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One time several years ago in graduate school, I simply could not remember the word "syrup", so I called it "pancake gravy". That title was already taken(!), so I added "cane" because when I was a child in the Panhandle of Florida (aka Lower Alabama), my family grew sugar cane and made our own cane syrup.

Tuesday, December 16, 2014

Infinite Regress

Achilles Penthesileia BM B209  
Some of the arguments for the existence of God as a First Cause depend on the assertion that there can be no infinite regress of causes.  It is safe to say that although such an assertion is plausible, it is not self-evident. I thought it would be just as well to attempt to construct an example.  My attempt fails, but it is an interesting failure (at least to me).

The idea is this:  Achilles throws his spear, which we will take to be made of continuous, infinitely divisible matter.  (Sorry Democritus!)  In making his through, he obviously does not hold the spearhead directly; he holds the spear by somewhere near the middle of the shaft, but the push of his hand is ultimately responsible for the motion of the spearhead.  Ultimately responsible, but not directly responsible!  We can divide the shaft between his and and the spearhead (of length L) into halves:  Achilles pushes the first half, the first half pushes the second half, and the second half pushes the spearhead.  We can divide this again, so that now we have quarters:   Achilles pushes the first quarter, which pushes the second quarter, which pushes the third quarter, which pushes the fourth quarter, which pushes the spearhead.  We can continue, a la Zeno, to divide the shaft indefinitely, but each time we do, there remains a well-defined chain of causes, with the last piece (ending at distance L) being pushed by the penultimate piece (ending at distance (1 - 2-N)L).  Isn't this an example of an infinite regress?

Well, no.  It is a finite regress of arbitrary length, and no one has ever had a problem with finite (though long) regress.  We are safe as long as the number of divisions of the shaft is an arbitrarily large but finite number, but what happens if we do what the Greeks would never feel comfortable in doing and "complete" the infinity of divisions? Then the last piece, at distance L, will be pushed by the penultimate piece at distance (the largest rational number less than 1)L.  But there is no such thing as "the largest rational number less than 1".

Of course, another way to avoid a first cause is to have a closed causal loop.  Those may be possible in General Relativity, but it is highly doubtful that they can describe the universe as a whole.  Worse, although the cause of each element in the loop may be well defined, the loop as a whole seems very ... artificial, a thing even more unsatisfying and in need of an explanation than a chain of events going back into the infinite past (with apologies to the Big Bang).

Thursday, December 4, 2014

Elgin Marbles on the Moon


Ac marbles
Author unknown [GFDL or CC-BY-SA-3.0], via Wikimedia Commons

Last night I dreamed that there were huge carvings on the surface of the moon.  They were similar in style to the Elgin Marbles, but each figure was at least 1 mile high, and were easily visible from Earth through sufficiently powerful telescopes.  Although there were heroes, centaurs, etc., the carvings did not correspond to any known characters or stories from any mythology; I had the vague feeling these might correspond to a mythology from the age of the Titans, before Zeus overthrew his father.  There was an accompanying inscription in very old Greek; a few people could read it, but I never found out what it said.  The whole display was clearly meant to be seen from Earth.  Naturally enough, there was a mission planned to visit the carvings in the hope of learning something about how they had been made, whether this meant that people had once lived on the moon and it once had (surprisingly) an atmosphere, etc. 

My dreams are still better than SyFy made-for-TV movies.

Wednesday, December 3, 2014

Is String Theory Too Timid?

Lately I've been watching the series of YouTube videos put out by Stanford University in which Leonard Susskind lectures about string theory and M-theory.  He really is an excellent lecturer, so even though I have had little cause to use advanced quantum mechanics over the past two decades, let alone particle physics or string theory, it's easy to follow his lectures.  (They are not lectures for the general public, though, because they do require having had at some time a pretty good background in physics, but they are OK for an advanced undergrad or someone who is very rusty.)

I have tended to be a skeptic regarding superstrings, mostly because it is too often presented to the general public in exactly the same way ancient Greek philosophers presented their physics theories:  long on an appeal to what a beautiful idea it is, but almost completely lacking any evidence from experiment or observation.  That is very bad form for a scientist!  It hasn't helped that some of the theory's proponents have even suggested that perhaps it is the ONLY possibility, so that "God had no choice" but to build a universe out of superstrings -- a statement that is at least borderline blasphemous and which displays a mind-boggling absence of imagination.  Happily, though, the actual science behind string theory is not quite so muddle-headed as the popularizations. 

One thing that is still surprising, though, is how reliant string theory seems to be on physics that is backed up mostly by our experience with molecules, atoms, and nuclei.  In particular, Susskind starts off with a string of masses connected by springs, considers that string in a reference frame in which it is moving close to the speed of light, then applies the standard techniques to quantize it.  This is all pretty basic stuff, very similar to what is used in the Debye model of a generic crystal.  The only thing is, he wants this to apply all the way down to the Planck scale.

To me that seems to be unjustified optimism.  Quantum mechanics has of course been phenomenally successful in explaining or predicting all kinds of phenomena, but there are, after all, a number of foundational problems about it, and it requires a huge jump to go from they physics of hadrons and mesons to the Planck scale.  Somehow, it seems likely to me that along the way, we will have to replace Quantum Mechanics itself with something new that will be even weirder.  Quantum Mechanics would remain as a "low energy" approximation for whatever comes next, just as Newtonian Mechanics remains as an approximation for Quantum Mechanics.

Sunday, October 12, 2014

Thinking in Dreams

Like most people, I suspect, my dreams come in different kinds.  Some of them are like short stories, and if I remember enough details these can be quite interesting.  Many are like a confused movie, except that the confusion is usually not noticed until I wake up.  In yet other dreams the main character really does seem to be much more identifiable as "me", partly because the people with whom the character interacts are often family or friends, or because the places the character visits are places I have been, and partly because he thinks much the same way my waking self thinks. 

The fact that this dream self thinks so much like me makes the differences all the more interesting.

One thing that stands out is that at some level -- something like the subconscious of my dreaming self -- I know that I am dreaming.  I do not have lucid dreams, but in some cases I end up debating with myself whether I can disregard an unpleasant event because it is just a dream or whether I am just in denial.  This happened twice over the past week:  in one dream I had accidentally backed my truck into a car behind me, and in another I was hunting with a friend (not anyone my waking self recognizes) and got into trouble both for shooting a moose on private property without the landowner's permission and for discharging a firearm too close to the road.  The fact that I have never hunted nor lived in a place with moose makes that second dream particularly strange.  I tend to wake up shortly after beginning to suspect that I am dreaming.

Geography is very confused in my dreams.  I know the layout of the US states pretty well -- the main mistake I am likely to make is confusing Vermont and New Hampshire.  Maps in my dreams are horribly confused.  The distances are much reduced, with the cities that are landmarks on my drives each lying about one hour or less from its neighbor, and the roads are much more north/south and east/west than in reality.  In my dreams, a good day's road trip would be from Tuscaloosa up into Indiana, then over to New Jersey and down to Philadelphia.  In the real world this would be a trip of about 1300 miles; in my dreams it is more like 250 miles, and I seem to have made many such trips just of the heck of it.

When I was a student I used to dream that I was studying for the test that was (in the real world) coming up the next day.  I would try to read from my textbook, but it was impossible to focus on it, either visually or mentally.  This usually happened just as it was time to get up, and eventually I realized I needed to wake up because the fuzziness of the textbook was a dead giveaway.

Something similar happens when I try to do math in my dreams.  For instance, just last night I dreamed I was talking to someone about the manganese nodules on the seafloor (why we would be talking about this, I have no idea), and he suggested that there were only a few thousand of them.  I knew that was much too small a number, but all my efforts to make an order-of-magnitude estimate were frustrated, even though I used dream paper to try writing it out.  I made all kinds of mistakes:  I mixed up the formula for the volume with the formula for the area, even though I knew I was doing something wrong; I estimated the oceans to cover half the earth, rather than 70%; and I used 4000 km as the radius of the earth, when it is 4000 miles.  I also estimated one nodule per square kilometer of ocean, but I knew that would be a generous lower bound.  I can do a calculation like this in my head in just a few seconds while awake, but it was quite beyond me while asleep.

The weird thing is that once, back in high school, I went to bed knowing there was a serious problem with the proof for a theorem I was trying to prove.  At about 3 am, I woke up knowing what the solution was to my difficulty, so I got up and wrote it down.  Somehow I had solved the problem in my sleep.  Sadly, this seems to have been a once-in-a-lifetime event.

Friday, September 5, 2014

Is My Office Haunted?

Well, no.  This is just a stupid trick of the light on some blank DVDs I had on my much-too-messy desk.  Still, I can kind of make out two eyes and a nose. 


What's really sad/funny is that this is actually as good as or better than many of the "ghost photos" one can find on the Internet.

Tuesday, August 5, 2014

Unconditional Surrender and a False Dilemma

HiroshimaGembakuDome6705.jpg
"HiroshimaGembakuDome6705". Licensed under Public domain via Wikimedia Commons

Wednesday will mark the 69th anniversary of the bombing of Hiroshima, which, together with the bombing of Nagasaki, killed well over a hundred thousand civilians.  That was according to plan; the bombings were intended to make it blatantly obvious to the Japanese that the war was unwinnable and the cost was unthinkable, so that they would promptly surrender.  If this was not terrorism, nothing is terrorism.  Please do not pretend that the target was a ball-bearings plant.

This much is generally conceded, but it is argued that it was the better of only two alternatives.  The other possibility was a D-Day-style invasion that was expected to result in a million American casualties, with even larger numbers of Japanese military and civilians killed.  It is easy to say that we must not do evil that good may result, it is argued, but if doing evil saves over three million lives, then the evil must be done. 

But were these the only two possible alternatives?  Actually, there was another choice available -- one that is so much more shocking than the deliberate slaughter of 100,000 civilians that it is overlooked:    admit that the president of the United States had made a mistake.

Franklin Roosevelt had insisted that the surrender of the Axis powers must be unconditional, and Churchill and Stalin had agreed.  This was in no small part bravado, which was necessary in the early part of the war, but it was also intended to make sure that the defeat of the Axis would be unambiguous.  The Allies did not want a repeat of the claim that Germany had not lost the First World War in the field, but rather was betrayed by cowards well behind the front.

Look at this from the perspective of the Japanese, though.  What could unconditional surrender mean, other than that if they knew what the Allies had in mind they would never surrender?  It would have been easy for them to imagine atrocities; all they had to do was remember how they had treated China and Korea.  The Japanese tendency to commit suicide rather than surrender was only partly a matter of honor; there was also a very practical fear of how the defeated were made to suffer.  What terrible things could the Allies have in mind that they were not willing to declare?

Of course, the reality was far milder than anyone, Japanese or American, could have imagined.  Tojo was hanged, as were a few others, but Japanese war criminals were pursued with nothing of the gusto applied to the hunt for German war criminals.  Japan surrendered the right to wage war, but a small self-defense force was retained.  Hirohito abandoned the claim to divinity, but both his life and his office were spared.  The occupation forces were well-disciplined, and Japan was welcomed as a trading partner and ally, leading to greater prosperity than at any earlier point in Japanese history.

What if the Japanese had been told what lay in store for them?  Would they have stubbornly insisted on continuing to fight, regardless of the costs?  Probably not: even before the atomic bombs were dropped, about half the Japanese cabinet favored surrender.

Would this have allowed Japanese militarists to insist that Japan had not "really" been beaten?  Possibly, but that kind of person will make outrageous claims no matter what the facts may be.  The German perception that their armies had not lost World War I in the field had less to do with the rise of the Nazis than the terms of surrender and (above all) the Great Depression.

Americans have always had too great a tendency to deify our presidents, and FDR was an extreme example.  This often comes at a cost.  Let us pray that we never again consider the reputation of a president to be worth more than a hundred thousand civilian lives.

Sunday, July 20, 2014

Hidden Bloodlines

I just stumbled across a rather interesting documentary that argues that Edward IV of England was illegitimate, and then proceeds to track down the "real" king of England, who was (he seems to have passed away, if the YouTube comments are to be trusted) "real people", as my family would say. 



I think this sort of thing must be very common.  After all, St. Joseph was a direct descendant of King David, yet he was a carpenter with no apparent social or political significance.  More generally, although a tiny percentage of people descended from prominent families are able to trace one line of ancestors back two thousand years or so, I suppose no one can trace back all his ancestors that far.

In my case, I know I have ancestors from France, England, Ireland, and Germany -- presumably, then, basically the whole of northwestern Medieval Europe.  But what about before then?  Could one of my ancestors have been a Roman legionnaire recruited in Egypt and settling in Gaul, but descended from one of Ramses the Great's 96 sons?  Who knows?  Going back that far, we all have a lot of ancestors, and with all that has happened since then, just about anything is possible.

All this is well and good, but arguably of only trivial interest.  Things get more interesting, though much more controversial, when we get to the question of who may be descended from ancient Israel and Judah, and what that means.  An unbelievable amount of nonsense, much of it highly offensive to any thinking person, has been written on such topics.  Let me be clear from the outset that I am not in any way endorsing either the anti-Semitic pseudoscience that led to the Nazis and their successors, nor the comparatively quaint fantasy of British Israelism.

Instead, I want to focus primarily on Christian (and especially Catholic) writers who tend to take a few verses from Scripture (in particular, John 4:22 and Romans chapter 3) use them to draw unwarranted conclusions regarding the relationship of the Catholic Church to "the Jews".  (Quotation marks are actually necessary here, because the passages would have had a somewhat different meaning in the First Century than in the Twenty-first Century.)  The motivations of these authors are no doubt good; they seems to be a combination of curiosity about these particular verses, a wish to counteract the history of Antisemitism, and a desire to make the Gospel more palatable to their Jewish friends, but there are problems with their results.

First of all, in John 4:22, when Jesus said, "Salvation is from the Jews," He was kind of obviously talking about what was happening that very decade -- a time when there was not much mystery to the question of who is a Jew.  He was also building up to the very next two verses, which were about the end of Temple Judaism and the admission of non-Jews to proper worship:
But the hour cometh and now is, when the true adorers shall adore the Father in spirit and in truth. For the Father also seeketh such to adore him.  God is a spirit: and they that adore him must adore him in spirit and in truth.
As for the advantages St. Paul lists for being a Jew, they appear to fall into three categories. 

  1. Some advantages are apparently due to some spiritual aspect of biological descent.  Some societies vastly overestimate the importance of such a dimension -- in particular, caste-based and eugenic societies.  Today's society tends to deny any possibility of such a dimension, in part due to its materialist philosophy, and in part due to the outrages committed by caste-based and eugenic societies.  However, it is important to remember that the doctrine of Original Sin means that biological descent does have certain real spiritual consequences, even though they are not as extreme as some have believed.

    Also, every human being whatsoever has both good and bad in his ancestry.  The Hebrews accepted the Law at the foot of Mount Sinai; they also worshiped the Golden Calf at the foot of Mount Sinai.  The prophets came from and to them, and they are the ones who murdered the prophets.  This does not make them especially bad or especially good; it makes them a fitting representative for all of humanity.  (In fact, I suspect part of the reason God called the Hebrews is precisely because there was nothing very special about them.  If He had called the Egyptians, people might have thought it was because of their science or architecture.  If He had called the Greeks, it might have been thought to be because of Greek philosophy or art.  For a long time, though, the Hebrews had no very distinctive worldly success.)

    The main problem, though, is clear in Romans 3:3.  "For what if some of them have not believed?"  Because, of course, some of them did believe, and those who did entered the Christian community and no longer identified themselves as Jews.  At this point, only God knows who is actually descended from the Patriarch Jacob, just as only God knows who is actually descended from Ramses the Great.  I suppose that there are very few people in Europe with no Jewish ancestry at all, but there is apparently no way of knowing in this life.
  2. Other advantages listed by St. Paul were due to the fact that Jewish culture going back to Abraham had been shaped by the worship of the One True God for nearly two thousand years.  This is not such an advantage today, when modern Judaism has explicitly rejected the Christian Gospel for two thousand years but several national cultures have been shaped by the Gospel for up to the same length of time.
  3. Finally, at the time of St. Paul, only Jews would have been raised since childhood in the worship of the True God.  By the time he was martyred, though, he would already have known Gentile converts whose children had been raised in the Faith from childhood.
So two of the kinds of advantage really do not apply any more, whereas the third is a mixed blessing that might apply to just about anyone of European or Near Eastern descent.  This, to say nothing of the explicit statements of Scripture in precisely the passages that are cited, makes it perfectly clear that a recent convert from Judaism does not become a First Class Christian, with everyone else a Second Class Christian, which sadly is the implication of many of these books.

As regards ranking individuals or nations or cultures, I think the problem comes with assuming that there is one universal ranking, and everyone ranked "better" is better in every way.  This certainly creeps into much that has been written about the nine choirs of angels.  We know, though, that the Blessed Virgin Mary occupies a position in Heaven higher than that of any angel or any other mere human, and we also know that she was not eligible to become a priest or bishop.  We know that she comes first among created beings by order of grace, but that Lucifer came first by order of nature.  We even know that it is meaningless to ask if an oboist "outranks" a cellist, because there are both oboe concertos and cello concertos.