All I'm saying when speaking of such things Lloyd is that there are those things being satisfied within the macro and micro and the path to me is to understand what such things are whereby we might just find that with the proper paradigm and perspective it is the very same thing being satisfied at all scales due to conservation of c mechanics. Thus, the geometric asymmetry we see before us is conserving a deeper symmetry or at least attempting to. I have no problem with asymmetry existing because from my perspective the constant conservation of substance from structured to unstructured states by way of rad decay, absorption and such along with the opposing motion states which produce the surface interactions which establish charge and such are all evidence that symmetry is never maintained. There seem to be those things which are required to be satisfied and those actions which arise when such isn't satisfied.

It takes two opposing dynamics which can never be satisfied completely to make perpetual existence as anything less would resolve itself through time. There must remain the unsolvable problem of the fundamentals of matter, space and time which allows for the state changes that perhaps cycle such a universal volume as the one we find ourselves within. I'm speaking at the most fundamental level of course.

The progression of the universal system through time establishes one fundamental substance taking on all of the various forms of structured and unstructured states while its transitional actions back and forth between such account for all of the forces we measure and find in nature. It's merely how the volume morphs itself internally whereby we might find existence. Following such a progression through time and space allows for all asymmetries and symmetries which we know of to exist, but just as we often find laws which seem to be homogenous throughout the universe, all are plausibly relational due to an underlying function which is perhaps due to the very quantization aspects I was referring to or something similar. I'm not certain how we would have motion at all if an underlying rule was constantly satisfied per a maintained state of symmetry as every measurable aspect we know of is made possible due to the unsatisfied side of the equation and is testament thereof. When I speak of such things I'm only implying that there is a motion related entropy which the system strives for at all resolutions which we translate as being distinct actions depending on the scales at which we observe it, as seen when volumes begin to clump together in ever more massive volumes.

Best I can do on a sleepy mind which has been on vacation.

Why Fundamental Asymmetries Necessarily Exist…

Hi Tim, and in answer to your desires for the Universe to have a fundamental absolute symmetry__just let me show you why this is impossible with absolutely simple math, and its simply extended permutations through even simpler addition, and the fundamental rules of addition or combinatorics, as the same...

Take any absolute fundamental you choose, time, motion, matter, FS, energy, charge__and use any method you choose to convert such fundamentals to real mathematical representations, as per 1, 2, 3, __ positive & negative __ true & false, 1’s & 0’s, etc. It matters not how you work out the permutations, you must first work out the most fundamental logic of the permutations, and that is to logically consider what exactly is required to build these fundamental permutations or combinatorics from absolute scratch(as it's scratch we are usually theorizing from, in these areas)__as per applies to symmetries and asymmetries. The easiest to see is most likely the positive and negative charges, of say the fundamental em forces of the most fundamental photon mechanics, i.e., it's polarization and double polarization potentials, as was actually proved by Huygens, over 300+ years ago. Iff you have only absolute symmetry as your most fundamental logic and physical action, your method can never produce the asymmetries__we absolutely know makes up just about half of the Universe, as the negative and irregular forces__we plainly see. In order for such asymmetries to exist, which we know they do, they must be just as fundamental as the symmetries, or they can't possibly exist__Due to this absolute fundamental dynamics:

1. If you start any math with perfect symmetries, such symmetries can only produce more symmetries...

2. Only asymmetries are possible of producing both symmetries and still other asymmetries...
3. Simple example: 1+1=2_a symmetry... Only -1+1=0_an asymmetry... Yet, -1+-1=+2_a symmetry...
4. No matter how you set these fundamental charges up, only a fundamental -1+-1=+2 will create that first positive symmetry(two negatives produce a positive example), of a required combinatoric Universal permutation math, applied to Bose-Einstein Photonic Condensation__From An Absolute Fundamental Field...(thus the requirement of my 9 fundamental degrees of freedom)
5.The Absolute Fundamental Asymmetric and Symmetric Charges Are Necessitated to Primordially Exist, To Exist At All__Which we know, in the end result, they do...
6. No absolutely fundamental permutations exist, except as asymmetries/symmetries building symmetries/asymmetries, at the same time asymmetries are building more asymmetries, as it's the asymmetries which are responsible for either building All symmetries and asymmetries, due to the mechanical fact__symmetries can Never build asymmetries...(and herein lies the deep motion catch, to wrap one's mind around...)(this is probably better understood through Markov Chains... http://en.wikipedia.org/wiki/Markov_chain )
7. +1+1 only makes +2... 1+2 only makes a +3 charge, i.e., no negative asymmetric change possible from positive integers...
8. Only the asymmetric negatively charged numbers(photons or poles of photons) produce the required negative charges, to build any of the known to exist asymmetries...(asymmetries seem to be built into the fundamental photons, or FS-Field as such...)(Really, they'd have to be, wouldn't they Tim...?)(Seems as though that would be a basic necessity of any quantized field__No...?)
9. Combine the most fundamental permutations any way you wish, you can't possibly produce a fundamental asymmetry__unless your permutation maths and particle-waves include an 'absolute fundamental negative asymmetry'__no matter whether produced by colliding wave-particles or mathematical permutations, Markov Chains and/or any possible combinatorics...(you just can't get negatives outta positives, no matter how hard you try, but you can get positives outta two negatives__just mathematical, fs-motion and charge facts...)

'Absolute Asymmetry Is An Absolute Fundamental Necessity of FS-Motion'__By default of its fundamental necessity, which can not be divided or derived as any sort of smaller infinitesimal action of Reality__Possible...

Absolute divisions/differentiations within 'The Absolute Calculus' http://en.wikipedia.org/wiki/Tensor prevents any other possibilities...(Tim, imo people/scientists/logicians/mathematicians/physicists/whoever, just haven't looked deep enough into FS-Motions absolute necessities of fundamental actions...)

Tim, if you look at permutation math explanations, even here http://en.wikipedia.org/wiki/Permutation on Wiki, you'll see they've truly left out this most fundamental necessity, and probably due to a defunct logic, of not realizing, logic requires triadic proofs of all its actions, or it's simply invalid psychology, even as applied to the logic of math...

If you'll notice Tim, in the entire above Wiki article, there's no mention of the 'fundamental triadic necessity method' of the fundamental proofs needed... Logics and maths trying to prove themselves, within themselves, was proved by both Godel and Tarski to be impossible, back in the `30's, and the last half of the 20'th century, was spent trying to develop just such sound proofs, verifications and validities of fundamental logics. As far as my studies go, only the 'cross-product of triadic systems of proofs is valid'__to accomplish this very tickleish job__otherwise, you're left defending the impossibility of the purely psychological ego, which ain't valid in any logic and/or math systems' proofs, as it's simply a circular logic pertaining only to itself__a dis-allowed ego-logic, where any hard science is concerned...

The above 9 points have been worked out much better and more thoroughly by other mathematicians/logicians than myself, but I don't happen to have the information at my fingertips, as I take so many notes, it's too hard to find until I better organize my most recent notes, over the last 6 months__that's over 2000 pages long... Every time I try to use search, I come up with far too many links, until I better collate the notes into subject categories...(that's why category logic is oh so needed, but when I'm just research reading, I can't take the time to properly collate, on the fly, or I'd never finish my research... Btw, my research is finally coming to an end, and I'll be collating my notes over the winter__I've only about 10,000 pages of em... Last time I had about 50,000 pages of em__That took three years, to just collate...)

Tim, see if you can give me a 'mathematically changed system', that can be produced by only symmetries, which produce asymmetries__without such fundamental motions, already containing such fundamental asymmetries, to do so...(I don't think it possible...!!!)

That's my challenge to ya... 

http://en.wikipedia.org/wiki/Andrey_Markov

http://en.wikipedia.org/wiki/Gregorio_Ricci-Curbastro

http://en.wikipedia.org/wiki/Pafnuty_Chebyshev

http://en.wikipedia.org/wiki/Tullio_Levi-Civita
http://en.wikipedia.org/wiki/William_Kingdon_Clifford
http://en.wikipedia.org/wiki/Alexander_Bain
http://en.wikipedia.org/wiki/William_Rowan_Hamilton
http://en.wikipedia.org/wiki/Augustus_De_Morgan
http://en.wikipedia.org/wiki/Charles_Sanders_Peirce
P.s.
DeMorgan, Hamilton, Bain, Peirce and Clifford are excellent souces of the logic I draw from, as they be the founding fathers of the physics' logics and maths, more widely used in standard model physics, than all the others put together__and include the above logic discussions, at these most fundamental necessity levels...

The Importance of Hypothesis To Reality Correspondence…

Kepler's Conservation of Angular Momentum__1609...

Illustration of Kepler's second law. The planet moves faster near the Sun, so the same area is swept out in a given time as at larger distances, where the planet moves more slowly. The green arrow represents the planet's velocity, and the purple arrows represents the force on the planet...

Kepler's Scientific Method...

(Click to enlarge...)

The Uniformeity of Continuum Mechanics…

Gravity is proportionally co-ordinate to angular momentum__at all levels__CM à RM à QM…

http://en.wikipedia.org/wiki/Kepler's_laws_of_planetary_motion

Nikolai Ivanovich Lobachevsky (Russian: Никола́й Ива́нович Лобаче́вский) (December 1, 1792 – February 24, 1856 (N.S.); November 20, 1792 – February 12, 1856 (O.S.)) was a Russian mathematician and geometer, renowned primarily for his pioneering works on hyperbolic geometry, otherwise known as Lobachevskian geometry. William Kingdon Clifford called Lobachevsky the "Copernicus of Geometry" due to the revolutionary character of his work.

Chance & The Necessity of Free-Will...

(Hi Tim, check out Boethius, from the 6th century__a major logician-mathematician-physicist of antiquity...)

BOOK V.

I.

She ceased, and was about to pass on in her discourse to the exposition of other matters, when I break in and say: 'Excellent is thine exhortation, and such as well beseemeth thy high authority; but I am even now experiencing one of the many difficulties which, as thou saidst but now, beset the question of providence. I want to know whether thou deemest that there is any such thing as chance at all, and, if so, what it is.'

Then she made answer: 'I am anxious to fulfil my promise completely, and open to thee a way of return to thy native land. As for these matters, though very useful to know, they are yet a little removed from the path of our design, and I fear lest digressions should fatigue thee, and thou shouldst find thyself unequal to completing the direct journey to our goal.'

'Have no fear for that,' said I. 'It is rest to me to learn, where learning brings delight so exquisite, especially when thy argument has been built up on all sides with undoubted conviction, and no place is left for uncertainty in what follows.'

She made answer: 'I will accede to thy request;' and forthwith she thus began: 'If chance be defined as a result produced by random movement without any link of causal connection, I roundly affirm that there is no such thing as chance at all, and consider the word to be altogether without meaning, except as a symbol of the thing designated. What place can be left for random action, when God constraineth all things to order? For "ex nihilo nihil" is sound doctrine which none of the ancients gainsaid, although they used it of material substance, not of the efficient principle; this they laid down as a kind of basis for all their reasonings concerning nature. Now, if a thing arise without causes, it will appear to have arisen from nothing. But if this cannot be, neither is it possible for there to be chance in accordance with the definition just given.'

'Well,' said I, 'is there, then, nothing which can properly be called chance or accident, or is there something to which these names are appropriate, though its nature is dark to the vulgar?'
'Our good Aristotle,' says she, 'has defined it concisely in his "Physics," and closely in accordance with the truth.'

'How, pray?' said I.

'Thus,' says she: 'Whenever something is done for the sake of a particular end, and for certain reasons some other result than that designed ensues, this is called chance; for instance, if a man is digging the earth for tillage, and finds a mass of buried gold. Now, such a find is regarded as accidental; yet it is not "ex nihilo," for it has its proper causes, the unforeseen and unexpected concurrence of which has brought the chance about. For had not the cultivator been digging, had not the man who hid the money buried it in that precise spot, the gold would not have been found. These, then, are the reasons why the find is a chance one, in that it results from causes which met together and concurred, not from any intention on the part of the discoverer. Since neither he who buried the gold nor he who worked in the field intended that the money should be found, but, as I said, ithappened by coincidence that one dug where the other buried the treasure. We may, then, define chance as being an unexpected result flowing from a concurrence of causes where the several factors had some definite end. But the meeting and concurrence of these causes arises from that inevitable chain of order which, flowing from the fountain-head of Providence, disposes all things in their due time and place.'

SONG I.
Chance.

In the rugged Persian highlands,
Where the masters of the bow
Skill to feign a flight, and, fleeing,
Hurl their darts and pierce the foe;
There the Tigris and Euphrates
At one source [O] their waters blend,

Soon to draw apart, and plainward
Each its separate way to wend.
When once more their waters mingle
In a channel deep and wide,
All the flotsam comes together
That is borne upon the tide:
Ships, and trunks of trees, uprooted
In the torrent's wild career,
Meet, as 'mid the swirling waters
Chance their random way may steer.
Yet the shelving of the channel
And the flowing water's force
Guides each movement, and determines
Every floating fragment's course.
Thus, where'er the drift of hazard
Seems most unrestrained to flow,
Chance herself is reined and bitted,
And the curb of law doth know.

FOOTNOTES:

[O] This is not, of course, literally true, though the Tigris and Euphrates rise in the same mountain district.

II.

'I am following needfully,' said I, 'and I agree that it is as thou sayest. But in this series of linked causes is there any freedom left to our will, or does the chain of fate bind also the very motions of our souls?'

'There is freedom,' said she; 'nor, indeed, can any creature be rational, unless he be endowed with free will. For that which hath the natural use of reason has the faculty of discriminative judgment, and of itself distinguishes what is to be shunned or desired. Now, everyone seeks what he judges desirable, and avoids what he thinks should be shunned. Wherefore, beings endowed with reason possess also the faculty of free choice and refusal. But I suppose this faculty not equal alike in all. The higher Divine essences possess a clear-sighted judgment, an uncorrupt will, and an effective power of accomplishing their wishes. Human souls must needs be comparatively free while they abide in the contemplation of the Divine mind, less free when they pass into bodily form, and still less, again, when they are enwrapped in earthly members. But when they are given over to vices, and fall from the possession of their proper reason, then indeed their condition is utter slavery. For when they let their gaze fall from the light of highest truth to the lower world where darkness reigns, soon ignorance blinds their vision; they are disturbed by baneful affections, by yielding and assenting to which they help to promote the slavery in which they are involved, and are in a manner led captive by reason of their very liberty. Yet He who seeth all things from eternity beholdeth these things with the eyes of His providence, and assigneth to each what is predestined for it by its merits:

'"All things surveying, all things overhearing."'

SONG II.
The True Sun.

Homer with mellifluous tongue
Phœbus' glorious light hath sung,
Hymning high his praise;
Yet his feeble rays
Ocean's hollows may not brighten,
Nor earth's central gloom enlighten.

But the might of Him, who skilled
This great universe to build,
Is not thus confined;
Not earth's solid rind,
Nor night's blackest canopy,
Baffle His all-seeing eye.

All that is, hath been, shall be,
In one glance's compass,
HeLimitless descries;
And, save His, no eyes
All the world survey—no, none!
Him, then, truly name the Sun.

III.
Then said I: 'But now I am once more perplexed by a problem yet more difficult.'

'And what is that?' said she; 'yet, in truth, I can guess what it is that troubles you.'

'It seems,' said I, 'too much of a paradox and a contradiction that God should know all things, and yet there should be free will. For if God foresees everything, and can in no wise be deceived, that which providence foresees to be about to happen must necessarily come to pass. Wherefore, if from eternity He foreknows not only what men will do, but also their designs and purposes, there can be no freedom of the will, seeing that nothing can be done, nor can any sort of purpose be entertained, save such as a Divine providence, incapable of being deceived, has perceived beforehand. For if the issues can be turned aside to some other end than that foreseen by providence, there will not then be any sure foreknowledge of the future, but uncertain conjecture instead, and to think this of God I deem impiety.

'Moreover, I do not approve the reasoning by which some think to solve this puzzle. For they say that it is not because God has foreseen the coming of an event that therefore it is sure to come to pass, but, conversely, because something is about to come to pass, it cannot be hidden from Divine providence; and accordingly the necessity passes to the opposite side, and it is not that what is foreseen must necessarily come to pass, but that what is about to come to pass must necessarily be foreseen. But this is just as if the matter in debate were, which is cause and which effect—whether foreknowledge of the future cause of the necessity, or the necessity of the future of the foreknowledge. But we need not be at the pains of demonstrating that, whatsoever be the order of the causal sequence, the occurrence of things foreseen is necessary, even though the foreknowledge of future events does not in itself impose upon them the necessity of their occurrence. For example, if a man be seated, the supposition of his being seated is necessarily true; and, conversely, if the supposition of his being seated is true, because he is really seated, he must necessarily be sitting. So, in either case, there is some necessity involved—in this latter case, the necessity of the fact; in the former, of the truth of the statement. But in both cases the sitter is not therefore seated because the opinion is true, but rather the opinion is true because antecedently he was sitting as a matter of fact. Thus, though the cause of the truth of the opinion comes from the other side,[P] yet there is a necessity on both sides alike. We can obviously reason similarly in the case of providence and the future. Even if future events are foreseen because they are about to happen, and do not come to pass because they are foreseen, still, all the same, there is a necessity, both that they should be foreseen by God as about to come to pass, and that when they are foreseen they should happen, and this is sufficient for the destruction of free will. However, it is preposterous to speak of the occurrence of events in time as the cause of eternal foreknowledge. And yet if we believe that God foresees future events because they are about to come to pass, what is it but to think that the occurrence of events is the cause of His supreme providence? Further, just as when I know that anything is, that thingnecessarily is, so when I know that anything will be, it willnecessarily be. It follows, then, that things foreknown come to pass inevitably.

'Lastly, to think of a thing as being in any way other than what it is, is not only not knowledge, but it is false opinion widely different from the truth of knowledge. Consequently, if anything is about to be, and yet its occurrence is not certain and necessary, how can anyone foreknow that it will occur? For just as knowledge itself is free from all admixture of falsity, so any conception drawn from knowledge cannot be other than as it is conceived. For this, indeed, is the cause why knowledge is free from falsehood, because of necessity each thing must correspond exactly with the knowledge which grasps its nature. In what way, then, are we to suppose that God foreknows these uncertainties as about to come to pass? For if He thinks of events which possibly may not happen at all as inevitably destined to come to pass, He is deceived; and this it is not only impious to believe, but even so much as to express in words. If, on the other hand, He sees them in the future as they are in such a sense as to know that they may equally come to pass or not, what sort of foreknowledge is this which comprehends nothing certain nor fixed? What better is this than the absurd vaticination of Teiresias?

'"Whate'er I sayShall either come to pass—or not."

In that case, too, in what would Divine providence surpass human opinion if it holds for uncertain things the occurrence of which is uncertain, even as men do? But if at that perfectly sure Fountain-head of all things no shadow of uncertainty can

possibly be found, then the occurrence of those things which He has surely foreknown as coming is certain. Wherefore there can be no freedom in human actions and designs; but the Divine mind, which foresees all things without possibility of mistake, ties and binds them down to one only issue. But this admission once made, what an upset of human affairs manifestly ensues! Vainly are rewards and punishments proposed for the good and bad, since no free and voluntary motion of the will has deserved either one or the other; nay, the punishment of the wicked and the reward of the righteous, which is now esteemed the perfection of justice, will seem the most flagrant injustice, since men are determined either way not by their own proper volition, but by the necessity of what must surely be.

And therefore neither virtue nor vice is anything, but rather good and ill desert are confounded together without distinction. Moreover, seeing that the whole course of events is deduced from providence, and nothing is left free to human design, it comes to pass that our vices also are referred to the Author of all good—a thought than which none more abominable can possibly be conceived. Again, no ground is left for hope or prayer, since how can we hope for blessings, or pray for mercy, when every object of desire depends upon the links of an unalterable chain of causation? Gone, then, is the one means of intercourse between God and man—the communion of hope and prayer—if it be true that we ever earn the inestimable recompense of the Divine favour at the price of a due humility; for this is the one way whereby men seem able to hold communion with God, and are joined to that unapproachable light by the very act of supplication, even before they obtain their petitions. Then, since these things can scarcely be believed to have any efficacy, if the necessity of future events be admitted, what means will there be whereby we may be brought near and cleave to Him who is the supreme Head of all? Wherefore it needs must be that the human race, even as thou didst erstwhile declare in song, parted and dissevered from its Source, should fall to ruin.'

FOOTNOTES:

[P] I.e., the necessity of the truth of the statement from the fact.

SONG III.
Truth's Paradoxes.

Why does a strange discordance break
The ordered scheme's fair harmony?
Hath God decreed 'twixt truth and truth
There may such lasting warfare be,
That truths, each severally plain,
We strive to reconcile in vain?

Or is the discord not in truth,
Since truth is self consistent ever?
But, close in fleshly wrappings held,
The blinded mind of man can never
Discern—so faint her taper shines—
The subtle chain that all combines?

Ah! then why burns man's restless mind
Truth's hidden portals to unclose?
Knows he already what he seeks?
Why toil to seek it, if he knows?
Yet, haply if he knoweth not,
Why blindly seek he knows not what?[Q]

Who for a good he knows not sighs?
Who can an unknown end pursue?
How find?
How e'en when haply found
Hail that strange form he never knew?
Or is it that man's inmost soul
Once knew each part and knew the whole?

Now, though by fleshly vapours dimmed,
Not all forgot her visions past;
For while the several parts are lost,
To the one whole she cleaveth fast;
Whence he who yearns the truth to find
Is neither sound of sight nor blind.

For neither does he know in full,
Nor is he reft of knowledge quite;
But, holding still to what is left,
He gropes in the uncertain light,
And by the part that still survives
To win back all he bravely strives.

FOOTNOTES:

[Q] Compare Plato, 'Meno,' 80; Jowett, vol. ii., pp. 39, 40.

IV.

Then said she: 'This debate about providence is an old one, and is vigorously discussed by Cicero in his "Divination"; thou also hast long and earnestly pondered the problem, yet no one has had diligence and perseverance enough to find a solution. And the reason of this obscurity is that the movement of human reasoning cannot cope with the simplicity of the Divine foreknowledge; for if a conception of its nature could in any wise be framed, no shadow of uncertainty would remain. With a view of making this at last clear and plain, I will begin by considering the arguments by which thou art swayed. First, I inquire into the reasons why thou art dissatisfied with the solution proposed, which is to the effect that, seeing the fact of foreknowledge is not thought the cause of the necessity of future events, foreknowledge is not to be deemed any hindrance to the freedom of the will. Now, surely the sole ground on which thou arguest the necessity of the future is that things which are foreknown cannot fail to come to pass. But if, as thou wert ready to acknowledge just now, the fact of foreknowledge imposes no necessity on things future, what reason is there for supposing the results of voluntary action constrained to a fixed issue? Suppose, for the sake of argument, and to see what follows, we assume that there is no foreknowledge. Are willed actions, then, tied down to any necessity inthis case?'

'Certainly not.'

'Let us assume foreknowledge again, but without its involving any actual necessity; the freedom of the will, I imagine, will remain in complete integrity. But thou wilt say that, even although the foreknowledge is not the necessity of the future event's occurrence, yet it is a sign that it will necessarily happen. Granted; but in this case it is plain that, even if there had been no foreknowledge, the issues would have been inevitably certain. For a sign only indicates something which is, does not bring to pass that of which it is the sign. We require to show beforehand that all things, without exception, happen of necessity in order that a preconception may be a sign of this necessity. Otherwise, if there is no such universal necessity, neither can any preconception be a sign of a necessity which exists not. Manifestly, too, a proof established on firm grounds of reason must be drawn not from signs and loose general arguments, but from suitable and necessary causes. But how can it be that things foreseen should ever fail to come to pass? Why, this is to suppose us to believe that the events which providence foresees to be coming were not about to happen, instead of our supposing that, although they should come to pass, yet there was no necessity involved in their own nature compelling their occurrence. Take an illustration that will help to convey my meaning. There are many things which we see taking place before our eyes—the movements of charioteers, for instance, in guiding and turning their cars, and so on. Now, is any one of these movements compelled by any necessity?'

'No; certainly not. There would be no efficacy in skill if all motions took place perforce.'

'Then, things which in taking place are free from any necessity as to their being in the present must also, before they take place, be about to happen without necessity. Wherefore there are things which will come to pass, the occurrence of which is perfectly free from necessity. At all events, I imagine that no one will deny that things now taking place were about to come to pass before they were actually happening. Such things, however much foreknown, are in their occurrence free. For even as knowledge of things present imports no necessity into things that are taking place, so foreknowledge of the future imports none into things that are about to come. But this, thou wilt say, is the very point in dispute—whether any foreknowing is possible of things whose occurrence is not necessary. For here there seems to thee a contradiction, and, if they are foreseen, their necessity follows; whereas if there is no necessity, they can by no means be foreknown; and thou thinkest that nothing can be grasped as known unless it is certain, but if things whose occurrence is uncertain are foreknown as certain, this is the very mist of opinion, not the truth of knowledge. For to think of things otherwise than as they are, thou believest to be incompatible with the soundness of knowledge.

'Now, the cause of the mistake is this—that men think that all knowledge is cognized purely by the nature and efficacy of the thing known. Whereas the case is the very reverse: all that is known is grasped not conformably to its own efficacy, but rather conformably to the faculty of the knower. An example will make this clear: the roundness of a body is recognised in one way by sight, in another by touch. Sight looks upon it from a distance as a whole by a simultaneous reflection of rays; touch grasps the roundness piecemeal, by contact and attachment to the surface, and by actual movement round the periphery itself. Man himself, likewise, is viewed in one way by Sense, in another by Imagination, in another way, again, by Thought, in another by pure Intelligence. Sense judges figure clothed in material substance, Imagination figure alone without matter. Thought transcends this again, and by its contemplation of universals considers the type itself which is contained in the individual. The eye of Intelligence is yet more exalted; for overpassing the sphere of the universal, it will behold absolute form itself by the pure force of the mind's vision. Wherein the main point to be considered is this: the higher faculty of comprehension embraces the lower, while the lower cannot rise to the higher. For Sense has no efficacy beyond matter, nor can Imagination behold universal ideas, nor Thought embrace pure form; but Intelligence, looking down, as it were, from its higher standpoint in its intuition of form, discriminates also the several elements which underlie it; but it comprehends them in the same way as it comprehends that form itself, which could be cognized by no other than itself. For it cognizes the universal of Thought, the figure of Imagination, and the matter of Sense, without employing Thought, Imagination, or Sense, but surveying all things, so to speak, under the aspect of pure form by a single flash of intuition. Thought also, in considering the universal, embraces images and sense-impressions without resorting to Imagination or Sense. For it is Thought which has thus defined the universal from its conceptual point of view: "Man is a two-legged animal endowed with reason." This is indeed a universal notion, yet no one is ignorant that the thing is imaginable and presentable to Sense, because Thought considers it not by Imagination or Sense, but by means of rational conception. Imagination, too, though its faculty of viewing and forming representations is founded upon the senses, nevertheless surveys sense-impressions without calling in Sense, not in the way of Sense-perception, but of Imagination. See'st thou, then, how all things in cognizing use rather their own faculty than the faculty of the things which they cognize? Nor is this strange; for since every judgment is the act of the judge, it is necessary that each should accomplish its task by its own, not by another's power.'

Francis Bacon__The Father of Modern Scientific Induction...

A Priori Induction…

Every Word Is A Method…!!!

The A Priori Perception…
Gravity = EM-Hydro-Dynamic Balance…
The Three Fundamental Forces…!!!

http://www.constitution.org/bacon/nov_org.htm
I

Man, being the servant and interpreter of Nature, can do and understand so much and so much only as he has observed in fact or in thought of the course of nature. Beyond this he neither knows anything nor can do anything.

II

Neither the naked hand nor the understanding left to itself can effect much. It is by instruments and helps that the work is done, which are as much wanted for the understanding as for the hand. And as the instruments of the hand either give motion or guide it, so the instruments of the mind supply either suggestions for the understanding or cautions.

III

Human knowledge and human power meet in one; for where the cause is not known the effect cannot be produced. Nature to be commanded must be obeyed; and that which in contemplation is as the cause is in operation as the rule.

IV

Toward the effecting of works, all that man can do is to put together or put asunder natural bodies. The rest is done by nature working within.

V

The study of nature with a view to works is engaged in by the mechanic, the mathematician, the physician, the alchemist, and the magician; but by all (as things now are) with slight endeavor and scanty success.

VI

It would be an unsound fancy and self-contradictory to expect that things which have never yet been done can be done except by means which have never yet been tried.

VII

The productions of the mind and hand seem very numerous in books and manufactures. But all this variety lies in an exquisite subtlety and derivations from a few things already known, not in the number of axioms.

VIII

Moreover, the works already known are due to chance and experiment rather than to sciences; for the sciences we now possess are merely systems for the nice ordering and setting forth of things already invented, not methods of invention or directions for new works.

IX

The cause and root of nearly all evils in the sciences is this — that while we falsely admire and extol the powers of the human mind we neglect to seek for its true helps.

X

The subtlety of nature is greater many times over than the subtlety of the senses and understanding; so that all those specious meditations, speculations, and glosses in which men indulge are quite from the purpose, only there is no one by to observe it.

XI

As the sciences which we now have do not help us in finding out new works, so neither does the logic which we now have help us in finding out new sciences.

XII

The logic now in use serves rather to fix and give stability to the errors which have their foundation in commonly received notions than to help the search after truth. So it does more harm than good.

XIII

The syllogism is not applied to the first principles of sciences, and is applied in vain to intermediate axioms, being no match for the subtlety of nature. It commands assent therefore to the proposition, but does not take hold of the thing.

XIV

The syllogism consists of propositions, propositions consist of words, words are symbols of notions. Therefore if the notions themselves (which is the root of the matter) are confused and overhastily abstracted from the facts, there can be no firmness in the superstructure. Our only hope therefore lies in a true induction.

XV

There is no soundness in our notions, whether logical or physical. Substance, Quality, Action, Passion, Essence itself, are not sound notions; much less are Heavy, Light, Dense, Rare, Moist, Dry, Generation, Corruption, Attraction, Repulsion, Element, Matter, Form, and the like; but all are fantastical and ill defined.

XVI

Our notions of less general species, as Man, Dog, Dove, and of the immediate perceptions of the sense, as Hot, Cold, Black, White, do not materially mislead us; yet even these are sometimes confused by the flux and alteration of matter and the mixing of one thing with another. All the others which men have hitherto adopted are but wanderings, not being abstracted and formed from things by proper methods.

XVII

Nor is there less of willfulness and wandering in the construction of axioms than in the formation of notions, not excepting even those very principles which are obtained by common induction; but much more in the axioms and lower propositions educed by the syllogism.

XVIII

The discoveries which have hitherto been made in the sciences are such as lie close to vulgar notions, scarcely beneath the surface. In order to penetrate into the inner and further recesses of nature, it is necessary that both notions and axioms be derived from things by a more sure and guarded way, and that a method of intellectual operation be introduced altogether better and more certain.

XIX

There are and can be only two ways of searching into and discovering truth. The one flies from the senses and particulars to the most general axioms, and from these principles, the truth of which it takes for settled and immovable, proceeds to judgment and to the discovery of middle axioms. And this way is now in fashion. The other derives axioms from the senses and particulars, rising by a gradual and unbroken ascent, so that it arrives at the most general axioms last of all. This is the true way, but as yet untried.

XX

The understanding left to itself takes the same course (namely, the former) which it takes in accordance with logical order. For the mind longs to spring up to positions of higher generality, that it may find rest there, and so after a little while wearies of experiment. But this evil is increased by logic, because of the order and solemnity of its disputations.

XXI

The understanding left to itself, in a sober, patient, and grave mind, especially if it be not hindered by received doctrines, tries a little that other way, which is the right one, but with little progress, since the understanding, unless directed and assisted, is a thing unequal, and quite unfit to contend with the obscurity of things.

XXII

Both ways set out from the senses and particulars, and rest in the highest generalities; but the difference between them is infinite. For the one just glances at experiment and particulars in passing, the other dwells duly and orderly among them.

The one, again, begins at once by establishing certain abstract and useless generalities, the other rises by gradual steps to that which is prior and better known in the order of nature.

XXIII

There is a great difference between the Idols of the human mind and the Ideas of the divine. That is to say, between certain empty dogmas, and the true signatures and marks set upon the works of creation as they are found in nature.

XXIV

It cannot be that axioms established by argumentation should avail for the discovery of new works, since the subtlety of nature is greater many times over than the subtlety of argument. But axioms duly and orderly formed from particulars easily discover the way to new particulars, and thus render sciences active.

XXV

The axioms now in use, having been suggested by a scanty and manipular experience and a few particulars of most general occurrence, are made for the most part just large enough to fit and take these in; and therefore it is no wonder if they do not lead to new particulars. And if some opposite instance, not observed or not known before, chance to come in the way, the axiom is rescued and preserved by some frivolous distinction; whereas the truer course would be to correct the axiom itself.

XXVI

The conclusions of human reason as ordinarily applied in matters of nature, I call for the sake of distinction Anticipations of Nature (as a thing rash or premature). That reason which is elicited from facts by a just and methodical process, I call Interpretation of Nature.

XXVII

Anticipations are a ground sufficiently firm for consent, for even if men went mad all after the same fashion, they might agree one with another well enough.

XXVIII

For the winning of assent, indeed, anticipations are far more powerful than interpretations, because being collected from a few instances, and those for the most part of familiar occurrence, they straightway touch the understanding and fill the imagination; whereas interpretations, on the other hand, being gathered here and there from very various and widely dispersed facts, cannot suddenly strike the understanding; and therefore they must needs, in respect of the opinions of the time, seem harsh and out of tune, much as the mysteries of faith do.

XXIX

In sciences founded on opinions and dogmas, the use of anticipations and logic is good; for in them the object is to command assent to the proposition, not to master the thing.

XXX

Though all the wits of all the ages should meet together and combine and transmit their labors, yet will no great progress ever be made in science by means of anticipations; because radical errors in the first concoction of the mind are not to be cured by the excellence of functions and subsequent remedies.

XXXI

It is idle to expect any great advancement in science from the superinducing and engrafting of new things upon old. We must begin anew from the very foundations, unless we would revolve forever in a circle with mean and contemptible progress.

XXXII

The honor of the ancient authors, and indeed of all, remains untouched, since the comparison I challenge is not of wits or faculties, but of ways and methods, and the part I take upon myself is not that of a judge, but of a guide.

XXXIII

This must be plainly avowed: no judgment can be rightly formed either of my method or of the discoveries to which it leads, by means of anticipations (that is to say, of the reasoning which is now in use); since I cannot be called on to abide by the sentence of a tribunal which is itself on trial.

XXXIV

Even to deliver and explain what I bring forward is no easy matter, for things in themselves new will yet be apprehended with reference to what is old.

XXXV

It was said by Borgia of the expedition of the French into Italy, that they came with chalk in their hands to mark out their lodgings, not with arms to force their way in. I in like manner would have my doctrine enter quietly into the minds that are fit and capable of receiving it; for confutations cannot be employed when the difference is upon first principles and very notions, and even upon forms of demonstration.

XXXVI

One method of delivery alone remains to us which is simply this: we must lead men to the particulars themselves, and their series and order; while men on their side must force themselves for a while to lay their notions by and begin to familiarize themselves with facts.

XXXVII

The doctrine of those who have denied that certainty could be attained at all has some agreement with my way of proceeding at the first setting out; but they end in being infinitely separated and opposed. For the holders of that doctrine assert simply that nothing can be known. I also assert that not much can be known in nature by the way which is now in use. But then they go on to destroy the authority of the senses and understanding; whereas I proceed to devise and supply helps for the same.

XXXVIII

The idols and false notions which are now in possession of the human understanding, and have taken deep root therein, not only so beset men's minds that truth can hardly find entrance, but even after entrance is obtained, they will again in the very instauration of the sciences meet and trouble us, unless men being forewarned of the danger fortify themselves as far as may be against their assaults.

XXXIX

There are four classes of Idols which beset men's minds. To these for distinction's sake I have assigned names, calling the first class Idols of the Tribe; the second, Idols of the Cave; the third, Idols of the Market Place; the fourth, Idols of the Theater.

XL

The formation of ideas and axioms by true induction is no doubt the proper remedy to be applied for the keeping off and clearing away of idols. To point them out, however, is of great use; for the doctrine of Idols is to the interpretation of nature what the doctrine of the refutation of sophisms is to common logic.

Also:
In the late 19th century, Charles Sanders Peirce proposed a schema that would turn out to have considerable influence in the further development of scientific method generally. Peirce's work quickly accelerated the progress on several fronts. Firstly, speaking in broader context in "How to Make Our Ideas Clear" (1878),^[66] Peirce outlined an objectively verifiable method to test the truth of putative knowledge on a way that goes beyond mere foundational alternatives, focusing upon both Deduction and Induction. He thus placed induction and deduction in a complementary rather than competitive context (the latter of which had been the primary trend at least since David Hume a century before). Secondly, and of more direct importance to scientific method, Peirce put forth the basic schema for hypothesis-testing that continues to prevail today. Extracting the theory of inquiry from its raw materials in classical logic, he refined it in parallel with the early development of symbolic logic to address the then-current problems in scientific reasoning. Peirce examined and articulated the three fundamental modes of reasoning that play a role in scientific inquiry today, the processes that are currently known as abductive, deductive, and inductive inference. Thirdly, he played a major role in the progress of symbolic logic itself — indeed this was his primary specialty.

Charles S. Peirce was also a pioneer in statistics. Peirce held that science achieves statistical probabilities, not certainties, and that chance, a veering from law, is very real. He assigned probability to an argument’s conclusion rather than to a proposition, event, etc., as such. Most of his statistical writings promote the frequency interpretation of probability (objective ratios of cases), and many of his writings express skepticism about (and criticize the use of) probability when such models are not based on objective randomization.^[67] Though Peirce was largely a frequentist, his possible world semantics introduced the "propensity" theory of probability. Peirce (sometimes with Jastrow) investigated the probability judgments of experimental subjects, pioneering decision analysis.

Peirce was one of the founders of statistics. He formulated modern statistics in "Illustrations of the Logic of Science" (1877–1878) and "A Theory of Probable Inference" (1883). With a repeated measures design, he introduced blinded, controlled randomized experiments (before Fisher). He invented an optimal design for experiments on gravity, in which he "corrected the means". He used logistic regression, correlation, and smoothing, and improved the treatment of outliers. He introduced terms "confidence" and "likelihood" (before Neyman and Fisher). (See the historical books of Stephen Stigler.) Many of Peirce's ideas were later popularized and developed by Ronald A. Fisher, Jerzy Neyman, Frank P. Ramsey, Bruno de Finetti, and Karl Popper.

Economic Models' Math__Applies To Physics, As Well__& Vice-Versa...

(P.s. added Tim...)

http://en.wikipedia.org/wiki/Economic_model

"The economics/(physics) profession appears to have been unaware of the long build-up to the current worldwide financial/(mathematical physics) crisis and to have significantly underestimated its dimensions once it started to unfold. In our view, this lack of understanding is due to a misallocation of research efforts in economics/(physics). We trace the deeper roots of this failure to the profession’s focus on models that, by design, disregard key elements driving outcomes in real-world markets/(physics models). The economics/(physics) profession has failed in communicating the limitations, weaknesses, and even dangers of its preferred models to the public. This state of affairs makes clear the need for a major reorientation of focus in the research economists/(physicists) undertake, as well as for the establishment of an ethical/(scientific) code that would ask economists/(physicists) to understand and communicate the limitations and potential misuses of their models."

Tim, I think it quite important to read David Hestenes' entire paper, to see where this paragraph links the maths of any and all model constructs together, and which ones are invalid and useless, verses, the truly valid and useful maths and models... Remember, at the most and absolute fundamental level, all these maths__being one of the fundamentals of all models__are all fully isomorphic, at limits__That's the real 'Conformality' of the entire 'House of Cards...' I think Hestenes has much better captured these facts with humor, than any serious post I could possibly make... The most important thing to recognize, is the fact that all these maths and models absolutely must be grounded in real World and Universal facts, parts, pieces and motions(the 9 degrees of freedom motions, i.e., vectors of real asymmetric wave actions, of the real fs-field...)__1st and foremost...!!!

http://geocalc.clas.asu.edu/pdf-preAdobe8/MathViruses.pdf

Imo Tim, you are going to have to understand the asymmetric/achiral control of the entire Universe's fundamental wave mechanics control mechanisms, in order to see how a Bose-Einstein Condensate truly forms and decays__over time__The true four dimensional aspects of FS-Matter, through its most fundamental wave-mechanics__Pure Wave-Mechanics as Vector-Phase-State-Spaces through Scalar Time Factors... Imo Tim, this takes a full understanding of the achiral actions of opposite handedness(the 3rd state), in a far deeper model of understanding chirality(left and right symmetric states), than you are presently looking at... I hate to keep chasing you back to this well worn point, but until you see what this model represents, I know it's not possible to see the Universe's most fundamental wave and motion mechanics(it's like a self-polarizing triadic orthogonality of the most fundamental hydrodynamic forces__the least understood of the least actions...) When you finally see what I'm truly saying here, the whole world of your personal Universal understanding will explode anew... Build the wire models Tim, and see the true Boogie-Man, in the Universe__It's far more fundamental than the analog-digital models, as they are thus far, interpreted almost entirely dyadically, and I'm constantly speaking about the triadicity of the fundamental polarizations__necessitated by the time scalar waves altered distance actions, in relation to the fundamental orthogonal polarizations, of the FS-Waves... This is more easily understood through 'Tensor Mechanics', as first started by Leibniz, and followed all the way through to Levi-Civita and the many more moderns, like Hestenes'(Geometrical Algebra...) Imo, math is absolutely necessary, but it must be the proper maths, and the even more proper use of the maths, in relation to real World and Universal facts...

A few years back, I named it: 'The Relational Geometry & Algebra of Responsible Intelligence…' It still holds...

A related link:
http://en.wikipedia.org/wiki/Nine-point_circle

The Achiral Non-Conformality, Within The Chiral Conformality...
The Achiral Non-Symmetries, Within The Chiral Symmetries...
The Non-Conservation of Time, Within The Conservation of Space…???

And Tim's Theorem:
http://en.wikipedia.org/wiki/Lester%27s_theorem
http://mathworld.wolfram.com/LesterCircle.html
http://en.wikipedia.org/wiki/Fermat_point
http://en.wikipedia.org/wiki/Circumcenter

And:
http://en.wikipedia.org/wiki/Binary_Golay_code
http://en.wikipedia.org/wiki/Ternary_Golay_code
http://en.wikipedia.org/wiki/Jakob_Steiner
http://en.wikipedia.org/wiki/Steiner_system
http://en.wikipedia.org/wiki/Steiner_triple_system
http://en.wikipedia.org/wiki/Steiner_tree_problem
http://en.wikipedia.org/wiki/Geometric_median
http://en.wikipedia.org/wiki/Ernst_Witt
http://en.wikipedia.org/wiki/Leech_lattice
http://en.wikipedia.org/wiki/%C3%89mile_L%C3%A9onard_Mathieu
http://en.wikipedia.org/wiki/Mathieu_group

P.s.
A few more of the notes I'm working with, Tim:

The Symmetry Illusion…

The Mechanics of Long Wave to Short Wave Photons__Radio to Gamma…
Peirce__The Teleological Logician…
Teleology__The 1^st Beginnings of Knowledge Gives Ya The Ends of Knowledge__Primitive Logic…
Peirce__The Father of True Teleological Pragmatic Logic…
Only Teleological Intelligence__Exists…!!!
The teleological past, present and future of entropy__Gas shrinks upon losing all heat…
A living organism holds a continuum of ideas, to form real intelligence…
Peirce__The Teleological Genius…
Thought mechanics is outside-in__Not inside-out…
Archetype Thought Modes__Pure_Category_Model Logics…
Modal Teleological Epistemic Pragmatic Logic…
The False Vector/Scalar Models of Physics…

Sherrington's philosophy as a teacher can be seen in his response to the question of what was the real function of Oxford University in the world. Sherrington said:  "after some hundreds of years of experience we think that we have learned here in Oxford how to teach what is known. But now with the undeniable upsurge of scientific research, we cannot continue to rely on the mere fact that we have learned how to teach what is known. We must learn to teach the best attitude to what is not yet known. This also may take centuries to acquire but we cannot escape this new challenge, nor do we want to."

Peirce solved Cantor’s, Frege’s and Russell’s paradoxes, before they were ever created__Deep Relational Algebra__Foundations to Tensor Algebra…

‘The Axiom of Choice’ vs. ‘The Axiom of Determinacy…’
Both Geometry & Nature Necessitate ‘The Axiom of Choice’, or No Universe Could Ever Exist__Difference Necessitates ‘The Axiom of Choice/Action…’
‘The Axiom of Difference’ Mandates Choice, or Random Action, As Same…
‘The Axiom of Difference’ Makes Strong Determinism__Impossible…
The Universe Requires ‘The Axiom of Difference’ to Produce Different Quarks and Protons…
Factual Ideas & Goals force logic to actions, occurences and events__which change the world…
Iff granted absolute power, then & only then, can I emplace law to solve all the world’s problems…
Science = A Provable Concept…

Professor Hochberg’s book is best characterized by his own words from the preface: The book attempts to sketch, not work out in detail, an account of reference, meaning, truth and intentionality that stays within the “linguistic turn” characterizing twentieth century analytic philosophy. But it seeks to avoid following the contemporary variants of analytic philosophy that have turned from the analysis of things and facts to a preoccupation with and virtual worship of language and its use. The classical focus on ontology, combined with careful and precise formulations, that marked the writings of the early founders of the analytic tradition, has degenerated into the spinning of intricate verbal webs of analysis. The latter supposedly yield “theories of meaning” but more often signal the rebirth of idealism in the guises of “anti-realism” and “internal realism.” The focus on the world, as what words are about, is often lost as “analytic philosophers” concentrate on language itself—the world being “well lost,” in Nelson Goodman’s honest words… . We shall also note examples of a remarkable combination of arrogance towards and ignorance of the philosophical tradition that is displayed in some writings within the analytic tradition, including influential works.

The Complete/Incomplete “Distinction…”

His paper “Universals”, which denies any fundamental distinction between universals and particulars, surmounts serious objections to a realist view of universals and, at the same time, solves several long-standing problems about them, dismissing other venerable enigmas as nonsense. Ramsey

 

Various reasons for making the distinction between universals and particulars – psychological, physical and logical – can be advanced. Ramsey argues that logic justifies no such ontological distinction. Allusion to the grammatical subject-predicate distinction will not do, since “Socrates is wise”, with the subject “Socrates” and the predicate “wise”, “asserts the same fact and expresses the same proposition” (p. 12) as “Wisdom is a characteristic of Socrates”, with subject “wisdom” and predicate “Socrates”.3

Moreover, there is, he argues, no essential difference between the (in)completeness of universals and that of particulars. “Wise” can, for example, be used to generate propositions not only of the atomic form “Socrates is wise”, but also of the molecular form “Neither Socrates nor Plato is wise”. But “Socrates” can also be used to generate propositions of both these forms: e.g. “Socrates is wise” and “Socrates is neither wise nor just”.

There is therefore a complete symmetry in this respect between individuals and basic properties (qualities). As Ramsey succinctly puts it, the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality what is merely a characteristic of language (p.13).

The Particular/Universal Distinction ¬…

One of his co-workers, Frank Ramsey, took Russell’s warning very much to heart. But Ramsey soon came to the conviction that philosophers had not only been misled by language to adopt and adhere to a subject-predicate logic and a denial of relations. Writing in his 1925 Mind paper “Universals” (hereafter U) Ramsey declared: “nearly all philosophers, including Mr Russell himself, have been misled by language in a far more far-reaching way than that; that the whole theory of particulars and universals is due to mistaking for a fundamental characteristic of reality, what is merely a characteristic of language.” (U: 13)

The Particular/Universal Distinction Illusion__The Language Illusion_At Limits…
“True” Is An Incomplete Symbol… Ramsey
Quantum Uncertainty & ‘The Axiom of Difference…’
Russell, Quine, Putnam, Chomsky__Purile Bastardizations of Peirce…
The Subjective Psychology & The Objective Philosophy…
Russell’s Phony Symbol Semiotics__A Logical Joke…
Language and Linguistic Non-Sense__A Running Series of Logical Jokes…
The Frege-Russell-Quine Psychological Era of Logic…
Russell’s False Symbol System__Confused and Conflated Semiotics…
The ‘One-Many’ ‘Universal-Particular’ Plays Out In Every Hand of Logic…
The ‘One-Many’ Central Logical Illusion… 
Russell’s Purile Tensor Logic…
The Mind Is A ‘One-Many Continuum’, Having To Interpret Both ‘Universals’ and ‘Particulars’__At Once__In Each Propositional Analysis…
The Central ‘One-Many Continuum’ Logic Problem Always Exists…
‘Formal Truth Formal Logic…’ Ramsey…
¬ () = X Is False…(let ¬ = the empty)
¬ {()} = X Is False…
1^st Methodological Tensor Choice Modality…
The Continuum of Triadic Choice Modalities…
All Knowledge Is Combinatoric From Its Initial State, Except Psychological Non-Knowledge Systems…
Psychology__The Modern-Day Anti-Knowledge System__Nietzsche On…
Psychology can not be added, subtracted, multiplied or divided…
Psychology, being non-mathematizable, must remain non-scientific…
Hard Knowledge vs. Soft Non-Knowledge…
The Methodology of Discovery__Science…
Weak Belief vs. Strong Knowledge…(from Hume on)
The Combinatoric Compositionality of All Real Hard Knowledge Systems…
Economics is primarily historically combinatoric, except for the slight and short anomalies of intermittent negative psychological events…
Modal Knowledge vs. Modal Belief…
‘The Difference Axiom’ of Knowledge vs. Belief…
The Continuum/s Obviously Create/s Difference…
Determinism requires symmetry, whereas the Universe is asymmetric, thus the asymmetric actual eliminates hard determinism…
Francis Bacon’s Eliminative Induction…
Eliminative Combinatoric Induction Mechanics…

http://en.wikipedia.org/wiki/Multinomial_theorem
This my help with this Tim:
The Universal Isomorphic Algorithm__UIA = ∑∫∏v -> IC:M Iff / ≡ ∑’s •…(The universal isomorphic algorithm equals the sum of the integral product variables, implying the isomorphic center of mass, if and only if divided identical to the sum’s center…)
Proof
This proof of the multinomial theorem uses the binomial theorem and induction on m.

First, for m = 1, both sides equal x₁ⁿ since there is only one term k₁ = n in the sum. For the induction step, suppose the multinomial theorem holds for m. Then

by the induction hypothesis. Applying the binomial theorem to the last factor,

which completes the induction. The last step follows because

as can easily be seen by writing the three coefficients using factorials as follows:

A related Pdf:
http://mathsci.kaist.ac.kr/~drake/pdf/towards-a-combinatorial-theory-of-multiple-orthogonal-polynomials.pdf

Best first source informations:
http://www.constitution.org/bacon/nov_org.htm
http://en.wikipedia.org/wiki/Pafnuty_Chebyshev
http://en.wikipedia.org/wiki/Andrey_Markov

And as Chebyshev's work relates analog to digital:
http://en.wikipedia.org/wiki/Chebyshev_filter
Chebyshev filters are analog or digital filters having a steeper roll-off and more passband ripple (type I) or stopband ripple (type II) than Butterworth filters. Chebyshev filters have the property that they minimize the error between the idealized and the actual filter characteristic over the range of the filter, but with ripples in the passband. This type of filter is named in honor of Pafnuty Chebyshev because their mathematical characteristics are derived from Chebyshev polynomials.