Monthly Archives: June 2009

Giving the Devil His Due

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I read The Devil Is in the Digits, an analysis of the Iranian voting results, and something doesn’t feel quite right about it. (And it’s not that these two political science student authors are being touted as mathematicians in some of the blogs linking to the story) Disclaimer: there seem to be lots of reasons to question the vote. I’m not addressing anything but the rigor of this analysis.

Now, I could be wrong about this, because anything past basic probability gives me trouble — I’m not particularly skilled (my lowest math grades were on probability exams. What are the odds of that?), and those feeble skills have atrophied for most anything beyond simple dice-rolling and poker calculations.

But I do recall that when you multiply probabilities together, it needs to be for independent events. And I question what’s going on here.

We find too many 7s and not enough 5s in the last digit. We expect each digit (0, 1, 2, and so on) to appear at the end of 10 percent of the vote counts. But in Iran’s provincial results, the digit 7 appears 17 percent of the time, and only 4 percent of the results end in the number 5. Two such departures from the average — a spike of 17 percent or more in one digit and a drop to 4 percent or less in another — are extremely unlikely. Fewer than four in a hundred non-fraudulent elections would produce such numbers.

OK, the premise seems fine. You expect each digit to show up 10% of the time, but you can deviate from that and still have a random distribution. But the relationship between the digits is not random — if you have too many 7s, you must have fewer of other numbers! So what I want to know is how they arrived at the four percent result.

Let me illustrate with an example that’s easier to see, and one I can work through: coin tosses. If you toss a coin twice, there are three outcomes: Two heads (25% of the time) a head and a tail (50%) and two tails (25% of the time). So while the expected, average result is one head, it only happens half the time — a result of either two heads or two tails isn’t evidence of anything fishy; we don’t have enough trials. But here’s the biggie: what is the probability of getting two heads, and no tails? It’s still 25%, because (heads) and (not tails) are not independent results. They have the maximum amount of correlation you can get, and since they aren’t independent results, you wouldn’t multiply the probabilities together to find the answer.

I found an analysis someone did using random numbers, and their model simulation gives the odds of a number appearing 5 or fewer times as about 20%, and appearing more than 20 time as 11%. But the odds of both shouldn’t simply be the product of the two, because the results would be correlated in some fashion that’s more involved than the coin-tossing.

So I wonder how they arrived at 4%. It’s not at all clear.

The second part of their analysis is of the last two digits, and whether they are adjacent (or identical) numbers or not, e.g. 54 (adjacent) vs 59 (not).

To check for deviations of this type, we examined the pairs of last and second-to-last digits in Iran’s vote counts. On average, if the results had not been manipulated, 70 percent of these pairs should consist of distinct, non-adjacent digits.

Not so in the data from Iran: Only 62 percent of the pairs contain non-adjacent digits.

Aha! They assume that the numbers are perfectly distributed, and we know the last digits are not; I didn’t see any mention of the second-to-last digit. So one has to wonder whether this analysis holds. I can certainly think of some examples where it fails: the second-to-last digits are all 5, and the last digits are all 4, 5 or 6. In that unlikely result, there would be zero pairs that were non-adjacent, rather than 70%. So I have to wonder how far the assumption holds and how badly it fails. And if these odds depend on the distribution, the digits and the pairings are not independent of each other, so multiplying the probabilities won’t give the right answer.

That’s what my gut and some basic probability math, dredged up from the recesses of my brain tell me. Perhaps someone who does math for a living can confirm that I’m right or tell me that I’m wrong and should stick to my day job. (or that I’m right and I should still stick to my day job)

Which One's Pink?

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Color and Reality. Another take on color vs. the brain’s interpretation of color, discussed (OK, linked to) previously in Color on the Brain

We were all taught about Sir Isaac Newton who discovered that a glass prism can split white light apart into its constituent colors.

While we consider this rather trivial today, at the time you’d be laughed out of the room if you suggested this somehow illustrated a fundamental property of light and color. The popular theory of the day was that color was a mixture of light and dark, and that prisms simply colored light. Color went from bright red (white light with the smallest amount of “dark” added) to dark blue (white light with the most amount of “dark” added before it turned black).

Candygram

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Great white sharks hunt just like Hannibal Lecter

Great white sharks have some things in common with human serial killers, a new study says: They don’t attack at random, but stalk specific victims, lurking out of sight.

The sharks hang back and observe from a not-too-close, not-too-far base, hunt strategically, and learn from previous attempts, according to a study being published online Monday in the Journal of Zoology. Researchers used a serial killer profiling method to figure out just how the fearsome ocean predator hunts, something that’s been hard to observe beneath the surface.

Just like the landshark

Tasty News

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Why taste is as regional as dialect

Prof Taylor said: “Taste is determined by our genetic make-up and influenced by our upbringing and experience with flavours.

“Just as with spoken dialects, where accent is placed on different syllables and vowel formations, people from different regions have developed enhanced sensitivities to certain taste sensations and seek foods that trigger these.”

The part I can’t quite wrap my head around is that this was a test done with British cuisine. One has to question if it is applicable to a broader population.

Is it Really Green?

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Sainsbury’s brings green power to the checkout with ‘kinetic plates’

Energy will be captured every time a vehicle drives over “kinetic road plates” in the car park and then channelled back into the store.

The kinetic road plates are expected to produce 30 kWh of green energy every hour — more than enough energy to power the store’s checkouts. The system, pioneered for Sainsbury’s by Peter Hughes of Highway Energy Systems, does not affect the car or fuel efficiency, and drivers feel no disturbance as they drive over the plates.

My first reaction is that somebody apparently thinks they can violate the first law of thermodynamics. If the energy comes from the car, then it will necessarily affect the car — it will slow it down. Now, this makes sense if you install it where the car was going to slow down anyway, like an approach to a stop sign. But not if the car is going to want to maintain speed, or if the slowdown/stopping is unnecessary.

Sincerely sustainable contains a quote which implies that these are being used as speed bumps. But harvesting energy from speed bumps is only green in a very abstract way, since the car is going to speed up again once past it — you’d be greener by not having the speed bumps there at all, which is one reason why you get better mileage on the highway — you eliminate those stops and starts. A car that is already going the desired speed is going to surrender energy to the device and slow down even though it didn’t need to. Green-wise, you’d be better served with an improved design of the traffic flow. (They also claim that they will generate 30 kW of electricity every hour, when they mean 30 kWh. Call the unit police.)

What they are doing is getting the customers to pay for some of their electricity.

Another example of this appears in Cocktail Party Physics : body heat (spoiler: it stars neither Kathleen Turner nor William Hurt)

Boesel has retrofitted much of his exercise equipment (stationary bikes, treadmills, elliptical machines) so that gym members can produce a little bit of usable energy during their workouts — not a lot, mind you, but enough to run the fans, for example, or the stereo system. Combine that with other strategies for improving energy efficiency, and Boege keeps his electricity costs to a bare minimum. In time, he thinks he can break even, and maybe even turn a small profit.

Tapping the energy from the exercise equipment is a fine goal for the owner, but calling it green is another thing. It’s being powered by the food we eat, via our physical exertion, and that means you have to look at the energy used to bring that food to the table. Dollars to donuts (or tofu) that energy is not green — the delivery trucks run on gas or diesel, the water may be bottled, etc. So once again, the circumstances matter. If you’re recovering otherwise wasted energy, fine, but don’t get on the treadmill for the purpose of generating energy. If someone needs to consume an extra few calories so they can go work out, they’ve basically become a very inefficient battery, and the energy they generate isn’t green. Much like the regenerative braking on Jennifer’s Prius: if you drive around the block, stopping and starting, in order to charge up the battery, then energy will have come from the gasoline.

I noticed the phrase “judicious use of the A/C.” If that means making the patrons sweat some more, there’s the cost of un-doing the dehydration. As I noted in my inaugural post, excess sweat is wasted, from a thermodynamic standpoint, and if you’re drinking bottled water, that’s one more consideration of how green this strategy is.

(and Jennifer also finds herself under investigation by the unit cops, for using “Watts per hour”)

This is reminiscent of the hydrogen economy that was touted a few years back, but about which we haven’t heard much lately. Why? One reason is that it’s not green, It sounds green, but that’s just because you’ve slapped a green-label veneer on something, but when you peel back that layer you find some very un-green components. When all is said and done, this is a little like money laundering — you’re just making it harder to trace the true source.

But there is a true source. The energy we use on this planet ultimately comes from one of two places: the sun, or radioactive materials leftover from the planet’s formation (which came from another sun). You have to trace your generation back to one of those, somehow. If that audit hits a “fossil fuel” source at any point, then your source isn’t green (assuming “green” here refers to sources that do not include sequestered Carbon). Anything involving food runs into issues of fertilization and transportation — even driving to the store to buy it — and packaging, all of which typically involve unsavory sources of energy from a “green” perspective.

So my objection is this: using “Green” makes it sound like you are having no or minimal impact on the environment, and it can be misleading. It can make you focus on a very small reduction in emissions, while distracting from the very large amount that’s already there, and other much more significant improvements that could be made. Be a little skeptical of the users of “Green” and its synonyms, because they may just be feeding you an advertising gimmick.

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Update (more space here than in the comments section. It’s good to be the king):

I don’t necessarily disagree with the comments from BlackGriffen and Jennifer — as I said, harnessing otherwise wasted energy is fine. But consider this scenario:

Someone (Not Jennifer, because I never meant to pick on her) is very impressed by such a gym that she decides to join up, and figures, “What the heck, it’s only a half mile out of my way on my commute. Just an extra mile round trip!” Now, Not Jennifer is a beast in the gym and works out for two hours a day and can manage 100W that whole time (along with 100% efficiency), and works out 25 days a month. That’s 200Whr x 25 = 5kWh of electricity generated (saving the gym owner perhaps 50 cents). And it’s only a mile extra on the commute, so that’s 25 miles of driving, and Not Jennifer drives a Prius, too, so that’s only a half gallon of gas a month. Unfortunately a gallon of gas contains more than 30 kWh of energy. So we’ve traded in excess of 15 kWh of fossil fuel for 5 kWh of human-generated energy in this (admittedly contrived, but certainly plausible) scenario.

That’s my worry — that things like this will happen, because the whole picture isn’t being considered. Yes, education is important. Human power is pretty feeble compared to the machines we have around us, which is why we have them around us. But I have trepidation about tagging things as “green” that may not be, and may not only foster a sense of community but a sense of “I’ve done my part” when that’s not really the case.

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Update II: Some numbers at Dot Physics and Hamiltonian Function for kinetic plates and humans, respectively.

Mathworld

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Some random thoughts on coordinate systems, math-y terminology and the real world.

I went into Bed, Bath & Beyond the other day, and wondered, “What’s beyond Bed, Bath & Beyond? The name does not specify how far beyond bed and bath it goes.

As you drive through northern Pennsylvania there’s a sign that reads “Endless Mountains, next 6 exits.” What? Only 6? They’re endless, right? It must be that they’re endless in some other dimension, and I’m just going through with some perpendicular component.

Back when I lived in Orlando, there was a novelty/gift store called The Infinite Mushroom. One day I stopped off and there was a sign on the door explaining that they had moved. But if they were infinite, how could you tell? To make matters even more confusing, they later expanded. Obviously they could not be infinite in all dimensions. I started to refer to them as the semi-infinite mushroom after that.

The Deluge of Sarcasm

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A risk you run with in the digital age is that if you do something stupid, it will almost certainly be recorded in a quasi-permanent way, in contrast to the ephemeral nature of a spoken conversation. You don’t even have the “I was misquoted” excuse when you’ve removed the human being from the equation.

Great example: Pete Hoekstra (R, Min) tweeting about the horrible mistreatment he and his colleagues have suffered.

Iranian twitter activity similar to what we did in House last year when Republicans were shut down in the House.

Not surprisingly, that set off the internet’s sarcasmotron. Lots of tweets, and a blog post devoted to it. If you don’t want to sift sort too much, here are some highlights

benhuh: @petehoekstra I had to sit in the last row of our corporate jet this morning. This is what Rosa Parks must have felt.

curtsmith: @petehoekstra, fell off my surfboard in Malibu today, now I know what D-day felt like.

donnahon: @petehoekstra Got some sand in my shoe. Now I know what it’s like to be on my third deployment in Iraq.