B. Lukács

CRIP RMKI 1525 Bp. 114. Pf. 49

Budapest, Hungary

To be sure (and causal), that is not I. (I do know that the English/American way is to tell: that is not me. However that form would be simply erroneous. Here "I" am the subject, not the object. So it should be in nominative, I, and not in objective or common case, me. In English such a construction seems unnatural because of the word order, English being an SVO language; in Latin and Hungarian word order is free, so for me a nominative after a verb is triviality.) I am a Béla and my family has come from the Eastermost Marches, still the deceased is only my half namesake.


In August 2001 the Society of Creative Anachronisms notified itsmembers that Sir Béla of Eastmarch died on 31st July. He wasa Court Baron of the Kingdom of the West, one of the founders, and a veryeminent Bard. His device was "azure, a saltire argent, in chief a sun inglory". (Since this is almost Norman, for GR people speaking everydayEnglish the shield is blue, with two intersecting diagonal silver strips, inthe above quadrant with a golden Sun with rays.) His wife is Lady Karina of the Far West.

Then: what is the Kingdom of the West, who was Sir Béla of Eastmarch, and why is it important for Hungarian General Relativity people? I am going to go into details, but first let us see another bit of information.


The Synod of Constance, in the second decade of XVth century, was along-lasting but effective synod, chaired by Sigismund I, Apostolic King ofHungary, King of Croatia (& Jerusalem); otherwise the Emperor of the HolyRoman Empire of the German Nation and pretender to the Bohemian throne. But Imust emphasize in the present circumstances (Hungary just going to theEuropean Union) that first he had been King of Hungary, who then ran for the Empire and not backwards. The Synod, for example, clarified the confusion with popes and counter-popes; there were 3 popes in a time. After a lot of arguments the Synod elected a single pope, and there were some law and order again.

Also, the Synod heard Jan Hus (John Huss), the turbulent Bohemian priest, who very much influenced the Hungarian orthography, as you can directly see it in the name of Sir Béla. Namely, Latin has 5 vowel sounds and 6 vowel letters altogether. That is not enough for Bohemian; and also not for Hungarian. It is not enough for English or French either, but they were not interested. But Hus suggested to use bars, primes, dots, hooks &c. on letters. Bohemians fully accepted the idea (and Bohemian is almost impossible on Netscape Navigator), Hungarians only for vowels (and there are only slight problems with the long counterparts of ö and ü). However this idea of Hus was not discussed in Constance.

But Hus had other ideas too. E.g. he insisted that at the eucharictics even the laymen should get a small quantity of wine. Church’s opinion was that the bread was enough; every good theologians knew that the popular idea, in which bread transfigured into Christ’s body and wine into His blood was oversimplification. Moreover, since 1348, epidemic Black Death made communal drinking rather hazardous. However, Hus’ idea was popular and he was adamant.

Also, he told dirty things about vices of Popes. Until they were 3, each of them told even more dirty things about the other 2; but now there was again law and order, so the only Pope did not like such slogans. Finally, the Emperor was against Hus, because Hus was against Sigismund I as King of Bohemia.

Maybe nobody is surprised that the Synod, at the end, decided that Hus was a dangerous heretic. He was told to revise his ideas, he did not do it, so was burnt. What else to do with a strong heretic, ethnic separatist (he was one of the leaders ousting the German professors from the Prague University), enemy of the King (-to-be) &c?

OK, but then some theologians told that the burning was only half measure: Hus got his ideas (indirectly) from Wyclif, of Lutterworth.

Wyclif, priest of the English parish Lutterworth, was already dead for 30 years. In some sense he had also been turbulent in theology. For example he also told dirty words about Popes. He even told that papal tithes were unnecessary. He told even more heretic things, which will come soon. And there were some connections between English and Bohemian Churches via a royal marriage. It is probable that some ideas of Wyclif triggered Hus, indeed. But, as an encyclopedia tells us, Wyclif remained in "the favor of the court and of parliament".

Of course. Wyclif started to broadcast his anti-papal ideas when Popes had their seats in Avignon, they were French, while London and Paris were mortal enemies in the Hundred Year War. Of course, a patriotic Englishman does not pay tax to a Frenchman and does not recognize his jurisdiction, be that Frenchman either King or Pope.

Now, this was not a live question anymore in 1415. Popes had gone home to Rome. English troops dominated France (in this time it is better to use this as a geographic term); Joan of Arc still kept the geese. However if Hus had been burnt, it was not easy to refuse the discussion of Wyclifism. The dead seldom has friends, so on May 4, 1415 the Synod decided that Wyclif indeed had been a heretic, and ordered his books and corpse to be burnt. Nobody did it for another 12 years, and probably nobody was interested at all, but a heretic is a heretic.

OK; but what was his heresy? According to the Synod, he had some Epicurean ideas, and most definitely, he spoke against Aristotle’s book "De Lineis Insecabilibus". That is utter heresy.

Theoretically Aristotle could not be a Church Father, being a pagan.However in practice he was. St. Thomas of Aquinas baptized Aristotelis OperaOmnia (with minor exceptions: e.g. before the advent of Christ Aristotle didnot recognize that God could not create a triangle in which the sum of angleswas not of 2 right angles; note that Aristotle and I can make such trianglesbut for me it is natural, being in General Relativity). Indeed, as the saidencyclopedia tells, Wyclif preferred Plato against Aristotle, and once toldthat "Democritus, Plato, Augustine, and Grosseteste far outrankedAristotle". I, together with the whole Synod of Constance, am shocked, believe that Wyclif was in serious error; but I am not surprised. Only natural scientists can see the order of magnitude difference between scientist Aristotle and philosopher and rhetor Plato, speaking about winged myriad year old souls flying above Sky, about four-feeted four-armed Primaeval Humans or about Great Years. While on the 338 Corinth Pan-Hellene Conference Aristotle was Chief Political Advisor to Chairman, the angry tyrant of Syracuse sold Plato to slavery when the Philosoph wanted to make a try with his Ideal State and consequently the concubines of the Bodyguard fought each other, endangering the safety of the Head of State. But do not go into unnecessary details. Aristotle was a wise guy, Plato much less, that is enough.

However De Lineis Insecabilibus is so boring that it is rather impractical for starting a heresy. While it is a part of the Canon Aristotelicum, between Bekker lines 968a1 & 972b32, it is hard to understand its points. The book(let) tells that you must be careful when you tell that a line consists of points, of infinitely many points; while indivisible lines do not exist at all. I cite here the last two sentences: "Again, nobody has an infinity of joints in his body or his hand, but he has an infinity of points. Moreover, there is no joint of a stone, nor has it any; but it has points."

Still, De Lineis Insecabilibus was important for ancient scientists.Namely, Aristotle wanted to tell them: you rather should IGNORE Zeno’sparadoxes. As you know, Zeno had two very influential paradoxes. In the firstswift Achilles could not pass a turtle if the turtle was once leading; in thesecond the arrow could not fly because in a moment it must have been in adefinite point and there are infinite many such points. The first paradox iseasy to solve up for US; indeed, already Archimedes could have solved it acentury after Aristotle (summation of infinite geometrical sequences); but thesecond needed a long evolution of mathematics, physics and mathematicalphysics. In first approach the (true) message of De Lineis Insecabilibus is:Ignore the problem! I can explain away, but even I am not truly satisfied; but paradoxes cannot forbid something. In the same time, they are signals; only I do not know, of what. Real scientists saw the arrow fly, so did not refute the idea of motion. Philosophers often did.

Medieval Church canonized the best available ancient scientist; and for dead Wyclif burning did not do any harm. But of course sooner or later the paradoxes should be eliminated also. Either by showing what was unnoticed in them, or by finding a Law forbidding the process leading to the paradox.

And now I start with the real body of text.


Sir Béla of Eastmarch is a person, whose given name isBéla. (In the Western Kingdom, where he was a Court Baron, it waswritten as "Bela"; but my form is the correct, as you will see soon). What kind of name is this?

Magyar. It is a name of honoured people. Westerners may know only Béla Bartók, famous composer and hard-neck Unitarian, but Hungary had 4 kings of this name, between 1060 and 1270 (see Appendix A). Even Roman Catholic Church uses the name in baptization, although strictly speaking I do not know about a Saint Béla. The trick is that by mirror translation Béla º Vojtech (Slovakian) º Adalbert (German) , and there is a Saint Adalbert. He was a White Croat,whose whole family had been massacred by the Bohemian Royal forces (if not,now there would be another Croatia instead of Bohemia?); he had strongconnections with the Magyar Court (not yet Hungary for some years) and thenwas killed by pagan Pomeranians (not Germans; kins of Poles) just before theprevious millenium. And Eastmarch is proper for a Béla. The Easternmarches of a Western Kingdom always were situated somewhere where lands ofBélas started. Before 795 just West of River Enns, then until 972 justWest of Vienna (yes; Vienna was Magyar until that time and still has its Magyar name Bécs, and the Croatian is Bec’), then just West of River Leutha.

And what does this name mean? If there was no Hebrew, Greek or Roman Béla protomartyr, the name should mean something. Yes, it does. Only, do not go into false directions. "Bela" would be "white" in Slavic languages, so "bright"; but in the feminine form. While Magyar has no genders, you may know that Béla Bartók was a male.

However "bél" means literally the guts, the insides of the body. The inside is more valuable than the skin. Human inside contains the real person., the essence.


Sir Béla of Eastmarch had a "civil" name in Californian life: Poul William Anderson, famous sci-fi writer. In the Saturn Game both he, Sir Bela of Eastmarch, and his wife, Karina of Far West, appear as legendary/literary persons. And observe that in his last but one essay, "Whitefist Béla", the name is of correct orthography (Unicode for Windows Word has already been created.)

Biographies repeat and repeat that Anderson was born from Danish parents in the USA, but as a youngster he lived years in Denmark. To a Dane an American is from the Far West. And Danish motifs are really abundant in his novels; Danish heroes, Danish places, Danish sentences. Indeed, in the Corridors of Time a big part of the story is going in Late Neolithic "Denmark", just when Nordic Indo-Germans arrive with chariots, and the non-Indo-Germanic (Late Maglemose) defend their homeland, with half-success.

OK. But: there are Magyar (and Hun) motifs too. Not so numerous, but quite enough. Huns, of course, were a very big power for some decades; everybody hears about Great King Attila. So it may be an accident that one of the 4 temporarily displaced persons in Dancer from Atlantis is a Hun; to be sure, before Attila. It is not so trivial that the No. 2 hero of The Star Fox is a modern Magyar, with whole (correct) Magyar sentences in the English text. However the most "fitting" story of Sir Béla (of Eastmarch) is Eutopia. There (I will return to the story after some proper General Relativity discussion) traveller Jason Philippou flees the Danish lands of Northern America into the Magyar territories, whose ruler is Voivode Bela.

So Sir Béla of Eastmarch was a Danish and American writer, surprisingly interested in Magyar and Hungarian topics (Magyar and Hungarian are not exactly synonymes, see Appendix B and some parts of the main text below). But Sir Béla/Anderson was also specialized on scholarly approaches on Time Travel, parallel realities and such. I will go into some details later.

Time Travel (or Acausality) is a much discussed topic in recent General Relativity. Physical arguments pro and contra are numerous (although far insufficient); but Time Travel leads to inevitable paradoxes, as we shall see in the next Chapter. Then everybody discussing the paradoxes from nonphysical viewpoint are welcome by GR people; and Sir Béla's work may have deserve the attention of all Hungarians.


Time travel in its modern sense was an idea quite foreign in Ancient and Medieval times; at least even definite speculations are unknown for me. One way travels to future sometimes were discussed as the legend of the Seven Dreamers of Ephesus, but such constructions do not lead to paradoxes. A (limited) knowledge of future, which definitely leads to paradoxes was more or less accepted by practically anybody (even Aristotle was unable to fully refuse the idea, see the Corpus Aristotelicum bw. Bekker numbers 462b13 – 464b18; as for the Arrow of Time 916a18 – a38. Some writers tried to deal with the paradox, and here it is enough to discuss the case of King Oidipus.

Oidipus, as Heir Apparent of Corinth, applies to the Delphi shrine for prophecy. Delphi is a very reliable shrine for prophecies. The priestess tells: go away, you will kill your father and cohabitate with your mother. So Oidipus does not return home, and becomes a nameless outlaw to avoid the specific prophecy. In due course he kills a traveler (who is, without his knowledge, the King of Thebes, saves the City of Thebes from calamities, finally marries the widow Queen. Later it turns out that he was the royal child of Thebes, but the King got a prophecy that the child would kill him, so he disposed the newborn; and after some steps the baby was adopted by the royal couple of Corinth. So the very attempts to avoid two embarrassing prophecies led to the fulfillment of them: no paradox appeared in the story, in spite of the partial knowledge of future.

The matter remained in this stage to the end of XIXth century. Very rarely travelers claimed to have come from the past, and ghosts were commonplace; but nobody ever claimed to have come from future. Prophecies were not very rare, but not so regular as at Delphi & Dodona. Catholic Church in principle accepted the existence of true prophecies but she was very cautious about them.

For physics deterministic equations of motion from Newton upwards led to the idea that Future may be exactly determined, but this was a school amongst many. Direct (subjective) experience about the existence of Free Will was a very strong counterargument. As for Time Travel fashionable Conservation Equations more or less ruled out the idea: Time Travel in the interval (t1,t2) would led to triple representation there: twice forward and once backward.

After some XIXth century trials the literary formulation of the Time Travel idea had been invented fully by H. G. Wells in Time Machine. The travel, on a poorly defined but dirigible machine, went to the far future, so direct paradoxes were practically avoided; however it was clear that the idea contained paradoxes inherently. As for Science, in mere 10 years the physical situation radically changed.

In 1905 via Einstein, and surely in 1908 via Minkowski the space-time continuum took over the role of space. In Relativity the Reality is not a changing 3-dimensional picture, but a 4-dimensional pattern. The fates of ideal point-like objects are world-lines; our languages with tenses, aspects &c. are improper for this view, but in it Future is as real as Past and Present, only we shall observe it at a later proper time. In this sense Time Travel is more natural than before 1905.

However Special Relativity excluded time travel more directly than any earlier physical theory/world picture. An object originally moving subluminally simply cannot be accelerated even to superluminal velocities: when the velocity goes to light velocity, mass goes to infinity.

A world line must be closed for temporal paradoxes; but it cannot be closed because of the light cone structure. Try to draw a closed loop on a paper if the maximal steepness of any tangent of the curve is 45°. Ergo: via SR Future is so real as Present, but SR itself forbids the return to Present from Future. (At least for the same individuum. In principle there may be effects propagating always backwards, although never anybody saw such signals. If they exist, Future can also be a topic of observation; for my knowledge this construction does not lead to known paradoxes.)

However a unification of Newtonian Gravitation and Special Relativity was reached in 1916; that is General Relativity and after 87 years we still do not know any experience against GR, while many unexpected predictions of the theory turned out to be true.

In GR the geometry of the space-time continuum is determined by the matter within, which is not surprising at all. However what is, when we solve the gravitational equations, the majority of the solutions can have closed loops of motions (on technical language, Closed Timelike Lines/Loops, henceforth CTL's exist in them). While I cannot make a worldwide statistics, surely the majority of solutions I got so far were of such geometry.

We do not like this; and are rather doubtful about the reality of these acausal geometries. Obviously not all solutions of the gravitational equations are realized in Nature. However: we cannot prevent the CTL's to come out from the equations.

So in GR temporal paradoxes are rather natural; we all try to remove such situations afterwards, but the attempts (e.g. "Cosmic Censorship") seem artificial so far, and they generally either remove too few or too much. I will not go into details: what I could tell would be too much for everybody not GR expert. I want to communicate only my viewpoint: GR seems to be correct and temporal paradoxes (not their solutions/interpretations, of course) are simply commonplace in GR.

Now: does Time Travel exist or not? And we have practically no experimental evidence into any direction.

The worldview is quite different (different, not opposite) in Quantum Mechanics. For that point I will return in due course, later. However just now it is impossible to synthetize a coherent worldview of even recent Physics. (I speak about the recent state of course, not about Final Truth, reachable, if any, in t=infinity.) Namely, recent physical experience leads to the idea that there are 3 fundamental phenomena all of general validity (not necessarily in their present forms of theories): Gravity, Relativity and Quantization. Separate theories, Newtonian Gravity, Special Relativity and Quantum Mechanics are all nice, but they are pairwise incompatible and all of them have become disproven.

Pairwise Unified Theories have been constructed as General Relativity (G*R), Quantum Field Theory/ies (R*Q) and Classical Quantum Gravity (Q*G; almost ready). Unified here means that the new theory does not even resemble the old ones, but in one limit it gives one of them and in other the other. So in General Relativity there is no more contradiction between Gravity and Relativity. However any two of the unified theories are still incompatible. So we cannot be sure in any very exotic prediction of our theories even as a matter of theories because in principle any evaluation of a situation would need the mutual use of (now) incompatible theories.

It is, e.g., possible that a temporal paradox of GR would be eliminated after proper inclusion of quantum phenomena, which we cannot rigorously do in 2003. Efforts for trial unifications without self-contradiction are heavy, but unsuccessful so far, although surely it will be made in the near future (say, a decade as an order of magnitude guess); and then we shall be able to check the predictions of the new trial theory. Note that not all possible theories are true, of course; but for any case self-contradictory theories are impossible and so cannot answer fundamental questions.

So: we never saw time travel, but we would greatly appreciate it. On the other hand, space-times permitting time travel are commonplace in our best present physical theory, but these time travels always can lead to paradoxes.

Zeno's two paradoxes plagued mathematical physics for two millenia, but they are eliminated now, so they have not proven impossibility of spatial motion in time. We do not yet know the fates of our paradoxes about time travel.

So everybody is welcome to discuss time travel paradoxes seriously, even if not with physical formalism. We are then understanding better and better the situation.

Poul Anderson did it many times with a method of ancient Greek mythographers/writers, but in infinitely more involved ways. So his works will be remembered by GR people.


Poul Anderson wrote 4 books in the Time Patrol scheme, Guardians of Time (1961), Time Patrolman (1983), The Year of the Ransom (1988) and The Shield of Time (1990); but all of them are composed of short stories woven together. The startpoint is rather simple. If there is at least some Free Will, if Time Travel is possible and if human knowledge is growing without bounds (of course all three conditions can be questioned) then Time Travel will be discovered, it is pointless to discuss when. However every Present is the Past of somebody. If you can travel and still cannot alter anything, then there is no paradox but then there is absolutely no Free Will either. (See Igor Novikov's recent physics works; one is very briefly recapitulated in App. C.) If some Free Will exists, then the discoverer can alter his Future, which is, however, the Past of another, more potent civilization, which must defend itself. So the logical consequence is a Temporal Police organized by far Uptime but recruited from various ages.

Obviously such stories are pictoresque and interesting; also, they are hard to be written in a coherent way and Anderson's stories seem the most coherent I read. Of course, self-contradictions will be identified only after clearing up the temporal paradoxes.

Here I discuss only 2 stories, Delenda est & The Amazement of the World; as for books the first was a part of Guardians of Time, the second that of The Shield of Time. Both stories discuss major alterations of Past, indeed disrupting the Time Patrol upwards from the alteration until the original history is not restored.

Delenda est deals with a simple enough situation. Two Patrolmen would like to make a happy weekend, so go to October 23, 1960, New York. However at arrival they are in a big enough city, but English is not spoken and the average technical level is slightly lower.

At Police Headquarters they see a World Map. Average state sizes are bigger than we had them in 1960, the alphabet is Phoenician, the language is Celtic. In Central Europe and Balkan some states seem to have Hunnish names. Hence the patrolmen have a guess which then they can check by a local historian: some uptime brigands joined Hannibal and eliminated the Scipios at Cannae. Indeed, they go back to Cannae, kill the brigands, and History jumps back to "normal": Time Patrol stations after Hannibal reappear. What is interesting, is the reasoning.

A hybrid of Phoenician and Celtic civilization indicates the role of Hannibal. Since average states are bigger, they seem older. So there was no Dark Ages. Still Hunnish migration happened. But note that the Hunnish migration originally was independent of European history: it was started by the desiccation of the steppe of Dzhungaria, and the Great Wall did not permit Eastern migration.

Note that after dealteration some personal details of the Cannae Battle remain different: some individual deaths are still different than in the "original". Still, History swings back because the Scipios were the key persons.

This is not proven, simply Anderson’s opinion. But, indeed, the Scipios were key persons in later history.

The second story is double-decked and 2 times & 3 places are involved: XII-XIIIth century Southern Italy and late XXth century Paris & California. It starts as follows.

In 1137 the defeated army of the Sicilian King limps back to Palermo, which is quite kosher History, except that the King is dead. The local Patrol observer tries to contact stations uptime, but they do not exist. A handful of experts are Downtime, either on stations or on holidays, so they try to reconstruct History. In itself the death of the King would be easy to be rectified, but two personal friends of the leading Patrolman are caught in the altered Future, in 1980 Paris & in 1990 San Francisco, so they must be rescued and transported first below 1137.

In 1990 California there is no radio & TV activity and no whites. White colonizers happen to be at East of Mississippi, and steamships do not exist. 1980 Paris is big enough, there was no Technical Revolution, there is an Anglo-French Kingdom, but Church leads.

Time Patrol agents appear above the Rignano battlefield, look for the knight going to kill the King, and stun him from above by a stunner with telescopic sight. Then the leader and the Californian agent go back to 1990 Frisco for a check. And History swung away, not back.

Still no radio & TV. There are whites iin California, but technical level is backward. Europe is full with slums, the general picture is roughly Early Industrial Age, and cathedrals are in neglect. Then the emergency Patrol Council puts together this and the experiences from the previous altered Reality and they guess that a reconnaisance is needed in the court of Frederick II of Hohenstaufen (he is the "Amazement of World", Stupor Mundi) in 1245.

It turns out that he is healthy; will have a long life; and he already tamed the Pope. The Investiture Struggle is practically over. Then they must go back again to the XIIth century Italy, to completely eliminate the knight who two realities ago tried to kill the King; and now indeed History swings back, and normal 1990 Frisco reappears. I do not want to tell more details; everybody should read The Shield of Time, and the exact details of the story are irrelevant from GR viewpoint. However the main line of the story is important.

Everything seemed simple at the first alteration. Frederick II would have been a grandson of the deceased King, and his birth needed some luck. So with the premature death of the King Frederick II was not born, and Papacy won the struggle against Empire. Now, according to historical thumb rules since Enlightment, Church dominance leads to no Rinascimento, so slowdown of scientific & technological evolution. And just this was seen in the first altered Reality.

Still, when the Patrolmen saved Empire, Frederick became too strong, and again Science starved. Why?

Because Science, while searches for the One and Unique Truth, does not like if somebody already knows Truth. That, very probably, will not be the true Truth. You cannot make effective scientific argumentations in a society with a single Power. It is a slight difference if it is Pope or Emperor. In Anderson’s story the technology is slightly higher with Emperor than with Pope; but this is trivial. Emperors are interested in cannons, artillery, and mathematics for ballistics. But this is not enough for electricity, Quantum Mechanics and such.

OK, this is interesting, but what about General Relativity? Now, the said example demonstrates that at some key moments the known history is (rather: seems to be; of course nothing is proven) not too probable. I will not tell here the whole plot, what a fine tuning is needed in this point according to Anderson; read The Shield of Time. However, I tell a purely physical story.

In our world there are some Fundamental Laws. We do not know, why these Laws hold; we do not know if other Laws might exist as alternatives. For simplicity let us assume that the forms could not be different.

However we have some fundamental constants. We definitely can calculate what would have happened with another set of constants. True, we do not exactly know, which are the independent constants. However we may accept a practical viewpoint that for us independent constants are which we cannot derive from others. Then in a minimal toy world model there are the 3 fundamental scales and a few particle masses plus interaction charges.

Let us see. The three fundamental scales are those of Gravity, G, of Relativity, c and of Quantization, h. In our World G=6.67*10-8 cm3/gs2, c=3.00*1010 cm/s and h=1.05*10-27gcm2/s. We do not know why these are the real values; but maybe this question is meaningless, because a change of one constant simply would alter the mass, length and time scales of Physics and everything would be the same on the new scales. We would be on different scales, our environment also, but relative to the environment everything would remain the same.

However this proportionality is not true with a fourth independent constant. There are particle masses around us; nobody was able up to now to derive them from the 3 scale constants and I shall be very, very much surprised seeing the good theory published. Surely, proton mass is M=1.66*10-24 g. Now, the scale constants yield a unique mass scale, but this universal mass is (hc/G)1/2, and (substitute!) this is 2.17*10-5 g, bigger by 19 orders of magnitude! We not only do not know the formula expressing M via G, c and h; we cannot even imagine the form of the formula. As for proton to electron mass M/m, it is 1836, and there were at least attempts to get this from theories, although they were unsuccessful up to now.

And there are interactions. Before 1962 even physicists told that there were a weak, an electromagnetic and a strong interaction; and all non-GR people spoke about a fourth, Gravity. But note that Gravity is not an interaction. For the 3 interactions language has changed, and for my present argumentation I need only two. Electric charge is e, and "nuclear, strong" force has another, say g.


e2 = (1/137.036)*hc

If we can derive 1/137.036 from fundamental theories, we are ready with electric charges. From the time of Eddington lots of attempts are known to get a number near to 137 from a formula not unbelievable. While it is easy to get such a formula, e.g.


no reliable theory of electromagnetism would lead to the particular formula, so the good value may well be a coincidence. So we do not know why the value of charge e is just the value we measure.

This is even more so for the "nuclear force". For it

g2 = (1-10)hc

the factor depending on the actual particles interacting. Since 1962 we believe that the strong force is a peripheric action of the QCD force binding quarks together, and this is the reason that it differs for different hadrons. Anyway, we are unable to derive the value of QCD charge from anything more fundamental, so let us imagine it which might be somewhat different as well. (For great differences, see I. Asimov's "The Gods Themselves...".)

Interestingly enough, there would not be life in the Universe if g were smaller by a mere 7%. Let us see.

Big Bang started with very high temperature, so there were no structures. Only quarks, leptons and coupling bosons were present. Entropy/baryon charge can be calculated from present observations and then we get that quarks were bound in triads between 8 and 15 microseconds.

At cca. 1 s temperature became less than Mn-Mp-me so neutrons started to decay. Since neutron half life time is cca. 10 minutes, after, say, 1 day no neutrons are expected. So when proto-galaxies, and later proto-stars, are being formed, one expects only hydrogen as building blocks (plus a minor amount of helium, you will see, how; but it is not too important).

The very first proto-stars were heating up via contraction: and then what? Now, we know deuteron, the nucleus of heavy hydrogen or deuterium, consisting of a proton and a neutron. But there was no neutron is the primordial gas some 1 billion years after Start.

No matter. We know a reaction

p+p -> (p+n)+e++n = d+e++n

so first deuterons are produced; later they form helium nuclei (and this process went between 1 s and 1 day, forming some original helium, but practically nothing else). When already a lot of helium is present in cores of stars, then another reaction can start forming carbon nuclei from each 3 helium nuclei; and then the cosmic nucleosynthesis starts. Result: C, N and O for life; Mg, Al and Si for planets and so on.

But the very existence of deuterons is a luck. It is rather loose; hardly bound. With a strong force only 7% weaker there were no deuterons. So at the proto-galaxy formation there would have been only hydrogen (and a negligible amount of helium, each nucleus formed at a rare 4-collision), and nucleosynthesis could not start in stars. The matter of world would remain hydrogen forever, with the H2 molecule as most complicated structure. No life ever.

Only because strong force is slightly weaker. Physics can calculate some other similar constraints for a world where mind or even life is possible at all, but this was the simplest to communicate. If we believe that some particle data could vary a little, it turns out that most variations would be worse. Are we lucky? Is a Providence present? Or there are many worlds but we know only these in which we can exist? It is an almost philosophic question, but can be formulated in Physics; read Rees' works.

OK, for anything, we have a world compatible with life. Then Evolution would (?) produce Mind sooner or later. However what is the probability that it produced a Frederick II Hohenstaufen during the Investiture Struggle?

Lot of people recognized that Frederick II was somewhat unique and thisis the reason that already his contemporaries called him Stupor Mundi. ButAnderson recognised how chancy had been his existence. I put the details intoAppendix D; here I repeat only the statement of The Shield of Time that his mother was the posthumous daughter of the King of Sicily.

For an average ruler the specific genes may not count too much. But if Frederick was Stupor Mundi, he must have been special. Anybody else could have been elected then Emperor; but without Frederick's valours and without the centralised Kingdom of Sicily as a reserve. Popes may have won against an average German Emperor. Now we see Anderson's claim. The existence of Frederick II was not guaranteed. But if he existed but the papal succession had been not so lucky between 1198 and 1241, Frederick might have won. In both cases: One Thruth, no Thruth.

Also, a fractionally higher entropy/baryon ratio, and...


Quantum Mechanics teaches us that particles are hazy: we cannot exactly know their positions, momenta &c. In the same time they are indivisible: if we catch a corner of an electron somewhere, we have caught the whole electron: it turns out that the whole was just there.

If we slowly send individual photons into a dark box through a double slot, it turns out that each photon took both slots, and was dispersed in the whole box, but then the photoplate at the other end got them and they appear at definite points. I am speaking about observed facts.

In 1932 physicists involved in QM told the problem of QM Measurement to margittai Neumann János, the witty mathematician (sorry, maybe you do not recognise his Magyar name; you know him as John von Neumann). The problem was: the wave function must evolve smoothly as the Schrödinger equation tells, otherwise hydrogen spectrum and such would be contrary to observations. But haziness does not hold anymore when the quantum system interacts with a macroscopic system measuring it. All the "potentialities" are in the system until measurement, but Measurement gives a unique result. Seems difficult.

No, told Neumann. If you need only this, I can make you axioms. With these axioms fulfilled the description of Measurement will satisfy your desires. (History of Science tells he did the axioms for a big piece of chocolate.)

Now 3 paragraphs will be true QM. If you do not understand everything, you need not be sad at all.

So you are measuring a definite physical quantity: in QM that quantity is an operator. You will get one of its eigenvalues.

But the wave function is generally not an eigenfunction of that operator, but a linear combination of eigenfunctions with some weights.

Then the Measurement is the following process: You have the probability pi to measure a value Xi where Xi is the ith eigenvalue and pi is the relative weight of the ith eigenfunction in the wavefunction; this is mathematically unequivocal. But when you got one result, simultaneously the wave function reduces to the respective eigenfunction; the others vanish forever, and the wave function develops from this eigenfunction thenceforth.

And no observations up to now contradict this.

Still some QM experts do not believe the scheme. Some for example tellthat the Schrödinger equation should contain small nonlinearities and bythese nonlinearities the "superposition breaks down" when amacroscopic system is attached as in the real measuring process. It is reallyeasy to make such a QM, but it is not easy to do this in such a way that all measurements be met. No satisfactory nonlinear model is known so far; I do not go into details (hidden parameters, Bell inequalities, &c.) here.

And there is the Everett proposition suggesting that nothing is lost in Measurement. Only, when I (or my Mind; or such) measure, my Mind takes the quantum state to which Xi belongs. So in the wave function there will be some weight of the state that X=Xi and I measured Xi, but also some that X=Xk and I measured Xk. Then, in everyday language, my Mind, and the World it observes, is split into a few at each Measurement. And I emphasize: up to now no decisive experiment has proven or disproven this scheme compared to the other. So now we do not know if Neumann or Everett is right; and Neumann did not claim to be right: he made axioms for physicists' need.

In some modern parts of physics it is not easy to tell what is and what is not. "To be" is a mere philosophical statement.


Now we can quietly enjoy Eutopia. By some accident 33 year old Alexander recovers from his illness in Babylon. Not many centuries after Aristotle Greeks united by long-living Alexander discover the Western Continent. Their society & science are developed according to the points of the Philosopher, tutor of the King, they establish his suggestions on the new land, which they call Eutopia, the True Place (or Good Place), where, on the shore of Pentalimne, the Five Seas (our Great Lakes), they built Neathenai.

After some more centuries they discover that other realities also existand develop a machine called parachronion (roughly: timelines beside eachother) by which the experimenter can be transposed into another reality. Theydiscover us, the timeline on which Alexander drank himself into death, hisempire fragmented and in posterity Aristotle must have shared with impracticalPlato & such, and where another Mediterranean religion got dominantposition. And, later, they discover still another reality, where Greeks areirrelevant at the Balkan, but after some centuries the new religion vanished too.

Assume that the Arabs won in Southern France in 732 against Charles Martell. Many years ago Gibbon wrote that then now we would learn the wisdom of Koran. I do not believe this. Ottoman Turks occupied 2/3 of Hungary for one and half centuries and still we did not learn Koran. However if Franks lost that battle, Christianity may have had problems. Back to the story of Eutopia!

Young history postgraduate Jason Philippou goes over and finds a reality. After the Arabs Atlantic Europe got the Vikings and the Frankish Kingdom was weakened. Arabs and Danes disrupted the Kingdom; then Arabs became interested in the internecine Omayyad/Abbaside War and decoupled from Global History. Then came the Magyars, raiding everywhere. For a while Europe became dominated by seafaring Danes and horseriding Magyars and Christianity vanished there. Then somebody discovered Westfall, the western continent, Danes, Magyars and some Turks migrated there, and live together with the Indians. Danes live of course on the North, on the shores and around the Great Lakes, Magyars (and Turks) live in the Mississippi/Missouri valley. Magyars; not Hungarians (maybe there is a Hungary in Old World?) because the name Hungarian comes from the territory there. But the new land of Magyars similarly is called Dakoty.

Jason Philippou flees from Danish lands and behind the Dakota border the Magyar who helps him is Kálmán, son of Árpád. The Prince taking him as guestfriend is Béla son of Zsolt. All old Magyar names. In our reality Árpád (Defender of the Throne) was the leader occupying Hungary, Zsolt was his son and successor (and the name is a variant of Sultan=Ruler), as I already told Béla was the name of 4 kings and Kálmán was also a king. No Christian names are used, not being Christianity. Some people honour the Triad: Wotan, Attila & Manitou.

I could comment the story in details for Hungarians, but for the international community I stop here and only tell: Sir Béla of Eastmarch commemorated his name featuring his namesake as Prince of Dakoty.


So far Anderson is not in contradiction with natural sciences, albeit is not conform with them either. If Everett is right, then sooner or later we may observe the other realities too.

And note that Sprague de Camp some 70 years ago used a similar idea (not in QM) to avoid temporal paradoxes. He told, OK, time travel is very rare. But if happens, a "new branch" of reality starts.

In "Lest Darkness Fall" a young American archaeologist is catastrophically pushed back 1400 years, into Gothic Rome, where an other Reality starts, simply with him in it. In some years he starts printing, optical telegraphs and bad telescopes.

Now we use a similar trick about Kerr spacetime. But Kerr spacetime was found in 1962, well after Lest Darkness Fall's publication (1939).

Kerr spacetime is a spacetime which is stationary, axially symmetric and valid in vacuum. So loosely speaking it is the spacetime around some unchanging rotating source. Kerr is not the general stationary axisymmetric vacuum spacetime; we are still unable to calculate that, but it is proven that it is the lest offending one (…"the only with regular event horizon"…). So we can visualize the situation as: there is first a very massive rotating star. It totally exhausts its fuel, so starts to collapse. It is too massive to stop (roughly more massive than 4 solar mass). After vehement transient changes a black hole is formed, with a ring-like singularity (infinite curvature) inside. No problem; rotation caused the matter to collapse to the ring. The plane of the ring is the original equatorial ring. If the angular momentum was not too high, this is a black hole.

Still, as Gautreau showed this in a classical article (R. Gautreau: Nuovo Cim. 50A, 120 (1967)) tossing stones or spaceships into this hole strange things may happen.

Gautreau calculated things falling freely along the North Pole. The fate depended on the initial height and velocity. With some initial data the spaceship goes below the equatorial plane, but is not on the other side of the ring. In some cases the spaceship reappears, which is rather strange from a black hole; but the problem is not this, but: there is a height and time occupied by both the ingoing and the outcoming spaceship. Does it meet itself?

Wait a moment. I told that we have the tendency to get acausal spacetimes; is there simply one more? No. Kerr is the most regular stationary rotating vacuum spacetime!

So what? All rotating black holes generate self-collisions? But there is a big one in the center of the Galaxy! Is the central hub full with time travelers and temporal paradoxes?

GR consensus does not exist, but the more conservative (!) alternative suggested is as: no; the spaceship goes to a new place; height is the same, time is the same, still elsewhere. ("A new Riemann leaf"…).

So does the formation of the black hole multiply the Space fourfold? (One the original. Another "below the plane but not on the other side". And doubling both to get new place to go out?)

No, it is not enough. The spaceship can make a pendulum-like motion (with appropriate initial velocity), coming out and then falling back again. But the paradox would appear at the next outcoming. So we need infinitely many seemingly identical spaces!

I do not like this way out. But: either I believe this, or I must take stoically the worst of paradoxes: meeting by myself. Really, the paradoxes should be clarified up. But: also, the situation is so messy that now even De Camp’s idea may be refreshing. And: Gautreau’s self-collision is not a tale but a result of honest calculation.

Self-meeting is discussed in details (but not in general) in Anderson’s The Dancer from Atlantis. A time-travelling research team is going from moderate future Hawaii to Pleistocene Africa; but the craft is damaged, so picks up in backward sequence Duncan, a XXth century American from a ship on Pacific, Oleg, a XIth century Russian from the North of Black Sea, Uldin (the „i" must be a back one, as in Turkish „basi"="chief, head"), a Hun of Walachia from 379 and Erissa, a Cretan woman from Rhodes. Then it meets the Santorin paroxysm, and cca. 1 years before (!; travelling Downtime) goes down in Libya. The crew is dead.

In that very moment Erissa exists in two copies. One is a young bull-dancer on the island Santorin/Atlantis, the other is 24 years older in Libya. They do not influence each other directly. However older Erissa knowns the American, knows his name, and starts to tell him bits of events.

The travellers first get to Athens, but Duncan can get to Santorin, and tries to suggest some measures against utter devastation of Cretan population/Navy; in a cryptic way to avoid paradoxes. During this he meets younger Erissa. Of course he does not inform her about her second occurrence; but this is the reason that Erissa knew his name back in Libya.

I do not go into details; you should read the book. Anderson is able totell a tale without bigger catastrophes than the Santorin eruption and end ofthe Cretan maritime power. He solves a task definitely greater than that ofthe classical Greek poets about Oedipus, and on higher artistic level (ofcourse he had 2400 more years of experience). But his success does notprove that the CTL world line is possible; only it demonstrates that it is not necessarily impossible.

Note that Physics could not observe CTL so far, so we do not know howeven a particle behaves while approaching itself. The closest analogon treatedtheoretically so far is one half of an indivisible particle to theother half. You can read an article of L. Diósi, e.g. Phys. Lett. 112A, 221 (1987) discussing the situation where a neutron can orbit itself. (Note that great Hungarian writer F. Karinthy once dreamed that he was two cats, playing with each other.)

I am not lunatic. The wave function of an indivisible particlecan be big at two separate points, and small in between; and he showed thatthen these points will orbit each other, exactly as predicted byNewton. But this is (almost) nothing in the present context; the two parts give one neutron. This is not one neutron meeting itself. The difference is enormous.

I stop here. The discussion needs General Relativity and Quantum Physics simultaneously, and the situation is unknown from practice. The task is not simply difficult. General Relativity and Quantum Physics are incompatible in their present forms. And no experience helps us, because there is not yet any experimental/observational experience.

Anderson/Sir Béla helped us to imagine the situation. Novikov showed a solution for balls without Free Will. And for two Erissas?


Yes, I believe, they are. But Anderson played with the idea: whatif old (obscure but numerous) reportss about magic, werewolves and such werehonest. You can find the construction in two Cappen Varra stories The Valor of Cappen Varra, and The Ladyof the Winds, in the first part of The UnicornTrade, the Fairy Gold, which happens in thehome city of Cappen Varra, in two Matuchek stories, Operation Chaos and OperationLuna, and also in Midsummer Tempest. In The Lady of the Winds the minstrel knows a magician, whogets books "through a gate" and some picture in a book shows Venice.In Midsummer Tempest some transreality travelerseven meet in an inn, e.g. Valerie Matuchek, Holger Danske/Carlsen, Prince Rupert and Clodia Pulcher. In all these stories some magic works or fairies exist.

I should not follow Anderson/Sir Béla there. First, I definitely do not like magic, second, I am a Hungarian. Sir Béla of Eastmarch still existed in the Kingdom of West; the Eastmarch of West. You immediately will see the differences between the East of West and West of Hungary.

But while I do not like magic, I must admit that Anderson is stillself-consistent. Note that if the traveler can go over, then not only theforms of Fundamental Laws must be the same but also the parameters (say,proton mass) must be very close in the two realizations, otherwise the personof Reality A would die, explode or dissolve in Reality B. And even minordifferences in electron charge e or Planck constant h wouldmake some complicated biomolecules of Reality A impossible, unstable or simplyineffective in Reality B. Think about enzymes whose tertiary (!) bounds arevery important for the shapes/working. I never calculated the permitted rangesin e, mp, me or h; I could do it, butnobody seems interested too much. But if we leave these 4 parameters vary evenin narrow ranges, for the very large majority of (AB) pairs human lives wouldbe mutually impossible. E.g. in Three Hearts andThree Lions Holger Carlsen is transferred from a reality with magicinto ours as an infant, so his body must grow, his cells multiply many times in our world with our h &c. Now, a DNA structure formed originally under slightly different fundamental constants would multiply erroneously, resulting in cell death or cancer, at least. (Quantum Mechanics permeates everything, but especially the helical structure comes directly from QM; hydrogen bonds have no classical valence counterparts at all. So the helical structure is directly influenced by the value of h.) The necessity of "closeness" is, indeed, intuitively mentioned in the prologue of Operation Chaos. So natural laws in Anderson’s "magic" worlds must be very, very near to those here.

And still Jason Philippou of Eutopia was able to live, eat &c. in our world and also in that of Westfall; Miss Matuchek of Magical USA and Prince Rupert of the Shakespearean Reality could drink the same beer, while Mr. Matuchek is a werewolf and Mrs. Matuchek is a witch. But the Fundamental Laws must be the same!

And they are. The trick of the magical world of Operation Chaos is explained. The idea is as follows. Natural laws permit magic; only iron inhibits it. So when iron became abundant (I would tell, from XIth century BC) magical practices started to fail. Indeed, in Three Hearts and Three Lions and in Midsummer Tempest fairies do not stand iron, and in Operation Chaos scientific magic becomes possible only when somebody discovers how to degauss iron’s bad power. So then: if we, in our Reality, learn, how to degauss, we shall be able to make magic too.

This may be good enough to Westerners. But we, in the Carpathian Basin never had the idea that iron would disturb anything. No Magyar tradition knows anything about iron disturbing Magyar Shamans. Great King Attila of the Huns had his Heavenly Sabre made of a heavenly iron found by the heifer Balmazka in the grass field near Szeged; and this heavenly iron made him lucky. Smiths, ironsmiths have great power and honour at Magyar, Turk and Mongol tribes; in 551 the Turk revolution in the Altai was led by a Gray she-Wolf (Boz Kurt, Bora Kovrat) and a master smith. Tarchans~Darhans denote simultaneously Princes and Smiths for Turks, Mongols and Magyars. And Slovakians of the Basin were the best iron- and steelworkers of whole Europe in the XIVth century.

But, what is more definite. Werewolves do not (or, at least, must not)exist. Our King Koloman (Kálmán) declared in 1102 that none can transform herself into animal, and no such case can be put to courts. He (definitely as King of Croatia, but the law went into the Hungarian Law Book too) told in the text of a new law about witches and such that "De strigiis, quae non sunt, nulla quaestio fiat!" (about strigas, since they do not exist, be no discussion; "striga" is definitely a magician able to turn into animal). Thenceforth in the Carpathian Basin there were no trials about magicians (either female or male) changing into animals. I know about one werewolf case from 16th century where some 95 witnesses were found but then the angry Royal Chancellery stopped the impossible legal process. All the cases happened in the West of Hungary, and then the Hungarian Royal Chancellery was even in Vienna.

Indeed, in the Basin witches may fly with broomsticks, but NOBODY is able to/may transform her/himself into any animal. Amongst the eastern mountains of my ancestry (the Eastmarch of the Basin) there is a tradition about the big and horrifying Copper Owl. Nobody returns after seeing Him; as for his sounds the very brave can even simulate them and answer their call (a brave man is not silent if an animal speaks, even of copper), but even this deadly Copper Owl is not a magician in animal disguise. In the Basin Steve Matuchek would be either a liar, or a very exotic human. (But he is from Bohemia.) Had Sir Béla not been from the Kingdom of the West (if even from its Eastmarch), he would have not even discussed such impossible beings. For any case, it is even a usurpation of Royal attributes to claim by somebody that he could turn into wolf or backwards; remember the royal Gray Wolf (some lateral ancestor of Kings of Hungary). Maybe the King could; but surely nobody else.

OK; the Basin is special. However it seems that the belief in the inhibitor nature of iron is general in the West. (Mermaids are not magic for Anderson; see Appendix E.) I stop here; honour and thanks for the deceased, for his help in GR Gedankenexperimente.

But still we do not know whether Reality is one or many; what is the true meaning of wave functions; whether the Cosmic Censor exists (to remove CTL’s and CTL-conform spacetimes, including Kerr, the best black hole spacetime) or not, and so on. At this moment Physics does not suggest anything at all in these fundamental questions. Maybe some years later…


Béla I was the son of Basil, close relative tp King Stephen I, the founder of the Kingdom Hungary (Hungaria), having no surviving sons. So, Basil’s sons Andrew, Béla & Levente had to flee (I skip the details). Andrew went to Kiev, Béla & Levente to Cracow. Andrew was the eldest, but under Greek Orthodox influence, and Levente was pagan. The result was a struggle of Andrew and Béla for the Crown; Béla ruled between 1060 & 1063.

Béla II, the Blind ruled 1131-1141. His father was Prince Álmos, brother of King Coloman (i.e. Kálmán). The ailing King ordered to eliminate the danger of Álmos to the trone, and a faithful attendant blinded father & son. Still, Béla ruled after one more King.

Béla III, 1172-1196, was one time the heir of the Byzantian throne, being close kin by marriage of Emperor Manuel I Komnenos. He came home and became one of the greatest Kings of Hungary (& Croatia).

Béla IV, 1235-1270, does not seem to have been either a successful or an inventive King; his original political & economic ideas were devastating. But he was the King of the time of Mongolian incursions, and he directed the restoration afterwards. I only tell here to Westerners that in 1240 he took also the title of King of Cumania, and some years later he wed his minor Heir Apparent to the minor Elisabeth, heir of killed Sublime Khan Kuthen of the Cumans. Hungary got some extra cavalry, and now 2 counties of Hungary have the partial names „Cuman". Just now the Cumans have some nice relations with related Kazakistan.


Modern foreigners (except for Slovakians and Roumanians) generally consider the two terms synonyms, as e.g. the names Ceylon and Sri Lanka. However it is not so.

The State of Hungary was formed on the Christmas of 1000 AD, by aninterplay of Eastern Magyars, autochtones of the Carpathian Basin (mainlyproto-Slovakians on the North, proto-Bunevatzes on the South andproto-Szeklers on the East), and middle-class immigrants mainly from Italy& Germany. The royal family came from the Magyars. (If you do not know howare Bunevatzes, you are with the overwhelming majority. Bunevatzes exist,their idiom is something between Croatian and Serbian, the Hungarian andCroatian statistics consider them Croatian, the Serbian ones Serbian; they areCatholic as Hungarians/Croatians in contrast to Greek Orthodox Serbians, and they never lived in either a Croatian or in a Serbian state (until 1920). I think this is enough for a Westerner.)

Since that time Hungary was the state, Hungarian a subject of the state. Official Hungarian state was Latin until 1841, biggest Hungarian language is Magyar. In Magyar language Magyar and Hungarian is very near to be synonyms (by a linguistic deficiency) but e.g. in Slovakian Magyar=mad'arsky, and Hungarian=uhorsky.

Very probably the term Hungarian comes from the Onogur Turks, inhabitating the Carpathian Basin in VIIIth century AD.

In Poul Anderson/Sir Béla's Eutopia,where Early Middle Age pagan Berbers/Arabs, Danes & Magyars eliminatedChristian European civilization and then Danes and Magyars occupied NorthernAmerica, after some centuries Magyars do have only original Magyar names (ofcourse there are no cosmopolitan European/Christian names of them), but thestate in the Mississippi/Missouri region is called Dakoty, from theautochtonous Dakotas. This is a nice parallel of Magyar/Hungarian.


The physicist’s approach to temporal paradoxes is to make the example as simple as possible, but to him "simple" means something which can be directly calculated, no matter how much calculation is needed. Novikov formulated a sequence of purely mechanical problems in an acausal spacetime. See I. Novikov: Phys. Rev. D45, 1989 (1992). I deal with only the simplest problem here: a billiard game in a space-time very similar to ours far from gravity centers, except an interconnected pair of "holes" separated by time.

Let the space-time Minkowskian everywhere except for 2 small 4-regions A & B interconnected by a "tunnel"; B is in the future of A. The statements are well defined in GR; here I give an explanation good for lay physicists. In Relativity "to be in the future of A" means that B can be reached from A via subluminal motions (say, superluminal ones do not exist). The statement is absolute: if one observer sees B in A’s future, all see so. The "tunnel" can be imagined on a 2-dimensional analogy. Take a sheet of paper, the left/right direction will be Space, the back/forth will be Time. Now, somewhere "in the middle" give an S turn to the sheet. You can check that geometric figures drawn on the sheet will not become distorted: the 2-dimensional surface is still uncurved! Now go within the S bend. The sheet has 3 layers above each other (but in the 3rd dimension, so sheetbound people do not observe that they are layered. Make two circular holes A and B, B just above A; and insert a tube between B and A. Then our surface is as follows. If the motions avoid both A and B, the holes cannot be observed. If something, say, a ball, drops into one hole, it immediately appears in the other (they are very near through the tube), moving into the original direction as if nothing happened (since, indeed, almost nothing happened).

Now back to space-time. We roll a ball, towards the past hole A. The ball vanishes in A, immediately appears in B, and continues. Although it went farther than we would have expected, no paradox happens. But if it drops into B, then it reappears in its own past!

Now comes a real billiard problem. "Originally" (and theexact meaning of this simple word now needs some thinking) or in the firstpart of the path the ball avoided hole A, but after B it reappears in A, so inan earlier moment. Try to give the initial push in such a way that the ballafter reappearing collides with itself still before B. This sounds as madnessbut it is not so; a physicist can devise such a path. So the ball collideswith itself (!) but that is not paradoxial in itself. However very probablyafter the self-collision its velocity and direction will change, and it willnot reach Hole B. But then it cannot go into B, so will not emerge (?; Wouldhave not emerged?) from A. But then there will not be collision, so it should go into B! If it drops into B then it cannot drop into B and vice versa!

Now comes Novikov and tells: no. The self-collision happens sometimes after A but before B. And from that moment the self-collision becomes a fact, so velocity and direction will (must; have to) change just so that when the ball later drops into B, it will come out of A with just the good velocity and direction. He shows that the laws of mechanics can be satisfied; so this will (must; have to) be happened.

This is OK. There is no more paradox. But there will be problems with Free Will. Substitute the ball with a spaceman on exploration, and assume that some very nasty happens just at B. Of course originally the explorer does not know this. He observes the first hole to open and close, and assumes it will open again, so he waits to go in. But in the meantime he sees his own ship and person (the person in a bad shape) and hears his own sound in the radio: "Do not go in; very bad!" Now, he, with Free Will, should be able to revise his goal; but then how has he got the warning?

Think about this; but rather not just before sleep.


Although Frederick was the son of a German Emperor, Henry VI of Hohenstaufen, the Imperial title was not hereditary; he took his power from the Kingdom of Sicily. Now let us see the steps to Frederick.

The Kingdom was organised as a Great County by the Norman Roger I(1072-1101) who died and left 2 very minor sons, Simon (1101-1105) & RogerII (1105-1154). Roger II left a successor son William, and some other childrenincluding posthumous daughter Constance (1155-1198), who in 1198 was the lastscion of the House. Constance was wed to the later Henry VI in 1186 andFrederick was born in 1194. Henry VI died in 1197, Constance in 1198.

Now let us count. In 1154 Roger II was surely younger than 61 (Simon was born in 1093), but older than 52. It seems that he died natural death and according to medical science of that time he might have died some months earlier as well and then no Constance at all.

Now, again, Constance was 31 (!) at marriage. While she was in childbearing age and indeed she produced Frederick in 39, this age was rather late for marriage. So, for any reason (temperament? lack of proper dowry?) Constance had marriage problems previously, and had a fat chance not to marry at all.

Then Frederick is born and when at age 4 (!), he is the single survivor of the royal line. What were his chances to survive until majority?

Now let us see the list of Popes from the time of Roger II until Frederick. This was the time of serious struggles between Pope and Emperor. Short-ruling popes of course were no matches for Emperors, and with counter-Popes Emperors had ample possibilities. So:




Innocent II


Anacletus II




Celestine II


Victor IV




Lucius II




Eugenius III




Anastasius IV




Adrian IV




Alexander III


Victor IV




Lucius III


Paschal III




Urban III


Callixtus III




Gregory VIII




Clement III




Celestine III






Innocent III

Parents die





Honorius III

King. Emperor





Gregory IX






Celestine IV





Mongol incursions





Innocent IV






Counter-popes definitely were utilized by e.g. Roger II. But note that fromInnocent III to Innocent IV, bw. 1198 and 1254 there are no counter-popes, theonly short rule is of irrelevant Celestine IV (not even consecrated) and theonly interregnum is in 1241-1243, coincident with the Mongolian raids.Frederick could not make use of this interregnum; while the Regno itself wasnot in any danger, the Empire was more disturbed than Rome. German troops hadto act in the very Western part of flat Poland.

Frederick became Innocent's ward in 1198. It then seems as if Popes won forever. Maybe this would have happened with another, average, Emperor, in his lack. He was able to fight, maybe because Freddy was a really though sonofabitch, however from this underdog position even his exceeding qualities could not raise him to final victory, and he died in digestion illnesses (from nerves?).


Merman’s Children is a story happening about 1310 where mermen can handle steel. So it is either an alternative reality, or according to Anderson’s opinion, mermen are not magic.

Now, even if that is an alternative reality, the Point of Divergence cannot be too far before 1310. Namely, some part of the story happens in Croatia/Dalmatia, and the King is Charles Robert, the Caroberto, and the Ban is Pavao Subic’, as in our timeline. Charles Robert would not have become King in (theoretically) 1301 if history changed before 1290. I would not go into the very exotic details of the rule of Ladislaus IV the Cuman (1272-1290), but must note that Pavao Subic’ is an ancestor of the famous Zrinskis/Zrinyis (of which no Westerner knows anything, except some Austrians; Austrians executed Petar Zrinski/Zrinyi Péter & Franjo Frankapan/Frangepán Ferenc in 1671, where the names are Croatian/Hungarian).

The described reality is rather strange. For example viljas are mentioned in Dalmatia. I checked this point on one of my Croatian woman colleagues (of Hungary) and of course she knew nothing about viljas. Remember what I told above about strigas. Viljas belong to Serbia and Montenegro; indeed, the famous Vilja Song of composer Lehár in operetta Merry Widow is sung at the Montenegro embassy in Paris. True, even Westerner Anderson recognizes at least that the Croatian aquatic ghosts are different from Russian ones.


Physics papers are referred in the text, emphasized. Anderson’s works are emphasized by Ariel font. You may read my newest paper B. Lukács: Acausality and Retrocausality in Four- and Higher-Dimensional General Relativity, in The Nature of Time: Geometry, Physics and Perception, ed. R. Buccheri & al., Kluwer Academic, 2003, pp. 277-288, if you can find the Volume.

My HomePage, with some other studies, if you are curious.