Works by James Blish referring to his character Adolph Haertel can be grouped as follows.
The Star Dwellers and Mission To The Heart Stars are the Jack Loftus diptych.
"Common Time," "Nor Iron Bars" and "This Earth Of Hours" are the Galactic Cluster trilogy. (They form a linear sequence and are collected in a volume of that title.)
A Case Of Conscience (ACOC) is Volume III of the After Such Knowledge (ASK) Trilogy. (ASK Vol I, Doctor Mirabilis, and Vol II, Black Easter/The Day After Judgement, are respectively historical and contemporary, thus pre-Haertel.)
Haertel, young in Welcome To Mars and old in "Common Time," is referred back to by:
Loftus in his diptych;
Arpe in "Nor Iron Bars";
Ruiz-Sanchez in A Case Of Conscience;
Wald in The Quincunx Of Time.
Thus, the Haertel Scholium comprises one single volume, one diptych, one trilogy and one tetralogy plus some loose ends:
a short story loosely connected to Welcome To Mars;
another, "A Dusk Of Idols" (see Anywhen cover, below), connected to The Star Dwellers;
earlier, shorter versions of Quincunx and "A Style In Treason."
Arpe and Wald, each appearing once;
Haertel and Loftus, each appearing twice;
conflict between sacred and secular knowledge, addressed thrice.
The characters' legacies are:
Roger Bacon in ASK I: scientific method;
magicians in ASK II: a changed relationship to deity;
Haertel and Arpe: interstellar drives, named after them;
Arpe: microcosmic exploration and the discovery that psi forces are characteristic of subatomic space as electromagnetism is of macrocosmic space;
Ruiz-Sanchez: the theological problem of sinless but Godless aliens;
Petard, also in ASK III: his instantaneous communicator, the circum-continuum radio (CirCon);
Wald: (i) his instantaneous communicator, named after Paul Dirac, which, unlike Petard's, receives messages not only from the present but also from the past and future; (ii) a metalanguage for scientific paradigms and multiple dimensions;
Loftus: the Haertel overdrive-using UN, dolphins, extrasolar races and star dwelling energy beings allied against the Heart Stars Empire;
Oberholzer in "This Earth Of Hours": the Terrestrial Matriarchy, using a post-Arpe Standing Wave, mobilized against the telepathic Central Empire;
Martels in Midsummer Century: a telepathically guided "Rebirth" of human civilization mobilized against an evolutionary challenge from intelligent Birds.
Thus, ASK and Haertel present:
two theories of telepathy (Arpe's and Martels');
two instantaneous communicators (Circon and Dirac);
three theology-science conflicts (Bacon, magicians and Ruiz-Sanchez);
three interstellar empires (Heart Stars, Green Exarchy and Central Empire);
four interstellar drives (Haertel, Arpe, Imaginary Drive and Standing Wave).
Circon, reaching around the continuum, detects and replies to radio waves currently transmitted light years away whereas the Dirac communicator controls the placement of an electron in the circuits of another Dirac communicator by controlling the frequency and path of a positron moving through a crystal lattice accompanied by de Broglie waves which are transforms of the waves of the electron so that a message is received by amplifying the bursts and reading the signal.
Dirac is not radio;
its effect is simultaneous, not wave-like;
CirCon and Dirac are not two names for the same device.
Bacon, wrongly accused of magic, is the historical forerunner of scientists including:
in several Blish futures, Haertel;
in different Haertel futures, Petard and Wald.
Blish's imagined scenarios are both extrapolative and exotic. ASK and Haertel are not a continuous sequence, except for ACOC, but Haertel etc as scientists are Bacon's successors.
Blish appropriately extends the theology-science issue from a medieval monk in ASK I through modern magicians in ASK II to a future Jesuit biologist and an atheist physicist in ASK III. However, despite the seriousness with which Blish treats this issue here, all his other fictitious scientists simply expand human knowledge of the galaxy, the universe, the microcosm and space-time without being troubled by theology.
Ruiz-Sanchez's contemporary, Petard, a lapsed Catholic, parallels the entirely secular Wald's invention of an instantaneous communicator but Wald goes further by also inventing a metalanguage for discussing the succession of scientific paradigms that had been initiated by Bacon in Doctor Mirabilis.
This article began as an attempt to group together the works of the Haertel Scholium but, because that Scholium overlaps with the After Such Knowledge Trilogy, it became a discussion of that Trilogy in relation both to the Scholium and to the Cities In Flight Tetralogy. For completeness, we should also mention Blish's shorter tetralogy collected as The Seedling Stars.
The Dirac transmitter first appeared in the Okie series that became Cities In Flight but the transmitter's capacity to receive messages from the future would not have fitted into Okie culture, where cities fly into the unknown, so it had to be developed separately in one of the Haertel timelines. Similarly, the Okies, interstellar traders, and the Adapted Men, extrasolar colonists, could have complemented each other in a single series but Blish wanted to show that the Okies, despite their anti-agathics, would not live forever and demonstrated this drastically by ending the universe in 4004 whereas the Adapted Men needed much longer to colonize the galaxy so these two series necessarily diverged despite some early common references:
pantropists, like Okies and Wald, have the faster than light ultraphone.
Okies and Wald, but not pantropists, have the instantaneous Dirac transmitter but only Wald and his colleagues receive the Dirac "beep" containing messages from the future and including messages from later stories. Thus, one potential series became three distinct series whose defining technologies are:
"spindizzies," gravitron polarity generators, moving spaceships and cities through space faster than light, later moving a planet between galaxies and to the Metagalactic Centre;
pantropy, adapting human beings to other planets;
The text of "A Style In Treason," and even the Dirac message received from that period, assume faster than light but not instantaneous communication, ultraphone but not Dirac. However, the politics of the period are somehow based on institutionalized deception and Blish would have been able to resolve any inconsistencies in his projected High Earth/Traitors' Guild/Green Exarchy novel.
The various series are also differentiated by their beginnings. Blish laid a sound basis for each series by describing the discoveries underlying his characters' later activities:
antigravity in "Bridge," incorporated into Cities In Flight, Vol I;
anti-agathics in "At Death's End," also incorporated into CIF, Vol I;
pantropy in The Seedling Stars, Book One;
antigravity, this time discovered by Haertel, in Welcome To Mars;
test flight of the Haertel overdrive in "Common Time";
test flight of the Arpe Drive in "Nor Iron Bars";
the theory of telepathy that later accounts for the Central Empire, also in "Nor Iron Bars";
the Dirac transmitter in "Beep," novelized as The Quincunx Of Time;
scientific method in Doctor Mirabilis.
when anti-gravity and antiagathics have been discovered and some extrasolar planets colonized, Russia wins the Cold War and bans space travel but, later, with anti-gravity rediscovered and the Vegan Tyranny defeated, a new confederation, roughly based on the former UN, rules Arm II until replaced by the Web of Hercules although New Earthmen continue to control the Greater Magellanic Cloud and the planet He explores the Andromeda galaxy;
the Greater Earth Port Authority, so enriched by tolls that its police force has absorbed the United States armed forces, aims to charge landing fees on terraformed planets and nearly suppresses pantropy but Adapted Men escape and occupy the galaxy;
ACOC's UN has imposed a world government in response to Corridor Riots in the self-sufficient city-sized underground nuclear air raid shelters controlled by Target Area Authorities derived from self-policing port authorities;
in Oberholzer's future, sperm electrophoresis enables parents to predetermine children's sex, causing a glut of males and a Matriarchy which discovers that planets of Population I stars in the galactic center and the clusters are populated by beings with hive mentalities and ganglia instead of brains and who regard brains as tumors so are hostile to the brained inhabitants of planets of Population II stars like Sol;
in the High Earth period, neither the ultraphone nor the Imaginary Drive permits hegemony over more than ten light years but a uniform interstellar economy is maintained with traitors as brokers in a bourse where planets seek financial advantage although half of the human worlds are ruled by the Green Exarch which draws tithes from six fallen empires older than man;
These are seven very differently imagined futures although the High Earth-Green Exarchy conflict is supposed to be incorporated somehow into the peaceful expansion supervised by Wald's successors - unless, contradicting both their theory and their policy, this Dirac message turns out after all to originate from a merely potential future which they prevent instead of causing? (I don't think so but there you are.)
ASK, Haertel, Okies and pantropy are not one series but they are a single coherent body of work: one diptych, two trilogies and three tetralogies. Uniform editions could comprise six volumes including a revised Galactic Cluster containing the short trilogy and the "loose ends."
Haertel's achievements, not necessarily mutually compatible, were:
to incorporate Einstein's relativity into Milne's and Milne's into his own (he did this in 2011, last year!);
to prove that there is only one fundamental particle;
to assume at the age of seventeen that a Pythagorean geometry of points, not a Euclidean geometry of lines, applies to ultimate particles like positrons;
also at age seventeen, to discover anti-gravity and fly a tree hut to Mars.
Loftus' mentor regards Haertel as the greatest theoretical physicist ever and Wald sometimes thinks that he must have been God so it is unsurprising that he is prominent in several timelines.
(1) Blish, James, Mission To The Heart Stars, London, 1980, p. 48.