Wild Math in Rain City
Last night I had dinner with my witness, the former emergency room physician and math Ph.D. My plans to visit the Sun Yat-Sen Garden in the afternoon after our lunch at Horseshoe Bay had been thwarted by a downpour but it had stopped raining by dinner time. We went to the aptly-named Rain City Grill. Rain City Grill is the Restaurant Nora of Vancouver. There was no cod on the menu so I ordered halibut.
People who know me well will find it stunning that I signed up for a solo dinner with a math Ph.D. I am the one who avoided having to take remedial math at Barnard by a mere 1 point on the matriculation test. I am the one who calculated in my Astronomy class that the moon weighs 90 pound and travels 35 millimeters above the surface of the earth. I have to ask my excellent secretary to do percent calculations for me (I can't even do them on a calculator). I am the one for whom a tax return is an impressionist exercise that occurs shortly before an entertaining and entirely inscrutable, months-long correspondence with the IRS. ("Box 37a should have contained the number 12," they say. Fine -- then you do my tax return, smarty pants.)
Earlier that day I had actually asked my witness his thoughts about tax returns. He said that he, too, found them obtuse and that he always did his own returns because he found it challenging to try to figure out WHY the IRS wanted you to add 13.5 to box 19 only to ask you three pages later to remove it. He approaches his returns as a logic game -- "if they want you to subtract line 19 from line 34 then there MUST be a situation in which line 19 is bigger than line 34. What situation could that be?" Etc. He said it lead him into an interesting philosophical rumination on the imaginary financial lives of others.
I learned more about his approach to math at dinner. I started with the basics. "Why do you like math?" "I think it's wild!" he said. "When I was young, I realized that 2+3 = 5 but that 3+2 also equals 5. It didn't matter which way you added up the numbers, the answer was always 5. And that's true no matter how long your list of numbers is. Addition is bi-directional! That's wild!" "I suppose that's true," I said.
Then he said he thought it was very satisfying to add up some numbers and get an answer and then to add them up several more times and always get the same answer. I said that did sound satisfying but that I could only speculate because that had never happened to me. Every time I add up a set of numbers more than once I get an entirely different answer each time. Sometimes I get 31. Sometimes I get 29. Sometimes I get 12. You see the problem. How do you know which one is right?
Instead of looking at me like I was an idiot, he said, "Ah, well, it sounds like no-one has ever taught you the trick of casting out nines." "That is most definitely true." So he taught me this trick and it didn't seem to have anything to do with the number nine but it is a way of figuring out whether you got the right answer. "You're kidding me -- all this time there was a TRICK to make sure you were RIGHT and NO-ONE EVER TOLD ME THIS?" Education today…..And it works for multiplication as well as addition.
We played more math games and they were all indeed "wild" and my witness became very animated and excited and after each game he would sit back in his chair with wide eyes and an impish grin and say, "isn't that WILD!" There was one where you did something with even integers and something else with odd integers and you kept going for a while until your paper was all covered up with numbers and it turned out you would always arrive eventually at the number 1. He said no-one has ever ended up with anything other than 1. Euclid figured this out, back in the day. He said, "whether you can end up with something other than 1 is still an open question in math." I looked at him, stunned. "Is this what math Ph.Ds do all day? Doing this over and over again to see if they come up with something other than 1?" The answer is yes, basically. Since the time of Euclid. I suggested it might be time to call it a day on that particular open question.
Which lead us to the discussion of which came first, math or nature -- math describes nature -- but we humans came up with it -- so how ironic that we just happened to have come up with a number system that also works in nature -- creepy -- WILD! -- if that's the case, why do we have to teach math -- if the concept of the number 2 is "natural," then how come we do not emerge from the womb able to do arithmetic -- you can't teach biology after all -- no, of course, you can't teach someone to sweat…. Etc.
Somehow in there we discussed how there is no such thing as sea level. Or rather, there is such a thing as sea level but it's different everywhere. The ocean on the west side of the Panama canal is six feet higher than the ocean on the east side. And that's true all around the world. Has to do with winds. So I came up with "Kim's Rule," "Sea level is only constant if you happen to be at sea." He thought that was pretty good.
My expert was happy to chat away for quite some time about Wild Math. The restaurant started to empty. It made me think maybe not everyone was interested in this. I said, "Do you find there are a lot of people in Vancouver with whom you can have this kind of discussion about math?" "No."
Then I asked him what the point of math was. WHY sit around in a room trying to come with an answer other than 1.
He said, "Well, that's part of the problem. That's why I went back to Harvard to become an emergency room physician."
There was a lot more to our dinner conversation of course, but that will give you the gist.
Visiting Vancouver
I am once again in Canadia. This time I'm on the West Coast, in Vancouver. I deplaned into an empty airport, as all airports seem to be in this basically unpopulated country. No people. No noise. No nothing. It is a beautiful empty airport. Inside it one walks through a little ecosystem with screeching loons and tall totems and a rain forest. On the walk to customs one passes several other large totems. At baggage claim, totems. Right outside of baggage claim is a huge totem guarding the parking lot. At the airport exit, a totem.
I rented a car and drove into town. There is no highway to Vancouver from the airport. One drives through a dingy neighborhood called Richmond, which smells like sushi, then over various bodies of water, and then one is in town. The architecture is identical to that of late- to post-dot-com San Francisco. A form of architecture I despise. My firm's old office in San Francisco was built in that style and we had to move out because, among other things, the floors were too flimsy to support real desks, etc.
It was a warm sunny day in Vancouver yesterday and it shocked the citizenry. The Canadians were wearing shorts, which I thought inadvisable. And sandals, a form of footwear to which they are unaccustomed, judging from their walking style.
I had dinner at the hotel bar, looking out over the water. I ordered something called "sablefish" and an unoaked, Canadian chardonnay. I tried to entertain the bartender by dropping fascinating facts on him, such as:
- At any given moment, 500,000 people are in the air.
- Of all the people in the world who have ever reached the age of 65, 2/3 of them are alive right now.
- The largest producer of quinoa is Peru.
- Ocean-going fish contain more Omega 3s than river fish.
- Thirty percent of all clinical trials for marketed anti-depressants fail.
He found that last fact the least interesting of them all. So I asked him a question, namely, "What is sablefish?" He said it was an ocean-going fish that is over-fished by the Japanese right across the way there and that the Canadians are grateful that at least the Japanese leave them a few to eat occasionally. I said I had never heard of it and that I kind of know my fish so was it possible it also goes by some other name. "Cod," he said.
Ha! Why didn't you say so? I know lots and lots about cod. I demonstrated:
- it's good luck to eat cod on New Year' Eve
- adolescent cods are called haddock
- cods eat crabs
- Newfoundland has a cod stamp
- lots of fishes called cods are actually groupers (see, e.g., coral cod, reef cod, rock cod),
- the Vikings traveled with dried cod
- William Pitt the Elder called cod 'British Gold"
Sablefish is a Pacific cod -- turns out to be three times bigger than an Atlantic cod. That's big.
After dinner I went to sleep and then got up this morning and went to have breakfast with my co-counsel who is from Alabama and his 10-year-old son, Jake. Jake was delightful though I thought he did not approach the buffet with the gusto and vigor that I would have, had I ordered the buffet (I ordered the buttermilk pancakes). When he came back with a dull, unemotional looking plate, I took him back up there and heaped it back up with sausage and salmon and cheeses, etc. He said he liked it all. He had just been in Turkey with his father (my co-counsel) and so I asked him what he thought of the food. "I really liked the pizza," he said. I told him that on his trip to Vancouver with his father he should make a rule to eat something new at each meal, or, if there was literally nothing new on the menu, something that his mother would be unlikely to make for him at home. His father approved of all this, of course. "See, Jake -- what have I been telling you. Miss Kim is right."
All three of us then drove out to West Vancouver, which is West of Vancouver, to meet with an expert witness who lives in a tiny house way up on a steep mountain. I should mention that the mountains in Vancouver are very steep. I don't think I've ever seen mountains this steep. And the trees are very tall. Jake sat quietly and read a book while we interviewed the witness, who is an FDA expert and also a math Ph.D and also a computer programmer. He had little boxes in his study that had labels that said things like "Mystery Hardware" and "Mysterious Nuts & Bolts." He once wrote a computer program that counted down the days until George W. Bush would be out of office. And he was also an emergency room physician. Almost forgot that.
He said he made databases and stuff and so I asked him if he had a recipe database. He said yes and that I could download it from his website. I asked him if it could tell me what to cook if I told it that all I had in the fridge were an onion, a fig, and a cod, let's say. He said I could sort it by ingredient. I asked him if it could come with me to the grocery store and tell me what other ingredients I needed to buy if I saw a yummy cod and wanted to make some sort of miso-sauce reduction with blanched zucchini confit (for example). He said no. I asked him if it could also tell me how much zucchini I already had in my kitchen and thus did not really need to buy anymore just for the cod confit. He said no. I said that sounded like a rather useless recipe database.
The expert also introduced me to an amazing artist named Peter Milton. I will write more about him tomorrow. And he used an excellent phrase that I had never heard before and likely won't again-- he was describing how to run a particular type of clinical trial and he said, "imagine you are trying to study dueling pistols...." I liked that. At one point his coffee pot beeped. He said, "the coffee is telling me that it no longer considers itself fresh."
Then it was time for lunch. We went to Horseshoe Bay -- a vertical semi-circular plunge into the Pacific that manages to squeeze into its narrowness three massive ferries (one carries 500 cars) that go from the mainland to Vancouver Island. It is creepy vertical -- granite straight down from very far up a high mountain covered in Fraser pines to who knows where in the center of the earth.
Jake was still with us of course and he ordered hot chicken wings. I told him this violated his new food rule. He said that was true, it did, so he changed his order and asked for his chicken wings to come with Thai sauce.
I ordered cod. Something called a "ling cod." (Not really a cod at all, as it turns out -- so confusing.)
On the way back to town after we dropped off our expert, Jake said he thought he might like to go on a gastronomic tour of the country of his choosing with me as his chaperone. This is what I have promised my nieces and my nephew for when they graduate from high school. The rule is we go to any country the child chooses but that upon arrival, the child must eat the local cuisine and not order pizza in Turkey, for example.
Jake selected Greenland.
