Monday, August 30, 2010

On that "ground zero mosque"

It's all over the news that some people want to build a mosque at ground zero in New York.  As other commentators have said, calling it the "Ground Zero mosque issue" is ironic, since it is not a mosque (it is a community center), it is not at Ground Zero (it is several blocks away), and it is not an issue.

Unfortunately, CFI went and made a press release placing themselves on the wrong side of the issue.  That is, the side that thinks it's an issue.
CFI also holds that the focus of the protests is too narrow; it would be inappropriate to build any new house of worship in the area immediately around Ground Zero, not just mosques. “The 9/11 attacks were an example of faith-based terrorism, and any institution that privileges faith above reason is an affront to those who were killed and injured in those attacks,” observes Ronald A. Lindsay, president and CEO of CFI.
It's almost like CFI is making a reductio ad absurdum argument.  If we oppose the mosque, we must also oppose all houses of worship in the area.  But instead of questioning their original premise, CFI decides they'd rather accept the absurd.

Orac of Respectful Insolence was also very unhappy with the press release, to the point that he was considering withdrawing his support of CFI.  As for me, I have never been particularly happy with CFI, but I still find this disappointing.  I've always been annoyed that CSI, a notable skeptical organization, is affiliated with CFI, a perpetually disappointing atheist organization.

Apparently, CFI got a lot of complaints from supporters, so they issued a clarification.  But CFI doesn't really retract anything, it just emphasizes that they support the legal right to build the community center.  Supporting the legal right to build a community center is just the bare minimum necessary to not be a flaming bigot.  But I have higher standards than that.

Honestly, even if it were a mosque, and if it were right across the street from the former location of the World Trade Center, I would not care.

I think people are assigning too much meaning to the location.  I'm reminded of the story of the serial killer's sweater.*  If you show people a sweater, and say that it used to belong to a serial killer, but has since been cleaned, people hesitate to wear it.  It's because people assign meaning to the sweater and its history.  Likewise, they assign positive meaning to family heirlooms and a whole mix of meanings to places like Ground Zero.

*I think I heard this story from psychologist Bruce Hood.  So I looked him up, and I saw on his blog he is talking about Ground Zero as a sacred site.

Sometimes, this superstition is okay, because it doesn't hurt anyone.  We could even use it to our advantage, for example by placing a memorial at Ground Zero.  The whole point of a memorial is to create a particular experience; knowing that it's located where the World Trade Center used to be can enhance that experience.  So what's the harm?

The harm is that people forget that it is superstition, and it messes up their priorities.  What's more important: the superstitious belief that Ground Zero and the surrounding privately owned land is somehow sacred, or letting people build religious community centers without having to cause a national dispute?

Mind you, CFI claims that they don't support the building of any houses of worship whatsoever.  But they're not thinking out the issue seriously enough.  Much bigger mosques, churches, and synagogues are built all the time, and they don't make a huge issue out of each one.  Nor should they.  Even if I agree that organized religion causes some problems in the world, I'm not convinced that any of these problems are solved by stopping people from building places where they can gather.

If you discourage Muslims from building mosques, you're not doing anything to persuade them that Islam is wrong, you're just oppressing them.

Let's just explicitly add two and two together.  There is a superstitious belief here, and there is oppression.  That makes it superstitiously motivated oppression.  As a skeptic, there are few things I oppose as strongly.

Friday, August 27, 2010

Ask questions

Readers!  Do you have any questions that you'd like me to blog about?  It can be a personal question, an opinion question, or a knowledge question.  It can even be on a topic that I don't normally blog about.

I can't guarantee that I will actually answer every question.

I'm doing this because I'm still somewhat busy even after my blogging break, and my working hypothesis is that this will require somewhat less time investment on my part.  Let's test that hypothesis.

Thursday, August 26, 2010


By reader request, I will explain superconductors.  But I have to be cautious about it.  I may understand the basics, but I don't have the deeper understanding of a professional.  I recommend the recent explanation on Uncertain Principles, which is written by a professional, though he doesn't specialize in superconductors.

A superconductor is a material with two characteristic properties: zero resistance and the Meissner Effect.

Zero resistance means that it conducts electricity perfectly.  When electricity flows through a superconductor, no energy is lost to heat.  This is obviously has many practical uses.  If we could just replace all of our transmission lines with superconductors, for instance, we could save so much electricity.

What's more, we can create persistent currents in a superconductor.  These are currents that just keep on going and going in a loop for an indefinite amount of time.  No energy is lost to heat, so the current never stops.  One of the practical applications of this are strong magnets.  A loop of current creates a magnetic field, and no material can maintain a current as efficiently as superconductors.  MRI machines, for instance, use superconducting magnets.

The Meissner Effect is a little trickier to describe.

If you've ever played with a bar magnet, you know that it attracts certain kinds of metals, even if those metals are not themselves magnets.  Materials that attract magnets are called paramagnetic.  They attract magnets because when they are in the presence of a magnet, they spontaneously form their own magnetic field in the same direction.  So when you put a magnet and a metal together, they behave like two magnets attracting each other.

However, many materials are not paramagnetic, but diamagnetic.  When they're in the presence of a magnet, they spontaneously form their own magnetic field in the opposite direction.  This causes them to be repelled by magnets.  Diamagnetism is usually very weak, so it's hard to see just by fooling around with refrigerator magnets.

The Meissner Effect means that a superconductor is a perfect diamagnet.  When a superconductor is in the presence of a magnet, it spontaneously forms a magnetic field in the opposite direction, just enough to cancel the magnetic field.  So when you put a superconductor near a magnet, the magnetic fields just go around the superconductor, never penetrating through.  This also means that superconductors repel magnets, strongly enough to create magnetic levitation.

The lines represent the magnetic field, which is going around the superconducting sphere. (Image courtesy of Geek3)

This is the classic superconductor demonstration of magnetic levitation.  (Image courtesy of David Monniaux)

As we now understand it, the reason for superconductivity has to do with fermions and bosons.  Fermions are particles that cannot occupy the same state.  For example, when you have a lot of electrons in a single atom, each electron must occupy a successively higher energy state, from the core electrons to the outer electrons.  Bosons, on the other hand, are allowed to crowd a single state.  If electrons were bosons, then they would all collapse to the smallest orbital around an atom.

The reason for fermions and bosons is complicated enough to devote a whole blog post complete with pictures.  Let's just say that single electrons are fermions, but paired electrons are bosons.  This is what happens in a superconductor.  The electrons pair up, and behave like bosons.

Pairing up electrons requires that there be some attractive force between the electrons.  This is hard to imagine, because electrons have like charges, and normally repel each other.  But remember that we don't just have negatively charged electrons, but positively charged atomic nuclei.  If we have an electron, it pulls nearby atomic nuclei towards it, creating an excess positive charge.  This positive charge weakly attracts a second electron.  The weak attractive force between electrons allows them to pair up.

This is known as BCS theory (named for the physicists who proposed it, Bardeen, Cooper, and Schrieffer).  It allows for superconductivity up to about 30 K above absolute zero (that's about -240 Celsius, or -400 Fahrenheit).  Above this temperature, the positively charged nuclei fluctuate too much from thermal energy for the mechanism to work properly.

The thing is, since 1986, we have observed superconductors at much higher temperatures!  The highest temperature superconductors work up to about 125 K* (-150 Celsius or -240 Fahrenheit), which is still really cold, but too hot for physicists.  It's a holy grail for physicists to figure out the correct explanation for high-temperature superconductors.  It's a guaranteed Nobel Prize.  With a good explanation, we may be able to create superconducting materials at even higher temperatures, perhaps even at room temperature.  Once we get room temperature superconductors, we will finally be able to create those perfect transmission lines that we were dreaming of, among other things.  Until then, all our superconductors have to be refrigerated by something like liquid nitrogen.  Unfortunately, this makes many possible applications of superconductors impractical.

*You might see claims of superconductivity at higher temperatures, but these aren't generally accepted.

One of the interesting things about these high temperature superconductors is that the Meissner Effect does not strictly hold.  Superconductors are divided into two types: Type-I and Type-II.  Above a certain magnetic field, Type-I superconductors stop behaving like superconductors.  This is because the Meissner Effect requires a certain amount of energy.  The stronger the magnetic field, the more energy it requires.  If the magnetic field is too strong, then it takes too much energy for the material to remain a superconductor.  Instead, it just becomes a regular material with electrical resistance.

But all high-temperature superconductors are Type-II.  Type-II superconductors remain superconductors even in stronger magnetic fields.  Once the magnetic field is strong enough, it starts to penetrate the superconductor in thin tubes.

Magnetic field penetrates Type-II superconductors in thin tubes.  (Image courtesy of Hyperphysics)

What's going on here is that the material is now a mix of superconducting and non-superconducting material.  The bulk of the material is superconducting, but the thin tubes are non-superconducting.  That's why the magnetic field can penetrate through the tubes, but not through the rest of the material.

The difference between a Type-I and Type-II superconductor is that a Type-I superconductor doesn't like having lots of boundaries between superconducting and non-superconducting material.  Having lots of little non-superconducting tubes wouldn't make sense in a Type-I superconductor because the boundaries would just require too much energy.  On the other hand, in a Type-II superconductor, boundaries don't require extra energy.

As far as practical applications go, Type-II superconductors are probably more useful, since they allow for the strong magnetic fields needed for MRIs, maglev trains, and any large currents.

And right about now, we're at the limit of what can be explained to a popular audience, also incidentally about the limit of my knowledge.  But if you have any questions, feel free to ask.

Thursday, August 19, 2010

Blogging break

I will probably be busy as grad school is starting up, so I am declaring an official blogging break for a week or so.

Saturday, August 14, 2010

Beyond sex-positive

Because I write to a skeptical and pro-science audience, I can be reasonably sure that most of my readers consider themselves sex-positive.  That is, most of you believe that sex is a good thing, as long as all parties give informed consent, and no one is harmed.  You probably think that abstinence-only education is ineffective, that porn can be positive, that premarital sex is a good thing.  You also probably believe that abortion should be legal, same-sex marriage should be legal, and perhaps even prostitution should be legal.

I consider myself sex-positive too.  I think that the best basis for a sexual ethic is informed consent and harm reduction.  Tradition is frequently wrong.  Purity is meaningless.  Gross-out reactions are not a moral compass.  God's intentions don't exist.

But "sex-positive" isn't consistently defined in any particular way, so many people use it to mean different things.  Many people also interpret sex-positive attitude as, "Sex! Rah rah rah!  Everyone should have more of it because clearly that's what everyone wants."

"Everyone wants sex" isn't necessarily meant as a universal rule. For example, no one thinks that rape victims wanted to be raped.  Indeed, the idea that "she was asking for it" is a repugnant myth fought by many who consider themselves sex-positive.  And yet, some people universalize the rule more than they should.

That people take "sex-positive" too far becomes clear the moment you step in the asexual community.  When you're asexual, coming out to people is a crapshoot.  Even liberal-minded people can have negative reactions.  Those liberal-minded people are usually sex-positive, and some sex-positive people just can't process asexuality.  What do you mean you don't want sex?  You must be attracted to someone, we just need to find who.  Were you abused as a child?  Do you have hormonal problems?  Did you just have a bad relationship?  It's okay if you're gay, so why don't you just come out already?  You're repressing yourself.  You've bought into a puritanical culture.

Why do people bring up all these objections?  It's not because they've seriously considered each one (as asexuals have).  It's because the idea that everyone wants sex is embedded too deeply in their heads, and anything that might dredge it up just bounces off.

Oh, there's more.  Sex-positive people are always fighting norms against sex.  They fight the idea that women are "sluts" while men are "pimps".  They fight the idea that premarital sex is dirty, that virgins are pure, that fetishes are freakish, that same-sex sex is unnatural.  But they sometimes replace it with the opposite norm, that everyone should have sex.  It's not a frequent thing, but frequent enough to be a problem.  When asexuals first enter the forums all insecure because they've felt broken and abnormal all they're lives, then we have a problem.  When some depressed asexuals declare that they must lose their virginity so that they will no longer face shame for being a virgin, then we clearly have a problem.

And you know what?  This isn't even about asexuality, or sexual orientation at all.  It doesn't matter that I only consider myself borderline asexual.  If there were no such thing as asexuality, this would still be a problem, it's just that we would have a harder time recognizing it as such.  The bottom line is that people have different levels of interest in sex, different kinds of interest in sex.  We need not deny it or treat it normatively.

Some people will react by saying, "those people aren't really sex-positive."  But I don't care about that.  I care about the people and norms that piss me off, I don't care what you call them.

Let's consider a specific issue: celibacy.  In the standard asexual presentation, celibacy is contrasted with asexuality, because asexuality is an orientation while celibacy is a choice.  I have made this contrast too, though I prefer to frame it as a difference between desire and behavior, rather than orientation vs choice.  In general, a behavior can be non-chosen, as is the case for involuntary celibates.

There is a pretty good reason that asexual rhetoric tends to distance itself from celibacy.  It's because the main audience of this rhetoric is sex-positive.  Sex-positive people tend to associate celibacy with bad things like clerical celibacy and abstinence-only education.  But they have it wrong.  Celibacy is not intrinsically good or bad.  Celibates are not unnatural, and not necessarily repressed.  It can be an entirely respectable decision, one that's available to people of all orientations I might add.

To accept asexuality and reject celibacy is a little like accepting gay people but rejecting gay sex (as the Catholic Church does).  It can hardly be considered proper acceptance at all.

That's not to say that we can't criticize clerical celibacy, which is a more specific kind of celibacy.  If celibacy is part of a religious vow, then the vow becomes the primary consideration, and the specifics of the individual are secondary.  It should be the other way around.  Furthermore, requiring all leaders to be celibate implicitly places undue value on celibacy.  Also, if these leaders want to talk about sexual moral values, they're going to have a very narrow perspective.  Finally, I am skeptical about the idea of sublimating sexual energy into other kinds of energy.  That just has pseudoscience written all over it.

But I cannot criticize clerical celibacy by declaring that celibacy in general is bad.  In general, celibacy passes the test of informed consent and harm reduction.  That's all we need ask for.

(Some influence for this post comes from Asexual Explorations)

Thursday, August 12, 2010

Update: Prop 8 stay

A little update on the prop 8 ruling last week.

Judge Walker finally ruled on whether prop 8 would remain in place or not during the appeals process.  The marriage ban will be lifted on August 18th, next Wednesday!*  Yay for marrying couples!

*ETA: unless the appeals court decides to issue another stay

By the way, here's a flowchart of what may happen during the Prop 8 appeals process.  I think I'm done with news blogging; go elsewhere for your news.

Update: The US 9th Circuit Court of Appeals decided to extend the stay until December.

Wednesday, August 11, 2010

"The Limits of Reason" in Newsweek

Newsweek just published an article called "The Limits of Reason: Why evolution may favor irrationality", by Sharon Begley.  It's a good article explaining many cognitive biases and fallacies with good concrete examples.

However, I note with some amusement that Begley got this bit wrong.
Consider the syllogism “No C are B; all B are A; therefore some A are not C.” Is it true? Fewer than 10 percent of us figure out that it is, says Mercier.
But the syllogism is wrong!  The syllogism is correct if we assume that there exist some B.  So what if B is unicorns?  Then the syllogism doesn't necessarily work:

No mammals are unicorns (because there are no unicorns).
All unicorns are horses (all existing unicorns anyway, which is to say none).
Therefore some horses are not mammals.

Begley continues...
Interestingly, syllogisms are easier to evaluate in the form “No flying things are penguins; all penguins are birds; so some birds are not fliers.” That’s because we are more likely to argue about animals than A, B, and C.
...Also because we know penguins exist.

But back on topic.  Sharon's main point is that evolution favors irrationality.  This is true.  It's a well-documented fact that humans have some irrational cognitive biases.  This irrationality must have been favored by evolution; nearly all of our biological traits are there because they were, in some sense, favored by evolution.  Empirical fact.

The explanation for why evolution favored irrationality is somewhat more suspect.
Failures of logic, he and cognitive scientist Dan Sperber of the Institut Jean Nicod in Paris propose, are in fact effective ploys to win arguments.
This explanation just raises so many questions.  Does irrationality help you persuade other people, or does it help other people persuade you?  If the latter, doesn't this require some sort of group selection?  What exactly is the mechanism connecting persuasiveness to evolutionary adaptiveness?

In general, I'm pretty suspicious of these evolutionary psychology narratives, because it's difficult to prove one narrative over another.  And yes, there are other narratives.  For instance, Michael Shermer often explains confirmation bias by saying that for early humans, it was more advantageous to mistake the wind for a tiger than mistake a tiger for the wind.  Come to think of it, does Shermer have any evidence for this narrative aside from its initial plausibility?  Another alternative hypothesis is that cognitive biases are not adaptive at all; a flawed brain was just the best that evolution could manage.

Which of these hypotheses, if any, are true?  I cannot imagine any evidence that would distinguish between them.  I wish popular explanations of evolutionary psychology would focus more on the kind of evidence they use, because whatever it is, it'd have to be really clever.  Believe me, I get that scientific evidence can often be really hard to explain to lay people, but this could be downright fascinating, almost too clever to exist.

Monday, August 9, 2010

A pair of parity puzzles

Create the above figure with 24 identical dominoes (or prove that this is impossible).  They may not overlap.

The above tetrominoes (as seen in Tetris) are sometimes called the O and N tetrominoes. There is a shape that can be built with four O tetrominoes OR with four N tetrominoes.  Is there a shape that can be built with an odd number of O tetrominoes OR with an odd number of N tetrominoes?  Find such a shape, or prove that it is impossible.  You may rotate and flip the tetrominoes, but they may not overlap.

If this sounds familiar, it's because I used a similar puzzle before.

There is a common theme with these two puzzles: parity.  Parity is the property of being odd or even.

See the solutions

Saturday, August 7, 2010

Solution to "Double Rock Paper Scissors"

See the original puzzle

Since Alice can't use paper, Bob has no reason to ever use scissors.  Rather than playing scissors, Bob can always achieve a better outcome with rock.  Given this knowledge, each player has four possible moves, and we can draw a table of the sixteen different outcomes.

From this table, it's clear that Alice has no reason to ever play RS or SR, because SS is always an improvement.  So we can cross out those columns.

Alice's best strategy is to pick RR or SS each with a 50% chance.  Bob's best strategy is to have a 50% chance of picking RR and a 50% chance of picking RP/PR/PP (it doesn't matter which).  The outcome is that both players have an even chance of winning.

I am making certain assumptions about what constitutes the best strategy.  I am assuming that Alice picks each choice with a certain probability.  She chooses those probabilities based on the assumption that Bob uses the best possible strategy to counter hers.  Likewise, Bob chooses probabilities based on the assumption that Alice uses the best possible strategy to counter his.

For example, if Alice picked RR with a 20% chance and SS with an 80% chance, then this strategy is suboptimal.  Bob can simply pick RR, and win 80% of the time.  Mind you, Bob doesn't necessarily know what Alice's strategy is, and thus doesn't know to pick RR.  But the fact remains that there exists some strategy which Bob could use to win 80% of the time.

Back in my high school days, I think I wrote a rock paper scissors type puzzle, except with six choices consisting of different "elements".  It was highly nontrivial.  I think I was pretty hardcore back then.

Plantinga responds to me

I've written a lot about the ontological argument, going through its internal details (as opposed to the typical atheist response, which is to dismiss it from the top).  I've found that the ontological argument is one of those topics which attracts dedicated commenters who disagree with me.  But that's okay, because I feel confident about defending my position on the Ontological argument.

It has happened again.  I had a long discussion with blogger Metacrock about the modal ontological argument.  At one point, Metacrock e-mailed Alvin Plantinga to get his response "just for grins".  Plantinga responded, though I don't think his response clears anything up.

I just thought I'd let you know about it.   If you want to read the discussion, follow the links.

I confess to being slightly starstruck at getting a response from Plantinga.  He's a very famous philosopher!  I mean, I may not like any of his philosophical positions, but... yeah...

Friday, August 6, 2010

US Puzzle Championship 2010

The US Puzzle Championship is an annual puzzle-solving competition conducted online. Typically, most puzzles are grid-based logic puzzles, like Battleships and Sudoku variants.

The test occurs on Saturday, August 21, 1 PM EDT.  You have two and a half hours to solve as many problems as possible.  The recommended way to do it is to print out all puzzles, and solve them on paper, then input the answers online.  Go register now.

Over the many years I've participated, my rankings have gradually improved.  But this year I have scheduling conflicts and I can't compete.  I'll be sure to solve all the puzzles on my own time anyway.

Wednesday, August 4, 2010

Prop 8 overturned, Same-sex marriage legalized

From CNN:
A federal judge in California on Wednesday overturned the state's ban on same-sex marriage, saying the voter-approved rule violates the constitutional rights of gays and lesbians.
And here's the judge's conclusion:
Proposition 8 fails to advance any rational basis in singling out gay men and lesbians for denial of a marriage license. Indeed, the evidence shows Proposition 8 does nothing more than enshrine in the California Constitution the notion that opposite sex couples are superior to same-sex couples. Because California has no interest in discriminating against gay men and lesbians, and because Proposition 8 prevents California from fulfilling its constitutional obligation to provide marriages on an equal basis, the court concludes that Proposition 8 is unconstitutional.
Being very California-centric, I wanted to know whether the ruling is effective immediately or delayed for the appeals process.  The appeals process could take a long time (years?), and though I don't expect to get married myself in that time, it seems like an important thing to know.

CNN says that Proposition 8 has a "stay", meaning that the same-sex marriage ban will temporarily remain.  However, CNN neglects to mention that this stay is only for two days.  On August 6, there will be a hearing to determine whether to grant a long-term stay.  So stay tuned for the results of that hearing.

One friend of a friend on Facebook* predicted that the hearing would probably be short, and that no stay will be granted.  The basis for this opinion is how strongly the judge came down against Proposition 8 in his decision.  That means that we may have same-sex marriages in California within a few days!

*Yes, I am using some random person on the internet as my expert.

Update: on the stay decision

Monday, August 2, 2010

Sunsara on morality and god(s)

I don't  know why I haven't bothered to mention this until now, but back in spring, I saw a discussion panel called "Morality and God(s): Can there be Ethics without Deities?"  I missed half of the panel, but I did at least see the introductory presentations by all the panelists.  Easily the loudest and most dominant panelist was Sunsara Taylor.  She's just that kind of speaker, she quickly becomes the focus of attention.

Sunsara said two things that stuck in my mind, even after several months.

The first was her answer to the question, "Is morality based on gods?"  The answer is no.  Because there are no gods.

Probably many people will first react by asking, "But what makes you think there are no gods?"  Sunsara went on to explain, in brief, why she thinks there are no gods.  In this explanation, morality is never mentioned.

I thought this was a simple and powerful statement, and I don't know if I can comment further without detracting from it.  The point is that, whatever morality we currently have cannot be based on gods, because there are none.  So every atheist knows it's silly to say morality requires gods.  And even if morality did require gods, that would have no bearing on whether gods exist.

The second thing Sunsara said, I disagreed with.  She was talking about a hypothetical person who believes there is an invisible heatless incorporeal dragon floating above us.  She said that we would question such a person's sanity and perhaps institutionalize them.  The implication was that we should have the same reaction to theists.

The invisible dragon is a classic skeptical example given by Carl Sagan.  So I saw Sunsara's comparison as one between a skeptical issue and an atheist issue.  I see these comparisons pretty often.  It goes in three steps:
  1. Religious claims aren't really all that different from pseudoscientific claims.
  2. Therefore, we should treat them in the same manner.
  3. Therefore, we should mock religious people the same way we mock pseudoscience.
I think all three of these steps are questionable.
  1. Religious claims tend to be more tangled up with philosophy than with science.  When countering religious claims, you have to delve much more into raw critical thinking rather than investigative skepticism.  There are exceptions, and varying degrees in between, but it's true in general.
  2. There are many powerful organizations supporting pseudoscience (eg alt med, intelligent design), but they don't compare to the sheer cultural and political power of religion.  This may call for different large-scale strategies against the two.  Even PZ Myers thinks that there should be division of labor between skeptics and atheists.
  3. The thing is, I don't mock pseudoscience quite as bad as Sunsara mocks religion.  That's not quite true, I probably do a lot of subtle mocking.  But I don't go so far as to say people who believe in pseudoscience should be institutionalized.  People usually don't believe weird things because they are crazy.  They believe weird things because they are mislead by normal thought processes.  So you see, if someone really believed that there was an invisible dragon floating above us, I would not think they were insane.  Just wrong.
This isn't the first time I've seen Sunsara speak.  Sunsara Taylor is a writer for Revolution newspaper, which is the "voice of the Revolutionary Communist Party".  Yes, that's a real political party, and yes, that makes Sunsara a communist.  I mention this at the end rather than the beginning, because some people I know groan at the very mention of communism.  I don't know, I may have some political disagreements, but they're not all that bad!  Maybe I can garner a little sympathy for Sunsara by showing this interview on The O'Reilly Factor.