## Innumeracy

August 24, 2010

So I just saw an article about Justin Bieber’s newly released song “U Smile 800% Slower.” This song was purportedly obtained by slowing down Bieber’s original “U Smile” song by 800%. Read that last sentence again and see if you can make sense of it. That’s what I thought. Slowing something down by 800% is gibberish, unless you allow for going in reverse.

See the original article for yourself by clicking here.

To be fair, what they mean is that the new version has been “stretched out” to be 8 times longer than the old version. Equivalently, its new speed is one eighth its old speed. But this is not the same as being slowed down by 800%. In fact, if your new speed is one eighth your old speed, then you’ve slowed down by 87.5%, not 800%, a fact which I’ll prove below.

To understand what’s going on, first consider increasing a quantity by a certain percentage. What does it mean to increase something up by 50%? Well, it’s new value should be 50% more than its old value. For example, if you increase 100 by 50%, what’s the new value? Answer: 150. What did you do? You added 50% of 100 to itself. More generally, if $x$ is the quantity we’re increasing by $p$ percent, its new value is $x+(p/100)x=(1+p/100)x$. Thus, to increase 100 by 75% is to multiply it by $1+75/100=1.75$, so its new value is 175, right? Right.

Now consider reducing something by a certain percentage. Say you’re driving down the highway at 100 mph. If you slow down by 50%, how fast are you going? Answer: 50 mph. If you slow down instead by 75% how fast are you going? Answer: 25 mph. What did you do? Answer: you subtracted the given percentage of the original quantity from itself. Generally, if $x$ is the quantity to be reduced by $p$ percent, its new value is $x-(p/100)x=(1-p/100)x$. In other words, to find the new (reduced) value, you multiply the original value by $1-p/100$. In the 75% case for example, the new value of $x$ is $(1-75/100)x=0.25x$. Similarly, if you slow down by 100% how fast are you going? Answer: 0 mph, since $(1-100/100)x=0x=0$. You’ve stopped.

Now, if you slow down by 800% how fast are you going? Answer: You’re going in reverse at 700 mph, since $x(1-800/100)=-7x$.

In any case, the new song is 1/8th as fast as the original song. If $x$ is the speed of the original song, its new speed is $(1/8)x$. By what percentage was the song slowed down? According to the formula developed above, we need to find a $p$ such that $(1/8)x=(1-p/100)x$. Solving for $p$ gives $p=87.5$. That is, the song was slowed down by 87.5%, not 800%.

Got it? Good.

August 19, 2009

My campus bookstore made a dramatic claim about reduced textbook pricing. Karen Natale, the “Bookstore & Licensing Program Manager” has this to say about the new bookstore and reduced prices:

In case you don’t have time to watch the video, here’s the relevant quote:

As you know, publishers set the prices, the bookstore doesn’t, on [new] textbooks. But bookstores add a margin, and the margin covers overhead, salaries, shipping and handling, all the things we need to do to stay in business. In the past, our margin was 23%, which is what the national average is. Many of the UNC campuses are at 25%. We are now, thanks to our new contract [with Barnes & Noble], at 18%. So that’s a significant savings that students are going to see staying in their pockets.

Wow! A margin of only 18%, when the national average is 23% and some UNC campuses are charging as much as 25%, according to her. Sounds great, right?

Suppose the publisher sells a book to the bookstore for the wholesale price of $105. With an advertised 18% margin, what do you think the shelf price should be? Pause for a moment and calculate this yourself. You probably came up with$123.90. You took $105 and multiplied it by 1.18, right? Unfortunately, that’s not how it’s done. What you’ve done (and what advertisers are counting on) is to confuse margin with markup. There’s quite a difference. To be brief, if you start with the sale price, the margin is percentage you *discount* to get the cost, whereas if you start with the cost, the markup is the percentage you *add* to determine the sale price. Thus markup and margin are “dual” to each other in some sense. To be definite, suppose $C$ is the wholesale cost of the item to the reseller. Let $M$ represent the percent margin or markup desired, with $0\leq M<1$. If $M$ represents markup, then the price $P$ of the item is $P=C(1+M)$. If $M$ represents margin, the formula is $P=C\frac{1}{1-M}$ instead. To summarize, $P_\text{markup}=C(1+M)$ $P_\text{margin}=C\frac{\displaystyle 1}{\displaystyle 1-M}$. So, back to our textbook example. Its wholesale cost to the bookstore was$105.00. Since they have an 18% margin, the price listed on the shelf will be $105\frac{1}{1-.18}=105\frac{1}{.82}=105(1.22)=128.05$. Did you notice? An 18% margin became a 22% markup!

In general, if the margin is $M$ then the markup is $\frac{M}{1-M}$. Here’s a short table showing the relationship in increments of 10%.

0% margin = 0% markup
10% margin = 11.1% markup
20% margin = 25% markup
30% margin = 42.9% markup
40% margin = 66.7% markup
50% margin = 100% markup
60% margin = 150% markup
70% margin = 233% markup
80% margin = 400% markup
90% margin = 900% markup

Assuming $0\leq M<1$, we may Taylor expand the margin factor as follows: $\frac{1}{1-M}=1+M+M^2+M^3+\cdots$. Thus we see that

$P_\text{markup}=C(1+M)$

$P_\text{margin}=C(1+M+M^2+M^3+\cdots)$

So the markup formula is really just a first order Taylor approximation to the margin formula. In using the margin formula, they’re benefitting from keeping all those higher order terms, and they can really add up over many, many sales.

What’s worse, the difference between the markup formula and the margin formula becomes more dramatic as the margin goes up. The formulas are identical for $M=0$, but the margin formula blows up to infinity as $M$ approaches 1 (i.e. 100%). Meanwhile, the honest markup formula remains “honest” no matter how high $M$ goes.

By the way, I don’t place any blame on Karen Natale. She’s been excellent in working with professors and publishers to get low prices and correct errors.

I’m guessing resellers advertise margin instead of markup since, for a fixed profit, the advertised margin will be smaller than the markup, making it sound like you’re getting a better deal than you really are. I suppose this tactic is par for the advertising world. Oh well. Now you know.

## The sensation of flight … again

August 5, 2009

Ahhhhhhhhhhhhhh… That’s what it felt like to finally jump again. On May 30, 2009, it had been 1,309 days since my last skydive (that’s just over 3.5 years if you’re not quick with mod 365 arithmetic). Since I’m hostage to Chicago this summer without my girlfriend, friends, family, or other hobbies to distract me, I decided it was a good time to start jumping again. And what better place than Skydive Chicago (SDC), a huge dropzone about an hour and a half southwest of the Windy City.

Planning for this, I showed up at SDC with my rig (Javelin Odyssey and PD Spectre) on my first full weekend here, but unfortunately it needed to be sent away for its 4 year AAD service, and then a main inspection and reserve repack. So I had to jump a rental rig until mine came back from its service.

For the first skydive that weekend, I jumped with Biff Bolen of SDC, one of the most laid back jumpers I’ve met (that’s saying a lot, since skydivers are a relaxed, generally hippy crowd). And he generously offered me free video, too! Here’s the jump, after I did some editing in Final Cut Express 4.

Although my exit was perfect (putting it modestly), you can see that I’m porpoising at a few points during the skydive. My track was a little unstable but basically on heading. Flying your body is not as easy as it looks. I don’t think it was too bad considering the 43 month hiatus.

I jumped at SDC a few times since this video, but not with anybody flying camera (or I would’ve posted footage of my much better and less embarrassing subsequent jumps instead!) The pro shop just called me and said my rig is back from Europe and ready to go, so I can’t wait to jump my Odyssey again.

Skydive Carolina, here I come again!

P.S.: As I browsed my iTunes library for the right music to accompany the video, I finally decided on Orbital’s “One Perfect Sunshine” track from their Blue Album. This got me to thinking about Shaun Kime, my good friend from high school who introduced me (among other things) to Orbital and Pink Floyd. Funny how, as the years go past, you remember the ways certain people influenced you. Tip of the hat to Shaun, and congrats again on getting married.

## Bill O’Reilly is full of baloney

August 2, 2009

If you know me at all, then you know I’m no fan of Fox News. But I love watching it because (1) it gets my heart rate up, burning some calories in the process, and (2) it continues to hone my bullshit detector. As a typical example, I’m going to eviscerate Bill O’Reilly’s “Talking Points Commentary” from 7/30/2009. Here it is.

If you’re a Fox News fan, and especially if you like demagogues such as Bill O’Reilly, Sean Hannity, Glenn Beck, Rush Limbaugh, and the like, then before reading further I entreat you to watch the video in its entirety. See if you can spot all the baloney for yourself. Maybe you’re more credulous than you think.

O’Reilly’s monologue is centered around the controversy Bill Maher stirred up after he called America a “stupid country” on CNN with Wolf Blitzer. Now, I don’t think America is a stupid country. I do think the average citizen is seriously uninformed, but not stupid. According to the New Oxford American Dictionary, stupid means “lacking intelligence or common sense,” and intelligence is defined as “the ability to acquire and apply knowledge and skills.” I think many people don’t make use of that ability, but this doesn’t mean they don’t have it.

Let’s begin with the substantive critique, shall we? At time 1:02 in the video, Bill’O says

“Why do uber liberals believe the USA is a dumb country?”

STOP! Who said uber liberals believe the USA is a dumb country? BILL MAHER said we are a stupid country, but don’t characterize the entire left wing as agreeing with Maher’s unkind remark. Of course, this sort of verbal prestidigitation does help your campaign against the left, but if you want to call yourself a news anchor, please stop distorting what you report.

At 1:09, O’Reilly says

“But the truth is, the governor (Palin) did a pretty good job on Alaska. Her approval rating when she left office was 54%. Despite spending a lot of time outside the state, Mrs. Palin is portrayed by the left as dumb, but how does that square with her solid performance in office? No, she didn’t study at an Ivy League college, graduating from the university of Idaho, but again, she did the job she was elected to do.”

First of all, favorable approval ratings are not evidence for doing a good job in office. They are evidence that you have a good public opinion, but that can be explained in other ways (say, having a shrewd public relations manager). Secondly, Bill’O keeps insinuating, just about every time he’s on the air, that graduating from top schools means you’re smart. Nope. It likely means you have a decent education, but I submit there are many folks who didn’t attend top schools that are nevertheless smarter than others who did. It’s well known that some who attend top schools get in (over better qualified applicants) because they know somebody important, they come from a long line of alumni, or their family members are generous benefactors. Finally, and this is not really germane to the discussion at hand, but I find O’Reilly’s inconsistent “reasoning” (if you can call it that) distressingly irritating: President Bush had the lowest approval rating when he left office in the nation’s hisotry, yet Bill’O thinks he did a bang-up job. Are approval ratings correlated with job performance or not? This is trademark O’Reilly style, arguing a point in two opposite ways when it suits his purpose.

Moving on, at 1:28 O’Reilly says

“So let’s compare her (Palin) to a darling of the left, (democratic) Massachusetts’ Governor Deval Patrick, Barrack Obama’s good friend. Governor Patrick has a law degree from Harvard, so obviously he’s a smart guy, but his approval rating now stands at an embarrassing 36%, and the state’s in chaos. So Pailn is dumb but Alaska is fine, and Patrick is smart but Massachusetts is failing. Don’t you hate it when the facts get in the way of the stupid theory?”

STRAW MAN ! Bill is presenting a distorted view of the opposition’s argument and then attacking that distorted view, as if doing so proves his point. Maher never said “Palin did a bad job because she’s stupid.” But this fabricated soundbite is what Bill’O is arguing against. Classic straw man. Next, why the “Barrack Obama’s good friend” reference? It has nothing to do with the discussion, but it does link Obama to what O’Reilly is characterizing as a failed governorship. Subtle and pernicious propaganda, as I’ve come to expect from Bill’O. And again, we see O’Reilly claiming that graduates of top schools are smart. I won’t bother to repeat myself in rebutting this point. But I will point out one possible explanation for why O’Reilly keeps putting this forward: Bill’O is fond of reminding his viewers that he has a masters degree from Harvard, so what should you conclude using his reasoning?

At 1:57 into the video we find the real disingenuous zinger. Bill’O says:

“87% of U.S. adults ages 25 to 64 have graduated from high school or college compared to 85% in Britain and 67% in France. Obviously, we the people are fairly well educated. The far left ignorance meter, I think, is simply driven by ideology. If you disagree with their policies, you’re a moron. Now, some on the right do that as well.”

Notice this carefully crafted statistic, in particular the or in “high school or college”. Pretty much anybody who’s graduated recently from high school in the U.S. will tell you their diploma isn’t worth its weight in toilet paper. Bill knows our college graduation rate is well behind the rest of the west, so he throws in “high school” in his statistic to bring our numbers up. Clever, but that won’t slip past the discerning viewer (did it slip past you?). If we focus on just college graduation percentages instead, arguably much more important, then we find that America is well behind Europe. Regarding his ideology comment, may I point out O’Reilly’s characteristic hypocrisy again? Bill’O frequently labels his interlocutors as “pinheads” if they disagree with him. Pot. Kettle. Black. I think O’Reilly’s pinhead meter is driven by his ideology.

For the record, Bill’O reveals what he’s really worried about in the next clip, namely America losing her “white Christian male power structure.” All at once, he’s racist, theocratic, and sexist. Sound outrageous? Don’t take my word for it:

As you’ve just seen above, “news” from Fox is anything but fair and balanced or spin free. Yet Fox News keeps chanting a mantra about how they deliver “fair and balanced news,” and O’Reilly’s program is outrageously subtitled “The No-Spin Zone.” Why the need to constantly remind us that they’re fair and balanced? Maybe they’re betting if you tell a lie often enough that people will start to believe it. Sadly, many already do.

## Healthcare Reform – Part I

August 2, 2009

I keep hearing critics cite the one thousand page length of the healthcare reform bill as evidence it is hopelessly complicated; that it will crush healthcare providers under the weight of government regulations. Quite frankly, I’m surprised it’s only a thousand pages long. I would’ve thought reforming a system as large and complicated as healthcare would take far more ink. It sounds daunting to the average citizen, but we’re talking about revamping a huge chunk of the nation’s economy. Too little (or too much) specificity in the bill is a recipe for loophole exploitation. It’s difficult to find the right balance, but I wouldn’t say a thousand pages, per se, is too much.

Rules and regulations will likely cut into the profit margins of healthcare providers. No doubt some insurance companies will lose customers to the government plan. Who knows, some businesses might even fold if they dip too far into the red.

But the critics are forgetting the powerful engine of capitalism. The great economic strength (and moral weakness) of capitalism is its ability to find and exploit opportunities for profit, wherever they may be. Profit opportunities in America are like weeds growing through cracks in a sidewalk. Where some die, others spring up. Those who claim health insurance companies will die out and become a shadow of the past are vastly underestimating the driving force behind capitalism, namely greed. And I don’t think history is on the critics’ side.

After the stock market crash of 1929, what did the government do? In 1934 it introduced the Securities and Exchange Commission (SEC) to crack down on fraud and corporate malpractice in the stock market. Did the SEC crush out our economy? No. Did corrupt companies fold under the SEC’s wrath? Yes they did (and they still do). And we should be glad for it. It has been strongly argued that a little more regulation of risky lending practices might have prevented this whole darned recession in the first place. But I digress.

If healthcare reform is passed, you can bet that lip-smackingly opportunistic business executives will find a way to cope with the new system and turn a profit. After all, the business (racket?) of insurance is inherently profitable — for every claim, there are thousands of healthy patients paying more in premiums than they receive in benefits.

Furthermore, I find it mildly ironic that those critizing reform and portending the doom of the entire health insurance market are the same people who argued that big banks and auto companies should be left to sink or swim, according to their ability to adapt. Which is it? Do we allow businesses to adapt and survive to changing circumstances or not? If so, then let the health insurance companies adapt to the new regulations, just as Wall Street adapted to the SEC.

I will speculate by positing a simpler, albeit cynical, explanation for all the doom and gloom you hear on Fox News: Health insurance companies don’t want healthcare reform to pass because it will eat into profit margins. They’re accustomed to lining their pockets with record profits while denying the most deserving customers their due care. The moment someone has a catastrophic claim, they give the patient’s medical history an enema, looking for the slightest reason to disqualify them, even irrelevant ones. Take, for example, the case of the California woman Tarsha Harris. After being diagnosed with leukemia, her insurance carrier, Blue Cross, gave her medical history the aforementioned enema and dropped her after discovering she failed to report a yeast infection several years earlier. What the HELL does a yeast infection have to do with her leukemia? Nothing, but she didn’t disclose it, and so they uncovered a fine print loophole to evade covering her much needed care (after she dutifully paid her premiums year after year). And insurance companies routinely tell doctors they won’t pay for prescribed medical procedures, in effect letting profit considerations dictate the level of patient care. You can guess who draws the shortest straw in this deal. So the scum of the healthcare system, fearing a cut in the spoils of their wicked racket, spill doom and gloom into conservative think tanks and leak pseudo statistics into the media about how awful reform will be, and that it will drive them into bankruptcy, causing more job losses. Then it goes straight to the talking heads on Fox News and into the hearts and minds of the credulous.

Plainly now: What’s more likely, that some government regulations will bankrupt the entire healthcare market and doom it to failure, or that greedy healthcare companies want you to believe doom and gloom in order to stymie the bill and keep up their record profits? I think Ockham is on my side.

## Letter from a Birmingham Jail

August 1, 2009

If you’ve never read Martin Luther King Jr. before, may I humbly suggest his “Letter from a Birmingham Jail?” Weighing in at just under 7,000 words, this memorable April 1963 essay manages to be simultaneously heart wrenching and uplifting. The essay, addressed to white Christian preachers, paints a striking picture of their indifference towards black suffering and oppression, and it’s bound to melt the heart of all but the most strident racist.

King lists the four components of nonviolent protest (fact gathering, negotiation, self-purification, and direct action), and makes the case forcefully for nonviolent protest. Citing Socrates the gadfly, he argues that nonviolent protests create tension, dramatizing the situation and thereby forcing the community to confront the issue instead of ignoring it.

Dr. King then repudiates the white’s tiresome call for King and his followers to “wait” for change. He does so by laying out a lengthy list of grievous injustices his people suffer daily, laying waste to the idea that anybody should “wait” under those awful circumstances. As his style is inimitable, I’ll just quote him directly…

King takes mainstream Christian churches to task, many of which were still segregated at the time, for dragging their feet on the most important civil rights, indeed human rights, issue of the time.

… I have heard numerous southern religious leaders admonish their worshipers to comply with a desegregation decision because it is the law, but I have longed to hear white ministers declare: “Follow this decree because integration is morally right and because the Negro is your brother.” In the midst of blatant injustices inflicted upon the Negro, I have watched white churchmen stand on the sideline and mouth pious irrelevancies and sanctimonious trivialities. In the midst of a mighty struggle to rid our nation of racial and economic injustice, I have heard many ministers say: “Those are social issues, with which the gospel has no real concern.” And I have watched many churches commit themselves to a completely other worldly religion which makes a strange, un-Biblical distinction between body and soul, between the sacred and the secular …

Yet King gives credit where it’s due, specifically naming several courageous whites (Ralph McGill, Lillian Smith, Harry Golden, James McBride Dabbs, Ann Brade, and Sarah Patton Boyle) with the moral and personal courage to stand tall beside their negro brothers in peaceful protest, suffering beatings and jail time right alongside them.

Probably an underappreciated result of Dr. King’s nonviolent protest movement, and one that he only briefly mentions in his essay, is the garnering of support from innumerable blacks who might have otherwise turned to racial and nationalistic movements. One doesn’t have to stretch the imagination too far to speculate what might have happened if King’s followers had chosen a more radical leader to follow.

King’s essay is powerful. Read it: Letter from a Birmingham Jail.

## Chicago – Sunday, 07/26/2009

July 28, 2009

We had a tough time getting up Sunday morning, being exhausted from walking many, many miles on concrete and asphalt the day before. I think by 8:00am we managed to be out of bed. The first order of business was breakfast, but this time I chose the Blueberry Hill Cafe (in historic LaGrange, IL), having been discovered by my keenly observant mother a few weeks earlier. You see, Mom, my sister Sarah, and my nephew Alec were visiting me in early July. Sarah and I wanted breakfast at IHOP. On the way, Mom spotted the Blueberry Hill Cafe with a decidedly subordinate comment like “Oh, that looks like a nice place to eat” as we drove past it. After we failed to locate a local IHOP, Mom asserted the Blueberry Hill Cafe again, knowing from her long experience that it’s better to eat at a local (vs. large chain) restaurant when traveling. I couldn’t agree with her more.

Sharing in Mom’s wisdom, I took Dad to the Blueberry Hill Cafe.  He loved the restaurant on the way in, but got an omelette he didn’t like, spoiling his impression.  We made it to the train station and headed for the Museum of Science & Industry.  On the basis of the transit map alone, we decided the shortest way to the museum was to take the green line towards Cottage Grove all the way to the end.

Exiting the train station and finding ourselves in the projects, I realized there’s a lot more to getting around a city than train stops and street names. You’d think I would have remembered this lesson from when I lived in the D.C. suburbs, but apparently not. We made a hair-raising 2 mile walk through this war zone, replete with gold-toothed thugs wearing wife-beaters and pants sagging down to their knees. We got more than a few hostile stares from street goons, but managed to avoid any tolls or beatings. Both of us were sweating bullets. Dilapidated and crumbling structures with barred doors and broken windows boxed us in at every turn, while chain link fences with barbed wire rounded out the scenery.

Emerging suddenly from the projects was the University of Chicago, which was at once both a visual and psychological safe-haven, but the damage was done to any desires I might have about a postdoc there.  It’s too close to the projects (literally, one street away).  Although the campus was lush and green and seemed safe, one needs only to stray down a wrong street or two to find oneself in trouble. Finding ourselves out of the danger area, our heart and perspiration rates returned to normal. My brain emerged from fight-or-flight mode, and its cognitive abilities were freed up enough for me to generate a good idea: Mark regions of high crime rate on maps, especially tourist maps. Somebody should do this. Maybe they already have.

A quick walk past UChicago and Hyde Park, we arrived at the Museum of Science and Industry, the largest science museum in the western hemisphere. Flashing our CityPass booklets again, we skipped lines and made it into the exhibit halls. Confronting us head-on was a Foucalt pendulum, and I couldn’t help but think of the Coriolis effect and noninertial reference frames.

Focault Pendulum

I surprised Dad by telling him I could calculate the length of the pendulum by just measuring the period of its swing (the period is the time for the pendulum to make one full swing back and forth). Indeed, the period of a simple pendulum is given by $T=2\pi\sqrt{\frac{L}{g}}$ where $L$ is the length of the pendulum and $g$ is the magnitude of the gravitational acceleration at the pendulum’s location. Solving this equation for $L$ we get $L=\frac{gT^2}{4\pi^2}$. I measured the period $T$ of the pendulum over several swings and averaged my result, getting $T=8.9\pm 0.1\textrm{~s}.$ Taking $g=9.81\textrm{~m/s}^2$ we get $L=19.7\pm 0.2\textrm{~m}.$ Thus the length of the pendulum shown in the picture is 64 feet 7 inches, with an uncertainty of about 7 inches. Thus just by measuring the period alone, I am able to calculate how long the wire is that connects the pendulum to the ceiling, several stories above. Even though this is freshman physics, I still think it’s pretty cool.

Our first major exhibit was the Henry Crown Space Center, where was saw the original Apollo 8 space capsule and the Apollo 11 training mock-up. Next were the giant LEGO models of Adam Reed Tucker and the Navy, Auto, and Ships exhibits. Passing by a whispering gallery, I mentioned the reflection property of an ellipse. But the real gem of our trip was the U-505 submarine. This is the german U-boat captured by the United States on June 4, 1944. We only toured a few compartments of the U-boat, but it was enough to give you a palpable feel for life in those conditions. The tour was timed and had visual and audio cues, which I thought might be hokey at first but were pretty effective. Das Boot was on my mind during the tour. If you haven’t seen it, you should rent it. English subtitles will get you through this compelling movie.

Exiting the U-boat, I saw some of the original German Enigma machines and told Dad a little about Alan Turing and the contributions made by mathematicians that helped end World War II, since this was largely neglected from the exhibit. I guess math isn’t sexy enough for museums, even a science one. After briefly seeing a few more exhibits, like the Genetics Lab, Chick Hatchery, and Earth Revealed, we focused our attention on the Transportation Gallery, which has a replica of the 1903 Wright Flyer. But the gallery has even more more important originals, such as one of the only two remaining German Stukas in existence, a Spitfire, the Piccard Gondala, and a Boeing 727, whereupon Dad couldn’t help but reciprocate by lecturing me about jet engines and telling me all about the instrument panels in the flight deck.

Transportation Gallery

After finishing our visit to the museum, we opted to take the #10 bus for the trip back to the loop, avoiding our harrowing experience earlier, which no doubt would be worse as dusk was coming on fast. Despite having to stand on the bus on account of crowdedness, it was well worth it in terms of personal safety.

Having had such a good experience the night before at Elephant & Castle, we decided not to risk anything new and repeated ourselves. We weren’t disappointed. Dinner conversation centered on organized religion again, and whether or not faith is a virtue (no need to say which way I argued that point). We left downtown around 6:30pm. Making it back to my car, I drove Dad through Westmont, IL and then on to Argonne National Laboratory, my reason for being in Chicago this summer. At 9:00pm we were back near the hotel, and Dad, with his characteristic generosity, insisted on filling my car up with gas despite having paid for almost everything so far the entire trip. Against my protestations to the contrary, he still filled it up. As the Borg say, resistance is futile.

Finally, I had the impulse to drive down the famous Lake Shore Drive at night, a scenic drive splitting Lake Michigan and the Chicago skyline. So we did.  The city was gorgeous at night time.  The trip up Lake Shore Drive was so nice, I surprised Dad by doing it twice. We made it home by around midnight again, and stayed up an hour or so talking, before fading to sleep.