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Oct 16
2007

Tim O'Reilly

Since I just made mention of Science News in my response to Scoble's comment on my blog entry about tech blogs all drinking at the same watering hole, I thought I'd point to an actual Science News story that might be of interest to the Radar audience: Math Trek: A Tangled Tale. Go read that article, about an experiment by Dorian Raymer and Douglas Smith at the University of California, San Diego, tumbling lengths of string into knots, and tell me you didn't learn more than you did from a story about one more me-too Web 2.0 startup....

A few tidbits:

• It takes only ten turns for a typical length of string tumbled at random to form a knot.

• For purposes of mathematical analysis, mathematicians create an "ideal form" of the knot by connecting its ends. Two knots are considered equivalent if you can transform one into another simply by moving the string around without cutting it.

 Although these three knots look quite unalike, they're all really just simple loops with no actual knots, meaning that each one can be pulled into a simple loop without cutting the string. Mathematicians call this the "unknot."Wikipedia, via Science News

• "Back in 1983, a mathematician named Vaughan Jones at the University of California, Berkeley devised a mathematical expression—now known as the Jones polynomial—that can be defined for any knot. The remarkable thing is that if two knots are equivalent, they'll each yield the same Jones polynomial. It's not a perfect way to classify all knots, because some complicated knots that aren't equivalent correspond to the same polynomial—so knot theorists still have plenty to keep them busy."

• A knot is considered "prime" if it can't be decomposed into two simpler knots. All of the knots generated by the tumbling experiment were prime.

Now, I'm waiting for the practical application: a headset for my phone that doesn't tie itself into knots. (And no, I don't want bluetooth. Having to remember to recharge another device is the only thing worse than untangling the headset cord. Universal recharging anyone? Mobilewise promised this back in 2002, but it never caught on.)

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Hmm, my bluetooth headset only needs charging every few weeks. It might be worth trying a modern one, or maybe it's just that I don't talk enough for the charging to become an issue.

[10.16.07 12:11 PM]

I think the moral of the story is that both ends of the cell phone headset cord should be attached to each other before storing. This way a simple loop is always guaranteed.

I was going to reflect on this with a bagel and a cup of coffee, but got distracted by their topological isomorphism, and never got around to it.

@Ross: How do you connect both ends of your cellphone headset before storing? As far as I can see both ends are not compatible.
Interesting post, though, Tim, this is what I love the Radar for.

It can only be a matter of time before we are offered a sub-cutaneous bluetooth headset that is powered off our nervous systems, meaning no more re-charging ever, but also meaning a lot of people wandering around apparently talking to themselves, which could be unsettling for the rest of us.

I'm already seeing a lot of that, just with hard-to-see headsets. In Berkeley it's significantly changed the odds in the guessing game of "schizophrenic, or on the phone?"

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