Scientists Crochet Chaos!
In science news, some scientists in the UK have done something that, to most folks, seems pretty much like magic.
They’ve made a crocheted version of the Lorenz Manifold. You can find a pdf of the paper’s abstract here.
Is that a big deal? Well, not to most of us, but it is pretty cool insofar since what they’ve done is made a three-dimensional model of a two-dimensional set of mathematical equations used to represent a three-dimensional space.
Got that? Good….now scoop up that little bit of brain that just leaked out of your ear.
Okay, here’s what that whole Lorenz thing is all about, as best I know how to explain it. Lorenz was a scientist who was interested in chaos theory. he’s also the fellow who coined the term “the butterfly effect” to sum up how small changes in a system – like a weather system – can produce huge and nearly unpredictable results farther along in the system. This uncertainty is why weather is impossible to predict 7 days down the road (and, by the way, any weatherman who says he can give you an accurate prediction for a date a week from todayis fibbing to you badly).
Lorenz believed that it was possible to build a set of mathematical equations which, if you input some initial data, would show you all the eventual possibilities in a system. In other words, it won’t show you what will happen, but it will show you everything that could happen. As a rough example. If you watch a leaf float down a stream, you con’t know exactly where it will finish a hundred yards downstream. It might flow undisturbed all the way down the river, or it may wind up in a shoreside eddy, or it could zig-zag its way down, or any number of othre final results. Using the Lorenz equations and a couple other mathematical tools, you can figure out where the leaf could end up, though you won’t know where it will end up. But by changing the numbers as the leaf goes along, you’ll get a good picture of what could be likely to happen, which wil make your prediction more accurate, if not entirely accurate.
But that’s my layman’s explanation. IANAS, so I’ll defer to Mr. Science Guy whom I’m sure will find htis entry sometime in the next coupld days and, as a Legitimate, Certified, Science Guy, will be physically unable to resist correcting my hamhanded attempt at explanation. That way, at least we’ll know for sure why this crocheting job is such a cool thing and wouldn’t make a very good hat.
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Category: Hey, Mr. Science Guy!
Argh–I hate it when you're right, Jimmie. In this case, what you're right about is that I'm physically unable to resist correcting your explanation.
The good news is, there are just a few details to change in your outline. Most important is that the Lorenz equations aren't specifically designed to show you all the possibilities. They're an attempt to model (or predict) chaotic (or unpredictable) behavior. (And that sentence shows just how hard it is to translate math into English. It's not 100% prediction, and it's also not 100% unpredictable; chaos theory is about finding predictable patterns in a sea of unpredictable data.) The Lorenz equations are useful as a tool in that effort, because they generate that class of not-quite-random data, and they can be used to model quite a few kinds of chaos. I'm not going to go into all the interesting properties and behaviors of those equations, because whole books are written on the subject.
Anyway–your rough example regarding all the places where a leaf might end up (all possible outcomes for a given system), falls more into the field of probability and applied statistics. Chaos theory is a way of determining what the probabilities are, for a given outcome–in other words, all the possible paths a leaf might take, to get to the same place.
Even now, I'll admit that I'm not doing justice to the subject, but I can only do so much writing on my lunch break….
You're my go-to guy and I shamelessly exploit the fact that if I get an explanation near the hole, you'll be able (nay, compelled!) to putt it in!
If you had to pick the neatest or perhaps the application most immediately observed by the common mook like me, what would it be?