Saturday, March 30, 2013

First Interview with F.E.D. Co-Founder & '''Mathematics of Dialectics''' Discoverer Karl Seldon.

Full Title:   First Interview with F.E.D. Co-Founder & '''Mathematics of Dialectics''' Discoverer Dr. Karl Seldon.

Dear Readers,

I have posted below the transcript of the first public interview ever granted by Karl Seldon, the co-founder of Foundation Encyclopedia Dialectica [F.E.D.], and the discoverer, in 1996, of the first dialectical arithmetic -- also the first 'contra-Boolean algebra'; the first algebraic dialectical logic -- and of the dialectic of the dialectical arithmetics, a dialectical progression of systems of dialectical arithmetic, modellable using the algebra of the first dialectical arithmetic, and hence also the discoverer of the '''mathematics of dialectics''' entire.

This interview is a wonderful reflection of a life of 'practical dialectics' -- of dialectics applied, to consciously '"change the world"', not just to '''interpret the world''' [Marx].

The URLs by which you may access the original text of this interview transcript are the following --,29DEC2012,re-edited_02APR2013.pdf

This interview is a rare opportunity  -- indeed, an almost unique opportunity -- to glimpse directly the self-movement of the mind of the person behind the subject-matter of this blog, and behind all of the manifold works of Foundation Encyclopedia Dialectica [F.E.D.]!

For a similar view of the "Antihumanism" of the descendance-phase Ruling Class, with much historical background, see the new book [published in 2012] by Robert Zubrin, title:  MERCHANTS OF DESPAIR -- Radical Environmentalists, Criminal Pseudo-Scientists, and the Fatal Cult of Antihumanism.



P.S.  F.E.D.-unfamiliar readers take note:  The title of this interview -- "Terran Humanity at the Brink" -- is a reference to Dr. Seldon's famous First Afterword to the partially-extant e-Book Dialectical Ideography, co-authored by Dr. Seldon and F.E.D. co-founder Sophya St. Germain:

F.E.D. Interview #1 --

Terran Humanity at the Brink

First Published Interview with F.E.D. Co-Founder Karl H. Seldon [KHS]

Interviewer: [WM]

WM:  Welcome, Doctor Seldon.  Let me begin by, first of all, thanking you, and the F.E.D. General Council, for granting me this first-ever to-be-published interview with you.  I've been waiting for this moment, with anticipation, ever since the F.E.D. General Council's first letter to this web site, dated June 5th, 2004.

KHS:  You are most welcome, and also most deserving!  I also know, from our many conversations over the years since that first letter, that you know that the timing of such events is a matter for the most careful psychohistorical calculation.  Also, I know that you are aware that this first interview may not be able to go on for as long -- or into as much depth -- as you and I both would like, because the global situation is so utterly delicate as of this present moment, and we of F.E.D. are ethically committed do everything in our power, however minute that power may be, and whatever the risks to our persons, to help "swerve" the present situation away from the precipice of a New/Final Dark Age, and toward the take-off point for Terran humanity's first Global Renaissance.

WM:  Yes, and, given our situation, I propose that we "cut to the chase", so that I will ask you for your most urgent bottom line recommendations to the world wide web public of this web site first -- jumping ahead to a question which might have otherwise been my last question, or, at least, a later question, in this interview, had our situation not been so urgent.   

After that, we can see how far we can get into my "lower priority" questions. 

So, my first question to you is this one:  What is the most urgent message that you and the rest of the F.E.D. General Council wish to convey to the guests of this web site tonight?

KHS: The core-plutocracy-orchestrated "Fiscal Cliff"/Sequestration/Federal Government Spending Limit drama, now nearing its climax in the U.S., may be designed to provide cover for the core plutocracy to trigger a new, drastically-deeper phase of their engineered 'Global Great Depression II', a la, in their 'Global Great Depression I', their 1931 Credit-Anstalt default trigger, that plunged the global financial system into the pit of 1933, and beyond.

It is of crucial importance, at this juncture, that the peoples of Europe, the U.K., and the U.S. continue to demonstrate their firm opposition to the draconian, Depression-worsening, viciously-descending spirals of the "austerity" regimes that the core plutocracy is attempting to impose, most savagely in Greece, so far, but, soon, equally, or even more savagely, elsewhere in Europe, and in the U.K., and in the U.S. as well -- and, of course, also in China, India, Brazil, and Russia, etc., through the catastrophic contraction of global trade entailed by the collapse of effective demand in the E.U./U.K./U.S. --  if that core plutocracy are not frightened into putting the brakes on their present time-table, precisely by such popular resistance. 

If the core plutocracy is running a similar time-table to that they ran for their 'Global Great Depression I', then 2013 corresponds to 1934, so that they have already been forestalled, since 2010, if it corresponds to 1931, from "pulling the trigger" for the deeper phase of their 'Global Great Depression II', by the beginnings of a popular "catching on" to their machinations, as expressed by the massive anti-plutocracy demonstrations in Europe, and, to a lesser extent, in the U.K./U.S., the latter being the very home turfs of the ruling, "Eugenics" faction of the core plutocracy.

It is equally crucial, however, that these popular demonstrations avoid the initiation of violence.

Nonviolence is a key to the effectiveness of efforts for social betterment, because violence corrupts its initiators, converting them, even if their violence is "successful" in overthrowing the violent tyranny that they had opposed, into but the new incumbents of the very evil that they had intended to overthrow -- reinstating that evil through them, as them -- and thus resulting, for them, and for humanity as a whole, in a defeat which could not be more complete.

Of course, the agents of the core plutocracy will initiate violence, against peaceful demonstrators, and will attempt to provoke a violent reaction from such demonstrators.  

Such provocations provide opportunities for these agencies of the core plutocracy to apply their crippling and maiming "technologies", and their "population reduction" methods -- and to "justify" martial law, etc., etc., a la the core plutocracy’s Syrian erstwhile 'servant-dictator'.

Given all of this, we recommend immediate -- and increasing -- recourse to methods of effective protest that do not require citizens to expose themselves to maiming, mayhem, and murder, on the public streets, by the core plutocracy's proto-police-state apparatuses.   

Massive global boycotts of the products and "services" of core-plutocracy-owned mega-corporations can still exercise tremendous leverage over the core plutocracy, hitting them where they "live", wallowing in filthy lucre.

In our opinion, such boycotts should target those mega-corporations that are prostituting the executive, the legislative, and the judicial branches of national governments, across the Northern temperate zone, to impose the core plutocracy’s eugenics solution’, in particular, by means of ‘stealth genocide’, including via draconian "austerity", via their global, pseudo-food-induced obesity/diabetes epidemic, and via naked aggression -- variously-excused military assaults upon, invasions of, and occupations of other countries -- countries that have not attacked the U.S./U.K.. 

Some main objectives of these invasions is ‘stealth genocide’ via “collateral damage” -- ultra-high levels of “accidental” civilian casualties -- and to recruit more revenge-seeking enemies of the U.S. among the survivors [e.g., with the rate of rape committed by U. S. soldiers against their female comrades-in-arms being so high, just imagine the rate of rape against the occupied civilian population], to help “justify” keeping the military-industrial complex budget “booming” -- as well as to achieve some ‘stealth genocide’ also against the young, plutocracy-impoverished citizens of the U.S., who the plutocracy has made sure will have few job options other than those in the military, and who, thus, populate the U.S. “volunteer” army -- e.g., via suicides, e.g., due to PTSD induced by witnessing, and by being forced to participate in, war crimes, and other crimes against humanity -- rapes, tortures, mass murders, etc., etc. -- of the occupied civilian populations.  

These are all only particular instances of the plutocracy’s general “divide & rule” method, e.g., inducing people that the plutocracy has impoverished in one part of the world to kill other people that it has impoverished in another.   

The value that the plutocracy truly places upon U.S. volunteer soldiers can be inferred by how immediately these former soldiers are discarded, denied any help, denied their Veterans Administration medical care rights, etc., once they return from the occupied territories.

Hypothesis:   Boycott targets should include the major oil companies, the largest financial corporations, the [pseudo-]food’ companies [i.e., ‘diabetes, heart disease, stroke, kidney disease, cancer, auto-immune disease, and Alzheimers’ disease producers/inducers’], [the ‘pseudo-medicines’] pharmaceutical drug companies ['lethal side-effects-cascades producers/inducers'], mass media corporations [‘ideology-inducers/reproducers’], etc.  

[It is our theory that the rank and file levels, and even senior executive levels, of these mega-corporations are typically not privy to the “eugenics”/‘stealth genocide’ intent of their corporate operations and products, being motivated mainly by the amplified profits attendant thereupon.  That is, nutrition-emptied and/or toxic, processed ‘pseudo-foods’ that generate disease-inducing addictive binge consumption, and pharmaceutical drugs that induce cascades of dangerous, potentially lethal side-effects, requiring yet further pharmaceutical drugs to mitigate those side effects -- further drugs each of which has its own dangerous side-effects, thus requiring further such “medication”, etc. -- can, indeed, drive huge profits, but these are profits upon the contraction, not upon the expansion, of human social reproduction.  It is, we believe, the few but highly influential controllers of these corporations, at the [interlocking] Boards of Directors levels, banker levels, and beyond, who consciously prosecute the “eugenics”/‘stealth genocide’ agenda.  But these “agents of influence” of the core plutocracy must promote their ‘stealth genocide’ operations under the cover of profitability -- and these operations must in fact deliver mega-profits -- to keep their corporate-executive underlings in line, and to keep those underlings able to keep their underlings in line, ..., i.e., all of them in effective, if unconscious, alignment with the core plutocracy’s ‘‘‘eugenocidal’’’ plan.] 

Such mass boycotts would tell the core plutocrats that the public is becoming aware of the plutocracy's global war on humanity, and is beginning to fight back against that "population reduction" strategy, including against the ‘stealth genocide’ producers referenced above, with effective non-violent weapons.

If the people of Europe and of North America do not give such evidence of their awakening to the plutocracy's war upon them, and upon the rest of humanity, then the core plutocracy will be encouraged to accelerate their tightening of the nooses that they have placed around the necks of the rest of humanity, worldwide.

If your site guests here wish more in-depth background about this global situation, I recommend that they study the serialization, by F.E.D.’s  Miguel Detonacciones, of the Equitist Advocacy group’s manifesto entitled "Malady and Remedy", via the following URLs --

WM:  It sounds as if you, and Miguel, and the Equitist Advocacy group, are all alleging a multi-genocidal conspiracy by what you term “the core plutocracy” -- is that correct?

KHS:  That, yes we are.   

But not simply that.   

We are not asserting that the conspiracy of the core plutocracy is the final cause of what is now unfolding in Terran human history.   

It is but a secondary cause, one which is itself caused by a far deeper cause.   

Now, of course, the “core plutocracy” is the present “ruling faction” of the present, global “ruling class”, and a ruling class is, by fact, and by definition, always a conspiracy against the interests of the rest of the society that it rules, for the perceived differential benefit of itself, at the expense of all others.   

But the ‘humanocidal mania’ of the present core plutocracy is a consequence of the unintended “laws” of a total human social practice that is based upon humanity valuing economic “value” -- monetary “value”, capital-“value”, profitability-“value”, and the social power, and the “perks”, that the ownership of this “value” brings with it -- above all else. 

The ‘humanocidal mania’ of the core plutocracy, since ~1900, is the predictable response, by human Nature, especially by the Nature of the core plutocracy, to the prospect of their massive loss of social power, due to their prospective loss of “value” -- due to the prospective loss of the profit-“value”, and, therefore, of the power-“value”, of the core capital-“value” that they own, due to ‘technodepreciation’-driven loss, or fall, of their rate of profit on their ‘techno-obsolescent’ fixed-capital-“value” -- especially on that of their petroleum “value”, in the face of the increasingly irrepressible advent of fusion power and of other ‘oil-obsoleting’ scientific and technological innovations.   

Look what a mere pipsqueak ‘servant-dictator’ like al-Assad has done, and is still doing, in response to a non-violent challenge, by his people, to his power:  turning his weapons of mass destruction on their cities, on their homes, and on their bodies.   

Then guess how much more viciously the ultra-dictators of the global petroleum-finance plutocracy will respond to a proximate threat to their power, such as is 'technodepreciation' in the '''descendance phase''' of the capitals-system.

The way things are, broadly speaking, is, in this sense, the only way that they could be, given the nature and process of Terran human origins, the conditions of Terran human life, and the human-genomic and human-phenomic consequences thereof, throughout all of human prehistory to-date.  

Our science of psychohistory enables us to see that this entire descendant-phase ‘metafinite singularity’ of the global capitals-system, this looming ‘Meta-Darwinian Planetary Selection Test’ of the Terran human phenome/human genome totality, this ultra-degeneration and ‘Meta-Darwinian ultra-unfitness’ of the contemporary ruling class, have all been, broadly speaking, essentially and broadly inevitable ever since human social productivity breached the level where exchange-value emerged from use-value, and, in actuality, ever since the human genome itself first emerged. 

Likewise, this total history is now bringing, to the threshold of possibility, humanity’s power to put an end to this prehistory, for the first time ever in that prehistory.

The Foundation values the role in the world, and the heritage, of the United States of America, despite its many sins and shortcomings -- even if, broadly, inevitable ones.   

We have located both of our main centers of operation on U. S. soil -- one on the Western extremity of the North American continent, at Terminious, California, and the other one on its Eastern extremity, at Stars’ End, New York. 

I now ask your guests of this site, especially those who are citizens of the United States of America, to ask themselves what, today, is left of the legacy and of the heritage of liberty in the U.S.A.; what is left of the U. S. Constitution and of its Bill of Rights. 

Under the recent U. S. Federal Government administrations -- administrations of the [both ‘misnomered’] “Republican” Party & “Democratic” Party alike, as if they have been working to a common plan, despite all of their dividing-&-conquering theatrics of supposedly unalloyed mutual hostility and opposition -- the U. S. Constitution/Bill of Rights has been utterly shredded, in essence, if not yet fully in practice, ‘til essentially nothing of it remains in recent “law”:

  • By the recent “eminent domain” decision by the U. S. Supreme Court, any sufficiently influential private corporation, enlisting the support of “your” municipal government, can confiscate your personal and/or your private property, e.g., your home, with but pennies on the dollar in “compensation” to you.  “Eminent domain” takings of private and personal property were intended to achieve overriding public good, not merely private corporate profit, but, no more!  [Kelo v. City of New London, 545 U.S. 469 (2005), ];

  • By recent U. S. Supreme Court decision, U. S. corporations now have the “right”, as ‘virtual persons’, hence also as ‘virtual citizens’, to apply their effectively unlimited monetary wealth so as to effectively buyU. S. elections.  This decision is expected to increasingly nullify the voting rights of the actual citizens of the United States, at all levels of government -- local, state, and national -- and to prostitute, to corporate special interests, an ever greater proportion of those candidates who wish to be able to win elections -- by buying more mass media mud-slinging ads than their opponents, etc. -- which requires those candidates, if they are not independently wealthy, to accept millions in corporate de facto bribery  [Citizens United v. Federal Election Commission, 558 U.S. 310 558 (2010), ];

  • By recent Congressional legislation, signed into law by President Obama, the government, by its sole order, has the “right” to imprison any U. S. citizen indefinitely -- even for the rest of their lives -- without charge(s), without trial, without conviction of any crime, by any jury of their peers, and without any habeas corpus access, or other access, to the U. S. Courts, for that “citizen”, a “citizen” thereby reduced, ipso facto, to a kind of non-citizen” slave of the [‘‘‘corporatist’’’] government [ ]

Clearly, these new corporate and government “rights” are really wrongs, and total violations of the U. S. Constitution and Bill of Rights.  

These developments instantiate the horror that is heralded by our psychohistorical, technical prediction: the law of motion of descendant-phase capital-based society is a sociotaxis to totalitarian, humanocidal state-capitalism.

They come at the same time that the Wall Street ‘‘‘R.I.C.O.’’’ corporations and their criminal CEOs have stolen, from so many millions of Americans, and without a single Big Bank CEO prosecution, those citizens’ pensions, their 401(k)s, their life savings, their jobs, and their homes.   

Moreover, these same CEOs  have also absconded -- via the complicity of the many ruling class members who are also federal government appointees at the highest levels, and of their lower-level political prostitutes in the U. S. federal government -- with trillions of dollars of U. S. taxpayers funds, and also with the proceeds of trillions of dollars of new taxpayer debt, created to “bail out” those CEOs, which they then used to pay themselves even more exorbitant salaries and bonuses than they used to do before they launched their Global Great Depression II, as well as to buy even more elections -- so that they have effectively robbed the Social Security Trust Fund, and the U. S. Treasury as a whole, of the funds previously promised to actually benefit majority taxpayers, and so that they can now say -- ‘‘‘we really just can’t afford the promised Social Security and Medicare benefits [that workers pay for from every paycheck], Medicaid, Head Start, Pell Grants, U. S. Federal Government Pensions to federal government workers, or any social safety net at all’’’, and so that they can continue to buy elections to put into office enough prostitute politicians to repeal these programs, and to repeal virtually every other government program that actually benefits the U.S. majority [ ].

The “representative-democratic” political system of the United States of America has become increasingly reduced to a system of legalized corporate bribery, to a system of intellectual and political, policy prostitution to mega-corporate Big Money, by which the major corporations write the laws of the land, and thereby also “legalize” their mounting criminality. 

The houses of legislature have become houses of prostitution, together with the executive mansions and the court houses -- especially the White House and the “house” of the “corporatist” U. S. Supreme Court. 

The horrific results, sampled above, are hardly surprising. 

And the ruling corporate whores have far more horror still in store for you and your family.

So, we ask our U. S. citizen friends:  What is left of your America?  

Is this “bi-partisan” shredding of the founding contracts of the United States of America simply an accident?   

Or, does it reflect the intention, the agenda, and the plan of the ruling, core plutocracy, which wields both major political parties like a limp pair of soulless marionettes?

WM:  Why, then -- as you have described, in part, above -- is the human world on Earth today such a horrible place, so bad, so retrogressive?   

Why do all efforts to improve it seem to end in failure, or, even worse, in even further worsening  -- e.g., the recent pro-democracy revolutions across the Arab world? 

KHS:  The primary reason for this is that the most powerful institutionalized social force that has ever existed on Earth, in all of Earth's known human history to date -- today's global, core, petroleum-finance plutocracy -- is hell-bent on preventing, or reversing, any improvement of human life for the vast majority of humanity, and on making life worse for that vast majority, until that plutocracy has made life literally impossible for most of that majority.   

They are hell-bent on "population reduction" -- to the extent of eliminating 95% of the human race [see, for example, quoted public statements to that effect from plutocracy 'spokes-servant'/CNN-founder Ted Turner, e.g.: ].

The deeper causes, behind that primary reason, have their sources in the 'intra-duality' of the capitals-system of human-societal self-reproduction, combined with the human "power-sickness" that afflicts Terran humanity, both genomically and 'phenomically'.

As the capitals-system develops, the growth of social productivity -- "the growth of the human social forces of production" -- is expressed in both the growing physical mass of the fixed capital plant and equipment used in production, relative to the mass of labor-power also mobilized therein, and also in the increasing concentration, consolidation, and centralization of the ownership of the largest agglomerations of that fixed capital, and of the socio-economic and political power that goes with the monetary returns upon that ownership, in ever fewer hands.

Those “fewer hands” eventually become the global, core, ruling, petroleum/finance faction of the global plutocracy.

At a certain point in this development -- at the turning point from the ascendant phase to the descendant phase of the capitals-system -- further productivity-increasing innovations obsolete, hence devalue, more “sunk” fixed capital value than the incremental profit value that they add, especially for this ultra-fixed-capital-intensive core plutocratic faction. 

Think what fusion power would do to the value of oil itself, and to that of the global capital infrastructure used to "produce" it -- fusion power that yields, from a gram of its fuel, energy equivalent to that from 8 tons of oil.

Those who have experienced near absolute socio-political power, and who have succumbed to the "power-sickness" that such experience typically breeds in Terran humans, will do anything in their power to hold on to that power.  

No level of crimes against humanity, no amount of murder, is too much to perpetrate for the monsters that such people become, if they think that those mega-crimes will enable them to retain their socio-political-economic power. 

As I mentioned earlier, erstwhile 'servant-dictator' Bashar al Assad foreshadows, on a smaller -- but now openly-visible -- scale, the "power-sickness" of the core plutocracy that we are pointing out, and the ultra-vicious actions that it breeds in them.

So, starting in the late 1800s, the plutocracy moves to crush incipient industrialization in the global periphery to the core regions of earliest capitals-system development -- e.g., the U.K., France, and the U.S. core -- suppressing those regions under military dictatorships, 'servant-dictatorships' -- "servant" to the core plutocracy, "dictator" to their own people -- thereby turning that periphery into the modern "Third World" -- since competition from the most advanced vintages of fixed capital, installed "from the git-go" in newly-industrializing regions -- and also operated by the initially cheaper labor-power located there, to boot -- would devastate the capital value and profitability of the legacy fixed capital in the old capitalist core regions, especially that owned directly by the core plutocracy, or financed by, e.g., the largest banks, also owned, by then, by the core plutocracy.

The core plutocracy likewise suppresses technological innovation within the original industrial core region, the U.S., the U.K., and Western Europe, and invests in anti-technology and anti-science ideologies, sparing only those sciences and technologies that they can harness to turn technologies of production -- "productive forces" -- into "forces of destruction"; into "destructive forces" -- e.g., into military means of mass destruction, into engineered world wars, into [“eu”]genocides -- and to transition from an ascendant-phase regime of profit predominantly on expansion of social reproduction to a descendant-phase regime, more and more profiting on their deliberately-induced contraction of social reproduction. 

Of course, the core plutocracy also happily allows ‘technodepreciation’ to proceed unabated in industrial sectors in which they have limited investments or loans outstanding, and/or in which the ‘technodepreciation’-driven bankruptcies of small corporations there will allow the core plutocrats to send in their carpetbaggers to acquire those small corporations, and/or their assets, for pennies on the dollar, when they perceive advantages to their power in so doing.

E.g., they thereby eliminate components of citizen freedom, and/or consolidate their concentrated ownership and control over the economy and over the polity even further -- e.g., in the book publishing industry, and via the more recent, internet-driven ‘technodepreciation’ bankruptcies in the public post offices, in the private newspaper and magazine publishing industries, in the audio-recording publishing industry, etc.

But their suppression of industrialization in the periphery has the effect of also suppressing the "demographic transition", in most of the world, e.g., in the "Third World", and of preventing the development of industrial-productivity-based prosperity there, thus, in effect, recruiting an ever-growing population of plutocracy-impoverished people who the plutocracy fears are increasingly ripe to rise up in anger and overthrow its power, world-wide. 

The core plutocracy therefore feels compelled, in order to retain its vicious, vampiric power over the rest of humanity, to resort to a global pogrom of "Eugenics" -- of "population reduction", beginning with various forms of 'stealth genocide', but intended and planned, by the core plutocracy, to escalate into a global regime of concentration/extermination-camp-based ‘‘‘humanocide’’’, once they have succeeded in imposing national state-capitalisms/totalitarian rule globally. 
The catastrophic contraction of global social reproduction via the core-plutocracy-orchestrated ‘Global Great Depression I’, with its proliferation of their fascist state-capitalist ‘servant-dictatorship’ regimes throughout the planetary temperate zones, and with the Stalinist, quasi-autarkic, proto-state-capitalist “gulag regime” in Russia, was their first attempt at this. 

This first attempt was defeated by the ‘Franken-dictator’ turn, against them, of their erstwhile ‘servant-dictatorship’, the Hitler Eugenics Regime that they had installed in Germany, a Regime which switched to an attempt to wrest world dictatorship away from the U.K./U.S. plutocrats, and, thereafter, by the contest for global power with the Stalinist ‘Franken-dictators’, until the 1989 fall of Stalinism across Eastern Europe.
Since then, the plutocracy has, to a considerable degree, lost control of their Third World, even while they have regained considerable control of the erstwhile Stalinist “Second World”, especially in Eastern Europe.   

That is, China, India, and Brazil have been able to industrialize, and new middle/working classes are burgeoning there, with increasing numbers of their citizens receiving advanced training in advanced technology and in "high-tech" engineering. 

This has induced a state of unprecedented panic in the core plutocracy.   

They feel that they have only a little time left to abort this progress before accelerating technological development, rising living standards, advancing education -- and ‘technodepreciation’ -- put a final end to their global rule, and to all of their prized “perks of rule” -- to their lives of pillage, torture, rape, and mass murder.   

In particular, their global efforts to suppress the invention -- hence also the inventors -- of fusion power, are, they feel, in increasing jeopardy of imminent failure.

The above, prose rendition of our psychohistorical-dialectical ideographical 'meta-model' -- a vast compression of that full psychohistory ‘meta-model’ -- brings us to the global situation we face today.

WM:  What do you and the rest of the Foundation do to mitigate, among yourselves, the universal "power-sickness" that you have just identified?

KHS:  We are a cloistered, secular monastic order, precisely in order to combat that "power-sickness" within each of us, and among ourselves.  

The disciplines that we use to evoke, and to confront, that potential sickness within ourselves, and within our community, include the following --

  •  We accept no contributions of money from non-members.

  • No Foundation publications are authored in our "real names", but only pseudonymously”, lest the pursuit of power in the form of personal fame pervert and corrupt our motivations, and the very content of our work;

  • The fruits of our research are typically offered free of any monetary charge, to every person in the global community of the world wide web, lest pursuit of power in the form of monetary wealth pervert and corrupt our motivations, and the very content of our work;

  • We advise our www public as to how they might move in socio-political and economic ways to bring about a Global Renaissance, and to avert a New/Final Dark Age, with the pledge that no member of the Foundation will ever seek, or accept, election or appointment to political power / political office, lest the pursuit of political power pervert and corrupt our motivations, and the very content of our work.

Moreover, once a trans-capitalist regime -- e.g., one of Economic Democracy, such as that defined by Prof. David Schweickart, or one of Political-Economic Democracy, such as that defined by the Equitist Advocacy group -- “comes to power” by popular election, as we fully hope and intend that it should do -- and as we work, with every resource at our disposal, to help to bring that revolution about -- we will serve and support that regime only with the greatest possible contribution that we could ever provide to it -- that of helping to expose, to criticize, to check, to balance -- to “whistle-blow” against -- all of the tendencies that this new regime may exhibit toward abusing their new-found power, and, thereby, toward self-inducing their own failure and demise, and, along with that ‘self-induced demise’, probably inducing also thereby the demise of Terran humanity as a whole.

In both of these two roles -- both that of this new regime’s “proponent” and “promoter”, and that of this new regime’s critic and “whistle-blower” -- we would be working to overcome the tendencies toward the failure/extinction of Terran humanity, in its looming ‘Meta-Darwinian Planetary Selection Test’. 

This "Test" is a ‘“Natural Selection Test”’, not just of the human genome, but of the ‘‘‘complex unity’’’ of the human phenome/human genome entire.

The tendencies that we work to overcome are incarnated, most maximally, in the ‘meta-Darwinian ultra-unfitness’ of the ruling, ‘‘‘humanocidal’’’ core plutocracy, which actually pursues the anti-fitness aim of plunging the rate of human social reproduction deep into the negative domain.

The tendencies that we work to reinforce are Terran humanity’s tendencies to successfully pass this looming ‘‘‘Test’’’, thereby entering into its first Global Renaissance, founded upon a resurgent re-acceleration in the growth of the human-societal self-forces of expanding human-societal self-re-production, including in the human harnessing of the ‘pre-atomic power’ of nuclear fusion, and also, thereby, entering upon the threshold of Terran humanity’s ‘trans-planetary’, ‘meta-planetary’, and interplanetary potential higher destiny. 

WM:  What’s the "back story" behind Karl H. Seldon, Sophya St. Germain, and F.E.D. as a whole?

KHS:  ... One moment please ... I am being called, right now, into an emergent session of the F.E.D. Special Council of Psychohistorians.  We will have to now suspend this interview, for the present.  Please let me thank you, once again -- and publicly, this time, Webmaster -- for all that you do for the upkeep of your crucial website, in particular, and for all that you do on behalf of the highest good of Terran humanity, in general!

WM:  Thank you.  Let me simply say that I stand ready to resume this interview whenever developments allow.

Thursday, March 28, 2013

'''Number''' Theory -- Ancient versus Modern versus 'Trans-Modern'

Dear Readers,

I have excerpted, below, parts of the forthcoming F.E.D. Vignette #11, by F.E.D. Public Liaison Officer Aoristos Dyosphanthos, entitled '''Number''' Theory, Ancient vs. Modern vs. 'Trans-Modern', below, for your reading and learning pleasure.

P.S.  I have sometimes had to render, below, Greek letters, and other Ancient Greek symbols, in ways that could be accommodated within the available typography, or even as blank character-strings -- _______ -- when I found no more adequate way to render them.

F.E.D. Vignette #11 --



Ancient vs.  

Modern vs.  


 by Aoristos Dyosphainthos

Authors Preface.  The purpose of F.E.D. Vignette #11 is to present F.E.D.’s «Arithmos» Theory -- a psychohistorical dialectical synthesis of Ancient «Arithmos» Theory &/with Modern ‘‘‘Number Theory’’’ -- without recourse to numbers.

A Note about the On-Line Availability of Definitions of F.E.D. Key Technical Terms.  Definitions of Encyclopedia Dialectica technical terms and ‘neologia’ are available on-line via the following URLs --

-- by clicking on the links associated with each such term, listed, alphabetically, on the web-pages linked above.

The Encyclopedia Dialectica special terms most fundamental to this vignette are indicated below, together with links to their E.D. definitions --

«arithmos» and «arithmoi»




NQ dialectical arithmetic/algebra

self-meta-monad-ization or self-meta-individual-ization

-- we plan to expand these definitions resources as the F.E.D. Encyclopedia Project unfolds.

q1 <---]  I.  Ancient «Arithmos» Theories.

Exemplary Ancient, Quanto-Qualitative Definitions of ‘“Number’’’ as «Arithmos»:  E.g., by Euclid and by Aristotle.

Not generally realized by we Moderns is the psychohistorical fact that the Ancients’ concept of ‘‘‘Number’’’ -- named, in ancient Greek, by the word «Arithmos», the ancient Greek word from which the modern English word Arithmetic” descends -- as proven by the ‘psychoartefacts’ that the Ancients left behind, and that have come down to us, still extant, was qualitatively, ideo-ontologically’ different from our Modern concept of “Number”.

Summarily we can say that Ancients defined an «Arithmos» as an ‘‘‘assemblage of qualitative -- of multiple-qualities-exhibiting -- units/things of a given, single kind’’’.  «Arithmoi» are thus bothquanto-qualitative’, and sensuous and ideational, phenomena, not “purely quantitative”, ‘quantifier-only’ ideo-phenomena, such as, e.g., 2, 3, 4, 5, 6, and 7, ... .

Herein we will take, as representative of the Ancients’ concept of ‘‘‘Number’’’, in its philosophical and/or mathematically technical form, the still-extant recorded thoughts of Euclid and Aristotle.

For Euclid [third Century B.C.E.]:  “Euclid defines in the Elements, VII, 2, a number as “the multitude made up of units” having previously (Elements, VII, 1) said that a unit is “that by virtue of which each of existing things is called one.”  As a unit is not composed of units, neither EUCLID nor ARISTOTLE regard a unit as a number, but rather as “the basis of counting, or as the origin [i.e., as the «arché» -- A.D.] of number.”  There is an echo of this Euclidean definition in CANTOR’s definition of the cardinal number as a set composed of nothing but units ... .” [H. Hermes, et al., Numbers, Springer Verlag, [NY:  1991], p. 12].

Note that this -- “self-evident?” -- claim that “a unit is not composed of units” posits a radical duality between multiplicity / number on the one hand, and unity on the other, i.e., between «arithmos» & «monad».  The Ancients excepted a single «monad» from their category of ‘‘‘number’’’ simply because a single «monad» is not an assemblage of «monads» -- is not plural.

This claim ignores the fact that reality is rife with ‘assemblages of metan+1-units, each of which is composes of a sub-assemblage of metan-units -- e.g., as a population with molecules as its units is one of each of whose units is composed of atoms as its sub-units, as a population with atomic nuclei as its units is one each of whose units is composed of “sub-atomic particles” [e.g., protons] as its sub-units, and as a population of “sub-atomic particles” is one each of whose units is composed of “pre-sub-atomic particles” [e.g., quarks and gluons] as its sub-units.

For Aristotle [circa 335 B.C.E]:  “Apart from this definition of number, which is oriented towards the idea of counting, one can find in ARISTOTLE the following statement:  that which is divisible into discrete parts is called [A.D.:  «plethos»] _____ (multitude), and the bounded (finite) multiplicity is called the number (ARISTOTLE [1], 1020a, 7.14).  The [A.D.:  Ancient] Greeks thus regarded as numbers, only the natural numbers, excluding unity; fractions were treated as ratios of [A.D.: “natural”] numbers, and irrational numbers as relationships between incommensurable magnitudes in geometry ... .  [Ibidem].

Actually, the statement above is an anachronism, a ‘moderno-morphism’, and a ‘retro-projection’ of the Modern meme of “number” back upon the Ancient one:  the Ancients did not hold the modern conception of the “natural” number, as pure, unqualified quantifier”.  On the contrary, as we shall show herein, via Diophantus’s circa 250 C.E. treatise The Arithmetica, the ancient meme of ‘‘‘number’’’ was a hybrid, quanto-qualitative’ one.

Attending closely to the qualitative, ‘ideo-ontological’ distinction of the Ancient concept of ‘‘‘number’’’ from the Modern can enable one to solve -- with both speed and clarity -- mysteries that still baffle many scholars of philosophy, e.g. --

arithmos:  number; arithmêtikê:  the science of number.  Zero was unknown as a number and one also was not counted as a number, the first number being duas [A.D.:  or ‘dyos’] -- two.  From the Pythagoreans, ton arithmon nomizontes arkhên einai -- who consider number to be the first principle (Ar. Met. 986a15) -- number played a great part in metaphysics, especially in Plato’s unwritten doctrines, involving obscure distinctions of e.g. sumblêtoi and asumblêtoi -- addible and non-addible numbers.” [J. O. Urmson, The Greek Philosophical Vocabularly, Duckworth [London: 2001], pp. 31-32].

The «Arithmoi Eide-tikoi» of Plato’s static, eternal dialectic, or ideo-taxonomy, were, in his conception, «arithmoi» of «Eide-Monads» -- Assemblages of «Idea»-Units -- for Plato’s reified, deified «Ideas», which he supposed to be the immutable, perfect, Parmenidean Causes behind the imperfect copies of them which somehow constituted and conducted the dynamic flux of our sensuous world. 

Per Plato, for each such Causal «Idea», call it I1, any perfect copy of It was redundant in terms of philosophical logic, and could not exist:   I1 + I1    ~=  2I1; instead,  I1 + I1   =   I1 [an algebraic property which Modern mathematics names “additive idempotency”]. 

Moreover, for any two -- heterogeneous, qualitatively/ontologically distinct -- such «Ideas», call them I1 and I2, their very apples versus oranges heterogeneity makes them “non-amalgamative” [cf. Dr. Charles Musès] if added together: 

I1 + I2    ~=  2I1, and I1 + I2   ~=   2I2; instead,
I1 + I2   =   I1 + I2, without further possibility of reduction within this language;

“apples plus oranges” equals “apples plus oranges”, irreducibly so, at this level.

Thus, in both ‘self-addition’ and ‘other-addition’, Plato’s «Eide»-Units are unaddible”, unsum-able’ -- «asumblêtoi».

Also, given that the original Pythagoreans held that «arithmoi» -- ‘‘‘assemblages of qualitative, multiple-qualities-exhibiting units/things of various single kinds’’’, i.e., ‘‘‘populations of individual things [including of physical, sensuous things]’’’ -- constitute reality, it is no longer sure that the original Pythagoreans were raving idealist mystics, as is so often presumed, based upon the ‘retro-projection’ of the modern meme of ‘‘‘number’’’ upon their Ancient «arithmos» idea.
Ancient Alexandria’s ‘Proto-Renaissance’, & Diophantus’s Qualifier-Quantifier Proto-Algebra’, at Dark Ages’ Door.

The first known ‘protoic’ emergence of “symbolical algebra”, as distinct from the already ancient ‘prose algebra’ -- or “rhetorical algebra” -- and of an algebra “symbolical” in the specific sense of ideogramic symbols’, not exclusively of either pictogramic symbols’ and/or of phonogramic [phonetic”] symbols’ [which, after all, would simply mean ‘prose algebra’, or “rhetorical algebra” again] -- was in a circa 250 C.E. work by Diophantus, entitled The Arithmetica.

This text, The Arithmetica [«Arithmêtikê»], taught the ‘‘‘art’’’, or ‘‘‘technology’’’ or ‘‘‘technique(s)’’’ [«tekhnê»], or ‘‘‘craft’’’, or ‘‘‘skill’’’, or ‘‘‘science’’’ of «Arithmoi» in general.

This text developed an intermediate stage between “rhetorical” algebra and full-blown “symbolical”, ‘equational’ algebra, which has often been termed “syncopated” [abbreviated] algebra, in which minimized abbreviations [“syncopations”] of words served as ‘proto-ideogramic’ symbols for arithmetical quantities, or ‘‘‘quantifiers’’’, and for arithmetical qualities or ‘‘‘qualifiers’’’, including for equations involving unknown quantities which Diophantus showed how to “solve” -- how to systematically render the unknown quantities known.

Diophantus’s particular style of “abbreviation” or “syncopation” -- an unprecedented style as far as is known -- was, apparently, to take the first letter of the Greek word to be abbreviated, and to place atop that first letter the second Greek letter of that word.  Thus, only two Greek letters -- the first two letters -- of the Greek word “survived” his abbreviation process.  Known numerical values were expressed using single Greek letters, with a dash or a “ prime” atop each letter, in ordinal correspondence [i.e., alpha = I, beta = II, gamma = III, etc.], in accord with longstanding Ancient arithmetical tradition.

The context of this work by Diophantus was the Ancient Egyptian city of Alexandria, after the zenith of the extraordinary, unprecedented Human-Phenomic -- scientific, technological, and institutional -- developments there, that Karl Seldon has described as the Western “Proto-Renaissance”.  Diophantus’s revolution in mathematics was cut short, in part, because it  arose circa 250 C.E., just a few centuries before the tidal wave of the fall of the Roman Empire, and the undertow dragging Ancient Hellenistic civilization down into the hellish abyss of the European Dark Ages, smashed into Alexandria, suppressing this progressive trend, and delaying its resumption, continuation, and supersession for another ~ ten centuries.

Regarding the mathematical aspect of this “Proto-Renaissance” in Ancient Alexandria, we find the following from the historical record:  “The earliest attempt to found a university, as we understand the word, was made at Alexandria.  ...  It was particularly fortunate in producing within the first century of its existence three of the greatest mathematicians of antiquity -- Euclid, Archimedes, and Apollonius.  They laid down the lines on which mathematics subsequently developed, and treated it as a subject distinct from philosophy:  hence the foundation of the Alexandrian Schools is rightly taken as the commencement of a new era.  Thenceforward, until the destruction of the city by the Arabs in 641 A.D. [i.e., C.E.], the history of mathematics centers more or less round that of Alexandria”.  [W. W. Rouse Ball, A Short Account of the History of Mathematics, Dover [New York:  1960], pp. 50-51].

Howard Eves describes, as follows, the lead-up to the founding of Alexandria --

“The period following the Peloponnesian War was one of political disunity among the Greek states, rendering them easy prey for the now strong kingdom of Macedonia which lay to the north.  King Philip of Macedonia was gradually extending his power southward and Demosthenes thundered his unheeded warnings.  The Greeks rallied too late for a successful defense and, with the Athenian defeat at Chaeronea in 338 B.C.[E.], Greece became a part of the Macedonian empire.  Two years after the fall of the Greek states, ambitious Alexander the Great succeeded his father Philip and set out upon his unparalleled career of conquest which added vast portions of the civilized world to the growing Macedonian domains.  Behind him, wherever he led his victorious army, he created, at well-chosen places, a string of new cities.  It was in this way, when Alexander entered Egypt, that the city of Alexandria was founded in 332 B.C.[E.]. ... It is said that the choice of the site, the drawing of the ground plan, and the process of colonization for Alexandria were directed by Alexander himself.  From its inception, Alexandria showed every sign of fulfilling a remarkable future.  In an incredibly short time, largely due to its very fortunate location at a natural intersection of some important trade routes, it grew in wealth, and became the most magnificent and cosmopolitan center of the world. ..." [Howard Eves, An Introduction to the History of Mathematics (3rd ed.), Holt, Rinehart & Winston (NY:  1969), pp. 112-113 emphasis added by A.D.].

-- and the institutional innovations which seeded its unprecedented destiny --

“After Alexander the Great died in 323 B.C.[E.], his empire was partitioned among some of his military leaders, resulting in the eventual emergence of three empires, under separate rule, but nevertheless united by the bonds of the Hellenistic civilization that had followed Alexander's conquests.  Egypt fell to the lot of Ptolemy. ... He selected Alexandria as his capital and, to attract learned men to his city, immediately began the erection of the famed University of Alexandria. This was the first institution of its kind. ... Report has it that it was highly endowed and that its attractive and elaborate plan contained lecture rooms, laboratories, gardens, museums, library facilities, and living quarters.  The core of the institution was the great library, which for a long time was the largest repository of learned works to be found anywhere in the world, boasting, within forty years of its founding, over 600,000 papyrus rolls.  It was about 300 B.C.[E.] that the university opened its doors and Alexandria became, and remained for close to a thousand years, the intellectual metropolis of the Greek race [and not of the Greek “race” alone, but of the Occidental Afro/Euro/Near-Asian hemisphere of humanity entire! -- A.D.]." [Ibid., page 113, emphasis added by A.D.].

In summary:  No other city has been the center of mathematical activity for so long a period as was Alexandria from the days of Euclid (ca. 300 B.C.[E.]) to the time of Hypatia (A.D. 415 [C.E.]).  It was a very cosmopolitan center, and the mathematics that resulted from Alexandrian scholarship was not all of the same type. ...” [Carl Boyer, Uta Merzbach, A History of Mathematics (2nd edition), John Wiley & Sons, Inc. (NY:  1991), p. 178, emphasis added by A.D.].

Morris Kline well-describes the mathematical, technological, economic, and cultural momenta that converged into the genesis of the Ancient Alexandrian “Proto-Renaissance” in the following passages.

After the early death of Alexander, the Ptolemaic emperors of Egypt carried forward with Alexander’s plans:  “After his death ... the empire was split into three independent parts. ... Egypt, ruled by the Greek Ptolemy dynasty, became the third empire.  Antigonid Greece and Macedonia gradually fell under Roman domination and became unimportant as far as the development of mathematics is concerned ... The major creations following the classical Greek period were made in the Ptolemaic empire, primarily in Alexandria.” 

“That the Ptolemaic empire became the mathematical heir of classical Greece was not accidental.  The kings of the empire ... pursued Alexander’s plan to build a cultural center at Alexandria. ... These rulers therefore brought to Alexandria scholars from all the existing centers of civilization and supported them with state funds.”

“About 290 B.C.[E.] Ptolemy Soter built a center in which the scholars could study and teach.  This building, dedicated to the muses, became known as the Museum, and it housed poets, philosophers, philologists, astronomers, geographers, physicians, historians, artists, and most of the famous mathematicians of the Alexandrian Greek civilization.”

“Adjacent to the Museum, Ptolemy built a library, not only for the preservation of important documents but for the use of the general public.  This famous library was said at one time to contain 750,000 volumes, including the personal library of Aristotle and his successor Theophrastus.  Books, incidentally, were more readily available in Alexandria than in classical Greece because Egyptian papyrus was at hand.  In fact, Alexandria became the center of the book-copying trade of the ancient world.”

“The Ptolemies also pursued Alexander’s plan of encouraging a mixture of peoples, so that Greeks, Persians, Jews, Ethiopians, Arabs, Romans, Indians, and Negroes came unhindered to Alexandria and mingled freely in the city.  Aristocrat, citizen, and slave jostled each other and, in fact, the class divisions of the older Greek civilization broke down.”  [Morris Kline, Mathematical Thought from Ancient to Modern Times, Volume I, Oxford University Press [New York:  1972], pp. 101-102, emphases added by A.D.].

Ancient Alexandria’s favorable locus, with respect to the concentration and centralization of ancient commerce and wealth there, also contributed crucially to the consummation of its peoples’ cultural ambitions:  “The civilization in Egypt was influenced further by knowledge brought in by traders and by the special expeditions organized by the scholars to learn more about other parts of the world.  Consequently, intellectual horizons broadened.  The long sea voyages of the Alexandrians called for far better knowledge of geography, methods of telling time, and navigational techniques, while commercial competition generated interest in materials, in efficiency of production, and in improvement of skills.  Arts that had been despised in the classical period were taken up with new zest and training schools were established.  Pure science continued to be pursued but was also applied.”  [ibid., pp. 102-103]. 

Part of what resulted was an unprecedented flowering of engineering and technology, even though not supported by strong incentives to apply this technology in production, given the still predominantly pre-capitalist, peasant-/serf-, ‘artisanal-’, and slavery basis of the prevailing social relations of production, especially after the Roman conquest of Egypt, in 31 B.C.E.:  The mechanical devices created by the Alexandrians were astonishing even by modern standards.  Pumps to bring up water from wells and cisterns, pulleys, wedges, tackles, systems of gears, and a mileage measuring device no different from what may be found in the modern automobile were used commonly.  Steam power was employed to drive a vehicle along the city streets in the annual religious parade.  Water or air heated by fire in secret vessels of temple altars was used to make statues move. ... Water power operated a musical organ and made figures on a fountain move automatically while compressed air was used to operate a gun.  New mechanical instruments, including an improved sundial, were invented to refine astronomical measurements.” [ibid.; pp. 103, emphases by A.D.].

The disparaging squeamishness and ‘needlessness’ of classical Greek “aristocratic” slave-holders with regard to ‘‘‘hands-dirtying work’’’ [‘‘‘fit only for slaves’’’] -- and with regard to practical and commercial applications of the fruits of intellectual labor -- was overcome in Ancient Alexandria:  “Proclus, who drew material from Germinus of Rhodes (1st cent. B.C.[E.]), cites the latter on the divisions of mathematics...:  arithmetic (our theory of numbers), geometry, mechanics, astronomy, optics, geodesy, canonic (science of musical harmony), and logistics (applied arithmetic).  According to Proclus, Germinus says:  The entire mathematics was separated into two main divisions with the following distinction:  one part concerned itself with the intellectual concepts and the other with material concepts.”  Arithmetic and geometry were intellectual.  The other division was material.  However, the distinction was gradually lost sight of ... One can say, as a broad generalization, that the mathematicians of the Alexandrian period severed their relation with philosophy and allied themselves with engineering.”  [ibid., pp. 104-105, emphases by A.D.]. 

Hero[n] of Alexandria, and his teacher, Ctesibius [who may have been responsible for the “Antikythera Mechanism”], incarnate this mathematico-technological momenta of the Ancient Alexandrian ‘Proto-Renaissance’:  “Proclus refers to Heron as mechanicus, which might mean a mechanical engineer today, and discusses him in connection with the inventor Ctesibius, his teacher.  Heron was also a good surveyor. ... The striking fact about Herons work is his commingling of rigorous mathematics and the approximate procedures and formulas of the Egyptians.  On the one hand, he wrote a commentary on Euclid, used the exact results of Archimedes (indeed he refers to him often), and in original works proved a number of new theorems of Euclidean geometry.  On the other hand, he was concerned with applied geometry and mechanics and gave all sorts of approximate results without apology.  He used Egyptian formulas freely and much of his geometry was also Egyptian in character. ...” 

“His applied works include Mechanics, The Construction of Catapults, Measurements, The Design of Guns, Pneumatica (the theory and use of air pressure), and On The Art of Construction of Automata.  He gives designs for water clocks, measuring instruments, automatic machines, weight lifting machines, and war engines.” [ibid., pp. 116-117, emphases added by A.D.].

Factors in the demise of this Ancient Alexandrian “Proto-Renaissance” are described, by Howard Eves, as follows --

“The city of Alexandria enjoyed many advantages, not the least of which was long-lasting peace.  During the reign of the Ptolemies, which lasted for almost 300 years, the city, although on occasion beset with internal power struggles, remained free from external strife.  This was ended by a short period of conflict when Egypt became part of the Roman empire ... The closing period of ancient times was dominated by Rome. ... The economic structure ... was essentially based on agriculture, with a spreading use of slave labor.  The eventual decline of the slave market, with its disastrous effect on Roman economy, found science reduced to a mediocre level.  The Alexandrian school gradually faded, along with the breakup of ancient society. [op. cit., p. 164, emphases added by A.D.].

-- and --

“Greek science reached its pinnacle at Alexandria ... The decline was caused by a combination of technological, political, economic, and social factors. ... The Romans used slave labor to an almost unprecedented degree, especially after the founding of the Empire by Augustus in 31 B.C.[E.].  More than half of the Empires inhabitants were slaves.  With slaves to do most of the backbreaking work, there was little perceived need for labor-saving devices, such as the pulleys and levers invented by Archimedes ... hence, scientists had little incentive to invent them.”  [op. cit., pp. 137-138, emphases added by A.D.].

-- and by Morris Kline thusly --

The fate of Hypatia, an Alexandrian mathematician of note and the daughter of Theon of Alexandria [the redactor of Euclid's Elements -- A.D.], symbolizes the end of the era.  Because she refused to abandon the Greek religion, Christian fanatics seized her in the streets of Alexandria and tore her to pieces. ... From the standpoint of the history of mathematics, the rise of Christianity had unfortunate consequences.  Though the Christian leaders adopted many Greek and Oriental myths and customs with the intent of making Christianity more acceptable to converts, they opposed pagan learning and ridiculed mathematics, astronomy, and physical science; Christians were forbidden to contaminate themselves with Greek learning.  Despite cruel persecution by the Romans, Christianity spread and became so powerful that the emperor Constantine (272-337 [C.E.]) was obliged to consign it a privileged position in the Roman Empire.  The Christians were now able to effect even greater destruction of Greek culture.  The emperor Theodosius proscribed the pagan religions and, in 392 [C.E.] ordered that the Greek temples be destroyed.  Pagans were attacked and murdered throughout the empire.  Greek books were burned by the thousands.  In that year Theodosius banned the pagan religions, the Christians destroyed the temple of Serapis [in Alexandria -- A.D.], which still housed the only extensive collection of Greek works.  It is estimated that 300,000 manuscripts were destroyed.  Many other works written on parchment were expunged by the Christians so that they could use the parchment for their own writings ... In 529 [C.E.], the Eastern Roman emperor Justinian closed all the Greek schools of philosophy, including Platos Academy. ... The final blow to Alexandria was the conquest of Egypt by the upsurging Moslems in ... 640 [C.E.].  The remaining books were destroyed on the ground given by Omar, the Arab conqueror:  “Either the books contain what is in the Koran, in which case we do not have to read them, or they contain the opposite of what is in the Koran, in which case we must not read them.”  And so for six months the baths of Alexandria were heated by burning rolls of parchment.  After the capture of Alexandria by the Mohammedans, the majority of the scholars migrated to Constantinople, which had become the capital of the Eastern Roman Empire.  Though no activity along the lines of Greek thought could flourish in the unfriendly Christian atmosphere of Byzantium, this flux of scholars and their works to comparative safety increased the treasury of knowledge that was to reach Europe eight hundred years later.  It is perhaps pointless to contemplate what might have been.  But one cannot help observe that the Alexandrian Greek civilization ended its active scientific life on the threshold of the modern age.  It had the unusual combination of theoretical and practical interests that proved so fertile a thousand years later.  Until the last few centuries of its existence, it enjoyed freedom of thought, which is also essential to a flourishing culture.  And it tackled and made major advances in several fields that were to become all-important in the Renaissance:  quantitative plane and solid geometry; trigonometry; algebra; calculus; and astronomy.”  [op. cit., pp. 180-181, emphases added by A.D.].

It is in the above-described ‘‘‘psychohistorical’’’ context that the work of Diophantus of Alexandria can be comprehended -- as a hybrid product of waning Hellenistic memes, and of a ‘protoic’, precocious, prevenient partial prefigurement of core components of the as yet unborn Human Phenome of Modernity. 

Morris Kline assesses the work of Diophantus in the following terms:

“The highest point of Alexandrian Greek algebra is reached with Diophantus. ... His work towers above that of his contemporaries; unfortunately, it came too late to be highly influential in his time because a destructive tide was already engulfing the civilization.  Diophantus wrote several books that are lost in their entirety. ... His great work is the Arithmetica which, Diophantus says, comprises thirteen books.  We have six [6 surviving in Greek, that is; 4 more were recently found, in Arabic, possibly translations into Arabic of Hypatia’s Greek commentaries on books 4 through 7, rather than of Diophantus' originals -- A.D.] ... One of Diophantus’ major steps is the introduction of symbolism [i.e., of proto-ideography -- A.D.] in algebra. ... The appearance of such symbolism is of course remarkable but the use of powers higher than three is even more extraordinary.  The classical Greeks could not and would not consider a product of more than three factors because such a product had no [then-recognized -- A.D.] geometrical significance [i.e., given the apparently 3-and-no-more/no-less-dimensional physical space of our world -- A.D.].  On a purely arithmetical basis, however, such products do have a meaning; and this is precisely the basis Diophantus adopts." [op. cit., pp. 138-139, emphases added by A.D.].

Diophantus symbolized a[ny], generic number, in a dual format, as a juxtaposition -- a ‘‘‘product’’’, in effect -- of two semantic  ‘‘‘co-factors’’’, called, by Karl Seldon, an ‘‘‘arithmetical qualifier’’’, and an ‘‘‘arithmetical quantifier’’’, viz. --


-- with the “syncopated” unit qualifier symbol M signifying the «Mo-nad», the generic, abstract [and quantifiable’] unit, or ‘‘‘one-ness”’, standing generically and indifferently for any specific kind of unit -- e.g., for an ontological unit, or for a metrical unit, or even for an undifferentiated combination of the two.

Examples include a unit of the kind of thing category -- or ‘‘‘ontological category’’’ -- of the quality of “apple-ness”, i.e., an apple unit, or an orange unit, or a pound unit as unit of measure or metrical unit, or the combined, undifferentiated unity of a metrical and an ontological quality unit, e.g., “a pound of apples”, or “a pound of oranges”.

The symbol s, is the generic quantifier symbol, often used by Diophantus to represent the unknown, and to-be-solved-for, value in one of Diophantus’s ‘proto-algebraic proto-equations’.   

This number symbol is drawn, as was typical in Ancient Greek ‘‘‘logistics’’’ [practical arithmetic], from the Greek alphabet.  It is the version of the Greek letter sigma, _, that is used when sigma is the final letter of a Greek word, e.g., in particular, s is the last letter of the Greek word «arithmos» ... .   

In modern English, it coincides with the final s, i.e., with English letter suffix that signifies plurality.

Thus, the expression above might stand, indifferently, for the prose representations “six apples” [or, literally, “apples six” -- qualifier first, or in first place, followed by quantifier second, or in second place], or “six oranges”, or “six pounds”, or “six pounds of apples”, etc.

That is, Diophantus, in keeping -- for the most part -- with Ancient «Arithmos» Theory, does not symbolize number in general simply as --

-- i.e., as an abstract, “pure” quantifier, without qualification, as would be the case if Diophantus had followed -- i.e., if he had anticipated -- the meme of European Renaissance humanity, after the world-historic Elision of the Qualifiers.

This world-historic Elisionwas brought about, ‘‘‘psychohistorically’’’, we hold, in the post-Dark-Ages European Human Phenome -- which was also the point-of-origin of the [psycho]historically-specific Capitalist Phenome, or «mentalité», by the intensive practice of the capital-relation by so much of the population:  of the monies-[capitals-]mediated exchanges of commodities[-capitals], that emerged, in the lead-up to the Western European Renaissance, as a far more intensive such praxis than was ever reached within the socio-economic limitations of Ancient Mediterranean times, and of their substantially slavery-based mode of social production. 

This ‘capital-praxis’ was captured, in its purest, simplest essence -- abstracting from its more concrete determinations, involving mediation by money [price] and by production processes, outside of the process of circulation of capitals, by Marx’s «arché» for «Das Kapital» as a whole, The Elementary or Accidental Form of Value, set forth by Marx from the beginning of that work, in Vol. I, Part I, Chapter I., Section 3.A. of, as the systematic-dialectical seed cell of that entire work, and expressed by Marx, in his ‘algebraic/rhetorical’ notation, in the form of the ‘‘‘exchange-equations’’’ --

"x commodity A  =  y commodity B"

                                                            or, e.g., as:   

"20 yards of linen  =  1 coat"

-- and, later, by Seldon, as --

{ cjCj   =  ckCk }

-- with commodity quantifiers cj  < or = or > ck, despite the fact that, for the Commodity qualifiers,  Cj is qualitatively unequal to Ck.

                                                                                        . . .

q2 <---] II.   Modern Number Theories.


q3 <---] III.   F.E.D.’s Seldonian, Trans-Modern -- Modern/Ancient Hybrid -- «Arithmos» Theories.

We of F.E.D.use the word ‘‘‘number’’’ in a far more concrete sense than has become habitual in the Modern World, and, in certain ways, with a sense much more like it had in the Ancient World.

In our ‘‘‘Number Theory’’, as a modernization of the ancient ‘«Arithmos»-Theory, or ‘«Monads»-Theory, ‘‘‘number’’’ means not an abstract, “purequantity as such, as per those number conceptions so central to the Modern [unconsciously, experientially law-of-capital-value-inculcated] «mentalité».

On the contrary, in our usage, ‘‘‘number’’’ means something far closer to sensuous empiricality.

It refers to a specific multiplicity of units/individuals/monads, akin to a plural but finite population of the individuals of the same kind, such that each individual is a concrete, determinate, ‘multi-qualitative’ [‘multi-quality’], attributes-rich [ev]entity, not a distilled, rarefied mental abstraction of “pure, unqualified quantity”.

In such a usage, ‘‘‘numbers’’’ thus no longer differ only quantitatively: such ‘‘‘numbers’’’ have different kinds.

And, Old ‘‘‘numbers’’’ create New ‘‘‘numbers’’’: they not only expand themselves quantitatively, as populations of their units, but qualitatively, ontologically as well.

That is, Old kinds of ‘‘‘numbers’’’ create New kinds of ‘‘‘numbers’’’ by means of self-meta-monad-ization, that is, via ‘self-meta-unit-ization’, or ‘self-meta-individual-ization’.

The process of self-meta-monad-ization is a self-«aufheben» process, which is to say, a dialectical process.

A theory of the progressive self-construction of our cosmos -- in the form of a single, recurrent, mounting, cumulative, helical dialectic of nature -- can be constructed on the basis of noticing that, e.g. --

The [self-changing] ‘‘‘number’’’ [cosmological population] of pre-nuclear “particles” [e.g., of non-Hadronic, “non-composite” bosons and fermions, such as quarks] created the [dynamical, “fluent” [cf. Newton] self-changing] ‘‘‘number’’’ of sub-atomic “particles” [e.g., of primordial protons and neutrons], by their own self-meta-monad-ization;

The [self-changing] ‘‘‘number’’’ [cosmological population] of sub-atomic “particles” [e.g., non-Hadronic, “non-composite” bosons and fermions, such as, quarks] created the [self-changing/other-changed/other-changing] ‘‘‘number’’’ of [ionic] atomic nuclei [e.g., primordial Deuterium, Tritium, Helium, and Lithium], by their self-meta-monad-ization;

The [self-changing] ‘‘‘numbers’’’ [galactic populations] of atomic nuclei created the [dynamical, “fluent”, self-changing/other-changed/other-changing] ‘‘‘numbers’’’ of molecules [e.g., of galactic “inter-stellar medium” accumulating H2, O2, CN, H2O, CO2, CH4, etc.], by their own brand of such self-meta-monad-ization;

The [dynamical, “fluent”, self-changing] ‘‘‘numbers’’’ [cosmological populations] of molecules created the [self-changing/other-changed/other-changing] ‘‘‘numbers’’’ of ‘pre-eukaryotic’ living cells, by their own, natural-historically-specific «species» of self-meta-monad-ization;


Our Marxian, immanent critique of both the Modern and the Ancient conceptions of ‘‘‘Number’’’ find their foundation in the ‘‘‘psychohistorical’’’ insights, into both the Modern and the Ancient human ideologies -- into the Modern versus the Ancient ‘Human Phenomes’ -- embodied in Marx’s immanent, dialectical critique of capitalist political economy.

In his Elementary Form of Value, Marx discovered something much more momentous than even the ultimate seed category -- the «arché» category -- from which there ‘‘‘descends’’’, in an ideo-meta-genealogical, dialectical method-of-presentation sense, the rest of his entire, vast, comprehensive critique of the political economy of capital; of the capital social-relation-of-production; of the capitals social system of global, prehistoric humanity.

He also discovered the universal unconscious paradigm of The Modern «mentalité»’, whose most characteristic symptom is the purely quantitative frame of mind, and, consequently, The Elision of the Qualifiers from conception, from perception, and from mathematical -- starting especially with arithmetical -- symbolic expression.

Marx therein and thereby discovered the secret, not just of The German Ideology, but of the total, global, human Modern Ideology entire -- of the totalHuman Phenome of a planetary humanity that embodies and incarnates Capital [i.e., that incarnates the "Capital-relation-of-production' as the predominant social relation of social reproduction].

We of F.E.D. have found working with the NQ arithmetic/algebra, as with its successor systems, to be a worthwhile and cognitively healing practice for we F.E.D. monastics.

In working with the NQ, one is working with ‘‘‘numbers’’’ that are purely qualitative.

A given, generic qk is interpreted, or specified, as “standing for” an «arithmos», anumber, in part, in the Ancient sense: as “standing for”, in effect, an ontological category representing the special ‘common-kind-ness’ that unites all of the individuals; that all of the «monads» which inhere in that ontological category share, like the ‘‘‘in-tension’’’ of an ‘‘‘ex-tension’’’, i.e., of a “set of elements”.

The generic symbol qk,  for a k in N, thus interpreted, means a number of indefinite/changing cardinality, creating a kind of Marxian version of the “intentional” variables of the original Boolean algebra.

The practice of the expression of experienced/experimented reality, using the language of the NQ numbers, is, we find, a liberating “spiritual practice” -- in the sense of a Marxian version of Hegel’s “Objective Spirit”: of The Human Phenome.

That is, this activity of ours is a healing modifier of our individual human phenomes, one that lifts us beyond the collective, ‘ideologized’ “Mind”, the typical «mentalité», of our time -- beyond the “Mind” of The Modern Ideology; beyond the Money Mind, beyond the one-sidedly, purely-quantitative «mentalité», the “Mind” of The Elementary Form of [Commodity] Value as unconscious universal paradigm -- in short, beyond ‘the capital-value «mentalité»’.

This practice thereby helps us to free our minds to see in new and wider ways -- to think beyond the blockages characteristic of The Modern Ideology, the ideology of capital-value as supreme value, or even as only-value.

If you believe that such seeing is a part of your life path, then we commend this practice also to you.

Links to definitions of additional Encyclopedia Dialectica special terms deployed in the discourse above --


Booles Algebra



dialectical categorial progression


ontological category