Halloween Fun

Time for some Halloween fun with numbers. In a paper written a few months ago, a University of Central Florida physics professor puts Halloween legends up to the scrutiny of modern science, offering critiques of the Hollywood portrayals of ghosts, zombies, and vampires. The latter is the most interesting. Using the (conservative by the movie's standards) assumption that each vampire feeds on one human and reproduces one vampire per month, the authors show that if the first vampire appeared in the year 1600, the human population would be approaching zero within about two years.

Of course, what he misses is that vampires may feed much more than they reproduce. In the Buffyverse, for instance, vampires seem to feed on humans almost nightly, but reproduce other vampires perhaps once a decade or less. And of course, he isn't considering the reduction in vampire population a Slayer or two might have....

Innateness and Syntactic Universals

This post doesn’t really belong on this blog since it has nothing to do with the intersection of science and faith. But recently I’ve been having interesting discussions over at Babel’s Dawn about the nature of language and its evolution in the human species. As in any such discussion, the topic of what aspects of language might be innate (meaning, ‘genetically programmed’) properties of the human species has arisen several times. Now, for those who don’t know, I’m a professional linguist, my subfield being generative syntactic theory. Even more specifically, I’m a theoretician who works within the Minimalist Program, a program for research built on the work of Noam Chomsky as well as others.. In minimalism, it is taken for granted that some parts of linguistic structure are innate. Discovering what those properties are (and what their sources might be) is a central part of minimalist goals.

Despite the consensus in my field, however, I have found that many non-linguists (and even linguists who are outside the subfield of formal grammar) have a strong resistance to the very idea of there being innate properties of language. Very often I think this resistance has its roots in an acute appreciation of the richness and cultural complexity of language. Anthropologists, literature experts, ethnologists, and linguists largely concerned with descriptivist goals (grammars, lexicographers, etc.) sometimes express the sentiment that formal linguistics (and syntactic theory in particular) is an effort to reduce the multi-faceted kaleidoscope of language to a simple system of computational rules. Anyone who knows the field, however, knows that this simply isn’t the case. Rather, syntactic theory focuses on a very specific set of principles – those that are responsible for the difference between well-formed and ill-formed sentences both in particular languages as well as in language universally. It is easy to see that these principles are largely isolable from cultural influence since grammaticality judgments often do not depend upon social or even discourse context.

Some of the principles responsible for sentence formation seem to have a universal character, being relevant for all human languages. It is these principles that Chomsky and those in the field he spawned have supposed to have an innate basis in the human genome. Most outside the field, however, have no idea what these principles are. Often those who argue for the implausibility of an innate language component are unaware of what linguists in fact claim is innate, making debate rather pointless.

Finally, to the point of the post: below I’m going to enumerate four principles for which there is a strong consensus as to their universality. That is, these are principles that almost no syntactician would deny are universal properties of human language. They are also four principles central to syntactic investigation and theorizing current in the field. After I enumerate them, I’ll say something more about the plausibility of their innate nature.

I. Hierarchical Structure. The relationship between words in a sentence in any language is not symmetric. Consider the sentences in (1) and (2). Note that John may precede himself in (1) and the sentence is grammatical. Reverse the order and the sentence is ungrammatical:

(1) John likes himself.

(2) *Himself likes John.

One might think this restriction is just about word order, but its easy to show this isn’t the case. Consider (3):

(3) I saw the picture of himself that John likes.

Here in (3) himself precedes John and the sentence is fine. What’s the difference? In (3) the phrase picture of himself is not in its original position which is as the grammatical object of the verb likes (in (3) the thing that John likes is the picture of himself). (3) is grammatical because John hierarchically dominates the original position of the phrase picture of himself before it is moved to its overt phonological position. All languages, even so-called ‘non-configurational’ languages, exhibit these hierarchical asymmetries.

II. Displacement/Movement. The data above also illustrate this principle. As I pointed out, the phrase picture of himself in (3) is interpreted in a position different from the one it is pronounced in. Displacement is also common in questions in many languages. In (4), the thing we are asking about, indicated by the word what, is actually the object of the verb read. What has ‘moved’ from its original position to the front of the sentence.

(4) What did John read?

All languages exhibit displacement in one form or another to varying degrees.

III. Recursion. Human language is a recursive system. This just means that we can combine phrases grammatically and iteratively to an infinite degree. Consider (5)

(5) John knows a man who lives in a house that has a new roof that was installed by my friend that used to date a woman that taught at the university that was attended by my brother that…

(5) is a simple sentence with an extremely long object that consists of an iterative sequence of subject relative clauses. One can easily see that this process could, in principle, continue forever without ever violating the principles of English grammar (though of course the capacities of individual memories come into play at some point, making such sentences unnatural and hard to follow). This is recursivity. Not only is it universal to human language, but it also seems to be unique to human language. No other species has been convincingly demonstrated able to detect or produce recursive patterns.

IV. Minimality. It is a surprising and universal fact about language that dependencies between two elements in a sentence cannot be interrupted by a third element of the same type. Consider the movement of question words to the front of the sentence like we saw back in (4). When more than one question word is present in the sentence, it is often the case that only one of them will move to the front. However, there are restrictions on which word it can be:

(6) Who do you think __ bought what?

(7) *What do you think who bought __?

The difference between (6) and (7) is that in (7) the question word who intervenes between the fronted what and its original position (indicated by the blank). In (6), however, no question word intervenes between who and its original position. (7) is said to be an instance of an intervention effect or minimality violation. The constraint doesn’t just apply to movement. Consider a language with object agreement such as Swahili. In this language, the verb shows agreement with objects that refer to humans. In (8), -mw- indicates agreement with the object mtoto. The sentence is ungrammatical without it.

(8) Juma a-li-mw-ona mtoto. ‘Juma saw the child.’

Now, consider a verb that takes two objects, the higher of which is non-human. Turns out it is impossible for the verb to agree with a human direct object in this configuration.

(9) *Juma a-li-m-pa dunia mtoto. ‘Juma gave the world a child.’

(10) Juma a-li-pa dunia mtoto. ‘Juma gave the world a child.’

The reason for (9)’s ungrammaticality is the same as the reason for (7)’s. In (9) dunia intervenes between the verb and the human direct object unlike in (8) where nothing intervenes between these two elements. Since its discovery, minimality has been found to play similar roles in a variety of constructions in dozens of languages. In fact, much of mimimalism is concerned with finding out just how much of linguistic structure minimality can explain.

All four of the above principles are central to current syntactic investigations and there is widespread consensus as to their universality. The question then becomes, what is the source of this universality? Does it come from the fact that all languages have a common ancestor? Unlikely, but even if that were the case, it would merely change the form of the question to why these particular properties have remained constant throughout language while many other properties of the original language have been lost. What about a shared construct of reality? Again, it is a possibility that must be considered, but if it is true, this certainly isn’t obvious. That is, there doesn’t seem to be an obvious reason why the necessities of interpreting reality or expressing internal thoughts would require properties like displacement or minimality or even hierarchical structure to be a part of language. We are left with the idea that the universality of these four properties (and possibly others) stems from genetic information that all humans share. This conclusion, however, isn’t the final one for linguists. Once we conclude some property is innate, the next question is whether that property is a principle specific to language only or whether it is a principle exapted from more general components of cognition. Recursion, for instance, seems to be not only a central part of language, but also counting, dancing, musical composition, and other cognitive activities. It is therefore unlikely that recursion is particular to language. Indeed, given the propensity for exaption that evolution generally exhibits, it is unlikely that any of the four principles above are wholly specific to language.

I know this has been long, but to those few who made it through, I hope it has served as an information source for a few of the basic claims modern syntacticians make for principles of language that are universal and plausibly innate. Discussion about the innateness of human language must deal with the specific arguments that center around specific claims about specific principles. It is useless to discuss the plausibility of innate linguistic principles philosophically since the questions about innateness are empirical question that can be (and have been) given plausible answers based on scientific inquiry. Any argument against innateness have to be similarly based on empirical investigations and claims.

Galileo and the Church, Part III

Now that we know the sequence of events that led up to Galileo's trial and conviction, we're ready to ask the question 'why.' Why did the church react so strongly to Galileo's teaching of the heliocentric theory of the cosmos? What was the big deal? And what does it mean for us today?

First, it is essential to recognize that the source of the conflict between Galileo and the Church was not Galileo's views on the solar system, but rather his views on Scripture. The church endorsed a geocentric view because a strict interpretation of scripture seemed to demand it (see Galileo and the Church, Part I for the relevant verses). Galileo might have simply accepted this as the church's view and decided to go his own way. He could have left Italy to teach in a part of Europe where the Vatican had less influence. He could have disassociated himself from Catholicism, become a Lutheran, and joined Kepler in Prague. But he didn't. Galileo's devotion to the Church was real, and he knew that though nature was telling him something that scripture seemed to refute, the two could not really be in conflict. He also realized that when scripture and science compete for the right to define physical reality, it is science that must win. This is so simply because defining physical reality is what science is all about, and because scripture contains many metaphors and much imagery that is open to interpretation (a fact that Galileo took to be a virtue of scripture, a tool used by scripture "in order to accommodate itself to the understanding of the majority"). It was Galileo's contention that the scientific story he was pushing and the teachings of scripture were not incompatible, and it was this contention that got him into trouble. "If Scripture cannot err," he wrote in his letter to Benedetto Castelli, "certain of its interpreters and commentators can and do so in many ways." In this view, Galileo was in good company. As St. Augustine wrote, "If it happens that the authority of Sacred Scripture is set in opposition to clear and certain reasoning, this must mean that the person who interprets Scripture does not understand it correctly. It is not the meaning of Scripture which is opposed to the truth but the meaning which he has wanted to give to it." (Epistula 143).

In the papal condemnation issued by the inquisition judges, the charges against Galileo were spelled out. He was condemned for holding the heliocentric view, for teaching it, and for "replying to the objections from the Holy Scriptures, which from time to time were urged against it [the theory], by glossing the said Scriptures according to your own meaning." The condemnation also addressed the theory itself, stating that "the proposition that the Sun is the center of the world and does not move from its place is absurd and false philosophically and formally heretical, because it is expressly contrary to Holy Scripture."

Today, the Catholich Church can clearly have been said to have learned from its mistakes in the Galileo trial, and in particular the mistake of insisting on an overly literal reading of Scripture. As John Paul II stated in a 1992 speech that addressed the Galileo trial, the church now recognizes that "it is a duty for theologians to keep themselves regularly informed of scientific advances in order to examine if such be necessary, whether or not there are reasons for taking them into account in their reflection or for introducing changes in their teaching." In that same speech, the pope warned that lessons from Galileo's trial must be learned for "It is therefore not to be excluded that one day we shall find ourselves in a similar situation..."

I would argue that that day has come. The controversy surrounding Galileo and his advocacy of the heliocentric model finds striking parallels in the popular debates today that concern the theory of evolution. The theory has been around in one form or another for over 150 years and has predecessors dating back centuries farther. Its basic tenets of evolution are undeniably true, there being no other natural explanation for the similarities and distinctions between the fossils of extinct species and their modern counterparts. Yet many Christians find it impossible to accept since it would mean abandoning a literal interpretation of the first few chapters of Genesis. Rather than re-examining their theological understanding, as Augustine and John Paul II suggested is necessary, they rather choose to reject evolutionary theory out of hand (in most cases without really understanding its claims).

Throwing the theory of Intelligent Design into the mix provides even more parallels. To be fair, most scientists who advocate ID would not themselves take a literal view on Genesis, and defending scripture is not their primary motivation. Rather, they are chiefly concerned with defending a direct role for God in creation, whatever that role may be. Nevertheless, the basic principle of ID - that God has directly designed creation - does at least allow for the possibility that the Genesis accounts are accurate. I think this is the reason why fundamentalist Christians have latched onto ID as an alternative to evolution. Recall that in Galileo's time, the exact same thing happened: the more widespread heliocentricism became, the more church was drawn to the Tychonian model of geocentricism. That system was designed by Tycho Brahe, the Danish scientist who tutored Kepler. The system was ugly, made some poor predictions, and clearly could not account for sunspots, but the church's allegiance to it had little to do with its scientific merit. It was merely advocated as a foil to the claims of heliocentricism. I have no doubt that this is the case with ID today. Few of its scientists, but most of its proponents advocate it simply to provide a way to ignore the claims of evolution and maintain a literal interpretation of Genesis. How else can we explain why non-scientist schoolboard members in towns across America are advocating its teaching in public schools? Today, as in Galileo's time, cries are continually heard for evolution to be treated as "merely a hypothesis" and not established truth.

Its clear that the culture of Galileo's day and the culture of modern Christian America aren't much different. True there is no Inquisition here, but in many evangelical churches there may as well be. Admitting that you take evolution to be basically true is tantamount to admitting to being an atheist. I was talking with another professor at the University here recently about designing a course on The Evolution of Language. She was clearly interested, but unsure since "evolution is such a controversial topic here [in the South]." Clearly we have some way to go.

Fortunately, this problem has been solved before. We have only to look to Galileo and the lessons the church has learned from that experience. As Pope Leo XIII said, "Truth cannot contradict truth." Therefore, when it appears that the teachings of science and the teachings of scriptures conflict, we needn't reject science or scripture. Rather, we must examine our understandings of these teachings, for that is likely where the fault lies.

Galileo and the Church, Part II

In 1543 the publication of Copernicus On the Revolutions of the Heavenly Spheres led to a revival of the idea of heliocentricism. Over the next 40 years the theory began gaining ground in spite of warnings from theologians that its assumptions were counter to scripture. By 1600, Galileo (then only thirty six years old) was convinced that the heliocentric model must be correct, even writing to Kepler in Prague, “Like you, I accepted the Copernician position several years ago and discovered from thence the causes of many natural effects which are doubtless inexplicable by the current theories.” By 1610, Galileo had become even more convinced when he became the first person to observe four moons revolving around Jupiter, and in 1611 he observed sunspots, concluding that they could only be explained if it was hypothesized that the sun revolved on an axis.

In the meantime, opposition to heliocentricism was growing in Rome following the burning of declared heretic Giordano Bruno who, among other dissenting beliefs, held the heliocentric view openly. Bruno’s trial and execution was overseen by the harsh inquisitor Cardinal Robert Bellarmine who refused to allow Bruno to partially recant his ideas. But Bellarmine was a man of great intelligence, open to scientific arguments. When he heard of Galileo’s discoveries concerning sunspots and the moons of Jupiter, he asks Jesuit mathematicians to confirm the scientists’ observations. They did so, but argued that the observations aren’t clear evidence for the motion of the earth. By 1613 arguments began to appear that explicitly condemned the Copernician theory.

By then Galileo is in residence in Rome, teaching at the Accademia dei Lincei and it is at this time that he makes a crucial decision. Or perhaps there wasn’t much of a decision to make. Galileo was a devout Catholic who took his allegiance to the church seriously. But he was also a scientist unwilling to compromise his intellectual honesty. In 1613 he wrote a letter to a professor at the University of Pisa offering his thoughts on how the heliocentric model and the integrity of Scripture could both be maintained, writing that the Holy Scriptures “…like nature, owe their origin to the Divine Word….It was necessary, however, in Holy Scripture, in order to accommodate itself to the understanding of the majority, to say many things which apparently differ from the precise meaning. Nature, on the contrary, is inexorable and unchangeable, and cares not whether her hidden causes and modes of working are intelligible to the human understanding or not, and never deviates on that account from her prescribed laws.”

Two years later the letter was used in a complaint reporting Galileo to the Roman Inquisition. In response, Bellarmine issued a caution for scientists to treat Copernicus’ views as unconfirmable hypotheses rather than fact. Galileo went to Rome to defend his views, writing a paper arguing that tidal motion proves that the earth revolves. Advisors to the Inquisition responded with an official declaration that the concept of a moving earth is ridiculous and formally heretical. Bellarmine admonished Galileo in 1616 not to hold the Copernician view (there is some debate about whether he was ordered not to teach the view at this point). Galileo agreed to accept heliocentricism only as a logically possibly hypothesis. That same year Copernicus’ famous text was banned by the Inquisition. That same month, Galileo met with Pope Paul V.

And then things went sort of quiet for a while. Galileo continued to teach and publish interesting papers on comets and sunspots supporting the Copernician view, but being careful to temper his explicit arguments. In 1623, Galileo saw hope in the ascension of the fair-minded Cardinal Baberini (who had opposed his admonition in 1616) as Pope Urbana VIII. He met with the pope and other cardinals six times to explain Copernican theory. Interested in the ideas, the Pope assured Galileo that he had nothing to fear in discussing Copernican theory so long as he treated it as a supposition and not an established fact. The Pope also granted Galileo’s request to write a book comparing the geocentric and heliocentric views openly and fairly. He completed the book in 1630 and went through all the necessary channels to get approval from the Vatican for its publication. In 1632 it was printed. Four months later the pope ordered its distribution stopped and ordered a special commission to examine the book. Based on the commission’s report, the pope referred Galileo’s case to the Inquisition.

So what had happened? The problem was Galileo’s inability to contain his theoretical bias as well as some personal pride on the part of the pope. The book Galileo had published, Dialogue Concerning the Two Chief World Systems, was formatted as an Aristotelian dialogue between two learned men, one of whom held the heliocentric view and the other the geocentric view. Unfortunately, in a few passages the man holding the latter view seemed to be portrayed as foolishly holding to his beliefs despite clear evidence to the contrary. In his depositions before the Inquisition, Galileo claimed this was completely unintentional, stating “with the said book I had neither held nor defended the opinion of the earth’s motion and sun’s stability; on the contrary, in the said book I show the contrary of Copernicus’s opinion and show that Copernicus’s reasons are invalid and inconclusive.” But it seems Galileo’s theoretical bias had slipped through. At his second deposition two weeks later, he had gone back and reread his own book which he claimed not to have read since he had written it three years before, stating that “I wanted to check very carefully whether, against my purest intention, through my oversight, there might have fallen from my pen not only something enabling readers or superiors to infer a defect of disobedience on my part, but also other details through which one might think of me as a transgressor of the orders of Holy Church.” His conclusion was a free confession that at some parts he could indeed see how someone might get the idea he was arguing for one side over the other rather than presented both views as valid, “in particular, two arguments, one based on sunspots and the other on the tides, are presented favorably to the reader as being strong and powerful, more than would seem proper for someone who deemed them to be inconclusive and wanted to confute them, as indeed I inwardly and truly did and do hold them to be inconclusive and refutable.” Galileo offered to write another book that would correct these misperceptions in Dialogues, an offer which was refused. Perhaps more damning, however, was the perception by the Pope that Galileo had placed the pope’s very words into the mouth of his geocentric-leaning literary character. The Pope therefore felt personally slighted by the passages which made this character appear as a fool. Whether this was intentional or a misperception on the pope’s part was isn’t known and wasn’t addressed in the depositions.

At his final deposition, Galileo was finally asked whether he held the Copernician view. He denied that he did, but claimed to hold the Ptolemaic geocentric view. He was asked repeatedly and under threat of torture to tell the truth. He repeated only that he did hold the Ptolemaic view and had held it since the injunction from Cardinal Bellarmine was issued against him. In the end, Galileo received a papal condemnation sentencing him to prison for an indefinite term (he was 70 years old at the time). After signing a formal recantation, he was allowed to serve his term under house-arrest where published the foundational Two New Sciences (despite the papal ban on his publishing anything). He died eight years later.

What exactly was Galileo’s crime? Was it really that he held and taught and wrote about the heliocentric view? It is doubtful since as I wrote before, the heliocentric view was quite commonly known amongst the public and even quite commonly believed in academic circles. In the next and final post, I’ll make the case that Galileo’s crime was not his scientific belief, but rather the fact that he challenged the church’s official interpretation of Scripture. I’ll also draw modern parallels, suggesting that Galileo’s experience can help us out of the quagmire between science and religion we are experiencing today.

Galileo and the Church, Part I

Talk about conflicts between science and religion and eventually Galileo's name will come up. But usually its merely an anecdotal mention: "We all know how the church hates science. Look at Galileo!" But what really did happen to Galileo? What was the nature of his conflict with the church? Are there any lessons we can learn from it?

As most are aware, Galileo was an Italian scientist in the early 1600s. He made invaluable contributions to mathematics and physics, paving the way for Newton, and invented various microscopes and telescropes. But perhaps his greatest contribution was methodological - Galileo was one of the first scientists to assume that lack of unity in the way we understand something is the result of gaps in our understanding rather than in the nature of the universe. Its because of this he is referred to as the 'father of science' and the 'father of physics,' or as Einstein called him, 'the father of us all.'

What got Galileo into trouble, though, were his views on astronomy. He was a staunch supporter of the Corpernician theory of the universe, which was heliocentric. In this model, the sun was a stable object near the center of the universe while the earth (and all the other planets) moved in a series of circles around it. Heliocentricism had actually been around a long time, going back at least to Aristarchus in Ancient Greece around 270 BC and having a long tradition in Indian culture and literature (in particular, the Vedas). Nevertheless, most astronomers even in Galileo's time were skeptical of the view, largely because it did not make as accurate predictions about the motions of the heavens as modern versions of the Ptolemaic geocentric system (the reason, of course, is that heliocentricism is also wrong - the sun is not the center of all the rotation of the heavens).

Heliocentricism got a second shot in 1543 when Nicolas Copernicus published his "On the Revolutions of the Heavenly Spheres." The work touted a revised heliocentric model in which the sun was not quite the center of the universe and, more importantly, which employed the concept of geometric simplicity and symmetry to arrive at results nearly as accurate as the geocentric models everyone used. So why wasn't Copernicus punished by the church for his views? Largely because he died the year the work was published (which wasn't a coincidence - there is evidence Copernicus had written most of the work a decade earlier and delayed publication due to fear of ridicule), but also because Copernicus dedicated the book to the Pope and backed off the claim that his theory was any more than a hypothesis chosen for its mathematical simplicity rather than its reflection of reality. In some sense, this was just being honest since there really was no way at the time to prove what body revolved around what, and Copernicus had indeed designed his system to get away from the inelegance of Ptolemy's equants.

The book made a splash, but not a big one and its self-disclamations allowed the church to dismiss it. Still, it did get people talking about heliocentricism again and sixty years later one of those people was Galileo. Galileo believed that the Copernician system had to be moving in the right direction largely because of its elegant mathematical solutions to the ancient problems it addressed. He recognized that no model with the earth at its center could achieve such consistency and that the basic structure of such models was being driven more by dogmatic belief than by observation. To show this is the case, one has only to consider the dominant model at the time, the Tychonian model developed by the metal-nosed Danish astronomer Tycho Brahe. In that model the earth is the center of the universe, the sun moves around the earth, and all the other planets revolved around the sun!

But why did any of this matter to the church? Why did they care whether the earth or the sun moved? The answer, of course, was Scripture. In several places, scripture suggests that the earth is immobile. Psalm 93:1: "The earth is firmly established, it cannot be moved," and Pslam 104:5 "He set the earth on its foundation, it can never be moved." Scripture also suggests that the sun moves as in Ecclesiastes 1:5, "The sun rises and the sun sets and hurries back to where it rises." And of course, there is the story of Joshua who, as Martin Luther pointed out, made the sun stand still, not the earth. These strict interpretations of scripture set the church, at least in principle, against the heliocentric view of the universe. But in fact there was very little hostility to the ideas until they began gaining ground in academic circles thanks to one teacher, Galileo Galilei.

Already an established scientists, Galileo moved to Rome in 1612 and began teaching at the famous Accademia dei Lincei where he not only began teaching heliocentricism and against geocentricism, but also taught that heliocentricism was not incompatible with Scripture. And herein lies the key to understanding why Galileo's teaching became so widely popular and why the wrath of the Roman Inquisition came down upon him. Galileo was a devout Catholic and was not content to keep his faith and scientific beliefs completely separate when they competed to explain the physical nature of the universe. Just as with his scientific theories, Galileo assumed that a lack of unity reflected a gap in understanding. The way he filled that gap was to take the Augustinian view that not all scripture is meant to be interepreted literally, in particular those parts meant as poetry. Before Galileo, it was very easy for the Church and its members to dismiss heliocentric viewpoints due to their dogmatic leanings. Galileo offered them a way to accept the best available science and still hold Scripture as the source of truth and light.

As we'll see in the next post, the Church was not entirley unsympathetic to Galileo's view, but a misunderstanding of the nature of science as well as simple prideful sin led religious leaders to try to silence the great scientist.