Sunday, June 28, 2020

Tau Day 2020

Happy Tau Day! What's this? Me remembering two interesting dates in a row? I'm as confused as you are! I guess it helps that both fell on weekends this year so I was less busy.

I've mentioned tau a few times before, but as a reminder, \(\tau=2\pi\). It's the ratio of a circle's circumference to its radius, and makes much more sense as the true circle constant rather than \(\pi\). I was reminded recently how much more sense when my mother asked for some help with some trigonometry problems (she's been teaching herself trig lately) and it was so confusing trying to think about the various unintuitive ½\(\pi\)'s and ¾\(\pi\)'s scattered about. With \(\tau\), a fractional value of \(\tau\) corresponds directly to a fraction of the way around a circle, which is so much simpler to remember. I think \(\tau\) makes more sense than \(\pi\) from a purely mathematical perspective, but the practical benefits to teaching and using trigonometry (and higher math that uses it) would be compelling all on their own—after all, we switched from Roman numerals to Arabic numerals primarily because the latter were easier to use and reason about; why shouldn't we do the same with other values? A hui hou!

Sunday, June 21, 2020

Happy [Winter/Summer] Solstice!

Happy [winter/summer] solstice, [southern/northern] hemisphere readers! As an astronomer I always feel like I should comment on these astronomically significant dates, and then I always end up forgetting or being too busy to write anything. This year, at least, it falls on a weekend and since I've been working from home I've been even more aware than usual of the lengthening nights the past few months. It's actually rather relieving to finally reach the solstice, to know that this is as dark as it gets, and the days will begin to lengthen again after today (even if it won't really be noticeable for a few weeks, and the actual coldest part of winter is yet to come).

On an astronomically-related note, I wanted to share a website I found recently, called The idea behind it is to allow you to compare countries' sizes on a map that takes into account the distortions present in the projection, specifically the very common Mercator projection. You can input a country (or U.S. state) name to create a transparent copy of it on the map, and drag it around. As it gets closer to or farther from the equator, it'll shrink or grow according to the distortion present at that latitude (none at the equator, and increasing towards the poles). I found it absolutely fascinating, since I'm aware that there is distortion, but don't have a mental idea of its magnitude.

Probably my favorite country to visualize the distortion is Greenland, which looks to be bigger than South America in the Mercator Projection due to its great distance from the equator. But actually drag a copy of it down to South America and you'll see it's much smaller than Brazil, and comparable in size to Argentina. Comparing it to the U.S., the distance from north to south across Greenland is actually only just larger than the distance from the southern tip of Mexico to the Canadian border.

Anyway, it's lots of fun to drag countries around the map and see how they compare (you can have multiple countries active at once and also rotate them, allowing you to play games like fitting as many countries into another continent as possible). Hopefully you too can enjoy appreciating just how big (or small!) the world can actually be. A hui hou!

Sunday, June 14, 2020

Satisfying Slug Shadows

Working from home as I have been the past few months, I've got a lot more time to appreciate the paintings I happened to have here with me when lock-down started. Or, to become more dissatisfied with my previous efforts, in some cases. Specifically, my blue glaucus painting, which has already gone through two different revisions. Turns out I still wasn't happy with the shadow I added (though I'm glad I added it), so I went back and reworked it a little more.

Primarily I found the shadow to be a bit too hard and sharp; it didn't seem like a shadow of something floating in shallow water, and being as sharp as it was it distracted the eye from the slug itself, muddying the focus of the composition. I've gained a fair bit of appreciation for the pigment transparent yellow oxide over the past few months (as it's one I have with me, and have been doing some experimenting with), so I decided to use a glaze of it to make the shadow look softer and less distinct. In the process I also ended up spreading some around on the sandy background too, to help the shadow blend in better. While I was checking reference images, I also noticed that on some the silvery coloration extended along the cerata, so I've gone over those with a thin silver glaze as well. Anyway, here's how all that turned out:

“Carefree Blue Dragon”, 18"×14", acrylic on canvas.

I think this shadow works a lot better now, being still visible but less distinct and not overpowering the main subject quite so much. At this point I think I'm finally satisfied with it, but then I've thought that three times before, haven't I? As the saying goes, “art is never finished, merely abandoned,” so we'll see if this truly is the final revision! A hui hou!

Monday, June 8, 2020

Orchestrating Handel's “The Harmonious Blacksmith”

Today I'm pleased to finally be able to share a new project I've been working on for a few months now. Back in February I mentioned I started learning LilyPond in order to engrave sheet music, and after finishing copying Ecossaise in E♭ Major by Beethoven as a warm-up exercise I was looking around for something new to practice with. I settled on Handel's piece known as The Harmonious Blacksmith, the name given to the fourth movement from his Suite No. 5 in E major for harpsichord. I discovered this fantastic piece last year, and in the process of writing the LilyPond code for it I listened to a whole bunch of different versions of it, including two versions of it orchestrated for a full orchestra. After copying a version for harpsichord(/piano), this inspired me to undertake something a bit more ambitious: making my own orchestrated version!

I settled on a sixteen-instrument ensemble, where two coincidences neatly dovetailed: MIDI handles channels in groups of 16, and the staves for those instruments also pretty nicely filled exactly one page vertically. It's scored, somewhat arbitrarily, for first and second violins, viola, cello, bass, harp, flute, oboe, English horn, bassoon, clarinet, trumpet, trombone, tuba, French horn, and xylophone. I started sometime in mid-March or so, and worked on it off and on for the next month and a half. In early May I gave a short talk at our astronomy department's weekly Monday lunch (which often features people talking about hobbies or interests) and gave the first public premiere of the (mostly) finished work by playing the synthesized MIDI audio. Since then I've tweaked a few little things (such as changing instrument parts to the correct keys for transposing instruments), and this weekend I finally worked out an easy way to render MIDI to audio. (Turns out there's a convenient Python package, midi2audio, which makes it a snap.)

Anyway, here's a video I made so I could display the sheet music along with the audio:

This was, obviously, my first such attempt at orchestration and I have to say, I really enjoyed it. I'm sure if I actually knew music theory I'd be able to weave even more beautiful passages, but even so I stumbled upon quite a few bits that still give me goosebumps, or which just sound lovely: the gentle introduction of the harp in the first variation, the punctuating xylophone taps on pages 8–10 (but especially on page 9) like little blacksmith's hammers, the interplay between trumpet and oboe (page 11), the pastoral, sublime repetition of the second variation (page 14) right after the bombastic introduction a page before, the staccato viola (page 17) interspersing with the flute*, the introduction of the third variation with its gentle, lilting interplay between the woodwinds and harp, the xylophone intermittently shadowing the oboe (page 23), the growing crescendo involving nearly all the instruments which ends that variation (page 24), those  two insistent growling low notes from the bassoon in the fourth variation (page 27), the trumpet making a surprise appearance in the fifth variation (page 34), the four-part instrument unison between the violins, viola, and trumpet on page 38 (never fails to bring out the goosebumps), and the entirety of the last two pages as everything slows, and builds, and crescendos before the final cascading descent to the finish. I've listened to this piece I don't know how many dozens of times at this point (both my version and others), and I have yet to tire of it.

Anyway, enough of my rambling. I hope you enjoy the music, and feel free to point out any musical mistakes I might have made—I did have an experienced violinist friend look it over so I'm fairly confident the strings don't have any unplayable notes (he found those already), but I might still have made mistakes with the other instruments. A hui hou!

*The staccato markings were one of the few liberties I took with the original notes along with adding a few trills in places, though there are a number of trills in the second variation in the original. The dynamics markings and tempi are also mine.

Saturday, May 30, 2020

If Beethoven Wrote Variations on Children's Tunes

A few days ago I came across this incredible impression of the familiar tune “Old MacDonald Had A Farm” played à la Beethoven by Polish-Canadian pianist Daniel Vnukowski, and it's so good I simply must share it. I've listened to enough Beethoven over the years—he's one of my favorite composers—to tell that this is absolutely spot-on:

Variations, or variational forms, were a great favorite of Beethoven's judging by the number of them he wrote, though he didn't publish many of them suggesting it was something he did for fun. The Diabelli Variations are probably his most famous among the ones he did publish, though I especially love the Eroica [Heroic] Variations, both the version for single piano and how they reappear in the final movement of his third symphony, the ‘Eroica.’ Anyway, apologies if this song gets stuck in your head as it has mine, but there are certainly worse pieces of music to have that happen with. A hui hou!

Monday, May 25, 2020

Flowery Australian Flora

This past Sunday, due to loosening lock-down restrictions, I went over to some friends' to catch our church livestream and have lunch. As I was leaving my house, the surprisingly nice weather caught my eye and caused me to take a few photos of some of the plants in the front yard with rain from the night before still sparkling on them. The Sun was unexpectedly out—it's been rainy or overcast the past few days—and it lit up the raindrops in a really lovely manner.

I haven't been taking too many photos the past few months, so I felt like playing around a bit and experimenting with angles. Here's a bottle-brush still be-speckled with raindrops, with the blue sky in the background. A lot of stuff is blooming out-of-season this year, which is strange: apparently, in the first four months of the year, we've had more rain in Melbourne than in the entirety of 2019, and were even on track for having the wettest such time period ever. And we missed breaking the lowest recorded temperature on May 1st by a single degree (Celsius)! So it's not like it's been unseasonably warm or anything, plants are just blooming at strange times.

I don't know what kind of plant this is, I'm afraid, other than that it's different from the previous one. I was really feeling like pushing the limits of how close I could get a photo, and with the Sun shining brightly on the water droplets this came out pretty nicely I think.

And here's the culmination of my attempts to get up-close-and-personal with the plants. This is, yet again, a different plant from the first two, and I similarly don't know what it's called. (Edit: Whoops! I checked my front yard this morning and realized this is actually part of the same bottle-brush plant from the first photo.) I love the back-lighting of the fine hairs on the leaves, though!

I'm sure for my northern hemisphere readers this flowery foliage is nothing special as you head into summer, but I thought it looked nice, so have a helping of Australian flora! A hui hou!

Sunday, May 17, 2020

A Magnetic Birthday

Today the Earth marks another revolution about the Sun and I turn a year older. Or is the act of turning older less of a discrete moment and instead spread throughout the year? Is a birthday merely the observation of—and subsequent collapsing of—the waveform?

Sorry, that got a bit philosophical. As I expect many of you, dear Readers, are, I've been working from home for about two months now. Since I'm spending a much larger fraction of my time at home, I've been ordering a few things online to make it a more pleasant experience, such as the office chair I got from Ikea to replace the borrowed kitchen chair I'd been sitting on.

This week I had two different packages come in on the same day in a sort of early-birthday-present surprise, and I wanted to share a bit about the contents of one of them, from a Kickstarter campaign I backed late last year by a company called Chargeasap. (If you're curious, the other was a pair of arm warmers to keep me warm as we go into winter in the southern hemisphere.)

For a bit of context (bear with me), I've had a heightened interest in magnets for about half a year now, ever since I bought a pair of wireless headphones back in August or so. In those headphones the battery resides in one earpiece beneath a molded plastic cover held on by a pair of magnets. For whatever reason, I found this to be a particularly elegant solution, and started noticing magnets used in various other places.

I first came across a company called Zubits which makes these nifty magnetic clasps which you can thread your shoelaces in such that you can replace tying your shoes with snapping a pair of powerful magnets together. This inspired me to make a piece of artwork involving magnets back in November, which I still think is a fantastic idea and which I'm eager to use in future projects somehow. I also picked up Xvida's wireless charger with automatic magnetic alignment, which I wrote about recently. For Christmas my brothers got me a Tie Mags magnetic tie clip, to hold your tie in place magnetically without needing to pierce it with a tie tack or something similar. And the list goes on, you get the idea. Magnets are a great way to hold things in place as firmly or weakly as you need without fading over time.

Anyway, the point of this long digression was that I came across a Kickstarter campaign back in September for what I thought was a really good idea: a set of cables, with a USB Type-C plug on one end, and a universal magnetic connector on the other which could connect to tips with either Apple's Lightning connector, Micro USB, or USB-Type C. These tips could then simply be left embedded in the thing to be connected, such as a phone or laptop. To make a long story short, I backed the project, and despite some slight delays from the unforeseen pandemic currently ravaging the world I got the cables I'd pledged for this week.

I was impressed with the standard of the packaging. Very professional-looking.

Chargeasap isn't the first company to come up with the idea of these universal, interchangeable, cables, and this also isn't their first iteration on the concept; I think it's their third or fourth. These Infinity cables incorporate a number of improvements from their previous designs, such as the brightness of the LED in the cable end letting you know it has power being lower so that it isn't as distracting if used to charge your phone overnight. The cables themselves are very nice-looking, being braided nylon in construction with durable plastic caps at both ends and the thoughtful inclusion of a little rubber strap to help hold them in place when coiled up. They feel very high quality, and seem durable enough to hold up to lots of abuse.

The (unfortunately a little blurry) photo above shows the end of a cable, with one each of the USB Type-C and Micro USB tips magnetically stuck to its sides. You can see the 10-pin design which allows the cables to transfer data as USB 2.0 speeds. Which I think I forgot to mention, these aren't just for charging, they'll fully be able to transfer data as well. In fact I used one while writing this post to get these photos off my phone, and they work very well.

They're also quite capable on the power front, however, with Chargeasap promising Power Delivery (PD) standard charging of up to 100 watts, enough to power and charge a laptop as I was testing above. In fact, one of the inspirations for these cables was Apple's old MagSafe connection for its Macbooks, which allowed the charging cable to come unattached instantly if snagged on something, without bringing the laptop down with it. (Chargeasap makes a special longer cable, two meters long, which is pretty much made for being used as a laptop power cord.)

Anyway, that's probably enough of me rambling on about cool new tech gadgets. I've had a few Kickstarter campaigns where I received the finished product and while it technically worked as advertised it just wasn't quite as cool or interesting as it'd seemed, but with these Infinity cables I'm still just as excited about the opportunities I can think of for using them. Unfortunately some of the things I'd like to connect are still at my desk at Swinburne, but I'm sure I can come up with something. I especially like being able to connect my phone to my computer with a single snap!—it should get me to actually transfer photos off it a bit more often as it won't be quite as much of a hassle anymore.

Stay safe everyone, and if you do decide to check out Chargeasap's lineup just be aware that they're based in Sydney so orders from overseas will be a bit slower to go out most likely. A hui hou!

Sunday, May 10, 2020

Ecossaise in E♭ Major by Beethoven (WoO 86)

Back in February I posted about the new hobby I've picked up of engraving music using the LilyPond markup language. I've thought for a while now that it would be nice to share what the music I'm engraving sounds like (especially for the musically non- or semi-literate such as myself), but it turned out to be more complicated process that I expected. Turning MIDI output into a waveform file format which I could include in a video is a bit tricky if you're coming to it fresh like I am, but I have a provisional method of doing so, so I made the short video below as a proof-of-concept for eventually making longer videos of some of the things I've done since. And I have been busy, but I'll leave it to a later post to go into more detail.

For now, just enjoy this short melody (seriously, it's less than thirty seconds long), and play along at home if you're so inclined and able. A hui hou!

Thursday, April 30, 2020

Filament-ary, My Dear Watson

Over the past week I've been playing a game that came out on Friday called Filament, and while I don't usually talk about my gaming hobby that much here on my blog, I have to write a glowing review of this game. It's a puzzle game with a very simple premise: you play a spacefaring traveler who comes upon a spaceship whose crew has disappeared, except for a disembodied voice over the radio from the pilot who's trapped in the cockpit. You wander about the rest of the ship and find “anchors,” where you control a little robot who can spool out an infinite amount of cable after itself in little puzzle rooms. They're explained as you “decrypting” the ship's logs to figure out what happened, and to progress you have to use the robots to wind cable around pegs in such a way that you've touched every one at least once in order to progress. However, you can never cross the cable you've already laid down, and those two simple rules combine to make a wide variety of puzzles from easy to brain-breakingly difficult.

A shot of a man standing in a futuristic-looking workshop.
The art style is also perfectly matched to my likes, very stylized and clean.

It's a very simple premise, but there are all kinds of additional obstacles added in various puzzles: sometimes literal obstacles, which block your path and force you think more outside the box, sometime more interesting puzzle conditions, like needing to have wrapped some pegs before being able to wrap others, having multiple robots (with multiple cables) in one room, or needing to run the cable over pads on the floor as well. The whole thing has strong connections to the mathematical fields of topology and graph theory; I often find myself, while stumped by a fiendishly difficult puzzle, thinking: “Surely there much be some theorem in topology to help me winnow out the impossible options here and narrow it down to the correct sequence of wraps to make to finish this level!”

A shot of a man standing in a futuristic library with a holographic globe.
Here I am in the library, trying to decipher what looks like a binary code on these servers.

Make no mistake, these puzzles get hard, and I am absolutely loving the experience. The story you unlock bit by bit is very engrossing, and keeps me coming back to throw myself at particularly difficult puzzles over and over again in hopes of finding out more about what happened. (I haven't finished the game yet, actually, so please no spoilers! I normally don't care about them but I find myself caring very much with this game for some reason—perhaps because the scraps of knowledge are so precious for having been so hard-won.) Here's a shot of a puzzle I've been stuck on for probably at least 20 minutes now:

This puzzle variety also requires you to run the cable through the four “light screens” you can see here.

I can't neglect to mention the music, which makes a soft, quiet, meditative background to your brain sparking and shorting out. It's very soothing, and loops so well that I could listen to it for hours. (And have!) I bought the “Marmalade Edition” which came with the soundtrack, and am looking forward to listening to it the next time I paint. (It's named after a particular character in the game, who all have color-themed nicknames assigned.)

The game is set up so that you can wander around at will and try any of the available puzzles, which helps negate the feeling of being stuck and unable to progress which is all-too-easy for puzzle games to fall into. If I'm having trouble with a particular type of puzzle, I can go and try a bunch of other different types instead. Sometimes I'll come back to a puzzle a day or two later and find the solution suddenly coming to mind. In fact…

After firing up the game to get this screenshot, I figured it out in about five minutes!

All in all, I can highly recommend Filament if you want to give your brain a real workout. And not just the puzzles; there are also secrets scattered liberally throughout the spaceship, in ways that make them incredibly satisfying to find. I once picked up a tray of seedlings in the botany lab, and discovered a secret code encoded in the way the plants' leaves were pointing at each other. I found another in the contents of a vending machine, and another as a binary pattern hidden in sets of four lights being on and off. There's a lot going on in this game under the surface, but the pleasant background music and engaging story make me want to keep coming back for another round of being thoroughly, utterly stumped.

Tuesday, April 14, 2020

Forget Princess, I Want to Be an Astrophysicist

Back in January I showed off the picture below of a Christmas present from my mother. I've finally finished painting it, and it came out quite well if I do say so myself. Here's the original canvas:

And here's the finished version:

I really, really like how this came out. There's a few minor blemishes—mostly invisible in the photo—where I over-painted the boundaries and need touch them up when I get access to the Midnight Blue I used for the background again, but on the whole this gives me joy every time I see it. You might notice that the stars are all colored as if their sizes correspond to their relative masses, with the smallest being reddish, then orange, yellow, etc. I had to get creative with some of the colors since I finished it at home in quarantine without my full range of pigments, but I think it looks good. I decided that what looked like a ringed planet with a star coming out of it was actually a black hole with accretion disk devouring a star, and since I happened to have my Black 2.0 at home I was able to make it work. I'm glad to finally be able to show this off, it's been an interesting exercise in constraints painting it. While I've gone for very simple, solid shading much of the time I've also gone for more subtle and realistic shading in places, but I've stayed within the lines everywhere without adding anything. (I thought about stretching the accretion disk into photon rings around the black hole, but decided to stick to the lines.) Anyway, I now have this hanging behind me at my computer desk at home to continually remind me of my vocational aspirations. A hui hou!