Dumb me. I went to the Zappa Plays Zappa concert last month. Great show, with Dweezil faithfully channeling his dad Frank. But I felt kind of dorky lugging my bicycle helmet around the theater.

You see, I had made the 10-mile round trip between lower Manhattan, where I live, and the Beacon Theatre on the Upper West Side, by bicycle. Burning a gallon of gas to go 20 miles makes 20 pounds of CO2, so I figure that by biking instead of taking a taxi I prevented 10 pounds of climate-altering greenhouse gases from going into the atmosphere. That may not be much, but it’s something.

But now I’m told that for 6 cents I could have been just as “climate-neutral” as I was by pedaling ten rather sweaty miles. Just a nickel and a penny could have purchased enough wind-generated electricity to keep the coal-fired power grid from burning a few lumps of bituminous and releasing 10 pounds of CO2 — the same climate-altering amount the cab ride would have made.

Says who? The very popular, and now supposedly climate-conscious, Dave Matthews Band. According to a link posted at the jam band’s website, the group is contributing $216,000 to a wind power investment fund to finance wind turbines, which over their operating life will offset 18,000 tons of CO2 that would otherwise have been produced with fossil fuels. Supposedly that’s as much carbon pollution as the DMB and its fans have produced by traveling 36 million car-miles since the band began touring in the early 1990s. This donation works out to 6/10 of a cent for each of those miles, or 6 cents for the 10 car miles I would have racked up if I’d taken a cab to the Zappa show.

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Want to try that again? Most electricity generation and all car driving make carbon dioxide, whereas wind power and bicycle riding do not. Just as biking can substitute for driving, wind-powered electricity displaces kilowatts that otherwise would have necessitated burning fossil fuels and making CO2.

So in my case — says the DMB — instead of bike-riding to the Beacon, I could have driven and still not produced any net carbon, as long as I paid a wind developer 6 cents to build a bit more wind power and displace enough coal-fired power to offset the emissions from my gasoline-fueled taxicab.

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Whew! That reasoning is almost as intricate as one of Mother Frank’s fiendish marimba parts. But is it equally logical? I’m not so sure.

First, a minor math matter: I ran the numbers and came up with only half of the carbon offsets the DMB is claiming. The $216,000 that the band is anteing up will only build enough wind capacity to offset the CO2 from 18 million car miles, rather than 36 million.

No big deal there. The offsets should be priced at 1.2 cents a mile, not 0.6 cents, which would bump up the cost to make my cab ride carbon-neutral to 12 cents from 6. Wowie Zowie, as Zappa might have said.

Intuitively, though, it feels like there’s something wrong with this picture. When you stop and think about it, the whole idea of driving a car, paying money into a green kitty to offset the CO2 from burning the gas, and then calling the car trip carbon-neutral, is ludicrous.

The windmills may offset the driving, mathematically, but so what? The windmills should, and likely could, have been built without my 6 cents or even Dave’s $216,000. (Indeed, wind turbines and other clean energy would be sprouting up everywhere, without green offsets, if the prices of fossil fuels included a charge for their climate destructiveness.) Crediting me or the DMB with climate neutrality for financing green energy, while the actual implementer — a wind developer here, an insulation installer or a mass transit builder there — also takes credit, is double-counting.

But it’s worse than padding the books. Carbon offsets are disturbingly redolent of the sale of indulgences in the Middle Ages, by which the wealthy could expiate their sins without prayer or good works by greasing the palms of the Church hierarchy. Leaving aside whether carbon emitting is “sinful,” the purchase of carbon offsets smacks of the same corruption that turned indulgences into “get out of Purgatory free” cards and helped set off the Protestant Reformation.

“Be the change you want to see in the world,” urged the 20th century’s greatest revolutionary. Gandhi wasn’t speaking about the climate crisis, but his words still apply. At the same time that we press for policy changes like carbon taxes and efficiency standards, we Americans must move individually toward low-carbon lives — bicycling instead of driving, replacing watt-wasting incandescent bulbs with compact fluorescents, and minimizing air travel. This personal commitment is essential, not just to deliver big reductions in carbon emissions but for the sake of moral consistency.

Preserving Earth’s climate isn’t a job that the environmentally concerned can subcontract. Telling others to cut back while we keep burning carbon will destroy our moral authority, no matter how many offsets we purchase.

We can’t buy the change we so desperately want to see in the world. As Gandhi said, we must be it.

Komanoff, an economist and Gristmill contributor, first saw Frank Zappa and the Mothers of Invention at the Garrick Theatre in Greenwich Village in 1967 in the company of his sister, percussionist Ruth Underwood, who went on to tour and record with the band.