Pareto Optimality

There are some solutions. (“If you don’t give a solution, you are part of the problem”). Most important: Human wealth should be set as the only goal in society and economy. Liberalism is ruinous for humans, while it may be optimal for fitter entities. Nobody is out there to take away the money of others without working for it. In a way of ‘revenge’ or ‘envy’, (basically justifying laziness) taking away the hard-work earnings of others. No way. Nobody wants it. Thinking that yours can be the only way a rational person can think. Anybody not ‘winning’ the game is a ‘loser’. Some of us, actually, do not even want to enter the game.

Yet – the big dilemma – that money-grabbing mentality is essential for the economy. Without it we would be equally doomed. But, what we will see now is that you’ll will lose every last penny either way, even without divine intervention.

Having said that, the solution is to take away the money. Seeing that the system is not stable and accumulates the capital on a big pile, disconnected from humans, mathematically there are two solutions:

1) Put all the capital in the hands of people. If profit is made M’-M, this profit falls to the hands of the people that caused it. This seems fair, and mathematically stable. However, how the wealth is then distributed? That would be the task of politicians, and history has shown that they are a worse pest than capital. Politicians, actually, always wind up representing the capital. No country in the world ever managed to avoid it.

2) Let the system be as it is, which is great for giving people incentives to work and develop things, but at the end of the year, redistribute the wealth to follow an ideal curve that optimizes both wealth and increments of wealth.

The latter is an interesting idea. Also since it does not need rigorous restructuring of society, something that would only be possible after a total collapse of civilization. While unavoidable in the system we have, it would be better to act pro-actively and do something before it happens. Moreover, since money is air – or worse, vacuum – there is actually nothing that is ‘taken away’. Money is just a right to consume and can thus be redistributed at will if there is a just cause to do so. In normal cases this euphemistic word ‘redistribution’ amounts to theft and undermines incentives for work and production and thus causes poverty. Yet, if it can be shown to actually increase incentives to work, and thus increase overall wealth, it would need no further justification.

We set out to calculate this idea. However, it turned out to give quite remarkable results. Basically, the optimal distribution is slavery. Let us present them here. Let’s look at the distribution of wealth. Figure below shows a curve of wealth per person, with the richest conventionally placed at the right and the poor on the left, to result in what is in mathematics called a monotonously-increasing function. This virtual country has 10 million inhabitants and a certain wealth that ranges from nearly nothing to millions, but it can easily be mapped to any country.

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Figure 1: Absolute wealth distribution function

As the overall wealth increases, it condenses over time at the right side of the curve. Left unchecked, the curve would become ever-more skew, ending eventually in a straight horizontal line at zero up to the last uttermost right point, where it shoots up to an astronomical value. The integral of the curve (total wealth/capital M) always increases, but it eventually goes to one person. Here it is intrinsically assumed that wealth, actually, is still connected to people and not, as it in fact is, becomes independent of people, becomes ‘capital’ autonomously by itself. If independent of people, this wealth can anyway be without any form of remorse whatsoever be confiscated and redistributed. Ergo, only the system where all the wealth is owned by people is needed to be studied.

A more interesting figure is the fractional distribution of wealth, with the normalized wealth w(x) plotted as a function of normalized population x (that thus runs from 0 to 1). Once again with the richest plotted on the right. See Figure below.

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Figure 2: Relative wealth distribution functions: ‘ideal communist’ (dotted line. constant distribution), ‘ideal capitalist’ (one person owns all, dashed line) and ‘ideal’ functions (work-incentive optimized, solid line).

Every person x in this figure feels an incentive to work harder, because it wants to overtake his/her right-side neighbor and move to the right on the curve. We can define an incentive i(x) for work for person x as the derivative of the curve, divided by the curve itself (a person will work harder proportional to the relative increase in wealth)

i(x) = dw(x)/dx/w(x) —– (1)

A ‘communistic’ (in the negative connotation) distribution is that everybody earns equally, that means that w(x) is constant, with the constant being one

‘ideal’ communist: w(x) = 1.

and nobody has an incentive to work, i(x) = 0 ∀ x. However, in a utopic capitalist world, as shown, the distribution is ‘all on a big pile’. This is what mathematicians call a delta-function

‘ideal’ capitalist: w(x) = δ(x − 1),

and once again, the incentive is zero for all people, i(x) = 0. If you work, or don’t work, you get nothing. Except one person who, working or not, gets everything.

Thus, there is somewhere an ‘ideal curve’ w(x) that optimizes the sum of incentives I defined as the integral of i(x) over x.

I = ∫01i(x)dx = ∫01(dw(x)/dx)/w(x) dx = ∫x=0x=1dw(x)/w(x) = ln[w(x)]|x=0x=1 —– (2)

Which function w is that? Boundary conditions are

1. The total wealth is normalized: The integral of w(x) over x from 0 to 1 is unity.

01w(x)dx = 1 —– (3)

2. Everybody has a at least a minimal income, defined as the survival minimum. (A concept that actually many societies implement). We can call this w0, defined as a percentage of the total wealth, to make the calculation easy (every year this parameter can be reevaluated, for instance when the total wealth increased, but not the minimum wealth needed to survive). Thus, w(0) = w0.

The curve also has an intrinsic parameter wmax. This represents the scale of the figure, and is the result of the other boundary conditions and therefore not really a parameter as such. The function basically has two parameters, minimal subsistence level w0 and skewness b.

As an example, we can try an exponentially-rising function with offset that starts by being forced to pass through the points (0, w0) and (1, wmax):

w(x) = w0 + (wmax − w0)(ebx −1)/(eb − 1) —– (4)

An example of such a function is given in the above Figure. To analytically determine which function is ideal is very complicated, but it can easily be simulated in a genetic algorithm way. In this, we start with a given distribution and make random mutations to it. If the total incentive for work goes up, we keep that new distribution. If not, we go back to the previous distribution.

The results are shown in the figure 3 below for a 30-person population, with w0 = 10% of average (w0 = 1/300 = 0.33%).

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Figure 3: Genetic algorithm results for the distribution of wealth (w) and incentive to work (i) in a liberal system where everybody only has money (wealth) as incentive. 

Depending on the starting distribution, the system winds up in different optima. If we start with a communistic distribution of figure 2, we wind up with a situation in which the distribution stays homogeneous ‘everybody equal’, with the exception of two people. A ‘slave’ earns the minimum wages and does nearly all the work, and a ‘party official’ that does not do much, but gets a large part of the wealth. Everybody else is equally poor (total incentive/production equal to 21), w = 1/30 = 10w0, with most people doing nothing, nor being encouraged to do anything. The other situation we find when we start with a random distribution or linear increasing distribution. The final situation is shown in situation 2 of the figure 3. It is equal to everybody getting minimum wealth, w0, except the ‘banker’ who gets 90% (270 times more than minimum), while nobody is doing anything, except, curiously, the penultimate person, which we can call the ‘wheedler’, for cajoling the banker into giving him money. The total wealth is higher (156), but the average person gets less, w0.

Note that this isn’t necessarily an evolution of the distribution of wealth over time. Instead, it is a final, stable, distribution calculated with an evolutionary (‘genetic’) algorithm. Moreover, this analysis can be made within a country, analyzing the distribution of wealth between people of the same country, as well as between countries.

We thus find that a liberal system, moreover one in which people are motivated by the relative wealth increase they might attain, winds up with most of the wealth accumulated by one person who not necessarily does any work. This is then consistent with the tendency of liberal capitalist societies to have indeed the capital and wealth accumulate in a single point, and consistent with Marx’s theories that predict it as well. A singularity of distribution of wealth is what you get in a liberal capitalist society where personal wealth is the only driving force of people. Which is ironic, in a way, because by going only for personal wealth, nobody gets any of it, except the big leader. It is a form of Prisoner’s Dilemma.

Atlantis

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After the Lemurians had existed for ages as beings not very different from the mankind of later times, yet more spiritual than intellectual, a gradual division took place into two well-marked sections, the Sons of Light and the Sons of Darkness. Selfish desire increased and the decline of the third race set in rapidly, but was not allowed to proceed too far. The law of progress prevented too great a downfall by the destruction of a large portion of the individuals through the breaking up of the Lemurian continent. Simultaneously with the decay of the third race civilizations, the beginnings of the new type of man, the fourth, began to appear, and new lands arose from the sea to take the place of the previous continent. Some of the islands of Polynesia are remains of some of the mountaintops of long-forgotten Lemuria, and the native traditions of a universal deluge, etc., greatly puzzled the early missionaries, who could not conceive how the ignorant savages, living in widely scattered islands, had obtained stories closely resembling those of the Creation and the Flood in the Bible. Australia and New Zealand are the largest parts of Lemuria now existing, but there are other portions, such as Ceylon or Lanka, which is a remnant of a northern highland of Lemuro-Atlantis, and the Polar lands, though the latter belong properly to the first and second continents.

Lemuria is said to have perished finally 700,000 years before the commencement of the Tertiary age of geology. The highest group of its inhabitants, the comparatively few “Sons of Light,” were not disturbed by the upheavals, for they had taken precautions and had moved away to safer regions; most of the small proportion of the average mankind that escaped centered towards land which is now under the waters of the North Atlantic. They formed the nucleus of the next root-race, the Atlantean, and from that land the coming great Atlantean civilization spread over the new continent that was rising. Nature never breaks the continuity of her processes, so no hard and fast line can be drawn as to when one race ends and another begins. For many thousands of years the first subrace of the fourth had been developing parallel with the culminating of the last subraces of the third, just as we see today a new subrace of our fifth root-race forming in America; so that the relic of mankind saved from destruction contained representatives in all degrees of advancement. It should be well remembered that it is not only mankind as a whole, but man as the individual ego, whose progress we are tracing. The races are the temporary vehicles of the larger life of the egos constituting them, and though they may perish when they have served their purpose, and before they have fallen too deeply into degradation, the immortal ego simply passes on to the next experience and will continue to do so until the succeeding manvantara or world period.

Atlantis gradually took form as Lemuria broke up under the turbulent disruptive forces of the adolescent period of earth’s growth, and as the portion of humanity which escaped the destruction spread afar, they peopled the newly risen lands and some of the old that were not submerged, with a race which subsequently touched the lowest depths of materiality that the world has seen. Since the Atlantean period man has been rising, though with many cyclic depressions, for the Atlantean civilization marked a turning point in the history of the Earth. Until then mankind was slowly descending into material conditions with a corresponding obscuration in spirituality. The Atlanteans stand as the apotheosis of matter, and it was in those far-distant days that the heaviest karma of the human race was generated, a karma which is holding us back from the advance we should otherwise make, and whose existence explains many of the difficulties and anomalies of life. Humanity reached its fullest physical development in the fourth race, the physical bodies themselves being much larger than at present. The old saying that “there were giants in those days,” was correct when applied to the Atlanteans. The curious decrease in the size of many organisms, which is so well marked in the case of the fearful saurians of the Secondary period — now represented by comparatively minute reptilian forms — also took place in the human kingdom; but as the practice of cremation was almost universal we are not likely to find many remains of gigantic human bones. Immense footprints have been found in the geologic strata of Nevada and Ohio, USA, which seem to be human, but geology has not definitely sanctioned the claim that they are so.

Legendary island of Atlantis.

The fourth race started under far less favorable conditions than the third, and towards its decline the story of Lemuria was repeated on lower levels; the same fight between the higher and lower natures within and without was waged, but more mercilessly; and as that was the age of passion and desire in excelsis and the eclipse of spirituality, the result was mainly in favor of the lower principles for a long time. But not forever, for, although the majority of the Atlanteans were not the descendants of the higher group of the third race, the “one third that remained faithful” fought such a good fight that they were enabled to escape before the Deluge from the lands that had been cursed by the evildoers, and to become the progenitors of the majority of our present humanity. The story of Noah’s Deluge is, in one of its aspects, a fanciful account of the great Atlantean submersion; but it also has deeper meanings, one of which allegorizes the primeval building of the world.

Full personal responsibility came to the man of the Atlantean period, and although the last or final choice between spiritual advancement on the one side, and materialism or personal aggrandizement on the other, “good and evil,” has not yet come for the mass of humanity, and will not until the next round, a long step in that direction was taken by the Atlanteans. But nature is merciful, and the world is not destined to perish ingloriously; so before the mischief had become irreparable, “the law that moves to righteousness” again arrested further degradation by giving a shock which allowed the egos to start anew with a fresh opportunity, upon new lands not soaked through with the evil memories of past sins. The majority of the Atlantean evildoers perished finally amid indescribable terrors, and the ocean soon obliterated all remains of that proud civilization which had misapplied greater powers than any with which we have since been entrusted. The last large destruction took place towards the close of the Meiocene age, when the Alps were upraised. Most of those then destroyed were of the giant race; but mankind was already diminishing in size, and when the final destruction of the few remaining islands upon which Atlanteans still existed took place, only about 11,000 years ago, men had long before assumed their present proportions. It was the latter destruction to which Plato refers when he handed on the tradition that the gods had caused the wicked Atlanteans to perish 9,000 years before his time. Airships of great perfection were used by the “White Adepts,” and the measures taken and the weapons spoken of illustrate a much deeper knowledge of natural forces — magic — than science has yet suspected, fortunately for us in this age of selfishness!

The fifth or Aryan race had started some time before the last destruction of Atlantis. Descended from the more spiritualized and better class of Atlanteans, a few had preserved the knowledge of their ancestors and were ready to revive it when the race demanded it. The institution of the Mysteries in all countries at a later period was an effort, and fortunately a successful one, to preserve the ancient wisdom from the profanation it had suffered in Atlantis. An example of the profound knowledge of the Atlanteans is shown in the astronomical computations of Indian astronomy, which are based upon a little that was permitted to escape from the guardianship of the Mysteries.

It was in Atlantis, too, that language took its inflectional form, after having passed from the stage of musical nature-sounds in the second race, to monosyllabic speech in the later third, and then to the agglutinative form in the fourth. Of course writing was well known to the fourth race, for during its long career it possessed civilizations higher than were those of Greece or Rome in their palmiest days, and even far higher than our own civilization today, though it may have been lost to the world at large during the period of confusion when the first subraces of the fifth were forming. The traces of writing in the “Stone Age ” (which belongs to our epoch) are not conclusive; and yet it is strange and entirely unexplained by modern science, that Palaeolithic man could draw animals upon antlers and cavern walls, etc., in a style that would not disgrace a good draughtsman of today, and which is certainly superior in accuracy to that of some of the Egyptian conventional representations of animals, or to the crude drawings of the famous Bayeux tapestry which was woven perhaps five hundred thousand years after the time of the supposed brutal “primitive” man — a savage that we are told was nearly on a level with his hypothetical ape-grandfather! Palaeolithic (ancient Stone Age) man was in reality carrying on some memories of the perished civilizations, as his artistic talent shows; the Neolithic (new Stone Age) man who followed him had lost this power, although he was improving in some other respects. The Palaeolithic drawings show no resemblance to the scrawls of children, but display concentrated observation and high technical skill — in other words, qualities of advanced civilization!

With this gradual break-up of the fourth race civilizations, which were varied and numerous, the dawn of what is known to science as the human period, begins. In actual years the distance is enormous from the first subrace of the fifth race to the present day, and what is generally supposed to be the whole history of man “does not go back. In the brief space at our disposal, only the most cursory reference can be made to the progress of humanity during the fifth race.

The destruction of the spiritually degraded Atlanteans gave a shock to the survivors which resulted in the sinking of material civilization for a long time over the main portion of the globe; we are not yet told exactly what proportion of the world kept some vestiges of the past greatness, but it cannot have been large. Anyway, the effect of the fresh start was good, for it provided conditions under which the later comparatively unsophisticated tribes could be helped by advanced souls who incarnated among them and taught them the elements of the arts and sciences. In every tradition that has come down to us from antiquity a Golden Age is spoken of — the “Garden of Eden” in the Bible — and, although in some cases this unmistakably refers to the first, second, and the early third races, when rudimentary mankind had not fallen into materiality, it may generally be taken to mean the dawn of the fifth when mankind was again comparatively pure and happy, and was guided by semi-divine kings, adepts of wisdom and compassion. In Egypt the traditions of many dynasties of gods and heroes were recorded by Manetho, and have actually come down to us, though the lists of names have been mutilated. While no doubt the details of the Greek, Hindu, Egyptian, Central American and Scandinavian cosmogonies and primitive histories of mankind are largely allegorical, their general agreement is not due to chance. By degrees the same old process of materializing came into action; and as the “family” races, or smaller divisions of the subraces, differentiated into the nations of the later ages, we arrive at “historic” and present times, with the numerous red, yellow, brown, black, and white representatives of the complex developments of the great evolutionary process of human expansion. Although we have descended into an age of moral and spiritual darkness (not intellectual), as compared with the Golden Ages it must not be forgotten that in the great journey of the soul from spiritual conditions through the material and back to a higher point, it is subject to a continual series of smaller cyclic ups and downs, and that even in the darkest time necessary experience is being gained. As we have long since passed the densest materiality of the fourth race, every step onwards is leading to higher conditions, and although the road seems to cross many a hill and descend into dark valleys, its general tendency is upwards all the time.

Planetary Spirit

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Cataclysm after cataclysm occurred, and the leaden slag of the fourth race sank to its doom, deluged by the waters of heaven and earth as they flooded the lands according to karmic law. Along with the sinking of Atlantis, which extended over several million years, new lands had been rising in other parts of the globe, and these became peopled as time went by with certain of the Atlanteans who settled there in two or three great migratory waves.

Thus the fourth root-race gave birth to the fifth whose cradleland was the Desert of Shamo or Gobi and surrounding tablelands — a country whose present sandy wastes give no hint of lands once rich with verdure, where forests and lakes witnessed a succession of civilizations as grand as any the world has ever known. Here for many millions of years, while Atlantis was involved in her death struggle, seeds of the new race were being sown in virgin soil.

Nature is beneficent in her workings. While the consequences of her human children must be met and faced by them through the working of karma and cyclic reimbodiment, yet at each new racial birth she casts her seed in freshly-turned soil, so that the child-race may be conceived in purity and nurtured in spirituality. Peopled thus with egos who had remained clean and strong through the Atlantean upheavals, and helped once again by the reentrance into their midst of semi-divine beings, the new race became a focus of spiritual light. As the Master Koot Hoomi (KH) wrote:

the highest Planetary Spirits, those, who can no longer err . . . appear on Earth but at the origin of every new human kind; at the junction of, and close of the two ends of the great cycle. And, they remain with man no longer than the time required for the eternal truths they teach to impress themselves so forcibly upon the plastic minds of the new races as to warrant them from being lost or entirely forgotten in ages hereafter, by the forthcoming generations. The mission of the planetary Spirit is but to strike the KEYNOTE OF TRUTH. — The Mahatma Letters to A. P. Sinnett, Letter IX,

Simultaneously with the establishment of the Mystery schools in Atlantis some four or five million years ago, the fifth or Aryan race was slowly coming into being, immensely aided by egos of spiritual refinement attracted there by ties of divine kinship. Gradually the soil was prepared and, the work of striking the “Keynote of Truth” having been accomplished, the demigods retired to their superior spheres. One million years ago the new race was ushered into adult existence impressed with the knowledge of “eternal truths.”

As the centuries passed and civilization succeeded civilization, the love of truth once again became dimmed in human hearts and the ancient precepts fell into disuse. The Mysteries were withdrawn even further, so that the knowledge once universal became the prized guerdon bestowed by the great Brotherhood upon that choice minority whose lives were dedicated to truth and truth alone, unstained by weakness or selfish ambition. With enduring consistency the ongoing purpose of the Mysteries has remained threefold in character:

(1) the persistent spiritualization of the thought-life of humanity so that knowledge of things spiritual may penetrate into the heart, and life in time may become a benediction of peace instead of a tragedy of conflict;

(2) seeding grounds of adepts, nurseries for future recruits, who through trial and initiation may become fit to receive the supreme dignity of membership in the great Brotherhood; and

(3) the preservation of truth for future races unsullied by human hand; and the polishing of the knowledge of truth through investigation by trained seers of the secrets of nature in worlds visible and invisible.

The first of these aims is fulfilled by the periodic appearance of world teachers, the inspirers of what later became the great religious and philosophical schools: messengers from the Lodge who come forth at cyclic periods to strike anew the “Keynote of Truth.” Hence every great religion, every noble philosophy, every fundamental scientific insight was born from the Sanctuary, to become a new religion, a new philosophy, a new science: fresh and new for the age and the people, but ancient beyond time because nurtured in the womb of esoteric antiquity.

All that is good, noble, and grand in human nature, every divine faculty and aspiration, were cultured by the Priest-Philosophers who sought to develop them in their Initiates. Their code of ethics, based on altruism, has become universal. — “The Origin of the Mysteries,” Blavatsky Collected Writings

The second of these aims is ages-long in accomplishment and deeply occult: to rouse the hidden fire of divinity in the human soul, and through the kindling of that flame burn the dross of imperfection, sloth, and unworthy desire from the heart. One of the impelling aims of such discipline is to restore to humanity inner sight, to free people “from every danger of being enslaved whether by a man or an idea”.

The disciple must become vajradhara (“diamond-bearer”), a title used for Bodhisattva Gautama, whose many-faceted heart was ever merciful in reflecting human sorrow, but whose spiritual essence was like a diamond, unyielding at its core to the subtle disguise of illusion (maya).

The third of these aims is made possible through the selection of new recruits into the Brotherhood, so that (a) truth may be preserved untarnished by human selfishness; and (b) investigation into the arcana of nature may go on unhindered, and the results of such examination by generations of trained seers be checked and rechecked, and only then recorded as occult fact for the benefit of humanity.

As far as the labor of the Masters is concerned, the following written by one of their number in 1881 speaks for itself:

If, for generations we have “shut out the world from the Knowledge of our Knowledge,” it is on account of its absolute unfitness; and if, notwithstanding proofs given, it still refuses yielding to evidence, then will we at the End of this cycle retire into solitude and our kingdom of silence once more. . . . We have offered to exhume the primeval strata of man’s being, his basic nature, and lay bare the wonderful complications of his inner Self — something never to be achieved by physiology or even psychology in its ultimate expression — and demonstrate it scientifically. It matters not to them, if the excavations be so deep, the rocks so rough and sharp, that in diving into that, to them, fathomless ocean, most of us perish in the dangerous exploration; for it is we who were the divers and the pioneers and the men of science have but to reap where we have sown. It is our mission to plunge and bring the pearls of Truth to the surface; theirs — to clean and set them into scientific jewels. And, if they refuse to touch the ill-shapen, oyster-shell, insisting that there is, nor cannot be any precious pearl inside it, then shall we once more wash our hands of any responsibility before human-kind.– Mahatma Letters, 

Unthanked, unknown, unconsidered, the Masters go on in their compassionate work for mankind’s enlightenment, a work that has never ceased in its outpouring of spiritual vitality for many millions of years, to continue another such period if necessity demand, until such time as humanity stirs from its lethargy and once again wills to unite its heart with truth. Master KH continues:

For countless generations hath the adept builded a fane of imperishable rocks, a giant’s Tower of INFINITE THOUGHT, wherein the Titan dwelt, and will yet, if need be, dwell alone, emerging from it but at the end of every cycle, to invite the elect of mankind to co-operate with him and help in his turn enlighten superstitious man. And we will go on in that periodical work of ours; we will not allow ourselves to be baffled in our philanthropic attempts until that day when the foundations of a new continent of thought are so firmly built that no amount of opposition and ignorant malice guided by the Brethren of the Shadow will be found to prevail.– Mahatma Letters.