What Is Zero?

 

Day 1

The Travel Day

Travelling to South Africa is no small feat of modern engineering and technology. To go 7894 miles from Washington DC to Capetown, SA, one needs either a very long time (it used to take weeks by boat) or a very powerful, sophisticated machine. We opted for the latter. Two GE jet engines (very high tech) put out 64,000 lb of thrust each, which allows a 500,000 lb chunk of metal to float in the air, carrying 381 passengers. Simply amazing. But as some wise guy once said: “Human problems are 20% technical and 80% social.” How true as we learned on our trip.

The flight from Indianapolis to DC was delayed due to some bad weather on the east coast, and our plane could not get to Indy from NY in a timely fashion. No big deal. We had a 2.5 hours layover in DC. Out of Indy, we were delayed 15 minutes – no, wait … 30 minutes – no, wait again … 45 minutes … OK finally after an hour, we were off and flying. Still no sweat for our connection in DC. Everything was smooth and comfy with only a slightly longer travel time as our pilot used modern navigational technology to maneuver around storm clouds etc. We landed at Washington Dulles airport, which is quite large and spread out. Our pilot announced that we were diverted to Gate A1 - no, wait … Gate A1c (how appropriate for a guy worked for Lilly on many diabetes trials 😊). About that time I was getting a friendly test from United Airlines that our flight to Capetown departed out of Gate D32. Another nice piece of modern technology, but hmmm. It also noted that it was an estimated 32 minutes between gates. Yes a link to the airport map (another piece of modern technology) showed that we were coming in and departing from the two gates that were absolutely the farthest apart as you can get at Dulles. OK, we were up for the hike, and we still had about an hour before our 6:30pm flight to Capetown.

Now, here is the social part of the problem. At 5:30pm (17:30 for the rest of the world), we pull up to Gate A1c, which is not really a Gate but a spot on the tarmac near Terminal A. OK, all still good. Then we stop and the pilot announces, “Please stay seated. We are waiting for a ground crew to guide us in.” OK, a little annoying, but not disastrous. But we wait … and wait … and wait [tensions rising; trying to keep anxiety at bay as our layover time is disappearing]. The we get pulled into our spot (recall not a Gate per se). Everyone stands and starts getting luggage – you know the routine. Then another announcement. “They are having trouble getting the bridge up to the door of the plane.” We wait. Next announcement, “They cannot position the bridge up to the plane and we will have to taxi back. We were pulled in too far. Everyone must get back in their seats.” What?!?! “We cannot move the plane until everyone is seated” with a little stern discipline on the tone of voice. There is a collective moan. Many people with connections are visibly sweating. We are taking deep breaths.

OK, here is the next thing. As everyone is just getting seated, a little girl of about 8 (I know these things since I have seen lots of kids and grandkids who are 8) comes walking back the aisle … TO USE THE RESTROOM. Really?! What mom holds up an already late plane of 150 passengers for another 5 minutes while their child goes to the bathroom? But she’s cute, untainted by worldly concern, and listening to the call of Nature. How can you be mad about that? But … the clock goes tick, tick, tick, …

So, now we are all re-settled and they start to move the plane. Mister “analytical mind” here has already scoped out the surroundings outside the plane because he is curious as to how far we have to move the plane back. Using a constant point of reference and the law of sines (from Geometry), I deduce that we moved about 6 feet backwards! One passenger says in surprise, “Did we move?” Yes, 6 feet. Holy cow – 25 minutes have elapsed since we arrived at our spot (remember, not really a Gate). Tick, tick, tick. We all stand up again. Now they get the bridge up to the door. Next announcement: “We are having a little trouble with the locking mechanism on the door, so please be patient.” Patient?!!! You’re lucky this plane is not called ‘The Bounty’ or you’d be having a mutiny on your hands. We finally get off the plane, only to discover that the “bridge” is one of those roll-up ramps that we have to walk down. What?!?! They couldn’t just roll that contraption 6 more feet up to the plane, which is sitting on a tarmac with nothing within a hundred feet of it?!?!

So, now the race is on. We are down to 25 minutes and the text message says our Gate is 30 minutes away. We are jogging through Dulles following the signs in Terminal A for how to get to Terminal D. Then we run into it – a dead end. To get to Terminal D, we need to take a shuttle bus and it just left! A timer pops up over the door where we are to board the bus and it says “Next shuttle in 15:00, 14:59, 14:58 …” Tick, tick, tick. Are we going to make it? OK, what do we do? The kids got time to find a bathroom since my grandkids didn’t take that opportunity on the plane, and I run back into Terminal A to a United gate and desk agent to explain what’s going on. That agent call Gate D32 and tells them that they got 5 passengers on the way – Ruberg and Browning. He says, “Please don’t so anything stupid like close the Gate before they get there. They are waiting for a shuttle and should be there just after 6:30.” THANKS, we feel better.

The shuttle bus arrives, we are transported to Terminal D and then have to go to the farthest end to get to the last Gate in the Terminal – Gate D32. We were hustling down the Terminal because we didn’t want to take any chance of something disastrous happening, and thankfully, the kids and Maria are in good enough shape to get ahead. As for me, well, hauling two backpacks and running is no longer my expertise, so my ‘run’ was more like a speed walk. Well, maybe a fast walk. OK, OK, OK, I walked as fast as I could! Stop thinking what you are thinking.

We got on the plane and sat in Rows 50 and 51, which amazingly, was nowhere near the back of the plane! Remember 381 passengers. The flight was long (about 15 hours), but reasonably comfortable with plenty of pretty good food and lots of entertainment options. I highly recommend the movie “A Man Called Otto” with Tom Hanks as the star. Maria suggested I watch it. She was spot on!

We landed in Capetown and Audley Travel took over from there (remember I get a commission if you contact them). We were met coming off the plane and escorted all the way through baggage claim and customs and driven to the hotel.

Unfortunately, the weather was quite rainy and the cloud cover very thick and low, so we did not get any good views of city or the harbor. We settled into the Victoria and Alfred Hotel (very nice renovated harbor warehouse from years past), and went to dinner at Baia very nearby. Wow! What a dinner it was – fresh local fish, langoustines, scallops, snails (I am not sure if there were local) all sauteed with vegetables and other toppings. We all agreed it was a 10 or something very close to 10. This led me to explain how 9.99999… is actually the number 10 just written in a different way. They are equal. However, that part of the dinner conversation was squelched pretty quickly.

                 

 By now we were full and tired and we retired to the V&A and it is affectionately known by the locals. It was easy to go to sleep.

Side Note: What is Zero? Just in case you want to know.

Notice that I called yesterday Day -1 since it was the day before our trip. That seems appropriate. And I called today Day 1 since it was the first day of our trip. Once again, wholly appropriate. OK, but what happened to Day 0. Interestingly (at least to me) is that this is a problem that came up in clinical trials in my early days in the industry. The day before a patient enters the trial is Day -1 but the day they start the trial is Day 1, it is the first day they get the experimental treatment. Where is Day 0. This is important for precisely calculating how long a patient has been on treatment. In my early days it was debated for statistical calculations. The solution is that statisticians defined "baseline" as that instant before a patient gets the first dose of the experimental treatment. A clinical measurement is taken at that time (blood pressure, tumor volume, cognition score, etc.) and then we measure the change from baseline to assess the effect of the treatment. The definition of baseline has evolved and is critical to clinical research as in some cases "baseline" might be an entire day or week or month (e.g., number of migraine headaches in the last month prior to the initiation of experimental treatment).

This also highlights the importance of the number zero. We didn't always have this concept in our mathematics. While some concepts similar to "zero" existed in ancient Babylon and other civilizations, it's formal use in mathematics appeared in the mid-700sAD in the middle east by the mathematicians who invented algebra. Others will claim that "zero" was invented by Hindu mathematicians 200 years earlier. Of course, this was all while the western world was deep in the so-called Dark Ages.