Sunday, July 5, 2015

The Most Holy Trinity and Self-Similar Fractals

One morning a few days ago, while I was still half awake, I found myself imagining a discussion of the Most Holy Trinity with a (rather rude) skeptic, and I thought of an analogy in terms of self-similar fractals, in particular the Mandelbrot set.

Notice that you see the same pattern at the very beginning (at 0:08) and three more times in this video (at 1:15, 2:29, and 5:03).  Note there  are other repetitions:  we zoom past the same pattern repeated many times before diving into it at 0:46, only to see yet more copies of it on the inside immediately thereafter.  At 1:27, we are once again zooming past more copies of this same pattern.  There is also a 4-armed pattern that we see several times, at 1:01, 1:38, 2:52, 3:11, and 3:48.  Each of these patterns is contained within the others and also contains the others, so whenever you see one, you know the others are also there.

My analogy is that these patterns are "like" the Divine Persons (the Father, the Son, and the Holy Ghost); the patterns are never really separated from each other, as the Divine Persons are not separated from each other.  Yet these patterns together form a unity, as there is only one God in three Persons.  Also, presumably the first pattern would correspond by analogy to God the Father, because although the other two Persons are co-eternal with Him, the Father is in some sense their origin, as He is neither begotten nor proceeding.

There are two other nice things about this analogy.  Firstly, the Mandelbrot set is beautiful, which is one of the reasons videos like the one above are produced.  Likewise, God is beautiful, or if you prefer, God is the ultimate perfection of beauty.  Secondly, although the Mandelbrot set seems infinitely complicated in such a video, in fact it is actually quite simple in its definition.  This might make philosophical statements about the simplicity of God a bit easier to accept.

Please understand that this is only an analogy, and all analogies have their limitations.  A much more careful explanation of what the Church actually teaches about the Trinity can be found in the Athanasian Creed.

Thursday, July 2, 2015

Red Storm Rising

A week ago I finished re-reading Red Storm Rising.  I first read it during the summer of 1989.  The book is now 28 years old, so it should not really be necessary for me to say this, but SPOILER ALERT.

The book holds up better over time than I had expected.  A few things are pretty obvious from the beginning, since this is (after all) a popular American novel from the Cold War.
  1. The USA wins.  Actually, it's more of a combined NATO "win", and "winning" mostly means "surviving".  That said, the Soviet Union took much more serious casualties and is economically and politically in tatters at the end of the book, so in a real (though not ultimate) sense they "lose".
  2. NATO are the good guys.  One of the book's heroes does something that is probably technically illegal, but it is not (under the circumstances) immoral.  All of the real crimes and unquestionably immoral acts are committed by not just Warsaw Pact personnel, but in fact Soviets.
  1. The conclusion of the war is not really a decisive "win", and the course of the war is very much an evenly-matched back-and-forth.  Part of this can be attributed to the need to tell a compelling tale, and part of it to contemporary estimates.  It is still refreshing, though, as compared to revisionist estimates after Desert Storm that assume that the Red Army is just the Iraqi Army scaled up and that a conventional World War III would have been a cakewalk for the USA, that the book assumes that the country that has produced so many world chess grand champions would not behave as complete strategic and tactical dunces.
  2. A number of "main characters" are introduced who are Soviets.  These are characters that still (for the most part) know right from wrong and generally choose to do what is right, and the reader is correctly expected to sympathize with them.  As with the NATO characters, these are ultimately survivors of the war.

Of course with hindsight it is clear that Clancy got many of the little details wrong, such as the appearance and capabilities of the (still classified at the time) F-117.  Much more striking, and in some cases more troubling, are the big things he got wrong, things that cast doubt on the USA and NATO actually being the "good guys".  Here are some of those things.
  • In Red Storm Rising, neither the USA nor its NATO allies are ever presented as torturing prisoners.  They do make use of psychological tricks, and they do make use of drugs (in one case, alcohol which the prisoners willingly "self-administer", and in two cases they exploit powerful pain-killers -- though in both cases, the prisoner had sustained injuries that required medical attention, which was the primary reason the pain-killers had been administered.

    Sadly, in the real world the USA has openly embraced "enhanced interrogation".  All manner of mental gymnastics are used in an attempt to justify this practice -- well, at least when the subject of the "enhanced interrogation" is not an American.  If he were an American, such actions would be torture, of course, just like when we capture someone, he is a "detainee" (not a prisoner of war, which would give him some rights, and not an accused criminal, which would give him some rights, but an Untermensch, with all that that word implies), but when our foes capture a uniformed American serviceman, he is always a "hostage".  These, at any rate, are the cases we know about and that are publicly defended; but given the culture and practice of secrecy that has come to surround the detention and interrogation of enemies of the state, it is doubtful we will ever know all that has been done.

    The situation is not improved by the knowledge of what happened at Abu Ghraib.  Supposedly, only low-ranking minions were involved in this, and supposedly, this did not represent the will of the US government.  As our British cousins would say, bollocks.  Senior members of the Bush administration (the same people who defended waterboarding) had given speeches (to rounds of applause) about how it was time for the US to "get tough" or "remove the kid gloves".  Only a moron could fail to see that this created an environment that encouraged such abuses, however much they later claimed never to have intended them.  There is, to be sure, a well-established practice of people in authority carefully avoiding all specifics, so that if there is negative fallout, they can claim that they did not authorize or even know about misdeeds carried out by their underlings.  The proverbial "wink and a nod" has been around for a long time!  Even Hitler had minimal contact with the details of the "Final Solution" -- but no one ever doubted that the Holocaust was a direct expression of the Führer's will.
  • The American intelligence community is beginning to resemble too closely institutions like the KGB and the East German Stasi.  I know too many silly people who, in the immediate aftermath of 9/11, were instantly willing to sell their birthright for a mess of pottage.  Actually, it was worse than that:  a mess of pottage is at least a concrete good, but all they got was an unsubstantiated, and highly questionable, claim that in some way they had a little more physical safety.  For that they were willing to spit on the grave of every serviceman who died in the hope that we would be free of secret police.

  • We used to hear that the Soviet Union was a nation of godless atheists, but now the US has become a nation of godless nones.  Or, if you prefer, the Soviet Union was full of people who practiced no religion and called themselves atheists, but now the USA is full of people who practice no religion and call themselves Christians.

    Yes, the trend towards a more godless nation is reflected in polls of religious affiliation, but it is reflected even more in the atmosphere of everyday life.  

    Let me first get out of the way two comparatively minor examples: the coarsening of the language and the ubiquity of tattoos.  By "coarsening of the language", I do not simply mean the use of crude and vulgar words; I also mean the glib discussion of crude and vulgar subjects with no consideration of whether they are appropriate for the time, place, and audience.  As for tattoos, I suspect that when they are used excessively it indicates a non-Christian attitude in which the body is regarded as clothing for the soul rather than as an integral part of the person.

    Perhaps an extreme example of what I mean happened in 2010, when a stalker posted to the web nude videos which he had surreptitiously taken of ESPN sideline reporter Erin Andrews.  This was discussed at length by a number of male ESPN employees on ESPN's national radio programs; many of these employees casually mentioned having seen the video.  (a)  Of course, these men should not have viewed the video.  (b)  If they did view it, they should have at least realized it was something they should feel ashamed for having done.  (c)  Even if they viewed the video and felt no shame, they should have realized that by flippantly discussing on air having viewed the video, they were creating a very uncomfortable, even hostile work environment for Ms. Andrews.  The really amazing thing was that there was absolutely no sense of shame, nor even any sense that there was a need to rationalize (probably on the basis of "we are journalists") what they had done.  There was no objection from anyone in the studio, and, at least during the time it took me to drive in to work, no objection from any guest or caller.

    (Two years later, Erin Andrews switched to Fox Sports.  Perhaps this was a contributing reason, though Fox Sports radio personalities seem to be cut from the same cloth as their ESPN counterparts.)

    I'll give just one more example of the change I am describing in the overall approach to life.  A few years ago, I was the principal investigator in a summer research program for college undergraduates.  Part of the program was an ethics component, which we satisfied by reading and discussing Fundamentals of Ethics for Scientists and Engineers by Edmund G. Seebauer (which I like because of its Aristotelian approach).  We ran into trouble at the very beginning:  at the point where it must be mentioned that we take for granted that there is something for ethics to study.  That is, ethics is the study of what ought to be done by a particular person in a particular set of circumstances, not a study of what people actually do (which is arguably history), nor what they say they should do (which is arguably cultural anthropology), nor how people feel about what they and others do (which is arguably psychology).  One student would have none of that; this student had a family member who was a philosophy grad student, and so knew that ethics is only what people actually do.  Most of the other students were noncommittal.  They have all grown up in a system that now teaches children that right and wrong are not concrete realities.  Of course their indoctrination is not consistent; I think they would all agree that James Earl Ray really ought not to have assassinated Martin Luther King, Jr., even though that is what he actually did, even though subcultures like the Ku Klux Klan would have said he did what he ought to have done, and even if the assassination made James Earl Ray feel better in some way.  They would "feel" that the assassination was in some way wrong, but they have been taught that there is no objective reality behind this feeling.  The Abolition of Man is nearly complete.