amoeba crunch / blog

The Casual Distractions

2009-01-13T22:12:00.003-05:00

Amoeba Crunch has teamed up with Instruction Shuttle (aka Lasers Shoot From Our Fangs) to form THE CASUAL DISTRACTIONS. Check us out at http://www.thecasualdistractions.com/. We've posted over 20 hours of electronic improv and counting! Beats, loops, vocoders, filter sweeps, shortwave radios, unidentifiable effects, big squarewave leads: we have it all except the Daft Punk helmets and those are on order. Coming soon: an index to help you find the good bits, like TC quoting the Cure's "Love Song" and JR accidentally sampling radio ads for Budweiser and John McCain. Classic stuff!

The Aleph Null Limited Edition

2008-12-23T06:27:00.008-05:00

Aleph Null, catalog number L9 314, is now available in an extremely limited edition of tangible packages. For just ten U.S. dollars you receive an individually numbered, hand stamped CD containing all seven tracks in full quality audio; a unique, handmade, biodegradable CD case constructed from recycled materials; new, extensive liner notes; and an obi band to hold everything together.

You may purchase it from this page using PayPal, which allows you to pay with most credit cards. Available while supplies last.

We are pleased that this package so well reflects the music within. Both have a beautiful, low key, DIY aesthetic that relishes unpredictable human touches. Corners are left rounded off. Edges do not meet at a crisp ninety degrees. There is ample evidence of scissors, fingerprints, and glue. The package was clearly born of a large mess that someone had to clean up.

The Aleph Null special edition is exclusive to amoebacrunch.com.

Let's Get Metaphysical

2008-10-21T21:10:00.009-04:00

It is obvious a person's consciousness is irrevocably tied to his or her physical body. Consider how these things influence the sense of self. Perhaps you can attest to some by personal experience.

Too little sleep
Fasting, or skipping meals
Shock and confusion after sustaining a serious injury
Too much alcohol
Too much coffee
Legal, mood altering drugs administered by a doctor after surgery
Legal, mood altering drugs administered by a doctor to treat depression
Illegal, mood altering drugs administered by yourself
The adrenaline rush during a confrontation
Distress caused by physical pain or discomfort
Delerium due to (oh, let's pick something..) vitamin B12 deficiency
A stroke
Alzheimer's disease
Old age

Some have temporary effects, some permanent, but clearly they all are physical in nature and all affect your "I" (as DRH calls it), some profoundly so. Who am "I" but a particular walking, talking bag of meat? But that begs the question, which "I" would I be without this earthly body in heaven, hell, purgatory, sheol, hades, or jannah?

On the other hand, we are not simply crude masses of atoms. To be strictly reductionist about it, 99% of the human body is composed of just six elements. Yet, some blend of pure oxygen, carbon, nitrogen, phosphorous, hydrogen, and calcium doesn't make me or you. Nor are "you" a result of the specific cells that compose you. The average age of your body's cells is just 10 years. So unless you are rather young (and precocious, reading this -- hey, get your mom's credit card and buy my record), you are not even the "you" you were during the Clinton administration.

So, who are "you" and who am "I"? Science suggests that "we" are nothing more or less than uncommon, persistent patterns of common physical matter. If that isn't pure magic, I don't know what is.

Now Introducing the Clear Crayon

2008-10-20T22:35:00.003-04:00

Aleph Null

2008-09-05T06:20:00.002-04:00

I am pleased to announce a new album, Aleph Null. It is 70+ minutes of completely spontaneous electronica, each track recorded live in a single take with no overdubs. You can download it for free from the link above.

It's a departure, aesthetically and sonically, from earlier Amoeba Crunch recordings, and represents a new focus on live performance.

It's also the harbinger of a cool new project, a collaboration with Todd of Instruction Shuttle. Aleph Null shows where my half of that new sound is going. More on this later.

Blue Semiotics Series, Part 1

2008-08-26T10:26:00.004-04:00

Blue Food Series, Part 2

2008-08-22T10:59:00.003-04:00

Hacking the DigiTech JamMan

2008-08-20T23:05:00.014-04:00

The DigiTech JamMan would be the perfect looper pedal if not for the fact that it's near impossible to sync to a specific rhythm. Not only does it not have MIDI capability for syncing to an external clock, it doesn't even show you the BPM. The best you can do is tap the tempo, and that's likely to drift in short order. It's useless in a live situation where someone else is setting the tempo.

Or is it? Here's a nice hack I came up with. For it to work you need to know the exact BPM. Hopefully there are some electronics in play that display it. It's not going to work if you're trying to loop to your pal's guitar noodling or worse yet, his JamMan. You're also SOL if you have to loop to anything other than a 4/4 time signature.

The big idea is to preset the JamMan with empty loops set for each BPM at which you're likely to play. The other folks in the band have to agree not to stray out the range you pick, so choose carefully. Me, I'm covered from 81 to 140 BPM. That leaves 39 loop slots to play with. I can use the extra slots for preloaded samples, making backups of common tempos, or recording tap stuff if I happen to be leading the band. Why 81 and not 80? Simpler math. I just add 80 to the loop number to get the tempo. Loop 01 is 81 BPM (1 + 80 = 81). Loop 40 is 120 BPM (40 + 80 = 120). Got it? The rest of this article uses my range as an example.

To start, connect the JamMan to a computer. The computer should recognize it as an external hard drive. The root folder is JAMMAN and there is a subfolder for each loop: LOOP01, LOOP02, etc. Copy the entire JAMMAN folder to your computer. That way if you screw this up you can undo the damage.

Next, make a LOOP subfolder for each tempo in the range. Start with LOOP01 and go up to LOOP60. It's fine if a folder is already there. Just make sure to delete the WAV file inside it. All that should be left is the LOOP.XML file.

When you have 60 subfolders, go through them and make sure each has a LOOP.XML file. If one isn't there, create one. It must be called LOOP.XML, with capital letters! If you misspell it or use lower case it won't work. Paste this bit of code into each new file:

<?xml version="1.0" encoding="utf-8">
<jammanloopsetup>
<loopmode>Loop</loopmode>
<tempo>21168</tempo>
<timesignature>2</timesignature>
<rhythmtype>1</rhythmtype>
<stopmode>Stop</stopmode>
</jammanloopsetup>

By the way, the leading space on the 3rd through 7th lines ought to be a tab, not a space, but it's a space above due to Blogger's limitations. Technically, the JamMan shouldn't choke on a space (whitespace is whitespace in XML) but I didn't write it's parser and can't say for sure. Use a space at your own risk.

Now you should have 60 subfolders named LOOP01 through LOOP60, each with its own LOOP.XML file. The next step is to edit each XML file to set the proper tempo. (You didn't have anything fun planned for the evening, did you? I didn't think so. Then again, I did this work for you if you happen to run Windows. Download the zip file here.)

Some genius figured out that the number inside the Tempo element is in fact the number of samples per beat. This bit of info plus the knowledge that the JamMan samples at the rate of 44,100 samples per second (CD quality) means we can calculate the proper Tempo for any BPM:

Tempo = 44100 * 60 / BPM

For example, 110 BPM yields a tempo around 24054.54545 samples per beat. How can you have a fractional number of samples? You can't, so round it to 24055. Even if you play a song for ten minutes, and I hope you don't, the difference won't amount to more than half a millisecond. So to review, you'd plug 24055 into Tempo under the subfolder for 110 BPM. In our example, that's LOOP30, because 30 + 80 = 110. Still with me? I recommend plugging the tempo formula into a spreadsheet for easy calculation.

Once you update all the XML files, copy the whole JAMMAN folder to another place on your computer. Put it in another folder called EMPTYLOOPS_81_140 or something that will remind you that it's a set of empty, precalibrated loops. This is to back up the work you just did and also insure yourself against accidentally hitting tap tempo and screwing up the JamMan. More on that later.

Copy JAMMAN from the computer to the JamMan and you're good to go. Disconnect the JamMan. Plug in your instrument and, if necessary, a rhythm source into the AUX jack. Remember, the goal is to sync the JamMan to an external rhythm given nothing more than the BPM.

Let's say you have a drum machine plugged into AUX. Set it to play something at 120 BPM. Dial up loop 40 on the JamMan. It's tempo light should be blinking along with the beat. Notice the pattern: One red light and three green. Your goal is to get the red light to blink on the first beat of the measure. The easy way to do this is to start the drum machine on the red light. If you have that luxury then it's all good in the hood. Otherwise, you have to use Auto Record.

As you may recall, in Auto Record mode the JamMan starts recording as soon as it receives an audio signal. Now it may go without saying, but for this to work there must not be any signal on the JamMan input at all until the moment you choose to play. This is obvious, yes, but must be stated. You can't expect to play a little bit of something and then start recording. The first sound you make had better be on the first beat. Note that you only have to do this the first time you record a loop -- you won't have to use Auto Record for overdubs.

Push the Auto Rec button (or tap the MODE button on the FS3X footswitch). You'll see the Auto Record button light up. Then tap the REC/PLAY/OVERDUB pedal. The Record light will blink red, telling you that the JamMan is armed. Listen to the drum machine. As soon as it hits the one, play something. Continue for two bars or whatever and hit REC/PLAY/OVERDUB again. If you're timing is good it's now looping seamlessly with the drums.

At this point you can overdub until your heart's content. There are two things to consider. First, do not hit tap tempo. Doing that will completely bung you up! You can't restore the tempo to what it was without re-connecting the computer. That's why it's handy to have some spare preset loops for tempos you plan to use a lot. Be extremely careful around the STOP/TEMPO switch. Second, if you want to save a loop you should first move to an empty slot (loops 61-99 in our example). That way you can erase the main loop and reuse the tempo. To do this, press STORE once, dial to the free loop, and press STORE again. Now dial back to the main loop, erase it (hold down STOP/TEMPO for a few seconds) and start over.

There are a lot of ways to optimize this hack. You can know in advance what tempos you plan to use. That way you use far fewer loop slots. If your range is small enough you can give adjacent loops the same tempo. This way you can create alternate loops and switch between them for a more complex arrangement. One scheme would be to assign a tempo to adjacent even-odd pairs. For example, from loops 01 to 06 the tempos might go 110, 110, 111, 111, 112, 112. If you're in a song that's at 110 BPM, you have loops 01 and 02 to fill up and switch between.

Happy looping. If you try this, drop me a line and let me know how it went.

Blue Food Series, Part 1

2008-08-15T10:53:00.003-04:00

Metainstrument

2008-08-12T11:18:00.007-04:00

Here's our live improv setup. It provides the ability to sample and loop anything, the ability to apply a wide range of effects, and gives us total control of the final stereo mix. Considerations have been made for portability and modularity, and it can change from a live rig to a recording studio just by moving a few cables.

Not pictured: Light show, smoke machine, video of bright, shiny things.

New Video

2008-07-31T00:35:00.003-04:00

Here is the new video for "Damn This Money."

Proof We're One People

2008-07-02T12:29:00.005-04:00

The fact that every person on earth is related to every other has nothing to do with religion or a creation myth. It's a simple matter of mathematics, and it's good to remember in the we vs. they social dynamics we increasingly find ourselves in.

Everybody has 2 parents, 4 grandparents, 8 great-grandparents, 16 great-great-grandparents, etc. Every generation back we go, we have twice as many lineal ancestors. You can see that this is very much a Persian chessboard kind of problem. If there are, say, 25 years to a generation, then 64 generations ago is 64 X 25 = 1,600 years ago, or just before the fall of the Roman Empire. So..., every one of us alive today had in the year 400 some 18.5 quintillion ancestors - or so it seems. And this says nothing about collateral relatives. But this is far more than the population of the Earth, then or now; it is far more than the total number of human beings who have ever lived. Something is wrong with our calculation. What? Well, we have assumed all those lineal ancestors to be different people. But this, of course, is not the case. The same ancestor is related to us by many different routes. We are repeatedly, multiply connected with each of our relatives - a huge number of times for the more distant relations.

Something like this is true of the whole human population. If we go far enough back, any two people on Earth have a common ancestor. Whenever a new American President is elected, there's bound to be someone - generally in England - to discover that the new President is related to the Queen or King of England. This is thought to bind the English-speaking peoples together. When two people derive from the same nation or culture, or from the same small corner of the world, and their genealogies are well-recorded, it is likely that the last common ancestor can be discovered. But whether it can be discovered or not, the relationships are clear. We are all cousins - everyone on Earth.

—Carl Sagan, Billions and Billions, p. 23.

Not for the Easily Distracted

2008-06-27T09:25:00.005-04:00

Line Rider: Draw lines on your screen and watch a little guy ride a sled over them. Marvel at the realistic physics and spectacular crashes. Wonder what happened to your afternoon.

BLDGBLOG: Fascinating stuff about design, secret passages, and urban environments; but it makes you wonder how a respected architect finds time for such frequent and heavily researched posting.

The Conet Project: 92358 04635 19248 93855 21985 28134 91248 59812 23589 12985 91245 95854 59382 23598 07315 52378 48923 12948 59238 85274 12744 58372 82357 24871 18247 92386 69262 90902 03523 59351 44412 59251 71112 52355 62369 59358 34872 12384 14818 59325 36962 39635 95325 35820 59589 99910 21120 24440 57897 89355 82884 28412 27855 68903 23494 12469 30598 29591 29353 58235 56776 67384 94686 83669 78342 85235 11223 47950 69435 96969 68993 67456 63368 84322 34567 58394 68023 52355 69046 64636 22004 ende

Cloose to the Edge

2008-06-23T14:27:00.006-04:00

I had a hypnagogic math moment last night, as we all do from time to time. I drifted off and imagined a geometric sequence s in which each term was exponentially larger than the last. For example, suppose s = n³ for n = 1, 2, 3, .... The 4th term is 81 and the 5th is 243. The numbers x = 90 and y = 700 are "close" in a sense because they're just one term of s apart, yet you might argue they are not close in absolute terms because they differ by an order of magnitude. My foggy brain decided the numbers were not close but cloose (that is, "loosely close," or close only with respect to s). I had the wherewithal to recognize cloose as neologism worthy of Hofstadter, whatever it was I thought it meant, and filed it away for the morning. Now the s I gave above is a simple example, but you can see that with a more extreme definition (say if it relied on factorials or the Ackermann function) cloose will cover far more territory on the number line than close. I started to wonder whether it made sense to define clooseness differently for things other than sequences, like functions or series, but then fell asleep and dreamt about appearing on Iron Chef America (presumably for Battle Toast, Battle Hot Water, or Battle Beer).

Mystery Blob

2008-06-20T21:59:00.010-04:00

What is this strange, fuzzy little thing? Plankton? A white blood cell? A jellyfish? A virus? Inscrutable Peter Saville album art? Paramecium poop? It looks kind of mossy, doesn't it? And it's surrounded by a thin, blue sheath that suggests a cell wall or the thin skin of a tiny aquatic animal.

All totally wrong, of course. It's a great big thing floating in space: The Tycho Supernova remnant, to be precise. We were only off by a few dozen orders of magnitude. How slick is it that it looks so much like something we'd see in a biology textbook or under a microscope?

It's a false color X-ray image, which perhaps explains it's unusually textured, 3-D appearance, as if you could reach out and poke it.

Amazon

2008-06-20T09:20:00.004-04:00

Alternate Worlds is now available on Amazon as an MP3 album. They also have Sixteen Worlds used CDs.

Random iPod Walk: Best Of

2008-06-18T10:57:00.008-04:00

This is today's random walk through our iPod Best Of playlist, the songs that make us shout "Yes!" and pump a fist when we hear them.

The KLF, "Kylie Said to Jason"
This was what the KLF was about, also known as the Justified Ancients of Mu Mu, furthermore known as the JAMMs.

Rush, "Time Stand Still"
Yes, '80's prog rock.

Joy Division, "Warsaw"
The first and last monster Joy Division riff.

808 State, "Spanish Heart"
The vocals by Bernard Sumner elevate this beyond the band's usual generic techno.

The Beatles, "Get Back"
A fantastic groove pinned down by Billy Preston's keyboards. We love George's understated rhythm guitar. It must have taken great discipline to keep it simple.

KMFDM, "Megalomaniac"
The second best track from the last great KMFDM album, the best being "Anarchy."

Nick Cave and the Bad Seeds, "Red Right Hand"
We imagine a barren western scene, continuously panning across bleached skulls, saguaros, and distant silhouetted figures.

Stevie Ray Vaughan and Double Trouble, "Cold Shot"
Recorded in the early morning after a long, otherwise fruitless session. The desperate energy is evident in this lucid, faultless take.

R.E.M., "Orange Crush"
The second best track from Green, the first being "Turn You Inside Out."

Keller Williams, "Freeker by the Speaker"
Silly, groovy pop with ultratight rhythm and Williams's liquid acoustic guitar work.

The Magnetic Fields, "Long Forgotten Fairytale"
The synthpop gem from the stylistically diverse triple album 69 Love Songs.

Sublime, "Get Ready"
The casual listener may be forgiven for assuming that the singer hailed from Jamaica. What a voice.

Frank Zappa, "Sexual Harassment in the Workplace"
A great Zappa blues guitar solo extracted from a live recording and given a typically goofy title.

They Might Be Giants, "Mr. Xcitement"
TMBG with a beat and an idiosyncratic guest rap from Mike Doughty.

The KLF, "3 A.M. Eternal (Original)"
From the unreleased soundtrack to their White Room film.

Edvard Grieg, "In the Hall of the Mountain King"
We hope Michael Binkley achieved his stated goal of dancing the lead in Peer Gynt.

Depeche Mode, "Enjoy the Silence (Single)"
It seems naive now, but in 1989 we high schoolers wondered how a band like this could make such a huge impact without a drummer.

Amoeba Crunch, "Weights and Measures"
This is an unreleased song from 2005, though we are looking into clearing its samples for a possible future release. Or so it seems. Mostly we're having fun exchanging emails with business associates of the late, great Richard Feynman.

The Beatles, "The Ballad of John and Yoko"
Notice how the repeated bass figure wraps around to the next bar, propelling the groove forward. This was just Paul and John. Paul is behind the drum kit, as he was on "Back in the U.S.S.R." when Ringo briefly quit the band. This reminds us of John's dry answer to the question of whether Ringo was the best drummer in the world: "He's not even the best drummer in the Beatles."

Venus Hum, "Soul Sloshing"
Venus Hum deserves to be more popular. They have a lot of talent and are nice folks to boot.

Mindless Drug Hoover, "The Reefer Song (Grass Garden of Child's Mix by the Orb)"
Hilarious lyrics and delivery, and much improved by the Orb's double time dance hall backing track. Give yourself a laugh and check this out. You'll be singing it for weeks.

Nine Inch Nails, "Sin (Long)"
Classic teenage angsty NIN.

The Magnetic Fields, "Epitaph For My Heart"
Another from Stephin Merritt's tour de force, 69 Love Songs. We admire anyone who can work product warranty legalese into a poignant lyric. The only fault is that it's too short.

Erasure, "A Little Respect"
The cover by Wheatus is even better.

New Order, "Ceremony (Trio Version)"
"Ceremony" is our second favorite N.O. song.

Venus Hum, "Hummingbirds"
Deep, deep bass drum. This was great live. Twice.

Massive Attack, "Angel"
Great song, great video, which was all the better for the surprise ending that proved they had a sense of humor after all.

The Doors, "Peace Frog"
The Doors did techno ten years ahead of everyone else.

Belle and Sebastian, "Step Into My Office, Baby"
This has a unique sound. We heard it on Philly's WXPN, ran out and got the Dear Catastrophe Waitress CD, and were not disappointed.

Medeski, Martin, & Wood, "Bubblehouse"
Supergroovable jazz funk track, frequently heard as NPR interstitial music.

Van Halen, "Hot For Teacher"
Anyone who grew up in the '80's can dig this.

Us3, "Cantaloop (Flip Fantasia)"
This popular cut from 1993 is based on Herbie Hancock's fantastic jazz number, "Cantaloupe Island."

iTunes Release

2008-05-29T21:41:00.006-04:00

Alternate Worlds is on iTunes. Here is the link, though you must have iTunes installed on your machine for it to do anything. They charge more than CD Baby, apply wacky digital rights management, and you don't even get a real product to hold in your hands, so if you are actually considering shelling out your hard earned giro for our measly product we recommend doing it with CD Baby. Or hell, if you ask politely we may just send you a free copy. Or send you something else.

Thank God the primaries are almost over. Now we can get back to making fun of Republicans. Remember them? They spit on privacy! They spit on the Constitution! They're gonna give you righteous swirlies until you pledge allegiance to the Presidency, Jesus, and Perpetual War, in that order! They're military-home-wreckin', gay-bashin', immigrant-hatin', environment-stompin', deficit-multiplyin', long-term-ignorin' crazies that are convinced the terrorists have infiltrated your mailbox! They are now declaring a War Against Your Mailbox! The Third Army is being deployed as you read this, led by General Patton who was resurrected as part of Dick Cheney's unholy pact with Satan! The Democrats aren't any better mind you but, man! Those wacky Republicans. How we missed 'em.

CD release!

2008-05-16T00:03:00.003-04:00

Alternate Worlds is now available for $5 from CD Baby. You can also get it as free 96k mp3s from the music page. It will be on iTunes and other retail sites shortly. It already has its own Wikipedia page thanks to our loyal fans (as does our first release).

CDs: Not Quite Dead Yet

2008-05-01T10:28:00.008-04:00

Some say the music industry is no longer based on physical CDs. We disagree.

It's true that it's shifting to an attention economy. There are more bands than ever thanks to improved technology. Any home computer is potentially a sophisticated music studio. Innovative software developers are forever making composition more accessible to the masses. Distribution is totally free over the Internet. These days the problem is getting listeners. There is some attention to be had through so-called Web 2.0 resources like MySpace and Facebook; however, in general one must purchase it like any other commodity.

How does that happen? Attention is intangible but buying it requires a physical product. Virtually all reviewers, broadcasters, and respected arbiters of taste demand a press kit: A color-printed CD in a jewel case, a 4" x 6" glossy, professional writeup, postcards, stickers, and other goodies. Listeners may be happy enough with MP3s but a band won't have listeners without promo material that can clutter up some reviewer's desk. All that stuff costs money, paid for by the artist.

How to defray the cost? Let's face it, listeners don't have much incentive to pay for audio in these days of unfettered digital copying. However, they do have some incentive to buy patronage. In other words, they pay because it feels good. It's a vote in favor of the artist, "I like what you're doing, keep doing it." Perhaps this is evolving into universal cost free, DRM free music and "Donate Here" links on every band's homepage, but for now CDs are part of the process. They're a thank you gift in exchange for a donation.

Artists are like public radio stations. The product is free and financial support comes from voluntary sponsorship. Just as NPR will "gift" you a tote bag, so does a band gift you a CD. And just as NPR offers cooler gifts over a range of price points, some bands offer more elaborate physical packages. The audio may be free, to capture your attention, but the goodies will cost you. This is interesting from an artistic standpoint since it expands the concept of a release from a handful of songs to whole bunch of stuff. Physical stuff. Again, the tendency toward physical objects.

At least musicians aren't subjecting you to pledge drives. Yet.

Bands that play live have one more reason to make CDs. They're a great souvenir, and listeners are more likely to buy after a couple of beers.

As for us, we give away our music to make it as easy as possible to get listeners. We make CDs for promotion but also because, hey, it's fun and cool to make CDs. We offer them for sale to make patronage possible.

Fun With Mirror Images

2008-04-25T21:37:00.040-04:00

Ever wonder why mirrors reflect left and right but not up and down? In other words, why does the mirror image of text appear backward instead of upside down?

Let's look at an example.

Here I am proudly displaying the latest Amoeba Crunch poster, designed by Chip Kidd and available in the store for $13. Look at that reflection. It sure looks like the text (and therefore the whole mirror image) has been flipped horizontally.

However, that's only compared to how we expect it to look:

We think the text has been "flipped" around an imaginary line going from the ceiling to the floor, like this:

The problem is, how does the mirror "know" which way is up? Why didn't it just as easily do this?

(Of course, that's not quite right. The whole image would be flipped so I'd be on my head, but bear with me.)

The faulty assumption is that forward text factors into things at all. You'll notice that easily readable, forward text does not appear in the original photograph. In fact, it's backward both in front of the mirror (albeit viewed through the paper) and in the mirror image. This is easier to see if I take another photo with the paper turned around.

Now it ought to be clear that the text reads forward both in the original and the reflection, though in the reflection you're looking through the paper to text written on the other side. So in a sense the mirror hasn't flipped anything at all -- it's the same on both sides.

Another example: Consider my left hand, which has a wedding ring. To be overly pedantic, from my perspective the ring is on the hand that's to the left of my body. When I look in the mirror, as in the photo above, it also appears to the left (from my own perspective) of my body's mirror image. There is no left to right flip here. It's left and left on both sides of the glass. Likewise, the mirror hasn't changed the text. It's readable on both sides.

I can hear some of you crying foul. After all, from my mirror image's perspective he's wearing the ring on his right hand -- that's the flip. If you're thinking that, what you've done is redefine "left" and "right" in terms of his perspective. You're considering him as if here were someone in the real world. But he isn't!

Let's think about this. If in the real world a friend and I stand toe to toe facing each other, it's no stretch for us to agree her right hand is, from my perspective, to the left of her body. Without thinking, I assume the same is true for anyone facing me, including my mirror image. The trouble is, my mirror image is not in the real world. There is no guy over there! It's just me over here. The world in the mirror image is not an extension of the room I'm in. The fact is, the definitions of left and right don't change across a mirror and neither do the definitions of up and down. The left hand has the hand with the wedding ring on both sides. This can be hard to get around. We're hard wired to deal with people as real beings, and it sure looks like the guy in the mirror is a real guy standing there facing me with his right hand where I'd expect it to be. But the key is that my mirror image is just that, an image, a trick of light. The usual assumptions about people don't apply.

So if the mirror isn't swapping left to right or up to down, what is it doing? Is it showing you what you'd see if you were standing in place of the mirror? No, because if that were true the ring would be on the opposite hand (from your perspective, on the hand to the right of the body).

What a mirror does is flip things in to out. Specifically, along the imaginary line that is normal to (that is, perpendicular to) the mirror's surface. If you're facing it as I am here your mirror image is not merely you turned around, as if you stood facing the opposite way, but is you flipped through your belly to your back. (That would make a great animation. If someone has the time and expertise to put it together I'll include it.)

Notice that the unmarked side of the paper is toward the mirror in both the real world and the mirror image. Likewise, the paper is always between the mirror and me. There is not so much an axis of symmetry as a plane of symmetry, the plane of the mirror. So the reflection has nothing to do with the mirror "knowing" left from right or which way is up. The only direction it "knows" about is toward or away from its surface.

In mathematical terms, we can define a mirror's behavior with a Cartesian coordinate system having its origin on the mirror's surface and your eyeball on the positive z-axis, like so:

The negative z-axis extends into the mirror image world. For any point (x, y, z) in the real world you can find the corresponding point (x', y', z') on the far side using these equations, suitable even for the mathophobic:

x' = x
y' = y
z' = -z

This page explains mirror images in a slightly different way that you might find more clear.

Mathematics: Expect the Unexpected

2008-04-25T15:29:00.010-04:00

Did you know...

...there are just as many points in a unit square as on a unit line? In other words, the square is not "bigger" despite having a nonzero area.
...infinite sets come in different sizes? For example, there are demonstrably more real numbers than integers.
...the recurring decimal 0.999... is equivalent to one. It's not a smidge less than one, it is one. Don't buy it? What would you say is the decimal of 1/3? That's right, 0.333... Now, just as 3 times 3 is 9, 3 times 0.333... is 0.999..., which is one as surely as 3 times 1/3 is one.

Exposures

2008-04-07T11:20:00.005-04:00

Composing music is like taking photographs. As the time between a camera shutter opening and closing dictates the sharpness of the image, so does the time a recording is in flux dictate its relevance to the composer's ever changing tastes and circumstances. There is a tradeoff between perfecting the record, which takes time, and crystallizing it as an artifact of the moment.

Of course, it's not every composer's goal to capture moments in time, and it's not to say every piece of music that's taken a long time to create winds up unfocused. After all, long photographic exposures can reveal subtle details. But it takes great care, like high tech telescopes that track the stars, to get a clear image.

Alternate Worlds is shaping up to be a snapshot compared to the long exposure of Sixteen Worlds.

They're photos of the same subject taken a year apart, but it's surprising how different they feel. If the photography metaphors don't work for you, consider two acting companies performing Waiting For Godot. The words, themes, and characters are the same in each case. Yet the people involved, their interpretation, and the quality of the popcorn couldn't be more different.

Hot Wax From 1860

2008-03-31T07:53:00.007-04:00

Scientists at Lawrence Berkeley Laboratory teamed up with audio historians to play back the earliest known recording of the human voice, a woman singing the French folk song "Au Clair de la Lune." Parisian inventor Édouard-Léon Scott de Martinville made the 11-second recording in 1860, a full 17 years before Thomas Edison recorded "Mary Had A Little Lamb" and a shocking 127 years before "Pump Up the Volume."

You can listen to the recording here.

Edison buffs tripped over themselves to reassure the Francophobic U.S. public that Scott is no challenge to Edison's legacy. After all, Scott was merely first to record the human voice. Edison recorded it and played it back. Freedom fries, anyone?

Free Music!

2008-03-26T13:38:00.005-04:00

You can now download all our songs for FREE from the music page. All the files are 96k MP3s. Full-quality versions and actual CDs are available from CD Baby and iTunes, among other retailers. The Sixteen Worlds CD is just $4.95 from CD Baby.