## Physics culture and theistic cosmology models

A reader asks this question, testing the boundaries between physics culture and religious belief:

How hostile do you think a learning institution would be to someone in their Physics department looking at the Horizon problem via the Universe being an Ex Nihilo creation of God, where matter was purposefully set in place and then a God-caused spacetime expansion? (As opposed to the thought experiment of assuming a singularity and a "Theistic or Non-Theistic Big-Bang" requiring another speculation (inflation) to explain one of the shortcomings of the theory.)
Dean C

Dean,

Most physicists aren't actually militant atheists, but all of us (whatever our views on religion) have been exposed to numerous "crackpots" who think that they have found major flaws in conventional physics and have a completely new and revolutionary way of doing things.  I discussed this pathology here and here. At least 99.99% of time, outsiders making such grandiose claims are totally wrong (or "not even wrong", because their ideas aren't precise enough to be testable), and so we filter out pretty automatically anything which pattern-matches onto typical crackpot-seeming claims and behaviors.

But this is not to say that simply criticizing inflation, all by itself, would get you lumped into the "crackpot" category.  Even among respectable mainstream physicists, inflation isn't completely uncontroversial.  While most of us believe it is true, this hasn't been established with total certainty.

A lot of the original arguments for inflation (e.g. the flatness and horizon problems) are a little bit philosophical in nature, and it's understandable if you don't find them completely convincing.  But it's not just generic arguments like that.  Inflation also makes some very specific predictions about the state of the universe after inflation ends, and these predictions seem to match very closely to what we actually observe (as the graph in that article shows).  There are respectable researchers (such as Neil Turok and Paul Steinhardt) who have philosophical objections to inflation (not based on religion) and are working on alternatives which may predict the same features in the microwave background.  But they are able to do that only because they fully understand the mathematics of inflation and the observational tests that it passes.

If somebody said something like "For philosophical reasons I am skeptical of inflation, and therefore I am interested in exploring alternatives to inflation such as X, Y," and if this person understood the mathematics of inflation (so they weren't just criticizing something they didn't know well enough), and if X and Y were mathematically-precise models with equations (such that even somebody who didn't believe in God could manipulate the equations and work out the predictions of the model), and if there was some hope that in the future, that model could be confirmed by empirical observations, then if all of these conditions are met, I think at most places this would be regarded as acceptable though eccentric.  Even if the "philosophical reasons" included some religious considerations.

It would be even better if this person had the ability to "suspend their disbelief" by sometimes having useful conversations with other people that presupposed the truth of inflation, without bringing up their reasons for skepticism every single time.  (Because that would make them a more useful colleague, and its scientifically it's an important skill to be able to work out the consequences of hypotheses even if you aren't convinced by them yet, as a way of keeping a open mind and understanding the relationship between ideas.)   Such a person would be capable of interfacing with other scientists who don't share his conviction.

(Which is not to say you could actually obtain a research job simply by working on X, Y, since there also need to be a sufficiently large number of other people who think work on X, Y is valuable enough to pay somebody money to do it.  In practice, people who work on long-shot alternatives to standard physics also need to work on more conventional topics, in addition, to be viable.  There are limited resources and funding in science, and not everyone can be supported.  But not getting a job is quite different from being excommunicated as a heretic!)

On the other hand, if X and Y can't be understood without reference to a Creator, and have phrases like "and then God miraculously caused this to happen" in them, or if the model doesn't lead to any mathematically precise predictions that could in principle be tested by future experiments, then this would not be anything like Science as it is traditionally practiced, and it would be dismissed off-hand by almost all scientists as a scientific theory.

And rightly so, because it would, at the very least, involve an enormous paradigm shift in what it even means to practice the scientific method, and justifying such a change would require overwhelmingly convincing evidence.  Of course, as a Christian I believe that miracles have happened in history, and that the universe was created by God. But in the field of Cosmology as practiced in Physics departments, the job is to mathematically model the universe using a set of natural processes described by equations.

It's hard to see how "matter was purposefully set in place and then a God-caused spacetime expansion" could, all by itself, be a mathematically predictive theory.  Because if the matter was just spontaneously created, there are almost an infinite number of configurations it could have appeared in.  Without some physical process or principles to limit it, it could have been anything!  And a "God-caused spacetime expansion" must either be described by a set of specific equations like that of Einstein's (in which case, an atheist could also use those same equations, while denying the existence of God) or else it means we (not having access to God's "hidden counsels") simply can't predict exactly how the size of the early universe changed with time.  But then how do you get any quantitative predictions for what you see when you point your telescope into the sky?

But if all you mean is that, in the ordinary course of doing science, scientists should not a priori rule out mathematically well-defined hypotheses (such as the fine-tuning of the constants of nature in a way that happens to permit life, or a net nonzero number of baryons coming out of an initial singularity), simply because those hypotheses seem "unnatural" in the absence of an intelligent creator, then I agree with this.  Nor, obviously, should a theist rule out the possibility that God might have created our universe using inflation (I don't see why not).  Such scientific hypotheses should stand or fall on their own individual merits, as the case may be.  It's okay (and indeed essential) to be guided by our own individual sense of parsimony, but we shouldn't be so biased that we rule out sensible models which explain the facts better.

(Incidentally, if inflation did happen, then the hypothesis that the universe just "started off" with more matter than antimatter can't work.  Even if there were more baryons than antibaryons coming out of the initial singularity, the universe expanded so rapidly during inflation that the initial baryons would have been diluted to homeopathic proportions.  For this reason, physicists generally prefer models of baryogenesis, in which the baryons are created by some specific physical process some time after inflation ends.)

Posted in Scientific Method | 16 Comments

## God's will

Aron,
How is it possible that God is in control of all things and their will is always done, assuming that we are free?

First, why are we free in the first place?  Because God wants us to be free, and he always gets what he wants!  (Unless he wants something else more which conflicts with it; then he gets that instead.)

Some theologians distinguish between God's permissive will and his perfect will.  If God wants you to freely choose to love him.  Since he wants you to be free, that means his permissive will involves creating a world in which you are allowed to love other things instead of him, and even to become enslaved by these things and lose your freedom for a time.  So our Father permits people to love e.g. pornography and greed, but his perfect will is that we should turn to him and become pure and holy through his Son Jesus Christ.  God "wants all men to be saved and to come to a knowledge of the truth." (1 Tim 2:4)

So there is one sense in which God's will is always done—nothing happens unless he permits it to happen, according to his wisdom in accomplishing his ultimate goals.  But that does not mean he is equally pleased by everything that happens.  "Do I take any pleasure in the death of the wicked? says the Lord YHWH.  Rather, am I not pleased when they turn from their wicked ways and live?" (Ez 18).

Hence we need to pray every day that "your will be done", because our Father has freely chosen (it is his absolute, iron will) that some graces will be given only when we ask for them, and cooperate with the lavish grace which has already been given, before we even knew to ask.

In the end times, after Jesus comes back, God's kingdom will come and so his perfect will is going to extend throughout the entire universe, just as it is now in heaven.  But even then, there will be some rebels who refuse to give up their hatred and pride, who will end up being excluded from the Lord's perfect will, because he permits them to be the kind of person they want to be, instead of the kind of person he wants them to be (Rev 22:15).  So God will not, in fact, get every single thing he wants.

Yet he is clever enough to work everything which happens towards the final blessedness of those who love him, according to his plan from before time began.  "For those whom he foreknew, he also predestined to become conformed to the image of his Son" (Rom. 8:29).

Posted in Theology | 12 Comments

## Keeping the faith in college

Anyway, my kids are in 6th and 7th grades in a gifted school and in Florida, we have a prepaid college program and they both have 4 years tuition paid for.  How do I avoid sending them to the Dawkins and Krauses in academia.  I'm not saying it needs to be a christian school, but I'd like to avoid the atheist agendas if possible.  I'm accused online of believing in an old man in the sky, flying spaghetti monsters, Santa Claus, etc, and I don't know what I could expect a college student to withstand.  Any suggestions on how to identify these institutions, or suggestions on how to prepare my kids for the "smart people don't believe in silly things like God" mentality?

First of all, you're already doing a good job being a parent who is interested in science and open to truth in every area!  That will serve your kids well.

Not to panic you, but it's true that a LOT of kids who were raised in the Church fall away when they go off to secular colleges.  (Though many of these people come back to the Church later in life, when they settle down and have kids of their own.)  But I don't think this is usually because they get argued (or more likely mocked) out of it by people like Krauss or Dawkins.  In person, most atheists aren't all that evangelical about it, actually.  Atheists who argue about it on the internet aren't a typical sample!

Anyway, I think freshman college students are more likely to stop going to Church, and slowly drift away.  Or they'll get drunk and have sex with somebody at a party, and then feel like they can't really call themselves a Christian anymore.  Which is sad, because it indicates that they never really understood that salvation is by God's mercy, and not based on them being a good person who never makes serious mistakes!

A lot of Christian parents think they are raising their children with Christian values, but they're only really teaching them to be a "good kid", and then when they become an adult, it isn't real to them anymore.  It's biblical and proper for children to be obedient and responsible, but this is not the same thing as having a personal relationship with Christ.  Obviously you can't do this for them.  You can only show by example what it looks like.

So a lot of parents get into a panic and think they have to send their kids to a Christian college or else they'll stop being Christian.  But that might just be postponing the time when the person has to choose to follow God themselves, without people telling them what to do!  (For all I know, your kids are already like that, and you don't need to worry about it.)

There's nothing wrong with going to a Christian school, if that's what your kids end up wanting to do, but what's even better is if your children could be the kind of people who are secure in their faith and who have lots of nonreligious friends that they lead towards Christ.  Actually that goes for right now as well.

Anyway, I agree with St. Scott that the exposure method is best.  They'll eventually hear it anyway, so talk to them about it now (in limited quantities and in an age appropriate way, of course).  Talk to them about why you believe what you believe, and why other people believe differently.  Show them one of these online comments, and see if you can get them to explain to you why it's a misunderstanding of what we believe.  Teach them the skill of separating out the good from the bad (for example, it often happens that a writer says some nifty things about science but throws in a jibe at religion, so you can ask whether the one thing really follows from the other).

But of course, also give them a lot of good Christian books, for example by Sts. C.S. Lewis, G.K. Chesterton, N.T. Wright, Dorothy Sayers, A.W. Tozer, E. Stanley Jones, Augustine, George MacDonald, J.R.R. Tolkien, or, if they like historical fiction, Elizabeth Goudge.  Of course there are many more authors to choose from; it depends on their particular interests.  (Encouraging them to study the Bible goes without saying, of course.  But you could see if your church denomination has a Bible quizzing program or something like that for teenagers.)

Just having encouragement from a parent who is interested in science and open to truth is already a lot!  Teach them to ask questions and don't be afraid of saying "I don't know" instead of giving pat answers.  It's better to teach your kids that you can trust in Christ even when you have a lot of questions, then to give them a long list of answers and make it seem like faith depends on getting every one of them right.

The way a lot of Christians are raised, if they start doubting whether e.g. the Noah story was 100% literal in all of its details, they feel like they may as well be disbelieving in the Resurrection of Jesus!  But one of these two events is at the core of our faith, and the other is at the periphery.

Which college your kids go to should obviously depend on their own choices and interests, and it's a long time before this decision has to be made.  If they are truly seeking God's will, the Holy Spirit may guide them in a direction which neither they nor you expect.

In general, Ivy Leagues and other elite universities tend to have the academic environment which is most hostile to Christian faith.  I would not recommend places like Harvard, Yale, or U. Chicago as places to study theology, for instance.  But they might be fine for the sciences.  In my experience, secular science departments are more accepting of religious people than the humanities departments, actually.  Maybe not in Biology, because of all the conflicts involving Evolution.

A lot of secular schools have strong Christian social groups such as InterVarsity or Cru which can provide support for Christian students.  Really, it depends a lot on the school.  And there will always be some churches in the area where people are willing to pick students up from the college dorms, if one inquires sufficiently.

There are many fine Christian colleges out there, though some are Christian-in-name only, or so fundamentalist as to be embarrassing.  As good examples, I have family members who attended Seattle Pacific and Westmont, which are excellent liberal arts colleges, seriously Christian but not fundamentalist.  But they're over on the West Coast.  I'm not familiar with the situation near Florida, but a good high school counselor would know.  Very few Christian schools are also highly ranked research universities (although there are a few, like Notre Dame or Baylor).  Although this matters more for graduate education than college.

I went to St. John's College, which I would say is a rare example of a school where most students aren't religious, yet theological books (including the Bible) are on the curriculum and taken seriously.  This is a really weird college, not for most people (and rather expensive without financial aid) but for a few people, it's one of the best things that ever happened to them.

There are no wrong choices here.  What matters is where God is leading them as individuals.

It's a little tricky to give advice here, because some parents are over-protective, and some are under-protective, and the advice that is right for one, is wrong for the other.  If you're worrying about college when they're in 7th grade, you probably belong more to the first category. :-)  I'd advise you to relax and trust God, who knows better than any of us do what each of us need.

Posted in Education | 13 Comments

## God and Time III: General Relativity

Imagine if somebody said that only one height exists at once—whichever elevation you happen to be in at the moment, only things at that elevation really existThe moles in the ground are can be asserted to be "below", but that just means that they used to exist when you were in your basement.  And the birds in the trees are "above" you, but that just means that they will exist after you indulge your habit of climbing to the attic.

(Unlike the case of time, I can go either up or down, but who cares?  Time may flow like a river, but space flies like a bumblebee, wobbling around in random directions.)

This is clearly uncommonly silly, and there are several retorts one might make to it.  If the ground beneath us doesn't exist, then what on earth is holding us up and supporting us?

Also, there is no such thing as a perfectly flat human being.  Your brain occupies several different planes of elevation at once, and there is no good reason to think that any horizontal slice of your brain would be capable of thinking, independently of all the other slices.

Another possible retort would be to critique the language, and say that there is really no meaning to it.  If I say that the birds will exist after I go into the attic, I am implicitly and illegitimately assuming that my attic exists, and that I can therefore go up to it.  But if I really took my philosophy completely seriously, I would have to believe that the attic doesn't exist either.  To say that up exists upwards is a circular definition, which can hardly console us if things that are up do not exist in the first place.

But if none of these "philosophical" arguments are persuasive, I can always crack out the "Argument from Geophysics".  Our most advanced scientific theories suggest that the world is in fact round.  It turns out that up and down are relative concepts, you see.  In Australia, they fall in a different direction than we do.  What they call down is different from what we call down.  The actual laws of physics are rotationally symmetric.  There is a symmetry which mixes up the up-down axis with the right-left axis and the forwards-backwards axis.  We can call "down" the direction which points to the Earth, but the earth is a contingent object which might not have existed.  Out in space, there is no reason to adopt a geocentric coordinate system.

And certainly, if we start doing theology, it would be presumptuous to think that the God who created the whole universe, all the stars and galaxies, is confined to existing at some particular elevation.  Whatever limitations we may ascribe to created beings, we should not ascribe them to the unlimited Creator, who made them all out of nothing.

(Some ideas, e.g. the idea that God is a really old man with a long white beard who lives in the sky, really do become ridiculous when you consider the size and proportions of the Universe as discovered by modern Science.  But garden variety Internet Atheists are always trying to manufacture this feeling artificially, in situations where it's a non sequitur.  If you can't tell the difference between Classical Theism and belief in a sky-fairy or an invisible garage dragon, that shows your intellectual limitations, not mine.)

This analogy summarizes the previous posts in this series, only I was talking about Time instead of Height:

It turns out that there is also a "rotational symmetry" so to speak (called a Lorentz boost) which mixes Space and Time.  It works a little bit differently from a regular rotation, since it involves rotating along hyperbolas instead of circles.  Mathematically, it's just a matter of throwing in a minus sign.  A result of this is that there is a lightcone which is unaffected by the symmetry transformation.  Some pairs of points are timelike separated (one point can affect the other) and others are spacelike separated (neither can affect the other), but there is no such thing any more as simultaneity.  From the perspective of somebody who is stationary, time goes slower for somebody who is moving; this is called "time dilation".

But in General Relativity, things get more wild, since space and time can themselves be affected by the behavior of matter.  Thus the distances and durations become a function of where and when you are.  Time runs slightly slower near the earth than it does in outer space.  (Believe it or not, this is why things fall down.  An object in free-fall always takes the path which maximizes the amount of time to get from point A to point B.  This is a compromise between SR and GR time dilation effects.)

In Special Relativity, space and time are a unity, but they have a fixed geometry.  The distances and the times are the same regardless of what matter does.  They are unaffected, and therefore they might possibly (by a Materialist, not by a Classical Theist) be taken to be a fundamental, necessary, and immutable feature of reality, which limits other entities but is not itself affected by them.

In General Relativity, by contrast, the spacetime metric $g_{ab}$ not only affects matter, it is in turn affected by matter.  This implies that the causal structure  (which tells you which points can affect which other points by signals) is itself causally affected by stuff.  So we learn that the particular geometry of spacetime is a contingent, mutable feature of reality.

From a philosophical point of view, the Absolute Spacetime of Newton (or Special Relativity) was never very satisfying.  Even if it is Absolute, an empty Spacetime can hardly itself be the source of all that is real.  Thus there must also be some other principles besides those of space and time, threatening an unparsimonius proliferation of fixed principles.  It has seemingly arbitrary features, and yet if it is really immutable and necessary it is difficult to explain it in terms of other things, other than just God's will.  Many philosophers such as St. Leibnitz and Mach rejected absolute spacetime, and tried to reduce it to the status of merely relative data relating various material objects.  Newton and his followers, on the other hand, tried to identify Space and Time with the necessary attributes of God, his Immensity and Eternity, but this doesn't work very well theologically.

Einstein was influenced by Mach in the creation of GR, but it doesn't really meet Mach's original aspirations since spacetime is still a reality independent of matter in his theory.  Mach would have said that spacetime has no independent reality; that it is just a way of keeping track of the relationships between material objects.  (He thought that the water would run to the sides of a rotating bucket only because the bucket was rotating compared to the distant stars).  But in GR, it is possible to have a geometry apart from any matter, e.g. empty Minkowski space, or a spacetime with gravitational waves.

There is indeed a sense in which the curved spacetime of GR is relational—there is no absolute fixed coordinate system to measure everything else by.  Thus it is only meaningful to  measure the locations and times and velocities of objects relative to other objects, indeed unlike SR we must even specify a specific path through spacetime between the two objects, in order to meaningfully compare them.  But, even though GR is relational, the spacetime metric $g_{ab}$ is itself one of the entities which may be used to construct relational observables.

Thus I would say that Spacetime in GR is neither absolute in the Newtonian sense (more fundamental than matter), nor relative in the Leibnitz/Machian sense (less fundamental than matter), but rather has the same status as matter.  It is real in the same concrete, tangible way that a rock or a tree is real.  It is one of several different fields in Nature, all with equal status, all capable of affecting and being affected.

As some physicist I can't track down right now (Carlo Rovelli?) once said, if an intense gravity wave passed by and destroyed your house, you would think of it as being just as real as any other kind of matter.

Now, if Spacetime (and therefore Time) is real in the same sense that a rock or a tree are real, that meas that it is also a contingent, created being.  Time is just one of the many things that God has created.  But the Creator, blessed be he, is not dependent on rocks or trees for his existence.  He is not measured or parcelled out by units of space, therefore he is also not measured by time.  Time is just something he created, which need not have existed.  Before they were created, and afterwards, he exists just the same as he ever was.  He is the Absolute, the Fundamental Reality which everything else depends on, but which does not itself depend on anything.  God's divine attributes (his necessity, eternity, and unity) imply that he cannot change with time, nor can he consist of distinct parts at each time.  He is the Alpha and the Omega, the Beginning and the End!

But I digress, since I was planning to discuss the Scriptures in the next post.  This one is supposed to be about how GR makes it even harder to say that God is in Time.  I've already talked about the contingency of the spacetime geometry.  Now let's talk about the arbitrariness of selecting what you mean by a single moment of time.

In SR, there is still a preferred notion of "simultaneity" if you pick a particular reference frame.  I drew a picture of that in the previous post:

Here Sue and Martha don't agree on whether $p$ or $q$ came first.  But maybe Sue is objectively right and Martha objectively wrong?  Somebody could still argue that there is a special inertial frame of reference with respect to which God happens to exist.  In other words, God has no position, and yet he has a velocity?  He is not an idol, a piece of wood or stone carved into an anthropomorphic form.  Why should he be limited in this way.

But in GR, spacetime is curved, and there are no inertial coordinate systems defined on the whole spacetime.  You can divide Spacetime into Space and Time in any way you like, using wiggly surfaces (although one might want to restrict to surfaces which are everywhere spacelike).  For example, the relationship between 2 coordinate systems could look like this:

In GR is not always any particular connection between a given coordinate system and a given observer, so I have not drawn Sue and Martha in this picture, but I have still drawn the spacelike separated points $p$ and $q$ which are in an ambiguous time relation.  (Since spacetime is 4 dimensional, the time slices I've drawn actually represent 3 dimensional surfaces.)

Of course, nothing stops you from choosing a funky coordinate system in Newtonian mechanics or SR either.  For example, it is often convenient to choose a rotating frame of reference to follow a rotating body such as the Earth.  Or a coordinate system which tracks an accelerating observer.  (Many pop descriptions of GR give the false impression that you need GR to describe accelerating coordinate systems; this is obviously false since objects can accelerate even in Newtonian mechanics, and nobody can prevent you to choosing coordinates however you like no matter what the correct theory of physics is.)

The difference in GR is that none of the coordinate choices are particularly nice or special.  It looks from the picture above like the gray coordinate system is nicer than the apricot one, but that's just because your computer screen is flat.  On a typical curved spacetime, all time slices are bent in one place or another.  Thus, instead of having a 3 parameter family of "nice" time slices, we have an infinite dimensional family.  (The details depend on which particular curved spacetime we have.)

Do we really want to say that God's experience of time depends on making an arbitrary choice about how to respond to the gravitational field of each and every star?  An choice which, from the perspective of physics, is a completely meaningless choice of coordinate system?  God's perspective on the universe should not be more provincial and limited than the perspective of a mere physicist such as myself.  The Glory of Israel does not change, so why does he need a time coordinate?

Now it is true that on some specially nice spacetimes, there is a naturally nice choice of time coordinate.  For example in an FRW expanding universe, there is a "cosmic time" coordinate which tracks the overall size (the "redshift factor") of the universe.  Some philosophers, such as St. William Lane Craig, have suggested that God's "time" might simply be this "cosmic time".

But this is a misunderstanding of the physics of our universe.  The FRW metric is a just an approximation to reality.  It describes a universe which is completely uniform (the same in everywhere) and isotropic (the same in every direction).  This is a very good approximation on large distance scales (billions of light years), but on shorter distance scales (e.g. the solar system, or the milky way, or your living room) you may have noticed that matter is not distributed uniformly.  It comes in clumps, and each of these clumps has a gravitational field which distorts the spacetime metric, making the FRW metric no longer correct.  On a lumpy spacetime, the notion of "cosmic time" is not well-defined.

With sufficient effort, one might be able to define a different time coordinate which is well defined.  Perhaps the maximum proper time since the Big Bang, or something.  But reformulating GR in a way that makes special reference to such quantities spoils the beauty of Einstein's theory.  It is ugly.  As for a blind and lame theory like that, I hate it in my soul.  Why should our physical theory describing gravitation get uglier when we describe how it relates to God?

The closest thing I know about to an elegant reformulation of GR with a special time coordinate is called "shape dynamics".  (I say know about, since I don't understand it).  Apparently this is equivalent to GR in a coordinate system where you pick your time slices to be CMC ("constant mean curvature") slices.  I won't explain that right now, except to say that the soap films in your bubble bath are also CMC surfaces.  But given a GR spacetime metric, there might be many possible choices of CMC slicings, or none.  So the equivalence to GR is not complete.

It is of course always possible that a new theory of physics (such as Hořava gravity) might reimpose something like absolute time.  But I wouldn't count on it.

I think this is a good illustration of the point I made in Models and Metaphysics:

But it seems to me that the correct view is in the middle, that Physics has some bearing on Metaphysics but it doesn't fully determine it.

There are always going to be ways to force physics into being compatible with an A-theory metaphysics of time, but it doesn't look elegant or pretty.  The B-theory seems to fit much more naturally.  Physics can't usually rule out metaphysical ideas, but it can make them look a lot clunkier.

But in this case, physics isn't telling us anything we couldn't have learned from good philosophical theology.  Or from scriptural exegesis—which will be the subject of my next post in this series.

Posted in Physics, Theology | 29 Comments

## Challenge Solution #1

I've posted the solution for the First Challenge Question in the comments section to that post.  St. Jack Spell's comment here is the winner, and my answer key is here, along with some secret knowledge which I promised to "Andrew2" (St. Andrew II?)

Congratulations to Jack---As a prize, he may suggest the topic for a post.  (But no promises about when I would do that post.)

Posted in Challenge Questions | 8 Comments