Mathematically Proven Fact: Accelerate While Turning

Today I was chit chatting with my mentor about curvature and other differential-geometry-related shtuff, when she told me a most surprising fact. Unfortunately I can not explain it without relying on abstract mathematical concepts, because I myself can only understand it in those terms. It's really counterintuitive. Imagine you're driving on an exit ramp (or any any curved road for that matter). You want your acceleration vectors to point towards where you want your car to go, which in this case would be centripetally, towards the center of the circle in which you're driving. If you speed up, the acceleration vector gets longer, and pushes you more strongly to the center. If you decelerate, however, your acceleration vectors point backwards, away from where you want to go, so your car starts to skid. Of course it's good to slow down before making a turn. But once you start turning, you want to speed up. I'm talking nonsense? Well, that's what SHE said.

To understand this, do the following experiment:
Take a deep breath.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
Oh no! You're going to fast! You gently push the break.
Visualize it.
What do you feel happening?
I feel the tail of car swerving off the road.

Now let's try this again.
Pretend you're in a car.
You're driving down the highway.
You approach a curve in the road.
You head straight into the curve.
As you start curving, you press the accelerator.
Visualize it.
What do you feel happening?
I feel the car griping the road.

These thought experiments are really worthless. It's possible that the reason I connect decelerating with losing control is because I usually slow down only if I'm going too fast to begin with. And I connect accelerating with control because I usually accelerate only if I started off at a slow enough speed. It's a shame she didn't tell me about this when I met with her last Wednesday. That way I could have experimented when I drove to Pittsburgh last Thrusday. All my passengers were screaming that I drive too fast. Wouldn't they love it if I told them that taking curves fast is safer? And then proceeded to demonstrate it experimentally?

But the bottom line is: you should definitely slow down before the curve. And if you are pulled over for speeding through a curve, explain to the cop that if you would have slowed down, you would have skidded off the road. Then pull out a pad and draw the acceleration vectors. The cop should excuse you, because math never lies.

I'm Proud to be an American / At Least Phelps is Free

Isn't it neat that the John Galliano thing happened within a few days of the Snyder v. Phelps verdict? Where would you rather be? In France where you can be locked up for calling someone a fucking kike, or the U.S.A., where you you can tell grieving parents that god hates them and their recently killed son is in Hell.

I choose the latter. I'm proud of my right to be rude. The First Amendment tells us, "You guys are big boys and girls. As long as nobody is physically hurting anyone else, I trust you to fight it out between yourselves."

But even in America, Land of the Free and Home of the KKK, people on their own are forcing this you-can't-offend-anybody pussiness on others. Recently an anti-abortion group put up an ad drawing attention to the prevalence of abortion among Niggers (Yes! This is America! That word is still legal!)

You don't like it? Big deal. Pro-abortion people are never going to like anti-abortion ads. I don't like HSBC's ads where they misuse numbers and quote irrelevant statistics (There are more vineyards in Turkey than in South Africa. Bank with HSBC). I'm also offended with those gruesome ads trying to get you not to drink soda. But I don't make a fuss. I just try to ignore them. We are adults. Part of life is getting offended. Deal with.

But apparently I'm wrong. Apparently it's an outrage that anyone ever needs to endure offence related to race (or sexual orientation, to a lesser extent). The mother of the girl in picture is "furious," "devastated," and wants an apology. Well lady, when you took your kid to the stock-photo studio, you signed away your rights to the picture. Too bad. Honor your agreement, and live with it. This ad is just pointing out a fact, that lots of Black fetueses are aborted. No, Daily News, they are not comparing abortion to genocide. (Seriously, where did the Daily News see anything about genocide?) They are pointing out a statistical fact in a provocative way. Isn't that standard for advertising?

Together with the right to free speech comes the possibility of getting offended. Live with it.

Dammed Lies and Statistics, or, Context, Context, Context

"1 MILLION WORKERS. 90 MILLION iPHONES. 17 SUICIDES" screams the front cover of this month's Wired Turns out that there's this huge company called Foxconn that produces some huge chunk of the world's electronics. And 17 of their employees committed suicide. Now we're supposed to feel guilty that our insatiable desire for electronics drove them to death. There's only one problem with this story. Foxconn has one million employees. Seventeen out of a million is actually quite small. American college students are four times more likely to commit suicide. The non-sensational fact is that Foxconn is a better place to work than other Chinese factories (which is not saying much). Sure, some of the things which make Foxconn a better place to work were done in response to the public outcry caused by the suicides. But even before the suicides, it was better than the other factories. So leave Foxconn alone, and let them rake in the cash in peace.

The morals of this story are:
Without context, numbers mean nothing.
People do not know what a million is.

Do You Believe these Statistics?

People are jamming MetroCard machines, keeping people from buying MetroCards, and then illegally selling MetroCard swipes. According to the New York Post, "In Brooklyn, vandals at the Utica Avenue station that serves the 3 and 4 trains broke machines 198 times in December alone -- second only to Nostrand Avenue, where vandals took out 228 Metrocard machines, according to MTA data requested by The Post."

198/31 > 6. So if they broke machines 198 times in December, they'd need to break more than 6 machines a day. These criminals only jam the slot through which one puts bills. If I recall correctly, at the Schenectady Ave. entrance there are only two machines that accept bills. I don't know how many machines there are on the Utica Ave. side, but I imagine that no more than four accept bills. So to get 198 breakages in a month, they'd need to basically break every single machine every single day. I don't doubt that these criminals are up to that. I just can't believe that the MTA fixes the machines so quickly that they're ready to broken every day--even on weekends and holidays.

The next statistic is even more disturbing. 228 "broken machines" at Nostrand? That's not possible, considering there aren't 228 machines at Nostrand. Presumably they mean 228 breakages, distributed among much fewer machines. Fine. Now which Nostrand are they talking about? If it's the Nostrand Ave 3 station, there are only two bill-accepting machines there. To break two machines 228 times in one month requires breaking each machine (228/31)/2 = 3.67741935 times each day. There is no way the MTA could fix a machine more than three times a day, so how could vandals break the machines that often? Perhaps they meant the Nostrand Ave A/C line? I'm not familiar with that station, but I don't think it's such a huge station that 228 breakages would be plausible. Maybe the 228 breakages weren't all in December? Maybe they meant 228 breakages on the entire Nostrand Ave, which would include the A/C station, the 3 station, and all the 2/5 stations between President and Flatbush Ave-Brooklyn College? 228 breakages between all those stations is plausible. But if that's what they meant, then why the hell can't the Post write that? And if that's what meant, then how can they say that Utica is second to Nostrand? Maybe they should compare the entire Eastern Parkway to Nostrand Avenue?

Unlike the innumeracy I mentioned in the previous posts, this article does not talk about any huge numbers. Everyone has a pretty good grasp of magnitutes like 198 and 228. So then how could the Post publish these numbers without thinking about what these numbers mean? These numbers came from "MTA data requested by the Post." If the MTA coughed up the numbers just for them, can't they report the numbers in context?

PEOPLE!! Numbers are not conceptual art! You can not just play with them to make them mean whatever you want them to mean!

Thousand-Dollar Light Fixtures and Highly Informative Ads

So apparently the city isn't spending $708 billion on new light fixtures. It's only spending $708 million. WTF? $708 million for 772 schools is approximately $917,100 per school. According to Gothamist they're replacing 564,000 fixtures. That's approximately $1,255 per fixture. WTF? Seriously. Doesn't the city know how to shop around for a good deal?

Once I'm complaining about the city wasting money, what is up with these obnoxious ads on the subway how you shouldn't drink too much. Please. It is not a recent discovery that by drinking too much you might get into a fight or pass out. Humankind has been aware of the dangers of excessive drinking for thousands of years. I don't need NYC to tell me how much to drink. Do they think I'm stupid and I have no common sense? What's next? Ads with a picture of a guy lying in bed and a caption, "7 p.m. is not 7 a.m.--always make sure you've set your alarm clock correctly"? Maybe they should have ads telling us to call our mothers every week? And ads reminding us write thank-you notes when we get gifts? This is not a joke. The federal government already sponsors ads telling people to stay married.

Numeracy Please!

To the editors of Metro,

In Thursday's paper you write that Bloomberg will devote $708 billion to replacing dangerous light fixtures in 772 city schools. Do you have any idea what $708 billion is? The U.S. Department of Defense's 2011 budget is $721.3 billion. If there are 1,000 rooms in every one of the 772 schools, and each room has 100 light fixtures, $708 billion will leave nearly eight million dollars per light fixture. I'm not surprised that Metro's typists made a mistake. I'm surprised that the rest of Metro's staff was so innumerate as to not notice it.

Still a devoted reader,

e
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More on numeracy and large numbers:

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