Wednesday, April 16, 2008

dandelions are the white trash flower bed

I imagine that when the inventor of the folding bicycle first showed it around to his friends there may have been some confusion about the whole idea.

Friend: Oh my god, I'm so sorry. You worked so hard on that, and now look at it.

Inventor of Folding Bicycle: No, no. It's supposed to collapse like that. That's what it does.

Friend: All that planning and time and hard work for nothing. So sad. What are you going to do now? Go back to grad school?

Inventor of Folding Bicycle: No, you dolt. That's how it works. It's a folding bicycle.

Friend: Oh.... Ummm, I don't get it.

The point of the extremely boring above dialogue is that sometimes an idea takes some getting used to but that don't give up just because you're misunderstood by your friends and contemporaries.

For example, when I custom build an accordion with three changes in the treble to switch between a mildly pleasant vibrato with 12 equal half steps between octaves on the first switch and fifths tuned in a perfect 3:2 ratio with half steps being the seventh root of 3 halves on the second switch, and a third switch where the half steps are the fourth root of 4 thirds and the third tones in the scale are tuned in a perfect 4:3 ratio then all you naysayers won't be laughing anymore.

No. No, you won't.

Thursday, April 10, 2008

Advice for you

If you want to avoid pedal strike on your fixed gear (which I'm sure that you, sensible reader, most certainly do) one thing to take into account is your gear ratio.

Imagine a stretch of curb with an obstacle positioned briefly alongside it (this could be anything: a speed bump, an old lady with a walker, or perhaps a small infant (and really, aren't all infants small).)

Imagine further that the gap between the curb and the obstacle is wide enough to fit the bicycle tires but not wide enough to guarantee that your pedal won't hit the curb. --A certain percentage of your pedal arc will be too wide to fit in the gap.

Assume that the position of the pedals when you arrive at the gap is a uniform random variable (meaning all positions will be equally likely.) Then, whatever your gear ratio, the percentage of your pedal arc that is too wide for the gap will be the probability that your pedal is hitting the curb at any given time.

This is admittedly not all that profound and smacks of pretentious washed-up-math-major posturing. Which is what it is. The crucial insight comes, however, when you realize that if your gear inches are less than the length of the curb/obstacle gap, then your pedal is guaranteed to strike the curb. --You cannot get through the gap without making more than one complete revolution of the pedals, and part of your pedal revolution is too wide to get through.

Therefore, fixed-gear cyclists arriving at gaps between curbs and small infants (or whatever) can maximize the probability of successfully navigating such gaps by making their gear ratio as high as possible. For example, with an infinitely high gear ratio, one could potentially navigate between an infinitely long curb and infinitely long old lady and her walker.

...Just something to keep in mind while you're shopping for girl pants or listening to Sufjan Stevens.

A moral line in the sand

My editor's been hounding me to cut down on the math content. She says we're losing readership.

Me: Readership?

My Editor: Yeah.

Me: Readership?

My Editor: Yep. So can it with the heady math stuff, OK.

Me: Readership? Wait, wait. I'm sorry. Heady?

Her claim is that the number of readers gets cut in half for every post with any math in it. I told her that's good, --pretty soon we're going to be bailed out by the fed for two dollars a share.

My Editor: I don't even exist. This is a free blogspot account. You do what you want. I'm out of here.

Me: I will not water down my content. The huddled masses are clamoring for a blog solution combining a healthy dose of mathematical musings with a fun size portion of cycling punditry. They will not be denied.

Wednesday, April 9, 2008

If only

One thing fixed gear riders have noticed is that if the number of teeth on your chainring and the number of teeth on your rear-cog are relatively prime, then for any given such combination you will maximize the number of skid patches on your tire. This is good because you will have to replace your tire less often.

What's more, you can achieve more versatility by making the number of teeth on the chainring prime. That way, you can have a one or two tooth difference in cog size on the flip-flop, (which will give a greater difference in gear ratio for each side than the same difference in teeth on the chainring,) --and no matter what number of teeth you have on either cog, it will be relatively prime with the front chainring. This is because any number of teeth on the rear-cog will be relatively prime with the (prime) number of teeth on the chainring.

As Stephen Colbert once said to our bow-tie sporting local congressperson: this borders on interesting.

If only there were some device, --some kind of mechanism that would allow you to regulate chain tension as well as achieve different gear ratios without flipping your wheel around or prime-factoring your chainring. Or maybe some other sort of invention that allowed you to brake without wearing out your tire.

Maybe science can come up with something. Science has done good things in the past, haven't they?

Yes. Yes, they have.

Tuesday, April 8, 2008

That's what I thought too

Hey, what's the deal here? I thought this was going to be a blog about cycling.

this whole mortgage thing

By now it's old news that some of the big financial players misunderestimated the risk involved with buying a lot of sub-prime mortgages.

And, sure, we can second-guess after the fact --but if we had been there at the time who's to say we wouldn't have been buying up the crappy mortgages like hot-cakes ourselves. I know I do love me some hot-cakes.

Besides the occasional hankering for some hot-off-the-grittle whole-wheat pancakes, my only other claim to a bit of expertise in the matter is having failed the actuarial exam four times.

As Larry David would say:

Pretty, pretty good.

You'd be hard-pressed to find anybody who has topped that little bit of shameless perseverance. Way to go, me.

It has been a little while, but I was thinking about it and I do remember that theorem where the sum of the standard deviations is greater than the standard deviation of the sum. --Allegedly standard deviation measures risk, so the idea is that if you pool all the risk it's less risky.

That's the idea anyway.