The 1001 Faces of the Permacold

Nathaniel is in daycare, and I have a cold.

This is a sentence that is true today, was true the first week we sent Nathaniel to daycare, and has been true virtually every day in between.

I had heard about that permacold -- that as a parent you just spend the first X number of years of your child's life sick as he brings every single mildly transferable virus home with him. I had heard about it, but didn't quite believe it. Nathaniel stayed home with us for his first year, so he wasn't really affected, and so neither were we. It was all rumor and legend. And just as we miraculously missed the travails of having a baby who wouldn't stay asleep, maybe we'd miss this too. Maybe all the terribles of raising a little one are rumors and exaggeration!

Nope. This one hit. And the interesting bit about the permacold is that it makes you vividly aware of all the different types of colds one can have (because one is essentially speed-running them in a rapid and never-ending cycle). Sometimes you have a dry cough, and sometimes it's a productive cough. Sometimes you're congested beyond belief, and sometimes your nose won't stop running. Sometimes your throat is scratchy, and sometimes it's swollen. Sometimes your teeth hurt, and sometimes you snore just from breathing. It's not that any of these symptoms are novel or unfamiliar, exactly. It's just that normally they're spaced out weeks or months apart. To oscillate between all of them in 24 hour shifts is very disorienting.

And the bonus irony is that Nathaniel is basically unaffected by any of the diseases he vectors into the house. He coughs and sneezes and has a runny nose, but it never really bothers him all that much. It's mom and dad who are shambling around the house like the night of the living dead. Even when he gets sent home from daycare for something more serious, like pink eye or hand-foot-mouth disease, we're the ones who really end up suffering while his behavior barely changes at all. Objectively, I know that's far better than the alternative. Subjectively, it's tough not to feel a twinge resentful.

Jill was out tonight to see a play, so I got to put Nathaniel to bed (Jill and I share the nighttime routine, but the very last part of it is Jill's time). He hadn't gotten the best nap in (and the nap was late -- from 4:15 - 5:15), so I was a bit nervous. But I did my best solo version of the nighttime winddown process, and Nathaniel was very obliging. I gave him his kisses and told him how much I loved him, and he snuggled up against me and rested his head on my chest. I put him down to sleep, and he went right down, and all is right in the world -- no matter how much I cough.

Pricing In Synagogue Attacks

I first heard of the attack on the Temple Israel Michigan synagogue from one of my students after my morning class. The attack has been variously described as a "shooting" or a "car-ramming" attack; from what I can tell the terrorist had a ton of explosives in his car that he was hoping to set off via crashing his vehicle into the synagogue building. He was shot dead by security, and thankfully he seems to be the only fatality.

It's been reported that the synagogue also runs a preschool that was in session at the time of the attack. I, of course, am also the parent of a baby who currently attends preschool/daycare at his synagogue, under a set up that is very similar to that of Temple Israel. We also have security posted outside the building on a daily basis; we also have a gate set up one needs to "swipe" into (twice!) in order to access the interior of the building. 

It is very, very easy to imagine that our synagogue and our preschool could have been the target of this attack. In fact, the other day I was idly imagining (in the way parents do) just such an attack on my synagogue, in circumstances where Nathaniel was present. And what was striking to me about my thought process -- both in the imaginative space, yesterday, and in responding to the very real attack in Michigan, today -- was how numb I felt to it. It should feel terrifying. I should be terrified. But my reaction was alarmingly muted, as if I've just "priced in" the possibility of attacks like this. This is what it means to live as a Jew.

I don't know. I can't say I mourn not feeling overwhelmed by crippling anxiety and fear. But also, what does it say about me that I'm past feeling anxious and fearful? And this isn't, to be clear, a sound assessment of actuarial risk -- that would give me too much credit. It's something more quiescent -- an atrophication of any sense that security and safety is something I could ever expect to have for me and my family. That feeling -- or lack thereof -- well, I don't think it's a good thing.

David's First Math Problem

Last night, I had a math problem.

Sort of. Not really. I'm not saying it's a hard math problem, or an interesting math problem. It may be a profoundly weird way to look at a math problem, and the way I solved it may be a really silly and convoluted solution to the math problem. But it stuck with me until I just had to tackle it -- and I haven't done any real math in about twenty years.

Okay, let's get to it.

At an auction, the amount an item sells for is known as the "hammer price". But it is not necessarily the case that either the buyer pays, or the seller receives, the hammer price. Rather, there is both a buyer's premium (BP) and a seller's premium (SP) that is calculated as a percentage of the hammer. The buyer pays the hammer plus the BP; the seller receives the hammer minus the SP. In other words:

• Final buyer's price = Hammer + (Hammer x BP)
• Final seller's final return = Hammer - (Hammer x SP)

Imagine two different auction premium models. In the first, the buyer pays no premium (BP = 0), and the seller pays a premium of 50% (SP = .5). In the second, the buyer pays a premium of 30% (BP = .3) and the seller plays a premium of 20% (SP = .2). Assuming the final buyer's price remains constant, which model is better for the seller?*

The answer is obviously the second -- but not by as much as might appear at first glance. Since the buyer pays no premium in the first model, they'll pay a higher hammer price than in the second, which partially offsets the first model's higher seller's premium. It's just not enough. To give an example, for a buyer willing to pay $130 for an item:

• In model one, the item would hammer for $130 (130 + (130 x 0)). The seller would get half of that, or $65 (130 - (130 x .5).
• In model two, the item would hammer for $100 to yield the same final buyer's price of $130 (100 + (100 x .3)). The seller would get 80% of the $100 hammer, or $80 (100 - (.2 x 100)).

So model two is better than model one for the seller by a ratio of 16/13 (80/65 = 160/130 = 16/13).

That was not the math problem.

I looked at that number: 16/13. And I thought, that's an ugly number. It expresses out to 1.23076923077 -- yuck!** Moreover, it's an ugly number that, at first glance, has relatively little to do with the relatively nice numbers we saw in the inputs -- .3, .2, .5. Where on earth did 16/13 come from?

16/13, I knew, was not just the ratio that applied to the particular example buyer's price I chose ($130). It was the ratio for any buyer's final price fed into these two premium models. The seller's return would always be 16/13 times higher in model two compared to model one.

What I wanted was (and this was the math problem) was to write some sort of equation or proof that would spit out that ugly 16/13 number, not just for one particular buyer's price but generally.

Now all of this thinking occurred last night, in bed, right around when the daylight's savings time switch happened. It was pretty unproductive.

But this afternoon, I decided to actually take out a pen and paper and really see if I could do this. Here were my steps.

Fb = Final Buyer's Price

Fs = Final Seller's return

H = Hammer.

(1) Fb1 = H + (H x 0) = H

(2) Fs1 = H - (H x .5) = Fb1 - (Fb1 x .5) = .5Fb1

Since The Final Buyer's Price in the first model is just the hammer, we can substitute it in for the hammer in calculating the first model's Final Seller's Return. The Seller pays a 50% premium, so they receive half the Final Buyer's Return aka half the hammer price.

(3) Fb2 = H + (H x .3) = 1.3H

(4) 10Fb2 = 13H, divide both by 13 --> (10/13)Fb2 = H

Not as neat as the first model, but that also lets us express H as a function of Fb2.

(5) Fs2 = H - (H x .2) = .8H

(6) Fs2 = .8((10/13)Fb2 = (8/13)Fb2

(7) Fs2 = (8/13)Fb2 and Fs1 = (1/2)Fb1.

But by stipulation, Fb1 and Fb2 are the same (the buyer is paying the same final price in each model). Meaning:

(8) The ratio of Fs2/Fs1 = (8/13)/(1/2), multiply those by 2 and you get (16/13)/1, or just 16/13.

Tada!

And listen: maybe you're good at math. Maybe you do math all the time. I'm not and I don't. I did not enjoy math in school, and I have generally avoided math as an adult. Indeed, I've written about my complex relationship with my own math educational trajectory, which while not exactly a tragedy was not exactly a triumphant tale either. So I felt very good about being able to work this out, and to stretch some muscles that had lain dormant for quite some time -- even though to be honest I'm still not entirely sure why this particular hypothetical sunk its claws into me so.

Yay me!

* If you're wondering where these two "models" came from, model two represents the rough premiums charged by a standard commercial auction house, and model one represents a charity auction where returns are split 50/50 between the consigner and the charity beneficiary. My initial inquiry was to ask just how much the consigner is losing by doing the charity auction (with the answer being "they are losing, but not as much as they might think upon seeing that steep 50% seller's premium").

** In hindsight, while writing this post, I realized that just by flipping the ratio -- 13/16 -- it would be at least a little less ugly (13/16 = .8125).