The sine wave and quantum beats

s long as I'm mucking about trying to find parallels between quantum mechanics, set theory, and rythm, I set about with a bit of a musical experiment on my trusty korg electribe mx as piped through my soundcraft lexicon mixer's drum plate. The tubes in the electribe give the drums a predictable warmth, while the plate adds room overtones and depth.



The problem is no doubt simple from a purely musical or musician's perspective, but interesting from a mathematical one.



Just like an ordinary sine wave, we simply build a rythm that alternates parts from one measure to the next. For example, we can build a rhythm consisting of bass drum, snare, and decorate it up top with a constant closed hihat (with an open on the last half beat).

Our bass drum hits on [1, 5, 9, 13], where as our snare is on [3, 6, 9, 12]. What we end up with is a pretty straightforward bossa nova, with the intersection of both parts occuring on the half four [9]. Enter the sine wave: we alternate the bass and snare every other measure! (Incidentally, the effect that this has - if I first switch that opening snare to an opening kick - is a binary alternation between bossa nova and rock-steady beat!).

Granted this is the simplest way of looking at our beat composition and arrangement, but the best way I can think of to introduce the analogy. But think of the tapestry we could weave when we apply more sophistication to this schema? Like introducing limits, Integration/Differentiation, partial derivatives to the same set of numbers? (Note: I haven't figured all this out myself yet - still some of the results I've observed are really interesting - not to mention they groove, albeit in ways you probably don't expect!) It's probably possible to build this on e.g. complex functions, while keeping the groove. Then you're in uncharted territory, sweet stuff, you're sailing in blue oceans. Of course, there's more than just these musical variables to tweak.

When combined with acoustic instruments, the intent is hopefully to sincerely emulate "the groove" within the prescribed toolset with this added rythmic complexity as part of the mix. But like everything I'm into at the moment, I've kind of ripped the machine down to its parts to muse and dwell on particular small bits of the problem that fascinate me. Hopefully I'll get down to proper business with it soon enough!

Conservation - of energy and matter - would solve humanities major problem(s)...if we could just get there!

The key to all of this is about humans being able to convert matter into energy, transmit it, and reconvert it back into matter, perhaps conveniently reconfigured!

Yes, it's more or less right out of Star Trek (we could beam people around, we could project objects like holographs), is only remotely possible with our current understanding of quantum mechanics (but is apparently only as far away as our grasp of a grand unification theory) which is being stabbed at constantly by professionals and amateurs everywhere (which introduces a promising possibility that something will emerge). Which reminds me, I must look into whatever exists out there in terms of P2P scientific communities and start farming for ideas...same with my fractal art, my music, my programming, my performance style, and just about anything else I've ever smugly attempted to synthesize :P



When I was recently in Greenland, I was thinking about the simplicity of water, versus the apparent impossibility (technically speaking) to transform it into energy and back again - and how it would fundamentally transform the conditions of humans, and planet earth. Imagine...being able to take water gushing and streaming off the arctic and antarctic ice and make it bubble out of the ground across all the arid regions on planet earth - from the Sub Sahara across the 'stans to Mongolia. Certainly, the room full of Somalis, Kenyans and other Africans on Helsinki's north-east side agreed with me hands down that this is the major number one obstacle on earth: obviously it would feed and economically enable billions who are currently dormant. By the greening of the deserts, would transform back the environment into something far more oxygen rich and equally less CO₂ saturated.

And yet's what stopping it?


Humans have, in the 20th century, been able to convert very unstable matter into raw energy in the course of wiping out foes, and related pursuits. And we have harnessed the practical energy of grabbing electrons as they fly off bits of U²³⁸. This is used in many countries to supplement what we can't get from wind, solar, hydroelectric and other sources of free-in-nature kinetic energy, and wouldn't want to necessarily get from other carbon-based non-renewable sources. But the pure conversion of matter to energy (and back) still seems a long way off in spite of our best efforts. And I find that somewhat puzzling.

In browsing across the macro-patterns of human activity we observe attempts to get there, but, for whatever reason, no solution completely bridges the divide. Take
current recycling...what we are gaining in reduced quantities of discarded paper (and to a far lesser degree, plastics), we gain in e-waste. With what I call "next years junk" syndrome, technophiles and technophytes, eagerly snatch up the latest available doodad that has arrived to their point on the bell-curve. Off to the "recycling" center or in some cases, landfill, with 2001's latest. Stuff resells on the market for anything greater than junk value for only so long, and when last years doodad goes to Africa, it simply ends up in the ground and water there, because Africans like the latest and greatest, just like everyone else, and they raid their shopping malls in Lagos and Johannesburg just like we do ours in Helsinki, London or suburban LA. Anyone seen my track-pad iPod?

I'm not sure what the state of the art in e-recycling is, but I don't believe it goes far enough. What happens to non-renewable plastics, parts like transistors that are not easily reducible (except with the same sort of "expensive" equipment employed in their manufacture and assembly), etc. I have often said that for everything that is manufactured, there should be an equal and opposite demanufacturing process/facility waiting for it at the end of its life. To what extent we fall short of it, I cannot say, but any shortcoming in it's achievement sets the immutability of those physical laws to a different footlight.



"Gross bodies and light are convertible into one another..." Isaac Newton, 1704. But what's the catch? Personally I stick to my e=mc² as a matter of faith, but understand, that it's opposite, its anti-particle, the yin to its hang, is subtly transformed, like water, to patterns that our symmetrical approach to reason and practical implementation perhaps cannot yet fully grasp.

In-between moments

...when you care enough to give the very least.