Check it out here: Lenz on Learning: Reflections on parenting, education, kids, and creativity. Here are the article titles so far:
I’ll probably still blog here on miscellaneous topics on an occasional basis (as always), so feel free to subscribe to both.
I just began watching The Atheism Tapes (on Netflix), by Jonathan Miller, a series of interviews with prominent atheist intellectuals. In the first episode, Colin McGinn reviews some standard arguments for and against the existence of God.
He puts forward lack of positive evidence as his principal reason for not believing that God exists. Paraphrasing Bertrand Russell, he says, “there’s no more reason to believe in the Christian God than in the Greek gods.” I think this is a silly assertion. Nobody believes in the Greek gods today. However, many millions of people do believe in the Christian God today. He may not think that’s a good enough reason to believe in God, but it’s a big jump to say there’s “no evidence”. If he’s talking scientific evidence, then I grant him the argument. Scientific evidence is a very narrow sort of evidence, as science is a very narrow sort of inquiry. But the continuing faith of millions over thousands of years does constitute some sort of evidence.
Later in the interview, he admits that people do have a sort of “cosmic loneliness”, or angst. He sees this as an explanation for why people have such a need for believing in God. The belief appears to satisfy their deep need for connection. This is another sort of evidence. You can use it to either explain people’s need to believe despite God’s non-existence, or you can view it as another sort of evidence for God—a being which, when believed in, “satisfies a deep craving in the human soul”, as McGinn puts it.
McGinn is most persuasive, I think, when he brings up the problem of evil. This should be truly challenging to any Christian or anyone who believes in the existence of a good, all-powerful God. Why would a good, all-powerful God let evil things happen in the world? McGinn notes the standard, ultimately unsatisifying explanation offered by theologians: God gave us free will, and we’re the ones that mess it up. Then what about natural disasters? Ultimately, the problem of evil is a real problem for faith. One of my beliefs as a Christian is that whereas God is all-knowing, we are not. And we’re not particularly meant to be. There are things we don’t understand and won’t ever understand in this life. Atrocities such as holocausts happen. There is a profound potential for evil in the human heart. These are things we have to contend with, even if we can’t fully explain them. If you’re going to believe in a religion, make sure it’s one that acknowledges and contends with the reality of suffering in the world and evil in the human heart—even if you were born into a free, wealthy society such as America where we are protected from much of the world’s suffering.
I have friends, family members, and colleagues who are atheists, and I want to better understand their point of view. I also want to find ways to address my doubts and to bolster my own faith in the face of unbelief. Despite my natural affinity for philosophy and philosophical arguments, I don’t put my hope in them as a primary way to grow closer to God (which is a primary goal of mine). They do play a minor role though; they fit in somewhere. Otherwise, I wouldn’t feel compelled to write about this topic. Just know that I haven’t even begun to expound on why I do believe, and I can’t necessarily explain all the reasons why I’m compelled to believe. (For one thing, I believe God had a large role in my choosing to believe and continue to believe, and that’s hopelessly circular from a philosophical perspective.)
I have a project where I need to generate file names that are GUIDs. I’m using Saxon.NET. With the help of Google, I figured out how to do that, but it wasn’t immediately obvious. Hopefully this post will make the solution easier to find for other people trying to solve the same problem.
This is just one example of a .NET function you can access as an extension function in XSLT 2.0, so a more general-purpose treatment of .NET extension functions might be more useful. (I defer to “Writing extension functions for .NET” for that.) But if you’re like me, you spend most of your coding time within the safe, comfy confines of pure XSLT. And you do very little .NET development. So to ensure your continued comfort, here’s how you can generate a GUID in Saxon.NET (relevant parts highlighted):
<xsl:stylesheet version="2.0"
xmlns:xsl="http://www.w3.org/1999/XSL/Transform"
xmlns:guid="clitype:System.Guid?partialname=mscorlib"
exclude-result-prefixes="guid">
<xsl:output indent="yes"/>
<xsl:template match="/">
<guids>
<guid>
<xsl:value-of select="guid:NewGuid()"/>
</guid>
<guid>
<xsl:value-of select="guid:NewGuid()"/>
</guid>
<guid>
<xsl:value-of select="guid:NewGuid()"/>
</guid>
</guids>
</xsl:template>
</xsl:stylesheet>
Here’s an example result from applying this stylesheet (to any input document):
<guids> <guid>6dbd3a72-ad74-429d-97ca-3056e8940813</guid> <guid>cea97da4-9de5-4fb5-a35e-ba04a0dee906</guid> <guid>41c89105-6cf7-4fd6-b17a-ed04235a4804</guid> </guids>
All you do is call the .NET platform’s System.Guid.NewGuid() method as an extension function. The function’s namespace URI identifies for Saxon what assembly and object class you’re interested in (System.Guid in this case).
Thanks to M. David Peterson: I found this usage buried in a code example in his lucidly-titled blog post: if ((OOP + FP + AOP) == XSLT 2.0) then ‘Composable Language’ else ‘Try Again’.
Short blog post, in bullet points:
That’s all for now. See you again in 6 months. 
This is how the PianoNinja is feeling tonight after suffering a difficult blow:
We had a little setback involving lost code. Ironically, this happened when I was trying to set up version control to guard against this very thing. I’ve posted a message to the user’s list for the IDE that failed to give me a warning before deleting all this naive user’s code, in hopes that similar mistakes by other users can be prevented. Hindsight is 20/20. I should’ve backed it up before trying to…back it up. It would also have been good to have Time Machine set up already, but I hadn’t done that either.
Thankfully, I did still have an older version of the code from before I switched over to the development environment that I’m now using, so I don’t have to start totally all over. And you can be sure that I have already secured that code into version control on a server machine so that I can continue from now on from a solid base.
How bad is it? Well, we were on Video #7. Let’s just say we’ve now reverted back to Video #3. In other words, all the code I wrote in the last two weeks is gone.
Maybe this is a blessing in disguise. Sure, I learned a lesson and I won’t make this mistake again. But the blessing might be that my continued dependency on MIDI files as the game’s underlying format is now that much less alluring. The MIDI crutch has been snatched out from under me. I don’t need to wrest myself from the MIDI code so I can move onto a better way. The code has wrested itself from me…
I was going to add bar lines tonight. Oh well, those can wait.
Before you know it, the ninja will be feeling better than ever.
Okay, this post is just to complete the thought I’ve been exploring over the last couple of posts. I wasn’t up for much heavy thinking tonight, so I decided to just download a free MIDI editor and normalize the durations of the notes in the Chopin Waltz MIDI file so that it had no more staccato releases in the first section of the piece. Now the visual note releases reflect the actual notated durations (except that some Klavarskribo continuation dots are still missing; I haven’t implemented those yet). I wanted to see if this helped make it easier to “see” the beat:
Video #7: Notation-consistent note releases (Quicktime streaming)
I think it works pretty well for this piece of music. The sudden flash of each note release now coincides with the attack of the next note. I think it now looks smooth and rhythmic, which is what I was hoping for.
I haven’t made any progress since yesterday’s report, but I did finally track down our camera. This video shows what I was talking about yesterday: the MIDI Note OFF events are now visible.
Video #6: Note OFF events visualized (Quicktime streaming)
The game isn’t making any sound in this video, because I’m not playing along on the MIDI keyboard. It’s easier to see the note releases when I’m not playing along and adding all the green and red colors. The piece is the same one I’ve been using for the last few demos: Chopin Waltz in E-flat, Opus 18.
The molasses effect of lingering notes is gone, so that’s good. But the note releases are accented too much, in that the suddenness of the notes’ disappearance tends to be the most visually striking movement that’s going on. It’s also dependent on the interpretation of the person who rendered the performance in the MIDI file. My theory is that if performance-dependent note releases are ignored and instead the actual note value is reflected (regardless of whether the note should be played staccato), then the accented note releases will actually help rather than hinder the feeling of the beat, since they’ll most often coincide with the attack of the next note. I’m looking forward to testing my theory out (and then moving on past this academic theorizing).
Today, I tried to enable what I talked about in my last post about PianoNinja. I was able to get the MIDI Note OFF events to be reflected in each note’s visible duration: how long it remains stationary on its piano key before disappearing. (I would have posted a video, but I can’t seem to find the camera right now, and I really need to be getting to bed earlier anyway.) I have a couple of observations:
A MIDI file contains a rendition of a piece, not (necessarily) the authoritative musical information you’d need to reconstruct a score. Staccato durations, for example, get interpreted as short notes that obscure the actual notated value. I’m coming to terms with what I want PianoNinja to do: display a score (in Klavarskribo notation) that can be relied upon as containing the more-or-less canonical information that makes up the piece. While there might be many and varied MIDI files for the same Chopin Waltz, I don’t want PianoNinja to be subject to those variations.
So while I’m glad that I got the MIDI Note OFF events to be reflected, the associated note-vanishing is still a bit jumpy-looking, since they don’t always coincide with the attack of the following note. Before diving into using MusicXML instead, I might try to see what sorts of MIDI file quantization I could do to stretch each duration out for its full note value. I’m going for the path of least resistance here in keeping this project moving forward—without compromising the steady vision I have for what PianoNinja can be.
As I play around with PianoNinja, I’ve noticed so far that it’s fairly easy to get out of sync with the notes that I’m supposed to be playing. I tend to speed up when playing slowly, for example. (You might have noticed this in the last video I posted). Part of the problem is that I don’t have any strong cues as to where the beat falls. In games like Dance Dance Revolution, there’s a very strong beat—you simply dance to the music that you hear. Ultimately, I think PianoNinja will need auditory cues as well, whether as simple as a metronome sound or as complex as a full accompaniment. (That would make it a lot more fun too.)
But before I add any auditory hints, I want to see how far purely visual cues can get me. Of course, I’ve made the decision to go with Klavarskribo, so the question as to what visual cues to use has largely already been answered for me. (Basically, use solid and dotted bar lines to indicate the primary and secondary beats, respectively.) But what Klavarskribo doesn’t answer is how to display the notes once they reach the point where they’re supposed to be played.
The simplest approach would be to just keep scrolling the manuscript right off the screen, just as if it was a roll of sheet music continuing to unwind. In other words, apart from the scrolling movement, the display would be purely static. You’d know when to play the notes only according to when they cross a given (horizontal) line, but then they’d keep on scrolling off the screen and out of sight. In that case, perhaps the most natural place for that line would be the middle of the screen rather than the top. That way, you’d be able to see the notes come and go rather than immediately scroll off the screen at the top.
I’ve decided to take a more dynamic approach, placing that line at the top of the screen and representing it with a picture of a piano keyboard, so that, for one thing, the relationship between the notation and the piano keyboard is immediately obvious (I hope). The dynamic aspect is that the visible note then freezes and remains stationary on its corresponding piano key for the duration that it’s supposed to be played, while all along the rest of the music continues to scroll upward. Early on, I was experimenting with a grayscale fade-out approach for representing the decay of the note’s sound, but I found that keeping it solid and stationary and then suddenly making it disappear worked nicely—especially when followed immediately by another note in the same hand. The combination of the new note stopping in its tracks and the old note vanishing in the same instant creates a certain visceral perception of the rhythm. At least that’s my suspicion and hope; I haven’t fully put it to the test. Right now, the durations are all hard-coded to the length of one beat, which doesn’t fit well with the Chopin Waltz I’ve been using in my demos. The notes all linger far too long, giving a molasses-like visual effect which doesn’t help you feel the beat at all. So I think I’ll focus next on taking care of those note durations.
With this approach, the most “attack-like” movement that you see is when a note ends, not when it begins. What makes it work is the fact that the disappearance of one note often coincides with the attack of the next. For that reason, it may turn out to work well for some kinds of music, but not so well for others.
But now I’m just speculating. First I’ll get it to work correctly and try several pieces of music with it. If I still find it to be lacking, then maybe I’ll add some kind of “flash” to each note’s attack. I’m hoping that won’t be necessary though. I like the idea of a visually spare interface that still packs a punch—like Klavarskribo itself, and, I hope, like the new PianoNinja logo.
I’m trying to figure out what file format(s) to support in PianoNinja. Synthesia has gone the route of “blind devotion to MIDI files” and its attendant pitfalls when it comes to notating music. I’ve already gotten a glimpse of these drawbacks now that I’ve tried to add the left-hand/right-hand distinction to PianoNinja. Some MIDI files separate the hands into two different tracks, and some don’t. And there doesn’t seem to be a standard way of doing this. Also, there are other visual cues built into Klavarskribo that I want to include, like bar lines, note beams, rests, continuation dots, etc. These aren’t going to be easy to derive from simplistic MIDI ON and OFF events, especially since the best MIDI files as far as performance goes would tend to be the worst as far as deriving notation goes. That’s my suspicion anyway. I get the impression that there are features of MIDI files that could allow them to provide notational hints, but those are optional and so they can’t be totally relied on.
MusicXML, on the other hand, is designed for representing musical information that can be notated. The biggest disadvantage I see of using MusicXML is that it’s not nearly as widely available as MIDI files are. Where do I go to find MusicXML files anyway? Do I have to purchase them? Do they only exist transiently on their path from Finale to Sibelius or vice versa? If I can get sufficiently past that hurdle, then it seems that I should go with MusicXML.
But there might be some other disadvantages to MusicXML also. Traditional notation requires you to make certain decisions about things like key signatures, whereas key signatures are optional in Klavarskribo (represented by a circle or diamond at the beginning of the piece on the relevant line for major or minor keys, as well as other shapes for different modes IIRC). Are they optional in MusicXML? Or does MusicXML force you to make certain distinctions that Klavarskribo doesn’t require? If MusicXML files were as abundant as MIDI files, I wouldn’t worry so much about this. I’d just take what I need and leave what I don’t need. But if I want to promote the proliferation of PianoNinja music across the Web, would MusicXML raise the bar too high? The purist in me doesn’t want to have to decide whether a note is B-flat or A-sharp in the underlying format when that distinction may not ever appear on the screen in PianoNinja.
So maybe what’s needed is a new “KlavarML” format, along with a converter from MusicXML to KlavarML (using XSLT of course). I presume there are already converters from MIDI to MusicXML (insofar as they’re able to). I don’t want to reinvent the wheel. But I also don’t want to be held back by unnecessary technological limitations. Both MIDI and MusicXML provide too much information. MIDI has lots of performance/interpretation-specific information that’s not relevant to Klavarskribo (although theoretically could be relevant to PianoNinja insofar as the scroll speed could dynamically vary, but I digress). MusicXML makes distinctions that Klavarskribo and PianoNinja do not. And MIDI doesn’t provide enough information.
Whether a “KlavarML” becomes an interchange format or an internal format specific to PianoNinja, I still like the idea. At the very least, the exercise of designing it would help clarify the whole domain of what it is I need to represent in PianoNinja. And it would also give me another opportunity to use RELAX NG.
Whereas in the last video all the note stems pointed to the right (which made it difficult to tell which hand was supposed to play which notes), now I’ve associated MIDI events in one track with the left hand, and the other track in the right hand. For those of you who aren’t familiar with Klavarskribo (which is probably 99% of the population), if a stem points to the left, then that means the note is meant to be played with the left hand. If it points to the right, use the right hand.
PianoNinja Video #5: both hands (Quicktime streaming)
My 7-year-old son was holding the camera, while I was using both hands to play. He was trying his best to hold it still.
Tonight I got some scrolling notes to appear on the screen in response to MIDI events being played back from a MIDI file. Observe:
There are a number of deficiencies still:
Despite these deficiencies, I’m really stoked. I’m starting to get a sense of what it will be like to use this game and to practice sight-reading with it (using Klavarskribo notation, of course). My vision is starting to be realized!
Earlier this month, I decided to come up with a name for the Klavarskribo video game I’m working on, so I wouldn’t have to keep calling it the “Klavarskribo game”. I was planning on making the name public when I had a first version ready to download. But last night I came up with the coolest logo for it that I just couldn’t wait to share it. (You’ll have to be the judge; perhaps I’m just sleep-deprived.)
I’m no graphic designer, so I didn’t think I’d actually come close to anything I’d be happy with. I just thought I’d sketch out some concepts. Here’s what I started with:
I did a quick Google search for drawing programs for OS X and downloaded a trial copy of EazyDraw. Within an hour, I was liking how things were going, so I purchased a license. I added some finishing touches today, and here’s the final result:
Why “Piano Ninja”? Well, for one thing, ninjas are cool. My 7-year-old has taken a particular liking to them lately, so I already have ninjas on the brain. I wanted to juxtapose the word “piano” with something indisputably cool (ninjas), since, let’s face it, “practicing piano” and “piano lessons” don’t traditionally evoke the same sense of enthrallment someone gets when absorbed in a video game (such as Guitar Hero). Also, I already mentioned that I don’t plan to knock on many piano teachers’ doors anytime soon (I’m no glutton for punishment), so I’m not terribly concerned with making the name sound “respectable” to the music education world. Finally, I like the stealth component that’s built into the name.
Now I’ve got no excuse but to get moving on this game (heh, as if not having a logo is what was holding me back). Anyway, I’ll continue to chronicle my progress as I’ve been doing so far.
I discovered and joined the Google group for the MNMA. Now I’m reading lots of interesting discussions about alternative notations, 7-5 keyboards (traditional piano keyboard: 7 white, 5 black) vs. 6-6 keyboards (like Janko and Chromatone). One thing I really like about the general feel of these discussions is the openness with which people greet each other’s ideas. Rather than clamoring to promote their pet notation systems at the expense of others, they generally seem to embrace new ideas as contributing to progress. They seem to embody their declared purpose well:
The MNMA is an international nonprofit organization dedicated to exploring ways to make reading and playing music easier to learn and enjoy. This is our forum for open discussion of music notation improvement, alternative music notations, and related topics.
One thing I think is missing in the discussions is an explicit emphasis on use cases. Klavarskribo and some of the other ANs (which in the MNMA forum is shorthand for “alternative notation”) as well as TN (”traditional notation”) are each what I would call a general-purpose music notation system: a single system designed to support pretty much any piece of Western music, and any activity relating to that piece of music. But I wouldn’t assume that the same notation would be equally well-suited to the very different activities of sight-reading, learning a piece for the first time, and analyzing a piece, to name a few. Similarly, I wouldn’t assume that a given notation would serve equally well for all pieces of music. In one of the MNMA forum discussions, someone mentioned that:
One person on the LilyPond list wanted to see Bartók in a chromatic
staff in order to see the symmetry. With just accidentals, and no
vertical change of position, the symmetry is hidden, just as TN hides
the symmetry.
Each piece has a logic of its own. A one-size-fits-all approach to notation is guaranteed to obscure much of that logic. The extent to which the composer’s structural intentions are clearly revealed will be haphazard if the notation is designed or chosen independently of the piece being represented.
So along with “use cases” and “refactoring”, I’d like to borrow another term from software engineering: “domain-specific languages”. But let’s modify that slightly: PSLs (piece-specific languages). And PSLs would have a leg up on DSLs, because we wouldn’t necessarily have to make them dumb enough for a computer to understand.
I don’t have much to update tonight about my Klavarskribo game progress. I’m currently trying to find a free Java profiler that will help me isolate whatever code inefficiencies are causing the slight delay between pressed piano keys and visible feedback on the screen. Yes, I’m using Java for this project. Java wasn’t my first choice, but since I have some experience with it and since it has built-in MIDI support and books about game development with starter code to work from, I found that it was my fastest way to get started. Before that, I was contemplating using languages that I’d rather learn more about, like Haskell and Q. But for me right now, the elegance of those languages would be distracting. My current focus is on getting the thing to work, not writing beautiful code. I’m not sure if you could call what I have “working” yet, but I have definitely written–rather, splatted–plenty of non-beautiful code onto the screen already. So I’m right on track.
My MIDI-to-USB adapter arrived via UPS today, so I hooked it up to the Roland RD-600 that I’m borrowing from my wonderful neighbors. I’m pleased to see that it works right out of the box and I only needed to make one small modification to my code to make (what’s implemented of) the video game to work. (Whereas previously it was only expecting MIDI note off events to appear as “note on” with volume 0, now it will handle explicit “note off” events as well.)
(Please forgive the low recording quality. I was using one hand to hold the camera and one hand to play the keyboard.) As you can see, there’s a fairly significant delay between the sound (which is pretty immediate) of me striking a key and the visual (green or red) note response that appears on the screen. This is something I have to work on before the game will be close to release-worthy.
Now that I have a functioning MIDI keyboard, I’m really motivated to get some real music in there (instead of these hard-coded notes that rise up the screen).
Over Christmas break, I got inspired to work on the Klavarskribo game some more. The video below shows the color coding I mentioned in my last post. When a currently-played piano key overlaps with a supposed-to-be-played piano key, the note is green for the duration that it’s supposed to be played. If you play a wrong note or if you hold the note for longer than it’s supposed to be played, it will be red. Any supposed-to-be-played notes that you don’t play will simply be black, until you hit them and then they’ll turn green. So the object of the game, at least as currently realized, is to make things as green as possible.
You’ll notice that the notes rising on the screen (which include an ascending chromatic scale and some random chords) have nothing to do with the live MIDI input. It’s as if the user is ignoring the notes on the screen and instead playing a Chopin waltz. So you end up seeing mostly red notes with a couple of green notes where the two happen to line up. That’s because I don’t yet have an actual MIDI keyboard hooked up. I’m waiting for a MIDI-to-USB adapter to come in the mail on Monday…
I still don’t have a name for this game I’m working on, so I’m not sure how to refer to it yet. Also, I’m still on the inept side when it comes to video publishing, so this first offering is of pretty low quality.
What this shows is live MIDI input (from a keyboard, eventually). What it doesn’t show is the rising notes of a score, which I’m still working on. This is an early video, so things have already changed quite a bit from what you see here. But at least it conveys some idea of what it will look like (piano keyboard at the top of the screen, Klavarskribo groups of 3 and 2 vertical lines down the screen). I’ve since removed the stems from the live (currently-being-played) notes, but they will remain on the notes that rise up the screen. As with Dance Dance Revolution’s arrows, when a note hits the top of the screen, that’s when you’re supposed to play it. I’ve also added color-coding to the notes: red for wrong note, green for correct note, and black for missed note (not shown in the above video). The aim is to provide immediate visual feedback as to how closely you’re matching the prescribed notes as they hit the top of the screen.
Steven Wilson commented on my last blog post. I went to his site and found a remarkably similar thing that he’s working on, along with a video showing the system in action. It doesn’t use Klavarskribo notation; it looks more like Synthesia’s vertical bars (with length indicating note values). But unlike Synthesia (and like what I’m doing), the keyboard is at the top of the screen (as opposed to the bottom of the screen). The link to the video on Steven’s page appears to be disabled at the moment though.
In my almost-daily scouring of the Web for Klavarskribo-related information (in English, as I don’t yet speak Dutch), I came across a thread on the Cakewalk forums where Johannes Drinda was proposing a Klavar-like notation for MIDI editing. (I’m not a Cakewalk user, so I don’t really know the context.) Anyway, I admired this whistling philosopher’s persistence and enthusiasm, so I emailed him.
In his response, he pointed me to the Janko keyboard design. Quoting him (with his permission): “What a shame, that true revolutionary notions, such as Klavarskribo and Janko keyboard pattern have almost vanished. They are indeed invaluable tools to create a system, which offers/ enables any musically minded (hobby/ home) musician to play MIDI instruments the easiest way.” So he shares my passion to reduce the cognitive overhead that’s built into conventional notation (and/or instruments). He also has created instructions for a DIY Janko keyboard overlay project (PDF file), which I found quite impressive.
That led me to some YouTube videos about the Chromatone, which is based on the Janko keyboard. Pretty interesting stuff. If nothing else, it helps situate my understanding of the traditional piano keyboard. But I’m keeping my mind open to what role it might play in my investigations. I’m also keeping an eye on what Thumtronics is doing, and I subscribed to its founder’s blog, which has a bunch of fascinating reading.
If you have experience with Klavarskribo or are particularly interested in it, please contact me. I’m hoping to get feedback once I’m able to get an initial release of this game out, and more ideas and suggestions in the meantime.
I’ve been steadily learning to read and play piano music in Klavarskribo notation. I still feel like a beginner but the pace of learning is good. New observations are coming fast and furious.
From the start, I wanted to have a computer game to teach me Klavarskribo interactively a la Dance Dance Revolution. There are some games out there that come close: Piano Wizard and Synthesia. I even crashed the Synthesia forums to see if Nicholas Piegdon would consider adding support for Klavarskribo notation. He was very gracious, but he’s also got his plate full with lots of feature requests, including support for displaying traditional notation.
I couldn’t wait, so I’ve started to cobble something together, working on it on and off over the last couple of months. It’s not close to being ready to release. It’s more of a test to help me visualize the particulars and assess its feasibility. So far, I’m encouraged that I’m on the right track.
Here’s a screenshot of an early version:
I will post a video once I figure out the best way to do that using Wordpress and/or YouTube. Also, I plan to blog more about this throughout the rest of this first month of 2008.
