Reasonable Unfalsifiable Beliefs

by Aron Wall Posted on April 2, 2014

In a previous post, I argued that falsifiability is not the be-all and end-all of Science.   There are valid scientific beliefs that are not falsifiable.

However, there is something to the idea that beliefs should be falsifiable.  One way to make this precise is to use Bayes' Theorem.  This is a rule which says how to update your probabilities when you get some new evidence E.  It says that your belief in some idea X should be proportional to your prior probability (how strongly you believed in before the evidence), times the likelihood of having measured the new evidence given X.   (You also have to divide by the probability of having measured the new evidence, but this is the same no matter what X is, so it doesn't affect the ratio of odds between two competing hypotheses X and Y.  It's just needed to get the probabilities to add up to 1).  As an equation:

P(X|E) = P(X) P(E|X) / P(E).

We won't actually plug any numbers into this equation in this post.  Instead, I'll just point out a general property which this equation has.  Suppose you are about to perform an experiment.  On average, you expect that your probability is going to be the same after the experiment as before.

For example, suppose you believe there is a 1/50 chance that there exists a hypothetical Bozo particle (I just made that up right now).  And suppose you perform an experiment which has a 50% chance of detecting the Bozo if it exists.  Just for simplicity in this example let's suppose there are no false positives: if you happen to see the Bozo, it leaves a trail in your particle detector which can't be faked.

There are two possible outcomes: you see the Bozo or you don't.  In order to see the Bozo, it needs to (a) exist and (b) deign to appear, so you have a 1% chance of seeing it.  In that case, the probability that the Bozo increases to 1.

On the other hand, you have a .99 chance of not seeing the Bozo.  In that case, your probabilty ratio goes from 49:1 to 98:1 since the Bozo exists possibilities just got halved.  This corresponds to a 1/99 probability that the Bozo exists.

On average, your final probability is (.01 \times 1) + (.99 \times 1/99) = .02.  Miraculously, this is exactly the same as the intitial probability 1/50 of the Bozo existing! Or maybe it isn't so much of a miracle after all.  On reflection, it's pretty obvious that this had to happen.  If you could somehow know in advance that performing an experiment would tend to increase (or decrease) your belief in the Bozo, that would mean you that just knowing that the experiment has been done (without looking at the result) should increase or decrease your probability.  That would be weird.  So really, it had to be the same.

We call this property of probabilities Reflection, because it says that if you imagine yourself reflecting on a future experiment and thinking about the possible outcomes, your probabilities shouldn't change as a result.

Now Reflection has an interesting consquence.  Since on average your probabilities remain the same, if an experiment has some chance of increasing your confidence in some hypothesis X, it must necessarily also have some chance of decreasing your confidence in X.  And vice versa.  They have to be in perfect balance.

This means, you can show that it is impossible for an observation to confirm a hypothesis, unless it also had some chance of disconfirming it.  VERY ROUGHLY SPEAKING, we could translate this as saying that you can't consider a theory to be confirmed unless it could have been falsified by the data (but wasn't).

Even so, there are a number of important caveats.  In some situations in which we can and should believe things which are, in various senses, unfalsifiable.  This occurs either because (a) The Reflection principle doesn't rule them out, or (b) the Reflection principle has an exception and doesn't apply.  Here are all the important caveats I can think of:

  1. It could be that the probability of a proposition X is already high (or even certain) before doing any experiments at all.  In other words, we know some things to be true a priori.  For example, logical or mathematical results (such as 2+2 = 4) can be proven with certainty without using experiments.  Similarly, some philosophical beliefs (e.g. our belief that regularities in Nature suggest a similar underlying cause) are probably things that we need to believe a priori before doing any experiments at all.
    .
    Propositions like these need not be falsifiable.  This does not conflict with Reflection, because that only applies when you need to increase the probability that something is true using new evidence.  But these propositions start out with high probability.
    .
  2. It could be that a proposition has no reasonable chance of being falsified by any future experiment, because all the relevant data has already been collected, and it is unlikely that we will get much more relevant data.  Some historical propositions might fall into this category, since History involves unrepeatable events.  Such propositions would be prospectively unfalsifiable, but it would still be true that they could have been falsified.  This is sufficient for them to have been confirmed with high probability.
    .
  3. Suppose that we call a proposition verified if its probability is raised to nearly 1, and falsified if its probability is lowered to nearly 0.  Then it can sometimes happen that a hypothesis can be verifiable but not falsifiable.  The Bozo experiment above is actually an example of this.  There is no outcome of the experiment which totally rules out the Bozo, but there is an outcome which verifies it with certainty (*).
    .
    This doesn't contradict Reflection.  The reason is that Reflection tells us that you can't verify a hypothesis without some chance of lowering its probability.  But it doesn't say that the probability has to be lowered all the way to 0.  In the Bozo case, we balanced a small chance of a large probability increase against a large chance of a smaller probability decrease.
    .
    The Ring Hypothesis was another example of this effect.  We have verified the existence of a planet with a ring.  Had we looked at our solar system and not seen a planet with a ring, this would indeed have made the Ring Hypothesis less likely.  But not necessarily very much less likely.  Certainly not enough to consider the Ring Hypothesis falsified.
    .
  4. Suppose that, if X were false, you wouldn't exist.  Then merely by knowing that you exist, you know that X is true.  But X is unfalsifiable, because if it were false you wouldn't be around to know it.
    .
    For example, no living creature could ever falsify the hypothesis that the universe permits life.  Even though it didn't have to be true.  Nor could you (in this life) ever know that you just lost a game of Russian Roulette.
    .
    This type of situation is an exception to the Reflection principle.  The arguments for Reflection assume that you exist both before and after the experiment.  (You can also construct counterexamples to Reflection involving amnesia, or other such funny business.)

To conclude, these are four types of reasonable beliefs which cannot be falsified.  It is a separate question to what extent these types of exceptions tend to come up in "Science" as an academic enterprise (as opposed to other fields).  But I don't see any good reason why these exceptions can't pop up in Science.

(*) Footnote: Some fictitious person (let's call her Georgina) might say that the Bozo is still falsifiable since nothing stops us from doing the experiment over and over again, until the Bozo is either detected or made extremely improbable.  Hence, Georgina would argue, the Bozo IS falsifiable.

My answer to Georgina is that it actually depends on the situation.  Maybe the Bozo experiment can only be done once.  Maybe (since I'm making this story up, I can say whatever I want) the Bozo can only be detected coming from a particular type of Supernova, and it will be millions of years before the next one.  More realistically, maybe the Bozo is detected using its imprint on the Cosmic Microwave Background, and the phenomenon of Cosmic Variance means that you can't repeat the experiment (since there is only one observable universe, and you can't ask for a new universe).  More realistically still, maybe the experiment costs 100 billion dollars and Congress can't be persuaded to fund it more than once.

Georgina might not like the last example very much, since she might say that all she cares about is that the Bozo is in principle falsifiable.  Perhaps as a holdover from logical positivism, the Georginas of this world often talk as though this makes some kind of profound metaphysical difference.  But it's not clear to me why we should care about falsifiability in principle.  The only thing that really helps us is falsifiability in fact.

If a critical experiment testing the Bozo will not be performed until next year, for purposes of deciding what to believe now, we should behave in exactly the same way as if the experiment could never be done.  Experiments can't matter until we do them.

Posted in Scientific Method | 5 Comments

When God kills the Innocent

by Aron Wall Posted on March 8, 2014

A Christian reader named Paul wrotes to me from New Zealand with the following common question.  With permission, I am posting his question and my answer on my blog.

St. Paul writes:

A few months ago I discovered your blog via the Biologos website. It has been a real encouragement for me to read your articles and I can honestly say that I enjoyed everything that I've read.

Anyway, a Church friend and I have been meeting up every few weeks to have discussions about tricky issues in Christianity and something that has come up (and was always bound to...) is the depictions of God in the Old Testament. In the Old Testament, God is often depicted as acting violently and sometimes in ways that can seem barbaric. For example, God gives instructions for the Israelites to kill people. Likewise, an atheist friend of mine was shocked when I referred to God as "just" because he had just read about the exodus and the plagues.

The issue for me is not that God doesn't have a right to judge/ punish guilty people (for example the Canaanites), but the fact that innocent people are also involved in some of these situations. For example children and babies. In some verses they seem to be explicitly mentioned (i.e. 1 Samuel 15:3). I realise this is only a single example, but there are one or two other examples that are quite easy to find.

The most common response of Christians seems to be that God created all of us and therefore He can do whatever He wants. I agree that God is sovereign, but these actions seem inconsistent with the nature of God revealed clearly in Jesus.

I have some ideas about what to make of it all, but I thought that I would ask you what you make of these sorts of verses? I realise that you must be very busy (and you don't know me!) so please don't feel obligated to reply! However, if you have the time and the inclination I would really appreciate it.

My reply:

This is a tricky problem in theology, isn't it!  But it isn't just an Old Testament vs. New Testament thing.  The following verses are all God speaking in the Old Testament:

  1. "I, the Lord your God, am a jealous God, punishing the children for the sin of the parents to the third and fourth generation of those who hate me, but showing love to a thousand generations of those who love me and keep my commandments." (Ex. 20:5-6)
    .
  2. "My angel will go ahead of you and bring you into the land of the Amorites, Hittites, Perizzites, Canaanites, Hivites and Jebusites, and I will wipe them out." [including the children, as other parts of Scripture make clear] (Ex. 23:23)
    .
  3. "Fathers are not to be put to death for their children or children for their fathers; each person will be put to death for his own sin.  Do not deny justice to a foreigner or fatherless child, and do not take a widow's garment as security.  Remember that you were a slave in Egypt, and the Lord your God redeemed you from there. Therefore I am commanding you to do this." (Deut. 24:16-18)
    .
  4. "Yet you ask, 'Why does the son not share the guilt of his father?' Since the son has done what is just and right and has been careful to keep all my decrees, he will surely live. The one who sins is the one who will die. The son will not share the guilt of the father, nor will the father share the guilt of the son. The righteousness of the righteous will be credited to them, and the wickedness of the wicked will be charged against them." (Ezekiel 18:19-20)

The tension lies within the pages of Hebrew Scripture itself.  We have to understand in what sense all of these Scriptures can be true.

The Righteousness of God

Let me start by demolishing the idea that "God created all of us and therefore He can do whatever He wants."  If this were true, there would be no meaning in saying that God is just and righteous in how he treats us.  It wouldn't allow us to predict anything whatsoever about what he would do.  Yet St. Abraham—our father in faith—pleads for Sodom and Gommorah by asking: "Far be it from you to do such a thing--to kill the righteous with the wicked, treating the righteous and the wicked alike. Far be it from you! Will not the Judge of all the earth do right?" (Gen. 18:25).  God does not respond by saying "Whatever I do is just by definition".  Rather, he grants Abraham's requests, and goes beyond them to ensure that, in this case, the innocent are not punished alongside the guilty.  The fact that God is just, implies that there are some things which he won't do—because they are unfair.

Because of this, I reject any "divine command theory" in which morality is simply a matter of what God happens to arbitrarily command.  No, morality is rooted in God's own character, in his essential and immutable goodness and love!

As St. Geroge MacDonald wrote:

If you say, That may be right of God to do which it would not be right of man to do, I answer, Yes, because the relation of the maker to his creatures is very different from the relation of one of those creatures to another, and he has therefore duties toward his creatures requiring of him what no man would have the right to do to his fellow-man; but he can have no duty that is not both just and merciful.  More is required of the maker, by his own act of creation, than can be required of men. More and higher justice and righteousness is required of him by himself, the Truth;--greater nobleness, more penetrating sympathy; and nothing but what, if an honest man understood it, he would say was right.  If it be a thing man cannot understand, then man can say nothing as to whether it is right or wrong.  He cannot even know that God does it, when the it is unintelligible to him.  What he calls it may be but the smallest facet of a composite action.  His part is silence.  (Unspoken Sermons)

St. MacDonald himself was famously unwilling to accept any doctrine (however much theologians might claim it was supported by Scripture) that would paint God's character in a bad light.  I myself take a more conservative point of view regarding the reliability of Scripture, but this does not change the fact that, as I wrote in another post:

The doctrine that God is good is more fundamental even than the doctrine that the Scriptures are inspired.  So that if it were necessary to choose between them (which it is not!) one should certainly pick the former over the latter.  This is the faith of Abraham, who lived before any part of our current Bible was written.

Even Abraham, when he God asked him to sacrifice his son Isaac, started to obey God only because he believed that God intended it for good.  As the New Testament interprets the story:

By faith Abraham, when God tested him, offered Isaac as a sacrifice. He who had embraced the promises was about to sacrifice his one and only son, even though God had said to him, “It is through Isaac that your offspring will be reckoned.” Abraham reasoned that God could even raise the dead, and so in a manner of speaking he did receive Isaac back from death.  (Hebrews 11:17-19)

And this interpetation can be shown to be reasonable in the original text based on Abraham's own words:

He said to his servants, “Stay here with the donkey while I and the boy go over there. We will worship and then we will come back to you.”  (Genesis 22:5, emphasis added)

In other words, Abraham believed that Isaac would somehow be returned to him, even after having been sacrificed.  He made the decision to interpret even God's most terrible command in a way that was consistent with his goodness, and faithfulness to his promises.  In this way he is a microcosm of our decision, whether to obey God even when it may (falsely) appear that he is acting malevolently towards us, or another person.

Furthermore, as Christians, we interpret the entire Bible (as well as all the evil that appears in the world) in light of the love which Jesus showed on the Cross.  Jesus is the highest revelation from God, the place where God's character becomes most clear.  Every other place in the Bible (especially the Old Testament, where God was revealing himself in a more imperfect way to people at a lower stage of spiritual development) must be interpreted in light of this.

So in light of all this, what do we make of passages in which, e.g. God orders the genocide of various ancient Caananite tribes?

Wrestling with the text in silence is one possible answer, as St. MacDonald suggests above.  But I think there are at least a few things that can be said, from our own limited human perspective.  (If nothing else, we can always remind ourselves just how limited our own perspective must be, in comparison with that of God, who sees everything!)  As the sovereign Lord who loves humankind, God's orders to kill simply cannot be regarded as being at all similar to that of a human murderer.  This is true for at least four reasons:

I. God has rightful authority over human life, humans do not

God IS the ruler of the universe.  This gives him the authority to make decisions which ordinary human beings are not allowed to make.  Just like an earthly Governor or Judge has authority to do some things which ordinary citizens don't have the right to do, God has the authority to do anything, i.e. any type of act.  For example, everything belongs to God, so when he takes things from us it is not stealing, but doing what he likes with his own property.  Similarly, if God kills people it is not murder, because our lives belong to him (Deut. 32:39).

(This does not, I think contradict the point of the previous section, in which I rejected the theory in which morality reduces to arbitrary divine commands.  The scope of authority is different from how one uses that authority.  God has the authority to do anything, precisely because, since he is perfectly good, he never abuses this authority, but only does what is just and right.)

Note that, as the ruler of the universe God actually kills everyone.  All people are mortal, some of them die young, and God is responsible for this state of affairs.  Sometimes he does it miraculously in order to make a special point, but more often it he causes it to happen naturally.  Before I ask whether I can trust a God who killed the Caananite children, I first need to ask whether I can trust a God who will kill ME.  As Christians, we trust that God is using death as a tool in order to turn us into the people he wants us to become.  Partly, we trust him because he came to Earth as Jesus, and died for us on the Cross, so he isn't asking us to suffer anything which he hasn't gone through himself.

II. God is always benevolent, human killers are not

God's motivations for killing people are not the same as that of a human murderer.  Most of the time, people kill other people out of hatred, because they want something bad to happen to them, or because they don't care about them.  But God solemnly swears to us that this is not why he does it. "As surely as I live, declares the Sovereign Lord, I take no pleasure in the death of the wicked, but rather that they turn from their ways and live" (Ezekiel 33:11)

To illustrate this: Suppose that a baby is very sick and a surgeon cuts his chest open in order to operate on his heart and save his life.  Now the surgeon's act of cutting open the baby cannot be regarded as being in the same moral world as if he were a Nazi, cutting open the baby's chest cavity out of callous indifference.  It is in fact totally the opposite because it is done with the intention of healing, rather than harming, the innocent.

Now Jesus is "the Resurrection and the Life" (John 11:25).  So when he chooses to take a child to himself (ending its earthly life), this is because he is able to give it a heavenly life which is far superior to anything it would have on Earth, in the bosom of the Father who cares for him.  If we have faith in God, then we must believe that whenever he takes the life of an innocent person, he is much more like the diligent surgeon, then he is anything like the Nazi.  In other words, we believe that he is acting for the good of the person concerned.

Since we on this side of the curtain of death and can only speculate about what is on the other side, we do not have any such authority over the lives of our felow human beings.  God expects us to obey the commandment "Do not murder", which means that, apart from exceptional situations (just war, punishment for crime, etc) we are not to kill other human beings.  However, this situation does not obtain in biblical situations where God himself orders people to kill, since there God is exercising his own authority over life and death, and is using the humans involved only as his instruments.

III. God is incorruptible, humans are not

God is unchangable.  If you or I killed somebody, we would become more violent and hateful people who would be more likely to kill someone else.  Whereas God's character, being eternal, cannot be corrupted.  Paradoxically, this means that a perfectly good being may be more likely than a good human to do bad things in order to produce good consequences.  Unlike us, he doesn't need to worry about his motivations being wrong, or it producing bad habits of character.

(This consideration does not apply completely to cases in which, rather than taking a human life himself, God orders another person to do it; since that human being could certainly be norally corrupted.  In this case, it would have been important to make sure that the humans are acting solely based on obedience to God's command, and not for the sake of the benefits they might receive.  This may be why God strictly commanded the Israelites not to take any plunder from the Canaanite cities they conquered—a rule that was enforced in Joshua 7—in order to make it clear that they were acting as agents of divine wrath on those cities, and not for personally selfish reasons.)

IV. God has complete knowledge, humans do not

God is omniscient, so he knows when a group of people have become so wicked that it would be bad for them, and for their children, and for the rest of the world, if they remain alive to keep sinning.  For example, the Canaanites sacrificed their children as part of their religion, and if God hadn't put an end to them, we might still be doing that today.  It may seem ironic that God also ordered that their innocent children be killed, but remember that they would not have remained innocent if they had been able to come to maturity.  Instead they went to Heaven, which might not have been possible if they had been corrupted by the religion of their parents.

We humans, on the other hand, have a very limited ability to guess the future.  Therefore no human being could ethically order a genocide on his own cognizance, because we are never really in a good position to be morally certain that the speculative goods arising from the elimination of a culture outweigh the immediate and obvious evils involved in killing a large cultural group.  Furthermore any such decision would almost certainly be tainted by prejudice and racism, rather than being an act of impartial justice.

Unlike humans, God is free from such favoritism (Acts 10:34), and only acts in ways that he knows are just and merciful (even if his reasons may sometimes be obscure to us).

Group vs. Individual Justice

This brings us back to the group justice vs. individual justice question.  Ultimately, I believe God is committed to bring justice and vindication to every innocent person, including those who were victims of bad circumstances.  On the other hand, God has also set up the world in such a way that our good or bad actions can have an effect on other people: if we sin against others, they are harmed, and can be tempted either to hate or to imitate us.  This is especially true in the case of our parents, who bring us into being and choose what enviornment we will come to maturity in.  Because of this strong moral influence, it is inevitable that to some extent our moral and cultural condition is inherited from others.  Alcoholic parents often have alcoholic children.  We may resist this influence and become different people than our parents, but there is a correlation which cannot be entirely removed.

As a result, in his role as Judge of the Earth, Guardian of Human Culture and Supervisor of the Gene Pool, God must necessarily engage in some amount of group justice as well as individual justice, because that is the nature of how humans propagate ourselves (and our ideas).  He does not, however, delegate this authority to us.  The ordinary Israelite judicial system was based strictly on individual actions (although even there, indirect punishment of others is inevitable: see the story in 2 Samuel 14:6-7 for an example).  Apart from this, the Israelites were also commanded to exterminate certain people groups, but had no authority to decide which ones—God provided them with a specific and limited list.

In the end, God will provide us all with individual justice.  But I think that once everything is revealed, our moral interdependence will prove to have been a means of grace.  If no innocent people ever suffered punishment for guilty people, then Christ could not have saved us, and we would be dead in our sins.  If we ourselves struggle, if sins have been transmitted to us by others, or if the punishment of others has ruined our lives as well, then what?

I think that by forgiving our forbears, and by seeking God's help for our problems, we become imitators of Jesus, as St. Peter says:

For you were called to this,
because Christ also suffered for you,
leaving you an example,
so that you should follow in His steps.
He did not commit sin,
and no deceit was found in His mouth;
when He was reviled,
He did not revile in return;
when He was suffering,
He did not threaten
but entrusted Himself to the One who judges justly.
He Himself bore our sins
in His body on the tree,
so that, having died to sins,
we might live for righteousness;
you have been healed by His wounds.
For you were like sheep going astray,
but you have now returned
to the Shepherd and Guardian of your souls. (1 Peter 2:21-25)

If Christ—the Innocent One—suffered for the sins of others and brought about the redemption of the world, then all of us who in lighter measure bear the sin of others, will also recieve through Christ this redemption.  From the the infants killed by St. Joshua for the sins of the guilty Canaanites, to the infants killed by wicked Herod in place of the innocent Christ-child, everyone who has a share in the sufferings of Christ will also rise with him in eternal glory.  This is both a justice and a mercy beyond our comprehension.

[Note: I expanded this blog post significantly on Aug 16, 2021. 

Also, there are a lot of people who have read this post and comment on it solely for purposes of expressing their anger against the God of the Bible, or that anyone could believe in such a Deity.  Most of these comments don't engage in any substantive way with the things I've written.  If you wish to make an argument against this blog post, please make sure to re-read the four sections labelled I-IV and then make sure that what you are saying is actually responsive what I've written.  Thanks!—AW]

Posted in Theology | 114 Comments

My take on Loop Quantum Gravity

by Aron Wall Posted on March 8, 2014

A friend of mine from St. John's College, who was recently accepted to a physics doctoral program at Penn State, asked me what my opinion of Loop Quantum Gravity is.  I replied be email, and then I decided, why not tell the world!

Now, Loop Quantum Gravity is the main rival to String Theory as an attempt to quantize gravity, although it only commands about a tenth of the resources that String Theory does.  The people who work on it tend to have more of a General Relativity background than a Particle Physics background, and this tends to influence what types of problems they are trying to solve.

Warning: Unlike my other physics posts, I have made no attempt to make my commentary here accessible to non-physics people.  (Yes, that means every other time I wrote a physics post and nobody understood it, I was the one to blame for not making it accessible enough!)

Einstein's theory of general relativity is background free, meaning that it does not start with any absolute background space or time, but instead allows the spacetime geometry to be dynamically constructed from the evolution of the metric.  A theory of quantum gravity ought to be similar---it ought to be expressed in a way which doesn't depend on the prior specification of any spacetime metric.  I think this is really important, but no one really knows how to do this.  There are many ideas, but they all have various difficulties.

In principle, I think the idea of LQG---to build spacetime out of a discrete, quantum structure---is a very elegant and moving idea.  (I first got interested in quantum gravity by reading the online writings of John Baez, who used to work on LQG.)  Also, the LQG people have a very beautiful quantization of space at one time, in terms of spin networks.  Essentially, by doing a step-by-step quantization of GR at one time (minus the dynamics), making only a few arbitrary choices, they were able to obtain spin networks.  I'm sure you [i.e. the friend I was writing to---AW] know what these are, but let me assure you that they are beautiful and have some deep connections to geometrical ideas.

The next step in the construction of LQG is to decide what the dynamics are.  Technically, this is done either (A) by choosing a "Hamiltonian constraint" in parallel with the Hamiltonian formulation of GR, or (B) in the spin-foam formalism, by postulating some sort of sum over histories assigning an action to each spin foam.  It is here which we encounter the major problem: There is no agreement over how to implement the dynamics!  There are many ideas, but no consensus on what to do.  Implementing dynamics seems to involve some arbitrary choices.  Some of the proposed solutions seem to me obviously wrong (e.g. see Smolin's criticism of Thiemann's Hamiltonian constraint: arXiv:gr-qc/9609034).  There is also a serious danger that by choosing the wrong dynamics, one breaks the diffeomorphism invariance of the theory.  In the Hamiltonian approach this manifests itself in so-called "anomalies in the constraint algebra", while in the spin foam approach it is unclear whether the inner product obtained from the sum over histories really has the necessary gauge invariance.  I summarized these problems in passing, with citations, in the Introduction to this article of mine: arxiv:1201.2489.

Thus---even leaving aside the critical hard problem of whether and how a continuum spacetime can emerge from a discrete description (a problem aggravated by the fact that it is difficult to see how any discrete model of spacetime besides causal sets could possibly preserve Lorentz invariance, see arXiv:gr-qc/0605006)---I would say that LQG really doesn't exist yet as a well-defined theory.  Unless you consider dynamics to be an unimportant part of a theory.  And finding sensible dynamics is a really hard problem, perhaps impossible.

Yet, despite the lack of dynamics, there's no end of papers where people do specific applications, like count black hole entropy, or even attempt to do quantum cosmology (basically by truncating the theory to a finite number of degrees of freedom, and then quantizing those degrees of freedom in a way which is "loopy" in spirit).  But all of these things are totally provisional until one can embed them in an actual theory with dynamics.   People used to be really interested in solving these hard problems, but I feel like a lot of them have now given up and are seeking more limited goals.  This is a shame, since I think progress can only come by facing the hard issues head on.  And maybe by showing some flexibility in how the theory is formulated.

Once one has the dynamics, again one can say nothing about the real world until one has identified the correct vacuum state.  An arbitrarily constructed "weave" state that happens to look like some Riemannian geometry doesn't cut it.  You have to figure out how to identify the right vacuum state---the one with lowest energy (once you figure out how to define that!).  Many deep questions here!  I think most people in LQG are asking all the wrong questions.

One can put too much emphasis on quantizing gravity---really that's backwards, we need the classical theory to emerge from the quantum theory, not vice versa.  When people calculate discrete area and volume spectra for spin network edges and vertices, they've got things backwards.  These are just some operators at the Planck scale.  The really interesting question is not, how much "area" is associated with each spin, but how many of each type of spin crosses a given area of the vacuum state (if such a thing even exists).

I despise the ignorant bigotry which most string theorists show towards LQG, even though LQG barely exists as a theory.  Their contempt is undeserved.  The LQG people are trying to do something genuinely harder---to reconstruct spacetime from first principles.  We don't know how to formulate string theory except by means of strings propagating in some background spacetime, or via dualities like AdS/CFT.  Since the theory has gravitons, with a diffeomorphism gauge symmetry, it's clear to me there has to be some background free formulation of string theory, but no one has any idea what this would look like.  And most string theorists don't even understand why it is important.

Personally (and unexpectedly for me) I've found that as someone who studies black hole theormodynamics, I can interface better with string theorists than with LQG people---the ones who are really interested in fundamental concepts, like Don Marolf and others at UCSB, for example---even though I don't really consider myself a string theorist.  This may be a bit of a conceit at this point, since I've now written multiple papers on AdS/CFT.  My heart is more strongly devoted to the types of ideas LQG people explore, but my mind recognizes that they really haven't made all that much progress.

Posted in Physics | 34 Comments

Yet More Random Stuff

by Aron Wall Posted on February 25, 2014

I've been staying home sick with some horrible cough for about 3 weeks now.  One would think that this would be quite conducive to blogging, but when I'm running a fever I find it hard to concentrate enough to produce mental output.  (Mental input, like books and movies, is fine).

Fortuantely—either because of taking antibiotics, or for some other reason—I'm beginning to feel much better, so here's a post, consisting of links which I've found interesting since the last time I did links:

  • Of This and Other Worlds blogs on the Problem of Susan in the Narnia books.  The Superversive adds some interesting personal testimony.
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  • A New York Times article on computer software that supposedly grades essays.  Anyone who thinks that computer programs can substitute for human graders is completely misinformed about the point of essays.  Which is always to communicate some sort of meaning through organized thought.  This is something that no computer can do, prior to the development of some actual AI overlords.  The best it could possibly do is check for pretentious vocabulary, correct bad grammar (badly) and enforce meaningless and stupid rules about how many paragraphs there must be.   No machine could possibly check for the presence of an interesting thesis supported by coherent argument based on plausible evidence.  There are probably some things you could measure which are corollated with being a good writer, but even this will cease once students learn how to flatter the machine.
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    The sad thing is that there are probably human teachers who grade this superficially.  Although, even they could probably tell if the sentences didn't actually fit together in any way (besides beginning with words like "Moreover").
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    Out of curiosity, I just went and checked the webpage of the discern program to see what their alogorithm was.  It's machine learning based on sample essays which are already graded.  Oh my.  That means neither the student nor the classroom instructor will even know what criterion the machine is using.
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  • What St. Lewis (in his capacity as a literary scholar) thought of the Puritans.
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  • You've probably heard how the first man in space, Soviet cosmonaut Yuri Gagarin, said that didn't enocunter God there.  As if God were literally located in the sky.  Well, it turns out, the whole story was a Soviet lie; St. Yuri was an Orthodox Christian.  More details here.
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  • A haunting article, by and about a woman who acts the part of a sick patient for medical students.  This is one of the best written narratives I've read in quite some time.
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  • An interesting (and to me inspiring) letter from missionary St. Anthony Norris Groves (1795-1853) to crankish schismatic (St?) John Nelson Darby (1800-1882) on the topic of Christian unity.
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    Darby was one of the first people to teach that Christians would be raptured into heaven 7 years prior to the Second Coming of Christ, a belief almost completely unheard of prior to Darby.  This is part of a detailed scheme called Dispensationalism, popular in American Fundamentalist circles, which is based on that idea that apparent contradictions in the Bible should be resolved by assigning different texts to one of seven different covenants or "dispensations" in which God treats people differently.  This way of thinking leads them to construct an elaborate timeline of End Times events (a suprise Rapture, followed by 7 years of Tribulation, followed by the Second Coming, followed by 1000 years of The Milennium [this one at least has a  foundation in a literal reading of the Book of Revelation], and then finally the Final Judgement).  Oddly enough, people think that this elaborate scheme comes from reading the Bible literally as a fundamentalist should, even though no one who read the Bible without influence from Darby would ever come to this elaborate scheme on their own.
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    More relevantly to this letter, Darby went on to found a small denomination of his own which excommunicated nearly everybody else.
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  • St. Maxime is a Stylite monk with a much better way to isolate himself from the World.  Make sure to click through the slide show.
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  • An article about my grand-advisor (i.e. the Ph.D. advisor of Ted Jacobson, my advisor) Cécile DeWitt-Morette.
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  • An article on the simplicity of God (hint: it doesn't mean that he is easy to understand).  Consider me firmly in the "classical theism" camp.  I consider the idea that God is just a person like us, but pure spirit and infinitely powerful etc., to be idolatrous.  True, we humans are the image of God.  The converse is not true: God is not to be conceived as being in our image.
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  • The New York magazine interviews St. Antonin Scalia.  There was an interesting moment where Scalia brings up that he believes in the Devil.  The interviewer acts a bit incredulous, and asks:

Isn’t it terribly frightening to believe in the Devil?
You’re looking at me as though I’m weird. My God! Are you so out of touch with most of America, most of which believes in the Devil? I mean, Jesus Christ believed in the Devil! It’s in the Gospels! You travel in circles that are so, so removed from mainstream America that you are appalled that anybody would believe in the Devil! Most of mankind has believed in the Devil, for all of history. Many more intelligent people than you or me have believed in the Devil.

Posted in Links | 3 Comments

Must Science be Falsifiable?

by Aron Wall Posted on January 29, 2014

There's a common notion floating around, due to Karl Popper, that scientific theories are characterized by the fact that they are falsifiable.  The idea is that it is never possible to verify a scientific theory (i.e. the sun always comes up) because one day it might not happen.  But it is possible that the sun might not come up some day, and then the theory is falsified.  It must then be rejected, and replaced with something more complicated.

Now, let me confess right away that I have not gotten this idea by reading any of Popper's writings.  It is an idea which has been popularized in the scientific community.  You see, everyone knows what Popper said without having read any of it ourselves.  It could be that if I actually read Popper's books, my idea of what he said would be falsified.  So let me confine myself in this post to discussing Popperism as commonly understood.

If a theory is unfalsifiable (that is, if no experiment you could possibly perform would rule it out, then according to Popperism it is not a scientific theory.  Among those who subscribe to Scientism, this is usually assumed to be A BAD THING™.  (The way some people talk, if a theory is unfalsifiable, that means it is false!)

People often characterize bogus pseudoscientific ideas as unfalsifiable, because of the tendency of people who believe in them not to subject them to rigorous scrutiny.  But this is clearly an oversimplification.  True, there is such a thing as mystical Woo-Woo from which no definable predictions can be made, either because the ideas are not precise enough or because they don't relate to any actually observable phenomena.  But many psuedoscientific ideas, such as homeopathy, reflexology, or astrology, can be tested experimentally, it's just that the people who believe in them don't like the results when people do!)  I've heard people refer to Young Earth Creationism (YEC) as unfalsifiable.  I think their reasoning must be the following:

1. YEC is unscientific and wrong.

2. I've been taught that when ideas are unscientific, the reason is because they are unfalsifiable.

3. Therefore, YEC is unfalsifiable.

In fact, though, the real problem with YEC is that it IS falsifiable, and in fact has been falsified many time over. If the universe were created about 6,000 years ago and we have to get all of the layers of fossils and rock from a single planet-wide Flood about 4,500 years ago, then there are a gazillion problems with observation.  It contradicts the results of almost every branch of science which tells us anything about the past.  (Adding bizarre extra ideas, like God created the earth with fossils in it in order to trick us into believing in evolution, may make YEC unfalsifiable, but it might be better to characterize this as pigheaded refusal to accept reasonable falsification.)

[Fun fact: if you interpret all of the genealogies in Genesis as being literal, with no gaps—which of course I don't—then it follows that when Abraham was born, all of his patrilineal ancestors were still alive, back to the tenth generation (Noah)!  (This is using the Masoretic Hebrew text that omits Cainan, who is included in the Septuagint Genesis and Luke.)]

All right, digression over.

Clearly there is something right about the idea that theories ought to be falsifiable, yet not confirmable with certainty.  Major scientific theories usually deal with generalities: they make predictions for a large (perhaps infinite) number of different situations.  Normally, it is not possible to verify them in all respects, because even if it works well in many cases, it could always be an approximation to something else.

On the other hand, I think there are some scientific ideas which are verifiable but not falsifiable.  Here's an example:

Ring Hypothesis: Somewhere in this universe or another, there exists a planet with a ring around it.

I submit to you that: 1) our observation of Saturn verifies the Ring Hypothesis, 2) when scientists verify a proposition by looking through a scientific instrument, that counts as Science, and 3) no possible observation could have falsified the Ring Hypothesis.  (Even restricting to the Milky Way, eliminating planets with rings would be a tall order, impossible with current technology.)  Therefore, there are scientific propositions which are verifiable but not falsifiable.

On the other hand, even if an experiment "falsifies" a theory, it could be that the experiment rather than the theory is wrong. As Einstein once said "Never accept an experiment until it is confirmed by theory".  This witticism may seem to turn science on its head, but nevertheless it has a bit of truth to it.  A while back, there was an experimental observation which seemed to suggest that neutrinos travel faster than light.  Soon there were many papers on the arxiv trying to explain the anomaly.  But it turned out, not surprisingly, that there was an error in the measuring devices.  Usually, when a well-tested theory is in conflict with an experiment, and the anomaly has no particularly good theoretical explanation, it is the experiment which is wrong.  Not always, but usually.

What this means is that we need a more flexible set of ideas in order to discuss falsification and verification.  In particular, we ought to accept that falsification and verification can come in degrees—observations can make an idea more or less probable, without reducing the probability to exactly 0 or 1.  The accumulation of enough experimental data against a theory should make you reject it, but it may be able to withstand one or two anomalous measurements.

The quick answer is that one ought to use Bayes' Theorem instead.  This is a general rule for updating beliefs, taking into account both our prior expectations and observation.  This goes not just for Science, but also for everything else.  The only thing that makes Science special is that, due to a number of special circumstances, the process of testing through observation is particularly easy to do.

Even though falsification is not the best way to think about Science, it still works pretty well in many cases.  In a later post, I hope to explain the connection between Bayes' Theorem and falsification.  Usually we should expect good theories of the universe to be falsifiable, but in certain situations they don't have to be.  Bayes' Theorem can be used to understand both the general rule, and why there are exceptions.

Posted in Scientific Method | 36 Comments