Quick Interstellar Thoughts

I’m teaching a Gen Ed course on relativity this term, which means I’m spending the last few weeks of the term discussing black holes. Which, in turn, means there was no way I couldn’t use that story about Kip Thorne calculating the appearance of a black hole for the movie. Especially since I have the students reading Thorne’s book.

And that, in turn, meant I needed to see the movie. So we got a sitter for the kids Saturday night, and went to the local theater to check it out. And, you know, it’s pretty much what it’s advertised as: A very pretty giant SF movie, with all that implies, both good and bad.

On the good side, they really did take some pains to get actual science content in there. There’s the black hole from the promo stuff, a wormhole, and even some old-school orbital mechanics. More relevant to my current obsessions is the fact that scientists and engineers are unambiguously the heroes of the piece, and the day is saved by people who stop and think things through in a systematic way.

On the bad side… well, the failure mode of grand cosmic SF is and always has been mystical twaddle, a narrative force whose attraction is more inescapable than gravity. And Interstellar doesn’t even come close to avoiding that problem. There’s a whole bunch of “fifth dimension” hooey, and that’s even before you get to the Power of Loooove transcending time and space.

And those flaws are somewhat magnified by the fact that a lot of the science is badly bent for narrative purposes. They fit gravitational time dilation in there, but the degree of time dilation they see is ridiculous, and real gravity isn’t like Angry Birds Space, with effects that cut off a fixed distance from the center of the black hole. And the characters are kind of stupid for not realizing that there was a problem with the water-planet probe, and the Blight doesn’t make any sense, and blah, blah, blah. Many of these questionable elements are also delivered in speeches that strain to rise to the heights of clunky dialogue. If you’re inclined to poke holes in the science and story, there are no end of holes you can poke.

But, to bring it back around to the good side, I don’t think any of those holes are any harder to retcon away than any other SF movie. A lot of them probably should’ve been addressed with an extra line or two of dialogue here or there, but it’s not hard to imagine off-screen conversations (and while it’s a very long movie, there are conversations off screen…) that could plug a bunch of the holes.

And I greatly appreciate the movie for what it isn’t, which is any of the things we saw in the trailers. Which, for our showing, were for the seventh Fast and Furious movie, the third Hunger Games movie, the second Avengers movie, and Ridley Scott remaking The Ten Commandments. (We also got trailers for a MLK biopic and a dreadful-looking Mark Wahlberg movie, but those aren’t relevant here.) For all Interstellar’s flaws, it’s at least got ambition– it’s an original story, not a sequel or a remake or based on something that was successful in another medium. And those are depressingly rare these days. The flaws of Interstellar are, for the most part, present in pretty much every big-budget movie, but at least it’s trying to do something ambitious and original.

So, I’m overall pretty happy with the movie. It also helps that Christopher Nolan’s general directorial style works well for me, making me more inclined to forgive the plot holes and bending of science to serve dramatic purposes– if you’re allergic to the Inception horns, you’ll probably feel less charitable. But it’s a great-looking movie, with spectacular design work, and while it takes liberties with astrophysics, it presents a very positive view of science on the whole. I’m glad I saw it in the theater, and I hope it makes a giant pile of money, mostly so people in Hollywood will keep giving Nolan the resources to make movies that aim high.

Particle Fever and Modern Art

As mentioned last week, I was the on-hand expert for the Secret Science Club’s foray into Massachusetts, a screening of the movie Particle Fever held at MASS MoCA. This worked out nicely in a lot of respects– it gave me an excuse to visit the newly renovated Clark Art Institute in Williamstown and check out the spiffy new library at Williams (where they have my second book on the shelves, but not my first; I may need to send them an author copy in lieu of a check this year…). I also did some random nostalgia things like grabbing dinner at Colonial Pizza (now in a strip mall halfway to North Adams, not the same vibe) and going up to the overlook above the famous hairpin turn (the view from which is one of the things that convinced me I wanted to go to Williams). And, of course, I got to see the much-buzzed-about movie, which I hadn’t gotten my act together to check out when it was in theaters. So, all kinds of winning.

The movie is very well done, following a handful of scientists from the days just before the first circulating beam at the LHC in 2008 to the announcement of the Higgs discovery in 2012. The most dynamic characters are superstar theorist Nima Arkani-Hamed and CERN post-doc Monica Dunford. Arkani-Hamed is notable for being furiously intense about whatever he’s doing, whether it’s talking about his pet theories, ranting about the PR mistakes made by CERN, discussing the abstract sculpture outside his office, or ordering convenience store food. Dunford is mostly just really enthusiastic. Like most such things, I think it oversells the general importance of the Higgs, and it doesn’t really go into the physics quite enough, but it’s very well made, and does a nice job showing the highs and lows of research science. I think the biochemistry documentary Naturally Obsessed probably did it a bit better, because they caught a much more immediate response to the major setback; the LHC and its collaborations are so huge that the magnet failure remains pretty abstract.

The participatory part was the usual mix of terrifying and fun. I helped put together a trivia quiz to be done beforehand, and the organizers asked me to do some on-stage chatter to help fill time while they collected the answers. We agreed that they would ask about the “Will the LHC destroy the Earth?” thing, so I could have something in mind to talk about rather than just free-associating. And, of course, once I was on stage I thought of something completely different than what I had worked out in my head in advance, and was basically ad-libbing. Which started to bomb, but I managed to save it. So, like I said, terrifying and fun.

Post-movie, I did Q&A, which was a little odd given that particle physics isn’t really my thing. But I know enough to be able to give answers at the right general level, and I had the foresight during the movie to Google up Robert Wilson’s famous testimony about Fermilab and national defense, so I could bust that out with proper attribution when someone asked what economic benefit would come from all this. And I got in the obligatory local pandering with a joke about Arkani-Hamed re-arranging the abstract sculpture, and a Williams-Amherst reference when talking up tabletop searches for new physics. I might’ve been a little hyper, but I think that’s probably what was needed. Also, I might’ve had a couple of beers during the movie. There was a photographer taking pictures for MASS MoCA, but I haven’t seen any.

I spent something like half an hour or forty minutes answering questions from people after the event was officially done, including one enthusiastic high school student, which is always great. The adrenaline rush from all the performing carried me most of the way to Pownal, VT on the way home, at which point the giant Coke I bought on my way out of town kicked in and caffeine and sugar got me the rest of the way home.

So, all in all, a great time. I enjoyed the movie, and the overall event; their usual Boorklyn venus is a bit out of the way for me, but I’ll definitely consider making the trip down sometime when they have an event that’s relevant to my interests.

My favorite random bit from the event came before the film, though, when we were working the room. The organizers were a few tables ahead of me, asking people if they had questions for a physicist (i.e., me), and when I caught up to them, they said “Oh, this guy is a physicist, too,” indicating a guy sitting at a table way at the back with his teenage son. “Where do you work?” he asked me. “Union College,” I said. “Union… Wait, are you Chad Orzel?” he asked. I said that I was, and he said “Oh, we have your books. Nice to meet you, I’m Adam Falk.” And so I had a nice chat for a while with the president of my alma mater…

(I decided it would be tacky to complain to him about the library not having my first book…)

Uncertain Dots 25: The Lightning Round

I got the time for the regular hangout wrong, and then we had some weird computer difficulties, so we only had ten minutes for Uncertain Dots this week. Which was enough time for me to say disparaging things about comic book movies, so, you know, if that interests you…

Here’s the making of Interstellar story about Kip Thorne.

Here’s the Avengers 2 trailer.

Also, a program note: I will be at MASS MoCA tonight talking about Particle Fever, if you’d like to hear me talk about real physics on film, or just take issue with my slagging off comic-book movies in person…

Particle Physics in Western Mass.

That’s “Mass” as in Massachusetts, not the stuff associated with the Higgs field… specifically, North Adams, MA, where I’ll be this Saturday night, October 25th, at the Secret Science Club screening of Particle Fever. This will be at the MASS MoCA, tickets here.

The Secret Science Club is a regular gathering in New York City featuring mind-bending lectures, volatile experiments, and thematic chemical libations (special cocktails, that is). It’s like the coolest science class you’ve ever been to, but with drinks and a DJ. SSC rockets into MASS MoCA with a special screening of Particle Fever, a “dazzling, dizzying documentary” that follows six high-energy scientists as they seek to unravel the mysteries of the universe. Plus, get your brain on with our audience pop quiz. Door prizes!

This is really convenient, because I never actually got my act together to go see Particle Fever when it was in theaters. So I get to see the movie all my physics friends on social media raved about, and hang out in a cool space. This will also be a nice excuse to go to the newly renovated Clark Art Institute in Williamstown, and generally wax nostalgic about college for a bit…

Anyway, if you’re in the cool bits of New England, stop by.

Space Travel, Einstein, and GPS

Below you’ll find the slides from my Physics Day presentations at Space Center Houston, embedded via SlideShare. I was doing the TED-style minimal text thing, so they’re probably not all that comprehensible on their own.

The event was supposed to have a pop-culture connection, so I decided to use space travel and extrasolar planets as a hook for talking about relativity, thus all the movie images near the beginning. The original idea I had was to look at different fictional ways of evading the ban on faster-than-light travel, but they wanted something more in the half-hour range than the hour-long talk I was originally envisioning, so I had to cut it way back.

The problem with using space travel as an intro to relativity is that it’s easy to come off as a total killjoy, saying we’ll never reach other stars. My original plan was to offer causality as a reason why you ought to be happy about the ban on FTL travel– if you can move faster than the speed of light, than some observers will necessarily see effects happening before their causes, which would just be bizarre. I didn’t really have time for that, though, so instead I offered the Global Positioning System as an example of a useful application of the constant speed of light. With a bit of local pandering, as you can see from the maps toward the end.

I probably overshot the actual level of the audience– I was aiming for the upper end of middle school, but one of the larger groups in the audience on Friday was probably in fourth grade, so it pretty much went over their head. On the other hand, though, one of the actual middle-schoolers there (I’d guess about eighth grade) came up to me after the talk and said “Thank you so much! That’s the first time any of this made sense.” Which is a great feeling.

(I said “Thanks, that’s really great to hear. And, have I got a book for you…”)

So, anyway, that’s how I spent the latter part of my week. And if anybody would like an hour-long talk about relativity using fictional space travel as a hook, drop me a line, and we’ll see if we can make that work, because I’ve got the idea, now, and would like to actually do it at some point…

Superheros are Anti-Science

I’m not really a comic-book guy, but I’ve watched a bunch of comic-book movies recently. Kate was really fired up for the new Captain America movie, so I finally got around to watching the first one as background for that, then when I was sleep-deprived last week I watched the second Thor movie via on-demand cable, then Sunday evening Kate and I went to see Captain America: The Winter Soldier in the theater (her second time watching it– she’s really fired up).

Mostly, this has served to confirm that I’m not a comic-book guy. I’m just not invested enough in the idea of a movie about these characters to get past the staggering logical inconsistencies in most of the movies. They’re great spectacle, but as soon as I start to think about them at all, they just fall apart.

By itself, that wouldn’t be worth a post– Tastes Vary, end of story. But I was thinking about this while walking the dog this morning, and there’s a sense in which my dissatisfaction with the genre touches on a deeper issue connected to my current obsessions: in a very deep way, superhero stories are anti-scientific.

That may sound like a crazy thing to say, given that there are numerous blog posts and books by people I know using superheros to teach science at varying levels of plausibility. And an awful lot of superheroes, including most of those appearing in the current run of Marvel movies, supposedly originate in science– Captain America was made in a lab (see image above, which I grabbed from this blog post about superhero science) as were his adversaries. But as I’ve been banging on about for months now, science isn’t just about gadgets, it’s a process, and superhero stories in general are fundamentally incompatible with the process of science.

What I mean by this is that the essential nature of the superhero story requires the hero to be singular, or at most a part of a small team. It’s about one person overcoming impossible odds to save the world via their own personal awesomeness and comic-book-science enhancements. These are, at their core, somewhere between power fantasies and a testament to the human spirit.

Science, on the other hand, is all about duplication. One of the most essential– arguably the most essential– steps of the scientific process is telling other scientists what you discovered. Whereupon they go into their own labs and duplicate what you did, and tease out further implications of it, and so on. The sharing of results is what lets the next generation of scientists stand on the shoulders of past giants.

And that’s fundamentally incompatible with superhero stories. If you could really make superheroes by scientific means, they would quickly stop being superheroes, because they’d be everywhere in short order. Because that’s what science does— it starts with an unusual event, moves to a general principle, and then expands to go everywhere. Even when the original scientists don’t expect it– when Heinrich Hertz confirmed Maxwell’s prediction of electromagnetic waves, he famously shrugged it off as a curiosity: “It’s of no use whatsoever[…] this is just an experiment that proves Maestro Maxwell was right—we just have these mysterious electromagnetic waves that we cannot see with the naked eye. But they are there” (this particular wording via Wikipedia because I’m lazy). A decade or so later, we had radio.

There are ways to get around this, but they generally involve breaking the scientific process in some way. A common one is to invoke the mistaken notion of the ahead-of-their-time genius. Captain America is singular because the only guy who knew how to make super-soldiers was shot in the first movie. Nobody else could figure it out, because Dr. Erskine was a genius.

Except, that doesn’t work even within the context of the movies. Erskine was one of three people who had some success with super-soldier research, the others being Johann Schmidt and Arnim Zola– granted, they were less successful than Erskine was, but the notion that nobody in the intervening seventy years could do better beggars belief. And there have to be people who know an understand bits of the process– note all the folks in white lab coats in the image up top. Surely some of them could build on that knowledge.

And if you try to look in history for evidence of ahead-of-their-time geniuses, the evidence is scant. Feynman is touted as a genius, except Schwinger and Tomonaga solved QED at the same time, and Stueckelberg got there earlier but failed to communicate his ideas. And Feynman’s real genius lay in making QED comprehensible to non-geniuses– that is, in communicating it to others. Dyson played a pretty major role with that, as well, showing that all three versions were equivalent, and nailing down the loose ends in Feynman’s approach.

Einstein gets hailed as a genius, but Poicaré and Lorentz were close to Special Relativity, and Hilbert almost scooped him on General Relativity by virtue of understanding the math better. And within a couple of months of the publication of General Relativity, Schwarzchild worked out a detailed solution to a real situation while in the trenches on the Eastern Front of WWI. That’s not an indicator that Einstein was miles ahead of his contemporaries. Either that, or there was an unusually high genius density in 20th century physics.

There are a few myths in the history of technology that might seem to resemble comic-book super-science, but none of them really pan out. Nikola Tesla has an army of fanboys, but the great ideas he had that actually worked were not all that advanced– and usually got tied up in nasty priority disputes with other inventors who claimed to have the same idea. The ideas that were uniquely his mostly didn’t work, and some of them were just nutty. Leonardo Da Vinci is another example that gets busted out– he invented the helicopter!– but most of his “inventions” were more inspirational than technological. He had nifty ideas that sorta-kinda resemble modern inventions, if you tilt your head and squint like a confused dog, but he didn’t build working versions of any of them, because it wasn’t possible to make working examples with the technology he had available.

To find genuine examples of inventions or discoveries that were developed once and not replicated, you need to go back to before the beginnings of institutional science– things like the ancient Chinese camera obscura of Mozi cited in last week’s Cosmos, or Cornelis Drebbel maybe inventing air conditioning. But those are kind of dubious examples in a lot of ways, and nothing like you see in superhero stories. And the fact that they’re pre-modern supports the general point.

The other way to fix this is to push the story wholly out of the realm of science. So, for example, you could claim that the reason the very public existence of magic Nazi technology in 194mumble hasn’t transformed the world in a more comprehensive way is that all those disintegrator guns Hydra was using need to be powered by magic blue-glowing alien technology that operates on principles beyond human science, blah blah, Clarke’s Law. Except the principles behind that technology were evidently completely understandable by Dr. Zola in 194mumble, who built all that alien-powered stuff in the first place. Given seventy years and the many dozens of examples of working alien-powered gadgets from all the magic Nazis who get gunned down in the first movie, it’s a little hard to believe that movie-present technology isn’t way more advanced.

(You can maybe claim that all of this was suppressed by SHIELD/ Hydra/ The Illuminati, but then you get into the inherent implausibility of grand secret conspiracies. which is a whole different argument…)

The final way out is to attribute things to the singular properties of individuals, which is the route the first Captain American movie seems to be taking. That is, there’s only one Captain America because Steve Rogers’s personal qualities are so great that he alone could survive the super-soldier process without becoming a monster. Which, okay, I guess you can go there. But that pushes you into an entirely different category, the Chosen One story, which is itself fundamentally unscientific.

So, again, there’s a very deep sense in which superhero stories– even stories about technologically created superheros– are fundamentally incompatible with science. Which, now that I’ve realized this, I think is a big part of why I’m not really a comic book guy in the first place.

————

Please note: I’m not saying that the incompatibility between the superhero genre and science means that superhero stories are Bad, or that the millions of people who enjoy these stories are Bad People. There’s no requirement that everything be scientific at the core, and certainly no requirement that everyone share my tastes. I read and enjoy lots of fiction that is every bit as non-scientific as the core superhero story– I’m rather fond of epic fantasy of the Chosen One variety, for example. But I think there is this tension at the core of the stories, and that seemed like something worth poking at a bit.

The Sound of Simulated Bombs

So, last week I idly wondered about the canonical falling-bomb whistle. The was originally intended to be a very short post just asking the question, but I got caught up in thinking about it, and it ended up being more substantial. And leaving room for further investigation in the form of, you guessed it, VPython simulations.

This one isn’t terribly visual, so you don’t get screen shots, just a link to the code at Gist. It’s a simulation of a falling bomb, with air resistance, tracking the velocity as a function of time. Then it calculates a “Doppler shift” using the velocity as a fraction of the speed of sound for an observer standing on the point of impact, and another some distance away.

Putting this together required some guesstimated numbers, so I gave the bomb a mass of 1000kg, a radius of 30cm (which don’t seem wildly unrealistic from this page about WWII munitions) and dropped it from a height of 6000 m (around 20,000 ft, which is a reasonable value for high-altitude WWII bombing; I’m using WWII as a reference point because the whistling-bomb noise dates back at least that far).

What I wanted to see was how significant the shift would be for somewhat realistic conditions, and whether this could make a sound like the canonical falling-bomb whistle, decreasing in pitch. Looking at the physics, as in the diagram above, it ought to– the falling bomb starts out coming toward the observer, shifting up in pitch, but an observer off to the side should see the velocity become more tangential as it drops, eventually coming back to whatever the default whistle frequency is. The question I wasn’t sure about is how significant this change in pitch could be.

So, what does the simulation show? Well, the primary output is this graph:

Doppler shift due to a 1000kg falling bomb with a 30cm radius.
Doppler shift due to a 1000kg falling bomb with a 30cm radius.

There are three curves here. The black points show the shift as seen by an unlucky person at the impact point, and it increases through the whole fall. In the absence of air resistance, this would be a straight line, but with air resistance, there’s a little bit of curvature. The red points are for an observer who starts out 6000m away (the same distance as the height the bomb drops from), and first increases in pitch, then decreases. The green points are for an observer 3000m away from the impact point, and the shift is more dramatic, because the bomb has a velocity toward them for longer than in the more distant case.

The shift here is fairly substantial, because the bomb is falling very fast. It also does exactly the sort of thing you expect from looking at the velocity components above: first goes up, then down. So, you could get a falling-bomb whistle with the canonical decreasing pitch provided you’re standing off to the side of the impact point. The closer you get to the impact point, the more dramatic the shift, both in terms of amplitude and speed– if you make the distance to the observer just 600m, the shift goes from 70% above the original pitch to zero in just six seconds (not plotted here).

Now, this obviously presumes a particular size and shape, and thus an effect of air resistance. So, if we change the size, what happens? I tried doubling the radius for the same mass, and you can see what that does here:

The Doppler shift of a falling bomb for two different sizes, showing the effect of air resistance.
The Doppler shift of a falling bomb for two different sizes, showing the effect of air resistance.

A bigger radius means more air resistance, and thus a slower terminal speed (this almost reaches terminal speed), which in turn means that it takes longer to hit, and has a smaller peak shift. You still get the reversal in pitch, though.

The other question that came to mind back when I was thinking about this was whether the decreasing-pitch whistle was a result of imagining things from the perspective of the person dropping the bombs rather than the person being bombed. I’ve seen clips of bombs being dropped where they seem to whistle as they leave the plane, but that might’ve been a dubbed-in effect, for all I know.

Anyway, just for fun, I thought it would be interesting to compare the decreasing-pitch whistle of bombs observed from a safe distance to that of a bomb dropped directly from a plane, which led to this graph:

Doppler shift of a falling bomb during the decreasing-pitch phase compared to the shift heard by the person who dropped it.
Doppler shift of a falling bomb during the decreasing-pitch phase compared to the shift heard by the person who dropped it.

The Doppler shift just depends on the velocity, which is initially increasing at a steady rate due to the acceleration of gravity, so we expect the points for the pilot’s perspective to fall on a straight line, and they do. The others are decidedly non-linear, but again, we expect that, because it should go like the cosine of the angle to the line of sight.

So, does this accurately reproduce the falling-bomb whistle? I had hoped to make Mathematica reproduce the sound pattern here, but it’s very picky about which users it’s friends with, and life is just too short to keep wrestling with that program. We can turn to some eyewitness testimony, though, in the form of a comment that must have a good story behind it, left by Time Eisele:

I can vouch for the ‘descending whistle’ sound in the case of falling bowling balls, at least. From an estimated peak altitude of about 1500 feet, and standing approximately 1000 feet away from the ultimate impact point, the sequence goes:

– Whistle starts by getting gradually louder at a more or less constant pitch.

– In the last few seconds of the drop, the pitch drops noticeably, all the way down to the ground.

And, you know, that looks pretty much like what we see in this graph: a slow decrease from the peak at first, that rapidly speeds up toward the end of the drop. So, I think this works out nicely. I’d like to know why Tim was being bombarded with bowling balls, though…

Uncertain Dots, Episode 8

In which Rhett and I talk about Cosmos. What, you thought there would be another topic? We have contractual obligations, you know…

Okay, there were some other topics like Battlestar Galactica (both versions), why so much of what’s on Discovery Channel and TLC sucks these days, the flawed astrophysics of Firefly, speculation about how those little infrared thermometers work, and why some kinds of labs are hard.

And Cosmos again. Because, really, how could we not?

Nostalgia and the Next Generation

“Daddy, I wanna play with the robot dog!”

“It’s not a dog, honey, it’s an Imperial walker. An AT-AT. A fearsome armored assault transport used to overwhelm the Rebel defenses in the battle of Hoth.”

“…”

“…”

“…”

“OK, fine, you can play with the robot dog.”

We came down to my parents’ for Thanksgiving this year, because both Kate and I are really busy with work at the moment, and didn’t need the additional stress of planning and hosting a big dinner. On Friday morning, my dad went up into the attic and dug out the bags containing the vast collection of Star Wars toys my sister and I amassed in the late 70’s and early 80’s:

The larger toys from our Star Wars collection.
The larger toys from our Star Wars collection.

I was right in the prime demographic for this– I was six when the first movie came out– and my sister is four years younger than me, so we had a good long run with Lucasfilm and Kenner. We didn’t quite have a complete set of all the original action figures, but were pretty close. Some of these have gone missing, and the original Lando Calrissian’s head snapped off at some point, but my dad found most of them up in the attic, and then SteelyKid spent a happy hour or so carefully washing two decades worth of dust off them (as seen in the “featured image”), and asking me to name them all (a lot of the character names are totally gone from my memory, though I know when they appeared in which movie). And I still vividly remember how all the ships go together (though a lot of pieces are broken or missing, and some of the springs and catches have worn out). She particularly enjoyed the speeder-bike that blows apart when you press a button on the back.

She’s never actually seen any of the movies, thus the dialogue snippet above, but she’s sort of vaguely aware of Star Wars as a cultural force, thanks to various classmates. The original movie is probably a little too scary for her still, but maybe one of these days…

(Assuming it’s possible to get a version where Han shoots first, that is. I have principles…)

Anyway, I spent a good deal of Friday back in 1981. Hope the end of your week was half as good.

Favorite Quantum Physics in Science Fiction?

I’m doing a bit of work on an idea for physics outreach, which would involve tying a discussion of modern physics to science fiction stories. I have Opinions about this sort of thing, of course, but I also have readers who might think of things I don’t. So, let me throw this out to you all:

What is your favorite example of a science fiction story (here meaning print, movie, or television) making use of ideas from quantum physics? What’s your least favorite?

My favorite stories invoking QM ideas are probably Robert Charles Wilson’s brilliant “Divided by Infinity” (which I will draw heavily on if I ever go nuts and start a cult), and Ted Chiang’s “Story of Your Life,” which I guest lectured on some time ago (by the way, the transition to WordPress a while back broke all internal links, so here’s a working link to the hypothetical scenario).

But I’m curious to know what other people think, if anybody still reads and comments on blogs.