring mind. It is the one topic boundary that has no boundary we can define!

The inspiration of the very word fractal was like the buzz created by Eric De Bono's new connective "po". Suddenly everything could make fractal sense!

But Mandelbrot laconically defined fractal as having at least this one property: almost self similarity! Every spiral is almost self similar, while a circle is ubiquitously self similar.

Grassmann said "Keine Abweichung", no giving in, no yielding, no wobbling! And yet life is all about wobbling, isn't it? That is why things that appear invariant are so special, remarkable and worth passing on to the next generation.

Most of these invariant things are subjective states of mind, experiences in and of consciousness. Of these, Fractal is the pinnacle and the foundation.

Newtonian Motive has given me a greater insight into Newton, Fluid Mechanics and The fundamental connection between fractal formulas and motive laws in nature.

Mandelbrot's insightful Almost self similar, recent apprehension of the Logos Analogos logic of Eudoxus' means that i view the fractal sculptures differently. They represent fluid dynamic sculptures.

As a consequence power 2 motives and above are descriptors of turbulent fluid dynamics, while power 1 represent streamline flows in julia mode, higher powers represent pressure heads on turbulent flows, i think. In mandelbrot mode we get complex turbulent pressure dynamics

just wanted to let you know that this thread is very close to what I have been thinking the last months. we are on the same path. It is great to find likeminded people.
I'm quite busy right now, and this topic consumes so much time, as I find it hard to get in that mindset and find a good way to convey my ideas with understandable words/analogies, as I'm by no means a scientist or mathematician.
but I needed to tell you that this thread was really exiting, gave me new ideas and that I'm looking forward to discussing and sharing thoughts with you! I'll have to comment so many things in this thread - it's a bit overwhelming.. :)

--edit--
pictures are a fast and easy way to show where I'm coming from:
http://www.fractalforums.com/fractals-in-nature/comprehensive-collection-of-fractals-in-our-universe/
----

Hello, Chillhelmer.

You are welcome to post as the title suggests, and i will try to get back to you to discuss in a reasonable time.

Maybe you can encourage others who you discuss with to contribute.

There is a vast amount of historical and philosophical material to comment on. We have the opportunity to humbly review and redact a lot of good and bad thinking and philosophy.

Whether we will be able to set out a view for future generations , i do not know. It is a big task, but someone needs to have a go.

I am in discussion with a person who is arguing the ontological or cosmological argument Aristotle developed to conclude the existence of a prime mover.

I mentioned the alternative conclusion of a fractal as a prime mover, referring particularly to the endless zooming we find in the Mandelbrot fractal.mthis was meant to be n analogy of how our mind endlessly zooms into this question of , who made god ?

I know some do not like that question, but I think it deserves some time in our meditations.

I go along with St. Augustine and his reply to the question of "What was god doing before he created the universe?"

He deemed it a meaningless question, and completely unanswerable, because the word "Before" implies the passage of time - and time is a function of the universe to which god would be immune and outside of.

I extrapolate the concept further and state that ANYTHING outside of our universe is not subject to the rules  (guidelines?)  of our universe and therefore cannot properly be addressed from within it's confines.

Once we find the way out of our universe we can begin to meaningfully address these concepts - but until then I find any considerations of things outside our universe to be pure speculation and, in the words of Our Hero, Bertrand Russell : "The idea of existence of god can no more be proven or disproven than the idea that there is a fine china tea set in orbit between Earth and Mars"

Lol! When I come across the china I will toast BR with the first cup, and call him a visionary!

The point of interest to me is that he makes the statement that such considerations are legitimate metaphysics.
As a fractalists, and a free thinker I like that assertion better than BR's.

The value judgement that seems to underlying the objection is that it is a waste of time that does not eleven exist in the subject of focus! This value judgement I allow, and I allow the opinions based on it, but what I do not allow is coercion into any particular world view or value judgement. I allow free assent as much as that is possible.

In one thread there was a conclusion I drew that within a deterministic framework of sufficient complexity freedom of choice exists. It may not be freedom to choose any or every of the infinite possibilities of choice , but it is a type of an undefined motion of free choice..

The discussion dies not go further simply because there is no one autistic or anal enough to split such hairs, for no purpose that is seemingly pragmatic, or even utilitarian. That does not mean that we have arrived at an inevitable conclusion to the train of thought. It means, thank god, that we can choose to truncate these infinite loops by a pragmatic interrupt command!

When we do that we notice that our processing in pragmatic experience avoids too many infinite loops, but not all.mthus zeno's and Parmenides paradix's have a pragmatic truncation, and the tortoise is passed easily by the Athlete, and the arrow does fly to the target.
 Similarly when we introduce cause and effect , these are pragmatic truncations of endless iterative sequences upon analysis.

Somehow does it benefit us that we have this infinite loop tendency? I think that Fractal iteration and synthesis at each iteration are the answer to this age old question. We see the structures that fractal generators produce, and we see them in a freeze frame, a truncated sequence has preceded that frame.
We make movies of many such frames and sit in amazement. It is as if we are watching our natural world experiences in some instances.

The complexity of what we produce in a video should not go unackneledged, but rather I apprehend that my experience is constructed by his pragmatic truncating process which feeds into a synthesis process to provide me with a dynamic experience of reality.

While I have not " got out of the box" the process has enlarged and enriched my view and transformed the box boundary into a potential Wada basin. Instead of feeling confined I instead feel constrained by an infinitely receding boundary.
I can speculate what is beyond that receding boundary  but in fact my best guess should be more of what leads into the boundary on a fractal analogy.
In a sense Aristotle came to the same conclusion, in that the prime movers were unmoved movers from our perspective, but from their perspective he speculates, they enjoy arn eternal blissful life of existence not at all mpecisrly ours, but described in analogous terms with proprieties caveats.

To then go on to define this as theological Truth is the biggest coercive Machiavellian propaganda ploy of the ages!

I have no issues discussing, speculating, and even believing such things if one chooses to do so.

I only take issue with drawing conclusions as if they constitute any sort of "proof" of these concepts.

Another fun concept related to this comes from another Great 20th Century Philosopher, Douglas Adams :


So the moral of the story is have fun debating, discussing, speculating, and all that - but don't actually draw any conclusions on this topic, because none are possible.

Possible in the sense they will exhibit in physical phenomena independent of an individual. By this I exclude the psycho somatic effects of meditation.

However I do want to include psychosomatic effects as real  benefits, or curses, of engaging in this kind of speculative enquiry. In a sense engaging with fractals in thought generate a sense of awe and beauty which I would not want to be belittled.

I am sure some fractals can screw you up too! :dink:

This section in the Metaphysics is of particular interest.

Any comments?
This section is of interest, assuming it is an accurate apprehension of the Greek.
"
        It is not as easy as it may at first seem to argue that the universe could include an infinite regress of causes.  But let the point be conceded for the sake of discussion.  Aquinas did not commit the fallacy of circular argument, for he drew from a principle best stated in  Book II, Chapter 2 of the Metaphysics, where Aristotle said,   
 
 
 
 
      "In any series of causes, we must have a first cause, then one or more intermediate  causes, then the last term. If we had to say which of these three terms is the real cause of the whole, we should say that it is the first cause, for the last term is as yet the cause of nothing, nor can it be said that the whole is produced by the intermediate cause or causes. It does not matter whether there be only one or more than one intermediate cause, nor even whether there be a finite or infinite number of intermediate causes.  For even if the series included an infinite number of causes, all causes down to the present moment would be only intermediate causes which would still need a first cause, so that, if there were no first cause, there would be no causes at all."       
"
there are certain value judgements and presentation structures that I do not assent to and I will discuss how.


I have found a Greek source text and will examine it in the Greek, but I would welcome any opinions especially if you have read Aristotle which I have not.

I don't feel I can form my opinion until I do.

I've read my share of Aristotle, and was surprised by the sheer number of wild assumptions he made without ever testing them for accuracy.  Everything from the number of teeth women had  (all he had to do was count 'em fer gawrsh sakes!) to spontaneous generation of mice in piles of unwashed laundry  (yes, he believed the laundry to Cause the mice to appear from nothing!).

I was much more impressed with my namesake, Socrates  (even if he spelled it funny).

But as for his "Cause" thingy you quoted - consider a circle  (This may or may not be circular reasoning, but it's the first idea that came to mind). Assume each point on the circle to cause the next point  (no more far-fetched a concept than the assumption that the universe cannot contain an infinite regression of causes).  So your starting point causes the next, and so on.  But once you complete the circle and continue on...  well, the idea of first causes becomes ambiguous.

The chosen starting point originally appeared to be a First Cause  (Prime Mover), but once the "Eternity" of the circle was completed it became apparent that it was no such thing at all.

To expand this analogy to our universe, it's first cause may not be understood until it has "run it's course" and then our perspective changes.

It comes back to the idea of being limited by our very existence within this universe and the only way to truly understand it is to escape it and view it from another frame of reference.

That's why I call all attempts to define such things Doo-Doo.  Whatever caused this universe will never be understood from within it's confines  (similar to Godel's incompleteness concept - it will always prove insufficient to make any such effort).

That is not to say such efforts have no value, just that placing any more worth to them than their amusement quotient is folly.

Thanks Sockratease.

I am sympathetic to your presentation and example. I am aware of the unempirical notions of some of our revered forefathers! The circle or sphere is precisely the point. I can not determine a first cause except by fiat. It is most likely by exhaustion, really. Not by removing all alternatives but by losing the will to continue endlessly uncovering so called causes.

Whrn I learned of the fractal zoom it immediately suggested a terminologically appropriate container in which I could wrap this endless experience and yet talk about it precisely and identifiably.

I too value Socrates and Pato's presentation of the Pythgorean school of thought, and sense Aristotle was a diversion from this line of philosophy . Nevertheless I owe his work a little consideration in order to better understand Newtons's derived concept of motive..

Also, this is a consideration of everyday cause and effect. Philosophically we can never know an absolute cause of anything, even voluntary actions.

Chinese philosophy holds Yin and Yang as the structure of cause and fortune.

Yeah, I guess Logical Positivism would be the closest "School Of Thought" I can claim an affinity to  (without fully embracing, as I find it difficult to fully embrace any school of thought I was exposed to while stumbling my way to a Philosophy Degree)  (I may be the only person to ever Accidentally get a Philosophy Degree! - I was taking Philosophy as electives and bouncing from major to major before settling into Chemistry, when one semester I went to look for another Phi elective, and found that I had taken them all and got an A in every one...  so I just said "Gimme the degree" and that was that).

But my thing for Socky wasn't his presentation of the Pythagorean ideas, but more his "Socratic Method" which I still tend to use in most discussions and debates.  

Plus, I am still rather tickled by the notion that nobody really knows if Socrates ever really existed or not.  Some say he was just Plato's "character" used to get ideas across.

As for Ultimate Causes, I do believe that there must have been a First Cause, but I just don't think we can make any meaningful assertions as to it's nature.  I simply accept that it's a limitation of our existence and try to make do with the rest of the stuff in the universe...

 :rotfl:
It tickles me too! And I love your way of getting a philosophy degree!
I know something of what you mean about our limitations. For some reason some do not want to acknowledge that means of communication can only go so far, and that by consent.
 I decide, as it were, to believe an impossible thing every so often, just for the Socratic Platonic conundrum!
Recognising the limitations of analysis, and so philosophical enquiry Socrates decides to play a game , or Plato decides to make a game. The theory of Forms or Ideas is like one of those character games. You chose which kind or kinds of reality you want to live in, and then you play the game of life.

Unfortunately some play to win, and that means coercion of others. Some do not know they have a choice within the game and they tend to limit their own opportunities. Some invent their own worlds, like Aristotle, and they are either hailed as geniuses or imprisoned in lunatic asylums .

I guess Socrates wanted to see what the outcome was for those who chose one reality. Or Plato preached a powerful utopian positivism based on accepting these ideals as real.
I see it as a free choice, especially when everything else seems to be heavily or unconsciously deterministic.

Somedays I will assent to a first cause, other days I assent to an endless recursive cause, a fractal zoom of analysis of preceding iterative status. Just depends on how tired I am!

I certainly embed consciousness in my concept of space, but at the level of a sensitivity to an environment. It seems to me that analysis of consciousness , at the extreme end of analysis, frays into this generalised notion, which is fractal. One fractal region acts on and reacts to all fractal regions in its immediate neighbourhood.

I recolgnise this is very akin to Newton's third law of motion of bodies, but in fact I now understand that Aristotle considered all kinds of motion in causal relationships. I know Newton admired Aristotle and I see his concepts in the Newtonian concept of Motive.

The Newtonian concept of Motive underpins all his ideas of accelerations. What I believe Newton did was to reduce the agency of gods, spirits and djin, daemonia and demiurge into a abstract concept he called motive. In so doing he squeezed the natural conscious intelligence of these entities into a physical measure called acceleration!

Of course modern scientists are hardly aware of Newton's Principia let alone his metaphysics. I still have to go to a historian of classical thought or classical science to apprehend what Newton had actually done to the intellectual discussions of his time. If only because it allowed him to measure and calculate so much more than his fellows, his view was set to become dominant in a technological age.

He is rightly respected in my view, but he was no saint! He attempted to bury Hookes work. This is usually described as a vengeful act, but it now comes to light, that Hooke was no mean philosopher himself, and in fact as a scientist substantiated all his claims with powerful demonstrations. Hooke above all could demonstrate the " wave" nature of light by his micrographical studies. One wonders if Newton recognised this falsified his optics and thus got rid of the evidence.

Hooke it appears had read Grimaldis treatise on Diffraction, something Newton had not had opportunity to read when formulating his Optics.

However, my point is, we use Newtonian ideas everyday now as part of our fractal reality. Newton was not afraid to think fractally about everything, and his method of Fluxions is his highest accomplishment in fractal thinking.

It suddenly dawned on me that Bruce Lipton has a fractal message relevant to this thread.

Hopefully it wii stimulate some discussion.

http://youtube.com/watch?v=qy29WIZxUOU

So now to Hegel!  :dink:
I guess that now I have come across Hegels philosophy in particular Hermann Grassmanns version and application of it I should discuss its relevance here in detail.

It's funny to me that I have avoided Aristotle despite his absolutely massive influence on Islamic and Western philosophical and Scientific thought: Newton, Hamilton and Hegel as well as Kant use him as a jumping off point. If it were not for Hegel I probably would still avoid him as a digression from the Pythagorean school of thought and philosophy. But Hegel invites these contradicting or contradictory positions, and that interests me a lot.

However I will approach Aristotle via Hegels treatment of him and thus in passing, because really it is Hermann Grassmanns use of Hegel that I feel is most relevant to this forum. Grassmanns use is sufficiently distinct to attract the label Grassmann Philosophy. This is a quintessential Fractal philosophy in my opinion.

Chadafrican and Gregory B Sadler are my recommended commentators on Hegel.

http://youtu.be/cqCzWP6hWio
http://www.youtube.com/watch?v=cqCzWP6hWio

Chadafrican Encyclopedia of Logic

http://youtu.be/6L6zndZs8Js
http://www.youtube.com/watch?v=6L6zndZs8Js

Chadafricans Phenomenology of Geist

http://youtu.be/RNOrAi_QCs4
http://www.youtube.com/watch?v=RNOrAi_QCs4

Carlton Heston narrating on Hegel

http://youtu.be/Jr4jOsAmcYg
There are 2 videos so look for the other on LordXenus channel.

Also listen to the 2 on Ariztotle.

http://youtu.be/oLREMBw6uJg
http://www.youtube.com/watch?v=oLREMBw6uJg

The problem arose in pplynomial geometry. The solution to a cubic involved using a polynomial that had a negative square root!  What could that mean beyond drunken and licentious nonsense, for which Cardano was well known.

However Bombelli was a respected engineer  and he soon drew attention to the algebraic rules of these adjugate magnitudes and their conjugate relations. Despite his brilliant work, Descartes was the one to scoffingly rename them as imaginary, reducing Bombelli and bigging up his own intellect, which to be fair was quite big!

However Newton knew a thing or two about these magnitudes, secrets that he shared only with DeMpivre and Cotes. These two created the theory of the roots of unity!

It was Newton  DeMoivre and Cotes together who advanced the study of multinomial geometry and buried in that was the theory of trigonometric roots, this was a great secret that Newton and De Moivre shared with Cotes Who on learning it solved the rhumb line problem and went on to extend a theorem of DeMoivre regarding powers of trig ratios with a conjugate form . Using this he uncovered the Cotes Euler formula for Napierian logarithms . He was ecstatic because he felt sure it was the key to gravity . But he died before he could explain . However in his work on the integrals of arcs he stated that i was a measure of the quantity of arc

The negative numbers were received with rancour . To add insult to injury the imaginary numbers were proposed to solve polynomial geometric problems . It seemed a step too far and imaginary magnitudes became a mathematical scorn in Britain in particular. On the continent Cauchy and Argand studied them with all seriousness making steady headway with niche applications . Gauss had given them considerable thought but was doubtful of the impact on his reputation. Wessel published a ground breaking study showing how the imaginary numbers had a 1 to 1 correspondence with directions and so were undeniably really useful magnitudes for surveyors .  Gauss who has been surveying Prussia for the emperor immediately understood their validity and published his work reticent about the metaphysics of these magnitudes.

At this time Euler was challenged to define the logarithm of a negative number by his Mentor one of the Bernoulli's who was engaged in a long and vitriolic correspondence with Cauchy over the logarithmic curve. Eulers careful redaction of Integral calculus and Differential calculus not only established the modern approach to calculus, it also took it into new applications, particularly the calculation of arc lengths. In setting that up he rediscovered Cotes formula but in the exponential form. Thus he confirmed that I was a magnitude of arc length, but not as explicitly as Cotes had stated. However his derivation was algebraic and undeniable . He had established once again the imaginaries as really important magnitudes.

The studies of Cauchy Argand , Gauss and Euler were absorbed by LaGrange and LaPlace who took them to places others would not go.

In Britain Hamilton and his friend studied and were impressed by the words of LaGrange and vowed to set algebra on the sound footing of the doctrine(mathesis) of the imaginaries. For this ambition they were lampooned and vilified from one end of the British empire to the other, and were it not for Hamiltons other important works to science he would have been buried in the dung pile of History's crazies.

But the other student of LaGrange faired no better. Grassmann was buried by circumstance and geopolitical instability in the mire of the 100 years wars in Europe. Nobody wanted to read philosophy when scientific and technological revolution was producing so much power and wealth. Gauss certainly did not want to invest time in correcting mathematics which was clearly in trouble. Instead he asked Riemann to take on the task, some 9 years after critiquing a draft of Hermanns manuscripts. He probably even forgot he had read them, or who had written them, favouring his own protogé within the academic system.

But as far as I know Hermann is the only man to state clearly and unequivocally that the imaginary magnitudes are magnitudes of arc, besides Sir Roger Cotes.

What we have just toured through is the historical dialectic process which has eventually in this year 2009 to 2014 led to the unequivocal notion that i is a magnitude of quarter rotation of the unit circle, a quarter arc magnitude. Thus the Hegelian philosophical method and analysis is found to be powerfully vindicated in this matter.

An informed critique of Hegels philosophy of history and such as given in his lectures
http://youtu.be/iTAb64QtzdQ

http://www.youtube.com/watch?v=iTAb64QtzdQ

However he does review Hegels method of analysis and synthesis, not only Hegels shortcomings which are to be expected even from the viewpoint of the philosophy.

He adopts an Aristotelian logic to criticise Hegels logic but describes Hegels logic of categories inaccurately. Ultimately Hegels argument leads to an apprehension of the whole but particular characteristics only ever give a partial truth. While a statement may be true it is not the whole truth. Knowing the whole truth allows the dialectical adjustment of ones understanding, but an Aristotelian would present this as the premise from which to deduce all knowledge! The dialectic does not lead to a first cause, but rather to an infinite regress of greater apprehension of the whole as cause.

Clearly one cannot know the whole and deduce therefrom because one would then be the absolute whole. So in adopting the pretense of absolutes one fails to recognise the truth.

Yes Hegel shows his failings but he des so against the backsrop of the clear power of his own identified method.thus he expects to be challenged and to be dialectically improved.

In addition the reader should be aware of the ad Hominem logic employed in critiquing which is part of the standard toolset of logicians including Hegel . The whole contains some very unpleasant aspects to be sure.so while generally one may subscribe to being nice one hides ones wholesale support of the slaughter of animals and the cutting down of harvests to supply the food chain in which one participates.

Clear thinking in a confused age!

http://youtu.be/mR1SLQwHDog

http://www.youtube.com/watch?v=mR1SLQwHDog

The Hegelian philosophy corrects the Consequences of the Aristotelian methodology.

Explaining the dialectic as a gradual revealing of deeper and wider contexts through comparing and contrasting and perceiving a lack which drives a search for a deeper truth.

http://youtu.be/yjuELzK7-u0

http://www.youtube.com/watch?v=yjuELzK7-u0

The trinity of revelations is a fractal development pattern that ultimately should lead to the truth about The Triune God, whether that be a Christian or other religious or even philosophical one .

Chadafrican on Ziszjeks praxis of Hegelian philosophy.
http://youtu.be/lDkQeTlkpBA

http://www.youtube.com/watch?V=lDkQeTlkpBA

Clear, but not easy listening.

I take from it an overview of Hegelian Philosophy In a historical developmental context, really showing how Hegelian philosophy in the west is still the dominant research tool and explanatory model for philosophy.

I think it dominates because it is fundamentally Fractal in structure.

The divine fractal order of Boethius

http://youtu.be/zQvH8S6nCbw
http://www.youtube.com/watch?v=zQvH8S6nCbw

Newtons Charge
Charge is a concept not often explained
It is a potential to force, accelerate or give motive to objects , inherent in space
Newton devised a system of absolute charge based on the Galilean observations of the Jovian system
The concept was given 3 intimately connected descriptors. The first emphasises the absolute nature of charge or force it is the nearest to zero point energy that Newton gets and in fact is a link between the divine and the mundane. Later he philosophises about the electrical nature of charge in this absolute sense. So he asks us to assume absolute charge exists
The second is the centrally acting nature of charge . Because it is absolute it is central to a point but not just one point every point in a system. This complex notion was expressed poetically by Galileo in the Dialogo . Today we call it fractally scale free or even zero point! The important aspect of this central action was that it was accelerative throughout the sphere of its influence . The law of acceleration was for philosophers to determine . Few know that Neeton tried many
Laws before announcing the inverse square law as most appropriate for gravity, even fewer know that Sir Roger Cotes was about to propose a logarithmic law !
In general the binomial series expansion was
The most convenient calculative svhema to base measurment systems on

The third aspect of charge in this absolute system
Was motive
This was how Neeton brought these general principles into the everyday methods of weights
And measures . Within this
Centrally acting sphere of influence material bodies were given motive or motion in such a way that comparisons of the actions could be made by balance and spring force. This was achieved by using a geometric product if material bulk and accelerative displacement .
These measurements of motive or motion by dynamic equilibrium thus combinatorially encapsulated/ summed the total effect of charge both locally and within the specified absolute system . This meant for each observed absolute system the same laws could be applied and the ensemble Of absolute systems could be calculated as a combinatorial sum for which it was found the same laws seemed to apply
That is until further observations gave a lie to this assumption 
Dark energy and dark matter was born as an alternative charge! Xx

http://m.youtube.com/watch?v=fePQdJNVF9g
When Newton set out his absolute system he based it spatiometrically on the sphere. In fact all Pythagorean Astrologers base their explanations on the sphere . Because of this Euclids last Stoikeia deals ŵith geodesic measurements on the sphere. Newton Halley and all competent Geometers including Wren were conversant with the frame of reference required to describe spherical regions. Thus Newtons framework was richer than the standard Cartesian framework including the circular arc and tangent.

Most scholars off Newton at the time therefore failed to grasp the complex interconnection between the components of his framework and insisted that Ohysicsvand forces and accelerations could only act in straight lines!
Simply put Newtons pulley and rope Mechnics assumes tension acts circularly around a pulley !

It was not until Örsted that a philosopher was brave enough to consider nature was more rotational than his peers believed. He was able to demonstrate a rotational force exists in space around a conductor/ inductor under charge of a battery or voltaic cell .

It is known that his peers were largely mystified by his philosophy, only Ampère understood accepted and demonstrated this circular force of magnetism.

In Newtons systèm the natural path of a celestial body is curved" the Right or Good line is not always straight! As one progresses through his acioms at the beginning of the Astrological Principles the right path changes from straight at ground level to curved at celestiàl level.

Motion in Newtons system is thus geodesic and trochoidal.
Now Einstein reworked Newton using Modern Mathematics . Basically he said the curvature of the sphere and within the sphere is equated to the Gravitational product!
However the mathematics is the same as curvature is equated the spherical form.
Because Einstein used a 4 tensor as a model of space-time " this means that the structure of the equations will be similar to those that include  measures for density! Consequently they give the same result!

The circle is the fundamental form by which we construct all others .
This is the Pythagorean " secret " universal structure.
The line segment that is so called good is constructed by intersecting circle and sphere boundaries. A circle boundary itself requires only a stiff object that contacts a surface ( any surface) in two places. Providing that "point" of contact on the stiff object remains the same during the rotation process around the other "fixed" point of contact a figure within a spherical shell can be " dragged out".  These drawn lines or skesis are not necessarily good or regular or straight but they are consistent by the stiffness constraint.
By intersecting these lines drawn from the two poits of contact we construct a set of intersections that form a circular Plane , and it is this citcular plane that is the ideal plane whose intersection points we use to construct plain straight lines and rectilinear figures .

We note parallelism in this plane and quarter arcs of the plane boundary reference Ortho-gonality.
We note the orthogonal intersection of the diameter based triangles with points on the perimeter.

There are many other invariant constructions we note within these circular constraints based on stiffness.

How do we record some of the important ratios?
Using a diameter we can mark off ratios as segments of the diameter, and we can carry the information on a knotted rope, which when stretched taut can form the basis for unfolding these proportions by cut les of those proportions .
In particular we can unfold the segments into rectangles , parallelograms or other complex combinatorial patterns like opening a penknife, or set of blades.

And so logos( ratio) and arithmod( rectangular mosaics) are related by counting the number of arc segments between each manifestation of an Arithmos. This count is now called the logarithm or exponent based on Bruges work, but understood by Napiers and Briggs exposition of the system.

From this we can grasp how Cotes in his Harmonium Mensuram  noted
Ix= ln(cosx + isinx)
That is the arc associated with the right triangle whose sides are lines cosx and sinx is in fact x!  Here I is used to signify an arc measure within an orthogonal scheme, but also to signify a magnitude that squares to -1 . Placing it before the sin indicates this length is different to the cos length by a direction of a quarter turn! These magnitudes are not homogenous and so can be combined but not subsumed in a larger magnitude of the same kind.

Why -1?
Because our homogenous lines have 2 directions running into each other! O e direction we can call +1 the other -1 and now we have a Dynamic system that records rotations and translations . Of course the totations are semi circular so not very general. introduces a quarter turn into this notation by means of the surd sign.

The surd sign represents processes that involve circular arc constructions so it has always indicated a rotational aspect of our Spaciometry . We were just blinded by the incredulous opinion of our forebears who never expressed processes in symbolic arithmetic and so never used the surd sign. Instead they used completing the square or making into a square technically in Latin "ex quadrature " from which we derived our square radix or square root idea.

Of course we forgot about the underlying circle Spaciometry, and thus symmetry of rotation!
All units are expressible in Eulers magical notation but that notation expresses rather than discovers a practice we have always used, sometimes called neusis of adjusting lines in space by rotation until they pass through 2 points!

This is where we started ,2 points in space associated with citcular( stiff) rotation.

How we express non stiff dynamics is the subject of fluid dynamics .

http://m.youtube.com/waych?v=ZijhIaJQILE
Here the problem of classical physics is well explained .
Note how the wave concept was not sufficient .
Why?

The answer is the incredible misguided notion of a " wave"!
The sine curve was adopted as typifying a wave ! This was a complete mistaken use of the sine curve.
The sine curve traditionally was related to the circle, that is to circular rotation. The sine is a quarter arc rotation decomposition onto an orthogonal axis . The cosine , versine and many other ratios are derived from circular rotation .
Newton had centuries before resolved circular kinematics into sine and cosine measures on orthogonal axes!

Laplace LaGrange and others assumed natural laws were based on straight lines, there were no circular forces. The result was that rotation was considered to be torque!

Circular forces of course rotate freely and therefore accelerated rotation would spin up to unimaginable rotational FREQUENCIES! . Note how velocity is replaced by frequency.

But frequency is related to complete rotations, not pendulum swings!

What is a wave? Well clearly a pendulum swing !
No!

Careful observation of water waves revels they are rotating cylindrical forms or vortices by another name!

When you realise that vortices are fundamental natural phenomna at all scales then quantum becomes understandable .
Fractal distribution in space also becomes very important to become familiar with.
DeMoivre took the first stps to develop a measure of probability that was based on rotation!
Both Newton and thus his student DeMoivre knew that the sine and cosine values could be used to solve certain types of Multinomials ( later called polynomials) . This meant that certain polynomials could be used to describe rotations and that meand periodical or cyclical events! This attracted DevMoivre to apply the sine and cosine tables to the prediction of card game results. This was the notion of likelihood or probability, first explored by Cardano.
DeMoivre was in fact in competition with another Natural Philosopher with regard to the laws of probability but it was agreed that ade Moivre took primacy.
Later Boltzman, Gauss and others worked on the statistical problem of errors in calculations . Again this stochastic problem was similar to probability . The intention to get an accurate result bounds the error and makes the errors cyclical in a probability sense that STATISTCAL.

Boltzmnn statistical approach produced accurate results but it took a while for Statistics to be put on a sound footing of weighted measures normal distributions expected values and standard deviations.

The crossover between statistics and probability is in the unit interval! Between 0 and 1 the results of probability can be applied to statistical situation. This is a strange interval as is -1 to 0. But this is the realm of quantum Mechnaics where statistics, probability and rotation combine, fracially .

We cn best apply our measures to natural phnomena if we assume a vorticular structure is fundamentally what is measurable by our systems.

Entanglement is explained as two counter rotating systems, Einstins left nd tight gloves only they are rotating like spinning coins in opposite patterns! When we determine one we impute the other as Einstein suspected but we do not know the frequency or mplitude of the paired phenomena ,
The event that creates the dual rotating( roulette patterned) phenomena creates counter rotating phenomena . Such phenomena re in superposition that is a tru true made up of rotations in multiple interference patterns . When we measure we collapse this rotional  complex we determine one of its major rotational modes . We then impute a counter major rotational mode in the entangled phenomena. This will be there because rotation demands counter rotation for contiguous regions of space.

Einsteins quantum explanation of photoelectric response is indicative of rotationl frequencies of vortices required to create smaller vorticular events. The quantum is a rotationl complex a vortex very confusingly called a particle!  A lump of energy, and many other descriptors like corpuscle etc are reduced to the term particle. Scientists can only deal with a certain level of complexity. Fortunately rotation compresses complexity into a simple vorticular notion that looks like a conical form.

http://m.youtube.com/watch?v=7GSUrPUFuEs

Sprites are such events and as you see the two counter phenomena are created together, when an upward sprite is seen a downward sprite is always there too, rather the rotational wave exhibits reflection, refraction and diffraction .
Amplitude is the other factor in quantum Mechanics, and this is the diameter of the region in coherence with a vorticular description . Amplitudes will form a fractal distribution that is bell curved shaped and of course this is a plot against frequency . Taking this information we can Fourier transform it by inverse Fourier into a Fourier " petiod"  that is a confined spatial form

http://m.youtube.coe/watch?v=VJ6MAFkP6wQ
The problems of Hubble expanding space are indicators of rotational symmetry . If a galaxy remains in the same spatial position either it is moving proportional to its radial distance or they do not move but we rotate relative to those fixed galaxies!
Einsteins relativity is first proposed by Newtin. Newton takes a view that systems are fractally absolute, based on Galileos observations . Einstein wanted to get away from this absolute premise/ assumption. It turns out if you do then you can only make sense of local events by classical physics. You have to spit a sphere of observation and an absolute of the speed of light . Using this and other assumptions or principles he constructs an alternative way to describe physical phenomna in non absolute terms.
The question is : was it useful? Increasingly it seems to be seen as flawed
Bohr sets out a rotational description of atomic structure . Because of the assumption that particles were solid and waves were not the understnding of the measurements stopped right there.

The simplest explanation was and is to use a fluid dynamic paradigm and vortices .
The vortex is a complex structure which is fractal and contains vortices within it! Where these vortices are is not determined because of rotational superposition that is constructive nd destructive interference of rotations.

The uncertainty principle does not deny the certainty principle! At the quantum level vortices are paramount. You cannot use straight lines! Classicl mechanics cam to rely on straight lines. At the macro level scientists can fudge most explanations into straight line resolutions but at the quantum levlma straight line is a non physical construct. The circular RC is the best measure we can use and that means the sine ratio, the probability laws and the statistical measures are our best means of measuring phenomna.
Quarks are a little bit like Alice in Wonderlands cat! So now we have Schtoedingers Cat and Alices cat.
My friends we mouses are in trouble! Xxx

What simplifies all of these observations for measurement is rotation, that is trochoidal rotation .

http://m.youtube.com/watch?v=RnaG6T-C14Q
When I chose the title Newtons Charge it was because we are taught  that Newton discovered the laws of Gravity. In factvNewton simply constructed a geometric algebra of sufficient flexibility to describe gravitational behaviour by positing a space influence that was absolute to some central point in a fractal way and in a fractal system. Thus the 3 descriptors of force behaviour give no causal framework, and Newton knew this well enough to not commit the mistakes of his students!
He in turn searched for a causative active principle Alchemically and perhaps found a solution in the nascent notions of the Electric Fluid perceived in space itself, but he directly asserted magnetism as a candidate. this was in line with Gilberts suggestion.
Charge thus was and is a potential to drive or exert force on objects, and scientists discovered that this potential came in opposites.
The simple plus and minus is simple precisely because philosophically we can not derive cause beyond these observations. Thus by distinguishing them as fundamental Elementaries we signal no further fruitful exploration is possible.
In fact we never do go behind this fundamental but rather use them judiciously to describe ore complex structures.
Now we think the label electric changes things, but it does not. Wecan replace any label by magnetic and reach the same descriptive conclusions.

However one further characteristic of Newtons absolute system in my mind favours magnetism as more fundamental than electricism, and that is rotation.

Using rotations I can develop a system of multiple charges that model complex magnetic, sonic, thermic electic and gravitics behaviours, but the fundamental structure is rotational/ vorticular. Magnetic behaviours are demonstrably rotational.
Gerald Pollocks gentle musings make so much sense of dat that is currently bathed in highly suspect and complex descriptors .
Amplitude,Freauency and Phase of rotation are fundamental descriptors of a trochoidal model of behaviour. Such a model potentially enables us to describe every o served behaviour by one system

http://magneticuniverse.com/discussion/129/a-sound-magnetic-base#latest
The magnetic universe forum is a collection of individuals who study zed Leedskalnins elegant ideas on magnetism. That is because Ed is just like you and me full of smarts, philosophical, and interested in natural powers, but not interested in being squashed by the academic machine!
The Electric Universe however is waiting in the wings vying to take over the lead position when the current scientific paradigm collapses. Either way they both refuse to start again from scratch!
As a philosopher of the foundations of Thought patterns I find myself drawn to the less busy forums that help me explore and think through my observations . I like to start at the roots. This would be hopeless if in fact the way we construct out patterns of thought were not inductive, iterative,self referential, tautological and thus fractal in the sense that Benoit used to describe it as " almost self similarity".

There are many strict definitions of fractal, but Benoit named the field on the toughness of the forms he was perceiving, forms that could not be described by regular geometrical forms, but yet by forms almost similar to the regular ones, repeated, recurred,iterated into fascinating patterns that achieved some invariance .
If the Mandelbrot set was unrecognisably chaotic we would not be celebrating the nature of fractals! At the same time the iconic image appears only in specific  circumstances showing us that we can pick out invariance but it is still only ever a small part of the possibilities out there.

The tools we use here to generate art and pattern and structure are the thing! Developing expertise with these tools and developing new tools may help us explain natural behaviours in a complex but consistent way.
What it won't do is give me absolute reality. Newton describes how he set up reasonable absolutes for his philosophical project. But he was clear that these assumptions though reasonable, have to prove their utility.
To this day we have barely varied these assumptions, except in the case of Einstein and Bohr, and these variations are of detail not fundamental generality.
The one aspect of Newtons assumptions, that of a rotational action, be it a trochoidal force path or a lineal impulse path in multiple orientations, that has not been explored as Newton envisaged, that is using the circular arc, that one is my obsession
we cn restate, and I sometimes do Newtons first axiom of motion: an object will remain: at rest or in a uniform motion in a trochoidal arc!  That Newton chose the straight line from among all the trochoids is a rhetorical concession to nagger the minds of his audience unfamiliar with advance Apollonian 'Geometry'.

http://plato.stanford.edu/entries/newton-stm/
A detailed discussion of Newtons solution to many philosophical disputes and disagreements.
The problems are identified but not empathised with.
What is space ? What is place ? What is motion ?

Maybe you dont think about such things but are you real? What is "You"?
In that context where to explain in words your apprehension of the answer to these questions is the task you will grasp the slipperiness of nailing these ideas down.

The concept of the Truth also factors into this: what is The Truth and why should we pursue it? The belief innGods in am immanent yet other reality a spiritual reality . What is spirit?
The platonic game of Form or Idea intrigued philosophers of all religious persuasions : you choose whether you accept forms as real and impressive on the soul or idea as real and reified through the soul .
Again in this context the questions about space, time and motion resonate.

The word absolute means "away to sole ", that is to strip away everything and reveal the singular nature of a thing its independence of any other thing . God of course is absolute andvthusbhe dwells in absolute space and time . And only he/she knows the true motion of all things .
That is a religious answer, what is a philosophers answer?
Newton tries to supply that .

http://m.youtube.com/watch?v=S1CB3_1KQGI
In fractal foundations of Mathematics I posited that the fundamental measurement schemes are fractals. They may be uniformly constructed, and so special, but nevertheless they possess self similarity one of the features Benoit identified in his exploration of fractals. To be clear he tweaked it a bit and used the peturbation: almost self similar.
This small change leads to dynamism under iterative calculations, making Calculayion process a driver for small sunthesised differences that add up to a limit sculpture if a cut off or bail out regime is imposed.

This calculative iteration then informs a geometrical application or interpretation.

Some more direct synthetical approaches to fractals involve using a form repeated( iterated) via translation, rotation or reflection, projection or some combination of these spatial transforms, into the entirety of space.
Projection is the general notion of magnification with straight lines or circles used to do the projecting.
Geometries are often characterised by the kind of projection utilised in synthesis of spatial forms and patterns.

Here Norman simply demonstrates that what we may call number has a pattern of representation even in the symbolic format. What you should realise is that Arithmoi are geometric mosaics and it is the count symbols of these mosaics that have come to be thought of as numbers . However the Indian Shunya cyclical systems simply arrange a set ofv9 symbols according to the pattern of gear wheels either concentrically arranged or systematically in contiguous relation in space,
The decimal place value system is a gear chain of ratios that recognise that when the symbol0 is reached the next gear up moves one tooth.the Shunya means "Everything" or in this specific case " full "

It is no mean observation to assert that we are not capable of perceiving" nothing", thus any notion of absolute space based on Nothing is not apprehensible. Absolute space is something whole and entire and independent of its parts, that is why it is absolute that is washed away of all influences absolved of any dependency, sole and totally the prime of all things which being part of it are causatively influenced by it but can not influence it . It is Aristotles prime mover conception . It is the ground of all analysis and the summit of all synthesis , and is often called the Monad in Neo Pythagorean philosophy, the Monad is Shunya , but prejudice seeks to demote Shunya to " nothing"
Shunya is Everything , it is absolute, The Absolute symbolised by an intact w-hole spherical / circular symbol

When I begin to analyse Shunya, or the Absolute I impose experience of extension and intension onto my experiential continuum . I impose surface and side and orientation and direction on extension, and intensity on intension , and in that experience Panta Rhei and I experience rhythm and rhyme the variation of the flowing change from which I derive first the sensations of motion as well as place and then by memories the notion of recorded Tyme.
To impose an absolute time requires a conception of The Absolutte which remembers and is conscious of all it's variations but the independent cause of them all : that is Newtons God, but corvally the fractally distributed conscious universe that is entire. And the prime Cause.
If we ask what is beyond this we show a lack of apprehension of the notion absolute, but we may be satisfied by a fractal synonymous conception that as the magnitude extension scale increases the perceived patterns re occur at larger and larger scales! We therefore rest our enquiry on what may be known, accepting that it is a copy or reflection or consequence of a much greater similarity which may be ascribed to a mysterious nation ofvGods or one Sole Deity reigning Absolutely.

Our systematic "Logic" therefore is merely language that describes as fact or myth or both the perceptions of the found( that is sensed by visual, auditory kinaesthetic and proprioceptive sensory meshes) " reality" .

This reality we must still chose according to Platos game of Idea or Form .
Do I express another reality through my " soul" in my reality, constructing imperfect copies, or do the forms in my reality so impress on my soul that I construct an ideal reality to apprehend and comprehend them in general? Or Both?
I accept as I choose and thus decide by that acceptance of the choice I made. And this then reifies my reality . Not your reality but solely mine!

What is  the meaning of m in Newtons philosophy?

Most miss this out and jump straight to the second law to explain it.
https://www.phas.ubc.ca/~berciu/PHILIP/TEACHING/PHYS340/SLIDES/PDF/Newton-Leibniz.pdf

Of course Newton explains it in the definitions to his Philoophy
m is defined as the quantity of matter and is the product of a measure called bulk or volume and the density of the object measured hydrostaticaily.

This the quantity of matter Is a quantity of standard volumes of water .

So why is mass so enigmatic? It is because the absolute system is fundamental to the accelerative centrifugal and centripetal forces that are part of its design and definition. Thus the standard volume of water has a standard mass if and only if it is N incompressible fluid . The compressibility of fluid may differ on different planetary systems so I compressibility is fundamental to a universal quantity.

Rest mass, kinetic mass, inertial mass all adjectively alter the compressibility of water under those conditions.

http://m.youtube.com/watch?v=qvyiq0S5nyw
A short course worth looking into

Do you understand Zenos Paradox?
Parmenides and Zeno like Socrates and Plato loved to play games with people's minds to teach them to think!
So the tortoise and the athlete, the flight of the arrow are analytical lessons!
How do you Analyse anything! You loose it from the top down( ana: above, top, new, again)
Thus you engage in a process of fractal distribution.
The ancient Greeks of Zenos time announced the principle of exhaustion! We have to stop when we are exhausted!
But then we have to re synthesise all the fractal parts we have analysed!
So if you say: the athlete can never pass the tortoise or the arrow can never move, you have simply forgotten the process you started, an analysis from the top down to its fractal parts, and you have more importantly forgotten to re synthesis all the parts!
For example the athlete is running at a constant pace, as is the tortoise . If you analyse from the point of view of the tortoise the athlete moves in that proportion to its movements, similarly, if you analyse from the point of view of the athlete the tortoise moves in that proportion to his movements. The analyses( plural)are consistent in the proportion and show the athlete covers more ground than the tortoise but always in the same proportion. In addition the tortoise always co ers less an less ground as the athlete approaches unti
 The athlete. At he's and surpasses the tortoise. Our infinite analysis has a finite resolution a limit even if we want to continue the analysis forever!
Time and exhaustion can not be excluded from our ability to process an analysis or synthesise a resolution.

The arrow?
Fundamentally our measures are local. We extend them to dynàmic and universal scales, not always justifiably!
So Einsteins postulate that the speed of light is constant is no more than this measurement issue. We can o ly measure the speed of light in one fixed reference frame . We have to assume that the answer is independent of any reference frame! But we know the speed of light is a bulk property of materials! Thus it is not a constant unless the material is uniformly constant, and our reference frame is made of s h material!

We have no reason to expect a length in dynamic motion will measure the same as a length in relative rest, because the measurement scheme is different, but that is not the same as saying a fixed length physically alters in straight line translation in uniform motion . We just do t know!

High speed photography is our best tool for measuring this phenomenon. We know from frame analysis that physical length is on average maintained in stiff materials, but in liquids the deformations are obvious and interesting.
Quantum mechanics, the black body curve all have a rotational explanation in particular whole number relationships between the measured outputs.

http://m.youtube.com/watch?v=OFzl37nX58A
At this stage Norman has established a coherent view on a representational form depicted on page by certain marks but thought of a responsive process of comparing, matching and verbally expressing: lego,analego, summetro, sumbolo in greek.
To call this Mathematics is deference to a subject name rather than to a description of the process . Mathematikos was a Qulification in scientific thinking really in astrological thinking.

The thought forms utilised by Noman are those from a broader subject called computational science in particular in application to computing mechanisms.
Processes of  listing or collecting are explored prior to a process of sequencing or ordering or succeeding.
The use of the concept of multiplication though tackled is finessed, because hardly anyone now comprehends factoring or fractioning a form by another!

Designing the factoring process defines what a particular style of multipliction could be.
Grasmann in my purview is the only philosopher who tackles this issue.
Here Norman defines multiplication as a kind of addition and this is the only real fundamental definition that cab apprehend the concepts of multiplication!

http://m.youtube.com/watch?v=7NefUTyUNuc
Here Nomn, indulgently, connects his thought forms to his Vexel idea.
The advantage is that he manages to embed his mathmatics in the over arching subject of computational science. That I concur with and find I have a long standing affinity for.

Of course this is a constructionist approach and some might wrongly claim intuition is excluded. Norman may harp on bout logical clarity etc, but the true process involves intuition, design, analogy, definition  And pragmatism .
Hermann Grassmann explains this in detail in the Ausdehnunglehre 1844.

http://m.youtube.com/Watch?v=bGJU9S3i8y8
Technical I know, but wht it is saying is that dropping the quantum theory element gives better results! So if quantum theory is the most accurate model we have thn it can be discarded in the short term nd certainly at the atosecond duration!
In fact the probability glasses we think it fashioble to wear obscures as much as it illuminates. It is a statistical process which works best on large data sets not so good on individual specific situation.
I worry that the mathematical measure that probability is is not understood as a global distortion of data. When renormalised to fit between values 0 and 1 actual data is distorted. Care must be taken to make the experimental outcome sit in the central part of the Bell distribution if classical results are desired!
Is the distorted outcome ever useful?
Pragmatically no,,but for experimental design it helps to minimise errors due to random effects of poor design or poor experimental control , or even  logical oversights . It mayt also indicate areas for additional research. ,
We are very human, we make mistakes, we measure incorrectly we design flawed processes , quantum theory takes that into account by using the probability distribution over the unit interval. . What is significant stands out, whether it be phenomenon or error!

Zeno's conundrum, the tortoise and the athlete teaches us something about our analytical and synthetical methods.
Firstly acknowledge anm8th sense, that of duration the analytical process is a process of cutting from above or over and over anew or again. The purpose to penetrate what lies within a form or structure, to reveal its constituents, the elements whose composition generates the analysed form, or the combinatorial arrangement of those elements that generate the same or new forms and structures.

Our sense of duration is often suspended, sometimes compounded into a false weight ( wait?) or eked out over massive accomplishments that seem to take no time at all! This unreliability in our sense encourages us to devise objective time keepers. the pendulum essentially..

So zenosnanalysis of the stages of motion suspend the sense of duration. In the meantime the analytical elements are increased in number without bound. .
This creates an issue for re synthesis! Suddenly the sense of duration kicks back in and the nalysed realises that it is not possible to finish the resynthesis!

The principle ofvexhaustionnremindsbthe analyser  he is part of the process!

We can also learn from Zeno that fractals are a natural requirement of analysis.
Firstly analysis is a scale free process! Thus it is up to the analyser to select an appropriate scale. . Fractals whether regular , irregular or dynamic set an upper and lower bound for analysis. The elements can be usefully identified by self similarity to the larger synthesised body. . In the case of dynamic bodies we can use the almost self similarity principle.

Ampere for example took a current in a circuit as his dynamic model of the elements of a rotational magnetic field around a current carrying wire in a circuit!

These elements ave been variously interpreted ad atomic structures with electrons circulating, to electrons themselves in some way rotating. , Biot and Savot just elected to use rectangular magnetic force arrows!
 . Consequently their model is accurate enough but limited to the circumstance they depicted"

Rayleigh in fluid mechanics proposed a scale factor determined by the ratio of momentum to viscosity effects,  the Rayleigh number guides application of the same principles at different scales. .thus synthesis and analysis of any fluid dynàmic investigations nd explanations.

http://m.youtube.com/watch?v=0BUR9mKvmi4
Norman clarifies his discussion of a theory of numbers and other mathmatical conventions.

The difficulties are related to scale. The issues go away when we renormalise or redefine the scale unit.
This is essentially a psychological application of fractal philosophy. We state that the arithmetic definitions illmapply to units. That leaves a unit undefined and therefore free to be set by the perpetrator!

In addition we use nalogues to justify or gain insight in applying this schema to almost self similar situations.

So our limitations naturally invoke this cyclical application of a methodology . This is innate within the development of fractals , the recursion or iteration of a defined process .

The distinctive structures ( topological) generated by such iterated processes are what Benoit called fractal. Some rigorous definitions initially limited the powerful applicability of this term, but I for one accept a looser set of defining properties.

We my not be able to prove Mathematically things which we intuitively recognise as fractal but that is no great loss co,pared to the ability to construct these topological patterns either as a resynthesis or as an experiential outcome .

Normns technical problem arises because he bases his foundation on numbers however captured. But his technical difficulty is pragmatically avoided by rescaling. .

The Pythgoreans based their philosophical treatment on topological forms . From foms we define counting and measuring , and these counting/ measuring practices give rise to mosaics called Arithmoi . It is one aspect ofvarithmoi that has come to be called numbers. By forgetting these connections moden Mathematicians including Norman, try to found their ideas on logic and a Minimal symbolic label or marker.

Grassmann particularly Justus attempted to found mathematics on logic and natural topological forms ( not the supposed ideal forms of the Greek philosophers) . However, natural forms are not regular , but irregularity is not without structure, Benoit by coining the term fractal sought to portray the roughness of natural forms but not as random roughness . In fact the complexity of randomness as a notion is redefined in the light of fractal topology.

http://m.youtube.com/watch?v=rCDRCGjmaO8

The Axioms of the Stoikeia do not exist! Axiom derives from the notion of an axle . These notions became identified as central tenets of any subject, that is the central dogma! . When classicists invented and used the term it was not to develop a Euclidean/ Pythgorean Teaching scheme or curriculum.  Instead it was more in keeping with a Platonic or Aristotelian discoursive approach where the central or axiomatic topics of a philosophical debate or discussion is where the continuing discussion starts anew,
Thus axioms originally required prior knowledge , learning or experience in a subject.
So what are the 5 in the Stoikeia?
They are Demands ( aitema) placed on the student to enter the course!
The word postulate means to beg or request with supplications! In polite society this is equivalent to demanding!
A list of items is a list of things required!

We therefore must not downplay the abolute embarrassment Mathematicians feel,about spending centuries trying to "prove" the 5th postulate!!!
It was and is a simple requirement on students or urveyors!
To do the course you need to be able to provide a straight edge that can join two points with a straight line! .,we take such rulers for granted, but if you do not have one how to you make one? It is not as easy as you might think!
You need to be able to extend a straight line, you need to be able draw a circle of a given segment size. Given a stiff segmnt and a fixed point a circle can easily be drawn, but to draw any circle you need to be able to provide this type of implement.

The 5th requirement is actually a requirement to draw straight lines that intersect however far they have to go to intersect! Surveyors need to be able to measure long distances and use straight lines that intersect . You can't use a curved line!

However spherical geometry assumes curved lines that intersect, that is a different more advanced philosophical discussion tackled in ancient times. 

Cantors demonstration of the continuum being a different infinity to the natural numbers infinity collapses to nothing when you realise that it is impossible to list all the real numbers so called and impossible to list all the natural numbers.
But we can structure the natural numbers but we can't structure the continuum? Well yrs we can structure the continuum by adopting a fractal structure . It might seem that structure must be larger than the natural number infinity, but of course we can not prove that , only assert it.

However this structure is nothing new. We have extensive magnitudes and intensive magnitudes and fractals are on the interplay between intensive and extensive magnitudes.
We know qualitatively intensity is different to extensivity.

I hear the conceit of potential infinity and actual infinity, but that is semantics. People want to keep the number infinity concept rather than the endless process.

http://m.youtube.com/watch?v=5rDxNjouzdg

http://m.youtube.com/watch?v=ywSQRggFjVg
These methods as explained are flawless! They indicate how thoroughly Newton apprehended the algorithm of Euclid in Stoikeia 7.
The setting out  and the algebra are 2 modern intrusions to try to " clarify" the rhetorical explanation usually given.
Of course in introducing these notations students tended to forget the process for continuing fractions or power series etc. thus they believed the = sign , not given in the original, meant actual equality! Thus we get into the Berkley misunderstanding of these Newtonian quantities, and the modern concern about convergence of series.

The long division arithmetical example is in fact a lay out established around the time of Brahmagupta, and promoted by him, but his layout relies on the power series base 10! Thus the polynomial reduction calculates the coefficients for this serie! Convergence is not an issue!

The second example highlight how to do a power series to a different base  and again convergence is not an issue.

If one uses the negative index for the powers less than one then the coefficients are relative to those.. Note how in calculating 1/8 the coefficients of the powers of 10 are calculated as a whole number by using not the next decimal place value but 10 times the next decimal at each stage.

One very important practice not explained here and again misunderstood when infinitesimals are mentioned the quantitative size of the magnitude and of the procedural product of a multiplication process with that magnitude are kept in mind!! So the product of any magnitude less than 1 in size with any other magnitude gives an output that is less in size than the product with 1 !!

Hence when reducing by Euclids algorithmic method the divisor is continually reduced in relative size until a whole count results . This is true in polynomial " division" as in ordinary arithmetic with " numbers". The practice of writing in power series is to acknowledge the structure on which numeral systems are based . The Hindu Arabic is a base 10 polynomiàl series, but of course other bases may be used and frequently are.

In addition the reduction from larger divisor/ factor to smaller factor does not have to proceed from left to right . In the case of 1/1-x where x is bigger than one the reduction can be performed the other way as the size is clearly larger than the item being factored. Alternatively one can proceed with negative powers ( a modern alternative) and negative size. In Newtons time these representations would not be understood unti Wallis established a consistent Algebraic notation for fractional and negative logarithms/ exponents / powers.

Today's emphasis on convergence etc is due to this fact , symbols completely mystify students who can not then relate the notation to actual quantities in their experience . Early Astrologers were taught better than we often are and so were not explicit about many obvious things.

http://m.youtube.com/watch?v=i5TFXyI4UMM

I am grateful for this video, which is why I posted the previous post. Newton never created a flawed system or method, he just lived in a time when others would steal or corrupt another's ideas fir financial or social or political gain. His academic papers written in Latin were sometimes written in code for that reason .

Here we see how the fulmination of Betkely to this day clouds the apprehension of Newtons method!

Suffice to say Berkely was well refuted by Cotes aad others at the time,mbut in a time of clerics, clerics rule! And Berkleys ferment had his intended effect regardless of its effect on Newtons reputation: religious philosophers came to heel while those who were atheistic we're forced into a semantic cubbyhole from which they to this day have not emerged!

The ideas of infinite / endless is well defined in philosophy, but in religion it is by design mysterious! Thus to some clerics it is blasphemous to even talk about infinity without acknowledging God or Jesus! But the Greeks did just that , because it is a semantic label for a human experience not a divine one! To any clear thinking Astrologer just as we can count without end, so we can factor without end. But Lucretius and Democritus insisted that there Must be an end to cutting a material object , even if we can continue to break it into parts in our minds! Thus the word atom was given its material significance as the material that can not be divided further!

To accept this stance is to immediately distinguish between matter and spirit. This basic asserted dichotomy underpins the argument between materialists and those who accept an immaterial reality. Clerics of course favoured the latter, but as Berkeley observed many philosophers were abandoning the tenets of the church for a materialist point of view.
Logically there is no irrefutability or either position, and this is what Berkeley was driving home. No one cn deny the other by the tenets of the dichotomous stances, both demand an equal faith response!

However, as logic was intended when designed by the greek schools of Rhetoric, one may present an argument to persuade by fair means or foul, and ridicule, ad Hominem, and many other logical devices were outlined and taught in the schools of rhetorical logic.

Berkeley picked on Newtons infinitesimal notion because he knew his audience did not understand it! He was careful not to claim Newton said, for libel was a serious issue in his day, but cleverly he points out that an apparent contradiction lies at the heart of Newtons method.
Then he asks in an attempt to ridicule : what are fluents,Fluxions and these vanishing quantities?

Now in Europe infinitesimals were considered as a joke ! But this again wasvduevo trying o call them numbers!
Everyone thinks they know what a number is!! Clerics were of the opinion they were ( whatever they are) divinely revealed by God and set out sensibly in the bible and in Nature. Thus infinitesimals were undoubtedly the  work of Error or at worst of the devil.

I can not emphasise just how tiring this kind of thinking is! For a classicist to read the Ancient Greek clear exposition of arithmos and how to philosophise quantity with them must have been a huge relief.

So infinitesimals for Newton, like infinity were semantic word labels for endless processes! Once you stop such a process it is by force no longer infinite!!! Thus to use a symbol is not to make it an Arithmos!
 2 other things highlight Newtons explanations . Fluents or fluids were time dependent, and his symbol is gor a small moment in time. While an extensive unity may be objectified, time is n intuitive srns that I highly subjective. The sense of duration requires such LanguGe as nascent, evanescent, vanishing etc. a clock, or pendulum do not replace our time sense, they merely provide a scaffolding in which to erect a onsidtent and conventional measure.

The second was a concept of dynamic variation. Even classical philosophers considered forms in static poses or stages of pause. Zeno sets aside time intervals in his famous argument to focus on the clear stages for comparison , thus fluidity is not incorporated in classical Mechanics.

It is still difficult to get this idea across even today! Fortunately we cn use the high speed camera metaphor to capture Newtons vision of fluents and fluxions. We can now visually track a fluid action and see the intensity of a Fluxions by comparing 2 sequential frames in such a movie.

Newton did not divide either. He factored. When you factor you do not Divide you look for the factor that gives a certain quantity, that is you look orthe Quotient!.

Often the concept of multiplication is used to explain quotients, but it is in fact the concept of counting factors of a given form that we need to inculcate. Our understanding of factors is codified in the binomial theorem but essentially the mosaics of old or a pile of bricks demonstrates factors and their equivalent topologies.

The rule not to divide by nothing is therefore patently nonsensical, but when you set up such algorithmic presentations of the factoring process and systematic synthesis or Combinatorial schemes these rules of thumb often pop up.

.let us now consider newtons fancy: suppose we have an infinitesimal moment in a fluid situation. This is like taking a snapshot at a trillion frames a second . The infinitesimal momnt is between frame 1 and 2 ! But that is at a trillion frames a second. What if we increase the frame rate to 10 trillion ? Then frames 1 and 2 now show a different relationship. If the quantities were not fluent there would be no change.

The symbol for this time step can not be fixed and it can not be evaluated because once you do you are no longer fluid! We know how high spped cameras Freeze fluid motion. The concept of freezing fluid motion is entirely novel to Newton. Leibniz still clung to the notion of a differential and that in an extension. Newton realised a differential in time might freeze a fluent and reveal its Fluxions or freeze frame changes.

So what about a term which contains an infinitesimal as a factor? In this case Newton new they were pragmatically useless. They can not be measured but if they could they would make the product so small as to be vanishingly small! Newton does not drop them, he just works with approximations from that point on
There is no need to go to a limit because a fluent is dynamic, continuous and clearly flows before nd after any chosen time frame. The Fluxion for a constant flow should be the same no matter when measured . The tiny piece he ignored in approximating is vanishingly small and not measurable in practice, especially if working at the limit of ones ability to measure.

The approximations of Newtons methods have served a pragmatic technology well.

http://m.youtube.com/watch? V=eOPpZ7eOAtA
The Sandkrit philosophy of the Upanishads heavily influenced Greek thought and then the Prussian and European intellectuals.
This clear explanation of Brahman also explicated the central role of Shunya that is Everything .
Shunya is the substratum from which all forms derive.