German translations

I am honored that St. Patrick Zimmerman has chosen to translate some of my blog posts into the German language.  His translation website, now included in my sidebar, includes the following posts so far:

Bei der Liebe Gottes!

Ist die Sühnung ethisch nachvollziehbar?

Wenn Gott die Unschuldigen tötet

Fragen zu Adam

Die Einheit der Kirche suchen

This is now the second language into which my blog posts have been translated; the first being Portuguese.  As Patrick finishes more translations, I will update the list on this post (without making any other announcement).  I'm grateful for his efforts.

Posted in Blog | 6 Comments

St. Antonin Scalia

As Charles de Gaulle is reputed to have remarked when his aides told him he could not resign as president of France because he was the indispensable man:
"Mon ami, the cemeteries are full of indispensable men."
Justice St. Antonin Scalia, "God's Justice and Ours".

I was deeply saddened this weekend to hear of the death of Justice Scalia, the most engaging, provocative, and brilliant of all of the justices on the Supreme Court.  As someone who reads Supreme Court decisions for fun, I will definitely miss his wit and humor and crankiness, and the way he made the job fun.  However, I also feel quite strongly that his loss is a significant blow to the Court and to my country.

There are countries in which the fundamental principle is rule by some human being or set of human beings.  The United States is not such a country; we are a constitutional republic.  In our country the fundamental legal principle is a document, the Constitution, which outlines the divisions of power between different branches of government, limits the powers of government, and provides for certain fundamental rights which cannot be abridged.

Of course no document interprets itself, and therefore there is a need for human beings to read the Constitution and decide what it means.  Sometimes the meaning is clear; other times there is an ambiguity which must be settled somehow or another.

It would be lovely if Congress and the Executive Branch could be trusted to police the boundaries of their own limited powers.  In principle, there is no inherent logical reason why this could not work.  In practice, politicians are too venal to be trusted with this; the general tendency is for people to interpret things in their own favor, expanding their role in the system until there are no restrictions at all.  There were only 9 years between the time that Congress proposed the First Amendment (1789) and the time when Congress passed the manifestly unconstitutional Alien and Sedition Acts (1798).  Hence the importance of judicial review from an outside body designed to be as neutral as possible.  In our system, that role is played by the Supreme Court.

When settling a dispute between two parties requires resolving an ambiguity in a statute or the Constitution, the Court is supposed to resolve the ambiguity with the most reasonable interpretation that is consistent with previous judicial precedents.  These decisions are binding on lower courts.  (On rare occasions the Supreme Court may reverse their previous decisions, if they are clearly wrong or prove to be unworkable.)  In cases where a statute is inconsistent with the Constitution, the Court has not only the power but also the obligation to strike down or modify the statute to make it conform to the higher law.

There is obviously a danger here, that the judges might substitute their own political will instead of trying to find the most reasonable interpretation.  This is a form of corruption, because they are there as judges, not politicians.  If we had wanted a tribunal with the power to strike down Congressional acts for political reasons (and sometimes to invent new pseudo-legislation), it is unclear why a democracy would want nine unelected Ivy League lawyers with lifetime tenure get to decide for the whole country, based on the arguments of two other lawyers hired by the two parties who lobby for their preferred position—our own American version of the "House of Lords"!  The only possible legitimacy the Court has, comes from the idea that generally speaking (aside from the inevitable but regrettable exceptions), the Court is engaged in acts of interpretation, not naked partisan will.

I am prepared to be quite generous here.  I do not require that all constitutional rules be explicitly spelled out, so long as there is some fair and reasonable argument that they are implied by structure or context.  But there are limits to this.  Many decisions which can hardly be called interpretation by the most generous stretch of the imagination.

The danger of misinterpretation becomes greater when one remembers that our legal system is based on precedent.  A single wrong precedent can become a launching pad for even greater departures, and when you stack them together the final result can be the complete and total erosion of some provision or right spelled out in the Constitution, or  the generation of some completely new provision or right almost out of whole cloth.  Like a rough stone becoming smooth after lying under a riverbed, it is easy for a system of laws to lose its distinctive features over a couple centuries.

For the past few decades the most dominant school of legal interpretation in the legal academy has been that this is not a bug but a feature.  (I have even found this view endorsed by textbooks written for Middle School students.)  The idea is that there is a "living constitution" which grows and adapts to the needs and ideals of each new generation.

To which I would reply: one may as well not have a Constitution at all, as to have one which is flexible enough to adapt itself to each new generation at the mere whim of judges.  If the duly elected representatives of the people pass a piece of legislation, then clearly the mores of the current generation are consistent with that law existing.  If, nonetheless, a bunch of unelected politicians decide to strike it down because it is incompatible with the current social mores of legal scholars, well that is merely a minority of the people exercising will-to-power over the majority.  Unless, of course, the legal scholars were actually using their legal expertise to interpret the text of the Constitution, which is of course the reason why we select them for the role in the first place.  I don't care whether you call it Originalism or Textualism or something else.  There are multiple reasonable ideas about how to do interpretation but Living Constitutionalism is not one of them.

In fact, it is only what these scholars might call a "dead constitution" which could actually exert a meaningful influence on the body politic.  It is the Constitution with definite meaning that should be called "alive", while the one whose flavor conforms to its surroundings like tofu is "dead".  As St. Chesterton said in another context:

A dead thing can go with the stream, but only a living thing can go against it.  A dead dog can be lifted on the leaping water with all the swiftness of a leaping hound; but only a live dog can swim backwards.

The rule of law is, simply speaking, the idea that there are certain written ideals which the government is permanently responsible to.  The idea of a "living constitution" is pernicious because it subverts our ability to have such permanent ideals.  A living constitution is an erasable Constitution.  If you value your rights to criticize the government or to have a fair trial, then this can continue to exist only if the government believes in the ideal of upholding the Constitution even when it is inconvenient .

You may ask, why should a few people who lived in 1787 or 1866 (when the 14th Amendment radically changed the balance of power between the federal government and the states) have more power than the rest of us to decide what should be the fundamental rules of society?  Haven't we developed morally since then?  The people in 1787 even allowed slavery!  (Although admittedly this has since been fixed.)  Well I should hope we have improved, but this objection is not to the point.  The Constitution is not perfect, but it is the one we have.  Therefore, until the next political revolution, it defines what is legal and illegal.  Furthermore it contains a number of very important principles about due process and so on, which I would rather not have forgotten.

And if there is a powerfully strong consensus that the Constitution should be changed, it contains procedures allowing the people to do so.  But it needs to be a stable bipartisan consensus, not the blowing of fickle political winds.

Nothing prevents Congress and the Presidency from acting based on the most up-to-date and progressive understanding of morality.  These are progressive, forward-looking institutions.  But the Supreme Court is backwards-looking: to make sure we are obeying the ground rules for American politics as traditionally defined by text and precedent.  Brown v. Board revolutionized American society, not by inventing a new racial ideal, but by holding the people to the ideal of racial equality which had already been incorporated into the Constitution a hundred years before.

Lawlessness has a general tendency to breed more lawlessness.  A given activist court may vote to increase your rights in some particular area, but if those rights are not based on sound legal construction, then at the same time it erodes the rule of law, which is a necessary to protect the existence of legal rights in the first place.  It's a shortsighted trade.  As St. Thomas More says in the brilliant play "A Man for All Seasons":

William Roper: So, now you give the Devil the benefit of law!

Sir Thomas More: Yes! What would you do? Cut a great road through the law to get after the Devil?

William Roper: Yes, I'd cut down every law in England to do that!

Sir Thomas More: Oh? And when the last law was down, and the Devil turned 'round on you, where would you hide, Roper, the laws all being flat? This country is planted thick with laws, from coast to coast, Man's laws, not God's! And if you cut them down, and you're just the man to do it, do you really think you could stand upright in the winds that would blow then? Yes, I'd give the Devil benefit of law, for my own safety's sake!

Let me give some specific examples of legal BS.  There are many historical examples such as Dred ScotPlessy, Cruikshank, Korematsu and Lochner, which have since been repudiated.

The most infamous currently valid precedent is of course Roe v. Wade, which reads more like a rambling college essay than anything resembling legal analysis.  Leaving aside your moral views on abortion (mine is that it is deeply evil, but that has nothing whatsoever to do with my current point), no reasonable person reading the actual text of the Constitution would ever guess that this is a protected constitutional right, implicit in "nor shall any State deprive any person of life, liberty, or property, without due process of law".  Even many liberal scholars agree that Roe is indefensible from a legal standpoint.  Wikipedia's article on Roe has a nice collection of quotes:

In a highly cited 1973 article in the Yale Law Journal,[81] Professor John Hart Ely criticized Roe as a decision that "is not constitutional law and gives almost no sense of an obligation to try to be."[82] Ely added: "What is frightening about Roe is that this super-protected right is not inferable from the language of the Constitution, the framers’ thinking respecting the specific problem in issue, any general value derivable from the provisions they included, or the nation’s governmental structure." Professor Laurence Tribe had similar thoughts: "One of the most curious things about Roe is that, behind its own verbal smokescreen, the substantive judgment on which it rests is nowhere to be found."[83] Liberal law professors Alan Dershowitz,[84]Cass Sunstein,[85] and Kermit Roosevelt[86] have also expressed disappointment with Roe.

Jeffrey Rosen[87] and Michael Kinsley[88] echo Ginsburg, arguing that a legislative movement would have been the correct way to build a more durable consensus in support of abortion rights. William Saletan wrote, "Blackmun’s [Supreme Court] papers vindicate every indictment of Roe: invention, overreach, arbitrariness, textual indifference."[89] Benjamin Wittes has written that Roe "disenfranchised millions of conservatives on an issue about which they care deeply."[90] And Edward Lazarus, a former Blackmun clerk who "loved Roe’s author like a grandfather," wrote: "As a matter of constitutional interpretation and judicial method, Roe borders on the indefensible.... Justice Blackmun’s opinion provides essentially no reasoning in support of its holding. And in the almost 30 years since Roe’s announcement, no one has produced a convincing defense of Roe on its own terms."[91]

If you support legal abortion as a policy matter, imagine how you would feel if the Supreme Court had decided that the state allowing abortions was a violation of the 14th Amendment right to "life" and "equal protection of the laws".  This is not about who is right as a policy matter, this is about not resorting to BS interpretations to short-circuit the political process.

Or consider the Congressional power to "regulate commerce....among the several states" has now become so broad that it includes the power to regulate literally almost anything.  One time, Congress passed a law that forbade anyone to bring a gun within 1,000 feet of a school.  The point has nothing to do with whether you like guns or hate them, the question is whether this was within the powers of Congress (as opposed to the relevant State Legislature).  Their justification was that guns cause violence, violence causes students to feel scared and disrupts education, which leads to a worse-trained workforce, negatively impacting interstate commerce.  Clearly, if that counts as interstate commerce, then everything counts as interstate commerce, and there are actually no limits on Congress' legislative powers, aside from the handful of explicit prohibitions in the Bill of Rights and other places.  The other sections of the Constitution need not have been written.

In United States v. Lopez, the majority (including Justice Scalia) ruled that this was a bridge too far.  This was the first time since FDR stacked the Court that they had ever struck down a law for this reason.  Yet it was only a 5-4 decision.  4 Justices were willing to buy the absurd argument, in order to obtain their preferred policy result.  The decision was considered a legal revolution for drawing any lines at all, even though in practice it led to very few consequences or future decisions placing limits on what Congress can do.  Congress simply re-passed the law to apply to any firearm "that has moved in or that otherwise affects interstate or foreign commerce", and the courts looked the other way.

It is very strange that the Framers would have enumerated 18 different powers of Congress in Article I section 8, if one of them turns out to give them the power to do anything at all.  The original idea proposed by the Federalists, was that these 18 powers would be so limited that there would be no need for a Bill of Rights.  The rights would simply be everything not covered by one of the limited powers.  (Of course, this would still leave you in the soup if a State tried to violate one of your rights, but I guess the idea was that the States would have constitutions of their own.)  We can see how that idea worked out.  So I'm glad the Anti-Federalists gave us the Bill of Rights.  (Nowadays the 14th Amendment has been interpreted—correctly in my opinion, although to be honest I wouldn't want it overrule this even if it had been bullshit—to mean that the States to also obey most of the provisions the Bill of Rights.)

For some more recent examples, consider Kelo v. City of New London, which ruled by a 5-4 decision that the government to use its power of eminent domain, which is supposed to be for "public use" only, to repossess "economically blighted" property in order to turn it over to private developers.  In other words, the government is allowed to give property from one private owner to another, but only when it steals from the poor and gives to the rich.   Amazingly the five more "liberal" justices were in favor of this approach, while the conservatives (including of course Justice Scalia) were against it.

Or United States v. Comstock, which ruled that the "necessary and proper" clause allows the federal government to keep people in prison indefinitely, after they have completed their prison sentence.  Under a federal law which incidentally applies retroactively to people who were jailed beforehand.  There are few laws which are more obviously unconstitutional than this—it is a more interesting game to try to count the number of different constitutional norms which it violates—and yet it was a 7-2 decision, with only Sts. Scalia and Thomas dissenting!  Oh, I forgot to mention that the law in question only applies to child molesters.  So far.  Remember that line about knocking down all the laws in order to get the Devil?

(To be fair, the justices were considering only whether this law was within the Article I powers of Congress, completely separating out the question of whether it violated the Bill of Rights, trial by jury, or the ex post facto clause.  But in this case, separating the two analyses is completely absurd.  How can an extension of Congressional power possibly be considered "proper" if every imaginable application of that power would violate other provisions of the Constitution?)

I admit I have aesthetic objections to this kind of bullshit as well as moral objections.  I remember being in the 5th grade, reading through the Constitution after finishing the in-class assignments.  I would like to believe that the words I read then have some relevance to what actually happens.  There is a limit to my populism: if some word had a different meaning in 1787 than it does today, or if I was unaware of its traditional legal context, then I don't insist that the courts defer to any accidental misconceptions I may have had.  But I would like to think that a citizen who reads the Constitution even today, would have a pretty decent idea of what it means, and would only need to consult a lawyer for the hard cases.

I really don't want to paint too bleak of a picture here.  I am deliberately focussing on the bad examples here.  There are many examples of Supreme Court decisions which were correctly decided, and there are many constitutional rights (including the all-important First Amendment) which are alive and well.  Taken as a whole, the country is far better off with judicial review, then it would have been without it.  That is exactly my point—the rule of law is a good thing, more important than the outcome of the individual cases, and we need to protect it.

Believe it or not, it is actually possible to be too cynical about politics.  In fact, excessive cynicism is actually the cause of our current political dysfunction; if everyone assumes the worst about a class of individuals, then they have no incentive to be better than that.  (Even Members of Congress have to have mostly started out with some real ideals buried under all their dissembling and compromises, or they wouldn't have entered politics in the first place.  I can't believe they did it for the pay or the job security!)

Lots of people would say that all judicial decisions are just politics, and any pretense of jurists to be principled and neutral are just hypocrisy.  But this is patently untrue.  Even if all of life were just "shades of grey", you can still usually tell which greys are whiter and which are blacker, when you hold them up right next to each other in the same light.  And right now—historically it has sometimes been the other way around—it is the "conservatives" on the Court who are clearly much more principled in their reading of the texts, and the "liberals" who are just trying to get their preferred policy outcomes.

(Here I am speaking only about the judicial philosophies labeled "conservative" and "liberal", and not about the merits of the Republican and Democratic political platforms in general.  It would be perfectly possible for someone with Democratic policy beliefs to be a judicial "conservative", it just tends not to happen in the current political environment.)

There are many examples where conservative judges say things like "I would prefer a different result if I were a legislator, but I think this is the law".  Liberal justices are much less likely to say things like that, and much more likely to appeal to vague or nebulous standards in order to get outcomes they obviously prefer personally.  In other words they are cheating.

I say this as somebody who has read most of the Supreme Court decisions written in the last decade, and several of the more notable ones before that.  Nor am I a knee-jerk conservative; when the court splits 5-4 I agree with the liberals about a quarter of the time.  For example, I strongly support habeas corpus rights even for suspected terrorists.  There are some constitutional principles I like, which might get less protection if the Court got more Republican appointees.

I do not doubt that there have been several times when conservative judges have, hypocritically, ruled in accordance with their conservative political principles (which they have no right to do) instead of in accordance with their claimed principle of interpreting the text fairly.  But it is better to sometimes fall short of a claimed standard of goodness, than not to have any standard at all.  "Living constitutionalism" is just a name for anything goes, it is not actually a coherent standard that one can fall short of.

I am not one of those partisan hacks who believes that somehow one of the two parties has an monopoly on dirty tricks and shoddy reasoning.  But I do believe that it makes a difference what our stated ideals are, and that a nebulous gas of constititual flexibility cannot act as a solid foundation for freedom, but principled reasoning from a black-and-white text can.

Now in the last 30 years, nobody has done a better job of promoting the rule of law than Justice Scalia, who has continually fought against all manner of sophistry, and given it the mocking it so richly deserves.  More than anything else his opinions, often his dissents, have made Originalism a viable interpretation in the academy.  He was not a "rebel without cause"; his cynicism was that of a wounded idealist, who stood for something quite definite.  His goal was not to revert decades of precedent back to some imaginary time when the Constitution was followed perfectly (although there are a few specific howlers he would have liked to kill).  Instead his goal was to contain the unprincipled exceptions, and to leave the law clearer than he found it.

Scalia was also a tremendously insightful person.  Hard as it is to imagine, given the current political environment, he was confirmed 98-0 by the Senate back in 1986.  Even jurists with radically different takes on the law recognized that he had some valid and interesting points to make about the law.  For example, his warnings on the dangers of relying too much on legislative history to decide what laws mean (if you do that, Congress will notice, and people will try to influence future legal decisions by means of their speeches before the house, subverting majority rule.)

True, his acid tongue made him some enemies.  In light of his professed Roman Catholic faith, some might wonder whether his bitter (and sometimes unfair) sarcasm was really compatible with a meek Christian spirit.  On the other hand, if we define Christianity by the behavior of Jesus in the Gospels, one could argue that it is actually very Christlike to react with hyperbolic outrage when you see people trying to legalistically distort the rules, in a way that subverts their actual meaning!

Yet Justice Scalia would be the first to admit that there is a distinction between the Kingdom of God and the kingdoms of this world.  In comparison with his faith, his life's work to to help improve the American system of law was of minor importance.  It would be wrong to reduce him as a person to his role as a judge.  His famous friendship with Justice Ginsburg (see elephant below) shows him to have been broad enough to like those who disagreed with his judicial philosophy.

Goodbye, St. Antonin Scalia, and God rest your soul.  I will miss you.

Posted in Politics | 11 Comments

Ratio Christi talk [UPDATED]

This Monday, I will be giving a talk on "Science and the Resurrection" at Rutgers University.  In my talk, I will describe the basic principles of Science and compare them to Christianity to see how it measures up.  Then there will be a Q&A period.  It is being hosted by a chapter of Ratio Christi, an apologetics organization (their blog is here).

The talk will be on this upcoming President's Day, Monday evening, Feb 15 at 8pm in the Busch Student Center, Room 174.  This is located in the Busch campus of the New Brunswick campus of Rutgers.  Non-students are welcome to attend, and I think there is going to be pizza as well.  So if any of my readers happen to be in the neighborhood, you are welcome to come!

However, if you do plan to come, please register at the Facebook event page, so that they can have an approximate estimate of how many people to prepare for.  This will prevent us from needing to pray for a miraculous multiplication of food.

The talk is free.  However if you plan to park your vehicle in Lot 51 right next to the Busch Student Center you will need to get a parking permit for $5 from this website.  Alternatively, you can park for free in Lot 48 by the Vistor Center, and then walk 15 minutes north.

Posted in Talks | 8 Comments

Black Swans

A reader asks:

After a lot of reading, I've come to realize that the Bayes factor for the resurrection is quite high that if the event in question wasn't a supernatural occurrence, no rational person would think that the event did not occur. However, I've stumbled upon an argument by a philosopher who argues against the resurrection argument by using bayes theorem as well.

I've included a link of a debate where he presented his arguments in a long mathematical form in case you wanted to refer to it, but the gist of his argument is that the prior probability of God raising Jesus from the dead is always going to be magnitudes lower than that of God *not* raising Jesus from the dead. He is a theist himself, so he argues that he does't follow Hume in his argument against miracles, but rather he claims to be making an argument from natural theology: Every experimental confirmation of a scientific theory that we observe counts as evidence of the fact that God created and ordered the world in an orderly and causally closed way and does not intervene. In another presentation, he puts forth a statistical inference of this sort(I didn't copy and paste it so it might be a flawed syllogism, but I think it captures the gist of what he's saying):

(1) For every dead person, 99.9999...% of the time God does not intervene

(2) Jesus died

(3) Therefore, we can be 99.9999....% certain that God did not intervene in Jesus' death

He argues that for every instance of a "miracle" being reported, we have experimental confirmations of the laws of nature of a much higher frequency. So, he concludes from all of this that the prior probability that God would raise Jesus from the dead is so astronomically low that however high our Bayes factor is *for* the resurrection, the prior improbability of God wanting to intervene with the laws of nature is always going to be much higher such that the posterior probability (or final probability) of the resurrection is always going to be really low.

This argument is unlike any other because it doesn't assume naturalism, in fact it assumes theism. It doesn't assume that God cannot or could not have raised Jesus from the dead, but that it is highly improbable that God would have intervened.

As a scientist, what do you think of this argument (Since your career involves seeing confirmations of God's love for order in the universe everyday?)

https://www.youtube.com/watch?v=XCCmDqQ7qgI
[Dr. Robert Cavin vs. St. Calum Miller]

(He presents his argument from the 14th minute to the 30 minute mark)

What do you think of this argument?

(1) For every American citizen who lives during a presidential election, 99.9999...% of the time they do not become President.
(2) St. Barack Obama was a living American citizen in 2008.
(3) Therefore, we can be 99.9999....% certain that Barack Obama did not become President of the United States.

Clearly there is something wrong with this argument.  What's wrong with it is that Obama is not a randomly selected [or typical] citizen.  He belonged to a special class of people who is unusually likely to become President (a Senator, a charismatic speaker, wanted to become president, went on to receive the nomination of a major party...).  Since we have additional information, it is fallacious to use the background rate to decide the chances of him becoming President.  [And of course, we also have excellent posterior evidence, coming from the period after the election, that he did in fact become President.]

In the same way, Jesus is not a randomly selected human being.  He was a person who claimed to be the Jewish Messiah and the Son of God, fulfilled certain prophesies, did other miracles, and so on.  So the prior probability that God will dramatically intervene shortly after Jesus' death, is a lot larger than the probability that he will dramatically intervene when one of my uncles dies.  (Although, actually God DOES plan to raise 100% of human beings from the dead when Jesus returns, the difference in the case of Jesus is that he did it right away.)

The reasonable question is, what is the prior probability that God would make some special person to be the Messiah and raise that person from the dead?  (Just like, we could ask what is the probability that any person becomes President.)  Once we believe that somebody is going to be President, or that somebody is going to be the Messiah, we shouldn't be all that surprised to learn that any one particular person turns out to be President, or the Messiah, so long as they are qualified for the position.)

The argument in the video is even more fallacious.  First of all, I should say you should be VERY SUSPICIOUS of any person who starts their argument by making concessions that huge to the other side. Factors of 10^{297} are ridiculous numbers that should never be thrown around in almost any real life situations, and if he concedes something that ridiculous to his opponent, he ought to be guaranteed to lose, plain and simple.  He's like a stage magician who makes a big show of how he's blindfolded and his hands are tied behind his back and so on.  You can be very sure there's a trick somewhere, and that all that patter is there to distract you from the way he actually does the trick.

(The other guy, St. Calum Miller, is also making a fallacy, when he quotes a liklihood factor of 10^{43} for the Resurrection; this number incorrectly assumes that the evidence from each apostle's testimony counts independently.  The odds of a group conspiracy to lie are certainly bigger than 10^{-43}, which is an astronomically tiny number.  No real historical event is ever that certain.  That being said, he's right that the evidence for the Resurrection is extremely strong, as far as historical evidence goes!  It's just that nothing in life is really that certain.)

By the way, Cavin is derisive about St. Craig Keener's statement that there are a hundred million miracle reports, but this is not actually all that silly of a number.  If 2% of the world's population claims to have seen a miracle, that's 140 million right there, assuming none of the events are redundant.  So I don't think this claim can be dismissed quite so easily.

Anyway, in his argument, Cavin compares the likelihood ratios of L (the laws of nature are always valid), M (at least once, God acts miraculously), and ~(M v L) (neither one is true).  The last comes in because L and M are not exhaustive, since there might be neither laws of nature nor divine interventions.

The actual fallacy in his argument is displayed on the slides at the 33:45 mark of the video.  He claims that ~M (i.e. not M, which would include both L and ~(M v L)), because it is maximally unspecific and does not necessarily predict that there are any laws of nature at all, is disconfirmed every time anything happens in accordance with a natural law.  Then he claims that M, because it only adds to ~M the claim that at least one miracle happens, is at least as bad off as ~M!

But this is clearly quite absurd.  Not even the most ardent believer in the supernatural thinks that every time I drop a ball, there is a 50% chance that it will miraculously fall up instead of down.  Not even the most tempestuous skeptic really halves their chance that God does miracles, every single time they see a ball drop!

Obviously, miracles don't happen all the time.  What Christians actually believe is:

M': the usual laws of Nature are almost always valid, but on rare occasions (especially at important moments in salvation history) God intervenes to perform miracles.

(By important moments in salvation history, I mean things like: critical events in ancient Israel, the ministry of Jesus and the Apostles, times when missionaries preach the Gospel to a group of people for the first time, or sometimes for the conversion of a particular individual.  Aside from this, sometimes God heals people in answer to prayer and so on, but my point is that miracles are not randomly tossed into history like darts shot into a dartboard; they tend to happen in specific kinds of situations.)

Now M' clearly does predict that balls will normally fall down.  So it is just as good as L (the laws of nature always hold) for purposes of everyday life.  So his huge probability factor of 2^{gazillion} goes away.  But M' is better than L in situations like Jesus' ministry, where there is significant historical evidence that miracles really occurred.

Incidentally, this implies that he was quite wrong to rank the probability of ~M (no miracles) so low.  Even though it is a very unspecific hypothesis, we shouldn't consider randomly selected examples of ~M, instead we should focus on whatever are the most plausible versions of ~M.  And clearly, the most plausible versions of ~M are scenarios where the laws of nature are followed, at least most of the time.  In fact, the most plausible version of ~M is L.  Thus he is guilty of a clear-cut violation of the laws of probability theory here, since he simultaneously argues that ~M is very improbable, and L very probable, even though L actually implies ~M!  This is an example of the Conjunction Fallacy:

https://en.wikipedia.org/wiki/Conjunction_fallacy

Had St. Miller realized this, he could have totally eviscerated Cavin's argument in a couple seconds, in a way that would have been completely humiliating and decisive.  However as far as I can tell (I skimmed through his remarks very quickly) he mostly just ignored that argument and presented the positive case for the Resurrection.

Similarly, the most plausible version of M is not a scenario where God intervenes half the time we do a science experiment (I agree THAT is ruled out), instead it is a scenario along the lines of M' or similar.

To give another illustration, consider the famous proposition

W: All swans are white.

For a long time, Europeans noticed that every swan they ever looked at was white.  You could take this as huge experimental confirmation for W.  Every time you look at a swan, W predicts it is white and therefore is confirmed by a factor of at least 2 over ~W (and that's if there was only one other color besides white), which says the swan could be any color.  Since there were millions of observations of white swans, doesn't this mean that W is a gazillion times more probable than ~W?

And yet, there are black swans!
https://en.wikipedia.org/wiki/Black_swan

The fallacy is to assume that the most plausible version of ~W is that each individual swan's color is random.  In fact all the swans in Europe are white; the black swans are not only rarer, they live in Australia.  So it is no surprise the Europeans didn't notice them until they came to Australia.  So actually ~W was almost as good of a theory as W, aside from being slightly more complicated.

As a scientist, what do you think of this argument (Since your career involves seeing confirmations of God's love for order in the universe everyday?)

That is indeed the exact point.  We worship a God who loves order, and therefore he does not do miracles haphazardly.  No scientific experiment can ever be evidence against miracles, unless you have some theological reason to believe that God would have been likely to intervene in that particular experiment.  For most experiments, the opposite is true—it would frustrate the ability of his creatures to learn about the world, without providing any particular benefit.

(I am assuming here that the goal of the particular experiment was not specifically to look for evidence of God, as in e.g. prayer experiments.  In that case, we all know that God does not usually respond to challenges to show his existence by striking a nearby tree with a lightning bolt.  The fact that he doesn't do that may be evidence against a certain sort of deity, but even there I don't see what is gained by dressing up the challenge with a veneer of science, when the whole point is simply to challenge God to act.)

Note: I only answered this question as a special favor to the particular reader in question.  I hate watching long web videos, and I tried to watch as few seconds of this one as I possibly could, to answer the question accurately!  I much prefer to interface with texts, which can be read at the speed I want, and then quoted accurately using the copy-and-paste function!

[Edit: In an earlier version of this blog post I misspelled the name "Cavin"; I apologize for this mistake.  Also, I would like to make it clear that, except in the portions of this blog post where I respond directly to the video debate, I am responding to the arguments as presented by my interlocutor, without asserting that it is necessarily an accurate summary of Cavin's position.

A few other changes made after the fact are in square brackets.]

Posted in Reviews, Theological Method | 20 Comments

Quantum Mechanics II: Decoherence & States

Strictly speaking, most of the other rules about QM are already implicit in what I've already said.  But a few implications of this setup are worth pointing out.

First note that, in QM, the "state" includes information about every single object in the system.  So, when you add up the different histories, they only interfere if the final states are exactly the same in every respect.  If even one tiny particle is in a different place than it otherwise would be, then they don't interfere.  In that case, you just add up the probabilities normally.

This is why measurement is such a significant thing in QM.  If you try to catch out Nature by explicitly measuring which slit the particle went through, then YOU are now different as a result of you knowing which slit it went through.  As a result, the two histories don't interfere.  But it needn't be a person which does the "measurement".  Even if you refuse to look at it, the detector being different still prevents the interference from happening.  As far as we know experimentally, there is no special relationship between consciousness and QM (although some people have proposed interpretations of QM in which there is a connection between the two.).

Usually, once histories become sufficiently different from each other, for a long enough period of time, their random interactions with the environment will tend to be different, so that the chances of getting everything perfectly the same become tiny, and the histories won't interfere anymore.  This phenomenon is called decoherence.  People argue about what this tells us about the interpretation of QM, but the phenomenon itself can be studied in the laboratory, so my use of this word should not be regarded as an endorsement of any particular interpretation.

Secondly, if you have two or more distinct states, then it's possible to take a quantum superposition of the two states, formed by adding them up with complex coefficients.  For example, if X and Y are two distinct states, then

(\mathbf{X} + \mathbf{Y}) / \sqrt{2}

or

(\mathbf{X} - \mathbf{Y}) / \sqrt{2}

or

(2\mathbf{X} +i \mathbf{Y}) / \sqrt{5}

are all equally valid states!  (The reason for the square root in the denominator, is to make it so that, by the Born Rule, the total probability of the state is still 1.)  These states are just as much valid states as X or Y themselves would be.

The possibility of quantum superpositions is implicit in the quantum probability rules, since if you start with a particular state A, in general it will evolve to a superposition of different states as time passes.  And there's no particularly good reason you couldn't also have started out the experiment with a quantum superposition.

(Note that if we take any state like (\mathbf{X} + \mathbf{Y}) / \sqrt{2}, and we multiply it by a phase (a number on the unit circle of complex numbers, e.g. i, or -1, or (1+i)/\sqrt{2}) then we can't tell the difference between that and the original state in any way!  That's because, when we work out the patterns of interference, we only care about the relative phases between different histories, not the absolute phase of the whole system.  So it's good to remember that there is a slight redundancy in our description here: two states that differ by a phase are really the same state.)

Now if we have a system with N possible states, then we can imagine a higher dimensional geometry consisting of all possible superpositions of these N possible states (including, for mathematical convenience, those for which the probability doesn't add to 1).  This is called the Hilbert Space of that system.  It is a kind of vector space with N complex dimensions, which means in terms of real numbers it's a 2N-dimensional space.  But don't worry about these details for the moment.

(It's kind of hard to visualize a Hilbert space when N is greater than about 2, but it's still very useful mathematically!)

The simplest nontrivial Hilbert Space is the one with N = 2 states.  (I'll give a physical example in a moment.)  This would normally involve a 4-dimensional space, but to keep things as simple as possible, I give you permission to ignore the bit about complex numbers and just think about a 2-dimensional plane.  (This is the space of all states of the form

a\mathbf{X} + b\mathbf{Y}

where a and b are now real numbers.)  Then we can think of X as a unit vector pointing along the x-axis, and Y as a unit vector pointing along the (wait for it...) y-axis.

Perhaps a picture will help:

The Hilbert space for a system with 2 states.

As you can see, the Hilbert space has an origin, which is the point in the middle which represents "zero".  Each state is a represented by a vector coming out of the origin, pointing in some direction.  (But remember that -X is really the same state as +X, since they differ by a -1 phase.  I didn't draw -X on the picture, but if I had it would be 180º around from X.)  The Born Rule tells us that length = total probability squared.  That means that in order for a vector to be a state-in-good-standing, it needs to be length 1.  (In other words, by the Pythagorean Theorem, the sum of the squares of its (x,y) coordinates needs to add up to 1).  So don't ask me what the physical meaning of the "zero" vector is, since it doesn't have one.

A physical example of an N = 2 state system would be the polarization of a photon coming straight at you from your computer screen.  Light can be either horizontally polarized (the X state, corresponding to an electric field that points in the x direction) or it can be vertically polarized (the Y state, corresponding to an electric field that points in the y direction).  Now since physics is rotationally symmetric, it's obvious that if light can be horizontal or vertical, it can also be diagonal.  So you might have naïvely thought the photon would have infinitely many possible states.  And in a sense this is true, but each of these diagonal states is really just a quantum superposition of the X and Y states.

Yet on a plane, the choice of axes is arbitrary.  You can rotate the coordinate system by 45º, and it would be just as good as the original coordinate axis.  In the same way, we are currently thinking of X and Y as the two possible states of the system (with every other state being a superposition of X and Y)—but this is an arbitrary choice!  We could just as well say that every state is a superposition of (\mathbf{X} + \mathbf{Y}) / \sqrt{2} and (\mathbf{Y} - \mathbf{X}) / \sqrt{2}!  So actually every state is a quantum superposition, of certain other states.

Although the choice of coordinate axis is arbitrary, it is important that the states you pick are all "orthogonal" to each other (i.e. at right angles in the Hilbert space).  That is what tells you that it represents a set of  mutually exclusive possibilities.  Any such set of N orthogonal states is called a basis of the Hilbert space.  (The plural of "basis" is "bases", pronounced BASE-EES.  Just like the plural of "index" is "indices".)  A basis gives the possible set of outcomes for some particular way to measure the system.

For example, suppose we start with a diagonal photon in the (\mathbf{X} + \mathbf{Y}) / \sqrt{2} state, and we measure it to see whether it is horizontally or vertically polarized.  (Maybe by passing it through some kind of material in which these two polarizations follow different trajectories.)  What happens?

Well, people disagree about interpretation (what is ultimately going on), but everyone agrees on the practical set of rules you'd use in the laboratory.  We just look at the state (\mathbf{X} + \mathbf{Y}) / \sqrt{2}.  It has an amplitude of 1/\sqrt{2} to be X, and also 1/\sqrt{2} to be Y.  By the Born Rule, we've got to square these numbers, so we get a 1/2 chance for it to be horizontal, and a 1/2 chance for it to be vertical.

Let's suppose it turns out to be vertical (the Y state).  Then from now on, the particle behaves just as if it had been in the Y state all along.  (This is called "projection" or sometimes "collapse of the wavefunction"; but see my remarks on decoherence earlier in this post.)  For example, if we measure it a second time to see if it is in the Y state.  If we check to see whether it is in the X state, it is definitely not.

But now we can ask a separate question: is it in the (\mathbf{X} + \mathbf{Y}) / \sqrt{2} state, or the (\mathbf{Y} - \mathbf{X}) / \sqrt{2} state?  This corresponds to sending it through a different kind of filter, which discriminates between the two 45° diagonal polarization choices.  We would then find a 1/2 chance of it being the former, and a 1/2 chance of it being the latter.

Supposing it turns out to be (\mathbf{Y} - \mathbf{X}) / \sqrt{2}, this is a bit paradoxical.  Since if we had just started off asking whether the (\mathbf{X} + \mathbf{Y}) / \sqrt{2} photon was in the (\mathbf{Y} - \mathbf{X}) / \sqrt{2} state, Nature's answer would have been "Nope.  Definitely not.  Those states are orthogonal and therefore if it's the one, it's not the other!"

But somehow, merely by answering a series of questions about the photon's polarization, we managed to trick Nature into converting the photon from its original polarization to one 90° away, which is inconsistent with the first.  By measuring the photon we have affected it!

So we see that, somehow, we can get the photon to be definitely - or | polarized, or definitely / or \ polarized.  But we can't get both of these things to be definite simultaneously.  This is an uncertainty relationship.  It's analogous to the "Heisenberg uncertainty principle" where you can't measure position and momentum at the same time; so that measuring one makes the other uncertain.  (Although it's not exactly the same, since position and momentum are continuous variables, while each polarization choice is a yes-no question.)

In the case we are considering, we're been lucky that the Hilbert space is directly related to two dimensions of the physical space.  That means that the rotation of axes in the Hilbert space is the same thing as a rotation of physical space.  In general, however, we are not so lucky and the Hilbert space is more abstract.  But it is still true that there are a bunch of different possible bases of the Hilbert space, that are related by rotations in the Hilbert space.  (Since the Hilbert space is complex, we are really only interested in those rotations that don't mess with the notion of "multiplying-by-i".  These are called unitary transformations.)

As long as I'm talking about complex numbers, I should mention that there's also such a thing as circularly polarized photons, which involve complex superpositions like (\mathbf{X} \pm i \mathbf{Y}) / \sqrt{2}.  But most of the bizarreness of superpositions can be illustrated without thinking about complex numbers.

Posted in Physics | 28 Comments